%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWW216+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 : n010.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 09:04:51 AM UTC 2026
% Result : Theorem 165.19s 165.56s
% Output : Proof 165.29s
% 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_I1_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
file('theBenchmark.p',fact_m_I1_J) ).
fof(fact_H_I3_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
file('theBenchmark.p',fact_H_I3_J) ).
fof(fact_assms,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_e),
file('theBenchmark.p',fact_assms) ).
fof(fact_H_I1_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____),
file('theBenchmark.p',fact_H_I1_J) ).
fof(fact_H_I2_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('theBenchmark.p',fact_H_I2_J) ).
fof(fact_dm_I2_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_d____),v_m____),v_e),
file('theBenchmark.p',fact_dm_I2_J) ).
fof(fact_d_I3_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
file('theBenchmark.p',fact_d_I3_J) ).
fof(fact_dm_I1_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_d____),v_m____)),
file('theBenchmark.p',fact_dm_I1_J) ).
fof(fact_em0,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
file('theBenchmark.p',fact_em0) ).
fof(fact_real__mult__commute,axiom,
! [V_w,V_z] : hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z),V_w) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_w),V_z),
file('theBenchmark.p',fact_real__mult__commute) ).
fof(fact_real__mult__assoc,axiom,
! [V_z3,V_z2,V_z1] : hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1),V_z2)),V_z3) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2),V_z3)),
file('theBenchmark.p',fact_real__mult__assoc) ).
fof(fact_d_I1_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____),
file('theBenchmark.p',fact_d_I1_J) ).
fof(fact_times_Oidem,axiom,
! [V_a,T_a] :
( class_Lattices_Oab__semigroup__idem__mult(T_a)
=> 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(c_Groups_Otimes__class_Otimes(T_a,V_x),V_x) = V_x ),
file('theBenchmark.p',fact_mult__idem) ).
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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b) = 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_mult__left__idem,axiom,
! [V_b,V_a,T_a] :
( class_Lattices_Oab__semigroup__idem__mult(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b) ),
file('theBenchmark.p',fact_mult__left__idem) ).
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(c_Groups_Otimes__class_Otimes(T_a,V_lx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),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_d_I2_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('theBenchmark.p',fact_d_I2_J) ).
fof(fact_one0,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('theBenchmark.p',fact_one0) ).
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_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(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_I10_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> 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(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_real__mult__1,axiom,
! [V_z] : 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__left__cancel,axiom,
! [V_b_2,V_a_2,V_ca_2] :
( V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ca_2),V_a_2) = 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__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(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a_2),V_ca_2) = 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__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(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z),V_x),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z),V_y)) ) ),
file('theBenchmark.p',fact_real__mult__less__mono2) ).
fof(fact_real__mult__order,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_y)) ) ),
file('theBenchmark.p',fact_real__mult__order) ).
fof(fact_real__mult__less__iff1,axiom,
! [V_y_2,V_x_2,V_za_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2),V_za_2))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_real__mult__less__iff1) ).
fof(fact_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(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_rx)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ly),V_ry)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),V_ry)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ly),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry))) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),V_rx) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_rx)),V_ly) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [V_rx,V_ly,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),V_rx) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ly),V_rx)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [V_ry,V_rx,V_lx,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,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__096_B_Bthesis_O_A_I_B_Bd_O_A_091_124_A0_A_060_Ad_059_Ad_A_060_A1_059_Ad_A_060_Ae_A_P_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [B_d] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_d,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_d,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ) ),
file('theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bd_O_A_091_124_A0_A_060_Ad_059_Ad_A_060_A1_059_Ad_A_060_Ae_A_P_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact__096EX_Aea_0620_O_Aea_A_060_A1_A_G_Aea_A_060_Ae_A_P_Am_096,axiom,
? [B_e] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_e,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_e,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e) ),
file('theBenchmark.p',fact__096EX_Aea_0620_O_Aea_A_060_A1_A_G_Aea_A_060_Ae_A_P_Am_096) ).
fof(fact_divide__strict__left__mono__neg,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))
=> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ),
file('theBenchmark.p',fact_divide__strict__left__mono__neg) ).
fof(fact_divide__strict__left__mono,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))
=> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ),
file('theBenchmark.p',fact_divide__strict__left__mono) ).
fof(fact_neg__divide__less__eq,axiom,
! [V_a_2,V_b_2,V_ca_2,T_a] :
( class_Fields_Olinordered__field(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,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2)
<=> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) ) ) ),
file('theBenchmark.p',fact_neg__divide__less__eq) ).
fof(fact_neg__less__divide__eq,axiom,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( class_Fields_Olinordered__field(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,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) ) ) ),
file('theBenchmark.p',fact_neg__less__divide__eq) ).
fof(fact_mult__imp__less__div__pos,axiom,
! [V_x,V_z,V_y,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y),V_x)
=> c_Orderings_Oord__class_Oless(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ),
file('theBenchmark.p',fact_mult__imp__less__div__pos) ).
fof(fact_mult__imp__div__pos__less,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y))
=> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z) ) ) ),
file('theBenchmark.p',fact_mult__imp__div__pos__less) ).
fof(fact_pos__divide__less__eq,axiom,
! [V_a_2,V_b_2,V_ca_2,T_a] :
( class_Fields_Olinordered__field(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,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2)
<=> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) ) ) ),
file('theBenchmark.p',fact_pos__divide__less__eq) ).
fof(fact_pos__less__divide__eq,axiom,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( class_Fields_Olinordered__field(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,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) ) ) ),
file('theBenchmark.p',fact_pos__less__divide__eq) ).
fof(fact_divide__less__eq,axiom,
! [V_a_2,V_ca_2,V_b_2,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_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_ca_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) ) ) ) ),
file('theBenchmark.p',fact_divide__less__eq) ).
fof(fact_less__divide__eq,axiom,
! [V_ca_2,V_b_2,V_a_2,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_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_ca_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_ca_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_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(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) ) ) ) ),
file('theBenchmark.p',fact_less__divide__eq) ).
fof(fact_times__divide__times__eq,axiom,
! [V_w,V_z,V_y,V_x,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)),c_Rings_Oinverse__class_Odivide(T_a,V_z,V_w)) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_z),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_w)) ),
file('theBenchmark.p',fact_times__divide__times__eq) ).
fof(fact_divide__strict__right__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ) ),
file('theBenchmark.p',fact_divide__strict__right__mono__neg) ).
fof(fact_divide__strict__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ) ),
file('theBenchmark.p',fact_divide__strict__right__mono) ).
fof(fact_divide__neg__neg,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ),
file('theBenchmark.p',fact_divide__neg__neg) ).
fof(fact_divide__neg__pos,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_divide__neg__pos) ).
fof(fact_divide__pos__neg,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_divide__pos__neg) ).
fof(fact_divide__pos__pos,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ),
file('theBenchmark.p',fact_divide__pos__pos) ).
fof(fact_divide__less__0__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
<=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ),
file('theBenchmark.p',fact_divide__less__0__iff) ).
fof(fact_zero__less__divide__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))
<=> ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ),
file('theBenchmark.p',fact_zero__less__divide__iff) ).
fof(fact_frac__eq__eq,axiom,
! [V_wa_2,V_x_2,V_za_2,V_y_2,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_za_2 != c_Groups_Ozero__class_Ozero(T_a)
=> ( c_Rings_Oinverse__class_Odivide(T_a,V_x_2,V_y_2) = c_Rings_Oinverse__class_Odivide(T_a,V_wa_2,V_za_2)
<=> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_za_2) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_y_2) ) ) ) ),
file('theBenchmark.p',fact_frac__eq__eq) ).
fof(fact_mult__divide__mult__cancel__left,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_mult__divide__mult__cancel__left) ).
fof(fact_mult__divide__mult__cancel__right,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_mult__divide__mult__cancel__right) ).
fof(fact_divide__eq__eq,axiom,
! [V_a_2,V_ca_2,V_b_2,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2) = V_a_2
<=> ( ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
=> V_b_2 = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2) ) ) ) ),
file('theBenchmark.p',fact_divide__eq__eq) ).
fof(fact_eq__divide__eq,axiom,
! [V_ca_2,V_b_2,V_a_2,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)
<=> ( ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2) = V_b_2 ) ) ) ),
file('theBenchmark.p',fact_eq__divide__eq) ).
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(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_right__inverse__eq,axiom,
! [V_a_2,V_b_2,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a)
=> ( c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_a)
<=> V_a_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_right__inverse__eq) ).
fof(fact_divide__self,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ),
file('theBenchmark.p',fact_divide__self) ).
fof(fact_divide__self__if,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring__inverse__zero(T_a)
=> ( ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a) )
& ( V_a = c_Groups_Ozero__class_Ozero(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_divide__self__if) ).
fof(fact_eq__divide__imp,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> ( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c) = V_b
=> V_a = c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c) ) ) ),
file('theBenchmark.p',fact_eq__divide__imp) ).
fof(fact_divide__eq__imp,axiom,
! [V_a,V_b,V_c,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_b = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c)
=> c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c) = V_a ) ) ),
file('theBenchmark.p',fact_divide__eq__imp) ).
fof(fact_nonzero__divide__eq__eq,axiom,
! [V_a_2,V_b_2,V_ca_2,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
=> ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2) = V_a_2
<=> V_b_2 = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2) ) ) ),
file('theBenchmark.p',fact_nonzero__divide__eq__eq) ).
fof(fact_nonzero__eq__divide__eq,axiom,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)
<=> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2) = V_b_2 ) ) ),
file('theBenchmark.p',fact_nonzero__eq__divide__eq) ).
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(c_Groups_Otimes__class_Otimes(T_a,V_m),V_n)) ) ) ),
file('theBenchmark.p',fact_less__1__mult) ).
fof(fact_zero__less__one,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ),
file('theBenchmark.p',fact_zero__less__one) ).
fof(fact_not__one__less__zero,axiom,
! [T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ),
file('theBenchmark.p',fact_not__one__less__zero) ).
fof(fact_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_divisors__zero,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Ono__zero__divisors(T_a)
=> ( 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_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(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_mult__eq__0__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Rings_Oring__no__zero__divisors(T_a)
=> ( 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_mult__zero__right,axiom,
! [V_a,T_a] :
( class_Rings_Omult__zero(T_a)
=> 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__zero__left,axiom,
! [V_a,T_a] :
( class_Rings_Omult__zero(T_a)
=> 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_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_divide__zero__left,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_divide__zero__left) ).
fof(fact_divide__zero,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring__inverse__zero(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_divide__zero) ).
fof(fact_times__divide__eq__right,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),V_c) ),
file('theBenchmark.p',fact_times__divide__eq__right) ).
fof(fact_divide__1,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a ),
file('theBenchmark.p',fact_divide__1) ).
fof(fact_real__divide__square__eq,axiom,
! [V_a,V_r] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r),V_a),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r),V_r)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_a,V_r),
file('theBenchmark.p',fact_real__divide__square__eq) ).
fof(fact_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(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__strict__left__mono__neg) ).
fof(fact_mult__strict__right__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)) ) ) ),
file('theBenchmark.p',fact_mult__strict__right__mono__neg) ).
fof(fact_comm__mult__strict__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__comm__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_comm__mult__strict__left__mono) ).
fof(fact_mult__strict__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__strict__left__mono) ).
fof(fact_mult__strict__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)) ) ) ),
file('theBenchmark.p',fact_mult__strict__right__mono) ).
fof(fact_mult__neg__neg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__neg__neg) ).
fof(fact_mult__neg__pos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_mult__neg__pos) ).
fof(fact_mult__less__cancel__left__neg,axiom,
! [V_b_2,V_a_2,V_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(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),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_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(c_Groups_Otimes__class_Otimes(T_a,V_b),V_a))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ),
file('theBenchmark.p',fact_zero__less__mult__pos2) ).
fof(fact_zero__less__mult__pos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ),
file('theBenchmark.p',fact_zero__less__mult__pos) ).
fof(fact_mult__pos__neg2,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_mult__pos__neg2) ).
fof(fact_mult__pos__neg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_mult__pos__neg) ).
fof(fact_mult__pos__pos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__pos__pos) ).
fof(fact_mult__less__cancel__left__pos,axiom,
! [V_b_2,V_a_2,V_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(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),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__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(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),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__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(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),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_not__square__less__zero,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__ring(T_a)
=> ~ c_Orderings_Oord__class_Oless(T_a,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_d1_I2_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____),
file('theBenchmark.p',fact_d1_I2_J) ).
fof(fact_divide_Ozero,axiom,
! [V_y,T_a] :
( class_RealVector_Oreal__normed__field(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_divide_Ozero) ).
fof(fact_mult_Ocomm__neutral,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__mult(T_a)
=> 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(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
file('theBenchmark.p',fact_mult__1__right) ).
fof(fact_mult__1,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__mult(T_a)
=> hAPP(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(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_mult__right_Ozero,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mult__right_Ozero) ).
fof(fact_mult_Ozero__right,axiom,
! [V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> 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__left_Ozero,axiom,
! [V_y,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> 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__left,axiom,
! [V_b,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> 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_real__le__refl,axiom,
! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w),
file('theBenchmark.p',fact_real__le__refl) ).
fof(fact_real__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__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__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__less__def,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
<=> ( V_x_2 != V_y_2
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_real__less__def) ).
fof(fact_less__eq__real__def,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
<=> ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_less__eq__real__def) ).
fof(fact_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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_split__mult__neg__le) ).
fof(fact_split__mult__pos__le,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) ) ),
file('theBenchmark.p',fact_split__mult__pos__le) ).
fof(fact_mult__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d)) ) ) ) ) ),
file('theBenchmark.p',fact_mult__mono) ).
fof(fact_mult__mono_H,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_d)) ) ) ) ) ),
file('theBenchmark.p',fact_mult__mono_H) ).
fof(fact_mult__left__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__left__mono__neg) ).
fof(fact_mult__right__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)) ) ) ),
file('theBenchmark.p',fact_mult__right__mono__neg) ).
fof(fact_comm__mult__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__comm__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_comm__mult__left__mono) ).
fof(fact_mult__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__left__mono) ).
fof(fact_mult__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Oordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)) ) ) ),
file('theBenchmark.p',fact_mult__right__mono) ).
fof(fact_mult__nonpos__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__nonpos__nonpos) ).
fof(fact_mult__nonpos__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,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__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(c_Groups_Otimes__class_Otimes(T_a,V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_mult__nonneg__nonpos2) ).
fof(fact_mult__nonneg__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__cancel__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,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__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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__nonneg__nonneg) ).
fof(fact_mult__le__0__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,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_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(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_b_2))
<=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ),
file('theBenchmark.p',fact_zero__le__mult__iff) ).
fof(fact_zero__le__square,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__ring(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a)) ),
file('theBenchmark.p',fact_zero__le__square) ).
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__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_divide__right__mono__neg,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c)) ) ) ),
file('theBenchmark.p',fact_divide__right__mono__neg) ).
fof(fact_divide__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ) ) ),
file('theBenchmark.p',fact_divide__right__mono) ).
fof(fact_divide__le__0__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
<=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ),
file('theBenchmark.p',fact_divide__le__0__iff) ).
fof(fact_zero__le__divide__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))
<=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ),
file('theBenchmark.p',fact_zero__le__divide__iff) ).
fof(fact_real__0__le__divide__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x_2,V_y_2))
<=> ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ),
file('theBenchmark.p',fact_real__0__le__divide__iff) ).
fof(fact_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(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),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(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),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(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),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(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),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(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),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_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(c_Groups_Otimes__class_Otimes(T_a,V_y),V_x),V_x) ) ) ) ),
file('theBenchmark.p',fact_mult__left__le__one__le) ).
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(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y),V_x) ) ) ) ),
file('theBenchmark.p',fact_mult__right__le__one__le) ).
fof(fact_divide__nonpos__neg,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ),
file('theBenchmark.p',fact_divide__nonpos__neg) ).
fof(fact_divide__nonpos__pos,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_divide__nonpos__pos) ).
fof(fact_frac__le,axiom,
! [V_z,V_w,V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_w,V_z)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)) ) ) ) ) ),
file('theBenchmark.p',fact_frac__le) ).
fof(fact_frac__less,axiom,
! [V_z,V_w,V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_w,V_z)
=> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)) ) ) ) ) ),
file('theBenchmark.p',fact_frac__less) ).
fof(fact_frac__less2,axiom,
! [V_z,V_w,V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
=> ( c_Orderings_Oord__class_Oless(T_a,V_w,V_z)
=> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)) ) ) ) ) ),
file('theBenchmark.p',fact_frac__less2) ).
fof(fact_divide__nonneg__neg,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_divide__nonneg__neg) ).
fof(fact_divide__nonneg__pos,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ),
file('theBenchmark.p',fact_divide__nonneg__pos) ).
fof(fact_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_real__mult__le__cancel__iff1,axiom,
! [V_y_2,V_x_2,V_za_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2),V_za_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_za_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_za_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_za_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_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(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)),V_c) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),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_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_le__divide__eq,axiom,
! [V_ca_2,V_b_2,V_a_2,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_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_ca_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) ) ) )
& ( 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(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) ) ) ) ),
file('theBenchmark.p',fact_le__divide__eq) ).
fof(fact_divide__le__eq,axiom,
! [V_a_2,V_ca_2,V_b_2,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_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_ca_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_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__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) ) ) ) ),
file('theBenchmark.p',fact_divide__le__eq) ).
fof(fact_pos__le__divide__eq,axiom,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( class_Fields_Olinordered__field(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,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) ) ) ),
file('theBenchmark.p',fact_pos__le__divide__eq) ).
fof(fact_pos__divide__le__eq,axiom,
! [V_a_2,V_b_2,V_ca_2,T_a] :
( class_Fields_Olinordered__field(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,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) ) ) ),
file('theBenchmark.p',fact_pos__divide__le__eq) ).
fof(fact_mult__imp__div__pos__le,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z) ) ) ),
file('theBenchmark.p',fact_mult__imp__div__pos__le) ).
fof(fact_mult__imp__le__div__pos,axiom,
! [V_x,V_z,V_y,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y),V_x)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ),
file('theBenchmark.p',fact_mult__imp__le__div__pos) ).
fof(fact_neg__le__divide__eq,axiom,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( class_Fields_Olinordered__field(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,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) ) ) ),
file('theBenchmark.p',fact_neg__le__divide__eq) ).
fof(fact_neg__divide__le__eq,axiom,
! [V_a_2,V_b_2,V_ca_2,T_a] :
( class_Fields_Olinordered__field(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,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) ) ) ),
file('theBenchmark.p',fact_neg__divide__le__eq) ).
fof(fact_divide__left__mono,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ),
file('theBenchmark.p',fact_divide__left__mono) ).
fof(fact_divide__left__mono__neg,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ),
file('theBenchmark.p',fact_divide__left__mono__neg) ).
fof(fact_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_linorder__not__less,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ),
file('theBenchmark.p',fact_linorder__not__less) ).
fof(fact_linorder__not__le,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
<=> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ),
file('theBenchmark.p',fact_linorder__not__le) ).
fof(fact_linorder__le__less__linear,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_order__less__le,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> ( V_x_2 != V_y_2
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_order__less__le) ).
fof(fact_less__le__not__le,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_less__le__not__le) ).
fof(fact_order__le__less,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
<=> ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_order__le__less) ).
fof(fact_leI,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ),
file('theBenchmark.p',fact_leI) ).
fof(fact_not__leE,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_not__leE) ).
fof(fact_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__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_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_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_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__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_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_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__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_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_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_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_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_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_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_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_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_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_field__le__mult__one__interval,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( ! [B_z] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),B_z)
=> ( c_Orderings_Oord__class_Oless(T_a,B_z,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,B_z),V_x),V_y) ) )
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_field__le__mult__one__interval) ).
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(c_Groups_Otimes__class_Otimes(T_a,V_u),V_x),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_v),V_y)),V_a) ) ) ) ) ) ),
file('theBenchmark.p',fact_convex__bound__lt) ).
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(c_Groups_Otimes__class_Otimes(T_a,V_u),V_x),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_v),V_y)),V_a) ) ) ) ) ) ),
file('theBenchmark.p',fact_convex__bound__le) ).
fof(fact_one__le__inverse__iff,axiom,
! [V_x_2,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) ) ) ),
file('theBenchmark.p',fact_one__le__inverse__iff) ).
fof(fact_inverse__less__1__iff,axiom,
! [V_x_2,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
<=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_inverse__less__1__iff) ).
fof(fact_one__le__inverse,axiom,
! [V_a,T_a] :
( class_Fields_Olinordered__field(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_a,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ),
file('theBenchmark.p',fact_one__le__inverse) ).
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__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_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_inverse__inverse__eq,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring__inverse__zero(T_a)
=> c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = V_a ),
file('theBenchmark.p',fact_inverse__inverse__eq) ).
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_inverse__eq__iff__eq,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Rings_Odivision__ring__inverse__zero(T_a)
=> ( c_Rings_Oinverse__class_Oinverse(T_a,V_a_2) = c_Rings_Oinverse__class_Oinverse(T_a,V_b_2)
<=> V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_inverse__eq__iff__eq) ).
fof(fact_inverse__eq__imp__eq,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Odivision__ring__inverse__zero(T_a)
=> ( c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Oinverse(T_a,V_b)
=> V_a = V_b ) ),
file('theBenchmark.p',fact_inverse__eq__imp__eq) ).
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_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oab__semigroup__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ),
file('theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(fact_add__left__cancel,axiom,
! [V_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_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__imp__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
=> V_b = V_c ) ),
file('theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_add__imp__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Ocancel__ab__semigroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
=> V_b = V_c ) ),
file('theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__right__imp__eq,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
=> V_b = V_c ) ),
file('theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_inverse__add,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_a))),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) ) ) ),
file('theBenchmark.p',fact_inverse__add) ).
fof(fact_division__ring__inverse__add,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) ) ) ),
file('theBenchmark.p',fact_division__ring__inverse__add) ).
fof(fact_field__inverse__zero,axiom,
! [T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_field__inverse__zero) ).
fof(fact_nonzero__inverse__eq__imp__eq,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Oinverse(T_a,V_b)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> V_a = V_b ) ) ) ),
file('theBenchmark.p',fact_nonzero__inverse__eq__imp__eq) ).
fof(fact_inverse__zero__imp__zero,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Groups_Ozero__class_Ozero(T_a)
=> V_a = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_inverse__zero__imp__zero) ).
fof(fact_nonzero__inverse__inverse__eq,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = V_a ) ),
file('theBenchmark.p',fact_nonzero__inverse__inverse__eq) ).
fof(fact_nonzero__imp__inverse__nonzero,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> c_Rings_Oinverse__class_Oinverse(T_a,V_a) != c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_nonzero__imp__inverse__nonzero) ).
fof(fact_inverse__nonzero__iff__nonzero,axiom,
! [V_a_2,T_a] :
( class_Rings_Odivision__ring__inverse__zero(T_a)
=> ( c_Rings_Oinverse__class_Oinverse(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_inverse__nonzero__iff__nonzero) ).
fof(fact_inverse__zero,axiom,
! [T_a] :
( class_Rings_Odivision__ring__inverse__zero(T_a)
=> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_inverse__zero) ).
fof(fact_inverse__mult__distrib,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) ),
file('theBenchmark.p',fact_inverse__mult__distrib) ).
fof(fact_inverse__eq__1__iff,axiom,
! [V_x_2,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( c_Rings_Oinverse__class_Oinverse(T_a,V_x_2) = c_Groups_Oone__class_Oone(T_a)
<=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ),
file('theBenchmark.p',fact_inverse__eq__1__iff) ).
fof(fact_inverse__1,axiom,
! [T_a] :
( class_Rings_Odivision__ring(T_a)
=> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_inverse__1) ).
fof(fact_inverse__divide,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_b,V_a) ),
file('theBenchmark.p',fact_inverse__divide) ).
fof(fact_INVERSE__ZERO,axiom,
c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('theBenchmark.p',fact_INVERSE__ZERO) ).
fof(fact_add_Ocomm__neutral,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
file('theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_add__0__right,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
file('theBenchmark.p',fact_add__0__right) ).
fof(fact_double__zero__sym,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_double__zero__sym) ).
fof(fact_add__0,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ),
file('theBenchmark.p',fact_add__0) ).
fof(fact_add__0__left,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ),
file('theBenchmark.p',fact_add__0__left) ).
fof(fact_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_add__le__imp__le__left,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_add__le__imp__le__right,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_add__le__imp__le__right) ).
fof(fact_add__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ),
file('theBenchmark.p',fact_add__mono) ).
fof(fact_add__left__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) ) ),
file('theBenchmark.p',fact_add__left__mono) ).
fof(fact_add__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__ab__semigroup__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ),
file('theBenchmark.p',fact_add__right__mono) ).
fof(fact_add__le__cancel__left,axiom,
! [V_b_2,V_a_2,V_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__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__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_Oadd__right,axiom,
! [V_b_H,V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> 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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),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(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(c_Groups_Otimes__class_Otimes(T_a,V_xa),V_x),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_xa),V_y)) ),
file('theBenchmark.p',fact_mult__right_Oadd) ).
fof(fact_mult_Oadd__left,axiom,
! [V_b,V_a_H,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> 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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),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(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(c_Groups_Otimes__class_Otimes(T_a,V_x),V_ya),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_ya)) ),
file('theBenchmark.p',fact_mult__left_Oadd) ).
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(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(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y),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_db_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_db_2
& V_a_2 != V_b_2 )
<=> c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_db_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_db_2),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(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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_m),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_m)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_crossproduct__eq,axiom,
! [V_za_2,V_x_2,V_y_2,V_wa_2,T_a] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_y_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_za_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_y_2))
<=> ( V_y_2 = V_za_2
| V_wa_2 = V_x_2 ) ) ),
file('theBenchmark.p',fact_crossproduct__eq) ).
fof(fact_comm__semiring__class_Odistrib,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring(T_a)
=> 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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)) ),
file('theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
fof(fact_combine__common__factor,axiom,
! [V_c,V_b,V_e,V_a,T_a] :
( class_Rings_Osemiring(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,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_divide_Oadd,axiom,
! [V_ya,V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__field(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya)) ),
file('theBenchmark.p',fact_divide_Oadd) ).
fof(fact_add__divide__distrib,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) ),
file('theBenchmark.p',fact_add__divide__distrib) ).
fof(fact_real__add__left__mono,axiom,
! [V_z,V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y)) ),
file('theBenchmark.p',fact_real__add__left__mono) ).
fof(fact_real__add__mult__distrib,axiom,
! [V_w,V_z2,V_z1] : hAPP(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(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1),V_w),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2),V_w)),
file('theBenchmark.p',fact_real__add__mult__distrib) ).
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__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_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__mult,axiom,
! [V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__div__algebra(T_a)
=> c_Groups_Osgn__class_Osgn(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y)) = 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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = 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_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_inverse__nonpositive__iff__nonpositive,axiom,
! [V_a_2,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(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)) ) ),
file('theBenchmark.p',fact_inverse__nonpositive__iff__nonpositive) ).
fof(fact_inverse__nonnegative__iff__nonnegative,axiom,
! [V_a_2,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,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_inverse__nonnegative__iff__nonnegative) ).
fof(fact_inverse__less__imp__less__neg,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_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_b,V_a) ) ) ),
file('theBenchmark.p',fact_inverse__less__imp__less__neg) ).
fof(fact_inverse__less__imp__less,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(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,V_b,V_a) ) ) ),
file('theBenchmark.p',fact_inverse__less__imp__less) ).
fof(fact_inverse__negative__imp__negative,axiom,
! [V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_inverse__negative__imp__negative) ).
fof(fact_less__imp__inverse__less__neg,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ),
file('theBenchmark.p',fact_less__imp__inverse__less__neg) ).
fof(fact_less__imp__inverse__less,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ),
file('theBenchmark.p',fact_less__imp__inverse__less) ).
fof(fact_negative__imp__inverse__negative,axiom,
! [V_a,T_a] :
( class_Fields_Olinordered__field(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_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_negative__imp__inverse__negative) ).
fof(fact_inverse__positive__imp__positive,axiom,
! [V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_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_a) ) ) ),
file('theBenchmark.p',fact_inverse__positive__imp__positive) ).
fof(fact_positive__imp__inverse__positive,axiom,
! [V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ),
file('theBenchmark.p',fact_positive__imp__inverse__positive) ).
fof(fact_inverse__negative__iff__negative,axiom,
! [V_a_2,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(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_inverse__negative__iff__negative) ).
fof(fact_inverse__positive__iff__positive,axiom,
! [V_a_2,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(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_inverse__positive__iff__positive) ).
fof(fact_nonzero__inverse__mult__distrib,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ),
file('theBenchmark.p',fact_nonzero__inverse__mult__distrib) ).
fof(fact_inverse__unique,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b) = c_Groups_Oone__class_Oone(T_a)
=> c_Rings_Oinverse__class_Oinverse(T_a,V_a) = V_b ) ),
file('theBenchmark.p',fact_inverse__unique) ).
fof(fact_field__divide__inverse,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Ofield(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) ),
file('theBenchmark.p',fact_field__divide__inverse) ).
fof(fact_divide__inverse,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) ),
file('theBenchmark.p',fact_divide__inverse) ).
fof(fact_field__class_Onormalizing__field__rules_I2_J,axiom,
! [V_a,T_a] :
( class_Fields_Ofield(T_a)
=> c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a) ),
file('theBenchmark.p',fact_field__class_Onormalizing__field__rules_I2_J) ).
fof(fact_inverse__eq__divide,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a) ),
file('theBenchmark.p',fact_inverse__eq__divide) ).
fof(fact_add__nonpos__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(fact_add__increasing2,axiom,
! [V_a,V_b,V_c,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
file('theBenchmark.p',fact_add__increasing2) ).
fof(fact_add__increasing,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
file('theBenchmark.p',fact_add__increasing) ).
fof(fact_add__nonneg__eq__0__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ),
file('theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(fact_add__nonneg__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ),
file('theBenchmark.p',fact_add__nonneg__nonneg) ).
fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
file('theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_add__neg__neg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_add__neg__neg) ).
fof(fact_add__pos__pos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ),
file('theBenchmark.p',fact_add__pos__pos) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
file('theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_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__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_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(c_Groups_Otimes__class_Otimes(T_a,V_r),V_c)) != c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_r),V_d)) ) ) ),
file('theBenchmark.p',fact_add__scale__eq__noteq) ).
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_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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_m),V_m) = 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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_m)) = 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(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_divide__real__def,axiom,
! [V_y,V_x] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,V_y) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_y)),
file('theBenchmark.p',fact_divide__real__def) ).
fof(fact_real__divide__def,axiom,
! [V_S,V_R] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_R,V_S) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_R),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_S)),
file('theBenchmark.p',fact_real__divide__def) ).
fof(fact_real__two__squares__add__zero__iff,axiom,
! [V_y_2,V_x_2] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_x_2),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_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_inverse__le__imp__le__neg,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))
=> ( 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_b,V_a) ) ) ),
file('theBenchmark.p',fact_inverse__le__imp__le__neg) ).
fof(fact_inverse__le__imp__le,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(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__eq(T_a,V_b,V_a) ) ) ),
file('theBenchmark.p',fact_inverse__le__imp__le) ).
fof(fact_le__imp__inverse__le__neg,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(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__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ),
file('theBenchmark.p',fact_le__imp__inverse__le__neg) ).
fof(fact_le__imp__inverse__le,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Olinordered__field(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_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ),
file('theBenchmark.p',fact_le__imp__inverse__le) ).
fof(fact_inverse__le__1__iff,axiom,
! [V_x_2,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_inverse__le__1__iff) ).
fof(fact_one__less__inverse,axiom,
! [V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ) ),
file('theBenchmark.p',fact_one__less__inverse) ).
fof(fact_one__less__inverse__iff,axiom,
! [V_x_2,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))
<=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) ) ) ),
file('theBenchmark.p',fact_one__less__inverse__iff) ).
fof(fact_field__inverse,axiom,
! [V_a,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_a) = c_Groups_Oone__class_Oone(T_a) ) ),
file('theBenchmark.p',fact_field__inverse) ).
fof(fact_left__inverse,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_a) = c_Groups_Oone__class_Oone(T_a) ) ),
file('theBenchmark.p',fact_left__inverse) ).
fof(fact_right__inverse,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = c_Groups_Oone__class_Oone(T_a) ) ),
file('theBenchmark.p',fact_right__inverse) ).
fof(fact_nonzero__inverse__eq__divide,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a) ) ),
file('theBenchmark.p',fact_nonzero__inverse__eq__divide) ).
fof(fact_add__nonpos__neg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_add__neg__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__strict__increasing2,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
file('theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_add__strict__increasing,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
file('theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_add__nonneg__pos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ),
file('theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__pos__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ),
file('theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_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_add__frac__eq,axiom,
! [V_w,V_x,V_z,V_y,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_y != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_w,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_z),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_w),V_y)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_z)) ) ) ),
file('theBenchmark.p',fact_add__frac__eq) ).
fof(fact_divide__add__eq__iff,axiom,
! [V_y,V_x,V_z,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y)),V_z) ) ),
file('theBenchmark.p',fact_divide__add__eq__iff) ).
fof(fact_add__frac__num,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( V_y != c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y)),V_y) ) ),
file('theBenchmark.p',fact_add__frac__num) ).
fof(fact_add__divide__eq__iff,axiom,
! [V_y,V_x,V_z,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_x),V_y),V_z) ) ),
file('theBenchmark.p',fact_add__divide__eq__iff) ).
fof(fact_add__num__frac,axiom,
! [V_x,V_z,V_y,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( V_y != c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y)),V_y) ) ),
file('theBenchmark.p',fact_add__num__frac) ).
fof(fact_real__mult__inverse__left,axiom,
! [V_x] :
( V_x != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_real__mult__inverse__left) ).
fof(fact_gt__half__sum,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_b) ) ),
file('theBenchmark.p',fact_gt__half__sum) ).
fof(fact_less__half__sum,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)))) ) ),
file('theBenchmark.p',fact_less__half__sum) ).
fof(fact_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_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(c_Groups_Otimes__class_Otimes(T_a,V_x),V_x),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(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),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__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(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),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_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(c_Groups_Otimes__class_Otimes(T_a,V_x),V_x),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_y))) ),
file('theBenchmark.p',fact_sum__squares__ge__zero) ).
fof(fact_real__mult__inverse__cancel2,axiom,
! [V_u,V_y,V_x1,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_x1)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x1),V_y),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_u))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_u),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x1))) ) ) ),
file('theBenchmark.p',fact_real__mult__inverse__cancel2) ).
fof(fact_real__mult__inverse__cancel,axiom,
! [V_u,V_y,V_x1,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_x1)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x1),V_y),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_u))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),V_y),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x1)),V_u)) ) ) ),
file('theBenchmark.p',fact_real__mult__inverse__cancel) ).
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(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),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_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_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_field__le__epsilon,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( ! [B_e] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),B_e)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Oplus__class_Oplus(T_a,V_y,B_e)) )
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_field__le__epsilon) ).
fof(fact_ln__add__one__self__le__self,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,hAPP(c_Transcendental_Oln,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)),V_x) ),
file('theBenchmark.p',fact_ln__add__one__self__le__self) ).
fof(fact_ln__mult,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)
=> hAPP(c_Transcendental_Oln,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x),hAPP(c_Transcendental_Oln,V_y)) ) ),
file('theBenchmark.p',fact_ln__mult) ).
fof(fact_ln__less__cancel__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x_2),hAPP(c_Transcendental_Oln,V_y_2))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_ln__less__cancel__iff) ).
fof(fact_ln__inj__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
=> ( hAPP(c_Transcendental_Oln,V_x_2) = hAPP(c_Transcendental_Oln,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_ln__inj__iff) ).
fof(fact_ln__less__self,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x),V_x) ),
file('theBenchmark.p',fact_ln__less__self) ).
fof(fact_ln__one,axiom,
hAPP(c_Transcendental_Oln,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('theBenchmark.p',fact_ln__one) ).
fof(fact_ln__le__cancel__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x_2),hAPP(c_Transcendental_Oln,V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_ln__le__cancel__iff) ).
fof(fact_ln__ge__zero,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x)) ),
file('theBenchmark.p',fact_ln__ge__zero) ).
fof(fact_ln__gt__zero__imp__gt__one,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,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_Oone__class_Oone(tc_RealDef_Oreal),V_x) ) ),
file('theBenchmark.p',fact_ln__gt__zero__imp__gt__one) ).
fof(fact_ln__less__zero,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
file('theBenchmark.p',fact_ln__less__zero) ).
fof(fact_ln__less__zero__iff,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
file('theBenchmark.p',fact_ln__less__zero__iff) ).
fof(fact_ln__eq__zero__iff,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> ( hAPP(c_Transcendental_Oln,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> V_x_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
file('theBenchmark.p',fact_ln__eq__zero__iff) ).
fof(fact_ln__gt__zero__iff,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x_2))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2) ) ),
file('theBenchmark.p',fact_ln__gt__zero__iff) ).
fof(fact_ln__gt__zero,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x)) ),
file('theBenchmark.p',fact_ln__gt__zero) ).
fof(fact_ln__ge__zero__imp__ge__one,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,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__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x) ) ),
file('theBenchmark.p',fact_ln__ge__zero__imp__ge__one) ).
fof(fact_ln__ge__zero__iff,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,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_ln__ge__zero__iff) ).
fof(fact_divide__le__eq__number__of1,axiom,
! [V_a_2,V_wa_2,V_b_2,T_a] :
( ( class_Int_Onumber(T_a)
& class_Fields_Olinordered__field__inverse__zero(T_a) )
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)
<=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2) ) ) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))) ) ) ) ),
file('theBenchmark.p',fact_divide__le__eq__number__of1) ).
fof(fact_divide__le__eq__number__of,axiom,
! [V_wa_2,V_ca_2,V_b_2,T_a] :
( ( class_Int_Onumber(T_a)
& class_Fields_Olinordered__field__inverse__zero(T_a) )
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_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_ca_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) )
& ( 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(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_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__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)) ) ) ) ),
file('theBenchmark.p',fact_divide__le__eq__number__of) ).
fof(fact_le__divide__eq__number__of,axiom,
! [V_ca_2,V_b_2,V_wa_2,T_a] :
( ( class_Int_Onumber(T_a)
& class_Fields_Olinordered__field__inverse__zero(T_a) )
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_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_ca_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(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,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)) ) ) )
& ( 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(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2) ) ) ) ),
file('theBenchmark.p',fact_le__divide__eq__number__of) ).
fof(fact_le__divide__eq__number__of1,axiom,
! [V_wa_2,V_b_2,V_a_2,T_a] :
( ( class_Int_Onumber(T_a)
& class_Fields_Olinordered__field__inverse__zero(T_a) )
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))
<=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))) ) ) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2) ) ) ) ),
file('theBenchmark.p',fact_le__divide__eq__number__of1) ).
fof(fact_DERIV__ln__divide,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,V_x_2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2)) ),
file('theBenchmark.p',fact_DERIV__ln__divide) ).
fof(fact_add__number__of__left,axiom,
! [V_z,V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_z) ),
file('theBenchmark.p',fact_add__number__of__left) ).
fof(fact_add__number__of__eq,axiom,
! [V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)) ),
file('theBenchmark.p',fact_add__number__of__eq) ).
fof(fact_number__of__add,axiom,
! [V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ),
file('theBenchmark.p',fact_number__of__add) ).
fof(fact_less__number__of,axiom,
! [V_y_2,V_x_2,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_less__number__of) ).
fof(fact_eq__number__of,axiom,
! [V_y_2,V_x_2,T_a] :
( ( class_Int_Oring__char__0(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_eq__number__of) ).
fof(fact_number__of__reorient,axiom,
! [V_x_2,V_wa_2,T_a] :
( class_Int_Onumber(T_a)
=> ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = V_x_2
<=> V_x_2 = c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) ) ),
file('theBenchmark.p',fact_number__of__reorient) ).
fof(fact_mult__number__of__left,axiom,
! [V_z,V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v)),hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)),V_z)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_w))),V_z) ),
file('theBenchmark.p',fact_mult__number__of__left) ).
fof(fact_arith__simps_I32_J,axiom,
! [V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_w)) ),
file('theBenchmark.p',fact_arith__simps_I32_J) ).
fof(fact_number__of__mult,axiom,
! [V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Int_Onumber__class_Onumber__of(T_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_w)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ),
file('theBenchmark.p',fact_number__of__mult) ).
fof(fact_le__number__of,axiom,
! [V_y_2,V_x_2,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_le__number__of) ).
fof(fact_le__number__of__eq__not__less,axiom,
! [V_wa_2,V_v_2,T_a] :
( ( class_Orderings_Olinorder(T_a)
& class_Int_Onumber(T_a) )
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
<=> ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2)) ) ),
file('theBenchmark.p',fact_le__number__of__eq__not__less) ).
fof(fact_left__distrib__number__of,axiom,
! [V_v,V_b,V_a,T_b] :
( ( class_Rings_Osemiring(T_b)
& class_Int_Onumber(T_b) )
=> hAPP(c_Groups_Otimes__class_Otimes(T_b,c_Groups_Oplus__class_Oplus(T_b,V_a,V_b)),c_Int_Onumber__class_Onumber__of(T_b,V_v)) = c_Groups_Oplus__class_Oplus(T_b,hAPP(c_Groups_Otimes__class_Otimes(T_b,V_a),c_Int_Onumber__class_Onumber__of(T_b,V_v)),hAPP(c_Groups_Otimes__class_Otimes(T_b,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v))) ),
file('theBenchmark.p',fact_left__distrib__number__of) ).
fof(fact_right__distrib__number__of,axiom,
! [V_c,V_b,V_v,T_b] :
( ( class_Rings_Osemiring(T_b)
& class_Int_Onumber(T_b) )
=> hAPP(c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Oplus__class_Oplus(T_b,V_b,V_c)) = c_Groups_Oplus__class_Oplus(T_b,hAPP(c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_b),hAPP(c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_c)) ),
file('theBenchmark.p',fact_right__distrib__number__of) ).
fof(fact_eq__divide__eq__number__of1,axiom,
! [V_wa_2,V_b_2,V_a_2,T_a] :
( ( class_Int_Onumber(T_a)
& class_Fields_Ofield__inverse__zero(T_a) )
=> ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
<=> ( ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Groups_Ozero__class_Ozero(T_a)
=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) = V_b_2 ) ) ) ),
file('theBenchmark.p',fact_eq__divide__eq__number__of1) ).
fof(fact_eq__divide__eq__number__of,axiom,
! [V_ca_2,V_b_2,V_wa_2,T_a] :
( ( class_Int_Onumber(T_a)
& class_Fields_Ofield__inverse__zero(T_a) )
=> ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)
<=> ( ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
=> c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2) = V_b_2 ) ) ) ),
file('theBenchmark.p',fact_eq__divide__eq__number__of) ).
fof(fact_divide__eq__eq__number__of,axiom,
! [V_wa_2,V_ca_2,V_b_2,T_a] :
( ( class_Int_Onumber(T_a)
& class_Fields_Ofield__inverse__zero(T_a) )
=> ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2) = c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)
<=> ( ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
=> c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
=> V_b_2 = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2) ) ) ) ),
file('theBenchmark.p',fact_divide__eq__eq__number__of) ).
fof(fact_divide__eq__eq__number__of1,axiom,
! [V_a_2,V_wa_2,V_b_2,T_a] :
( ( class_Int_Onumber(T_a)
& class_Fields_Ofield__inverse__zero(T_a) )
=> ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) = V_a_2
<=> ( ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Groups_Ozero__class_Ozero(T_a)
=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) != c_Groups_Ozero__class_Ozero(T_a)
=> V_b_2 = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) ) ) ) ),
file('theBenchmark.p',fact_divide__eq__eq__number__of1) ).
fof(fact_inverse__eq__divide__number__of,axiom,
! [V_w,T_b] :
( ( class_Rings_Odivision__ring(T_b)
& class_Int_Onumber(T_b) )
=> c_Rings_Oinverse__class_Oinverse(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_w)) = c_Rings_Oinverse__class_Odivide(T_b,c_Groups_Oone__class_Oone(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ),
file('theBenchmark.p',fact_inverse__eq__divide__number__of) ).
fof(fact_divide__less__eq__number__of1,axiom,
! [V_a_2,V_wa_2,V_b_2,T_a] :
( ( class_Int_Onumber(T_a)
& class_Fields_Olinordered__field__inverse__zero(T_a) )
=> ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)
<=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2) ) ) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
=> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))) ) ) ) ),
file('theBenchmark.p',fact_divide__less__eq__number__of1) ).
fof(fact_divide__less__eq__number__of,axiom,
! [V_wa_2,V_ca_2,V_b_2,T_a] :
( ( class_Int_Onumber(T_a)
& class_Fields_Olinordered__field__inverse__zero(T_a) )
=> ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_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_ca_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_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,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_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,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)) ) ) ) ),
file('theBenchmark.p',fact_divide__less__eq__number__of) ).
fof(fact_less__divide__eq__number__of,axiom,
! [V_ca_2,V_b_2,V_wa_2,T_a] :
( ( class_Int_Onumber(T_a)
& class_Fields_Olinordered__field__inverse__zero(T_a) )
=> ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_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_ca_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(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,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_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(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_2) ) ) ) ),
file('theBenchmark.p',fact_less__divide__eq__number__of) ).
fof(fact_less__divide__eq__number__of1,axiom,
! [V_wa_2,V_b_2,V_a_2,T_a] :
( ( class_Int_Onumber(T_a)
& class_Fields_Olinordered__field__inverse__zero(T_a) )
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))
<=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))) ) ) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
=> c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2) ) ) ) ),
file('theBenchmark.p',fact_less__divide__eq__number__of1) ).
fof(fact_DERIV__ln,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,V_x_2,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x_2)) ),
file('theBenchmark.p',fact_DERIV__ln) ).
fof(fact_DERIV__cmult__Id,axiom,
! [V_x_2,V_ca_2,T_a] :
( class_RealVector_Oreal__normed__field(T_a)
=> c_Deriv_Oderiv(T_a,c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_x_2,V_ca_2) ),
file('theBenchmark.p',fact_DERIV__cmult__Id) ).
fof(fact_number__of__succ,axiom,
! [V_k,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Int_Onumber__class_Onumber__of(T_a,c_Int_Osucc(V_k)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_k)) ),
file('theBenchmark.p',fact_number__of__succ) ).
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_exp__ge__add__one__self__aux,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x)) ),
file('theBenchmark.p',fact_exp__ge__add__one__self__aux) ).
fof(fact_exp__less__mono,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y)) ),
file('theBenchmark.p',fact_exp__less__mono) ).
fof(fact_plus__numeral__code_I9_J,axiom,
! [V_w,V_v] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),
file('theBenchmark.p',fact_plus__numeral__code_I9_J) ).
fof(fact_less__number__of__int__code,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ),
file('theBenchmark.p',fact_less__number__of__int__code) ).
fof(fact_times__numeral__code_I5_J,axiom,
! [V_w,V_v] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_w)),
file('theBenchmark.p',fact_times__numeral__code_I5_J) ).
fof(fact_minus__number__of__mult,axiom,
! [V_z,V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w))),V_z) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))),V_z) ),
file('theBenchmark.p',fact_minus__number__of__mult) ).
fof(fact_number__of__minus,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)) ),
file('theBenchmark.p',fact_number__of__minus) ).
fof(fact_arith__simps_I30_J,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) ),
file('theBenchmark.p',fact_arith__simps_I30_J) ).
fof(fact_less__eq__number__of__int__code,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ),
file('theBenchmark.p',fact_less__eq__number__of__int__code) ).
fof(fact_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_exp__le__cancel__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ),
file('theBenchmark.p',fact_exp__le__cancel__iff) ).
fof(fact_exp__minus,axiom,
! [V_x,T_a] :
( ( class_SEQ_Obanach(T_a)
& class_RealVector_Oreal__normed__field(T_a) )
=> hAPP(c_Transcendental_Oexp(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Transcendental_Oexp(T_a),V_x)) ),
file('theBenchmark.p',fact_exp__minus) ).
fof(fact_exp__inj__iff,axiom,
! [V_y_2,V_x_2] :
( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2) = hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y_2)
<=> V_x_2 = V_y_2 ),
file('theBenchmark.p',fact_exp__inj__iff) ).
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_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_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_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_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_square__eq__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Rings_Oidom(T_a)
=> ( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_a_2) = 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(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(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(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = 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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = 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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = 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_mult__left_Ominus,axiom,
! [V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> 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(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y)) ),
file('theBenchmark.p',fact_mult__left_Ominus) ).
fof(fact_mult_Ominus__left,axiom,
! [V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> 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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) ),
file('theBenchmark.p',fact_mult_Ominus__left) ).
fof(fact_mult__right_Ominus,axiom,
! [V_x,V_xa,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> 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(c_Groups_Otimes__class_Otimes(T_a,V_xa),V_x)) ),
file('theBenchmark.p',fact_mult__right_Ominus) ).
fof(fact_mult_Ominus__right,axiom,
! [V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> 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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) ),
file('theBenchmark.p',fact_mult_Ominus__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_minus__divide__left,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) ),
file('theBenchmark.p',fact_minus__divide__left) ).
fof(fact_minus__divide__right,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
file('theBenchmark.p',fact_minus__divide__right) ).
fof(fact_minus__divide__divide,axiom,
! [V_b,V_a,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ),
file('theBenchmark.p',fact_minus__divide__divide) ).
fof(fact_divide_Ominus,axiom,
! [V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__field(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ),
file('theBenchmark.p',fact_divide_Ominus) ).
fof(fact_inverse__minus__eq,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring__inverse__zero(T_a)
=> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ),
file('theBenchmark.p',fact_inverse__minus__eq) ).
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_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_exp__less__cancel__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y_2))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ),
file('theBenchmark.p',fact_exp__less__cancel__iff) ).
fof(fact_exp__less__cancel,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y) ),
file('theBenchmark.p',fact_exp__less__cancel) ).
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_zmult__1,axiom,
! [V_z] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z,
file('theBenchmark.p',fact_zmult__1) ).
fof(fact_zmult__1__right,axiom,
! [V_z] : hAPP(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__assoc,axiom,
! [V_z3,V_z2,V_z1] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1),V_z2)),V_z3) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2),V_z3)),
file('theBenchmark.p',fact_zmult__assoc) ).
fof(fact_zmult__commute,axiom,
! [V_w,V_z] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z),V_w) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w),V_z),
file('theBenchmark.p',fact_zmult__commute) ).
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__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(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k),V_i),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k),V_j)) ) ),
file('theBenchmark.p',fact_zmult__zless__mono2) ).
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(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_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_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_succ__def,axiom,
! [V_k] : c_Int_Osucc(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('theBenchmark.p',fact_succ__def) ).
fof(fact_zadd__0,axiom,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z,
file('theBenchmark.p',fact_zadd__0) ).
fof(fact_zadd__0__right,axiom,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z,
file('theBenchmark.p',fact_zadd__0__right) ).
fof(fact_zless__add1__eq,axiom,
! [V_za_2,V_wa_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> ( V_wa_2 = V_za_2
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) ) ),
file('theBenchmark.p',fact_zless__add1__eq) ).
fof(fact_odd__less__0,axiom,
! [V_za_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2),V_za_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('theBenchmark.p',fact_odd__less__0) ).
fof(fact_zadd__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_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__zmult__distrib,axiom,
! [V_w,V_z2,V_z1] : 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(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1),V_w),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2),V_w)),
file('theBenchmark.p',fact_zadd__zmult__distrib) ).
fof(fact_zadd__zmult__distrib2,axiom,
! [V_z2,V_z1,V_w] : 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(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w),V_z1),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w),V_z2)),
file('theBenchmark.p',fact_zadd__zmult__distrib2) ).
fof(fact_int__one__le__iff__zero__less,axiom,
! [V_za_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_za_2) ),
file('theBenchmark.p',fact_int__one__le__iff__zero__less) ).
fof(fact_zle__add1__eq__le,axiom,
! [V_za_2,V_wa_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,V_za_2) ),
file('theBenchmark.p',fact_zle__add1__eq__le) ).
fof(fact_add1__zle__eq,axiom,
! [V_za_2,V_wa_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_za_2)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) ),
file('theBenchmark.p',fact_add1__zle__eq) ).
fof(fact_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_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_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_zless__le,axiom,
! [V_wa_2,V_za_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_wa_2)
<=> ( V_za_2 != V_wa_2
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_za_2,V_wa_2) ) ),
file('theBenchmark.p',fact_zless__le) ).
fof(fact_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_ln__exp,axiom,
! [V_x] : hAPP(c_Transcendental_Oln,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x)) = V_x,
file('theBenchmark.p',fact_ln__exp) ).
fof(fact_exp__ln__eq,axiom,
! [V_x,V_u] :
( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_u) = V_x
=> hAPP(c_Transcendental_Oln,V_x) = V_u ),
file('theBenchmark.p',fact_exp__ln__eq) ).
fof(fact_ln__unique,axiom,
! [V_x,V_y] :
( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y) = V_x
=> hAPP(c_Transcendental_Oln,V_x) = V_y ),
file('theBenchmark.p',fact_ln__unique) ).
fof(fact_exp__not__eq__zero,axiom,
! [V_x,T_a] :
( ( class_SEQ_Obanach(T_a)
& class_RealVector_Oreal__normed__field(T_a) )
=> hAPP(c_Transcendental_Oexp(T_a),V_x) != c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_exp__not__eq__zero) ).
fof(fact_DERIV__exp,axiom,
! [V_x_2,T_a] :
( ( class_SEQ_Obanach(T_a)
& class_RealVector_Oreal__normed__field(T_a) )
=> c_Deriv_Oderiv(T_a,c_Transcendental_Oexp(T_a),V_x_2,hAPP(c_Transcendental_Oexp(T_a),V_x_2)) ),
file('theBenchmark.p',fact_DERIV__exp) ).
fof(fact_minus__le__self__iff,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
file('theBenchmark.p',fact_minus__le__self__iff) ).
fof(fact_neg__le__0__iff__le,axiom,
! [V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
file('theBenchmark.p',fact_neg__le__0__iff__le) ).
fof(fact_le__minus__self__iff,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_le__minus__self__iff) ).
fof(fact_neg__0__le__iff__le,axiom,
! [V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_neg__0__le__iff__le) ).
fof(fact_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_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__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_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_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_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(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_square__eq__1__iff,axiom,
! [V_x_2,T_a] :
( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( 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_nonzero__minus__divide__divide,axiom,
! [V_a,V_b,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) ) ),
file('theBenchmark.p',fact_nonzero__minus__divide__divide) ).
fof(fact_nonzero__minus__divide__right,axiom,
! [V_a,V_b,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ),
file('theBenchmark.p',fact_nonzero__minus__divide__right) ).
fof(fact_nonzero__inverse__minus__eq,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) ) ),
file('theBenchmark.p',fact_nonzero__inverse__minus__eq) ).
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(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_u),V_u)),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__eq__0__iff,axiom,
! [V_y_2,V_x_2] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> V_y_2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2) ),
file('theBenchmark.p',fact_real__add__eq__0__iff) ).
fof(fact_real__add__minus__iff,axiom,
! [V_a_2,V_x_2] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> V_x_2 = V_a_2 ),
file('theBenchmark.p',fact_real__add__minus__iff) ).
fof(fact_exp__ge__zero,axiom,
! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x)),
file('theBenchmark.p',fact_exp__ge__zero) ).
fof(fact_not__exp__le__zero,axiom,
! [V_x] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('theBenchmark.p',fact_not__exp__le__zero) ).
fof(fact_exp__gt__zero,axiom,
! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x)),
file('theBenchmark.p',fact_exp__gt__zero) ).
fof(fact_not__exp__less__zero,axiom,
! [V_x] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('theBenchmark.p',fact_not__exp__less__zero) ).
fof(fact_exp__eq__one__iff,axiom,
! [V_x_2] :
( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
<=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_exp__eq__one__iff) ).
fof(fact_exp__zero,axiom,
! [T_a] :
( ( class_SEQ_Obanach(T_a)
& class_RealVector_Oreal__normed__field(T_a) )
=> hAPP(c_Transcendental_Oexp(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_exp__zero) ).
fof(fact_exp__add,axiom,
! [V_y,V_x,T_a] :
( ( class_SEQ_Obanach(T_a)
& class_RealVector_Oreal__normed__field(T_a) )
=> hAPP(c_Transcendental_Oexp(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Transcendental_Oexp(T_a),V_x)),hAPP(c_Transcendental_Oexp(T_a),V_y)) ),
file('theBenchmark.p',fact_exp__add) ).
fof(fact_mult__exp__exp,axiom,
! [V_y,V_x,T_a] :
( ( class_SEQ_Obanach(T_a)
& class_RealVector_Oreal__normed__field(T_a) )
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Transcendental_Oexp(T_a),V_x)),hAPP(c_Transcendental_Oexp(T_a),V_y)) = hAPP(c_Transcendental_Oexp(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) ),
file('theBenchmark.p',fact_mult__exp__exp) ).
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__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__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_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_exp__le__one__iff,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(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_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('theBenchmark.p',fact_exp__le__one__iff) ).
fof(fact_one__le__exp__iff,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
file('theBenchmark.p',fact_one__le__exp__iff) ).
fof(fact_exp__gt__one,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x)) ),
file('theBenchmark.p',fact_exp__gt__one) ).
fof(fact_exp__less__one__iff,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('theBenchmark.p',fact_exp__less__one__iff) ).
fof(fact_one__less__exp__iff,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
file('theBenchmark.p',fact_one__less__exp__iff) ).
fof(fact_exp__ln,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x)) = V_x ),
file('theBenchmark.p',fact_exp__ln) ).
fof(fact_exp__ln__iff,axiom,
! [V_x_2] :
( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x_2)) = V_x_2
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
file('theBenchmark.p',fact_exp__ln__iff) ).
fof(fact_DERIV__unique,axiom,
! [V_E_2,V_D_2,V_x_2,V_f_2,T_a] :
( class_RealVector_Oreal__normed__field(T_a)
=> ( c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_D_2)
=> ( c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_E_2)
=> V_D_2 = V_E_2 ) ) ),
file('theBenchmark.p',fact_DERIV__unique) ).
fof(fact_DERIV__cong,axiom,
! [V_Y_2,V_X_2,V_x_2,V_f_2,T_a] :
( class_RealVector_Oreal__normed__field(T_a)
=> ( c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_X_2)
=> ( V_X_2 = V_Y_2
=> c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_Y_2) ) ) ),
file('theBenchmark.p',fact_DERIV__cong) ).
fof(fact_Deriv_Olemma__DERIV__subst,axiom,
! [V_E_2,V_D_2,V_x_2,V_f_2,T_a] :
( class_RealVector_Oreal__normed__field(T_a)
=> ( c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_D_2)
=> ( V_D_2 = V_E_2
=> c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_E_2) ) ) ),
file('theBenchmark.p',fact_Deriv_Olemma__DERIV__subst) ).
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_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_ln__inverse,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> hAPP(c_Transcendental_Oln,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x)) ),
file('theBenchmark.p',fact_ln__inverse) ).
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(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q),V_r) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,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(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(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(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(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q),V_r) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,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(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(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(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_minus__numeral__code_I5_J,axiom,
! [V_w] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),
file('theBenchmark.p',fact_minus__numeral__code_I5_J) ).
fof(fact_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_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_zmult__zminus,axiom,
! [V_w,V_z] : 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(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z),V_w)),
file('theBenchmark.p',fact_zmult__zminus) ).
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_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_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_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_number__of__is__id,axiom,
! [V_k] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k) = V_k,
file('theBenchmark.p',fact_number__of__is__id) ).
fof(fact_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(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(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_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(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_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(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_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(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_I1_J,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y)) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_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_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_eq__number__of__eq,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Int_Onumber__ring(T_a)
=> ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
<=> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))) ) ),
file('theBenchmark.p',fact_eq__number__of__eq) ).
fof(fact_DERIV__pos__inc__right,axiom,
! [V_l_2,V_x_2,V_f_2] :
( c_Deriv_Oderiv(tc_RealDef_Oreal,V_f_2,V_x_2,V_l_2)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_l_2)
=> ? [B_d] :
( ! [B_h] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_h)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_h,B_d)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(V_f_2,V_x_2),hAPP(V_f_2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,B_h))) ) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d) ) ) ),
file('theBenchmark.p',fact_DERIV__pos__inc__right) ).
fof(fact_DERIV__neg__dec__right,axiom,
! [V_l_2,V_x_2,V_f_2] :
( c_Deriv_Oderiv(tc_RealDef_Oreal,V_f_2,V_x_2,V_l_2)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_l_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> ? [B_d] :
( ! [B_h] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_h)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_h,B_d)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(V_f_2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,B_h)),hAPP(V_f_2,V_x_2)) ) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d) ) ) ),
file('theBenchmark.p',fact_DERIV__neg__dec__right) ).
fof(fact_iszero__def,axiom,
! [V_za_2,T_a] :
( class_Rings_Osemiring__1(T_a)
=> ( c_Int_Oiszero(T_a,V_za_2)
<=> V_za_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_iszero__def) ).
fof(fact_iszero__0,axiom,
! [T_a] :
( class_Rings_Osemiring__1(T_a)
=> c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ),
file('theBenchmark.p',fact_iszero__0) ).
fof(fact_not__iszero__1,axiom,
! [T_a] :
( class_Rings_Osemiring__1(T_a)
=> ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ),
file('theBenchmark.p',fact_not__iszero__1) ).
fof(fact_eq__special_I3_J,axiom,
! [V_x_2,T_a] :
( class_Int_Onumber__ring(T_a)
=> ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls)))) ) ),
file('theBenchmark.p',fact_eq__special_I3_J) ).
fof(fact_eq__special_I1_J,axiom,
! [V_y_2,T_a] :
( class_Int_Onumber__ring(T_a)
=> ( c_Groups_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
<=> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))) ) ),
file('theBenchmark.p',fact_eq__special_I1_J) ).
fof(fact_number__of__pred,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Int_Onumber__class_Onumber__of(T_a,c_Int_Opred(V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ),
file('theBenchmark.p',fact_number__of__pred) ).
fof(fact_less__nat__number__of,axiom,
! [V_v_H_2,V_v_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))
<=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2)
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_H_2) ) ) ),
file('theBenchmark.p',fact_less__nat__number__of) ).
fof(fact_less__0__number__of,axiom,
! [V_v_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_2) ),
file('theBenchmark.p',fact_less__0__number__of) ).
fof(fact_eq__0__number__of,axiom,
! [V_v_2] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ),
file('theBenchmark.p',fact_eq__0__number__of) ).
fof(fact_eq__number__of__0,axiom,
! [V_v_2] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ),
file('theBenchmark.p',fact_eq__number__of__0) ).
fof(fact_le__nat__number__of,axiom,
! [V_v_H_2,V_v_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,V_v_H_2)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) ) ),
file('theBenchmark.p',fact_le__nat__number__of) ).
fof(fact_minus__Pls,axiom,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls) = c_Int_OPls,
file('theBenchmark.p',fact_minus__Pls) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_Pls__def) ).
fof(fact_semiring__norm_I113_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
file('theBenchmark.p',fact_semiring__norm_I113_J) ).
fof(fact_nat__number__of__Pls,axiom,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_nat__number__of__Pls) ).
fof(fact_add__Pls__right,axiom,
! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_OPls) = V_k,
file('theBenchmark.p',fact_add__Pls__right) ).
fof(fact_add__Pls,axiom,
! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,V_k) = V_k,
file('theBenchmark.p',fact_add__Pls) ).
fof(fact_rel__simps_I2_J,axiom,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
file('theBenchmark.p',fact_rel__simps_I2_J) ).
fof(fact_mult__Pls,axiom,
! [V_w] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls),V_w) = c_Int_OPls,
file('theBenchmark.p',fact_mult__Pls) ).
fof(fact_rel__simps_I19_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
file('theBenchmark.p',fact_rel__simps_I19_J) ).
fof(fact_succ__pred,axiom,
! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x,
file('theBenchmark.p',fact_succ__pred) ).
fof(fact_semiring__norm_I112_J,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls) ),
file('theBenchmark.p',fact_semiring__norm_I112_J) ).
fof(fact_number__of__Pls,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_number__of__Pls) ).
fof(fact_add__numeral__0__right,axiom,
! [V_a,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) = V_a ),
file('theBenchmark.p',fact_add__numeral__0__right) ).
fof(fact_add__numeral__0,axiom,
! [V_a,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls),V_a) = V_a ),
file('theBenchmark.p',fact_add__numeral__0) ).
fof(fact_bin__less__0__simps_I1_J,axiom,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('theBenchmark.p',fact_bin__less__0__simps_I1_J) ).
fof(fact_zero__is__num__zero,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),
file('theBenchmark.p',fact_zero__is__num__zero) ).
fof(fact_add__nat__number__of,axiom,
! [V_v_H,V_v] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
=> ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_v_H)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v) ) ) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H) ) ),
file('theBenchmark.p',fact_add__nat__number__of) ).
fof(fact_nat__number__of__mult__left,axiom,
! [V_k,V_v_H,V_v] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
=> hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)),V_k)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_v_H))),V_k) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
=> hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)),V_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__number__of__mult__left) ).
fof(fact_mult__nat__number__of,axiom,
! [V_v_H,V_v] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
=> hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_v_H)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
=> hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_mult__nat__number__of) ).
fof(fact_iszero__Numeral0,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) ),
file('theBenchmark.p',fact_iszero__Numeral0) ).
fof(fact_nat__1__add__number__of,axiom,
! [V_v] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__1__add__number__of) ).
fof(fact_nat__number__of__add__1,axiom,
! [V_v] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__number__of__add__1) ).
fof(fact_le__iff__pred__less,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(V_k_2),V_l_2) ),
file('theBenchmark.p',fact_le__iff__pred__less) ).
fof(fact_divide__Numeral0,axiom,
! [V_x,T_a] :
( ( class_Int_Onumber__ring(T_a)
& class_Fields_Ofield__inverse__zero(T_a) )
=> c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_divide__Numeral0) ).
fof(fact_le__special_I1_J,axiom,
! [V_y_2,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_y_2) ) ),
file('theBenchmark.p',fact_le__special_I1_J) ).
fof(fact_le__special_I3_J,axiom,
! [V_x_2,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OPls) ) ),
file('theBenchmark.p',fact_le__special_I3_J) ).
fof(fact_less__special_I1_J,axiom,
! [V_y_2,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_y_2) ) ),
file('theBenchmark.p',fact_less__special_I1_J) ).
fof(fact_less__special_I3_J,axiom,
! [V_x_2,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OPls) ) ),
file('theBenchmark.p',fact_less__special_I3_J) ).
fof(fact_number__of2,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
file('theBenchmark.p',fact_number__of2) ).
fof(fact_eq__special_I4_J,axiom,
! [V_x_2,T_a] :
( class_Int_Onumber__ring(T_a)
=> ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Groups_Oone__class_Oone(T_a)
<=> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))) ) ),
file('theBenchmark.p',fact_eq__special_I4_J) ).
fof(fact_eq__special_I2_J,axiom,
! [V_y_2,T_a] :
( class_Int_Onumber__ring(T_a)
=> ( c_Groups_Oone__class_Oone(T_a) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
<=> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))) ) ),
file('theBenchmark.p',fact_eq__special_I2_J) ).
fof(fact_Numeral1__eq1__nat,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)),
file('theBenchmark.p',fact_Numeral1__eq1__nat) ).
fof(fact_nat__numeral__1__eq__1,axiom,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('theBenchmark.p',fact_nat__numeral__1__eq__1) ).
fof(fact_rel__simps_I39_J,axiom,
! [V_l] : c_Int_OPls != c_Int_OBit1(V_l),
file('theBenchmark.p',fact_rel__simps_I39_J) ).
fof(fact_rel__simps_I46_J,axiom,
! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls,
file('theBenchmark.p',fact_rel__simps_I46_J) ).
fof(fact_less__eq__int__code_I16_J,axiom,
! [V_k2_2,V_k1_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ),
file('theBenchmark.p',fact_less__eq__int__code_I16_J) ).
fof(fact_rel__simps_I34_J,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ),
file('theBenchmark.p',fact_rel__simps_I34_J) ).
fof(fact_rel__simps_I17_J,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ),
file('theBenchmark.p',fact_rel__simps_I17_J) ).
fof(fact_less__int__code_I16_J,axiom,
! [V_k2_2,V_k1_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ),
file('theBenchmark.p',fact_less__int__code_I16_J) ).
fof(fact_rel__simps_I51_J,axiom,
! [V_l_2,V_k_2] :
( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
<=> V_k_2 = V_l_2 ),
file('theBenchmark.p',fact_rel__simps_I51_J) ).
fof(fact_rel__simps_I22_J,axiom,
! [V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) ),
file('theBenchmark.p',fact_rel__simps_I22_J) ).
fof(fact_bin__less__0__simps_I4_J,axiom,
! [V_wa_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('theBenchmark.p',fact_bin__less__0__simps_I4_J) ).
fof(fact_rel__simps_I12_J,axiom,
! [V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) ),
file('theBenchmark.p',fact_rel__simps_I12_J) ).
fof(fact_Bit1__def,axiom,
! [V_k] : c_Int_OBit1(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k),V_k),
file('theBenchmark.p',fact_Bit1__def) ).
fof(fact_minus__Bit1,axiom,
! [V_k] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(V_k)) = c_Int_OBit1(c_Int_Opred(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k))),
file('theBenchmark.p',fact_minus__Bit1) ).
fof(fact_iszero__number__of__Bit1,axiom,
! [V_w,T_a] :
( ( class_Int_Oring__char__0(T_a)
& class_Int_Onumber__ring(T_a) )
=> ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(V_w))) ),
file('theBenchmark.p',fact_iszero__number__of__Bit1) ).
fof(fact_succ__Pls,axiom,
c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
file('theBenchmark.p',fact_succ__Pls) ).
fof(fact_number__of__Bit1,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ),
file('theBenchmark.p',fact_number__of__Bit1) ).
fof(fact_mult__numeral__1,axiom,
! [V_a,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))),V_a) = V_a ),
file('theBenchmark.p',fact_mult__numeral__1) ).
fof(fact_mult__numeral__1__right,axiom,
! [V_a,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_a ),
file('theBenchmark.p',fact_mult__numeral__1__right) ).
fof(fact_numeral__1__eq__1,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_numeral__1__eq__1) ).
fof(fact_semiring__norm_I110_J,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Oone__class_Oone(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)) ),
file('theBenchmark.p',fact_semiring__norm_I110_J) ).
fof(fact_divide__Numeral1,axiom,
! [V_x,T_a] :
( ( class_Int_Onumber__ring(T_a)
& class_Fields_Ofield(T_a) )
=> c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_x ),
file('theBenchmark.p',fact_divide__Numeral1) ).
fof(fact_divide__numeral__1,axiom,
! [V_a,T_a] :
( ( class_Int_Onumber__ring(T_a)
& class_Fields_Ofield(T_a) )
=> c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_a ),
file('theBenchmark.p',fact_divide__numeral__1) ).
fof(fact_inverse__numeral__1,axiom,
! [T_a] :
( ( class_Int_Onumber__ring(T_a)
& class_Fields_Ofield(T_a) )
=> c_Rings_Oinverse__class_Oinverse(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)) ),
file('theBenchmark.p',fact_inverse__numeral__1) ).
fof(fact_rel__simps_I29_J,axiom,
! [V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) ),
file('theBenchmark.p',fact_rel__simps_I29_J) ).
fof(fact_rel__simps_I5_J,axiom,
! [V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) ),
file('theBenchmark.p',fact_rel__simps_I5_J) ).
fof(fact_one__is__num__one,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)),
file('theBenchmark.p',fact_one__is__num__one) ).
fof(fact_not__iszero__Numeral1,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) ),
file('theBenchmark.p',fact_not__iszero__Numeral1) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
fof(fact_le__special_I2_J,axiom,
! [V_y_2,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2) ) ),
file('theBenchmark.p',fact_le__special_I2_J) ).
fof(fact_le__special_I4_J,axiom,
! [V_x_2,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)) ) ),
file('theBenchmark.p',fact_le__special_I4_J) ).
fof(fact_less__special_I2_J,axiom,
! [V_y_2,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2) ) ),
file('theBenchmark.p',fact_less__special_I2_J) ).
fof(fact_less__special_I4_J,axiom,
! [V_x_2,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)) ) ),
file('theBenchmark.p',fact_less__special_I4_J) ).
fof(fact_add__special_I3_J,axiom,
! [V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Int_OBit1(c_Int_OPls))) ),
file('theBenchmark.p',fact_add__special_I3_J) ).
fof(fact_add__special_I2_J,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_w)) ),
file('theBenchmark.p',fact_add__special_I2_J) ).
fof(fact_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_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_mult__le__cancel1,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),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_less__not__refl,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n),
file('theBenchmark.p',fact_less__not__refl) ).
fof(fact_nat__neq__iff,axiom,
! [V_n_2,V_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_linorder__neqE__nat,axiom,
! [V_y,V_x] :
( V_x != V_y
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x) ) ),
file('theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_less__irrefl__nat,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n),
file('theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_less__not__refl2,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
=> V_m != V_n ),
file('theBenchmark.p',fact_less__not__refl2) ).
fof(fact_less__not__refl3,axiom,
! [V_t,V_s] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)
=> V_s != V_t ),
file('theBenchmark.p',fact_less__not__refl3) ).
fof(fact_nat__less__cases,axiom,
! [V_P_2,V_n_2,V_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_nat__add__commute,axiom,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),
file('theBenchmark.p',fact_nat__add__commute) ).
fof(fact_nat__add__left__commute,axiom,
! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z)),
file('theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_nat__add__assoc,axiom,
! [V_k,V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)),
file('theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_nat__add__left__cancel,axiom,
! [V_n_2,V_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_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_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_nat__mult__assoc,axiom,
! [V_k,V_n,V_m] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_n)),V_k) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n),V_k)),
file('theBenchmark.p',fact_nat__mult__assoc) ).
fof(fact_nat__mult__commute,axiom,
! [V_n,V_m] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_n) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n),V_m),
file('theBenchmark.p',fact_nat__mult__commute) ).
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__nat__zero__code,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_less__nat__zero__code) ).
fof(fact_gr__implies__not0,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_gr__implies__not0) ).
fof(fact_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_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_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_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_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_less__eq__nat_Osimps_I1_J,axiom,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n),
file('theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(fact_le__0__eq,axiom,
! [V_n_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_le__0__eq) ).
fof(fact_mult__cancel2,axiom,
! [V_n_2,V_k_2,V_ma_2] :
( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2) = 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__cancel1,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2) = 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__is__0,axiom,
! [V_n_2,V_ma_2] :
( 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__0__right,axiom,
! [V_m] : 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__0,axiom,
! [V_n] : 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_add__lessD1,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k) ),
file('theBenchmark.p',fact_add__lessD1) ).
fof(fact_less__add__eq__less,axiom,
! [V_n,V_m,V_l,V_k] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ),
file('theBenchmark.p',fact_less__add__eq__less) ).
fof(fact_add__less__mono,axiom,
! [V_l,V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)) ) ),
file('theBenchmark.p',fact_add__less__mono) ).
fof(fact_add__less__mono1,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ),
file('theBenchmark.p',fact_add__less__mono1) ).
fof(fact_trans__less__add2,axiom,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ),
file('theBenchmark.p',fact_trans__less__add2) ).
fof(fact_trans__less__add1,axiom,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ),
file('theBenchmark.p',fact_trans__less__add1) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [V_n_2,V_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_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__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_le__neq__implies__less,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> ( V_m != V_n
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ),
file('theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_less__imp__le__nat,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_less__imp__le__nat) ).
fof(fact_le__eq__less__or__eq,axiom,
! [V_n_2,V_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__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__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__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__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_trans__le__add1,axiom,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ),
file('theBenchmark.p',fact_trans__le__add1) ).
fof(fact_trans__le__add2,axiom,
! [V_m,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ),
file('theBenchmark.p',fact_trans__le__add2) ).
fof(fact_add__le__mono1,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ),
file('theBenchmark.p',fact_add__le__mono1) ).
fof(fact_add__le__mono,axiom,
! [V_l,V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)) ) ),
file('theBenchmark.p',fact_add__le__mono) ).
fof(fact_add__leD2,axiom,
! [V_n,V_k,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ),
file('theBenchmark.p',fact_add__leD2) ).
fof(fact_add__leD1,axiom,
! [V_n,V_k,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_add__leD1) ).
fof(fact_add__leE,axiom,
! [V_n,V_k,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ),
file('theBenchmark.p',fact_add__leE) ).
fof(fact_add__mult__distrib,axiom,
! [V_k,V_n,V_m] : 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(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_k),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n),V_k)),
file('theBenchmark.p',fact_add__mult__distrib) ).
fof(fact_add__mult__distrib2,axiom,
! [V_n,V_m,V_k] : 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(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_m),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_n)),
file('theBenchmark.p',fact_add__mult__distrib2) ).
fof(fact_le__square,axiom,
! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_m)),
file('theBenchmark.p',fact_le__square) ).
fof(fact_le__cube,axiom,
! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_m))),
file('theBenchmark.p',fact_le__cube) ).
fof(fact_mult__le__mono1,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_k),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(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_i),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_j)) ),
file('theBenchmark.p',fact_mult__le__mono2) ).
fof(fact_mult__le__mono,axiom,
! [V_l,V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_k),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j),V_l)) ) ),
file('theBenchmark.p',fact_mult__le__mono) ).
fof(fact_nat__mult__eq__1__iff,axiom,
! [V_n_2,V_ma_2] :
( 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_nat__mult__1__right,axiom,
! [V_n] : 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(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(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_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__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(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__less__cancel1,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),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(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2),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__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(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_k),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(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_i),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_j)) ) ),
file('theBenchmark.p',fact_mult__less__mono2) ).
fof(fact_mult__eq__self__implies__10,axiom,
! [V_n,V_m] :
( V_m = 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_mult__le__cancel2,axiom,
! [V_n_2,V_k_2,V_ma_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2),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_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(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),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_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(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2) = 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_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(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),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__cancel__disj,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2) = 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_left__add__mult__distrib,axiom,
! [V_k,V_j,V_u,V_i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j),V_u),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,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_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_I2_J,axiom,
! [V_y,V_z,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ),
file('theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_termination__basic__simps_I1_J,axiom,
! [V_z,V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ),
file('theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(fact_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_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_one__code__numeral__code,axiom,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,c_Int_OBit1(c_Int_OPls)),
file('theBenchmark.p',fact_one__code__numeral__code) ).
fof(fact_zero__code__numeral__code,axiom,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,c_Int_OPls),
file('theBenchmark.p',fact_zero__code__numeral__code) ).
fof(fact_half,axiom,
! [T_a] :
( ( class_Int_Onumber__ring(T_a)
& class_Fields_Olinordered__field__inverse__zero(T_a) )
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('theBenchmark.p',fact_half) ).
fof(fact_incr__mult__lemma,axiom,
! [V_k_2,V_P_2,V_db_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_db_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_db_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(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k_2),V_db_2)))) ) ) ) ),
file('theBenchmark.p',fact_incr__mult__lemma) ).
fof(fact_iszero__number__of__Bit0,axiom,
! [V_wa_2,T_a] :
( ( class_Int_Oring__char__0(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_wa_2)))
<=> c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) ) ),
file('theBenchmark.p',fact_iszero__number__of__Bit0) ).
fof(fact_pred__Bit1,axiom,
! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k),
file('theBenchmark.p',fact_pred__Bit1) ).
fof(fact_pred__Bit0,axiom,
! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)),
file('theBenchmark.p',fact_pred__Bit0) ).
fof(fact_succ__Bit0,axiom,
! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k),
file('theBenchmark.p',fact_succ__Bit0) ).
fof(fact_succ__Bit1,axiom,
! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)),
file('theBenchmark.p',fact_succ__Bit1) ).
fof(fact_less__eq__int__code_I13_J,axiom,
! [V_k2_2,V_k1_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ),
file('theBenchmark.p',fact_less__eq__int__code_I13_J) ).
fof(fact_rel__simps_I31_J,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ),
file('theBenchmark.p',fact_rel__simps_I31_J) ).
fof(fact_mult__Bit0,axiom,
! [V_l,V_k] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k),V_l)),
file('theBenchmark.p',fact_mult__Bit0) ).
fof(fact_rel__simps_I14_J,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ),
file('theBenchmark.p',fact_rel__simps_I14_J) ).
fof(fact_less__int__code_I13_J,axiom,
! [V_k2_2,V_k1_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ),
file('theBenchmark.p',fact_less__int__code_I13_J) ).
fof(fact_Bit0__def,axiom,
! [V_k] : c_Int_OBit0(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_k),
file('theBenchmark.p',fact_Bit0__def) ).
fof(fact_add__Bit0__Bit0,axiom,
! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit0(V_l)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)),
file('theBenchmark.p',fact_add__Bit0__Bit0) ).
fof(fact_rel__simps_I50_J,axiom,
! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l),
file('theBenchmark.p',fact_rel__simps_I50_J) ).
fof(fact_rel__simps_I49_J,axiom,
! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l),
file('theBenchmark.p',fact_rel__simps_I49_J) ).
fof(fact_minus__Bit0,axiom,
! [V_k] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(V_k)) = c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k)),
file('theBenchmark.p',fact_minus__Bit0) ).
fof(fact_rel__simps_I48_J,axiom,
! [V_l_2,V_k_2] :
( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
<=> V_k_2 = V_l_2 ),
file('theBenchmark.p',fact_rel__simps_I48_J) ).
fof(fact_rel__simps_I44_J,axiom,
! [V_k_2] :
( c_Int_OBit0(V_k_2) = c_Int_OPls
<=> V_k_2 = c_Int_OPls ),
file('theBenchmark.p',fact_rel__simps_I44_J) ).
fof(fact_rel__simps_I38_J,axiom,
! [V_l_2] :
( c_Int_OPls = c_Int_OBit0(V_l_2)
<=> c_Int_OPls = V_l_2 ),
file('theBenchmark.p',fact_rel__simps_I38_J) ).
fof(fact_Bit0__Pls,axiom,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
file('theBenchmark.p',fact_Bit0__Pls) ).
fof(fact_add__Bit0__Bit1,axiom,
! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit1(V_l)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)),
file('theBenchmark.p',fact_add__Bit0__Bit1) ).
fof(fact_add__Bit1__Bit0,axiom,
! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit0(V_l)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)),
file('theBenchmark.p',fact_add__Bit1__Bit0) ).
fof(fact_rel__simps_I4_J,axiom,
! [V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_k_2) ),
file('theBenchmark.p',fact_rel__simps_I4_J) ).
fof(fact_rel__simps_I10_J,axiom,
! [V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) ),
file('theBenchmark.p',fact_rel__simps_I10_J) ).
fof(fact_bin__less__0__simps_I3_J,axiom,
! [V_wa_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('theBenchmark.p',fact_bin__less__0__simps_I3_J) ).
fof(fact_rel__simps_I16_J,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ),
file('theBenchmark.p',fact_rel__simps_I16_J) ).
fof(fact_less__int__code_I15_J,axiom,
! [V_k2_2,V_k1_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ),
file('theBenchmark.p',fact_less__int__code_I15_J) ).
fof(fact_rel__simps_I27_J,axiom,
! [V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OPls) ),
file('theBenchmark.p',fact_rel__simps_I27_J) ).
fof(fact_rel__simps_I21_J,axiom,
! [V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) ),
file('theBenchmark.p',fact_rel__simps_I21_J) ).
fof(fact_less__eq__int__code_I14_J,axiom,
! [V_k2_2,V_k1_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ),
file('theBenchmark.p',fact_less__eq__int__code_I14_J) ).
fof(fact_rel__simps_I32_J,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ),
file('theBenchmark.p',fact_rel__simps_I32_J) ).
fof(fact_number__of__Bit0,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) ),
file('theBenchmark.p',fact_number__of__Bit0) ).
fof(fact_rel__simps_I15_J,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ),
file('theBenchmark.p',fact_rel__simps_I15_J) ).
fof(fact_less__int__code_I14_J,axiom,
! [V_k2_2,V_k1_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) ),
file('theBenchmark.p',fact_less__int__code_I14_J) ).
fof(fact_rel__simps_I33_J,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ),
file('theBenchmark.p',fact_rel__simps_I33_J) ).
fof(fact_less__eq__int__code_I15_J,axiom,
! [V_k2_2,V_k1_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) ),
file('theBenchmark.p',fact_less__eq__int__code_I15_J) ).
fof(fact_mult__Bit1,axiom,
! [V_l,V_k] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit1(V_k)),V_l) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k),V_l)),V_l),
file('theBenchmark.p',fact_mult__Bit1) ).
fof(fact_add__Bit1__Bit1,axiom,
! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit1(V_l)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_Osucc(V_l))),
file('theBenchmark.p',fact_add__Bit1__Bit1) ).
fof(fact_double__number__of__Bit0,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) ),
file('theBenchmark.p',fact_double__number__of__Bit0) ).
fof(fact_number__of1,axiom,
! [V_n] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(V_n)))
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_n))) ) ),
file('theBenchmark.p',fact_number__of1) ).
fof(fact_eq__divide__2__times__iff,axiom,
! [V_za_2,V_y_2,V_x_2] :
( V_x_2 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_y_2,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_za_2))
<=> hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x_2) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_y_2,V_za_2) ),
file('theBenchmark.p',fact_eq__divide__2__times__iff) ).
fof(fact_mult__2__right,axiom,
! [V_z,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ),
file('theBenchmark.p',fact_mult__2__right) ).
fof(fact_mult__2,axiom,
! [V_z,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ),
file('theBenchmark.p',fact_mult__2) ).
fof(fact_one__add__one__is__two,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
file('theBenchmark.p',fact_one__add__one__is__two) ).
fof(fact_pos2,axiom,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('theBenchmark.p',fact_pos2) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
fof(fact_nat__mult__2__right,axiom,
! [V_z] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z),
file('theBenchmark.p',fact_nat__mult__2__right) ).
fof(fact_nat__mult__2,axiom,
! [V_z] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z),
file('theBenchmark.p',fact_nat__mult__2) ).
fof(fact_nat__1__add__1,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('theBenchmark.p',fact_nat__1__add__1) ).
fof(fact_real__less__half__sum,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('theBenchmark.p',fact_real__less__half__sum) ).
fof(fact_real__gt__half__sum,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_y) ),
file('theBenchmark.p',fact_real__gt__half__sum) ).
fof(fact_half__gt__zero,axiom,
! [V_r,T_a] :
( ( class_Int_Onumber__ring(T_a)
& class_Fields_Olinordered__field__inverse__zero(T_a) )
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_r,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ),
file('theBenchmark.p',fact_half__gt__zero) ).
fof(fact_half__gt__zero__iff,axiom,
! [V_r_2,T_a] :
( ( class_Int_Onumber__ring(T_a)
& class_Fields_Olinordered__field__inverse__zero(T_a) )
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_r_2,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r_2) ) ),
file('theBenchmark.p',fact_half__gt__zero__iff) ).
fof(fact_int__pos__lt__two__imp__zero__or__one,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> ( V_x = c_Groups_Oone__class_Oone(tc_Int_Oint)
| V_x = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ),
file('theBenchmark.p',fact_int__pos__lt__two__imp__zero__or__one) ).
fof(fact_real__sum__of__halves,axiom,
! [V_x] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = V_x,
file('theBenchmark.p',fact_real__sum__of__halves) ).
fof(fact_DERIV__real__sqrt__generic,axiom,
! [V_D_2,V_x_2] :
( 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),V_x_2)
=> V_D_2 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) )
=> ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> V_D_2 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) )
=> c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,V_x_2,V_D_2) ) ) ),
file('theBenchmark.p',fact_DERIV__real__sqrt__generic) ).
fof(fact_DERIV__const__average,axiom,
! [V_k_2,V_v_2,V_b_2,V_a_2] :
( V_a_2 != V_b_2
=> ( ! [B_x] : c_Deriv_Oderiv(tc_RealDef_Oreal,V_v_2,B_x,V_k_2)
=> hAPP(V_v_2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a_2,V_b_2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(V_v_2,V_a_2),hAPP(V_v_2,V_b_2)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) ),
file('theBenchmark.p',fact_DERIV__const__average) ).
fof(fact_real__sqrt__lt__1__iff,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('theBenchmark.p',fact_real__sqrt__lt__1__iff) ).
fof(fact_real__sqrt__gt__1__iff,axiom,
! [V_y_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2) ),
file('theBenchmark.p',fact_real__sqrt__gt__1__iff) ).
fof(fact_real__sqrt__ge__1__iff,axiom,
! [V_y_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2) ),
file('theBenchmark.p',fact_real__sqrt__ge__1__iff) ).
fof(fact_real__sqrt__le__1__iff,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('theBenchmark.p',fact_real__sqrt__le__1__iff) ).
fof(fact_real__sqrt__ge__one,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_x)) ),
file('theBenchmark.p',fact_real__sqrt__ge__one) ).
fof(fact_real__sqrt__eq__1__iff,axiom,
! [V_x_2] :
( hAPP(c_NthRoot_Osqrt,V_x_2) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
<=> V_x_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_real__sqrt__eq__1__iff) ).
fof(fact_real__sqrt__one,axiom,
hAPP(c_NthRoot_Osqrt,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('theBenchmark.p',fact_real__sqrt__one) ).
fof(fact_real__sqrt__le__mono,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),hAPP(c_NthRoot_Osqrt,V_y)) ),
file('theBenchmark.p',fact_real__sqrt__le__mono) ).
fof(fact_real__sqrt__le__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),hAPP(c_NthRoot_Osqrt,V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ),
file('theBenchmark.p',fact_real__sqrt__le__iff) ).
fof(fact_real__sqrt__less__mono,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),hAPP(c_NthRoot_Osqrt,V_y)) ),
file('theBenchmark.p',fact_real__sqrt__less__mono) ).
fof(fact_real__sqrt__less__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),hAPP(c_NthRoot_Osqrt,V_y_2))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ),
file('theBenchmark.p',fact_real__sqrt__less__iff) ).
fof(fact_real__sqrt__mult,axiom,
! [V_y,V_x] : hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_y)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)),hAPP(c_NthRoot_Osqrt,V_y)),
file('theBenchmark.p',fact_real__sqrt__mult) ).
fof(fact_real__sqrt__minus,axiom,
! [V_x] : hAPP(c_NthRoot_Osqrt,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)),
file('theBenchmark.p',fact_real__sqrt__minus) ).
fof(fact_real__sqrt__inverse,axiom,
! [V_x] : hAPP(c_NthRoot_Osqrt,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)),
file('theBenchmark.p',fact_real__sqrt__inverse) ).
fof(fact_real__sqrt__divide,axiom,
! [V_y,V_x] : hAPP(c_NthRoot_Osqrt,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),hAPP(c_NthRoot_Osqrt,V_y)),
file('theBenchmark.p',fact_real__sqrt__divide) ).
fof(fact_real__sqrt__eq__iff,axiom,
! [V_y_2,V_x_2] :
( hAPP(c_NthRoot_Osqrt,V_x_2) = hAPP(c_NthRoot_Osqrt,V_y_2)
<=> V_x_2 = V_y_2 ),
file('theBenchmark.p',fact_real__sqrt__eq__iff) ).
fof(fact_real__sqrt__gt__zero,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_x)) ),
file('theBenchmark.p',fact_real__sqrt__gt__zero) ).
fof(fact_real__sqrt__not__eq__zero,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> hAPP(c_NthRoot_Osqrt,V_x) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_real__sqrt__not__eq__zero) ).
fof(fact_real__sqrt__lt__0__iff,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('theBenchmark.p',fact_real__sqrt__lt__0__iff) ).
fof(fact_real__sqrt__gt__0__iff,axiom,
! [V_y_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2) ),
file('theBenchmark.p',fact_real__sqrt__gt__0__iff) ).
fof(fact_real__sqrt__ge__0__iff,axiom,
! [V_y_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2) ),
file('theBenchmark.p',fact_real__sqrt__ge__0__iff) ).
fof(fact_real__sqrt__le__0__iff,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('theBenchmark.p',fact_real__sqrt__le__0__iff) ).
fof(fact_real__sqrt__ge__zero,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_x)) ),
file('theBenchmark.p',fact_real__sqrt__ge__zero) ).
fof(fact_real__sqrt__eq__zero__cancel,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> ( hAPP(c_NthRoot_Osqrt,V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('theBenchmark.p',fact_real__sqrt__eq__zero__cancel) ).
fof(fact_real__sqrt__eq__0__iff,axiom,
! [V_x_2] :
( hAPP(c_NthRoot_Osqrt,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_real__sqrt__eq__0__iff) ).
fof(fact_real__sqrt__zero,axiom,
hAPP(c_NthRoot_Osqrt,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('theBenchmark.p',fact_real__sqrt__zero) ).
fof(fact_le__real__sqrt__sumsq,axiom,
! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_x),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y),V_y)))),
file('theBenchmark.p',fact_le__real__sqrt__sumsq) ).
fof(fact_real__sqrt__mult__self__sum__ge__zero,axiom,
! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_x),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y),V_y)))),
file('theBenchmark.p',fact_real__sqrt__mult__self__sum__ge__zero) ).
fof(fact_sqrt__divide__self__eq,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),V_x) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)) ),
file('theBenchmark.p',fact_sqrt__divide__self__eq) ).
fof(fact_real__sqrt__two__ge__zero,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('theBenchmark.p',fact_real__sqrt__two__ge__zero) ).
fof(fact_real__sqrt__two__gt__zero,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('theBenchmark.p',fact_real__sqrt__two__gt__zero) ).
fof(fact_real__sqrt__two__gt__one,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('theBenchmark.p',fact_real__sqrt__two__gt__one) ).
fof(fact_lemma__real__divide__sqrt__less,axiom,
! [V_u] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_u)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),V_u) ),
file('theBenchmark.p',fact_lemma__real__divide__sqrt__less) ).
fof(fact_DERIV__real__sqrt,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,V_x_2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('theBenchmark.p',fact_DERIV__real__sqrt) ).
fof(fact_lemma__sqrt__hcomplex__capprox,axiom,
! [V_y,V_x,V_u] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_u)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),V_u) ) ) ) ) ),
file('theBenchmark.p',fact_lemma__sqrt__hcomplex__capprox) ).
fof(fact_real__sqrt__sum__squares__mult__ge__zero,axiom,
! [V_ya,V_xa,V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_xa,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_ya,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
file('theBenchmark.p',fact_real__sqrt__sum__squares__mult__ge__zero) ).
fof(fact_real__sqrt__power,axiom,
! [V_k,V_x] : hAPP(c_NthRoot_Osqrt,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,V_k)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),V_k),
file('theBenchmark.p',fact_real__sqrt__power) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [V_q,V_p,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_p)),c_Power_Opower__class_Opower(T_a,V_x,V_q)) = 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_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)
=> c_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_p),V_q) = c_Power_Opower__class_Opower(T_a,V_x,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)
=> c_Power_Opower__class_Opower(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y),V_q) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_q)),c_Power_Opower__class_Opower(T_a,V_y,V_q)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(fact_power__eq__0__iff__number__of,axiom,
! [V_wa_2,V_a_2,T_a] :
( ( class_Rings_Ozero__neq__one(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Omult__zero(T_a)
& class_Power_Opower(T_a) )
=> ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_power__eq__0__iff__number__of) ).
fof(fact_power__0__left__number__of,axiom,
! [V_w,T_a] :
( ( class_Rings_Osemiring__0(T_a)
& class_Power_Opower(T_a) )
=> ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)) = c_Groups_Ozero__class_Ozero(T_a) )
& ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)) = c_Groups_Oone__class_Oone(T_a) ) ) ),
file('theBenchmark.p',fact_power__0__left__number__of) ).
fof(fact_power3__eq__cube,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a)),V_a) ),
file('theBenchmark.p',fact_power3__eq__cube) ).
fof(fact_zero__power2,axiom,
! [T_a] :
( class_Rings_Osemiring__1(T_a)
=> c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_zero__power2) ).
fof(fact_zero__eq__power2,axiom,
! [V_a_2,T_a] :
( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_zero__eq__power2) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
fof(fact_power2__eq__square,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a) ),
file('theBenchmark.p',fact_power2__eq__square) ).
fof(fact_one__power2,axiom,
! [T_a] :
( class_Rings_Osemiring__1(T_a)
=> c_Power_Opower__class_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_one__power2) ).
fof(fact_power2__minus,axiom,
! [V_a,T_a] :
( class_Rings_Oring__1(T_a)
=> c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
file('theBenchmark.p',fact_power2__minus) ).
fof(fact_power__even__eq,axiom,
! [V_n,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> c_Power_Opower__class_Opower(T_a,V_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
file('theBenchmark.p',fact_power__even__eq) ).
fof(fact_zero__le__power2,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('theBenchmark.p',fact_zero__le__power2) ).
fof(fact_power2__le__imp__le,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ),
file('theBenchmark.p',fact_power2__le__imp__le) ).
fof(fact_power2__eq__imp__eq,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> V_x = V_y ) ) ) ),
file('theBenchmark.p',fact_power2__eq__imp__eq) ).
fof(fact_zero__less__power2,axiom,
! [V_a_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
<=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_zero__less__power2) ).
fof(fact_power2__less__0,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ~ c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(T_a)) ),
file('theBenchmark.p',fact_power2__less__0) ).
fof(fact_sum__power2__eq__zero__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sum__power2__eq__zero__iff) ).
fof(fact_power2__eq__square__number__of,axiom,
! [V_w,T_b] :
( ( class_Int_Onumber(T_b)
& class_Groups_Omonoid__mult(T_b) )
=> c_Power_Opower__class_Opower(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_w),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ),
file('theBenchmark.p',fact_power2__eq__square__number__of) ).
fof(fact_power2__eq__1__iff,axiom,
! [V_a_2,T_a] :
( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a)
<=> ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
| V_a_2 = c_Groups_Oone__class_Oone(T_a) ) ) ),
file('theBenchmark.p',fact_power2__eq__1__iff) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
! [V_n,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Power_Opower__class_Opower(T_a,V_x,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n)),c_Power_Opower__class_Opower(T_a,V_x,V_n)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
fof(fact_ring__1__class_Opower__minus__even,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Oring__1(T_a)
=> c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Power_Opower__class_Opower(T_a,V_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) ),
file('theBenchmark.p',fact_ring__1__class_Opower__minus__even) ).
fof(fact_realpow__two__sum__zero__iff,axiom,
! [V_y_2,V_x_2] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('theBenchmark.p',fact_realpow__two__sum__zero__iff) ).
fof(fact_four__x__squared,axiom,
! [V_x] : hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('theBenchmark.p',fact_four__x__squared) ).
fof(fact_two__realpow__ge__one,axiom,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n)),
file('theBenchmark.p',fact_two__realpow__ge__one) ).
fof(fact_realpow__square__minus__le,axiom,
! [V_x,V_u] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_u,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('theBenchmark.p',fact_realpow__square__minus__le) ).
fof(fact_power2__less__imp__less,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ),
file('theBenchmark.p',fact_power2__less__imp__less) ).
fof(fact_sum__power2__ge__zero,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
file('theBenchmark.p',fact_sum__power2__ge__zero) ).
fof(fact_sum__power2__le__zero__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sum__power2__le__zero__iff) ).
fof(fact_not__sum__power2__lt__zero,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a)) ),
file('theBenchmark.p',fact_not__sum__power2__lt__zero) ).
fof(fact_sum__power2__gt__zero__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
<=> ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sum__power2__gt__zero__iff) ).
fof(fact_power2__sum,axiom,
! [V_y,V_x,T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Power_Opower__class_Opower(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ),
file('theBenchmark.p',fact_power2__sum) ).
fof(fact_even__power__le__0__imp__0,axiom,
! [V_k,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_k)),c_Groups_Ozero__class_Ozero(T_a))
=> V_a = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_even__power__le__0__imp__0) ).
fof(fact_zero__le__even__power_H,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) ),
file('theBenchmark.p',fact_zero__le__even__power_H) ).
fof(fact_power__minus1__even,axiom,
! [V_n,T_a] :
( class_Rings_Oring__1(T_a)
=> c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_power__minus1__even) ).
fof(fact_real__sqrt__unique,axiom,
! [V_x,V_y] :
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_x
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
=> hAPP(c_NthRoot_Osqrt,V_x) = V_y ) ),
file('theBenchmark.p',fact_real__sqrt__unique) ).
fof(fact_real__sqrt__pow2,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_x ),
file('theBenchmark.p',fact_real__sqrt__pow2) ).
fof(fact_real__sqrt__pow2__iff,axiom,
! [V_x_2] :
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_x_2
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
file('theBenchmark.p',fact_real__sqrt__pow2__iff) ).
fof(fact_real__sqrt__pow2__gt__zero,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('theBenchmark.p',fact_real__sqrt__pow2__gt__zero) ).
fof(fact_real__sqrt__sum__squares__ge1,axiom,
! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
file('theBenchmark.p',fact_real__sqrt__sum__squares__ge1) ).
fof(fact_real__sqrt__sum__squares__ge2,axiom,
! [V_x,V_y] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
file('theBenchmark.p',fact_real__sqrt__sum__squares__ge2) ).
fof(fact_real__sqrt__sum__squares__triangle__ineq,axiom,
! [V_d,V_b,V_c,V_a] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_c),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_b,V_d),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_b,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_c,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_d,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
file('theBenchmark.p',fact_real__sqrt__sum__squares__triangle__ineq) ).
fof(fact_real__sqrt__sum__squares__eq__cancel,axiom,
! [V_y,V_x] :
( hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) = V_x
=> V_y = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_real__sqrt__sum__squares__eq__cancel) ).
fof(fact_real__sqrt__sum__squares__eq__cancel2,axiom,
! [V_y,V_x] :
( hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) = V_y
=> V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_real__sqrt__sum__squares__eq__cancel2) ).
fof(fact_real__sqrt__sum__squares__mult__squared__eq,axiom,
! [V_ya,V_xa,V_y,V_x] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_xa,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_ya,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_xa,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_ya,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
file('theBenchmark.p',fact_real__sqrt__sum__squares__mult__squared__eq) ).
fof(fact_real__sqrt__sum__squares__ge__zero,axiom,
! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
file('theBenchmark.p',fact_real__sqrt__sum__squares__ge__zero) ).
fof(fact_real__inv__sqrt__pow2,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x) ),
file('theBenchmark.p',fact_real__inv__sqrt__pow2) ).
fof(fact_real__sum__squared__expand,axiom,
! [V_y,V_x] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)),
file('theBenchmark.p',fact_real__sum__squared__expand) ).
fof(fact_power__strict__mono,axiom,
! [V_n,V_b,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)) ) ) ) ),
file('theBenchmark.p',fact_power__strict__mono) ).
fof(fact_nat__power__less__imp__less,axiom,
! [V_n,V_m,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,V_i,V_m),c_Power_Opower__class_Opower(tc_Nat_Onat,V_i,V_n))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ),
file('theBenchmark.p',fact_nat__power__less__imp__less) ).
fof(fact_nat__zero__less__power__iff,axiom,
! [V_n_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,V_n_2))
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) ),
file('theBenchmark.p',fact_nat__zero__less__power__iff) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
! [V_n,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_n)) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(fact_zpower__zadd__distrib,axiom,
! [V_z,V_y,V_x] : c_Power_Opower__class_Opower(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_y)),c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_z)),
file('theBenchmark.p',fact_zpower__zadd__distrib) ).
fof(fact_zpower__zpower,axiom,
! [V_z,V_y,V_x] : c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_y),V_z) = c_Power_Opower__class_Opower(tc_Int_Oint,V_x,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_y),V_z)),
file('theBenchmark.p',fact_zpower__zpower) ).
fof(fact_zero__less__power__nat__eq,axiom,
! [V_n_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,V_n_2))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_zero__less__power__nat__eq) ).
fof(fact_zero__less__power__nat__eq__number__of,axiom,
! [V_wa_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_zero__less__power__nat__eq__number__of) ).
fof(fact_field__power__not__zero,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> c_Power_Opower__class_Opower(T_a,V_a,V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_field__power__not__zero) ).
fof(fact_power__mult__distrib,axiom,
! [V_n,V_b,V_a,T_a] :
( class_Groups_Ocomm__monoid__mult(T_a)
=> c_Power_Opower__class_Opower(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),V_n) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)),c_Power_Opower__class_Opower(T_a,V_b,V_n)) ),
file('theBenchmark.p',fact_power__mult__distrib) ).
fof(fact_power__commutes,axiom,
! [V_n,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)),V_a) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ),
file('theBenchmark.p',fact_power__commutes) ).
fof(fact_power__one,axiom,
! [V_n,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> c_Power_Opower__class_Opower(T_a,c_Groups_Oone__class_Oone(T_a),V_n) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_power__one) ).
fof(fact_power__divide,axiom,
! [V_n,V_b,V_a,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b),V_n) = c_Rings_Oinverse__class_Odivide(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)) ),
file('theBenchmark.p',fact_power__divide) ).
fof(fact_power__mult,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> c_Power_Opower__class_Opower(T_a,V_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_n)) = c_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),V_n) ),
file('theBenchmark.p',fact_power__mult) ).
fof(fact_power__inverse,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Odivision__ring__inverse__zero(T_a)
=> c_Rings_Oinverse__class_Oinverse(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)) = c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_n) ),
file('theBenchmark.p',fact_power__inverse) ).
fof(fact_power__one__right,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ),
file('theBenchmark.p',fact_power__one__right) ).
fof(fact_zero__le__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ),
file('theBenchmark.p',fact_zero__le__power) ).
fof(fact_power__mono,axiom,
! [V_n,V_b,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)) ) ) ),
file('theBenchmark.p',fact_power__mono) ).
fof(fact_zero__less__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ),
file('theBenchmark.p',fact_zero__less__power) ).
fof(fact_one__le__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ),
file('theBenchmark.p',fact_one__le__power) ).
fof(fact_power__eq__0__iff,axiom,
! [V_n_2,V_a_2,T_a] :
( ( class_Rings_Ozero__neq__one(T_a)
& class_Rings_Ono__zero__divisors(T_a)
& class_Rings_Omult__zero(T_a)
& class_Power_Opower(T_a) )
=> ( c_Power_Opower__class_Opower(T_a,V_a_2,V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_power__eq__0__iff) ).
fof(fact_power__inject__exp,axiom,
! [V_n_2,V_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)
=> ( c_Power_Opower__class_Opower(T_a,V_a_2,V_ma_2) = 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_nonzero__power__divide,axiom,
! [V_n,V_a,V_b,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b),V_n) = c_Rings_Oinverse__class_Odivide(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n)) ) ),
file('theBenchmark.p',fact_nonzero__power__divide) ).
fof(fact_power__0,axiom,
! [V_a,T_a] :
( class_Power_Opower(T_a)
=> c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_power__0) ).
fof(fact_power__add,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m)),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ),
file('theBenchmark.p',fact_power__add) ).
fof(fact_power__one__over,axiom,
! [V_n,V_a,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) = c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a),V_n) ),
file('theBenchmark.p',fact_power__one__over) ).
fof(fact_nonzero__power__inverse,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> c_Rings_Oinverse__class_Oinverse(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)) = c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_n) ) ),
file('theBenchmark.p',fact_nonzero__power__inverse) ).
fof(fact_power__less__imp__less__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_power__less__imp__less__base) ).
fof(fact_power__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(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Power_Opower__class_Opower(T_a,V_a,V_n))) ) ),
file('theBenchmark.p',fact_power__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,c_Power_Opower__class_Opower(T_a,V_a,V_n),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Power_Opower__class_Opower(T_a,V_a,V_n))) ) ),
file('theBenchmark.p',fact_power__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)
=> c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Oone__class_Oone(T_a) ) ) ),
file('theBenchmark.p',fact_power__0__left) ).
fof(fact_power__minus,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Oring__1(T_a)
=> c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),V_n)),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,c_Power_Opower__class_Opower(T_a,V_b_2,V_x_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_y_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_power__strict__increasing__iff) ).
fof(fact_power__less__imp__less__exp,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ),
file('theBenchmark.p',fact_power__less__imp__less__exp) ).
fof(fact_power__strict__increasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_a,V_N)) ) ) ),
file('theBenchmark.p',fact_power__strict__increasing) ).
fof(fact_power__increasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_a,V_N)) ) ) ),
file('theBenchmark.p',fact_power__increasing) ).
fof(fact_power__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(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ) ),
file('theBenchmark.p',fact_power__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,c_Power_Opower__class_Opower(T_a,V_a,V_N),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ) ) ),
file('theBenchmark.p',fact_power__strict__decreasing) ).
fof(fact_power__eq__imp__eq__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Power_Opower__class_Opower(T_a,V_a,V_n) = c_Power_Opower__class_Opower(T_a,V_b,V_n)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> V_a = V_b ) ) ) ) ),
file('theBenchmark.p',fact_power__eq__imp__eq__base) ).
fof(fact_power__decreasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_N),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ) ) ),
file('theBenchmark.p',fact_power__decreasing) ).
fof(fact_power__increasing__iff,axiom,
! [V_y_2,V_x_2,V_b_2,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_b_2,V_x_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_power__increasing__iff) ).
fof(fact_power__le__imp__le__exp,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ) ),
file('theBenchmark.p',fact_power__le__imp__le__exp) ).
fof(fact_one__less__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) ) ) ),
file('theBenchmark.p',fact_one__less__power) ).
fof(fact_csqrt,axiom,
! [V_z] : c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_z,
file('theBenchmark.p',fact_csqrt) ).
fof(fact_arctan__half,axiom,
! [V_x] : hAPP(c_Transcendental_Oarctan,V_x) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Transcendental_Oarctan,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))))),
file('theBenchmark.p',fact_arctan__half) ).
fof(fact_arctan__zero__zero,axiom,
hAPP(c_Transcendental_Oarctan,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('theBenchmark.p',fact_arctan__zero__zero) ).
fof(fact_arctan__minus,axiom,
! [V_x] : hAPP(c_Transcendental_Oarctan,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,V_x)),
file('theBenchmark.p',fact_arctan__minus) ).
fof(fact_arctan__monotone_H,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,V_x),hAPP(c_Transcendental_Oarctan,V_y)) ),
file('theBenchmark.p',fact_arctan__monotone_H) ).
fof(fact_arctan__monotone,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,V_x),hAPP(c_Transcendental_Oarctan,V_y)) ),
file('theBenchmark.p',fact_arctan__monotone) ).
fof(fact_DERIV__arctan,axiom,
! [V_x_2] : c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oarctan,V_x_2,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
file('theBenchmark.p',fact_DERIV__arctan) ).
fof(fact_cos__x__y__le__one,axiom,
! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('theBenchmark.p',fact_cos__x__y__le__one) ).
fof(fact_real__sqrt__sum__squares__less,axiom,
! [V_y,V_u,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),V_u) ) ),
file('theBenchmark.p',fact_real__sqrt__sum__squares__less) ).
fof(fact_zero__le__power__abs,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_n)) ),
file('theBenchmark.p',fact_zero__le__power__abs) ).
fof(fact_power__abs,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)) = c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_n) ),
file('theBenchmark.p',fact_power__abs) ).
fof(fact_abs__power__minus,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n)) = c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)) ),
file('theBenchmark.p',fact_abs__power__minus) ).
fof(fact_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(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_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(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(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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = 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_abs__of__nonpos,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ),
file('theBenchmark.p',fact_abs__of__nonpos) ).
fof(fact_abs__minus__le__zero,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a)) ),
file('theBenchmark.p',fact_abs__minus__le__zero) ).
fof(fact_abs__of__neg,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ),
file('theBenchmark.p',fact_abs__of__neg) ).
fof(fact_abs__if,axiom,
! [V_a,T_a] :
( class_Groups_Oabs__if(T_a)
=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
& ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ) ),
file('theBenchmark.p',fact_abs__if) ).
fof(fact_abs__div__pos,axiom,
! [V_x,V_y,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
=> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_x),V_y) = c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ),
file('theBenchmark.p',fact_abs__div__pos) ).
fof(fact_abs__one,axiom,
! [T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_abs__one) ).
fof(fact_real__sgn__eq,axiom,
! [V_x] : c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)),
file('theBenchmark.p',fact_real__sgn__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(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(c_Groups_Otimes__class_Otimes(T_a,V_c),V_d)) ) ) ),
file('theBenchmark.p',fact_abs__mult__less) ).
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_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).
fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).
fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
fof(arity_Int__Oint__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
fof(arity_Int__Oint__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
class_Rings_Osemiring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).
fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
fof(arity_Int__Oint__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
fof(arity_Int__Oint__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
fof(arity_Int__Oint__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
fof(arity_Int__Oint__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).
fof(arity_Int__Oint__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
fof(arity_Int__Oint__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
fof(arity_Int__Oint__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__Power_Opower,axiom,
class_Power_Opower(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Power_Opower) ).
fof(arity_Int__Oint__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
fof(arity_Int__Oint__Rings_Oring,axiom,
class_Rings_Oring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
fof(arity_Int__Oint__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
fof(arity_Int__Oint__Int_Onumber,axiom,
class_Int_Onumber(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Int_Onumber) ).
fof(arity_Int__Oint__Groups_Oone,axiom,
class_Groups_Oone(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
class_Rings_Osemiring__1(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).
fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
fof(arity_Nat__Onat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(arity_Nat__Onat__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
fof(arity_Nat__Onat__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(arity_Nat__Onat__Power_Opower,axiom,
class_Power_Opower(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
fof(arity_Nat__Onat__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(arity_Nat__Onat__Int_Onumber,axiom,
class_Int_Onumber(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).
fof(arity_Nat__Onat__Groups_Oone,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
fof(arity_HOL__Obool__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_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).
fof(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).
fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).
fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).
fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).
fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).
fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).
fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).
fof(arity_RealDef__Oreal__Rings_Oordered__ring__abs,axiom,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring__abs) ).
fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).
fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).
fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).
fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).
fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
fof(arity_RealDef__Oreal__Rings_Osemiring__1,axiom,
class_Rings_Osemiring__1(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__1) ).
fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).
fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).
fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
fof(arity_RealDef__Oreal__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).
fof(arity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).
fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).
fof(arity_RealDef__Oreal__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) ).
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fof(arity_RealDef__Oreal__Power_Opower,axiom,
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fof(arity_Complex__Ocomplex__Groups_Ouminus,axiom,
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fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
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file('theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
fof(arity_Complex__Ocomplex__Power_Opower,axiom,
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fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
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file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(arity_Complex__Ocomplex__SEQ_Obanach,axiom,
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fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
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fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
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fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
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( 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]) ).
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( U_1 = U_2
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inference(variable_rename,[status(thm)],[f_1_1]) ).
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( U_1 = U_2
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inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1(U_2,U_1))],[f_1_2]) ).
cnf(f_1_4,plain,
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inference(clausify,[status(thm)],[f_1_3]) ).
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inference(fof_nnf,[status(thm)],[fact_H_I3_J]) ).
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inference(clausify,[status(thm)],[f_3_1]) ).
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inference(fof_nnf,[status(thm)],[fact_assms]) ).
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c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact_H_I2_J]) ).
cnf(f_6_2,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_6_1]) ).
fof(f_7_1,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_d____),v_m____),v_e),
inference(fof_nnf,[status(thm)],[fact_dm_I2_J]) ).
cnf(f_7_2,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_d____),v_m____),v_e),
inference(clausify,[status(thm)],[f_7_1]) ).
fof(f_8_1,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
inference(fof_nnf,[status(thm)],[fact_d_I3_J]) ).
cnf(f_8_2,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_1,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_d____),v_m____)),
inference(fof_nnf,[status(thm)],[fact_dm_I1_J]) ).
cnf(f_9_2,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_d____),v_m____)),
inference(clausify,[status(thm)],[f_9_1]) ).
fof(f_10_1,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
inference(fof_nnf,[status(thm)],[fact_em0]) ).
cnf(f_10_2,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_11_1,plain,
! [V_w,V_z] : hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z),V_w) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_w),V_z),
inference(fof_nnf,[status(thm)],[fact_real__mult__commute]) ).
fof(f_11_2,plain,
! [U_4,U_3] : hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_3),U_4) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_4),U_3),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_3),U_4) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_4),U_3),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [V_z3,V_z2,V_z1] : hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1),V_z2)),V_z3) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z2),V_z3)),
inference(fof_nnf,[status(thm)],[fact_real__mult__assoc]) ).
fof(f_12_2,plain,
! [U_7,U_6,U_5] : hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_5),U_6)),U_7) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_5),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_6),U_7)),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_5),U_6)),U_7) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_5),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_6),U_7)),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____),
inference(fof_nnf,[status(thm)],[fact_d_I1_J]) ).
cnf(f_13_2,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____),
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
! [V_a,T_a] :
( 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_14_2,plain,
! [U_9,U_8] :
( hAPP(c_Groups_Otimes__class_Otimes(U_8,U_9),U_9) = U_9
| ~ class_Lattices_Oab__semigroup__idem__mult(U_8) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_8,U_9),U_9) = U_9
| ~ class_Lattices_Oab__semigroup__idem__mult(U_8) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [V_x,T_a] :
( 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_15_2,plain,
! [U_11,U_10] :
( hAPP(c_Groups_Otimes__class_Otimes(U_10,U_11),U_11) = U_11
| ~ class_Lattices_Oab__semigroup__idem__mult(U_10) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_10,U_11),U_11) = U_11
| ~ class_Lattices_Oab__semigroup__idem__mult(U_10) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [V_b,V_a,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b) = 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_16_2,plain,
! [U_14,U_13,U_12] :
( hAPP(c_Groups_Otimes__class_Otimes(U_12,U_13),U_14) = hAPP(c_Groups_Otimes__class_Otimes(U_12,U_14),U_13)
| ~ class_Rings_Ocomm__semiring__1(U_12) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_12,U_13),U_14) = hAPP(c_Groups_Otimes__class_Otimes(U_12,U_14),U_13)
| ~ class_Rings_Ocomm__semiring__1(U_12) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [V_b,V_a,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = 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_17_2,plain,
! [U_17,U_16,U_15] :
( hAPP(c_Groups_Otimes__class_Otimes(U_15,U_16),hAPP(c_Groups_Otimes__class_Otimes(U_15,U_16),U_17)) = hAPP(c_Groups_Otimes__class_Otimes(U_15,U_16),U_17)
| ~ class_Lattices_Oab__semigroup__idem__mult(U_15) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_15,U_16),hAPP(c_Groups_Otimes__class_Otimes(U_15,U_16),U_17)) = hAPP(c_Groups_Otimes__class_Otimes(U_15,U_16),U_17)
| ~ class_Lattices_Oab__semigroup__idem__mult(U_15) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [V_ry,V_rx,V_lx,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),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_18_2,plain,
! [U_21,U_20,U_19,U_18] :
( hAPP(c_Groups_Otimes__class_Otimes(U_18,U_19),hAPP(c_Groups_Otimes__class_Otimes(U_18,U_20),U_21)) = hAPP(c_Groups_Otimes__class_Otimes(U_18,U_20),hAPP(c_Groups_Otimes__class_Otimes(U_18,U_19),U_21))
| ~ class_Rings_Ocomm__semiring__1(U_18) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_18,U_19),hAPP(c_Groups_Otimes__class_Otimes(U_18,U_20),U_21)) = hAPP(c_Groups_Otimes__class_Otimes(U_18,U_20),hAPP(c_Groups_Otimes__class_Otimes(U_18,U_19),U_21))
| ~ class_Rings_Ocomm__semiring__1(U_18) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact_d_I2_J]) ).
cnf(f_19_2,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_d____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_19_1]) ).
fof(f_20_1,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact_one0]) ).
cnf(f_20_2,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_20_1]) ).
fof(f_21_1,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_real__zero__not__eq__one]) ).
cnf(f_21_2,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_21_1]) ).
fof(f_22_1,plain,
! [V_a,T_a] :
( 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_22_2,plain,
! [U_23,U_22] :
( hAPP(c_Groups_Otimes__class_Otimes(U_22,U_23),c_Groups_Oone__class_Oone(U_22)) = U_23
| ~ class_Rings_Ocomm__semiring__1(U_22) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_22,U_23),c_Groups_Oone__class_Oone(U_22)) = U_23
| ~ class_Rings_Ocomm__semiring__1(U_22) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [V_a,T_a] :
( 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_23_2,plain,
! [U_25,U_24] :
( hAPP(c_Groups_Otimes__class_Otimes(U_24,c_Groups_Oone__class_Oone(U_24)),U_25) = U_25
| ~ class_Rings_Ocomm__semiring__1(U_24) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_24,c_Groups_Oone__class_Oone(U_24)),U_25) = U_25
| ~ class_Rings_Ocomm__semiring__1(U_24) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [V_a,T_a] :
( 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_24_2,plain,
! [U_27,U_26] :
( hAPP(c_Groups_Otimes__class_Otimes(U_26,U_27),c_Groups_Ozero__class_Ozero(U_26)) = c_Groups_Ozero__class_Ozero(U_26)
| ~ class_Rings_Ocomm__semiring__1(U_26) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_26,U_27),c_Groups_Ozero__class_Ozero(U_26)) = c_Groups_Ozero__class_Ozero(U_26)
| ~ class_Rings_Ocomm__semiring__1(U_26) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
! [V_a,T_a] :
( 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_25_2,plain,
! [U_29,U_28] :
( hAPP(c_Groups_Otimes__class_Otimes(U_28,c_Groups_Ozero__class_Ozero(U_28)),U_29) = c_Groups_Ozero__class_Ozero(U_28)
| ~ class_Rings_Ocomm__semiring__1(U_28) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_28,c_Groups_Ozero__class_Ozero(U_28)),U_29) = c_Groups_Ozero__class_Ozero(U_28)
| ~ class_Rings_Ocomm__semiring__1(U_28) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [V_z] : 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_26_2,plain,
! [U_30] : hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_30) = U_30,
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_30) = U_30,
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [V_b_2,V_a_2,V_ca_2] :
( ( ( hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ca_2),V_a_2) = 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(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_ca_2),V_a_2) != 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_27_2,plain,
! [U_33,U_32,U_31] :
( ( ( hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_31),U_32) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_31),U_33)
| U_32 != U_33 )
& ( U_32 = U_33
| hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_31),U_32) != hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_31),U_33) ) )
| U_31 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( U_32 = U_33
| hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_31),U_32) != hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_31),U_33)
| U_31 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_27_2]) ).
cnf(f_27_4,plain,
( hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_31),U_32) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_31),U_33)
| U_32 != U_33
| U_31 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
! [V_b_2,V_a_2,V_ca_2] :
( ( ( hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a_2),V_ca_2) = 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(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_a_2),V_ca_2) != 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_28_2,plain,
! [U_36,U_35,U_34] :
( ( ( hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_35),U_34) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_36),U_34)
| U_35 != U_36 )
& ( U_35 = U_36
| hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_35),U_34) != hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_36),U_34) ) )
| U_34 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( U_35 = U_36
| hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_35),U_34) != hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_36),U_34)
| U_34 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_28_2]) ).
cnf(f_28_4,plain,
( hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_35),U_34) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_36),U_34)
| U_35 != U_36
| U_34 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [V_y,V_x,V_z] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z),V_x),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_29_2,plain,
! [U_39,U_38,U_37] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_37),U_38),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_37),U_39))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_38,U_39)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_37) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_37),U_38),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_37),U_39))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_38,U_39)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_37) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),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_30_2,plain,
! [U_41,U_40] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_40),U_41))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_41)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_40) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_40),U_41))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_41)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_40) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [V_y_2,V_x_2,V_za_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2),V_za_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2),V_za_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2) ),
inference(fof_nnf,[status(thm)],[fact_real__mult__less__iff1]) ).
fof(f_31_2,plain,
! [U_44,U_43,U_42] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_43),U_42),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_44),U_42))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_43,U_44) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_43,U_44)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_43),U_42),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_44),U_42)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_42) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_43,U_44)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_43),U_42),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_44),U_42))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_42) ),
inference(clausify,[status(thm)],[f_31_2]) ).
cnf(f_31_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_43),U_42),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_44),U_42))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_43,U_44)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_42) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_rx)),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_32_2,plain,
! [U_49,U_48,U_47,U_46,U_45] :
( hAPP(c_Groups_Otimes__class_Otimes(U_45,hAPP(c_Groups_Otimes__class_Otimes(U_45,U_46),U_47)),hAPP(c_Groups_Otimes__class_Otimes(U_45,U_48),U_49)) = hAPP(c_Groups_Otimes__class_Otimes(U_45,hAPP(c_Groups_Otimes__class_Otimes(U_45,U_46),U_48)),hAPP(c_Groups_Otimes__class_Otimes(U_45,U_47),U_49))
| ~ class_Rings_Ocomm__semiring__1(U_45) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_45,hAPP(c_Groups_Otimes__class_Otimes(U_45,U_46),U_47)),hAPP(c_Groups_Otimes__class_Otimes(U_45,U_48),U_49)) = hAPP(c_Groups_Otimes__class_Otimes(U_45,hAPP(c_Groups_Otimes__class_Otimes(U_45,U_46),U_48)),hAPP(c_Groups_Otimes__class_Otimes(U_45,U_47),U_49))
| ~ class_Rings_Ocomm__semiring__1(U_45) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),hAPP(c_Groups_Otimes__class_Otimes(T_a,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_33_2,plain,
! [U_54,U_53,U_52,U_51,U_50] :
( hAPP(c_Groups_Otimes__class_Otimes(U_50,hAPP(c_Groups_Otimes__class_Otimes(U_50,U_51),U_52)),hAPP(c_Groups_Otimes__class_Otimes(U_50,U_53),U_54)) = hAPP(c_Groups_Otimes__class_Otimes(U_50,U_53),hAPP(c_Groups_Otimes__class_Otimes(U_50,hAPP(c_Groups_Otimes__class_Otimes(U_50,U_51),U_52)),U_54))
| ~ class_Rings_Ocomm__semiring__1(U_50) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_50,hAPP(c_Groups_Otimes__class_Otimes(U_50,U_51),U_52)),hAPP(c_Groups_Otimes__class_Otimes(U_50,U_53),U_54)) = hAPP(c_Groups_Otimes__class_Otimes(U_50,U_53),hAPP(c_Groups_Otimes__class_Otimes(U_50,hAPP(c_Groups_Otimes__class_Otimes(U_50,U_51),U_52)),U_54))
| ~ class_Rings_Ocomm__semiring__1(U_50) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ly),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_34_2,plain,
! [U_59,U_58,U_57,U_56,U_55] :
( hAPP(c_Groups_Otimes__class_Otimes(U_55,hAPP(c_Groups_Otimes__class_Otimes(U_55,U_56),U_57)),hAPP(c_Groups_Otimes__class_Otimes(U_55,U_58),U_59)) = hAPP(c_Groups_Otimes__class_Otimes(U_55,U_56),hAPP(c_Groups_Otimes__class_Otimes(U_55,U_57),hAPP(c_Groups_Otimes__class_Otimes(U_55,U_58),U_59)))
| ~ class_Rings_Ocomm__semiring__1(U_55) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_55,hAPP(c_Groups_Otimes__class_Otimes(U_55,U_56),U_57)),hAPP(c_Groups_Otimes__class_Otimes(U_55,U_58),U_59)) = hAPP(c_Groups_Otimes__class_Otimes(U_55,U_56),hAPP(c_Groups_Otimes__class_Otimes(U_55,U_57),hAPP(c_Groups_Otimes__class_Otimes(U_55,U_58),U_59)))
| ~ class_Rings_Ocomm__semiring__1(U_55) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
! [V_rx,V_ly,V_lx,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),V_rx) = hAPP(c_Groups_Otimes__class_Otimes(T_a,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_35_2,plain,
! [U_63,U_62,U_61,U_60] :
( hAPP(c_Groups_Otimes__class_Otimes(U_60,hAPP(c_Groups_Otimes__class_Otimes(U_60,U_61),U_62)),U_63) = hAPP(c_Groups_Otimes__class_Otimes(U_60,hAPP(c_Groups_Otimes__class_Otimes(U_60,U_61),U_63)),U_62)
| ~ class_Rings_Ocomm__semiring__1(U_60) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_60,hAPP(c_Groups_Otimes__class_Otimes(U_60,U_61),U_62)),U_63) = hAPP(c_Groups_Otimes__class_Otimes(U_60,hAPP(c_Groups_Otimes__class_Otimes(U_60,U_61),U_63)),U_62)
| ~ class_Rings_Ocomm__semiring__1(U_60) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [V_rx,V_ly,V_lx,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),V_ly)),V_rx) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),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_36_2,plain,
! [U_67,U_66,U_65,U_64] :
( hAPP(c_Groups_Otimes__class_Otimes(U_64,hAPP(c_Groups_Otimes__class_Otimes(U_64,U_65),U_66)),U_67) = hAPP(c_Groups_Otimes__class_Otimes(U_64,U_65),hAPP(c_Groups_Otimes__class_Otimes(U_64,U_66),U_67))
| ~ class_Rings_Ocomm__semiring__1(U_64) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_64,hAPP(c_Groups_Otimes__class_Otimes(U_64,U_65),U_66)),U_67) = hAPP(c_Groups_Otimes__class_Otimes(U_64,U_65),hAPP(c_Groups_Otimes__class_Otimes(U_64,U_66),U_67))
| ~ class_Rings_Ocomm__semiring__1(U_64) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
! [V_ry,V_rx,V_lx,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_lx),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_rx),V_ry)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,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_37_2,plain,
! [U_71,U_70,U_69,U_68] :
( hAPP(c_Groups_Otimes__class_Otimes(U_68,U_69),hAPP(c_Groups_Otimes__class_Otimes(U_68,U_70),U_71)) = hAPP(c_Groups_Otimes__class_Otimes(U_68,hAPP(c_Groups_Otimes__class_Otimes(U_68,U_69),U_70)),U_71)
| ~ class_Rings_Ocomm__semiring__1(U_68) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_68,U_69),hAPP(c_Groups_Otimes__class_Otimes(U_68,U_70),U_71)) = hAPP(c_Groups_Otimes__class_Otimes(U_68,hAPP(c_Groups_Otimes__class_Otimes(U_68,U_69),U_70)),U_71)
| ~ class_Rings_Ocomm__semiring__1(U_68) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
? [B_d] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_d,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_d,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d) ),
inference(fof_nnf,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_Bd_O_A_091_124_A0_A_060_Ad_059_Ad_A_060_A1_059_Ad_A_060_Ae_A_P_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096]) ).
fof(f_38_2,plain,
? [U_72] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_72,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_72,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_72) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& 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_72,sK2)],[f_38_2]) ).
cnf(f_38_4,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK2),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_5,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_6,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
? [B_e] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_e,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_e,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e) ),
inference(fof_nnf,[status(thm)],[fact__096EX_Aea_0620_O_Aea_A_060_A1_A_G_Aea_A_060_Ae_A_P_Am_096]) ).
fof(f_39_2,plain,
? [U_73] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_73,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_73,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_73) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK3,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK3,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_73,sK3)],[f_39_2]) ).
cnf(f_39_4,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK3),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_5,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK3,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_6,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK3,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)),
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,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono__neg]) ).
fof(f_40_2,plain,
! [U_77,U_76,U_75,U_74] :
( c_Orderings_Oord__class_Oless(U_74,c_Rings_Oinverse__class_Odivide(U_74,U_77,U_75),c_Rings_Oinverse__class_Odivide(U_74,U_77,U_76))
| ~ c_Orderings_Oord__class_Oless(U_74,c_Groups_Ozero__class_Ozero(U_74),hAPP(c_Groups_Otimes__class_Otimes(U_74,U_75),U_76))
| ~ c_Orderings_Oord__class_Oless(U_74,U_77,c_Groups_Ozero__class_Ozero(U_74))
| ~ c_Orderings_Oord__class_Oless(U_74,U_75,U_76)
| ~ class_Fields_Olinordered__field(U_74) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( c_Orderings_Oord__class_Oless(U_74,c_Rings_Oinverse__class_Odivide(U_74,U_77,U_75),c_Rings_Oinverse__class_Odivide(U_74,U_77,U_76))
| ~ c_Orderings_Oord__class_Oless(U_74,c_Groups_Ozero__class_Ozero(U_74),hAPP(c_Groups_Otimes__class_Otimes(U_74,U_75),U_76))
| ~ c_Orderings_Oord__class_Oless(U_74,U_77,c_Groups_Ozero__class_Ozero(U_74))
| ~ c_Orderings_Oord__class_Oless(U_74,U_75,U_76)
| ~ class_Fields_Olinordered__field(U_74) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono]) ).
fof(f_41_2,plain,
! [U_81,U_80,U_79,U_78] :
( c_Orderings_Oord__class_Oless(U_78,c_Rings_Oinverse__class_Odivide(U_78,U_81,U_80),c_Rings_Oinverse__class_Odivide(U_78,U_81,U_79))
| ~ c_Orderings_Oord__class_Oless(U_78,c_Groups_Ozero__class_Ozero(U_78),hAPP(c_Groups_Otimes__class_Otimes(U_78,U_80),U_79))
| ~ c_Orderings_Oord__class_Oless(U_78,c_Groups_Ozero__class_Ozero(U_78),U_81)
| ~ c_Orderings_Oord__class_Oless(U_78,U_79,U_80)
| ~ class_Fields_Olinordered__field(U_78) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
( c_Orderings_Oord__class_Oless(U_78,c_Rings_Oinverse__class_Odivide(U_78,U_81,U_80),c_Rings_Oinverse__class_Odivide(U_78,U_81,U_79))
| ~ c_Orderings_Oord__class_Oless(U_78,c_Groups_Ozero__class_Ozero(U_78),hAPP(c_Groups_Otimes__class_Otimes(U_78,U_80),U_79))
| ~ c_Orderings_Oord__class_Oless(U_78,c_Groups_Ozero__class_Ozero(U_78),U_81)
| ~ c_Orderings_Oord__class_Oless(U_78,U_79,U_80)
| ~ class_Fields_Olinordered__field(U_78) ),
inference(clausify,[status(thm)],[f_41_2]) ).
fof(f_42_1,plain,
! [V_a_2,V_b_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__divide__less__eq]) ).
fof(f_42_2,plain,
! [U_85,U_84,U_83,U_82] :
( ( ( c_Orderings_Oord__class_Oless(U_82,c_Rings_Oinverse__class_Odivide(U_82,U_84,U_83),U_85)
| ~ c_Orderings_Oord__class_Oless(U_82,hAPP(c_Groups_Otimes__class_Otimes(U_82,U_85),U_83),U_84) )
& ( c_Orderings_Oord__class_Oless(U_82,hAPP(c_Groups_Otimes__class_Otimes(U_82,U_85),U_83),U_84)
| ~ c_Orderings_Oord__class_Oless(U_82,c_Rings_Oinverse__class_Odivide(U_82,U_84,U_83),U_85) ) )
| ~ c_Orderings_Oord__class_Oless(U_82,U_83,c_Groups_Ozero__class_Ozero(U_82))
| ~ class_Fields_Olinordered__field(U_82) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
( c_Orderings_Oord__class_Oless(U_82,hAPP(c_Groups_Otimes__class_Otimes(U_82,U_85),U_83),U_84)
| ~ c_Orderings_Oord__class_Oless(U_82,c_Rings_Oinverse__class_Odivide(U_82,U_84,U_83),U_85)
| ~ c_Orderings_Oord__class_Oless(U_82,U_83,c_Groups_Ozero__class_Ozero(U_82))
| ~ class_Fields_Olinordered__field(U_82) ),
inference(clausify,[status(thm)],[f_42_2]) ).
cnf(f_42_4,plain,
( c_Orderings_Oord__class_Oless(U_82,c_Rings_Oinverse__class_Odivide(U_82,U_84,U_83),U_85)
| ~ c_Orderings_Oord__class_Oless(U_82,hAPP(c_Groups_Otimes__class_Otimes(U_82,U_85),U_83),U_84)
| ~ c_Orderings_Oord__class_Oless(U_82,U_83,c_Groups_Ozero__class_Ozero(U_82))
| ~ class_Fields_Olinordered__field(U_82) ),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__divide__eq]) ).
fof(f_43_2,plain,
! [U_89,U_88,U_87,U_86] :
( ( ( c_Orderings_Oord__class_Oless(U_86,U_88,c_Rings_Oinverse__class_Odivide(U_86,U_89,U_87))
| ~ c_Orderings_Oord__class_Oless(U_86,U_89,hAPP(c_Groups_Otimes__class_Otimes(U_86,U_88),U_87)) )
& ( c_Orderings_Oord__class_Oless(U_86,U_89,hAPP(c_Groups_Otimes__class_Otimes(U_86,U_88),U_87))
| ~ c_Orderings_Oord__class_Oless(U_86,U_88,c_Rings_Oinverse__class_Odivide(U_86,U_89,U_87)) ) )
| ~ c_Orderings_Oord__class_Oless(U_86,U_87,c_Groups_Ozero__class_Ozero(U_86))
| ~ class_Fields_Olinordered__field(U_86) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
cnf(f_43_3,plain,
( c_Orderings_Oord__class_Oless(U_86,U_89,hAPP(c_Groups_Otimes__class_Otimes(U_86,U_88),U_87))
| ~ c_Orderings_Oord__class_Oless(U_86,U_88,c_Rings_Oinverse__class_Odivide(U_86,U_89,U_87))
| ~ c_Orderings_Oord__class_Oless(U_86,U_87,c_Groups_Ozero__class_Ozero(U_86))
| ~ class_Fields_Olinordered__field(U_86) ),
inference(clausify,[status(thm)],[f_43_2]) ).
cnf(f_43_4,plain,
( c_Orderings_Oord__class_Oless(U_86,U_88,c_Rings_Oinverse__class_Odivide(U_86,U_89,U_87))
| ~ c_Orderings_Oord__class_Oless(U_86,U_89,hAPP(c_Groups_Otimes__class_Otimes(U_86,U_88),U_87))
| ~ c_Orderings_Oord__class_Oless(U_86,U_87,c_Groups_Ozero__class_Ozero(U_86))
| ~ class_Fields_Olinordered__field(U_86) ),
inference(clausify,[status(thm)],[f_43_2]) ).
fof(f_44_1,plain,
! [V_x,V_z,V_y,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y),V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__imp__less__div__pos]) ).
fof(f_44_2,plain,
! [U_93,U_92,U_91,U_90] :
( c_Orderings_Oord__class_Oless(U_90,U_92,c_Rings_Oinverse__class_Odivide(U_90,U_93,U_91))
| ~ c_Orderings_Oord__class_Oless(U_90,hAPP(c_Groups_Otimes__class_Otimes(U_90,U_92),U_91),U_93)
| ~ c_Orderings_Oord__class_Oless(U_90,c_Groups_Ozero__class_Ozero(U_90),U_91)
| ~ class_Fields_Olinordered__field(U_90) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
( c_Orderings_Oord__class_Oless(U_90,U_92,c_Rings_Oinverse__class_Odivide(U_90,U_93,U_91))
| ~ c_Orderings_Oord__class_Oless(U_90,hAPP(c_Groups_Otimes__class_Otimes(U_90,U_92),U_91),U_93)
| ~ c_Orderings_Oord__class_Oless(U_90,c_Groups_Ozero__class_Ozero(U_90),U_91)
| ~ class_Fields_Olinordered__field(U_90) ),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,plain,
! [V_z,V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__less]) ).
fof(f_45_2,plain,
! [U_97,U_96,U_95,U_94] :
( c_Orderings_Oord__class_Oless(U_94,c_Rings_Oinverse__class_Odivide(U_94,U_96,U_95),U_97)
| ~ c_Orderings_Oord__class_Oless(U_94,U_96,hAPP(c_Groups_Otimes__class_Otimes(U_94,U_97),U_95))
| ~ c_Orderings_Oord__class_Oless(U_94,c_Groups_Ozero__class_Ozero(U_94),U_95)
| ~ class_Fields_Olinordered__field(U_94) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
( c_Orderings_Oord__class_Oless(U_94,c_Rings_Oinverse__class_Odivide(U_94,U_96,U_95),U_97)
| ~ c_Orderings_Oord__class_Oless(U_94,U_96,hAPP(c_Groups_Otimes__class_Otimes(U_94,U_97),U_95))
| ~ c_Orderings_Oord__class_Oless(U_94,c_Groups_Ozero__class_Ozero(U_94),U_95)
| ~ class_Fields_Olinordered__field(U_94) ),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_1,plain,
! [V_a_2,V_b_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__divide__less__eq]) ).
fof(f_46_2,plain,
! [U_101,U_100,U_99,U_98] :
( ( ( c_Orderings_Oord__class_Oless(U_98,c_Rings_Oinverse__class_Odivide(U_98,U_100,U_99),U_101)
| ~ c_Orderings_Oord__class_Oless(U_98,U_100,hAPP(c_Groups_Otimes__class_Otimes(U_98,U_101),U_99)) )
& ( c_Orderings_Oord__class_Oless(U_98,U_100,hAPP(c_Groups_Otimes__class_Otimes(U_98,U_101),U_99))
| ~ c_Orderings_Oord__class_Oless(U_98,c_Rings_Oinverse__class_Odivide(U_98,U_100,U_99),U_101) ) )
| ~ c_Orderings_Oord__class_Oless(U_98,c_Groups_Ozero__class_Ozero(U_98),U_99)
| ~ class_Fields_Olinordered__field(U_98) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
( c_Orderings_Oord__class_Oless(U_98,U_100,hAPP(c_Groups_Otimes__class_Otimes(U_98,U_101),U_99))
| ~ c_Orderings_Oord__class_Oless(U_98,c_Rings_Oinverse__class_Odivide(U_98,U_100,U_99),U_101)
| ~ c_Orderings_Oord__class_Oless(U_98,c_Groups_Ozero__class_Ozero(U_98),U_99)
| ~ class_Fields_Olinordered__field(U_98) ),
inference(clausify,[status(thm)],[f_46_2]) ).
cnf(f_46_4,plain,
( c_Orderings_Oord__class_Oless(U_98,c_Rings_Oinverse__class_Odivide(U_98,U_100,U_99),U_101)
| ~ c_Orderings_Oord__class_Oless(U_98,U_100,hAPP(c_Groups_Otimes__class_Otimes(U_98,U_101),U_99))
| ~ c_Orderings_Oord__class_Oless(U_98,c_Groups_Ozero__class_Ozero(U_98),U_99)
| ~ class_Fields_Olinordered__field(U_98) ),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__less__divide__eq]) ).
fof(f_47_2,plain,
! [U_105,U_104,U_103,U_102] :
( ( ( c_Orderings_Oord__class_Oless(U_102,U_104,c_Rings_Oinverse__class_Odivide(U_102,U_105,U_103))
| ~ c_Orderings_Oord__class_Oless(U_102,hAPP(c_Groups_Otimes__class_Otimes(U_102,U_104),U_103),U_105) )
& ( c_Orderings_Oord__class_Oless(U_102,hAPP(c_Groups_Otimes__class_Otimes(U_102,U_104),U_103),U_105)
| ~ c_Orderings_Oord__class_Oless(U_102,U_104,c_Rings_Oinverse__class_Odivide(U_102,U_105,U_103)) ) )
| ~ c_Orderings_Oord__class_Oless(U_102,c_Groups_Ozero__class_Ozero(U_102),U_103)
| ~ class_Fields_Olinordered__field(U_102) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
cnf(f_47_3,plain,
( c_Orderings_Oord__class_Oless(U_102,hAPP(c_Groups_Otimes__class_Otimes(U_102,U_104),U_103),U_105)
| ~ c_Orderings_Oord__class_Oless(U_102,U_104,c_Rings_Oinverse__class_Odivide(U_102,U_105,U_103))
| ~ c_Orderings_Oord__class_Oless(U_102,c_Groups_Ozero__class_Ozero(U_102),U_103)
| ~ class_Fields_Olinordered__field(U_102) ),
inference(clausify,[status(thm)],[f_47_2]) ).
cnf(f_47_4,plain,
( c_Orderings_Oord__class_Oless(U_102,U_104,c_Rings_Oinverse__class_Odivide(U_102,U_105,U_103))
| ~ c_Orderings_Oord__class_Oless(U_102,hAPP(c_Groups_Otimes__class_Otimes(U_102,U_104),U_103),U_105)
| ~ c_Orderings_Oord__class_Oless(U_102,c_Groups_Ozero__class_Ozero(U_102),U_103)
| ~ class_Fields_Olinordered__field(U_102) ),
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_1,plain,
! [V_a_2,V_ca_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2)
| ( ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
& ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( ~ c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_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,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) )
| ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_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,c_Groups_Ozero__class_Ozero(T_a),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,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_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,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_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,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__less__eq]) ).
fof(f_48_2,plain,
! [U_109,U_108,U_107,U_106] :
( ( ( c_Orderings_Oord__class_Oless(U_106,c_Rings_Oinverse__class_Odivide(U_106,U_107,U_108),U_109)
| ( ( ( ~ c_Orderings_Oord__class_Oless(U_106,c_Groups_Ozero__class_Ozero(U_106),U_109)
& ~ c_Orderings_Oord__class_Oless(U_106,U_108,c_Groups_Ozero__class_Ozero(U_106)) )
| ( ~ c_Orderings_Oord__class_Oless(U_106,hAPP(c_Groups_Otimes__class_Otimes(U_106,U_109),U_108),U_107)
& c_Orderings_Oord__class_Oless(U_106,U_108,c_Groups_Ozero__class_Ozero(U_106)) ) )
& ~ c_Orderings_Oord__class_Oless(U_106,c_Groups_Ozero__class_Ozero(U_106),U_108) )
| ( ~ c_Orderings_Oord__class_Oless(U_106,U_107,hAPP(c_Groups_Otimes__class_Otimes(U_106,U_109),U_108))
& c_Orderings_Oord__class_Oless(U_106,c_Groups_Ozero__class_Ozero(U_106),U_108) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless(U_106,c_Groups_Ozero__class_Ozero(U_106),U_109)
| c_Orderings_Oord__class_Oless(U_106,U_108,c_Groups_Ozero__class_Ozero(U_106)) )
& ( c_Orderings_Oord__class_Oless(U_106,hAPP(c_Groups_Otimes__class_Otimes(U_106,U_109),U_108),U_107)
| ~ c_Orderings_Oord__class_Oless(U_106,U_108,c_Groups_Ozero__class_Ozero(U_106)) ) )
| c_Orderings_Oord__class_Oless(U_106,c_Groups_Ozero__class_Ozero(U_106),U_108) )
& ( c_Orderings_Oord__class_Oless(U_106,U_107,hAPP(c_Groups_Otimes__class_Otimes(U_106,U_109),U_108))
| ~ c_Orderings_Oord__class_Oless(U_106,c_Groups_Ozero__class_Ozero(U_106),U_108) ) )
| ~ c_Orderings_Oord__class_Oless(U_106,c_Rings_Oinverse__class_Odivide(U_106,U_107,U_108),U_109) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_106) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
cnf(f_48_3,plain,
( c_Orderings_Oord__class_Oless(U_106,U_107,hAPP(c_Groups_Otimes__class_Otimes(U_106,U_109),U_108))
| ~ c_Orderings_Oord__class_Oless(U_106,c_Groups_Ozero__class_Ozero(U_106),U_108)
| ~ c_Orderings_Oord__class_Oless(U_106,c_Rings_Oinverse__class_Odivide(U_106,U_107,U_108),U_109)
| ~ class_Fields_Olinordered__field__inverse__zero(U_106) ),
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(f_48_4,plain,
( c_Orderings_Oord__class_Oless(U_106,hAPP(c_Groups_Otimes__class_Otimes(U_106,U_109),U_108),U_107)
| ~ c_Orderings_Oord__class_Oless(U_106,U_108,c_Groups_Ozero__class_Ozero(U_106))
| c_Orderings_Oord__class_Oless(U_106,c_Groups_Ozero__class_Ozero(U_106),U_108)
| ~ c_Orderings_Oord__class_Oless(U_106,c_Rings_Oinverse__class_Odivide(U_106,U_107,U_108),U_109)
| ~ class_Fields_Olinordered__field__inverse__zero(U_106) ),
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(f_48_5,plain,
( c_Orderings_Oord__class_Oless(U_106,c_Groups_Ozero__class_Ozero(U_106),U_109)
| c_Orderings_Oord__class_Oless(U_106,U_108,c_Groups_Ozero__class_Ozero(U_106))
| c_Orderings_Oord__class_Oless(U_106,c_Groups_Ozero__class_Ozero(U_106),U_108)
| ~ c_Orderings_Oord__class_Oless(U_106,c_Rings_Oinverse__class_Odivide(U_106,U_107,U_108),U_109)
| ~ class_Fields_Olinordered__field__inverse__zero(U_106) ),
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(f_48_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_106,c_Groups_Ozero__class_Ozero(U_106),U_108)
| c_Orderings_Oord__class_Oless(U_106,c_Groups_Ozero__class_Ozero(U_106),U_108)
| c_Orderings_Oord__class_Oless(U_106,c_Rings_Oinverse__class_Odivide(U_106,U_107,U_108),U_109)
| ~ class_Fields_Olinordered__field__inverse__zero(U_106) ),
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(f_48_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_106,U_108,c_Groups_Ozero__class_Ozero(U_106))
| c_Orderings_Oord__class_Oless(U_106,U_108,c_Groups_Ozero__class_Ozero(U_106))
| c_Orderings_Oord__class_Oless(U_106,c_Groups_Ozero__class_Ozero(U_106),U_108)
| c_Orderings_Oord__class_Oless(U_106,c_Rings_Oinverse__class_Odivide(U_106,U_107,U_108),U_109)
| ~ class_Fields_Olinordered__field__inverse__zero(U_106) ),
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(f_48_8,plain,
( ~ c_Orderings_Oord__class_Oless(U_106,c_Groups_Ozero__class_Ozero(U_106),U_109)
| c_Orderings_Oord__class_Oless(U_106,U_108,c_Groups_Ozero__class_Ozero(U_106))
| c_Orderings_Oord__class_Oless(U_106,c_Groups_Ozero__class_Ozero(U_106),U_108)
| c_Orderings_Oord__class_Oless(U_106,c_Rings_Oinverse__class_Odivide(U_106,U_107,U_108),U_109)
| ~ class_Fields_Olinordered__field__inverse__zero(U_106) ),
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(f_48_9,plain,
( ~ c_Orderings_Oord__class_Oless(U_106,U_108,c_Groups_Ozero__class_Ozero(U_106))
| ~ c_Orderings_Oord__class_Oless(U_106,hAPP(c_Groups_Otimes__class_Otimes(U_106,U_109),U_108),U_107)
| c_Orderings_Oord__class_Oless(U_106,c_Groups_Ozero__class_Ozero(U_106),U_108)
| c_Orderings_Oord__class_Oless(U_106,c_Rings_Oinverse__class_Odivide(U_106,U_107,U_108),U_109)
| ~ class_Fields_Olinordered__field__inverse__zero(U_106) ),
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(f_48_10,plain,
( ~ c_Orderings_Oord__class_Oless(U_106,c_Groups_Ozero__class_Ozero(U_106),U_109)
| ~ c_Orderings_Oord__class_Oless(U_106,hAPP(c_Groups_Otimes__class_Otimes(U_106,U_109),U_108),U_107)
| c_Orderings_Oord__class_Oless(U_106,c_Groups_Ozero__class_Ozero(U_106),U_108)
| c_Orderings_Oord__class_Oless(U_106,c_Rings_Oinverse__class_Odivide(U_106,U_107,U_108),U_109)
| ~ class_Fields_Olinordered__field__inverse__zero(U_106) ),
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(f_48_11,plain,
( ~ c_Orderings_Oord__class_Oless(U_106,c_Groups_Ozero__class_Ozero(U_106),U_108)
| ~ c_Orderings_Oord__class_Oless(U_106,U_107,hAPP(c_Groups_Otimes__class_Otimes(U_106,U_109),U_108))
| c_Orderings_Oord__class_Oless(U_106,c_Rings_Oinverse__class_Odivide(U_106,U_107,U_108),U_109)
| ~ class_Fields_Olinordered__field__inverse__zero(U_106) ),
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(f_48_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_106,U_108,c_Groups_Ozero__class_Ozero(U_106))
| c_Orderings_Oord__class_Oless(U_106,U_108,c_Groups_Ozero__class_Ozero(U_106))
| ~ c_Orderings_Oord__class_Oless(U_106,U_107,hAPP(c_Groups_Otimes__class_Otimes(U_106,U_109),U_108))
| c_Orderings_Oord__class_Oless(U_106,c_Rings_Oinverse__class_Odivide(U_106,U_107,U_108),U_109)
| ~ class_Fields_Olinordered__field__inverse__zero(U_106) ),
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(f_48_13,plain,
( ~ c_Orderings_Oord__class_Oless(U_106,c_Groups_Ozero__class_Ozero(U_106),U_109)
| c_Orderings_Oord__class_Oless(U_106,U_108,c_Groups_Ozero__class_Ozero(U_106))
| ~ c_Orderings_Oord__class_Oless(U_106,U_107,hAPP(c_Groups_Otimes__class_Otimes(U_106,U_109),U_108))
| c_Orderings_Oord__class_Oless(U_106,c_Rings_Oinverse__class_Odivide(U_106,U_107,U_108),U_109)
| ~ class_Fields_Olinordered__field__inverse__zero(U_106) ),
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(f_48_14,plain,
( ~ c_Orderings_Oord__class_Oless(U_106,U_108,c_Groups_Ozero__class_Ozero(U_106))
| ~ c_Orderings_Oord__class_Oless(U_106,hAPP(c_Groups_Otimes__class_Otimes(U_106,U_109),U_108),U_107)
| ~ c_Orderings_Oord__class_Oless(U_106,U_107,hAPP(c_Groups_Otimes__class_Otimes(U_106,U_109),U_108))
| c_Orderings_Oord__class_Oless(U_106,c_Rings_Oinverse__class_Odivide(U_106,U_107,U_108),U_109)
| ~ class_Fields_Olinordered__field__inverse__zero(U_106) ),
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(f_48_15,plain,
( ~ c_Orderings_Oord__class_Oless(U_106,c_Groups_Ozero__class_Ozero(U_106),U_109)
| ~ c_Orderings_Oord__class_Oless(U_106,hAPP(c_Groups_Otimes__class_Otimes(U_106,U_109),U_108),U_107)
| ~ c_Orderings_Oord__class_Oless(U_106,U_107,hAPP(c_Groups_Otimes__class_Otimes(U_106,U_109),U_108))
| c_Orderings_Oord__class_Oless(U_106,c_Rings_Oinverse__class_Odivide(U_106,U_107,U_108),U_109)
| ~ class_Fields_Olinordered__field__inverse__zero(U_106) ),
inference(clausify,[status(thm)],[f_48_2]) ).
fof(f_49_1,plain,
! [V_ca_2,V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_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_ca_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_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,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) )
| ( ~ c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_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_a_2,c_Groups_Ozero__class_Ozero(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,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_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,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) )
& ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_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_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__divide__eq]) ).
fof(f_49_2,plain,
! [U_113,U_112,U_111,U_110] :
( ( ( c_Orderings_Oord__class_Oless(U_110,U_111,c_Rings_Oinverse__class_Odivide(U_110,U_112,U_113))
| ( ( ( ~ c_Orderings_Oord__class_Oless(U_110,U_111,c_Groups_Ozero__class_Ozero(U_110))
& ~ c_Orderings_Oord__class_Oless(U_110,U_113,c_Groups_Ozero__class_Ozero(U_110)) )
| ( ~ c_Orderings_Oord__class_Oless(U_110,U_112,hAPP(c_Groups_Otimes__class_Otimes(U_110,U_111),U_113))
& c_Orderings_Oord__class_Oless(U_110,U_113,c_Groups_Ozero__class_Ozero(U_110)) ) )
& ~ c_Orderings_Oord__class_Oless(U_110,c_Groups_Ozero__class_Ozero(U_110),U_113) )
| ( ~ c_Orderings_Oord__class_Oless(U_110,hAPP(c_Groups_Otimes__class_Otimes(U_110,U_111),U_113),U_112)
& c_Orderings_Oord__class_Oless(U_110,c_Groups_Ozero__class_Ozero(U_110),U_113) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless(U_110,U_111,c_Groups_Ozero__class_Ozero(U_110))
| c_Orderings_Oord__class_Oless(U_110,U_113,c_Groups_Ozero__class_Ozero(U_110)) )
& ( c_Orderings_Oord__class_Oless(U_110,U_112,hAPP(c_Groups_Otimes__class_Otimes(U_110,U_111),U_113))
| ~ c_Orderings_Oord__class_Oless(U_110,U_113,c_Groups_Ozero__class_Ozero(U_110)) ) )
| c_Orderings_Oord__class_Oless(U_110,c_Groups_Ozero__class_Ozero(U_110),U_113) )
& ( c_Orderings_Oord__class_Oless(U_110,hAPP(c_Groups_Otimes__class_Otimes(U_110,U_111),U_113),U_112)
| ~ c_Orderings_Oord__class_Oless(U_110,c_Groups_Ozero__class_Ozero(U_110),U_113) ) )
| ~ c_Orderings_Oord__class_Oless(U_110,U_111,c_Rings_Oinverse__class_Odivide(U_110,U_112,U_113)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_110) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
cnf(f_49_3,plain,
( c_Orderings_Oord__class_Oless(U_110,hAPP(c_Groups_Otimes__class_Otimes(U_110,U_111),U_113),U_112)
| ~ c_Orderings_Oord__class_Oless(U_110,c_Groups_Ozero__class_Ozero(U_110),U_113)
| ~ c_Orderings_Oord__class_Oless(U_110,U_111,c_Rings_Oinverse__class_Odivide(U_110,U_112,U_113))
| ~ class_Fields_Olinordered__field__inverse__zero(U_110) ),
inference(clausify,[status(thm)],[f_49_2]) ).
cnf(f_49_4,plain,
( c_Orderings_Oord__class_Oless(U_110,U_112,hAPP(c_Groups_Otimes__class_Otimes(U_110,U_111),U_113))
| ~ c_Orderings_Oord__class_Oless(U_110,U_113,c_Groups_Ozero__class_Ozero(U_110))
| c_Orderings_Oord__class_Oless(U_110,c_Groups_Ozero__class_Ozero(U_110),U_113)
| ~ c_Orderings_Oord__class_Oless(U_110,U_111,c_Rings_Oinverse__class_Odivide(U_110,U_112,U_113))
| ~ class_Fields_Olinordered__field__inverse__zero(U_110) ),
inference(clausify,[status(thm)],[f_49_2]) ).
cnf(f_49_5,plain,
( c_Orderings_Oord__class_Oless(U_110,U_111,c_Groups_Ozero__class_Ozero(U_110))
| c_Orderings_Oord__class_Oless(U_110,U_113,c_Groups_Ozero__class_Ozero(U_110))
| c_Orderings_Oord__class_Oless(U_110,c_Groups_Ozero__class_Ozero(U_110),U_113)
| ~ c_Orderings_Oord__class_Oless(U_110,U_111,c_Rings_Oinverse__class_Odivide(U_110,U_112,U_113))
| ~ class_Fields_Olinordered__field__inverse__zero(U_110) ),
inference(clausify,[status(thm)],[f_49_2]) ).
cnf(f_49_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_110,c_Groups_Ozero__class_Ozero(U_110),U_113)
| c_Orderings_Oord__class_Oless(U_110,c_Groups_Ozero__class_Ozero(U_110),U_113)
| c_Orderings_Oord__class_Oless(U_110,U_111,c_Rings_Oinverse__class_Odivide(U_110,U_112,U_113))
| ~ class_Fields_Olinordered__field__inverse__zero(U_110) ),
inference(clausify,[status(thm)],[f_49_2]) ).
cnf(f_49_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_110,U_113,c_Groups_Ozero__class_Ozero(U_110))
| c_Orderings_Oord__class_Oless(U_110,U_113,c_Groups_Ozero__class_Ozero(U_110))
| c_Orderings_Oord__class_Oless(U_110,c_Groups_Ozero__class_Ozero(U_110),U_113)
| c_Orderings_Oord__class_Oless(U_110,U_111,c_Rings_Oinverse__class_Odivide(U_110,U_112,U_113))
| ~ class_Fields_Olinordered__field__inverse__zero(U_110) ),
inference(clausify,[status(thm)],[f_49_2]) ).
cnf(f_49_8,plain,
( ~ c_Orderings_Oord__class_Oless(U_110,U_111,c_Groups_Ozero__class_Ozero(U_110))
| c_Orderings_Oord__class_Oless(U_110,U_113,c_Groups_Ozero__class_Ozero(U_110))
| c_Orderings_Oord__class_Oless(U_110,c_Groups_Ozero__class_Ozero(U_110),U_113)
| c_Orderings_Oord__class_Oless(U_110,U_111,c_Rings_Oinverse__class_Odivide(U_110,U_112,U_113))
| ~ class_Fields_Olinordered__field__inverse__zero(U_110) ),
inference(clausify,[status(thm)],[f_49_2]) ).
cnf(f_49_9,plain,
( ~ c_Orderings_Oord__class_Oless(U_110,U_113,c_Groups_Ozero__class_Ozero(U_110))
| ~ c_Orderings_Oord__class_Oless(U_110,U_112,hAPP(c_Groups_Otimes__class_Otimes(U_110,U_111),U_113))
| c_Orderings_Oord__class_Oless(U_110,c_Groups_Ozero__class_Ozero(U_110),U_113)
| c_Orderings_Oord__class_Oless(U_110,U_111,c_Rings_Oinverse__class_Odivide(U_110,U_112,U_113))
| ~ class_Fields_Olinordered__field__inverse__zero(U_110) ),
inference(clausify,[status(thm)],[f_49_2]) ).
cnf(f_49_10,plain,
( ~ c_Orderings_Oord__class_Oless(U_110,U_111,c_Groups_Ozero__class_Ozero(U_110))
| ~ c_Orderings_Oord__class_Oless(U_110,U_112,hAPP(c_Groups_Otimes__class_Otimes(U_110,U_111),U_113))
| c_Orderings_Oord__class_Oless(U_110,c_Groups_Ozero__class_Ozero(U_110),U_113)
| c_Orderings_Oord__class_Oless(U_110,U_111,c_Rings_Oinverse__class_Odivide(U_110,U_112,U_113))
| ~ class_Fields_Olinordered__field__inverse__zero(U_110) ),
inference(clausify,[status(thm)],[f_49_2]) ).
cnf(f_49_11,plain,
( ~ c_Orderings_Oord__class_Oless(U_110,c_Groups_Ozero__class_Ozero(U_110),U_113)
| ~ c_Orderings_Oord__class_Oless(U_110,hAPP(c_Groups_Otimes__class_Otimes(U_110,U_111),U_113),U_112)
| c_Orderings_Oord__class_Oless(U_110,U_111,c_Rings_Oinverse__class_Odivide(U_110,U_112,U_113))
| ~ class_Fields_Olinordered__field__inverse__zero(U_110) ),
inference(clausify,[status(thm)],[f_49_2]) ).
cnf(f_49_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_110,U_113,c_Groups_Ozero__class_Ozero(U_110))
| c_Orderings_Oord__class_Oless(U_110,U_113,c_Groups_Ozero__class_Ozero(U_110))
| ~ c_Orderings_Oord__class_Oless(U_110,hAPP(c_Groups_Otimes__class_Otimes(U_110,U_111),U_113),U_112)
| c_Orderings_Oord__class_Oless(U_110,U_111,c_Rings_Oinverse__class_Odivide(U_110,U_112,U_113))
| ~ class_Fields_Olinordered__field__inverse__zero(U_110) ),
inference(clausify,[status(thm)],[f_49_2]) ).
cnf(f_49_13,plain,
( ~ c_Orderings_Oord__class_Oless(U_110,U_111,c_Groups_Ozero__class_Ozero(U_110))
| c_Orderings_Oord__class_Oless(U_110,U_113,c_Groups_Ozero__class_Ozero(U_110))
| ~ c_Orderings_Oord__class_Oless(U_110,hAPP(c_Groups_Otimes__class_Otimes(U_110,U_111),U_113),U_112)
| c_Orderings_Oord__class_Oless(U_110,U_111,c_Rings_Oinverse__class_Odivide(U_110,U_112,U_113))
| ~ class_Fields_Olinordered__field__inverse__zero(U_110) ),
inference(clausify,[status(thm)],[f_49_2]) ).
cnf(f_49_14,plain,
( ~ c_Orderings_Oord__class_Oless(U_110,U_113,c_Groups_Ozero__class_Ozero(U_110))
| ~ c_Orderings_Oord__class_Oless(U_110,U_112,hAPP(c_Groups_Otimes__class_Otimes(U_110,U_111),U_113))
| ~ c_Orderings_Oord__class_Oless(U_110,hAPP(c_Groups_Otimes__class_Otimes(U_110,U_111),U_113),U_112)
| c_Orderings_Oord__class_Oless(U_110,U_111,c_Rings_Oinverse__class_Odivide(U_110,U_112,U_113))
| ~ class_Fields_Olinordered__field__inverse__zero(U_110) ),
inference(clausify,[status(thm)],[f_49_2]) ).
cnf(f_49_15,plain,
( ~ c_Orderings_Oord__class_Oless(U_110,U_111,c_Groups_Ozero__class_Ozero(U_110))
| ~ c_Orderings_Oord__class_Oless(U_110,U_112,hAPP(c_Groups_Otimes__class_Otimes(U_110,U_111),U_113))
| ~ c_Orderings_Oord__class_Oless(U_110,hAPP(c_Groups_Otimes__class_Otimes(U_110,U_111),U_113),U_112)
| c_Orderings_Oord__class_Oless(U_110,U_111,c_Rings_Oinverse__class_Odivide(U_110,U_112,U_113))
| ~ class_Fields_Olinordered__field__inverse__zero(U_110) ),
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_1,plain,
! [V_w,V_z,V_y,V_x,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)),c_Rings_Oinverse__class_Odivide(T_a,V_z,V_w)) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_z),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_w))
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_times__divide__times__eq]) ).
fof(f_50_2,plain,
! [U_118,U_117,U_116,U_115,U_114] :
( hAPP(c_Groups_Otimes__class_Otimes(U_114,c_Rings_Oinverse__class_Odivide(U_114,U_115,U_116)),c_Rings_Oinverse__class_Odivide(U_114,U_117,U_118)) = c_Rings_Oinverse__class_Odivide(U_114,hAPP(c_Groups_Otimes__class_Otimes(U_114,U_115),U_117),hAPP(c_Groups_Otimes__class_Otimes(U_114,U_116),U_118))
| ~ class_Fields_Ofield__inverse__zero(U_114) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_114,c_Rings_Oinverse__class_Odivide(U_114,U_115,U_116)),c_Rings_Oinverse__class_Odivide(U_114,U_117,U_118)) = c_Rings_Oinverse__class_Odivide(U_114,hAPP(c_Groups_Otimes__class_Otimes(U_114,U_115),U_117),hAPP(c_Groups_Otimes__class_Otimes(U_114,U_116),U_118))
| ~ class_Fields_Ofield__inverse__zero(U_114) ),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono__neg]) ).
fof(f_51_2,plain,
! [U_122,U_121,U_120,U_119] :
( c_Orderings_Oord__class_Oless(U_119,c_Rings_Oinverse__class_Odivide(U_119,U_121,U_122),c_Rings_Oinverse__class_Odivide(U_119,U_120,U_122))
| ~ c_Orderings_Oord__class_Oless(U_119,U_122,c_Groups_Ozero__class_Ozero(U_119))
| ~ c_Orderings_Oord__class_Oless(U_119,U_120,U_121)
| ~ class_Fields_Olinordered__field(U_119) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
cnf(f_51_3,plain,
( c_Orderings_Oord__class_Oless(U_119,c_Rings_Oinverse__class_Odivide(U_119,U_121,U_122),c_Rings_Oinverse__class_Odivide(U_119,U_120,U_122))
| ~ c_Orderings_Oord__class_Oless(U_119,U_122,c_Groups_Ozero__class_Ozero(U_119))
| ~ c_Orderings_Oord__class_Oless(U_119,U_120,U_121)
| ~ class_Fields_Olinordered__field(U_119) ),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono]) ).
fof(f_52_2,plain,
! [U_126,U_125,U_124,U_123] :
( c_Orderings_Oord__class_Oless(U_123,c_Rings_Oinverse__class_Odivide(U_123,U_124,U_126),c_Rings_Oinverse__class_Odivide(U_123,U_125,U_126))
| ~ c_Orderings_Oord__class_Oless(U_123,c_Groups_Ozero__class_Ozero(U_123),U_126)
| ~ c_Orderings_Oord__class_Oless(U_123,U_124,U_125)
| ~ class_Fields_Olinordered__field(U_123) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
cnf(f_52_3,plain,
( c_Orderings_Oord__class_Oless(U_123,c_Rings_Oinverse__class_Odivide(U_123,U_124,U_126),c_Rings_Oinverse__class_Odivide(U_123,U_125,U_126))
| ~ c_Orderings_Oord__class_Oless(U_123,c_Groups_Ozero__class_Ozero(U_123),U_126)
| ~ c_Orderings_Oord__class_Oless(U_123,U_124,U_125)
| ~ class_Fields_Olinordered__field(U_123) ),
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))
| ~ c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__neg__neg]) ).
fof(f_53_2,plain,
! [U_129,U_128,U_127] :
( c_Orderings_Oord__class_Oless(U_127,c_Groups_Ozero__class_Ozero(U_127),c_Rings_Oinverse__class_Odivide(U_127,U_128,U_129))
| ~ c_Orderings_Oord__class_Oless(U_127,U_129,c_Groups_Ozero__class_Ozero(U_127))
| ~ c_Orderings_Oord__class_Oless(U_127,U_128,c_Groups_Ozero__class_Ozero(U_127))
| ~ class_Fields_Olinordered__field(U_127) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
( c_Orderings_Oord__class_Oless(U_127,c_Groups_Ozero__class_Ozero(U_127),c_Rings_Oinverse__class_Odivide(U_127,U_128,U_129))
| ~ c_Orderings_Oord__class_Oless(U_127,U_129,c_Groups_Ozero__class_Ozero(U_127))
| ~ c_Orderings_Oord__class_Oless(U_127,U_128,c_Groups_Ozero__class_Ozero(U_127))
| ~ class_Fields_Olinordered__field(U_127) ),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__neg__pos]) ).
fof(f_54_2,plain,
! [U_132,U_131,U_130] :
( c_Orderings_Oord__class_Oless(U_130,c_Rings_Oinverse__class_Odivide(U_130,U_131,U_132),c_Groups_Ozero__class_Ozero(U_130))
| ~ c_Orderings_Oord__class_Oless(U_130,c_Groups_Ozero__class_Ozero(U_130),U_132)
| ~ c_Orderings_Oord__class_Oless(U_130,U_131,c_Groups_Ozero__class_Ozero(U_130))
| ~ class_Fields_Olinordered__field(U_130) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
cnf(f_54_3,plain,
( c_Orderings_Oord__class_Oless(U_130,c_Rings_Oinverse__class_Odivide(U_130,U_131,U_132),c_Groups_Ozero__class_Ozero(U_130))
| ~ c_Orderings_Oord__class_Oless(U_130,c_Groups_Ozero__class_Ozero(U_130),U_132)
| ~ c_Orderings_Oord__class_Oless(U_130,U_131,c_Groups_Ozero__class_Ozero(U_130))
| ~ class_Fields_Olinordered__field(U_130) ),
inference(clausify,[status(thm)],[f_54_2]) ).
fof(f_55_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__pos__neg]) ).
fof(f_55_2,plain,
! [U_135,U_134,U_133] :
( c_Orderings_Oord__class_Oless(U_133,c_Rings_Oinverse__class_Odivide(U_133,U_134,U_135),c_Groups_Ozero__class_Ozero(U_133))
| ~ c_Orderings_Oord__class_Oless(U_133,U_135,c_Groups_Ozero__class_Ozero(U_133))
| ~ c_Orderings_Oord__class_Oless(U_133,c_Groups_Ozero__class_Ozero(U_133),U_134)
| ~ class_Fields_Olinordered__field(U_133) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
cnf(f_55_3,plain,
( c_Orderings_Oord__class_Oless(U_133,c_Rings_Oinverse__class_Odivide(U_133,U_134,U_135),c_Groups_Ozero__class_Ozero(U_133))
| ~ c_Orderings_Oord__class_Oless(U_133,U_135,c_Groups_Ozero__class_Ozero(U_133))
| ~ c_Orderings_Oord__class_Oless(U_133,c_Groups_Ozero__class_Ozero(U_133),U_134)
| ~ class_Fields_Olinordered__field(U_133) ),
inference(clausify,[status(thm)],[f_55_2]) ).
fof(f_56_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__pos__pos]) ).
fof(f_56_2,plain,
! [U_138,U_137,U_136] :
( c_Orderings_Oord__class_Oless(U_136,c_Groups_Ozero__class_Ozero(U_136),c_Rings_Oinverse__class_Odivide(U_136,U_137,U_138))
| ~ c_Orderings_Oord__class_Oless(U_136,c_Groups_Ozero__class_Ozero(U_136),U_138)
| ~ c_Orderings_Oord__class_Oless(U_136,c_Groups_Ozero__class_Ozero(U_136),U_137)
| ~ class_Fields_Olinordered__field(U_136) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
cnf(f_56_3,plain,
( c_Orderings_Oord__class_Oless(U_136,c_Groups_Ozero__class_Ozero(U_136),c_Rings_Oinverse__class_Odivide(U_136,U_137,U_138))
| ~ c_Orderings_Oord__class_Oless(U_136,c_Groups_Ozero__class_Ozero(U_136),U_138)
| ~ c_Orderings_Oord__class_Oless(U_136,c_Groups_Ozero__class_Ozero(U_136),U_137)
| ~ class_Fields_Olinordered__field(U_136) ),
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) )
& ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__less__0__iff]) ).
fof(f_57_2,plain,
! [U_141,U_140,U_139] :
( ( ( c_Orderings_Oord__class_Oless(U_139,c_Rings_Oinverse__class_Odivide(U_139,U_140,U_141),c_Groups_Ozero__class_Ozero(U_139))
| ( ( ~ c_Orderings_Oord__class_Oless(U_139,c_Groups_Ozero__class_Ozero(U_139),U_141)
| ~ c_Orderings_Oord__class_Oless(U_139,U_140,c_Groups_Ozero__class_Ozero(U_139)) )
& ( ~ c_Orderings_Oord__class_Oless(U_139,U_141,c_Groups_Ozero__class_Ozero(U_139))
| ~ c_Orderings_Oord__class_Oless(U_139,c_Groups_Ozero__class_Ozero(U_139),U_140) ) ) )
& ( ( c_Orderings_Oord__class_Oless(U_139,c_Groups_Ozero__class_Ozero(U_139),U_141)
& c_Orderings_Oord__class_Oless(U_139,U_140,c_Groups_Ozero__class_Ozero(U_139)) )
| ( c_Orderings_Oord__class_Oless(U_139,U_141,c_Groups_Ozero__class_Ozero(U_139))
& c_Orderings_Oord__class_Oless(U_139,c_Groups_Ozero__class_Ozero(U_139),U_140) )
| ~ c_Orderings_Oord__class_Oless(U_139,c_Rings_Oinverse__class_Odivide(U_139,U_140,U_141),c_Groups_Ozero__class_Ozero(U_139)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_139) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
cnf(f_57_3,plain,
( c_Orderings_Oord__class_Oless(U_139,U_140,c_Groups_Ozero__class_Ozero(U_139))
| c_Orderings_Oord__class_Oless(U_139,c_Groups_Ozero__class_Ozero(U_139),U_140)
| ~ c_Orderings_Oord__class_Oless(U_139,c_Rings_Oinverse__class_Odivide(U_139,U_140,U_141),c_Groups_Ozero__class_Ozero(U_139))
| ~ class_Fields_Olinordered__field__inverse__zero(U_139) ),
inference(clausify,[status(thm)],[f_57_2]) ).
cnf(f_57_4,plain,
( c_Orderings_Oord__class_Oless(U_139,c_Groups_Ozero__class_Ozero(U_139),U_141)
| c_Orderings_Oord__class_Oless(U_139,c_Groups_Ozero__class_Ozero(U_139),U_140)
| ~ c_Orderings_Oord__class_Oless(U_139,c_Rings_Oinverse__class_Odivide(U_139,U_140,U_141),c_Groups_Ozero__class_Ozero(U_139))
| ~ class_Fields_Olinordered__field__inverse__zero(U_139) ),
inference(clausify,[status(thm)],[f_57_2]) ).
cnf(f_57_5,plain,
( c_Orderings_Oord__class_Oless(U_139,U_140,c_Groups_Ozero__class_Ozero(U_139))
| c_Orderings_Oord__class_Oless(U_139,U_141,c_Groups_Ozero__class_Ozero(U_139))
| ~ c_Orderings_Oord__class_Oless(U_139,c_Rings_Oinverse__class_Odivide(U_139,U_140,U_141),c_Groups_Ozero__class_Ozero(U_139))
| ~ class_Fields_Olinordered__field__inverse__zero(U_139) ),
inference(clausify,[status(thm)],[f_57_2]) ).
cnf(f_57_6,plain,
( c_Orderings_Oord__class_Oless(U_139,c_Groups_Ozero__class_Ozero(U_139),U_141)
| c_Orderings_Oord__class_Oless(U_139,U_141,c_Groups_Ozero__class_Ozero(U_139))
| ~ c_Orderings_Oord__class_Oless(U_139,c_Rings_Oinverse__class_Odivide(U_139,U_140,U_141),c_Groups_Ozero__class_Ozero(U_139))
| ~ class_Fields_Olinordered__field__inverse__zero(U_139) ),
inference(clausify,[status(thm)],[f_57_2]) ).
cnf(f_57_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_139,U_141,c_Groups_Ozero__class_Ozero(U_139))
| ~ c_Orderings_Oord__class_Oless(U_139,c_Groups_Ozero__class_Ozero(U_139),U_140)
| c_Orderings_Oord__class_Oless(U_139,c_Rings_Oinverse__class_Odivide(U_139,U_140,U_141),c_Groups_Ozero__class_Ozero(U_139))
| ~ class_Fields_Olinordered__field__inverse__zero(U_139) ),
inference(clausify,[status(thm)],[f_57_2]) ).
cnf(f_57_8,plain,
( ~ c_Orderings_Oord__class_Oless(U_139,c_Groups_Ozero__class_Ozero(U_139),U_141)
| ~ c_Orderings_Oord__class_Oless(U_139,U_140,c_Groups_Ozero__class_Ozero(U_139))
| c_Orderings_Oord__class_Oless(U_139,c_Rings_Oinverse__class_Odivide(U_139,U_140,U_141),c_Groups_Ozero__class_Ozero(U_139))
| ~ class_Fields_Olinordered__field__inverse__zero(U_139) ),
inference(clausify,[status(thm)],[f_57_2]) ).
fof(f_58_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) )
& ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__divide__iff]) ).
fof(f_58_2,plain,
! [U_144,U_143,U_142] :
( ( ( c_Orderings_Oord__class_Oless(U_142,c_Groups_Ozero__class_Ozero(U_142),c_Rings_Oinverse__class_Odivide(U_142,U_143,U_144))
| ( ( ~ c_Orderings_Oord__class_Oless(U_142,U_144,c_Groups_Ozero__class_Ozero(U_142))
| ~ c_Orderings_Oord__class_Oless(U_142,U_143,c_Groups_Ozero__class_Ozero(U_142)) )
& ( ~ c_Orderings_Oord__class_Oless(U_142,c_Groups_Ozero__class_Ozero(U_142),U_144)
| ~ c_Orderings_Oord__class_Oless(U_142,c_Groups_Ozero__class_Ozero(U_142),U_143) ) ) )
& ( ( c_Orderings_Oord__class_Oless(U_142,U_144,c_Groups_Ozero__class_Ozero(U_142))
& c_Orderings_Oord__class_Oless(U_142,U_143,c_Groups_Ozero__class_Ozero(U_142)) )
| ( c_Orderings_Oord__class_Oless(U_142,c_Groups_Ozero__class_Ozero(U_142),U_144)
& c_Orderings_Oord__class_Oless(U_142,c_Groups_Ozero__class_Ozero(U_142),U_143) )
| ~ c_Orderings_Oord__class_Oless(U_142,c_Groups_Ozero__class_Ozero(U_142),c_Rings_Oinverse__class_Odivide(U_142,U_143,U_144)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_142) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
cnf(f_58_3,plain,
( c_Orderings_Oord__class_Oless(U_142,U_143,c_Groups_Ozero__class_Ozero(U_142))
| c_Orderings_Oord__class_Oless(U_142,c_Groups_Ozero__class_Ozero(U_142),U_143)
| ~ c_Orderings_Oord__class_Oless(U_142,c_Groups_Ozero__class_Ozero(U_142),c_Rings_Oinverse__class_Odivide(U_142,U_143,U_144))
| ~ class_Fields_Olinordered__field__inverse__zero(U_142) ),
inference(clausify,[status(thm)],[f_58_2]) ).
cnf(f_58_4,plain,
( c_Orderings_Oord__class_Oless(U_142,U_144,c_Groups_Ozero__class_Ozero(U_142))
| c_Orderings_Oord__class_Oless(U_142,c_Groups_Ozero__class_Ozero(U_142),U_143)
| ~ c_Orderings_Oord__class_Oless(U_142,c_Groups_Ozero__class_Ozero(U_142),c_Rings_Oinverse__class_Odivide(U_142,U_143,U_144))
| ~ class_Fields_Olinordered__field__inverse__zero(U_142) ),
inference(clausify,[status(thm)],[f_58_2]) ).
cnf(f_58_5,plain,
( c_Orderings_Oord__class_Oless(U_142,U_143,c_Groups_Ozero__class_Ozero(U_142))
| c_Orderings_Oord__class_Oless(U_142,c_Groups_Ozero__class_Ozero(U_142),U_144)
| ~ c_Orderings_Oord__class_Oless(U_142,c_Groups_Ozero__class_Ozero(U_142),c_Rings_Oinverse__class_Odivide(U_142,U_143,U_144))
| ~ class_Fields_Olinordered__field__inverse__zero(U_142) ),
inference(clausify,[status(thm)],[f_58_2]) ).
cnf(f_58_6,plain,
( c_Orderings_Oord__class_Oless(U_142,U_144,c_Groups_Ozero__class_Ozero(U_142))
| c_Orderings_Oord__class_Oless(U_142,c_Groups_Ozero__class_Ozero(U_142),U_144)
| ~ c_Orderings_Oord__class_Oless(U_142,c_Groups_Ozero__class_Ozero(U_142),c_Rings_Oinverse__class_Odivide(U_142,U_143,U_144))
| ~ class_Fields_Olinordered__field__inverse__zero(U_142) ),
inference(clausify,[status(thm)],[f_58_2]) ).
cnf(f_58_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_142,c_Groups_Ozero__class_Ozero(U_142),U_144)
| ~ c_Orderings_Oord__class_Oless(U_142,c_Groups_Ozero__class_Ozero(U_142),U_143)
| c_Orderings_Oord__class_Oless(U_142,c_Groups_Ozero__class_Ozero(U_142),c_Rings_Oinverse__class_Odivide(U_142,U_143,U_144))
| ~ class_Fields_Olinordered__field__inverse__zero(U_142) ),
inference(clausify,[status(thm)],[f_58_2]) ).
cnf(f_58_8,plain,
( ~ c_Orderings_Oord__class_Oless(U_142,U_144,c_Groups_Ozero__class_Ozero(U_142))
| ~ c_Orderings_Oord__class_Oless(U_142,U_143,c_Groups_Ozero__class_Ozero(U_142))
| c_Orderings_Oord__class_Oless(U_142,c_Groups_Ozero__class_Ozero(U_142),c_Rings_Oinverse__class_Odivide(U_142,U_143,U_144))
| ~ class_Fields_Olinordered__field__inverse__zero(U_142) ),
inference(clausify,[status(thm)],[f_58_2]) ).
fof(f_59_1,plain,
! [V_wa_2,V_x_2,V_za_2,V_y_2,T_a] :
( ( ( c_Rings_Oinverse__class_Odivide(T_a,V_x_2,V_y_2) = c_Rings_Oinverse__class_Odivide(T_a,V_wa_2,V_za_2)
| hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_za_2) != hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_y_2) )
& ( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_za_2) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_y_2)
| c_Rings_Oinverse__class_Odivide(T_a,V_x_2,V_y_2) != c_Rings_Oinverse__class_Odivide(T_a,V_wa_2,V_za_2) ) )
| V_za_2 = c_Groups_Ozero__class_Ozero(T_a)
| V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_frac__eq__eq]) ).
fof(f_59_2,plain,
! [U_149,U_148,U_147,U_146,U_145] :
( ( ( c_Rings_Oinverse__class_Odivide(U_145,U_148,U_146) = c_Rings_Oinverse__class_Odivide(U_145,U_149,U_147)
| hAPP(c_Groups_Otimes__class_Otimes(U_145,U_148),U_147) != hAPP(c_Groups_Otimes__class_Otimes(U_145,U_149),U_146) )
& ( hAPP(c_Groups_Otimes__class_Otimes(U_145,U_148),U_147) = hAPP(c_Groups_Otimes__class_Otimes(U_145,U_149),U_146)
| c_Rings_Oinverse__class_Odivide(U_145,U_148,U_146) != c_Rings_Oinverse__class_Odivide(U_145,U_149,U_147) ) )
| U_147 = c_Groups_Ozero__class_Ozero(U_145)
| U_146 = c_Groups_Ozero__class_Ozero(U_145)
| ~ class_Fields_Ofield(U_145) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
cnf(f_59_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_145,U_148),U_147) = hAPP(c_Groups_Otimes__class_Otimes(U_145,U_149),U_146)
| c_Rings_Oinverse__class_Odivide(U_145,U_148,U_146) != c_Rings_Oinverse__class_Odivide(U_145,U_149,U_147)
| U_147 = c_Groups_Ozero__class_Ozero(U_145)
| U_146 = c_Groups_Ozero__class_Ozero(U_145)
| ~ class_Fields_Ofield(U_145) ),
inference(clausify,[status(thm)],[f_59_2]) ).
cnf(f_59_4,plain,
( c_Rings_Oinverse__class_Odivide(U_145,U_148,U_146) = c_Rings_Oinverse__class_Odivide(U_145,U_149,U_147)
| hAPP(c_Groups_Otimes__class_Otimes(U_145,U_148),U_147) != hAPP(c_Groups_Otimes__class_Otimes(U_145,U_149),U_146)
| U_147 = c_Groups_Ozero__class_Ozero(U_145)
| U_146 = c_Groups_Ozero__class_Ozero(U_145)
| ~ class_Fields_Ofield(U_145) ),
inference(clausify,[status(thm)],[f_59_2]) ).
fof(f_60_1,plain,
! [V_b,V_a,V_c,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)
| V_c = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__left]) ).
fof(f_60_2,plain,
! [U_153,U_152,U_151,U_150] :
( c_Rings_Oinverse__class_Odivide(U_150,hAPP(c_Groups_Otimes__class_Otimes(U_150,U_151),U_152),hAPP(c_Groups_Otimes__class_Otimes(U_150,U_151),U_153)) = c_Rings_Oinverse__class_Odivide(U_150,U_152,U_153)
| U_151 = c_Groups_Ozero__class_Ozero(U_150)
| ~ class_Fields_Ofield__inverse__zero(U_150) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
cnf(f_60_3,plain,
( c_Rings_Oinverse__class_Odivide(U_150,hAPP(c_Groups_Otimes__class_Otimes(U_150,U_151),U_152),hAPP(c_Groups_Otimes__class_Otimes(U_150,U_151),U_153)) = c_Rings_Oinverse__class_Odivide(U_150,U_152,U_153)
| U_151 = c_Groups_Ozero__class_Ozero(U_150)
| ~ class_Fields_Ofield__inverse__zero(U_150) ),
inference(clausify,[status(thm)],[f_60_2]) ).
fof(f_61_1,plain,
! [V_b,V_a,V_c,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_c)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)
| V_c = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__right]) ).
fof(f_61_2,plain,
! [U_157,U_156,U_155,U_154] :
( c_Rings_Oinverse__class_Odivide(U_154,hAPP(c_Groups_Otimes__class_Otimes(U_154,U_156),U_155),hAPP(c_Groups_Otimes__class_Otimes(U_154,U_157),U_155)) = c_Rings_Oinverse__class_Odivide(U_154,U_156,U_157)
| U_155 = c_Groups_Ozero__class_Ozero(U_154)
| ~ class_Fields_Ofield__inverse__zero(U_154) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
cnf(f_61_3,plain,
( c_Rings_Oinverse__class_Odivide(U_154,hAPP(c_Groups_Otimes__class_Otimes(U_154,U_156),U_155),hAPP(c_Groups_Otimes__class_Otimes(U_154,U_157),U_155)) = c_Rings_Oinverse__class_Odivide(U_154,U_156,U_157)
| U_155 = c_Groups_Ozero__class_Ozero(U_154)
| ~ class_Fields_Ofield__inverse__zero(U_154) ),
inference(clausify,[status(thm)],[f_61_2]) ).
fof(f_62_1,plain,
! [V_a_2,V_ca_2,V_b_2,T_a] :
( ( ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2) = V_a_2
| ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)
& V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 != hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)
& V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
& ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_b_2 = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)
| V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) ) )
| c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2) != V_a_2 ) )
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__eq__eq]) ).
fof(f_62_2,plain,
! [U_161,U_160,U_159,U_158] :
( ( ( c_Rings_Oinverse__class_Odivide(U_158,U_159,U_160) = U_161
| ( U_161 != c_Groups_Ozero__class_Ozero(U_158)
& U_160 = c_Groups_Ozero__class_Ozero(U_158) )
| ( U_159 != hAPP(c_Groups_Otimes__class_Otimes(U_158,U_161),U_160)
& U_160 != c_Groups_Ozero__class_Ozero(U_158) ) )
& ( ( ( U_161 = c_Groups_Ozero__class_Ozero(U_158)
| U_160 != c_Groups_Ozero__class_Ozero(U_158) )
& ( U_159 = hAPP(c_Groups_Otimes__class_Otimes(U_158,U_161),U_160)
| U_160 = c_Groups_Ozero__class_Ozero(U_158) ) )
| c_Rings_Oinverse__class_Odivide(U_158,U_159,U_160) != U_161 ) )
| ~ class_Fields_Ofield__inverse__zero(U_158) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
cnf(f_62_3,plain,
( U_159 = hAPP(c_Groups_Otimes__class_Otimes(U_158,U_161),U_160)
| U_160 = c_Groups_Ozero__class_Ozero(U_158)
| c_Rings_Oinverse__class_Odivide(U_158,U_159,U_160) != U_161
| ~ class_Fields_Ofield__inverse__zero(U_158) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_4,plain,
( U_161 = c_Groups_Ozero__class_Ozero(U_158)
| U_160 != c_Groups_Ozero__class_Ozero(U_158)
| c_Rings_Oinverse__class_Odivide(U_158,U_159,U_160) != U_161
| ~ class_Fields_Ofield__inverse__zero(U_158) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_5,plain,
( U_160 = c_Groups_Ozero__class_Ozero(U_158)
| U_160 != c_Groups_Ozero__class_Ozero(U_158)
| c_Rings_Oinverse__class_Odivide(U_158,U_159,U_160) = U_161
| ~ class_Fields_Ofield__inverse__zero(U_158) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_6,plain,
( U_161 != c_Groups_Ozero__class_Ozero(U_158)
| U_160 != c_Groups_Ozero__class_Ozero(U_158)
| c_Rings_Oinverse__class_Odivide(U_158,U_159,U_160) = U_161
| ~ class_Fields_Ofield__inverse__zero(U_158) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_7,plain,
( U_160 = c_Groups_Ozero__class_Ozero(U_158)
| U_159 != hAPP(c_Groups_Otimes__class_Otimes(U_158,U_161),U_160)
| c_Rings_Oinverse__class_Odivide(U_158,U_159,U_160) = U_161
| ~ class_Fields_Ofield__inverse__zero(U_158) ),
inference(clausify,[status(thm)],[f_62_2]) ).
cnf(f_62_8,plain,
( U_161 != c_Groups_Ozero__class_Ozero(U_158)
| U_159 != hAPP(c_Groups_Otimes__class_Otimes(U_158,U_161),U_160)
| c_Rings_Oinverse__class_Odivide(U_158,U_159,U_160) = U_161
| ~ class_Fields_Ofield__inverse__zero(U_158) ),
inference(clausify,[status(thm)],[f_62_2]) ).
fof(f_63_1,plain,
! [V_ca_2,V_b_2,V_a_2,T_a] :
( ( ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)
| ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)
& V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2) != V_b_2
& V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
& ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2) = V_b_2
| V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) ) )
| V_a_2 != c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2) ) )
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__divide__eq]) ).
fof(f_63_2,plain,
! [U_165,U_164,U_163,U_162] :
( ( ( U_163 = c_Rings_Oinverse__class_Odivide(U_162,U_164,U_165)
| ( U_163 != c_Groups_Ozero__class_Ozero(U_162)
& U_165 = c_Groups_Ozero__class_Ozero(U_162) )
| ( hAPP(c_Groups_Otimes__class_Otimes(U_162,U_163),U_165) != U_164
& U_165 != c_Groups_Ozero__class_Ozero(U_162) ) )
& ( ( ( U_163 = c_Groups_Ozero__class_Ozero(U_162)
| U_165 != c_Groups_Ozero__class_Ozero(U_162) )
& ( hAPP(c_Groups_Otimes__class_Otimes(U_162,U_163),U_165) = U_164
| U_165 = c_Groups_Ozero__class_Ozero(U_162) ) )
| U_163 != c_Rings_Oinverse__class_Odivide(U_162,U_164,U_165) ) )
| ~ class_Fields_Ofield__inverse__zero(U_162) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
cnf(f_63_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_162,U_163),U_165) = U_164
| U_165 = c_Groups_Ozero__class_Ozero(U_162)
| U_163 != c_Rings_Oinverse__class_Odivide(U_162,U_164,U_165)
| ~ class_Fields_Ofield__inverse__zero(U_162) ),
inference(clausify,[status(thm)],[f_63_2]) ).
cnf(f_63_4,plain,
( U_163 = c_Groups_Ozero__class_Ozero(U_162)
| U_165 != c_Groups_Ozero__class_Ozero(U_162)
| U_163 != c_Rings_Oinverse__class_Odivide(U_162,U_164,U_165)
| ~ class_Fields_Ofield__inverse__zero(U_162) ),
inference(clausify,[status(thm)],[f_63_2]) ).
cnf(f_63_5,plain,
( U_165 = c_Groups_Ozero__class_Ozero(U_162)
| U_165 != c_Groups_Ozero__class_Ozero(U_162)
| U_163 = c_Rings_Oinverse__class_Odivide(U_162,U_164,U_165)
| ~ class_Fields_Ofield__inverse__zero(U_162) ),
inference(clausify,[status(thm)],[f_63_2]) ).
cnf(f_63_6,plain,
( U_163 != c_Groups_Ozero__class_Ozero(U_162)
| U_165 != c_Groups_Ozero__class_Ozero(U_162)
| U_163 = c_Rings_Oinverse__class_Odivide(U_162,U_164,U_165)
| ~ class_Fields_Ofield__inverse__zero(U_162) ),
inference(clausify,[status(thm)],[f_63_2]) ).
cnf(f_63_7,plain,
( U_165 = c_Groups_Ozero__class_Ozero(U_162)
| hAPP(c_Groups_Otimes__class_Otimes(U_162,U_163),U_165) != U_164
| U_163 = c_Rings_Oinverse__class_Odivide(U_162,U_164,U_165)
| ~ class_Fields_Ofield__inverse__zero(U_162) ),
inference(clausify,[status(thm)],[f_63_2]) ).
cnf(f_63_8,plain,
( U_163 != c_Groups_Ozero__class_Ozero(U_162)
| hAPP(c_Groups_Otimes__class_Otimes(U_162,U_163),U_165) != U_164
| U_163 = c_Rings_Oinverse__class_Odivide(U_162,U_164,U_165)
| ~ class_Fields_Ofield__inverse__zero(U_162) ),
inference(clausify,[status(thm)],[f_63_2]) ).
fof(f_64_1,plain,
! [V_x_2] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),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(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_64_2,plain,
! [U_166] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_166),U_166))
| U_166 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( U_166 = 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(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_166),U_166)) ) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
( ! [U_168] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_168),U_168))
| U_168 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_167] :
( U_167 = 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(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_167),U_167)) ) ),
inference(miniscope,[status(thm)],[f_64_2]) ).
cnf(f_64_4,plain,
( U_167 = 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(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_167),U_167)) ),
inference(clausify,[status(thm)],[f_64_3]) ).
cnf(f_64_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_168),U_168))
| U_168 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_64_3]) ).
fof(f_65_1,plain,
! [V_a_2,V_b_2,T_a] :
( ( ( c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2) = c_Groups_Oone__class_Oone(T_a)
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2) != c_Groups_Oone__class_Oone(T_a) ) )
| V_b_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_right__inverse__eq]) ).
fof(f_65_2,plain,
! [U_171,U_170,U_169] :
( ( ( c_Rings_Oinverse__class_Odivide(U_169,U_171,U_170) = c_Groups_Oone__class_Oone(U_169)
| U_171 != U_170 )
& ( U_171 = U_170
| c_Rings_Oinverse__class_Odivide(U_169,U_171,U_170) != c_Groups_Oone__class_Oone(U_169) ) )
| U_170 = c_Groups_Ozero__class_Ozero(U_169)
| ~ class_Rings_Odivision__ring(U_169) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
cnf(f_65_3,plain,
( U_171 = U_170
| c_Rings_Oinverse__class_Odivide(U_169,U_171,U_170) != c_Groups_Oone__class_Oone(U_169)
| U_170 = c_Groups_Ozero__class_Ozero(U_169)
| ~ class_Rings_Odivision__ring(U_169) ),
inference(clausify,[status(thm)],[f_65_2]) ).
cnf(f_65_4,plain,
( c_Rings_Oinverse__class_Odivide(U_169,U_171,U_170) = c_Groups_Oone__class_Oone(U_169)
| U_171 != U_170
| U_170 = c_Groups_Ozero__class_Ozero(U_169)
| ~ class_Rings_Odivision__ring(U_169) ),
inference(clausify,[status(thm)],[f_65_2]) ).
fof(f_66_1,plain,
! [V_a,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__self]) ).
fof(f_66_2,plain,
! [U_173,U_172] :
( c_Rings_Oinverse__class_Odivide(U_172,U_173,U_173) = c_Groups_Oone__class_Oone(U_172)
| U_173 = c_Groups_Ozero__class_Ozero(U_172)
| ~ class_Rings_Odivision__ring(U_172) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
cnf(f_66_3,plain,
( c_Rings_Oinverse__class_Odivide(U_172,U_173,U_173) = c_Groups_Oone__class_Oone(U_172)
| U_173 = c_Groups_Ozero__class_Ozero(U_172)
| ~ class_Rings_Odivision__ring(U_172) ),
inference(clausify,[status(thm)],[f_66_2]) ).
fof(f_67_1,plain,
! [V_a,T_a] :
( ( ( c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Oone__class_Oone(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a) )
& ( c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a)
| V_a != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Odivision__ring__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__self__if]) ).
fof(f_67_2,plain,
! [U_175,U_174] :
( ( ( c_Rings_Oinverse__class_Odivide(U_174,U_175,U_175) = c_Groups_Oone__class_Oone(U_174)
| U_175 = c_Groups_Ozero__class_Ozero(U_174) )
& ( c_Rings_Oinverse__class_Odivide(U_174,U_175,U_175) = c_Groups_Ozero__class_Ozero(U_174)
| U_175 != c_Groups_Ozero__class_Ozero(U_174) ) )
| ~ class_Rings_Odivision__ring__inverse__zero(U_174) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
cnf(f_67_3,plain,
( c_Rings_Oinverse__class_Odivide(U_174,U_175,U_175) = c_Groups_Ozero__class_Ozero(U_174)
| U_175 != c_Groups_Ozero__class_Ozero(U_174)
| ~ class_Rings_Odivision__ring__inverse__zero(U_174) ),
inference(clausify,[status(thm)],[f_67_2]) ).
cnf(f_67_4,plain,
( c_Rings_Oinverse__class_Odivide(U_174,U_175,U_175) = c_Groups_Oone__class_Oone(U_174)
| U_175 = c_Groups_Ozero__class_Ozero(U_174)
| ~ class_Rings_Odivision__ring__inverse__zero(U_174) ),
inference(clausify,[status(thm)],[f_67_2]) ).
fof(f_68_1,plain,
! [V_b,V_a,V_c,T_a] :
( V_a = c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)
| hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c) != V_b
| V_c = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__divide__imp]) ).
fof(f_68_2,plain,
! [U_179,U_178,U_177,U_176] :
( U_178 = c_Rings_Oinverse__class_Odivide(U_176,U_179,U_177)
| hAPP(c_Groups_Otimes__class_Otimes(U_176,U_178),U_177) != U_179
| U_177 = c_Groups_Ozero__class_Ozero(U_176)
| ~ class_Rings_Odivision__ring(U_176) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
cnf(f_68_3,plain,
( U_178 = c_Rings_Oinverse__class_Odivide(U_176,U_179,U_177)
| hAPP(c_Groups_Otimes__class_Otimes(U_176,U_178),U_177) != U_179
| U_177 = c_Groups_Ozero__class_Ozero(U_176)
| ~ class_Rings_Odivision__ring(U_176) ),
inference(clausify,[status(thm)],[f_68_2]) ).
fof(f_69_1,plain,
! [V_a,V_b,V_c,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c) = V_a
| V_b != hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c)
| V_c = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__eq__imp]) ).
fof(f_69_2,plain,
! [U_183,U_182,U_181,U_180] :
( c_Rings_Oinverse__class_Odivide(U_180,U_182,U_181) = U_183
| U_182 != hAPP(c_Groups_Otimes__class_Otimes(U_180,U_183),U_181)
| U_181 = c_Groups_Ozero__class_Ozero(U_180)
| ~ class_Rings_Odivision__ring(U_180) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
cnf(f_69_3,plain,
( c_Rings_Oinverse__class_Odivide(U_180,U_182,U_181) = U_183
| U_182 != hAPP(c_Groups_Otimes__class_Otimes(U_180,U_183),U_181)
| U_181 = c_Groups_Ozero__class_Ozero(U_180)
| ~ class_Rings_Odivision__ring(U_180) ),
inference(clausify,[status(thm)],[f_69_2]) ).
fof(f_70_1,plain,
! [V_a_2,V_b_2,V_ca_2,T_a] :
( ( ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2) = V_a_2
| V_b_2 != hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2) )
& ( V_b_2 = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)
| c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2) != V_a_2 ) )
| V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__divide__eq__eq]) ).
fof(f_70_2,plain,
! [U_187,U_186,U_185,U_184] :
( ( ( c_Rings_Oinverse__class_Odivide(U_184,U_186,U_185) = U_187
| U_186 != hAPP(c_Groups_Otimes__class_Otimes(U_184,U_187),U_185) )
& ( U_186 = hAPP(c_Groups_Otimes__class_Otimes(U_184,U_187),U_185)
| c_Rings_Oinverse__class_Odivide(U_184,U_186,U_185) != U_187 ) )
| U_185 = c_Groups_Ozero__class_Ozero(U_184)
| ~ class_Rings_Odivision__ring(U_184) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
cnf(f_70_3,plain,
( U_186 = hAPP(c_Groups_Otimes__class_Otimes(U_184,U_187),U_185)
| c_Rings_Oinverse__class_Odivide(U_184,U_186,U_185) != U_187
| U_185 = c_Groups_Ozero__class_Ozero(U_184)
| ~ class_Rings_Odivision__ring(U_184) ),
inference(clausify,[status(thm)],[f_70_2]) ).
cnf(f_70_4,plain,
( c_Rings_Oinverse__class_Odivide(U_184,U_186,U_185) = U_187
| U_186 != hAPP(c_Groups_Otimes__class_Otimes(U_184,U_187),U_185)
| U_185 = c_Groups_Ozero__class_Ozero(U_184)
| ~ class_Rings_Odivision__ring(U_184) ),
inference(clausify,[status(thm)],[f_70_2]) ).
fof(f_71_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)
| hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2) != V_b_2 )
& ( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2) = V_b_2
| V_a_2 != c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2) ) )
| V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__eq__divide__eq]) ).
fof(f_71_2,plain,
! [U_191,U_190,U_189,U_188] :
( ( ( U_190 = c_Rings_Oinverse__class_Odivide(U_188,U_191,U_189)
| hAPP(c_Groups_Otimes__class_Otimes(U_188,U_190),U_189) != U_191 )
& ( hAPP(c_Groups_Otimes__class_Otimes(U_188,U_190),U_189) = U_191
| U_190 != c_Rings_Oinverse__class_Odivide(U_188,U_191,U_189) ) )
| U_189 = c_Groups_Ozero__class_Ozero(U_188)
| ~ class_Rings_Odivision__ring(U_188) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
cnf(f_71_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_188,U_190),U_189) = U_191
| U_190 != c_Rings_Oinverse__class_Odivide(U_188,U_191,U_189)
| U_189 = c_Groups_Ozero__class_Ozero(U_188)
| ~ class_Rings_Odivision__ring(U_188) ),
inference(clausify,[status(thm)],[f_71_2]) ).
cnf(f_71_4,plain,
( U_190 = c_Rings_Oinverse__class_Odivide(U_188,U_191,U_189)
| hAPP(c_Groups_Otimes__class_Otimes(U_188,U_190),U_189) != U_191
| U_189 = c_Groups_Ozero__class_Ozero(U_188)
| ~ class_Rings_Odivision__ring(U_188) ),
inference(clausify,[status(thm)],[f_71_2]) ).
fof(f_72_1,plain,
! [V_n,V_m,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),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_72_2,plain,
! [U_194,U_193,U_192] :
( c_Orderings_Oord__class_Oless(U_192,c_Groups_Oone__class_Oone(U_192),hAPP(c_Groups_Otimes__class_Otimes(U_192,U_193),U_194))
| ~ c_Orderings_Oord__class_Oless(U_192,c_Groups_Oone__class_Oone(U_192),U_194)
| ~ c_Orderings_Oord__class_Oless(U_192,c_Groups_Oone__class_Oone(U_192),U_193)
| ~ class_Rings_Olinordered__semidom(U_192) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
cnf(f_72_3,plain,
( c_Orderings_Oord__class_Oless(U_192,c_Groups_Oone__class_Oone(U_192),hAPP(c_Groups_Otimes__class_Otimes(U_192,U_193),U_194))
| ~ c_Orderings_Oord__class_Oless(U_192,c_Groups_Oone__class_Oone(U_192),U_194)
| ~ c_Orderings_Oord__class_Oless(U_192,c_Groups_Oone__class_Oone(U_192),U_193)
| ~ class_Rings_Olinordered__semidom(U_192) ),
inference(clausify,[status(thm)],[f_72_2]) ).
fof(f_73_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_73_2,plain,
! [U_195] :
( c_Orderings_Oord__class_Oless(U_195,c_Groups_Ozero__class_Ozero(U_195),c_Groups_Oone__class_Oone(U_195))
| ~ class_Rings_Olinordered__semidom(U_195) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
cnf(f_73_3,plain,
( c_Orderings_Oord__class_Oless(U_195,c_Groups_Ozero__class_Ozero(U_195),c_Groups_Oone__class_Oone(U_195))
| ~ class_Rings_Olinordered__semidom(U_195) ),
inference(clausify,[status(thm)],[f_73_2]) ).
fof(f_74_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_74_2,plain,
! [U_196] :
( ~ c_Orderings_Oord__class_Oless(U_196,c_Groups_Oone__class_Oone(U_196),c_Groups_Ozero__class_Ozero(U_196))
| ~ class_Rings_Olinordered__semidom(U_196) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
cnf(f_74_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_196,c_Groups_Oone__class_Oone(U_196),c_Groups_Ozero__class_Ozero(U_196))
| ~ class_Rings_Olinordered__semidom(U_196) ),
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_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_75_2,plain,
! [U_199,U_198,U_197] :
( c_Orderings_Oord__class_Oless(U_197,U_199,U_198)
| c_Orderings_Oord__class_Oless(U_197,U_198,U_199)
| U_198 = U_199
| ~ class_Rings_Olinordered__idom(U_197) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
cnf(f_75_3,plain,
( c_Orderings_Oord__class_Oless(U_197,U_199,U_198)
| c_Orderings_Oord__class_Oless(U_197,U_198,U_199)
| U_198 = U_199
| ~ class_Rings_Olinordered__idom(U_197) ),
inference(clausify,[status(thm)],[f_75_2]) ).
fof(f_76_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(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_76_2,plain,
! [U_202,U_201,U_200] :
( U_202 = c_Groups_Ozero__class_Ozero(U_200)
| U_201 = c_Groups_Ozero__class_Ozero(U_200)
| hAPP(c_Groups_Otimes__class_Otimes(U_200,U_201),U_202) != c_Groups_Ozero__class_Ozero(U_200)
| ~ class_Rings_Ono__zero__divisors(U_200) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
cnf(f_76_3,plain,
( U_202 = c_Groups_Ozero__class_Ozero(U_200)
| U_201 = c_Groups_Ozero__class_Ozero(U_200)
| hAPP(c_Groups_Otimes__class_Otimes(U_200,U_201),U_202) != c_Groups_Ozero__class_Ozero(U_200)
| ~ class_Rings_Ono__zero__divisors(U_200) ),
inference(clausify,[status(thm)],[f_76_2]) ).
fof(f_77_1,plain,
! [V_b,V_a,T_a] :
( 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_77_2,plain,
! [U_205,U_204,U_203] :
( hAPP(c_Groups_Otimes__class_Otimes(U_203,U_204),U_205) != c_Groups_Ozero__class_Ozero(U_203)
| U_205 = c_Groups_Ozero__class_Ozero(U_203)
| U_204 = c_Groups_Ozero__class_Ozero(U_203)
| ~ class_Rings_Ono__zero__divisors(U_203) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
cnf(f_77_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_203,U_204),U_205) != c_Groups_Ozero__class_Ozero(U_203)
| U_205 = c_Groups_Ozero__class_Ozero(U_203)
| U_204 = c_Groups_Ozero__class_Ozero(U_203)
| ~ class_Rings_Ono__zero__divisors(U_203) ),
inference(clausify,[status(thm)],[f_77_2]) ).
fof(f_78_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( 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(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_78_2,plain,
! [U_208,U_207,U_206] :
( ( ( hAPP(c_Groups_Otimes__class_Otimes(U_206,U_207),U_208) = c_Groups_Ozero__class_Ozero(U_206)
| ( U_208 != c_Groups_Ozero__class_Ozero(U_206)
& U_207 != c_Groups_Ozero__class_Ozero(U_206) ) )
& ( U_208 = c_Groups_Ozero__class_Ozero(U_206)
| U_207 = c_Groups_Ozero__class_Ozero(U_206)
| hAPP(c_Groups_Otimes__class_Otimes(U_206,U_207),U_208) != c_Groups_Ozero__class_Ozero(U_206) ) )
| ~ class_Rings_Oring__no__zero__divisors(U_206) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
cnf(f_78_3,plain,
( U_208 = c_Groups_Ozero__class_Ozero(U_206)
| U_207 = c_Groups_Ozero__class_Ozero(U_206)
| hAPP(c_Groups_Otimes__class_Otimes(U_206,U_207),U_208) != c_Groups_Ozero__class_Ozero(U_206)
| ~ class_Rings_Oring__no__zero__divisors(U_206) ),
inference(clausify,[status(thm)],[f_78_2]) ).
cnf(f_78_4,plain,
( U_207 != c_Groups_Ozero__class_Ozero(U_206)
| hAPP(c_Groups_Otimes__class_Otimes(U_206,U_207),U_208) = c_Groups_Ozero__class_Ozero(U_206)
| ~ class_Rings_Oring__no__zero__divisors(U_206) ),
inference(clausify,[status(thm)],[f_78_2]) ).
cnf(f_78_5,plain,
( U_208 != c_Groups_Ozero__class_Ozero(U_206)
| hAPP(c_Groups_Otimes__class_Otimes(U_206,U_207),U_208) = c_Groups_Ozero__class_Ozero(U_206)
| ~ class_Rings_Oring__no__zero__divisors(U_206) ),
inference(clausify,[status(thm)],[f_78_2]) ).
fof(f_79_1,plain,
! [V_a,T_a] :
( 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_79_2,plain,
! [U_210,U_209] :
( hAPP(c_Groups_Otimes__class_Otimes(U_209,U_210),c_Groups_Ozero__class_Ozero(U_209)) = c_Groups_Ozero__class_Ozero(U_209)
| ~ class_Rings_Omult__zero(U_209) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
cnf(f_79_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_209,U_210),c_Groups_Ozero__class_Ozero(U_209)) = c_Groups_Ozero__class_Ozero(U_209)
| ~ class_Rings_Omult__zero(U_209) ),
inference(clausify,[status(thm)],[f_79_2]) ).
fof(f_80_1,plain,
! [V_a,T_a] :
( 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_80_2,plain,
! [U_212,U_211] :
( hAPP(c_Groups_Otimes__class_Otimes(U_211,c_Groups_Ozero__class_Ozero(U_211)),U_212) = c_Groups_Ozero__class_Ozero(U_211)
| ~ class_Rings_Omult__zero(U_211) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
cnf(f_80_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_211,c_Groups_Ozero__class_Ozero(U_211)),U_212) = c_Groups_Ozero__class_Ozero(U_211)
| ~ class_Rings_Omult__zero(U_211) ),
inference(clausify,[status(thm)],[f_80_2]) ).
fof(f_81_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_81_2,plain,
! [U_213] :
( c_Groups_Oone__class_Oone(U_213) != c_Groups_Ozero__class_Ozero(U_213)
| ~ class_Rings_Ozero__neq__one(U_213) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
cnf(f_81_3,plain,
( c_Groups_Oone__class_Oone(U_213) != c_Groups_Ozero__class_Ozero(U_213)
| ~ class_Rings_Ozero__neq__one(U_213) ),
inference(clausify,[status(thm)],[f_81_2]) ).
fof(f_82_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_82_2,plain,
! [U_214] :
( c_Groups_Ozero__class_Ozero(U_214) != c_Groups_Oone__class_Oone(U_214)
| ~ class_Rings_Ozero__neq__one(U_214) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
cnf(f_82_3,plain,
( c_Groups_Ozero__class_Ozero(U_214) != c_Groups_Oone__class_Oone(U_214)
| ~ class_Rings_Ozero__neq__one(U_214) ),
inference(clausify,[status(thm)],[f_82_2]) ).
fof(f_83_1,plain,
! [V_a,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__zero__left]) ).
fof(f_83_2,plain,
! [U_216,U_215] :
( c_Rings_Oinverse__class_Odivide(U_215,c_Groups_Ozero__class_Ozero(U_215),U_216) = c_Groups_Ozero__class_Ozero(U_215)
| ~ class_Rings_Odivision__ring(U_215) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
cnf(f_83_3,plain,
( c_Rings_Oinverse__class_Odivide(U_215,c_Groups_Ozero__class_Ozero(U_215),U_216) = c_Groups_Ozero__class_Ozero(U_215)
| ~ class_Rings_Odivision__ring(U_215) ),
inference(clausify,[status(thm)],[f_83_2]) ).
fof(f_84_1,plain,
! [V_a,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__zero]) ).
fof(f_84_2,plain,
! [U_218,U_217] :
( c_Rings_Oinverse__class_Odivide(U_217,U_218,c_Groups_Ozero__class_Ozero(U_217)) = c_Groups_Ozero__class_Ozero(U_217)
| ~ class_Rings_Odivision__ring__inverse__zero(U_217) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
cnf(f_84_3,plain,
( c_Rings_Oinverse__class_Odivide(U_217,U_218,c_Groups_Ozero__class_Ozero(U_217)) = c_Groups_Ozero__class_Ozero(U_217)
| ~ class_Rings_Odivision__ring__inverse__zero(U_217) ),
inference(clausify,[status(thm)],[f_84_2]) ).
fof(f_85_1,plain,
! [V_c,V_b,V_a,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)) = c_Rings_Oinverse__class_Odivide(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),V_c)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_times__divide__eq__right]) ).
fof(f_85_2,plain,
! [U_222,U_221,U_220,U_219] :
( hAPP(c_Groups_Otimes__class_Otimes(U_219,U_220),c_Rings_Oinverse__class_Odivide(U_219,U_221,U_222)) = c_Rings_Oinverse__class_Odivide(U_219,hAPP(c_Groups_Otimes__class_Otimes(U_219,U_220),U_221),U_222)
| ~ class_Rings_Odivision__ring(U_219) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
cnf(f_85_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_219,U_220),c_Rings_Oinverse__class_Odivide(U_219,U_221,U_222)) = c_Rings_Oinverse__class_Odivide(U_219,hAPP(c_Groups_Otimes__class_Otimes(U_219,U_220),U_221),U_222)
| ~ class_Rings_Odivision__ring(U_219) ),
inference(clausify,[status(thm)],[f_85_2]) ).
fof(f_86_1,plain,
! [V_a,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = V_a
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__1]) ).
fof(f_86_2,plain,
! [U_224,U_223] :
( c_Rings_Oinverse__class_Odivide(U_223,U_224,c_Groups_Oone__class_Oone(U_223)) = U_224
| ~ class_Rings_Odivision__ring(U_223) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
cnf(f_86_3,plain,
( c_Rings_Oinverse__class_Odivide(U_223,U_224,c_Groups_Oone__class_Oone(U_223)) = U_224
| ~ class_Rings_Odivision__ring(U_223) ),
inference(clausify,[status(thm)],[f_86_2]) ).
fof(f_87_1,plain,
! [V_a,V_r] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r),V_a),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_r),V_r)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_a,V_r),
inference(fof_nnf,[status(thm)],[fact_real__divide__square__eq]) ).
fof(f_87_2,plain,
! [U_226,U_225] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_225),U_226),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_225),U_225)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_226,U_225),
inference(variable_rename,[status(thm)],[f_87_1]) ).
cnf(f_87_3,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_225),U_226),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_225),U_225)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_226,U_225),
inference(clausify,[status(thm)],[f_87_2]) ).
fof(f_88_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),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_88_2,plain,
! [U_230,U_229,U_228,U_227] :
( c_Orderings_Oord__class_Oless(U_227,hAPP(c_Groups_Otimes__class_Otimes(U_227,U_230),U_229),hAPP(c_Groups_Otimes__class_Otimes(U_227,U_230),U_228))
| ~ c_Orderings_Oord__class_Oless(U_227,U_230,c_Groups_Ozero__class_Ozero(U_227))
| ~ c_Orderings_Oord__class_Oless(U_227,U_228,U_229)
| ~ class_Rings_Olinordered__ring__strict(U_227) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
cnf(f_88_3,plain,
( c_Orderings_Oord__class_Oless(U_227,hAPP(c_Groups_Otimes__class_Otimes(U_227,U_230),U_229),hAPP(c_Groups_Otimes__class_Otimes(U_227,U_230),U_228))
| ~ c_Orderings_Oord__class_Oless(U_227,U_230,c_Groups_Ozero__class_Ozero(U_227))
| ~ c_Orderings_Oord__class_Oless(U_227,U_228,U_229)
| ~ class_Rings_Olinordered__ring__strict(U_227) ),
inference(clausify,[status(thm)],[f_88_2]) ).
fof(f_89_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),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_89_2,plain,
! [U_234,U_233,U_232,U_231] :
( c_Orderings_Oord__class_Oless(U_231,hAPP(c_Groups_Otimes__class_Otimes(U_231,U_233),U_234),hAPP(c_Groups_Otimes__class_Otimes(U_231,U_232),U_234))
| ~ c_Orderings_Oord__class_Oless(U_231,U_234,c_Groups_Ozero__class_Ozero(U_231))
| ~ c_Orderings_Oord__class_Oless(U_231,U_232,U_233)
| ~ class_Rings_Olinordered__ring__strict(U_231) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
cnf(f_89_3,plain,
( c_Orderings_Oord__class_Oless(U_231,hAPP(c_Groups_Otimes__class_Otimes(U_231,U_233),U_234),hAPP(c_Groups_Otimes__class_Otimes(U_231,U_232),U_234))
| ~ c_Orderings_Oord__class_Oless(U_231,U_234,c_Groups_Ozero__class_Ozero(U_231))
| ~ c_Orderings_Oord__class_Oless(U_231,U_232,U_233)
| ~ class_Rings_Olinordered__ring__strict(U_231) ),
inference(clausify,[status(thm)],[f_89_2]) ).
fof(f_90_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),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_90_2,plain,
! [U_238,U_237,U_236,U_235] :
( c_Orderings_Oord__class_Oless(U_235,hAPP(c_Groups_Otimes__class_Otimes(U_235,U_238),U_236),hAPP(c_Groups_Otimes__class_Otimes(U_235,U_238),U_237))
| ~ c_Orderings_Oord__class_Oless(U_235,c_Groups_Ozero__class_Ozero(U_235),U_238)
| ~ c_Orderings_Oord__class_Oless(U_235,U_236,U_237)
| ~ class_Rings_Olinordered__comm__semiring__strict(U_235) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
cnf(f_90_3,plain,
( c_Orderings_Oord__class_Oless(U_235,hAPP(c_Groups_Otimes__class_Otimes(U_235,U_238),U_236),hAPP(c_Groups_Otimes__class_Otimes(U_235,U_238),U_237))
| ~ c_Orderings_Oord__class_Oless(U_235,c_Groups_Ozero__class_Ozero(U_235),U_238)
| ~ c_Orderings_Oord__class_Oless(U_235,U_236,U_237)
| ~ class_Rings_Olinordered__comm__semiring__strict(U_235) ),
inference(clausify,[status(thm)],[f_90_2]) ).
fof(f_91_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),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_91_2,plain,
! [U_242,U_241,U_240,U_239] :
( c_Orderings_Oord__class_Oless(U_239,hAPP(c_Groups_Otimes__class_Otimes(U_239,U_242),U_240),hAPP(c_Groups_Otimes__class_Otimes(U_239,U_242),U_241))
| ~ c_Orderings_Oord__class_Oless(U_239,c_Groups_Ozero__class_Ozero(U_239),U_242)
| ~ c_Orderings_Oord__class_Oless(U_239,U_240,U_241)
| ~ class_Rings_Olinordered__semiring__strict(U_239) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
cnf(f_91_3,plain,
( c_Orderings_Oord__class_Oless(U_239,hAPP(c_Groups_Otimes__class_Otimes(U_239,U_242),U_240),hAPP(c_Groups_Otimes__class_Otimes(U_239,U_242),U_241))
| ~ c_Orderings_Oord__class_Oless(U_239,c_Groups_Ozero__class_Ozero(U_239),U_242)
| ~ c_Orderings_Oord__class_Oless(U_239,U_240,U_241)
| ~ class_Rings_Olinordered__semiring__strict(U_239) ),
inference(clausify,[status(thm)],[f_91_2]) ).
fof(f_92_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),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_92_2,plain,
! [U_246,U_245,U_244,U_243] :
( c_Orderings_Oord__class_Oless(U_243,hAPP(c_Groups_Otimes__class_Otimes(U_243,U_244),U_246),hAPP(c_Groups_Otimes__class_Otimes(U_243,U_245),U_246))
| ~ c_Orderings_Oord__class_Oless(U_243,c_Groups_Ozero__class_Ozero(U_243),U_246)
| ~ c_Orderings_Oord__class_Oless(U_243,U_244,U_245)
| ~ class_Rings_Olinordered__semiring__strict(U_243) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
cnf(f_92_3,plain,
( c_Orderings_Oord__class_Oless(U_243,hAPP(c_Groups_Otimes__class_Otimes(U_243,U_244),U_246),hAPP(c_Groups_Otimes__class_Otimes(U_243,U_245),U_246))
| ~ c_Orderings_Oord__class_Oless(U_243,c_Groups_Ozero__class_Ozero(U_243),U_246)
| ~ c_Orderings_Oord__class_Oless(U_243,U_244,U_245)
| ~ class_Rings_Olinordered__semiring__strict(U_243) ),
inference(clausify,[status(thm)],[f_92_2]) ).
fof(f_93_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),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_93_2,plain,
! [U_249,U_248,U_247] :
( c_Orderings_Oord__class_Oless(U_247,c_Groups_Ozero__class_Ozero(U_247),hAPP(c_Groups_Otimes__class_Otimes(U_247,U_248),U_249))
| ~ c_Orderings_Oord__class_Oless(U_247,U_249,c_Groups_Ozero__class_Ozero(U_247))
| ~ c_Orderings_Oord__class_Oless(U_247,U_248,c_Groups_Ozero__class_Ozero(U_247))
| ~ class_Rings_Olinordered__ring__strict(U_247) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
cnf(f_93_3,plain,
( c_Orderings_Oord__class_Oless(U_247,c_Groups_Ozero__class_Ozero(U_247),hAPP(c_Groups_Otimes__class_Otimes(U_247,U_248),U_249))
| ~ c_Orderings_Oord__class_Oless(U_247,U_249,c_Groups_Ozero__class_Ozero(U_247))
| ~ c_Orderings_Oord__class_Oless(U_247,U_248,c_Groups_Ozero__class_Ozero(U_247))
| ~ class_Rings_Olinordered__ring__strict(U_247) ),
inference(clausify,[status(thm)],[f_93_2]) ).
fof(f_94_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,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_94_2,plain,
! [U_252,U_251,U_250] :
( c_Orderings_Oord__class_Oless(U_250,hAPP(c_Groups_Otimes__class_Otimes(U_250,U_251),U_252),c_Groups_Ozero__class_Ozero(U_250))
| ~ c_Orderings_Oord__class_Oless(U_250,c_Groups_Ozero__class_Ozero(U_250),U_252)
| ~ c_Orderings_Oord__class_Oless(U_250,U_251,c_Groups_Ozero__class_Ozero(U_250))
| ~ class_Rings_Olinordered__semiring__strict(U_250) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
cnf(f_94_3,plain,
( c_Orderings_Oord__class_Oless(U_250,hAPP(c_Groups_Otimes__class_Otimes(U_250,U_251),U_252),c_Groups_Ozero__class_Ozero(U_250))
| ~ c_Orderings_Oord__class_Oless(U_250,c_Groups_Ozero__class_Ozero(U_250),U_252)
| ~ c_Orderings_Oord__class_Oless(U_250,U_251,c_Groups_Ozero__class_Ozero(U_250))
| ~ class_Rings_Olinordered__semiring__strict(U_250) ),
inference(clausify,[status(thm)],[f_94_2]) ).
fof(f_95_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),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(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),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_95_2,plain,
! [U_256,U_255,U_254,U_253] :
( ( ( c_Orderings_Oord__class_Oless(U_253,hAPP(c_Groups_Otimes__class_Otimes(U_253,U_254),U_255),hAPP(c_Groups_Otimes__class_Otimes(U_253,U_254),U_256))
| ~ c_Orderings_Oord__class_Oless(U_253,U_256,U_255) )
& ( c_Orderings_Oord__class_Oless(U_253,U_256,U_255)
| ~ c_Orderings_Oord__class_Oless(U_253,hAPP(c_Groups_Otimes__class_Otimes(U_253,U_254),U_255),hAPP(c_Groups_Otimes__class_Otimes(U_253,U_254),U_256)) ) )
| ~ c_Orderings_Oord__class_Oless(U_253,U_254,c_Groups_Ozero__class_Ozero(U_253))
| ~ class_Rings_Olinordered__ring__strict(U_253) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
cnf(f_95_3,plain,
( c_Orderings_Oord__class_Oless(U_253,U_256,U_255)
| ~ c_Orderings_Oord__class_Oless(U_253,hAPP(c_Groups_Otimes__class_Otimes(U_253,U_254),U_255),hAPP(c_Groups_Otimes__class_Otimes(U_253,U_254),U_256))
| ~ c_Orderings_Oord__class_Oless(U_253,U_254,c_Groups_Ozero__class_Ozero(U_253))
| ~ class_Rings_Olinordered__ring__strict(U_253) ),
inference(clausify,[status(thm)],[f_95_2]) ).
cnf(f_95_4,plain,
( c_Orderings_Oord__class_Oless(U_253,hAPP(c_Groups_Otimes__class_Otimes(U_253,U_254),U_255),hAPP(c_Groups_Otimes__class_Otimes(U_253,U_254),U_256))
| ~ c_Orderings_Oord__class_Oless(U_253,U_256,U_255)
| ~ c_Orderings_Oord__class_Oless(U_253,U_254,c_Groups_Ozero__class_Ozero(U_253))
| ~ class_Rings_Olinordered__ring__strict(U_253) ),
inference(clausify,[status(thm)],[f_95_2]) ).
fof(f_96_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(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_96_2,plain,
! [U_259,U_258,U_257] :
( c_Orderings_Oord__class_Oless(U_257,c_Groups_Ozero__class_Ozero(U_257),U_258)
| ~ c_Orderings_Oord__class_Oless(U_257,c_Groups_Ozero__class_Ozero(U_257),U_259)
| ~ c_Orderings_Oord__class_Oless(U_257,c_Groups_Ozero__class_Ozero(U_257),hAPP(c_Groups_Otimes__class_Otimes(U_257,U_258),U_259))
| ~ class_Rings_Olinordered__semiring__strict(U_257) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
cnf(f_96_3,plain,
( c_Orderings_Oord__class_Oless(U_257,c_Groups_Ozero__class_Ozero(U_257),U_258)
| ~ c_Orderings_Oord__class_Oless(U_257,c_Groups_Ozero__class_Ozero(U_257),U_259)
| ~ c_Orderings_Oord__class_Oless(U_257,c_Groups_Ozero__class_Ozero(U_257),hAPP(c_Groups_Otimes__class_Otimes(U_257,U_258),U_259))
| ~ class_Rings_Olinordered__semiring__strict(U_257) ),
inference(clausify,[status(thm)],[f_96_2]) ).
fof(f_97_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(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_97_2,plain,
! [U_262,U_261,U_260] :
( c_Orderings_Oord__class_Oless(U_260,c_Groups_Ozero__class_Ozero(U_260),U_262)
| ~ c_Orderings_Oord__class_Oless(U_260,c_Groups_Ozero__class_Ozero(U_260),U_261)
| ~ c_Orderings_Oord__class_Oless(U_260,c_Groups_Ozero__class_Ozero(U_260),hAPP(c_Groups_Otimes__class_Otimes(U_260,U_261),U_262))
| ~ class_Rings_Olinordered__semiring__strict(U_260) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
cnf(f_97_3,plain,
( c_Orderings_Oord__class_Oless(U_260,c_Groups_Ozero__class_Ozero(U_260),U_262)
| ~ c_Orderings_Oord__class_Oless(U_260,c_Groups_Ozero__class_Ozero(U_260),U_261)
| ~ c_Orderings_Oord__class_Oless(U_260,c_Groups_Ozero__class_Ozero(U_260),hAPP(c_Groups_Otimes__class_Otimes(U_260,U_261),U_262))
| ~ class_Rings_Olinordered__semiring__strict(U_260) ),
inference(clausify,[status(thm)],[f_97_2]) ).
fof(f_98_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,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_98_2,plain,
! [U_265,U_264,U_263] :
( c_Orderings_Oord__class_Oless(U_263,hAPP(c_Groups_Otimes__class_Otimes(U_263,U_265),U_264),c_Groups_Ozero__class_Ozero(U_263))
| ~ c_Orderings_Oord__class_Oless(U_263,U_265,c_Groups_Ozero__class_Ozero(U_263))
| ~ c_Orderings_Oord__class_Oless(U_263,c_Groups_Ozero__class_Ozero(U_263),U_264)
| ~ class_Rings_Olinordered__semiring__strict(U_263) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
cnf(f_98_3,plain,
( c_Orderings_Oord__class_Oless(U_263,hAPP(c_Groups_Otimes__class_Otimes(U_263,U_265),U_264),c_Groups_Ozero__class_Ozero(U_263))
| ~ c_Orderings_Oord__class_Oless(U_263,U_265,c_Groups_Ozero__class_Ozero(U_263))
| ~ c_Orderings_Oord__class_Oless(U_263,c_Groups_Ozero__class_Ozero(U_263),U_264)
| ~ class_Rings_Olinordered__semiring__strict(U_263) ),
inference(clausify,[status(thm)],[f_98_2]) ).
fof(f_99_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,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_99_2,plain,
! [U_268,U_267,U_266] :
( c_Orderings_Oord__class_Oless(U_266,hAPP(c_Groups_Otimes__class_Otimes(U_266,U_267),U_268),c_Groups_Ozero__class_Ozero(U_266))
| ~ c_Orderings_Oord__class_Oless(U_266,U_268,c_Groups_Ozero__class_Ozero(U_266))
| ~ c_Orderings_Oord__class_Oless(U_266,c_Groups_Ozero__class_Ozero(U_266),U_267)
| ~ class_Rings_Olinordered__semiring__strict(U_266) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
cnf(f_99_3,plain,
( c_Orderings_Oord__class_Oless(U_266,hAPP(c_Groups_Otimes__class_Otimes(U_266,U_267),U_268),c_Groups_Ozero__class_Ozero(U_266))
| ~ c_Orderings_Oord__class_Oless(U_266,U_268,c_Groups_Ozero__class_Ozero(U_266))
| ~ c_Orderings_Oord__class_Oless(U_266,c_Groups_Ozero__class_Ozero(U_266),U_267)
| ~ class_Rings_Olinordered__semiring__strict(U_266) ),
inference(clausify,[status(thm)],[f_99_2]) ).
fof(f_100_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),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_100_2,plain,
! [U_271,U_270,U_269] :
( c_Orderings_Oord__class_Oless(U_269,c_Groups_Ozero__class_Ozero(U_269),hAPP(c_Groups_Otimes__class_Otimes(U_269,U_270),U_271))
| ~ c_Orderings_Oord__class_Oless(U_269,c_Groups_Ozero__class_Ozero(U_269),U_271)
| ~ c_Orderings_Oord__class_Oless(U_269,c_Groups_Ozero__class_Ozero(U_269),U_270)
| ~ class_Rings_Olinordered__semiring__strict(U_269) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
cnf(f_100_3,plain,
( c_Orderings_Oord__class_Oless(U_269,c_Groups_Ozero__class_Ozero(U_269),hAPP(c_Groups_Otimes__class_Otimes(U_269,U_270),U_271))
| ~ c_Orderings_Oord__class_Oless(U_269,c_Groups_Ozero__class_Ozero(U_269),U_271)
| ~ c_Orderings_Oord__class_Oless(U_269,c_Groups_Ozero__class_Ozero(U_269),U_270)
| ~ class_Rings_Olinordered__semiring__strict(U_269) ),
inference(clausify,[status(thm)],[f_100_2]) ).
fof(f_101_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),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(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),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_101_2,plain,
! [U_275,U_274,U_273,U_272] :
( ( ( c_Orderings_Oord__class_Oless(U_272,hAPP(c_Groups_Otimes__class_Otimes(U_272,U_273),U_274),hAPP(c_Groups_Otimes__class_Otimes(U_272,U_273),U_275))
| ~ c_Orderings_Oord__class_Oless(U_272,U_274,U_275) )
& ( c_Orderings_Oord__class_Oless(U_272,U_274,U_275)
| ~ c_Orderings_Oord__class_Oless(U_272,hAPP(c_Groups_Otimes__class_Otimes(U_272,U_273),U_274),hAPP(c_Groups_Otimes__class_Otimes(U_272,U_273),U_275)) ) )
| ~ c_Orderings_Oord__class_Oless(U_272,c_Groups_Ozero__class_Ozero(U_272),U_273)
| ~ class_Rings_Olinordered__ring__strict(U_272) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
cnf(f_101_3,plain,
( c_Orderings_Oord__class_Oless(U_272,U_274,U_275)
| ~ c_Orderings_Oord__class_Oless(U_272,hAPP(c_Groups_Otimes__class_Otimes(U_272,U_273),U_274),hAPP(c_Groups_Otimes__class_Otimes(U_272,U_273),U_275))
| ~ c_Orderings_Oord__class_Oless(U_272,c_Groups_Ozero__class_Ozero(U_272),U_273)
| ~ class_Rings_Olinordered__ring__strict(U_272) ),
inference(clausify,[status(thm)],[f_101_2]) ).
cnf(f_101_4,plain,
( c_Orderings_Oord__class_Oless(U_272,hAPP(c_Groups_Otimes__class_Otimes(U_272,U_273),U_274),hAPP(c_Groups_Otimes__class_Otimes(U_272,U_273),U_275))
| ~ c_Orderings_Oord__class_Oless(U_272,U_274,U_275)
| ~ c_Orderings_Oord__class_Oless(U_272,c_Groups_Ozero__class_Ozero(U_272),U_273)
| ~ class_Rings_Olinordered__ring__strict(U_272) ),
inference(clausify,[status(thm)],[f_101_2]) ).
fof(f_102_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),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(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),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_102_2,plain,
! [U_279,U_278,U_277,U_276] :
( ( ( c_Orderings_Oord__class_Oless(U_276,hAPP(c_Groups_Otimes__class_Otimes(U_276,U_277),U_278),hAPP(c_Groups_Otimes__class_Otimes(U_276,U_277),U_279))
| ( ( ~ c_Orderings_Oord__class_Oless(U_276,U_279,U_278)
| ~ c_Orderings_Oord__class_Oless(U_276,U_277,c_Groups_Ozero__class_Ozero(U_276)) )
& ( ~ c_Orderings_Oord__class_Oless(U_276,U_278,U_279)
| ~ c_Orderings_Oord__class_Oless(U_276,c_Groups_Ozero__class_Ozero(U_276),U_277) ) ) )
& ( ( c_Orderings_Oord__class_Oless(U_276,U_279,U_278)
& c_Orderings_Oord__class_Oless(U_276,U_277,c_Groups_Ozero__class_Ozero(U_276)) )
| ( c_Orderings_Oord__class_Oless(U_276,U_278,U_279)
& c_Orderings_Oord__class_Oless(U_276,c_Groups_Ozero__class_Ozero(U_276),U_277) )
| ~ c_Orderings_Oord__class_Oless(U_276,hAPP(c_Groups_Otimes__class_Otimes(U_276,U_277),U_278),hAPP(c_Groups_Otimes__class_Otimes(U_276,U_277),U_279)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_276) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
cnf(f_102_3,plain,
( c_Orderings_Oord__class_Oless(U_276,U_277,c_Groups_Ozero__class_Ozero(U_276))
| c_Orderings_Oord__class_Oless(U_276,c_Groups_Ozero__class_Ozero(U_276),U_277)
| ~ c_Orderings_Oord__class_Oless(U_276,hAPP(c_Groups_Otimes__class_Otimes(U_276,U_277),U_278),hAPP(c_Groups_Otimes__class_Otimes(U_276,U_277),U_279))
| ~ class_Rings_Olinordered__ring__strict(U_276) ),
inference(clausify,[status(thm)],[f_102_2]) ).
cnf(f_102_4,plain,
( c_Orderings_Oord__class_Oless(U_276,U_279,U_278)
| c_Orderings_Oord__class_Oless(U_276,c_Groups_Ozero__class_Ozero(U_276),U_277)
| ~ c_Orderings_Oord__class_Oless(U_276,hAPP(c_Groups_Otimes__class_Otimes(U_276,U_277),U_278),hAPP(c_Groups_Otimes__class_Otimes(U_276,U_277),U_279))
| ~ class_Rings_Olinordered__ring__strict(U_276) ),
inference(clausify,[status(thm)],[f_102_2]) ).
cnf(f_102_5,plain,
( c_Orderings_Oord__class_Oless(U_276,U_277,c_Groups_Ozero__class_Ozero(U_276))
| c_Orderings_Oord__class_Oless(U_276,U_278,U_279)
| ~ c_Orderings_Oord__class_Oless(U_276,hAPP(c_Groups_Otimes__class_Otimes(U_276,U_277),U_278),hAPP(c_Groups_Otimes__class_Otimes(U_276,U_277),U_279))
| ~ class_Rings_Olinordered__ring__strict(U_276) ),
inference(clausify,[status(thm)],[f_102_2]) ).
cnf(f_102_6,plain,
( c_Orderings_Oord__class_Oless(U_276,U_279,U_278)
| c_Orderings_Oord__class_Oless(U_276,U_278,U_279)
| ~ c_Orderings_Oord__class_Oless(U_276,hAPP(c_Groups_Otimes__class_Otimes(U_276,U_277),U_278),hAPP(c_Groups_Otimes__class_Otimes(U_276,U_277),U_279))
| ~ class_Rings_Olinordered__ring__strict(U_276) ),
inference(clausify,[status(thm)],[f_102_2]) ).
cnf(f_102_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_276,U_278,U_279)
| ~ c_Orderings_Oord__class_Oless(U_276,c_Groups_Ozero__class_Ozero(U_276),U_277)
| c_Orderings_Oord__class_Oless(U_276,hAPP(c_Groups_Otimes__class_Otimes(U_276,U_277),U_278),hAPP(c_Groups_Otimes__class_Otimes(U_276,U_277),U_279))
| ~ class_Rings_Olinordered__ring__strict(U_276) ),
inference(clausify,[status(thm)],[f_102_2]) ).
cnf(f_102_8,plain,
( ~ c_Orderings_Oord__class_Oless(U_276,U_279,U_278)
| ~ c_Orderings_Oord__class_Oless(U_276,U_277,c_Groups_Ozero__class_Ozero(U_276))
| c_Orderings_Oord__class_Oless(U_276,hAPP(c_Groups_Otimes__class_Otimes(U_276,U_277),U_278),hAPP(c_Groups_Otimes__class_Otimes(U_276,U_277),U_279))
| ~ class_Rings_Olinordered__ring__strict(U_276) ),
inference(clausify,[status(thm)],[f_102_2]) ).
fof(f_103_1,plain,
! [V_b_2,V_ca_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),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(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),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_103_2,plain,
! [U_283,U_282,U_281,U_280] :
( ( ( c_Orderings_Oord__class_Oless(U_280,hAPP(c_Groups_Otimes__class_Otimes(U_280,U_281),U_282),hAPP(c_Groups_Otimes__class_Otimes(U_280,U_283),U_282))
| ( ( ~ c_Orderings_Oord__class_Oless(U_280,U_283,U_281)
| ~ c_Orderings_Oord__class_Oless(U_280,U_282,c_Groups_Ozero__class_Ozero(U_280)) )
& ( ~ c_Orderings_Oord__class_Oless(U_280,U_281,U_283)
| ~ c_Orderings_Oord__class_Oless(U_280,c_Groups_Ozero__class_Ozero(U_280),U_282) ) ) )
& ( ( c_Orderings_Oord__class_Oless(U_280,U_283,U_281)
& c_Orderings_Oord__class_Oless(U_280,U_282,c_Groups_Ozero__class_Ozero(U_280)) )
| ( c_Orderings_Oord__class_Oless(U_280,U_281,U_283)
& c_Orderings_Oord__class_Oless(U_280,c_Groups_Ozero__class_Ozero(U_280),U_282) )
| ~ c_Orderings_Oord__class_Oless(U_280,hAPP(c_Groups_Otimes__class_Otimes(U_280,U_281),U_282),hAPP(c_Groups_Otimes__class_Otimes(U_280,U_283),U_282)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_280) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
cnf(f_103_3,plain,
( c_Orderings_Oord__class_Oless(U_280,U_282,c_Groups_Ozero__class_Ozero(U_280))
| c_Orderings_Oord__class_Oless(U_280,c_Groups_Ozero__class_Ozero(U_280),U_282)
| ~ c_Orderings_Oord__class_Oless(U_280,hAPP(c_Groups_Otimes__class_Otimes(U_280,U_281),U_282),hAPP(c_Groups_Otimes__class_Otimes(U_280,U_283),U_282))
| ~ class_Rings_Olinordered__ring__strict(U_280) ),
inference(clausify,[status(thm)],[f_103_2]) ).
cnf(f_103_4,plain,
( c_Orderings_Oord__class_Oless(U_280,U_283,U_281)
| c_Orderings_Oord__class_Oless(U_280,c_Groups_Ozero__class_Ozero(U_280),U_282)
| ~ c_Orderings_Oord__class_Oless(U_280,hAPP(c_Groups_Otimes__class_Otimes(U_280,U_281),U_282),hAPP(c_Groups_Otimes__class_Otimes(U_280,U_283),U_282))
| ~ class_Rings_Olinordered__ring__strict(U_280) ),
inference(clausify,[status(thm)],[f_103_2]) ).
cnf(f_103_5,plain,
( c_Orderings_Oord__class_Oless(U_280,U_282,c_Groups_Ozero__class_Ozero(U_280))
| c_Orderings_Oord__class_Oless(U_280,U_281,U_283)
| ~ c_Orderings_Oord__class_Oless(U_280,hAPP(c_Groups_Otimes__class_Otimes(U_280,U_281),U_282),hAPP(c_Groups_Otimes__class_Otimes(U_280,U_283),U_282))
| ~ class_Rings_Olinordered__ring__strict(U_280) ),
inference(clausify,[status(thm)],[f_103_2]) ).
cnf(f_103_6,plain,
( c_Orderings_Oord__class_Oless(U_280,U_283,U_281)
| c_Orderings_Oord__class_Oless(U_280,U_281,U_283)
| ~ c_Orderings_Oord__class_Oless(U_280,hAPP(c_Groups_Otimes__class_Otimes(U_280,U_281),U_282),hAPP(c_Groups_Otimes__class_Otimes(U_280,U_283),U_282))
| ~ class_Rings_Olinordered__ring__strict(U_280) ),
inference(clausify,[status(thm)],[f_103_2]) ).
cnf(f_103_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_280,U_281,U_283)
| ~ c_Orderings_Oord__class_Oless(U_280,c_Groups_Ozero__class_Ozero(U_280),U_282)
| c_Orderings_Oord__class_Oless(U_280,hAPP(c_Groups_Otimes__class_Otimes(U_280,U_281),U_282),hAPP(c_Groups_Otimes__class_Otimes(U_280,U_283),U_282))
| ~ class_Rings_Olinordered__ring__strict(U_280) ),
inference(clausify,[status(thm)],[f_103_2]) ).
cnf(f_103_8,plain,
( ~ c_Orderings_Oord__class_Oless(U_280,U_283,U_281)
| ~ c_Orderings_Oord__class_Oless(U_280,U_282,c_Groups_Ozero__class_Ozero(U_280))
| c_Orderings_Oord__class_Oless(U_280,hAPP(c_Groups_Otimes__class_Otimes(U_280,U_281),U_282),hAPP(c_Groups_Otimes__class_Otimes(U_280,U_283),U_282))
| ~ class_Rings_Olinordered__ring__strict(U_280) ),
inference(clausify,[status(thm)],[f_103_2]) ).
fof(f_104_1,plain,
! [V_a,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,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_104_2,plain,
! [U_285,U_284] :
( ~ c_Orderings_Oord__class_Oless(U_284,hAPP(c_Groups_Otimes__class_Otimes(U_284,U_285),U_285),c_Groups_Ozero__class_Ozero(U_284))
| ~ class_Rings_Olinordered__ring(U_284) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
cnf(f_104_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_284,hAPP(c_Groups_Otimes__class_Otimes(U_284,U_285),U_285),c_Groups_Ozero__class_Ozero(U_284))
| ~ class_Rings_Olinordered__ring(U_284) ),
inference(clausify,[status(thm)],[f_104_2]) ).
fof(f_105_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____),
inference(fof_nnf,[status(thm)],[fact_d1_I2_J]) ).
cnf(f_105_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____),
inference(clausify,[status(thm)],[f_105_1]) ).
fof(f_106_1,plain,
! [V_y,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_RealVector_Oreal__normed__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide_Ozero]) ).
fof(f_106_2,plain,
! [U_287,U_286] :
( c_Rings_Oinverse__class_Odivide(U_286,c_Groups_Ozero__class_Ozero(U_286),U_287) = c_Groups_Ozero__class_Ozero(U_286)
| ~ class_RealVector_Oreal__normed__field(U_286) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
cnf(f_106_3,plain,
( c_Rings_Oinverse__class_Odivide(U_286,c_Groups_Ozero__class_Ozero(U_286),U_287) = c_Groups_Ozero__class_Ozero(U_286)
| ~ class_RealVector_Oreal__normed__field(U_286) ),
inference(clausify,[status(thm)],[f_106_2]) ).
fof(f_107_1,plain,
! [V_a,T_a] :
( 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_107_2,plain,
! [U_289,U_288] :
( hAPP(c_Groups_Otimes__class_Otimes(U_288,U_289),c_Groups_Oone__class_Oone(U_288)) = U_289
| ~ class_Groups_Ocomm__monoid__mult(U_288) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
cnf(f_107_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_288,U_289),c_Groups_Oone__class_Oone(U_288)) = U_289
| ~ class_Groups_Ocomm__monoid__mult(U_288) ),
inference(clausify,[status(thm)],[f_107_2]) ).
fof(f_108_1,plain,
! [V_a,T_a] :
( 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_108_2,plain,
! [U_291,U_290] :
( hAPP(c_Groups_Otimes__class_Otimes(U_290,U_291),c_Groups_Oone__class_Oone(U_290)) = U_291
| ~ class_Groups_Omonoid__mult(U_290) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
cnf(f_108_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_290,U_291),c_Groups_Oone__class_Oone(U_290)) = U_291
| ~ class_Groups_Omonoid__mult(U_290) ),
inference(clausify,[status(thm)],[f_108_2]) ).
fof(f_109_1,plain,
! [V_a,T_a] :
( 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_109_2,plain,
! [U_293,U_292] :
( hAPP(c_Groups_Otimes__class_Otimes(U_292,c_Groups_Oone__class_Oone(U_292)),U_293) = U_293
| ~ class_Groups_Ocomm__monoid__mult(U_292) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
cnf(f_109_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_292,c_Groups_Oone__class_Oone(U_292)),U_293) = U_293
| ~ class_Groups_Ocomm__monoid__mult(U_292) ),
inference(clausify,[status(thm)],[f_109_2]) ).
fof(f_110_1,plain,
! [V_a,T_a] :
( 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_110_2,plain,
! [U_295,U_294] :
( hAPP(c_Groups_Otimes__class_Otimes(U_294,c_Groups_Oone__class_Oone(U_294)),U_295) = U_295
| ~ class_Groups_Omonoid__mult(U_294) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
cnf(f_110_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_294,c_Groups_Oone__class_Oone(U_294)),U_295) = U_295
| ~ class_Groups_Omonoid__mult(U_294) ),
inference(clausify,[status(thm)],[f_110_2]) ).
fof(f_111_1,plain,
! [V_x,T_a] :
( 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_111_2,plain,
! [U_297,U_296] :
( hAPP(c_Groups_Otimes__class_Otimes(U_296,U_297),c_Groups_Ozero__class_Ozero(U_296)) = c_Groups_Ozero__class_Ozero(U_296)
| ~ class_RealVector_Oreal__normed__algebra(U_296) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
cnf(f_111_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_296,U_297),c_Groups_Ozero__class_Ozero(U_296)) = c_Groups_Ozero__class_Ozero(U_296)
| ~ class_RealVector_Oreal__normed__algebra(U_296) ),
inference(clausify,[status(thm)],[f_111_2]) ).
fof(f_112_1,plain,
! [V_a,T_a] :
( 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_112_2,plain,
! [U_299,U_298] :
( hAPP(c_Groups_Otimes__class_Otimes(U_298,U_299),c_Groups_Ozero__class_Ozero(U_298)) = c_Groups_Ozero__class_Ozero(U_298)
| ~ class_RealVector_Oreal__normed__algebra(U_298) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
cnf(f_112_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_298,U_299),c_Groups_Ozero__class_Ozero(U_298)) = c_Groups_Ozero__class_Ozero(U_298)
| ~ class_RealVector_Oreal__normed__algebra(U_298) ),
inference(clausify,[status(thm)],[f_112_2]) ).
fof(f_113_1,plain,
! [V_y,T_a] :
( 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_113_2,plain,
! [U_301,U_300] :
( hAPP(c_Groups_Otimes__class_Otimes(U_300,c_Groups_Ozero__class_Ozero(U_300)),U_301) = c_Groups_Ozero__class_Ozero(U_300)
| ~ class_RealVector_Oreal__normed__algebra(U_300) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
cnf(f_113_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_300,c_Groups_Ozero__class_Ozero(U_300)),U_301) = c_Groups_Ozero__class_Ozero(U_300)
| ~ class_RealVector_Oreal__normed__algebra(U_300) ),
inference(clausify,[status(thm)],[f_113_2]) ).
fof(f_114_1,plain,
! [V_b,T_a] :
( 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_114_2,plain,
! [U_303,U_302] :
( hAPP(c_Groups_Otimes__class_Otimes(U_302,c_Groups_Ozero__class_Ozero(U_302)),U_303) = c_Groups_Ozero__class_Ozero(U_302)
| ~ class_RealVector_Oreal__normed__algebra(U_302) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
cnf(f_114_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_302,c_Groups_Ozero__class_Ozero(U_302)),U_303) = c_Groups_Ozero__class_Ozero(U_302)
| ~ class_RealVector_Oreal__normed__algebra(U_302) ),
inference(clausify,[status(thm)],[f_114_2]) ).
fof(f_115_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_115_2,plain,
! [U_304] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_304,U_304),
inference(variable_rename,[status(thm)],[f_115_1]) ).
cnf(f_115_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_304,U_304),
inference(clausify,[status(thm)],[f_115_2]) ).
fof(f_116_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_116_2,plain,
! [U_306,U_305] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_306,U_305)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_305,U_306) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
cnf(f_116_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_306,U_305)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_305,U_306) ),
inference(clausify,[status(thm)],[f_116_2]) ).
fof(f_117_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_117_2,plain,
! [U_309,U_308,U_307] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_307,U_309)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_308,U_309)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_307,U_308) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
cnf(f_117_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_307,U_309)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_308,U_309)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_307,U_308) ),
inference(clausify,[status(thm)],[f_117_2]) ).
fof(f_118_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_118_2,plain,
! [U_311,U_310] :
( U_310 = U_311
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_311,U_310)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_310,U_311) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
cnf(f_118_3,plain,
( U_310 = U_311
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_311,U_310)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_310,U_311) ),
inference(clausify,[status(thm)],[f_118_2]) ).
fof(f_119_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_119_2,plain,
! [U_313,U_312] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_312,U_313)
| U_312 = U_313
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_312,U_313) )
& ( ( U_312 != U_313
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_312,U_313) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_312,U_313) ) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
fof(f_119_3,plain,
( ! [U_317,U_315] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_315,U_317)
| U_315 = U_317
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_315,U_317) )
& ! [U_316,U_314] :
( ( U_314 != U_316
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_314,U_316) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_314,U_316) ) ),
inference(miniscope,[status(thm)],[f_119_2]) ).
cnf(f_119_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_314,U_316)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_314,U_316) ),
inference(clausify,[status(thm)],[f_119_3]) ).
cnf(f_119_5,plain,
( U_314 != U_316
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_314,U_316) ),
inference(clausify,[status(thm)],[f_119_3]) ).
cnf(f_119_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_315,U_317)
| U_315 = U_317
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_315,U_317) ),
inference(clausify,[status(thm)],[f_119_3]) ).
fof(f_120_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_120_2,plain,
! [U_319,U_318] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_318,U_319)
| ( U_318 != U_319
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_318,U_319) ) )
& ( U_318 = U_319
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_318,U_319)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_318,U_319) ) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
( ! [U_323,U_321] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_321,U_323)
| ( U_321 != U_323
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_321,U_323) ) )
& ! [U_322,U_320] :
( U_320 = U_322
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_320,U_322)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_320,U_322) ) ),
inference(miniscope,[status(thm)],[f_120_2]) ).
cnf(f_120_4,plain,
( U_320 = U_322
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_320,U_322)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_320,U_322) ),
inference(clausify,[status(thm)],[f_120_3]) ).
cnf(f_120_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_321,U_323)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_321,U_323) ),
inference(clausify,[status(thm)],[f_120_3]) ).
cnf(f_120_6,plain,
( U_321 != U_323
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_321,U_323) ),
inference(clausify,[status(thm)],[f_120_3]) ).
fof(f_121_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,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_121_2,plain,
! [U_326,U_325,U_324] :
( c_Orderings_Oord__class_Oless__eq(U_324,hAPP(c_Groups_Otimes__class_Otimes(U_324,U_325),U_326),c_Groups_Ozero__class_Ozero(U_324))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_324,c_Groups_Ozero__class_Ozero(U_324),U_326)
| ~ c_Orderings_Oord__class_Oless__eq(U_324,U_325,c_Groups_Ozero__class_Ozero(U_324)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_324,U_326,c_Groups_Ozero__class_Ozero(U_324))
| ~ c_Orderings_Oord__class_Oless__eq(U_324,c_Groups_Ozero__class_Ozero(U_324),U_325) ) )
| ~ class_Rings_Oordered__cancel__semiring(U_324) ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
cnf(f_121_3,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_324,U_326,c_Groups_Ozero__class_Ozero(U_324))
| ~ c_Orderings_Oord__class_Oless__eq(U_324,c_Groups_Ozero__class_Ozero(U_324),U_325)
| c_Orderings_Oord__class_Oless__eq(U_324,hAPP(c_Groups_Otimes__class_Otimes(U_324,U_325),U_326),c_Groups_Ozero__class_Ozero(U_324))
| ~ class_Rings_Oordered__cancel__semiring(U_324) ),
inference(clausify,[status(thm)],[f_121_2]) ).
cnf(f_121_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_324,c_Groups_Ozero__class_Ozero(U_324),U_326)
| ~ c_Orderings_Oord__class_Oless__eq(U_324,U_325,c_Groups_Ozero__class_Ozero(U_324))
| c_Orderings_Oord__class_Oless__eq(U_324,hAPP(c_Groups_Otimes__class_Otimes(U_324,U_325),U_326),c_Groups_Ozero__class_Ozero(U_324))
| ~ class_Rings_Oordered__cancel__semiring(U_324) ),
inference(clausify,[status(thm)],[f_121_2]) ).
fof(f_122_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),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_122_2,plain,
! [U_329,U_328,U_327] :
( c_Orderings_Oord__class_Oless__eq(U_327,c_Groups_Ozero__class_Ozero(U_327),hAPP(c_Groups_Otimes__class_Otimes(U_327,U_328),U_329))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_327,U_329,c_Groups_Ozero__class_Ozero(U_327))
| ~ c_Orderings_Oord__class_Oless__eq(U_327,U_328,c_Groups_Ozero__class_Ozero(U_327)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_327,c_Groups_Ozero__class_Ozero(U_327),U_329)
| ~ c_Orderings_Oord__class_Oless__eq(U_327,c_Groups_Ozero__class_Ozero(U_327),U_328) ) )
| ~ class_Rings_Oordered__ring(U_327) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
cnf(f_122_3,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_327,c_Groups_Ozero__class_Ozero(U_327),U_329)
| ~ c_Orderings_Oord__class_Oless__eq(U_327,c_Groups_Ozero__class_Ozero(U_327),U_328)
| c_Orderings_Oord__class_Oless__eq(U_327,c_Groups_Ozero__class_Ozero(U_327),hAPP(c_Groups_Otimes__class_Otimes(U_327,U_328),U_329))
| ~ class_Rings_Oordered__ring(U_327) ),
inference(clausify,[status(thm)],[f_122_2]) ).
cnf(f_122_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_327,U_329,c_Groups_Ozero__class_Ozero(U_327))
| ~ c_Orderings_Oord__class_Oless__eq(U_327,U_328,c_Groups_Ozero__class_Ozero(U_327))
| c_Orderings_Oord__class_Oless__eq(U_327,c_Groups_Ozero__class_Ozero(U_327),hAPP(c_Groups_Otimes__class_Otimes(U_327,U_328),U_329))
| ~ class_Rings_Oordered__ring(U_327) ),
inference(clausify,[status(thm)],[f_122_2]) ).
fof(f_123_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),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_123_2,plain,
! [U_334,U_333,U_332,U_331,U_330] :
( c_Orderings_Oord__class_Oless__eq(U_330,hAPP(c_Groups_Otimes__class_Otimes(U_330,U_331),U_333),hAPP(c_Groups_Otimes__class_Otimes(U_330,U_332),U_334))
| ~ c_Orderings_Oord__class_Oless__eq(U_330,c_Groups_Ozero__class_Ozero(U_330),U_333)
| ~ c_Orderings_Oord__class_Oless__eq(U_330,c_Groups_Ozero__class_Ozero(U_330),U_332)
| ~ c_Orderings_Oord__class_Oless__eq(U_330,U_333,U_334)
| ~ c_Orderings_Oord__class_Oless__eq(U_330,U_331,U_332)
| ~ class_Rings_Oordered__semiring(U_330) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
cnf(f_123_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_330,hAPP(c_Groups_Otimes__class_Otimes(U_330,U_331),U_333),hAPP(c_Groups_Otimes__class_Otimes(U_330,U_332),U_334))
| ~ c_Orderings_Oord__class_Oless__eq(U_330,c_Groups_Ozero__class_Ozero(U_330),U_333)
| ~ c_Orderings_Oord__class_Oless__eq(U_330,c_Groups_Ozero__class_Ozero(U_330),U_332)
| ~ c_Orderings_Oord__class_Oless__eq(U_330,U_333,U_334)
| ~ c_Orderings_Oord__class_Oless__eq(U_330,U_331,U_332)
| ~ class_Rings_Oordered__semiring(U_330) ),
inference(clausify,[status(thm)],[f_123_2]) ).
fof(f_124_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),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_124_2,plain,
! [U_339,U_338,U_337,U_336,U_335] :
( c_Orderings_Oord__class_Oless__eq(U_335,hAPP(c_Groups_Otimes__class_Otimes(U_335,U_336),U_338),hAPP(c_Groups_Otimes__class_Otimes(U_335,U_337),U_339))
| ~ c_Orderings_Oord__class_Oless__eq(U_335,c_Groups_Ozero__class_Ozero(U_335),U_338)
| ~ c_Orderings_Oord__class_Oless__eq(U_335,c_Groups_Ozero__class_Ozero(U_335),U_336)
| ~ c_Orderings_Oord__class_Oless__eq(U_335,U_338,U_339)
| ~ c_Orderings_Oord__class_Oless__eq(U_335,U_336,U_337)
| ~ class_Rings_Oordered__semiring(U_335) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
cnf(f_124_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_335,hAPP(c_Groups_Otimes__class_Otimes(U_335,U_336),U_338),hAPP(c_Groups_Otimes__class_Otimes(U_335,U_337),U_339))
| ~ c_Orderings_Oord__class_Oless__eq(U_335,c_Groups_Ozero__class_Ozero(U_335),U_338)
| ~ c_Orderings_Oord__class_Oless__eq(U_335,c_Groups_Ozero__class_Ozero(U_335),U_336)
| ~ c_Orderings_Oord__class_Oless__eq(U_335,U_338,U_339)
| ~ c_Orderings_Oord__class_Oless__eq(U_335,U_336,U_337)
| ~ class_Rings_Oordered__semiring(U_335) ),
inference(clausify,[status(thm)],[f_124_2]) ).
fof(f_125_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),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_125_2,plain,
! [U_343,U_342,U_341,U_340] :
( c_Orderings_Oord__class_Oless__eq(U_340,hAPP(c_Groups_Otimes__class_Otimes(U_340,U_343),U_342),hAPP(c_Groups_Otimes__class_Otimes(U_340,U_343),U_341))
| ~ c_Orderings_Oord__class_Oless__eq(U_340,U_343,c_Groups_Ozero__class_Ozero(U_340))
| ~ c_Orderings_Oord__class_Oless__eq(U_340,U_341,U_342)
| ~ class_Rings_Oordered__ring(U_340) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
cnf(f_125_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_340,hAPP(c_Groups_Otimes__class_Otimes(U_340,U_343),U_342),hAPP(c_Groups_Otimes__class_Otimes(U_340,U_343),U_341))
| ~ c_Orderings_Oord__class_Oless__eq(U_340,U_343,c_Groups_Ozero__class_Ozero(U_340))
| ~ c_Orderings_Oord__class_Oless__eq(U_340,U_341,U_342)
| ~ class_Rings_Oordered__ring(U_340) ),
inference(clausify,[status(thm)],[f_125_2]) ).
fof(f_126_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),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_126_2,plain,
! [U_347,U_346,U_345,U_344] :
( c_Orderings_Oord__class_Oless__eq(U_344,hAPP(c_Groups_Otimes__class_Otimes(U_344,U_346),U_347),hAPP(c_Groups_Otimes__class_Otimes(U_344,U_345),U_347))
| ~ c_Orderings_Oord__class_Oless__eq(U_344,U_347,c_Groups_Ozero__class_Ozero(U_344))
| ~ c_Orderings_Oord__class_Oless__eq(U_344,U_345,U_346)
| ~ class_Rings_Oordered__ring(U_344) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
cnf(f_126_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_344,hAPP(c_Groups_Otimes__class_Otimes(U_344,U_346),U_347),hAPP(c_Groups_Otimes__class_Otimes(U_344,U_345),U_347))
| ~ c_Orderings_Oord__class_Oless__eq(U_344,U_347,c_Groups_Ozero__class_Ozero(U_344))
| ~ c_Orderings_Oord__class_Oless__eq(U_344,U_345,U_346)
| ~ class_Rings_Oordered__ring(U_344) ),
inference(clausify,[status(thm)],[f_126_2]) ).
fof(f_127_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),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_127_2,plain,
! [U_351,U_350,U_349,U_348] :
( c_Orderings_Oord__class_Oless__eq(U_348,hAPP(c_Groups_Otimes__class_Otimes(U_348,U_351),U_349),hAPP(c_Groups_Otimes__class_Otimes(U_348,U_351),U_350))
| ~ c_Orderings_Oord__class_Oless__eq(U_348,c_Groups_Ozero__class_Ozero(U_348),U_351)
| ~ c_Orderings_Oord__class_Oless__eq(U_348,U_349,U_350)
| ~ class_Rings_Oordered__comm__semiring(U_348) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
cnf(f_127_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_348,hAPP(c_Groups_Otimes__class_Otimes(U_348,U_351),U_349),hAPP(c_Groups_Otimes__class_Otimes(U_348,U_351),U_350))
| ~ c_Orderings_Oord__class_Oless__eq(U_348,c_Groups_Ozero__class_Ozero(U_348),U_351)
| ~ c_Orderings_Oord__class_Oless__eq(U_348,U_349,U_350)
| ~ class_Rings_Oordered__comm__semiring(U_348) ),
inference(clausify,[status(thm)],[f_127_2]) ).
fof(f_128_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),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_128_2,plain,
! [U_355,U_354,U_353,U_352] :
( c_Orderings_Oord__class_Oless__eq(U_352,hAPP(c_Groups_Otimes__class_Otimes(U_352,U_355),U_353),hAPP(c_Groups_Otimes__class_Otimes(U_352,U_355),U_354))
| ~ c_Orderings_Oord__class_Oless__eq(U_352,c_Groups_Ozero__class_Ozero(U_352),U_355)
| ~ c_Orderings_Oord__class_Oless__eq(U_352,U_353,U_354)
| ~ class_Rings_Oordered__semiring(U_352) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
cnf(f_128_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_352,hAPP(c_Groups_Otimes__class_Otimes(U_352,U_355),U_353),hAPP(c_Groups_Otimes__class_Otimes(U_352,U_355),U_354))
| ~ c_Orderings_Oord__class_Oless__eq(U_352,c_Groups_Ozero__class_Ozero(U_352),U_355)
| ~ c_Orderings_Oord__class_Oless__eq(U_352,U_353,U_354)
| ~ class_Rings_Oordered__semiring(U_352) ),
inference(clausify,[status(thm)],[f_128_2]) ).
fof(f_129_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),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_129_2,plain,
! [U_359,U_358,U_357,U_356] :
( c_Orderings_Oord__class_Oless__eq(U_356,hAPP(c_Groups_Otimes__class_Otimes(U_356,U_357),U_359),hAPP(c_Groups_Otimes__class_Otimes(U_356,U_358),U_359))
| ~ c_Orderings_Oord__class_Oless__eq(U_356,c_Groups_Ozero__class_Ozero(U_356),U_359)
| ~ c_Orderings_Oord__class_Oless__eq(U_356,U_357,U_358)
| ~ class_Rings_Oordered__semiring(U_356) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
cnf(f_129_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_356,hAPP(c_Groups_Otimes__class_Otimes(U_356,U_357),U_359),hAPP(c_Groups_Otimes__class_Otimes(U_356,U_358),U_359))
| ~ c_Orderings_Oord__class_Oless__eq(U_356,c_Groups_Ozero__class_Ozero(U_356),U_359)
| ~ c_Orderings_Oord__class_Oless__eq(U_356,U_357,U_358)
| ~ class_Rings_Oordered__semiring(U_356) ),
inference(clausify,[status(thm)],[f_129_2]) ).
fof(f_130_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),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_130_2,plain,
! [U_362,U_361,U_360] :
( c_Orderings_Oord__class_Oless__eq(U_360,c_Groups_Ozero__class_Ozero(U_360),hAPP(c_Groups_Otimes__class_Otimes(U_360,U_361),U_362))
| ~ c_Orderings_Oord__class_Oless__eq(U_360,U_362,c_Groups_Ozero__class_Ozero(U_360))
| ~ c_Orderings_Oord__class_Oless__eq(U_360,U_361,c_Groups_Ozero__class_Ozero(U_360))
| ~ class_Rings_Oordered__ring(U_360) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
cnf(f_130_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_360,c_Groups_Ozero__class_Ozero(U_360),hAPP(c_Groups_Otimes__class_Otimes(U_360,U_361),U_362))
| ~ c_Orderings_Oord__class_Oless__eq(U_360,U_362,c_Groups_Ozero__class_Ozero(U_360))
| ~ c_Orderings_Oord__class_Oless__eq(U_360,U_361,c_Groups_Ozero__class_Ozero(U_360))
| ~ class_Rings_Oordered__ring(U_360) ),
inference(clausify,[status(thm)],[f_130_2]) ).
fof(f_131_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,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_131_2,plain,
! [U_365,U_364,U_363] :
( c_Orderings_Oord__class_Oless__eq(U_363,hAPP(c_Groups_Otimes__class_Otimes(U_363,U_364),U_365),c_Groups_Ozero__class_Ozero(U_363))
| ~ c_Orderings_Oord__class_Oless__eq(U_363,c_Groups_Ozero__class_Ozero(U_363),U_365)
| ~ c_Orderings_Oord__class_Oless__eq(U_363,U_364,c_Groups_Ozero__class_Ozero(U_363))
| ~ class_Rings_Oordered__cancel__semiring(U_363) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
cnf(f_131_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_363,hAPP(c_Groups_Otimes__class_Otimes(U_363,U_364),U_365),c_Groups_Ozero__class_Ozero(U_363))
| ~ c_Orderings_Oord__class_Oless__eq(U_363,c_Groups_Ozero__class_Ozero(U_363),U_365)
| ~ c_Orderings_Oord__class_Oless__eq(U_363,U_364,c_Groups_Ozero__class_Ozero(U_363))
| ~ class_Rings_Oordered__cancel__semiring(U_363) ),
inference(clausify,[status(thm)],[f_131_2]) ).
fof(f_132_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,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_132_2,plain,
! [U_368,U_367,U_366] :
( c_Orderings_Oord__class_Oless__eq(U_366,hAPP(c_Groups_Otimes__class_Otimes(U_366,U_368),U_367),c_Groups_Ozero__class_Ozero(U_366))
| ~ c_Orderings_Oord__class_Oless__eq(U_366,U_368,c_Groups_Ozero__class_Ozero(U_366))
| ~ c_Orderings_Oord__class_Oless__eq(U_366,c_Groups_Ozero__class_Ozero(U_366),U_367)
| ~ class_Rings_Oordered__cancel__semiring(U_366) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
cnf(f_132_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_366,hAPP(c_Groups_Otimes__class_Otimes(U_366,U_368),U_367),c_Groups_Ozero__class_Ozero(U_366))
| ~ c_Orderings_Oord__class_Oless__eq(U_366,U_368,c_Groups_Ozero__class_Ozero(U_366))
| ~ c_Orderings_Oord__class_Oless__eq(U_366,c_Groups_Ozero__class_Ozero(U_366),U_367)
| ~ class_Rings_Oordered__cancel__semiring(U_366) ),
inference(clausify,[status(thm)],[f_132_2]) ).
fof(f_133_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,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_133_2,plain,
! [U_371,U_370,U_369] :
( c_Orderings_Oord__class_Oless__eq(U_369,hAPP(c_Groups_Otimes__class_Otimes(U_369,U_370),U_371),c_Groups_Ozero__class_Ozero(U_369))
| ~ c_Orderings_Oord__class_Oless__eq(U_369,U_371,c_Groups_Ozero__class_Ozero(U_369))
| ~ c_Orderings_Oord__class_Oless__eq(U_369,c_Groups_Ozero__class_Ozero(U_369),U_370)
| ~ class_Rings_Oordered__cancel__semiring(U_369) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
cnf(f_133_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_369,hAPP(c_Groups_Otimes__class_Otimes(U_369,U_370),U_371),c_Groups_Ozero__class_Ozero(U_369))
| ~ c_Orderings_Oord__class_Oless__eq(U_369,U_371,c_Groups_Ozero__class_Ozero(U_369))
| ~ c_Orderings_Oord__class_Oless__eq(U_369,c_Groups_Ozero__class_Ozero(U_369),U_370)
| ~ class_Rings_Oordered__cancel__semiring(U_369) ),
inference(clausify,[status(thm)],[f_133_2]) ).
fof(f_134_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),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_134_2,plain,
! [U_374,U_373,U_372] :
( c_Orderings_Oord__class_Oless__eq(U_372,c_Groups_Ozero__class_Ozero(U_372),hAPP(c_Groups_Otimes__class_Otimes(U_372,U_373),U_374))
| ~ c_Orderings_Oord__class_Oless__eq(U_372,c_Groups_Ozero__class_Ozero(U_372),U_374)
| ~ c_Orderings_Oord__class_Oless__eq(U_372,c_Groups_Ozero__class_Ozero(U_372),U_373)
| ~ class_Rings_Oordered__cancel__semiring(U_372) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
cnf(f_134_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_372,c_Groups_Ozero__class_Ozero(U_372),hAPP(c_Groups_Otimes__class_Otimes(U_372,U_373),U_374))
| ~ c_Orderings_Oord__class_Oless__eq(U_372,c_Groups_Ozero__class_Ozero(U_372),U_374)
| ~ c_Orderings_Oord__class_Oless__eq(U_372,c_Groups_Ozero__class_Ozero(U_372),U_373)
| ~ class_Rings_Oordered__cancel__semiring(U_372) ),
inference(clausify,[status(thm)],[f_134_2]) ).
fof(f_135_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,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(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_135_2,plain,
! [U_377,U_376,U_375] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_375,hAPP(c_Groups_Otimes__class_Otimes(U_375,U_376),U_377),c_Groups_Ozero__class_Ozero(U_375))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_375,c_Groups_Ozero__class_Ozero(U_375),U_377)
| ~ c_Orderings_Oord__class_Oless__eq(U_375,U_376,c_Groups_Ozero__class_Ozero(U_375)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_375,U_377,c_Groups_Ozero__class_Ozero(U_375))
| ~ c_Orderings_Oord__class_Oless__eq(U_375,c_Groups_Ozero__class_Ozero(U_375),U_376) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_375,c_Groups_Ozero__class_Ozero(U_375),U_377)
& c_Orderings_Oord__class_Oless__eq(U_375,U_376,c_Groups_Ozero__class_Ozero(U_375)) )
| ( c_Orderings_Oord__class_Oless__eq(U_375,U_377,c_Groups_Ozero__class_Ozero(U_375))
& c_Orderings_Oord__class_Oless__eq(U_375,c_Groups_Ozero__class_Ozero(U_375),U_376) )
| ~ c_Orderings_Oord__class_Oless__eq(U_375,hAPP(c_Groups_Otimes__class_Otimes(U_375,U_376),U_377),c_Groups_Ozero__class_Ozero(U_375)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_375) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
cnf(f_135_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_375,U_376,c_Groups_Ozero__class_Ozero(U_375))
| c_Orderings_Oord__class_Oless__eq(U_375,c_Groups_Ozero__class_Ozero(U_375),U_376)
| ~ c_Orderings_Oord__class_Oless__eq(U_375,hAPP(c_Groups_Otimes__class_Otimes(U_375,U_376),U_377),c_Groups_Ozero__class_Ozero(U_375))
| ~ class_Rings_Olinordered__ring__strict(U_375) ),
inference(clausify,[status(thm)],[f_135_2]) ).
cnf(f_135_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_375,c_Groups_Ozero__class_Ozero(U_375),U_377)
| c_Orderings_Oord__class_Oless__eq(U_375,c_Groups_Ozero__class_Ozero(U_375),U_376)
| ~ c_Orderings_Oord__class_Oless__eq(U_375,hAPP(c_Groups_Otimes__class_Otimes(U_375,U_376),U_377),c_Groups_Ozero__class_Ozero(U_375))
| ~ class_Rings_Olinordered__ring__strict(U_375) ),
inference(clausify,[status(thm)],[f_135_2]) ).
cnf(f_135_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_375,U_376,c_Groups_Ozero__class_Ozero(U_375))
| c_Orderings_Oord__class_Oless__eq(U_375,U_377,c_Groups_Ozero__class_Ozero(U_375))
| ~ c_Orderings_Oord__class_Oless__eq(U_375,hAPP(c_Groups_Otimes__class_Otimes(U_375,U_376),U_377),c_Groups_Ozero__class_Ozero(U_375))
| ~ class_Rings_Olinordered__ring__strict(U_375) ),
inference(clausify,[status(thm)],[f_135_2]) ).
cnf(f_135_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_375,c_Groups_Ozero__class_Ozero(U_375),U_377)
| c_Orderings_Oord__class_Oless__eq(U_375,U_377,c_Groups_Ozero__class_Ozero(U_375))
| ~ c_Orderings_Oord__class_Oless__eq(U_375,hAPP(c_Groups_Otimes__class_Otimes(U_375,U_376),U_377),c_Groups_Ozero__class_Ozero(U_375))
| ~ class_Rings_Olinordered__ring__strict(U_375) ),
inference(clausify,[status(thm)],[f_135_2]) ).
cnf(f_135_7,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_375,U_377,c_Groups_Ozero__class_Ozero(U_375))
| ~ c_Orderings_Oord__class_Oless__eq(U_375,c_Groups_Ozero__class_Ozero(U_375),U_376)
| c_Orderings_Oord__class_Oless__eq(U_375,hAPP(c_Groups_Otimes__class_Otimes(U_375,U_376),U_377),c_Groups_Ozero__class_Ozero(U_375))
| ~ class_Rings_Olinordered__ring__strict(U_375) ),
inference(clausify,[status(thm)],[f_135_2]) ).
cnf(f_135_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_375,c_Groups_Ozero__class_Ozero(U_375),U_377)
| ~ c_Orderings_Oord__class_Oless__eq(U_375,U_376,c_Groups_Ozero__class_Ozero(U_375))
| c_Orderings_Oord__class_Oless__eq(U_375,hAPP(c_Groups_Otimes__class_Otimes(U_375,U_376),U_377),c_Groups_Ozero__class_Ozero(U_375))
| ~ class_Rings_Olinordered__ring__strict(U_375) ),
inference(clausify,[status(thm)],[f_135_2]) ).
fof(f_136_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(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(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_136_2,plain,
! [U_380,U_379,U_378] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_378,c_Groups_Ozero__class_Ozero(U_378),hAPP(c_Groups_Otimes__class_Otimes(U_378,U_379),U_380))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_378,U_380,c_Groups_Ozero__class_Ozero(U_378))
| ~ c_Orderings_Oord__class_Oless__eq(U_378,U_379,c_Groups_Ozero__class_Ozero(U_378)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_378,c_Groups_Ozero__class_Ozero(U_378),U_380)
| ~ c_Orderings_Oord__class_Oless__eq(U_378,c_Groups_Ozero__class_Ozero(U_378),U_379) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_378,U_380,c_Groups_Ozero__class_Ozero(U_378))
& c_Orderings_Oord__class_Oless__eq(U_378,U_379,c_Groups_Ozero__class_Ozero(U_378)) )
| ( c_Orderings_Oord__class_Oless__eq(U_378,c_Groups_Ozero__class_Ozero(U_378),U_380)
& c_Orderings_Oord__class_Oless__eq(U_378,c_Groups_Ozero__class_Ozero(U_378),U_379) )
| ~ c_Orderings_Oord__class_Oless__eq(U_378,c_Groups_Ozero__class_Ozero(U_378),hAPP(c_Groups_Otimes__class_Otimes(U_378,U_379),U_380)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_378) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
cnf(f_136_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_378,U_379,c_Groups_Ozero__class_Ozero(U_378))
| c_Orderings_Oord__class_Oless__eq(U_378,c_Groups_Ozero__class_Ozero(U_378),U_379)
| ~ c_Orderings_Oord__class_Oless__eq(U_378,c_Groups_Ozero__class_Ozero(U_378),hAPP(c_Groups_Otimes__class_Otimes(U_378,U_379),U_380))
| ~ class_Rings_Olinordered__ring__strict(U_378) ),
inference(clausify,[status(thm)],[f_136_2]) ).
cnf(f_136_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_378,U_380,c_Groups_Ozero__class_Ozero(U_378))
| c_Orderings_Oord__class_Oless__eq(U_378,c_Groups_Ozero__class_Ozero(U_378),U_379)
| ~ c_Orderings_Oord__class_Oless__eq(U_378,c_Groups_Ozero__class_Ozero(U_378),hAPP(c_Groups_Otimes__class_Otimes(U_378,U_379),U_380))
| ~ class_Rings_Olinordered__ring__strict(U_378) ),
inference(clausify,[status(thm)],[f_136_2]) ).
cnf(f_136_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_378,U_379,c_Groups_Ozero__class_Ozero(U_378))
| c_Orderings_Oord__class_Oless__eq(U_378,c_Groups_Ozero__class_Ozero(U_378),U_380)
| ~ c_Orderings_Oord__class_Oless__eq(U_378,c_Groups_Ozero__class_Ozero(U_378),hAPP(c_Groups_Otimes__class_Otimes(U_378,U_379),U_380))
| ~ class_Rings_Olinordered__ring__strict(U_378) ),
inference(clausify,[status(thm)],[f_136_2]) ).
cnf(f_136_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_378,U_380,c_Groups_Ozero__class_Ozero(U_378))
| c_Orderings_Oord__class_Oless__eq(U_378,c_Groups_Ozero__class_Ozero(U_378),U_380)
| ~ c_Orderings_Oord__class_Oless__eq(U_378,c_Groups_Ozero__class_Ozero(U_378),hAPP(c_Groups_Otimes__class_Otimes(U_378,U_379),U_380))
| ~ class_Rings_Olinordered__ring__strict(U_378) ),
inference(clausify,[status(thm)],[f_136_2]) ).
cnf(f_136_7,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_378,c_Groups_Ozero__class_Ozero(U_378),U_380)
| ~ c_Orderings_Oord__class_Oless__eq(U_378,c_Groups_Ozero__class_Ozero(U_378),U_379)
| c_Orderings_Oord__class_Oless__eq(U_378,c_Groups_Ozero__class_Ozero(U_378),hAPP(c_Groups_Otimes__class_Otimes(U_378,U_379),U_380))
| ~ class_Rings_Olinordered__ring__strict(U_378) ),
inference(clausify,[status(thm)],[f_136_2]) ).
cnf(f_136_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_378,U_380,c_Groups_Ozero__class_Ozero(U_378))
| ~ c_Orderings_Oord__class_Oless__eq(U_378,U_379,c_Groups_Ozero__class_Ozero(U_378))
| c_Orderings_Oord__class_Oless__eq(U_378,c_Groups_Ozero__class_Ozero(U_378),hAPP(c_Groups_Otimes__class_Otimes(U_378,U_379),U_380))
| ~ class_Rings_Olinordered__ring__strict(U_378) ),
inference(clausify,[status(thm)],[f_136_2]) ).
fof(f_137_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),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_137_2,plain,
! [U_382,U_381] :
( c_Orderings_Oord__class_Oless__eq(U_381,c_Groups_Ozero__class_Ozero(U_381),hAPP(c_Groups_Otimes__class_Otimes(U_381,U_382),U_382))
| ~ class_Rings_Olinordered__ring(U_381) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
cnf(f_137_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_381,c_Groups_Ozero__class_Ozero(U_381),hAPP(c_Groups_Otimes__class_Otimes(U_381,U_382),U_382))
| ~ class_Rings_Olinordered__ring(U_381) ),
inference(clausify,[status(thm)],[f_137_2]) ).
fof(f_138_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_138_2,plain,
! [U_383] :
( c_Orderings_Oord__class_Oless__eq(U_383,c_Groups_Ozero__class_Ozero(U_383),c_Groups_Oone__class_Oone(U_383))
| ~ class_Rings_Olinordered__semidom(U_383) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
cnf(f_138_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_383,c_Groups_Ozero__class_Ozero(U_383),c_Groups_Oone__class_Oone(U_383))
| ~ class_Rings_Olinordered__semidom(U_383) ),
inference(clausify,[status(thm)],[f_138_2]) ).
fof(f_139_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_139_2,plain,
! [U_384] :
( ~ c_Orderings_Oord__class_Oless__eq(U_384,c_Groups_Oone__class_Oone(U_384),c_Groups_Ozero__class_Ozero(U_384))
| ~ class_Rings_Olinordered__semidom(U_384) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
cnf(f_139_3,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_384,c_Groups_Oone__class_Oone(U_384),c_Groups_Ozero__class_Ozero(U_384))
| ~ class_Rings_Olinordered__semidom(U_384) ),
inference(clausify,[status(thm)],[f_139_2]) ).
fof(f_140_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__right__mono__neg]) ).
fof(f_140_2,plain,
! [U_388,U_387,U_386,U_385] :
( c_Orderings_Oord__class_Oless__eq(U_385,c_Rings_Oinverse__class_Odivide(U_385,U_387,U_388),c_Rings_Oinverse__class_Odivide(U_385,U_386,U_388))
| ~ c_Orderings_Oord__class_Oless__eq(U_385,U_388,c_Groups_Ozero__class_Ozero(U_385))
| ~ c_Orderings_Oord__class_Oless__eq(U_385,U_386,U_387)
| ~ class_Fields_Olinordered__field__inverse__zero(U_385) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
cnf(f_140_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_385,c_Rings_Oinverse__class_Odivide(U_385,U_387,U_388),c_Rings_Oinverse__class_Odivide(U_385,U_386,U_388))
| ~ c_Orderings_Oord__class_Oless__eq(U_385,U_388,c_Groups_Ozero__class_Ozero(U_385))
| ~ c_Orderings_Oord__class_Oless__eq(U_385,U_386,U_387)
| ~ class_Fields_Olinordered__field__inverse__zero(U_385) ),
inference(clausify,[status(thm)],[f_140_2]) ).
fof(f_141_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__right__mono]) ).
fof(f_141_2,plain,
! [U_392,U_391,U_390,U_389] :
( c_Orderings_Oord__class_Oless__eq(U_389,c_Rings_Oinverse__class_Odivide(U_389,U_390,U_392),c_Rings_Oinverse__class_Odivide(U_389,U_391,U_392))
| ~ c_Orderings_Oord__class_Oless__eq(U_389,c_Groups_Ozero__class_Ozero(U_389),U_392)
| ~ c_Orderings_Oord__class_Oless__eq(U_389,U_390,U_391)
| ~ class_Fields_Olinordered__field__inverse__zero(U_389) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
cnf(f_141_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_389,c_Rings_Oinverse__class_Odivide(U_389,U_390,U_392),c_Rings_Oinverse__class_Odivide(U_389,U_391,U_392))
| ~ c_Orderings_Oord__class_Oless__eq(U_389,c_Groups_Ozero__class_Ozero(U_389),U_392)
| ~ c_Orderings_Oord__class_Oless__eq(U_389,U_390,U_391)
| ~ class_Fields_Olinordered__field__inverse__zero(U_389) ),
inference(clausify,[status(thm)],[f_141_2]) ).
fof(f_142_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__le__0__iff]) ).
fof(f_142_2,plain,
! [U_395,U_394,U_393] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_393,c_Rings_Oinverse__class_Odivide(U_393,U_394,U_395),c_Groups_Ozero__class_Ozero(U_393))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_393,c_Groups_Ozero__class_Ozero(U_393),U_395)
| ~ c_Orderings_Oord__class_Oless__eq(U_393,U_394,c_Groups_Ozero__class_Ozero(U_393)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_393,U_395,c_Groups_Ozero__class_Ozero(U_393))
| ~ c_Orderings_Oord__class_Oless__eq(U_393,c_Groups_Ozero__class_Ozero(U_393),U_394) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_393,c_Groups_Ozero__class_Ozero(U_393),U_395)
& c_Orderings_Oord__class_Oless__eq(U_393,U_394,c_Groups_Ozero__class_Ozero(U_393)) )
| ( c_Orderings_Oord__class_Oless__eq(U_393,U_395,c_Groups_Ozero__class_Ozero(U_393))
& c_Orderings_Oord__class_Oless__eq(U_393,c_Groups_Ozero__class_Ozero(U_393),U_394) )
| ~ c_Orderings_Oord__class_Oless__eq(U_393,c_Rings_Oinverse__class_Odivide(U_393,U_394,U_395),c_Groups_Ozero__class_Ozero(U_393)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_393) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
cnf(f_142_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_393,U_394,c_Groups_Ozero__class_Ozero(U_393))
| c_Orderings_Oord__class_Oless__eq(U_393,c_Groups_Ozero__class_Ozero(U_393),U_394)
| ~ c_Orderings_Oord__class_Oless__eq(U_393,c_Rings_Oinverse__class_Odivide(U_393,U_394,U_395),c_Groups_Ozero__class_Ozero(U_393))
| ~ class_Fields_Olinordered__field__inverse__zero(U_393) ),
inference(clausify,[status(thm)],[f_142_2]) ).
cnf(f_142_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_393,c_Groups_Ozero__class_Ozero(U_393),U_395)
| c_Orderings_Oord__class_Oless__eq(U_393,c_Groups_Ozero__class_Ozero(U_393),U_394)
| ~ c_Orderings_Oord__class_Oless__eq(U_393,c_Rings_Oinverse__class_Odivide(U_393,U_394,U_395),c_Groups_Ozero__class_Ozero(U_393))
| ~ class_Fields_Olinordered__field__inverse__zero(U_393) ),
inference(clausify,[status(thm)],[f_142_2]) ).
cnf(f_142_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_393,U_394,c_Groups_Ozero__class_Ozero(U_393))
| c_Orderings_Oord__class_Oless__eq(U_393,U_395,c_Groups_Ozero__class_Ozero(U_393))
| ~ c_Orderings_Oord__class_Oless__eq(U_393,c_Rings_Oinverse__class_Odivide(U_393,U_394,U_395),c_Groups_Ozero__class_Ozero(U_393))
| ~ class_Fields_Olinordered__field__inverse__zero(U_393) ),
inference(clausify,[status(thm)],[f_142_2]) ).
cnf(f_142_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_393,c_Groups_Ozero__class_Ozero(U_393),U_395)
| c_Orderings_Oord__class_Oless__eq(U_393,U_395,c_Groups_Ozero__class_Ozero(U_393))
| ~ c_Orderings_Oord__class_Oless__eq(U_393,c_Rings_Oinverse__class_Odivide(U_393,U_394,U_395),c_Groups_Ozero__class_Ozero(U_393))
| ~ class_Fields_Olinordered__field__inverse__zero(U_393) ),
inference(clausify,[status(thm)],[f_142_2]) ).
cnf(f_142_7,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_393,U_395,c_Groups_Ozero__class_Ozero(U_393))
| ~ c_Orderings_Oord__class_Oless__eq(U_393,c_Groups_Ozero__class_Ozero(U_393),U_394)
| c_Orderings_Oord__class_Oless__eq(U_393,c_Rings_Oinverse__class_Odivide(U_393,U_394,U_395),c_Groups_Ozero__class_Ozero(U_393))
| ~ class_Fields_Olinordered__field__inverse__zero(U_393) ),
inference(clausify,[status(thm)],[f_142_2]) ).
cnf(f_142_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_393,c_Groups_Ozero__class_Ozero(U_393),U_395)
| ~ c_Orderings_Oord__class_Oless__eq(U_393,U_394,c_Groups_Ozero__class_Ozero(U_393))
| c_Orderings_Oord__class_Oless__eq(U_393,c_Rings_Oinverse__class_Odivide(U_393,U_394,U_395),c_Groups_Ozero__class_Ozero(U_393))
| ~ class_Fields_Olinordered__field__inverse__zero(U_393) ),
inference(clausify,[status(thm)],[f_142_2]) ).
fof(f_143_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
& c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_a_2,V_b_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__divide__iff]) ).
fof(f_143_2,plain,
! [U_398,U_397,U_396] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_396,c_Groups_Ozero__class_Ozero(U_396),c_Rings_Oinverse__class_Odivide(U_396,U_397,U_398))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_396,U_398,c_Groups_Ozero__class_Ozero(U_396))
| ~ c_Orderings_Oord__class_Oless__eq(U_396,U_397,c_Groups_Ozero__class_Ozero(U_396)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_396,c_Groups_Ozero__class_Ozero(U_396),U_398)
| ~ c_Orderings_Oord__class_Oless__eq(U_396,c_Groups_Ozero__class_Ozero(U_396),U_397) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_396,U_398,c_Groups_Ozero__class_Ozero(U_396))
& c_Orderings_Oord__class_Oless__eq(U_396,U_397,c_Groups_Ozero__class_Ozero(U_396)) )
| ( c_Orderings_Oord__class_Oless__eq(U_396,c_Groups_Ozero__class_Ozero(U_396),U_398)
& c_Orderings_Oord__class_Oless__eq(U_396,c_Groups_Ozero__class_Ozero(U_396),U_397) )
| ~ c_Orderings_Oord__class_Oless__eq(U_396,c_Groups_Ozero__class_Ozero(U_396),c_Rings_Oinverse__class_Odivide(U_396,U_397,U_398)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_396) ),
inference(variable_rename,[status(thm)],[f_143_1]) ).
cnf(f_143_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_396,U_397,c_Groups_Ozero__class_Ozero(U_396))
| c_Orderings_Oord__class_Oless__eq(U_396,c_Groups_Ozero__class_Ozero(U_396),U_397)
| ~ c_Orderings_Oord__class_Oless__eq(U_396,c_Groups_Ozero__class_Ozero(U_396),c_Rings_Oinverse__class_Odivide(U_396,U_397,U_398))
| ~ class_Fields_Olinordered__field__inverse__zero(U_396) ),
inference(clausify,[status(thm)],[f_143_2]) ).
cnf(f_143_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_396,U_398,c_Groups_Ozero__class_Ozero(U_396))
| c_Orderings_Oord__class_Oless__eq(U_396,c_Groups_Ozero__class_Ozero(U_396),U_397)
| ~ c_Orderings_Oord__class_Oless__eq(U_396,c_Groups_Ozero__class_Ozero(U_396),c_Rings_Oinverse__class_Odivide(U_396,U_397,U_398))
| ~ class_Fields_Olinordered__field__inverse__zero(U_396) ),
inference(clausify,[status(thm)],[f_143_2]) ).
cnf(f_143_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_396,U_397,c_Groups_Ozero__class_Ozero(U_396))
| c_Orderings_Oord__class_Oless__eq(U_396,c_Groups_Ozero__class_Ozero(U_396),U_398)
| ~ c_Orderings_Oord__class_Oless__eq(U_396,c_Groups_Ozero__class_Ozero(U_396),c_Rings_Oinverse__class_Odivide(U_396,U_397,U_398))
| ~ class_Fields_Olinordered__field__inverse__zero(U_396) ),
inference(clausify,[status(thm)],[f_143_2]) ).
cnf(f_143_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_396,U_398,c_Groups_Ozero__class_Ozero(U_396))
| c_Orderings_Oord__class_Oless__eq(U_396,c_Groups_Ozero__class_Ozero(U_396),U_398)
| ~ c_Orderings_Oord__class_Oless__eq(U_396,c_Groups_Ozero__class_Ozero(U_396),c_Rings_Oinverse__class_Odivide(U_396,U_397,U_398))
| ~ class_Fields_Olinordered__field__inverse__zero(U_396) ),
inference(clausify,[status(thm)],[f_143_2]) ).
cnf(f_143_7,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_396,c_Groups_Ozero__class_Ozero(U_396),U_398)
| ~ c_Orderings_Oord__class_Oless__eq(U_396,c_Groups_Ozero__class_Ozero(U_396),U_397)
| c_Orderings_Oord__class_Oless__eq(U_396,c_Groups_Ozero__class_Ozero(U_396),c_Rings_Oinverse__class_Odivide(U_396,U_397,U_398))
| ~ class_Fields_Olinordered__field__inverse__zero(U_396) ),
inference(clausify,[status(thm)],[f_143_2]) ).
cnf(f_143_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_396,U_398,c_Groups_Ozero__class_Ozero(U_396))
| ~ c_Orderings_Oord__class_Oless__eq(U_396,U_397,c_Groups_Ozero__class_Ozero(U_396))
| c_Orderings_Oord__class_Oless__eq(U_396,c_Groups_Ozero__class_Ozero(U_396),c_Rings_Oinverse__class_Odivide(U_396,U_397,U_398))
| ~ class_Fields_Olinordered__field__inverse__zero(U_396) ),
inference(clausify,[status(thm)],[f_143_2]) ).
fof(f_144_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x_2,V_y_2))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) )
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x_2,V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__0__le__divide__iff]) ).
fof(f_144_2,plain,
! [U_400,U_399] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_399,U_400))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_400,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_399) )
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_400)
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_399,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_400,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_399) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_400)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_399,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_399,U_400)) ) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
fof(f_144_3,plain,
( ! [U_404,U_402] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_402,U_404))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_404,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_402) )
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_404)
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_402,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
& ! [U_403,U_401] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_403,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_401) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_403)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_401,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_401,U_403)) ) ),
inference(miniscope,[status(thm)],[f_144_2]) ).
cnf(f_144_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_403)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_401,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_401,U_403)) ),
inference(clausify,[status(thm)],[f_144_3]) ).
cnf(f_144_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_403,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_401)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_401,U_403)) ),
inference(clausify,[status(thm)],[f_144_3]) ).
cnf(f_144_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_402)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_402,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_402,U_404)) ),
inference(clausify,[status(thm)],[f_144_3]) ).
cnf(f_144_7,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_404,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_402,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_402,U_404)) ),
inference(clausify,[status(thm)],[f_144_3]) ).
cnf(f_144_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_402)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_404)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_402,U_404)) ),
inference(clausify,[status(thm)],[f_144_3]) ).
cnf(f_144_9,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_404,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_404)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_402,U_404)) ),
inference(clausify,[status(thm)],[f_144_3]) ).
fof(f_145_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),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(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),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_145_2,plain,
! [U_408,U_407,U_406,U_405] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_405,hAPP(c_Groups_Otimes__class_Otimes(U_405,U_406),U_407),hAPP(c_Groups_Otimes__class_Otimes(U_405,U_406),U_408))
| ~ c_Orderings_Oord__class_Oless__eq(U_405,U_407,U_408) )
& ( c_Orderings_Oord__class_Oless__eq(U_405,U_407,U_408)
| ~ c_Orderings_Oord__class_Oless__eq(U_405,hAPP(c_Groups_Otimes__class_Otimes(U_405,U_406),U_407),hAPP(c_Groups_Otimes__class_Otimes(U_405,U_406),U_408)) ) )
| ~ c_Orderings_Oord__class_Oless(U_405,c_Groups_Ozero__class_Ozero(U_405),U_406)
| ~ class_Rings_Olinordered__ring__strict(U_405) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
cnf(f_145_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_405,U_407,U_408)
| ~ c_Orderings_Oord__class_Oless__eq(U_405,hAPP(c_Groups_Otimes__class_Otimes(U_405,U_406),U_407),hAPP(c_Groups_Otimes__class_Otimes(U_405,U_406),U_408))
| ~ c_Orderings_Oord__class_Oless(U_405,c_Groups_Ozero__class_Ozero(U_405),U_406)
| ~ class_Rings_Olinordered__ring__strict(U_405) ),
inference(clausify,[status(thm)],[f_145_2]) ).
cnf(f_145_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_405,hAPP(c_Groups_Otimes__class_Otimes(U_405,U_406),U_407),hAPP(c_Groups_Otimes__class_Otimes(U_405,U_406),U_408))
| ~ c_Orderings_Oord__class_Oless__eq(U_405,U_407,U_408)
| ~ c_Orderings_Oord__class_Oless(U_405,c_Groups_Ozero__class_Ozero(U_405),U_406)
| ~ class_Rings_Olinordered__ring__strict(U_405) ),
inference(clausify,[status(thm)],[f_145_2]) ).
fof(f_146_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),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(c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_a_2),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_146_2,plain,
! [U_412,U_411,U_410,U_409] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_409,hAPP(c_Groups_Otimes__class_Otimes(U_409,U_410),U_411),hAPP(c_Groups_Otimes__class_Otimes(U_409,U_410),U_412))
| ~ c_Orderings_Oord__class_Oless__eq(U_409,U_412,U_411) )
& ( c_Orderings_Oord__class_Oless__eq(U_409,U_412,U_411)
| ~ c_Orderings_Oord__class_Oless__eq(U_409,hAPP(c_Groups_Otimes__class_Otimes(U_409,U_410),U_411),hAPP(c_Groups_Otimes__class_Otimes(U_409,U_410),U_412)) ) )
| ~ c_Orderings_Oord__class_Oless(U_409,U_410,c_Groups_Ozero__class_Ozero(U_409))
| ~ class_Rings_Olinordered__ring__strict(U_409) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
cnf(f_146_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_409,U_412,U_411)
| ~ c_Orderings_Oord__class_Oless__eq(U_409,hAPP(c_Groups_Otimes__class_Otimes(U_409,U_410),U_411),hAPP(c_Groups_Otimes__class_Otimes(U_409,U_410),U_412))
| ~ c_Orderings_Oord__class_Oless(U_409,U_410,c_Groups_Ozero__class_Ozero(U_409))
| ~ class_Rings_Olinordered__ring__strict(U_409) ),
inference(clausify,[status(thm)],[f_146_2]) ).
cnf(f_146_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_409,hAPP(c_Groups_Otimes__class_Otimes(U_409,U_410),U_411),hAPP(c_Groups_Otimes__class_Otimes(U_409,U_410),U_412))
| ~ c_Orderings_Oord__class_Oless__eq(U_409,U_412,U_411)
| ~ c_Orderings_Oord__class_Oless(U_409,U_410,c_Groups_Ozero__class_Ozero(U_409))
| ~ class_Rings_Olinordered__ring__strict(U_409) ),
inference(clausify,[status(thm)],[f_146_2]) ).
fof(f_147_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),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_147_2,plain,
! [U_417,U_416,U_415,U_414,U_413] :
( c_Orderings_Oord__class_Oless(U_413,hAPP(c_Groups_Otimes__class_Otimes(U_413,U_414),U_416),hAPP(c_Groups_Otimes__class_Otimes(U_413,U_415),U_417))
| ~ c_Orderings_Oord__class_Oless__eq(U_413,c_Groups_Ozero__class_Ozero(U_413),U_416)
| ~ c_Orderings_Oord__class_Oless(U_413,c_Groups_Ozero__class_Ozero(U_413),U_415)
| ~ c_Orderings_Oord__class_Oless(U_413,U_416,U_417)
| ~ c_Orderings_Oord__class_Oless(U_413,U_414,U_415)
| ~ class_Rings_Olinordered__semiring__strict(U_413) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
cnf(f_147_3,plain,
( c_Orderings_Oord__class_Oless(U_413,hAPP(c_Groups_Otimes__class_Otimes(U_413,U_414),U_416),hAPP(c_Groups_Otimes__class_Otimes(U_413,U_415),U_417))
| ~ c_Orderings_Oord__class_Oless__eq(U_413,c_Groups_Ozero__class_Ozero(U_413),U_416)
| ~ c_Orderings_Oord__class_Oless(U_413,c_Groups_Ozero__class_Ozero(U_413),U_415)
| ~ c_Orderings_Oord__class_Oless(U_413,U_416,U_417)
| ~ c_Orderings_Oord__class_Oless(U_413,U_414,U_415)
| ~ class_Rings_Olinordered__semiring__strict(U_413) ),
inference(clausify,[status(thm)],[f_147_2]) ).
fof(f_148_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),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_148_2,plain,
! [U_422,U_421,U_420,U_419,U_418] :
( c_Orderings_Oord__class_Oless(U_418,hAPP(c_Groups_Otimes__class_Otimes(U_418,U_419),U_421),hAPP(c_Groups_Otimes__class_Otimes(U_418,U_420),U_422))
| ~ c_Orderings_Oord__class_Oless__eq(U_418,c_Groups_Ozero__class_Ozero(U_418),U_421)
| ~ c_Orderings_Oord__class_Oless__eq(U_418,c_Groups_Ozero__class_Ozero(U_418),U_419)
| ~ c_Orderings_Oord__class_Oless(U_418,U_421,U_422)
| ~ c_Orderings_Oord__class_Oless(U_418,U_419,U_420)
| ~ class_Rings_Olinordered__semiring__strict(U_418) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
cnf(f_148_3,plain,
( c_Orderings_Oord__class_Oless(U_418,hAPP(c_Groups_Otimes__class_Otimes(U_418,U_419),U_421),hAPP(c_Groups_Otimes__class_Otimes(U_418,U_420),U_422))
| ~ c_Orderings_Oord__class_Oless__eq(U_418,c_Groups_Ozero__class_Ozero(U_418),U_421)
| ~ c_Orderings_Oord__class_Oless__eq(U_418,c_Groups_Ozero__class_Ozero(U_418),U_419)
| ~ c_Orderings_Oord__class_Oless(U_418,U_421,U_422)
| ~ c_Orderings_Oord__class_Oless(U_418,U_419,U_420)
| ~ class_Rings_Olinordered__semiring__strict(U_418) ),
inference(clausify,[status(thm)],[f_148_2]) ).
fof(f_149_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),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_149_2,plain,
! [U_427,U_426,U_425,U_424,U_423] :
( c_Orderings_Oord__class_Oless(U_423,hAPP(c_Groups_Otimes__class_Otimes(U_423,U_424),U_426),hAPP(c_Groups_Otimes__class_Otimes(U_423,U_425),U_427))
| ~ c_Orderings_Oord__class_Oless(U_423,c_Groups_Ozero__class_Ozero(U_423),U_426)
| ~ c_Orderings_Oord__class_Oless__eq(U_423,c_Groups_Ozero__class_Ozero(U_423),U_424)
| ~ c_Orderings_Oord__class_Oless__eq(U_423,U_426,U_427)
| ~ c_Orderings_Oord__class_Oless(U_423,U_424,U_425)
| ~ class_Rings_Olinordered__semiring__strict(U_423) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
cnf(f_149_3,plain,
( c_Orderings_Oord__class_Oless(U_423,hAPP(c_Groups_Otimes__class_Otimes(U_423,U_424),U_426),hAPP(c_Groups_Otimes__class_Otimes(U_423,U_425),U_427))
| ~ c_Orderings_Oord__class_Oless(U_423,c_Groups_Ozero__class_Ozero(U_423),U_426)
| ~ c_Orderings_Oord__class_Oless__eq(U_423,c_Groups_Ozero__class_Ozero(U_423),U_424)
| ~ c_Orderings_Oord__class_Oless__eq(U_423,U_426,U_427)
| ~ c_Orderings_Oord__class_Oless(U_423,U_424,U_425)
| ~ class_Rings_Olinordered__semiring__strict(U_423) ),
inference(clausify,[status(thm)],[f_149_2]) ).
fof(f_150_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),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_150_2,plain,
! [U_432,U_431,U_430,U_429,U_428] :
( c_Orderings_Oord__class_Oless(U_428,hAPP(c_Groups_Otimes__class_Otimes(U_428,U_429),U_431),hAPP(c_Groups_Otimes__class_Otimes(U_428,U_430),U_432))
| ~ c_Orderings_Oord__class_Oless__eq(U_428,c_Groups_Ozero__class_Ozero(U_428),U_431)
| ~ c_Orderings_Oord__class_Oless(U_428,c_Groups_Ozero__class_Ozero(U_428),U_429)
| ~ c_Orderings_Oord__class_Oless(U_428,U_431,U_432)
| ~ c_Orderings_Oord__class_Oless__eq(U_428,U_429,U_430)
| ~ class_Rings_Olinordered__semiring__strict(U_428) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
cnf(f_150_3,plain,
( c_Orderings_Oord__class_Oless(U_428,hAPP(c_Groups_Otimes__class_Otimes(U_428,U_429),U_431),hAPP(c_Groups_Otimes__class_Otimes(U_428,U_430),U_432))
| ~ c_Orderings_Oord__class_Oless__eq(U_428,c_Groups_Ozero__class_Ozero(U_428),U_431)
| ~ c_Orderings_Oord__class_Oless(U_428,c_Groups_Ozero__class_Ozero(U_428),U_429)
| ~ c_Orderings_Oord__class_Oless(U_428,U_431,U_432)
| ~ c_Orderings_Oord__class_Oless__eq(U_428,U_429,U_430)
| ~ class_Rings_Olinordered__semiring__strict(U_428) ),
inference(clausify,[status(thm)],[f_150_2]) ).
fof(f_151_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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),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_151_2,plain,
! [U_436,U_435,U_434,U_433] :
( c_Orderings_Oord__class_Oless(U_433,U_434,U_436)
| ~ c_Orderings_Oord__class_Oless__eq(U_433,c_Groups_Ozero__class_Ozero(U_433),U_435)
| ~ c_Orderings_Oord__class_Oless(U_433,hAPP(c_Groups_Otimes__class_Otimes(U_433,U_434),U_435),hAPP(c_Groups_Otimes__class_Otimes(U_433,U_436),U_435))
| ~ class_Rings_Olinordered__semiring(U_433) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
cnf(f_151_3,plain,
( c_Orderings_Oord__class_Oless(U_433,U_434,U_436)
| ~ c_Orderings_Oord__class_Oless__eq(U_433,c_Groups_Ozero__class_Ozero(U_433),U_435)
| ~ c_Orderings_Oord__class_Oless(U_433,hAPP(c_Groups_Otimes__class_Otimes(U_433,U_434),U_435),hAPP(c_Groups_Otimes__class_Otimes(U_433,U_436),U_435))
| ~ class_Rings_Olinordered__semiring(U_433) ),
inference(clausify,[status(thm)],[f_151_2]) ).
fof(f_152_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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),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_152_2,plain,
! [U_440,U_439,U_438,U_437] :
( c_Orderings_Oord__class_Oless(U_437,U_438,U_440)
| ~ c_Orderings_Oord__class_Oless__eq(U_437,c_Groups_Ozero__class_Ozero(U_437),U_439)
| ~ c_Orderings_Oord__class_Oless(U_437,hAPP(c_Groups_Otimes__class_Otimes(U_437,U_438),U_439),hAPP(c_Groups_Otimes__class_Otimes(U_437,U_440),U_439))
| ~ class_Rings_Olinordered__semiring__strict(U_437) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
cnf(f_152_3,plain,
( c_Orderings_Oord__class_Oless(U_437,U_438,U_440)
| ~ c_Orderings_Oord__class_Oless__eq(U_437,c_Groups_Ozero__class_Ozero(U_437),U_439)
| ~ c_Orderings_Oord__class_Oless(U_437,hAPP(c_Groups_Otimes__class_Otimes(U_437,U_438),U_439),hAPP(c_Groups_Otimes__class_Otimes(U_437,U_440),U_439))
| ~ class_Rings_Olinordered__semiring__strict(U_437) ),
inference(clausify,[status(thm)],[f_152_2]) ).
fof(f_153_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(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),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_153_2,plain,
! [U_444,U_443,U_442,U_441] :
( c_Orderings_Oord__class_Oless(U_441,U_443,U_444)
| ~ c_Orderings_Oord__class_Oless__eq(U_441,c_Groups_Ozero__class_Ozero(U_441),U_442)
| ~ c_Orderings_Oord__class_Oless(U_441,hAPP(c_Groups_Otimes__class_Otimes(U_441,U_442),U_443),hAPP(c_Groups_Otimes__class_Otimes(U_441,U_442),U_444))
| ~ class_Rings_Olinordered__semiring(U_441) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
cnf(f_153_3,plain,
( c_Orderings_Oord__class_Oless(U_441,U_443,U_444)
| ~ c_Orderings_Oord__class_Oless__eq(U_441,c_Groups_Ozero__class_Ozero(U_441),U_442)
| ~ c_Orderings_Oord__class_Oless(U_441,hAPP(c_Groups_Otimes__class_Otimes(U_441,U_442),U_443),hAPP(c_Groups_Otimes__class_Otimes(U_441,U_442),U_444))
| ~ class_Rings_Olinordered__semiring(U_441) ),
inference(clausify,[status(thm)],[f_153_2]) ).
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__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),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_154_2,plain,
! [U_448,U_447,U_446,U_445] :
( c_Orderings_Oord__class_Oless(U_445,U_447,U_448)
| ~ c_Orderings_Oord__class_Oless__eq(U_445,c_Groups_Ozero__class_Ozero(U_445),U_446)
| ~ c_Orderings_Oord__class_Oless(U_445,hAPP(c_Groups_Otimes__class_Otimes(U_445,U_446),U_447),hAPP(c_Groups_Otimes__class_Otimes(U_445,U_446),U_448))
| ~ class_Rings_Olinordered__semiring__strict(U_445) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
cnf(f_154_3,plain,
( c_Orderings_Oord__class_Oless(U_445,U_447,U_448)
| ~ c_Orderings_Oord__class_Oless__eq(U_445,c_Groups_Ozero__class_Ozero(U_445),U_446)
| ~ c_Orderings_Oord__class_Oless(U_445,hAPP(c_Groups_Otimes__class_Otimes(U_445,U_446),U_447),hAPP(c_Groups_Otimes__class_Otimes(U_445,U_446),U_448))
| ~ class_Rings_Olinordered__semiring__strict(U_445) ),
inference(clausify,[status(thm)],[f_154_2]) ).
fof(f_155_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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),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_155_2,plain,
! [U_452,U_451,U_450,U_449] :
( c_Orderings_Oord__class_Oless__eq(U_449,U_450,U_452)
| ~ c_Orderings_Oord__class_Oless(U_449,c_Groups_Ozero__class_Ozero(U_449),U_451)
| ~ c_Orderings_Oord__class_Oless__eq(U_449,hAPP(c_Groups_Otimes__class_Otimes(U_449,U_450),U_451),hAPP(c_Groups_Otimes__class_Otimes(U_449,U_452),U_451))
| ~ class_Rings_Olinordered__semiring__strict(U_449) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
cnf(f_155_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_449,U_450,U_452)
| ~ c_Orderings_Oord__class_Oless(U_449,c_Groups_Ozero__class_Ozero(U_449),U_451)
| ~ c_Orderings_Oord__class_Oless__eq(U_449,hAPP(c_Groups_Otimes__class_Otimes(U_449,U_450),U_451),hAPP(c_Groups_Otimes__class_Otimes(U_449,U_452),U_451))
| ~ class_Rings_Olinordered__semiring__strict(U_449) ),
inference(clausify,[status(thm)],[f_155_2]) ).
fof(f_156_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(c_Groups_Otimes__class_Otimes(T_a,V_c),V_a),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_156_2,plain,
! [U_456,U_455,U_454,U_453] :
( c_Orderings_Oord__class_Oless__eq(U_453,U_455,U_456)
| ~ c_Orderings_Oord__class_Oless(U_453,c_Groups_Ozero__class_Ozero(U_453),U_454)
| ~ c_Orderings_Oord__class_Oless__eq(U_453,hAPP(c_Groups_Otimes__class_Otimes(U_453,U_454),U_455),hAPP(c_Groups_Otimes__class_Otimes(U_453,U_454),U_456))
| ~ class_Rings_Olinordered__semiring__strict(U_453) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
cnf(f_156_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_453,U_455,U_456)
| ~ c_Orderings_Oord__class_Oless(U_453,c_Groups_Ozero__class_Ozero(U_453),U_454)
| ~ c_Orderings_Oord__class_Oless__eq(U_453,hAPP(c_Groups_Otimes__class_Otimes(U_453,U_454),U_455),hAPP(c_Groups_Otimes__class_Otimes(U_453,U_454),U_456))
| ~ class_Rings_Olinordered__semiring__strict(U_453) ),
inference(clausify,[status(thm)],[f_156_2]) ).
fof(f_157_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,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_157_2,plain,
! [U_459,U_458,U_457] :
( c_Orderings_Oord__class_Oless__eq(U_457,hAPP(c_Groups_Otimes__class_Otimes(U_457,U_459),U_458),U_458)
| ~ c_Orderings_Oord__class_Oless__eq(U_457,U_459,c_Groups_Oone__class_Oone(U_457))
| ~ c_Orderings_Oord__class_Oless__eq(U_457,c_Groups_Ozero__class_Ozero(U_457),U_459)
| ~ c_Orderings_Oord__class_Oless__eq(U_457,c_Groups_Ozero__class_Ozero(U_457),U_458)
| ~ class_Rings_Olinordered__idom(U_457) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
cnf(f_157_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_457,hAPP(c_Groups_Otimes__class_Otimes(U_457,U_459),U_458),U_458)
| ~ c_Orderings_Oord__class_Oless__eq(U_457,U_459,c_Groups_Oone__class_Oone(U_457))
| ~ c_Orderings_Oord__class_Oless__eq(U_457,c_Groups_Ozero__class_Ozero(U_457),U_459)
| ~ c_Orderings_Oord__class_Oless__eq(U_457,c_Groups_Ozero__class_Ozero(U_457),U_458)
| ~ class_Rings_Olinordered__idom(U_457) ),
inference(clausify,[status(thm)],[f_157_2]) ).
fof(f_158_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,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_158_2,plain,
! [U_462,U_461,U_460] :
( c_Orderings_Oord__class_Oless__eq(U_460,hAPP(c_Groups_Otimes__class_Otimes(U_460,U_461),U_462),U_461)
| ~ c_Orderings_Oord__class_Oless__eq(U_460,U_462,c_Groups_Oone__class_Oone(U_460))
| ~ c_Orderings_Oord__class_Oless__eq(U_460,c_Groups_Ozero__class_Ozero(U_460),U_462)
| ~ c_Orderings_Oord__class_Oless__eq(U_460,c_Groups_Ozero__class_Ozero(U_460),U_461)
| ~ class_Rings_Olinordered__idom(U_460) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
cnf(f_158_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_460,hAPP(c_Groups_Otimes__class_Otimes(U_460,U_461),U_462),U_461)
| ~ c_Orderings_Oord__class_Oless__eq(U_460,U_462,c_Groups_Oone__class_Oone(U_460))
| ~ c_Orderings_Oord__class_Oless__eq(U_460,c_Groups_Ozero__class_Ozero(U_460),U_462)
| ~ c_Orderings_Oord__class_Oless__eq(U_460,c_Groups_Ozero__class_Ozero(U_460),U_461)
| ~ class_Rings_Olinordered__idom(U_460) ),
inference(clausify,[status(thm)],[f_158_2]) ).
fof(f_159_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))
| ~ c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__nonpos__neg]) ).
fof(f_159_2,plain,
! [U_465,U_464,U_463] :
( c_Orderings_Oord__class_Oless__eq(U_463,c_Groups_Ozero__class_Ozero(U_463),c_Rings_Oinverse__class_Odivide(U_463,U_464,U_465))
| ~ c_Orderings_Oord__class_Oless(U_463,U_465,c_Groups_Ozero__class_Ozero(U_463))
| ~ c_Orderings_Oord__class_Oless__eq(U_463,U_464,c_Groups_Ozero__class_Ozero(U_463))
| ~ class_Fields_Olinordered__field(U_463) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
cnf(f_159_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_463,c_Groups_Ozero__class_Ozero(U_463),c_Rings_Oinverse__class_Odivide(U_463,U_464,U_465))
| ~ c_Orderings_Oord__class_Oless(U_463,U_465,c_Groups_Ozero__class_Ozero(U_463))
| ~ c_Orderings_Oord__class_Oless__eq(U_463,U_464,c_Groups_Ozero__class_Ozero(U_463))
| ~ class_Fields_Olinordered__field(U_463) ),
inference(clausify,[status(thm)],[f_159_2]) ).
fof(f_160_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__nonpos__pos]) ).
fof(f_160_2,plain,
! [U_468,U_467,U_466] :
( c_Orderings_Oord__class_Oless__eq(U_466,c_Rings_Oinverse__class_Odivide(U_466,U_467,U_468),c_Groups_Ozero__class_Ozero(U_466))
| ~ c_Orderings_Oord__class_Oless(U_466,c_Groups_Ozero__class_Ozero(U_466),U_468)
| ~ c_Orderings_Oord__class_Oless__eq(U_466,U_467,c_Groups_Ozero__class_Ozero(U_466))
| ~ class_Fields_Olinordered__field(U_466) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
cnf(f_160_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_466,c_Rings_Oinverse__class_Odivide(U_466,U_467,U_468),c_Groups_Ozero__class_Ozero(U_466))
| ~ c_Orderings_Oord__class_Oless(U_466,c_Groups_Ozero__class_Ozero(U_466),U_468)
| ~ c_Orderings_Oord__class_Oless__eq(U_466,U_467,c_Groups_Ozero__class_Ozero(U_466))
| ~ class_Fields_Olinordered__field(U_466) ),
inference(clausify,[status(thm)],[f_160_2]) ).
fof(f_161_1,plain,
! [V_z,V_w,V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_w,V_z)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_frac__le]) ).
fof(f_161_2,plain,
! [U_473,U_472,U_471,U_470,U_469] :
( c_Orderings_Oord__class_Oless__eq(U_469,c_Rings_Oinverse__class_Odivide(U_469,U_470,U_473),c_Rings_Oinverse__class_Odivide(U_469,U_471,U_472))
| ~ c_Orderings_Oord__class_Oless__eq(U_469,U_472,U_473)
| ~ c_Orderings_Oord__class_Oless(U_469,c_Groups_Ozero__class_Ozero(U_469),U_472)
| ~ c_Orderings_Oord__class_Oless__eq(U_469,U_470,U_471)
| ~ c_Orderings_Oord__class_Oless__eq(U_469,c_Groups_Ozero__class_Ozero(U_469),U_470)
| ~ class_Fields_Olinordered__field(U_469) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
cnf(f_161_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_469,c_Rings_Oinverse__class_Odivide(U_469,U_470,U_473),c_Rings_Oinverse__class_Odivide(U_469,U_471,U_472))
| ~ c_Orderings_Oord__class_Oless__eq(U_469,U_472,U_473)
| ~ c_Orderings_Oord__class_Oless(U_469,c_Groups_Ozero__class_Ozero(U_469),U_472)
| ~ c_Orderings_Oord__class_Oless__eq(U_469,U_470,U_471)
| ~ c_Orderings_Oord__class_Oless__eq(U_469,c_Groups_Ozero__class_Ozero(U_469),U_470)
| ~ class_Fields_Olinordered__field(U_469) ),
inference(clausify,[status(thm)],[f_161_2]) ).
fof(f_162_1,plain,
! [V_z,V_w,V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_w,V_z)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_frac__less]) ).
fof(f_162_2,plain,
! [U_478,U_477,U_476,U_475,U_474] :
( c_Orderings_Oord__class_Oless(U_474,c_Rings_Oinverse__class_Odivide(U_474,U_475,U_478),c_Rings_Oinverse__class_Odivide(U_474,U_476,U_477))
| ~ c_Orderings_Oord__class_Oless__eq(U_474,U_477,U_478)
| ~ c_Orderings_Oord__class_Oless(U_474,c_Groups_Ozero__class_Ozero(U_474),U_477)
| ~ c_Orderings_Oord__class_Oless(U_474,U_475,U_476)
| ~ c_Orderings_Oord__class_Oless__eq(U_474,c_Groups_Ozero__class_Ozero(U_474),U_475)
| ~ class_Fields_Olinordered__field(U_474) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
cnf(f_162_3,plain,
( c_Orderings_Oord__class_Oless(U_474,c_Rings_Oinverse__class_Odivide(U_474,U_475,U_478),c_Rings_Oinverse__class_Odivide(U_474,U_476,U_477))
| ~ c_Orderings_Oord__class_Oless__eq(U_474,U_477,U_478)
| ~ c_Orderings_Oord__class_Oless(U_474,c_Groups_Ozero__class_Ozero(U_474),U_477)
| ~ c_Orderings_Oord__class_Oless(U_474,U_475,U_476)
| ~ c_Orderings_Oord__class_Oless__eq(U_474,c_Groups_Ozero__class_Ozero(U_474),U_475)
| ~ class_Fields_Olinordered__field(U_474) ),
inference(clausify,[status(thm)],[f_162_2]) ).
fof(f_163_1,plain,
! [V_z,V_w,V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w))
| ~ c_Orderings_Oord__class_Oless(T_a,V_w,V_z)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_frac__less2]) ).
fof(f_163_2,plain,
! [U_483,U_482,U_481,U_480,U_479] :
( c_Orderings_Oord__class_Oless(U_479,c_Rings_Oinverse__class_Odivide(U_479,U_480,U_483),c_Rings_Oinverse__class_Odivide(U_479,U_481,U_482))
| ~ c_Orderings_Oord__class_Oless(U_479,U_482,U_483)
| ~ c_Orderings_Oord__class_Oless(U_479,c_Groups_Ozero__class_Ozero(U_479),U_482)
| ~ c_Orderings_Oord__class_Oless__eq(U_479,U_480,U_481)
| ~ c_Orderings_Oord__class_Oless(U_479,c_Groups_Ozero__class_Ozero(U_479),U_480)
| ~ class_Fields_Olinordered__field(U_479) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
cnf(f_163_3,plain,
( c_Orderings_Oord__class_Oless(U_479,c_Rings_Oinverse__class_Odivide(U_479,U_480,U_483),c_Rings_Oinverse__class_Odivide(U_479,U_481,U_482))
| ~ c_Orderings_Oord__class_Oless(U_479,U_482,U_483)
| ~ c_Orderings_Oord__class_Oless(U_479,c_Groups_Ozero__class_Ozero(U_479),U_482)
| ~ c_Orderings_Oord__class_Oless__eq(U_479,U_480,U_481)
| ~ c_Orderings_Oord__class_Oless(U_479,c_Groups_Ozero__class_Ozero(U_479),U_480)
| ~ class_Fields_Olinordered__field(U_479) ),
inference(clausify,[status(thm)],[f_163_2]) ).
fof(f_164_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__nonneg__neg]) ).
fof(f_164_2,plain,
! [U_486,U_485,U_484] :
( c_Orderings_Oord__class_Oless__eq(U_484,c_Rings_Oinverse__class_Odivide(U_484,U_485,U_486),c_Groups_Ozero__class_Ozero(U_484))
| ~ c_Orderings_Oord__class_Oless(U_484,U_486,c_Groups_Ozero__class_Ozero(U_484))
| ~ c_Orderings_Oord__class_Oless__eq(U_484,c_Groups_Ozero__class_Ozero(U_484),U_485)
| ~ class_Fields_Olinordered__field(U_484) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
cnf(f_164_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_484,c_Rings_Oinverse__class_Odivide(U_484,U_485,U_486),c_Groups_Ozero__class_Ozero(U_484))
| ~ c_Orderings_Oord__class_Oless(U_484,U_486,c_Groups_Ozero__class_Ozero(U_484))
| ~ c_Orderings_Oord__class_Oless__eq(U_484,c_Groups_Ozero__class_Ozero(U_484),U_485)
| ~ class_Fields_Olinordered__field(U_484) ),
inference(clausify,[status(thm)],[f_164_2]) ).
fof(f_165_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__nonneg__pos]) ).
fof(f_165_2,plain,
! [U_489,U_488,U_487] :
( c_Orderings_Oord__class_Oless__eq(U_487,c_Groups_Ozero__class_Ozero(U_487),c_Rings_Oinverse__class_Odivide(U_487,U_488,U_489))
| ~ c_Orderings_Oord__class_Oless(U_487,c_Groups_Ozero__class_Ozero(U_487),U_489)
| ~ c_Orderings_Oord__class_Oless__eq(U_487,c_Groups_Ozero__class_Ozero(U_487),U_488)
| ~ class_Fields_Olinordered__field(U_487) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
cnf(f_165_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_487,c_Groups_Ozero__class_Ozero(U_487),c_Rings_Oinverse__class_Odivide(U_487,U_488,U_489))
| ~ c_Orderings_Oord__class_Oless(U_487,c_Groups_Ozero__class_Ozero(U_487),U_489)
| ~ c_Orderings_Oord__class_Oless__eq(U_487,c_Groups_Ozero__class_Ozero(U_487),U_488)
| ~ class_Fields_Olinordered__field(U_487) ),
inference(clausify,[status(thm)],[f_165_2]) ).
fof(f_166_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_166_2,plain,
! [U_491,U_490] :
( ( ( c_Groups_Ozero__class_Ozero(U_490) = U_491
| U_491 != c_Groups_Ozero__class_Ozero(U_490) )
& ( U_491 = c_Groups_Ozero__class_Ozero(U_490)
| c_Groups_Ozero__class_Ozero(U_490) != U_491 ) )
| ~ class_Groups_Ozero(U_490) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
cnf(f_166_3,plain,
( U_491 = c_Groups_Ozero__class_Ozero(U_490)
| c_Groups_Ozero__class_Ozero(U_490) != U_491
| ~ class_Groups_Ozero(U_490) ),
inference(clausify,[status(thm)],[f_166_2]) ).
cnf(f_166_4,plain,
( c_Groups_Ozero__class_Ozero(U_490) = U_491
| U_491 != c_Groups_Ozero__class_Ozero(U_490)
| ~ class_Groups_Ozero(U_490) ),
inference(clausify,[status(thm)],[f_166_2]) ).
fof(f_167_1,plain,
! [V_y_2,V_x_2,V_za_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2),V_za_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(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y_2),V_za_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2) ),
inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff1]) ).
fof(f_167_2,plain,
! [U_494,U_493,U_492] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_493),U_492),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_494),U_492))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_493,U_494) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_493,U_494)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_493),U_492),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_494),U_492)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_492) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
cnf(f_167_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_493,U_494)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_493),U_492),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_494),U_492))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_492) ),
inference(clausify,[status(thm)],[f_167_2]) ).
cnf(f_167_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_493),U_492),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_494),U_492))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_493,U_494)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_492) ),
inference(clausify,[status(thm)],[f_167_2]) ).
fof(f_168_1,plain,
! [V_y_2,V_x_2,V_za_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_za_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_za_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(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_za_2),V_x_2),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_za_2),V_y_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2) ),
inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff2]) ).
fof(f_168_2,plain,
! [U_497,U_496,U_495] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_495),U_496),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_495),U_497))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_496,U_497) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_496,U_497)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_495),U_496),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_495),U_497)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_495) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
cnf(f_168_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_496,U_497)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_495),U_496),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_495),U_497))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_495) ),
inference(clausify,[status(thm)],[f_168_2]) ).
cnf(f_168_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_495),U_496),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_495),U_497))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_496,U_497)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_495) ),
inference(clausify,[status(thm)],[f_168_2]) ).
fof(f_169_1,plain,
! [V_c,V_b,V_a,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)),V_c) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),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_169_2,plain,
! [U_501,U_500,U_499,U_498] :
( hAPP(c_Groups_Otimes__class_Otimes(U_498,hAPP(c_Groups_Otimes__class_Otimes(U_498,U_499),U_500)),U_501) = hAPP(c_Groups_Otimes__class_Otimes(U_498,U_499),hAPP(c_Groups_Otimes__class_Otimes(U_498,U_500),U_501))
| ~ class_Groups_Oab__semigroup__mult(U_498) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
cnf(f_169_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_498,hAPP(c_Groups_Otimes__class_Otimes(U_498,U_499),U_500)),U_501) = hAPP(c_Groups_Otimes__class_Otimes(U_498,U_499),hAPP(c_Groups_Otimes__class_Otimes(U_498,U_500),U_501))
| ~ class_Groups_Oab__semigroup__mult(U_498) ),
inference(clausify,[status(thm)],[f_169_2]) ).
fof(f_170_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_170_2,plain,
! [U_503,U_502] :
( ( ( c_Groups_Oone__class_Oone(U_502) = U_503
| U_503 != c_Groups_Oone__class_Oone(U_502) )
& ( U_503 = c_Groups_Oone__class_Oone(U_502)
| c_Groups_Oone__class_Oone(U_502) != U_503 ) )
| ~ class_Groups_Oone(U_502) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
cnf(f_170_3,plain,
( U_503 = c_Groups_Oone__class_Oone(U_502)
| c_Groups_Oone__class_Oone(U_502) != U_503
| ~ class_Groups_Oone(U_502) ),
inference(clausify,[status(thm)],[f_170_2]) ).
cnf(f_170_4,plain,
( c_Groups_Oone__class_Oone(U_502) = U_503
| U_503 != c_Groups_Oone__class_Oone(U_502)
| ~ class_Groups_Oone(U_502) ),
inference(clausify,[status(thm)],[f_170_2]) ).
fof(f_171_1,plain,
! [V_ca_2,V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
| ( ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
& ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_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,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) )
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_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__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(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,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_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,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_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__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__divide__eq]) ).
fof(f_171_2,plain,
! [U_507,U_506,U_505,U_504] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Rings_Oinverse__class_Odivide(U_504,U_506,U_507))
| ( ( ( ~ c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Groups_Ozero__class_Ozero(U_504))
& ~ c_Orderings_Oord__class_Oless(U_504,U_507,c_Groups_Ozero__class_Ozero(U_504)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_504,U_506,hAPP(c_Groups_Otimes__class_Otimes(U_504,U_505),U_507))
& c_Orderings_Oord__class_Oless(U_504,U_507,c_Groups_Ozero__class_Ozero(U_504)) ) )
& ~ c_Orderings_Oord__class_Oless(U_504,c_Groups_Ozero__class_Ozero(U_504),U_507) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_504,hAPP(c_Groups_Otimes__class_Otimes(U_504,U_505),U_507),U_506)
& c_Orderings_Oord__class_Oless(U_504,c_Groups_Ozero__class_Ozero(U_504),U_507) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Groups_Ozero__class_Ozero(U_504))
| c_Orderings_Oord__class_Oless(U_504,U_507,c_Groups_Ozero__class_Ozero(U_504)) )
& ( c_Orderings_Oord__class_Oless__eq(U_504,U_506,hAPP(c_Groups_Otimes__class_Otimes(U_504,U_505),U_507))
| ~ c_Orderings_Oord__class_Oless(U_504,U_507,c_Groups_Ozero__class_Ozero(U_504)) ) )
| c_Orderings_Oord__class_Oless(U_504,c_Groups_Ozero__class_Ozero(U_504),U_507) )
& ( c_Orderings_Oord__class_Oless__eq(U_504,hAPP(c_Groups_Otimes__class_Otimes(U_504,U_505),U_507),U_506)
| ~ c_Orderings_Oord__class_Oless(U_504,c_Groups_Ozero__class_Ozero(U_504),U_507) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Rings_Oinverse__class_Odivide(U_504,U_506,U_507)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_504) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
cnf(f_171_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_504,hAPP(c_Groups_Otimes__class_Otimes(U_504,U_505),U_507),U_506)
| ~ c_Orderings_Oord__class_Oless(U_504,c_Groups_Ozero__class_Ozero(U_504),U_507)
| ~ c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Rings_Oinverse__class_Odivide(U_504,U_506,U_507))
| ~ class_Fields_Olinordered__field__inverse__zero(U_504) ),
inference(clausify,[status(thm)],[f_171_2]) ).
cnf(f_171_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_504,U_506,hAPP(c_Groups_Otimes__class_Otimes(U_504,U_505),U_507))
| ~ c_Orderings_Oord__class_Oless(U_504,U_507,c_Groups_Ozero__class_Ozero(U_504))
| c_Orderings_Oord__class_Oless(U_504,c_Groups_Ozero__class_Ozero(U_504),U_507)
| ~ c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Rings_Oinverse__class_Odivide(U_504,U_506,U_507))
| ~ class_Fields_Olinordered__field__inverse__zero(U_504) ),
inference(clausify,[status(thm)],[f_171_2]) ).
cnf(f_171_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Groups_Ozero__class_Ozero(U_504))
| c_Orderings_Oord__class_Oless(U_504,U_507,c_Groups_Ozero__class_Ozero(U_504))
| c_Orderings_Oord__class_Oless(U_504,c_Groups_Ozero__class_Ozero(U_504),U_507)
| ~ c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Rings_Oinverse__class_Odivide(U_504,U_506,U_507))
| ~ class_Fields_Olinordered__field__inverse__zero(U_504) ),
inference(clausify,[status(thm)],[f_171_2]) ).
cnf(f_171_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_504,c_Groups_Ozero__class_Ozero(U_504),U_507)
| c_Orderings_Oord__class_Oless(U_504,c_Groups_Ozero__class_Ozero(U_504),U_507)
| c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Rings_Oinverse__class_Odivide(U_504,U_506,U_507))
| ~ class_Fields_Olinordered__field__inverse__zero(U_504) ),
inference(clausify,[status(thm)],[f_171_2]) ).
cnf(f_171_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_504,U_507,c_Groups_Ozero__class_Ozero(U_504))
| c_Orderings_Oord__class_Oless(U_504,U_507,c_Groups_Ozero__class_Ozero(U_504))
| c_Orderings_Oord__class_Oless(U_504,c_Groups_Ozero__class_Ozero(U_504),U_507)
| c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Rings_Oinverse__class_Odivide(U_504,U_506,U_507))
| ~ class_Fields_Olinordered__field__inverse__zero(U_504) ),
inference(clausify,[status(thm)],[f_171_2]) ).
cnf(f_171_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Groups_Ozero__class_Ozero(U_504))
| c_Orderings_Oord__class_Oless(U_504,U_507,c_Groups_Ozero__class_Ozero(U_504))
| c_Orderings_Oord__class_Oless(U_504,c_Groups_Ozero__class_Ozero(U_504),U_507)
| c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Rings_Oinverse__class_Odivide(U_504,U_506,U_507))
| ~ class_Fields_Olinordered__field__inverse__zero(U_504) ),
inference(clausify,[status(thm)],[f_171_2]) ).
cnf(f_171_9,plain,
( ~ c_Orderings_Oord__class_Oless(U_504,U_507,c_Groups_Ozero__class_Ozero(U_504))
| ~ c_Orderings_Oord__class_Oless__eq(U_504,U_506,hAPP(c_Groups_Otimes__class_Otimes(U_504,U_505),U_507))
| c_Orderings_Oord__class_Oless(U_504,c_Groups_Ozero__class_Ozero(U_504),U_507)
| c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Rings_Oinverse__class_Odivide(U_504,U_506,U_507))
| ~ class_Fields_Olinordered__field__inverse__zero(U_504) ),
inference(clausify,[status(thm)],[f_171_2]) ).
cnf(f_171_10,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Groups_Ozero__class_Ozero(U_504))
| ~ c_Orderings_Oord__class_Oless__eq(U_504,U_506,hAPP(c_Groups_Otimes__class_Otimes(U_504,U_505),U_507))
| c_Orderings_Oord__class_Oless(U_504,c_Groups_Ozero__class_Ozero(U_504),U_507)
| c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Rings_Oinverse__class_Odivide(U_504,U_506,U_507))
| ~ class_Fields_Olinordered__field__inverse__zero(U_504) ),
inference(clausify,[status(thm)],[f_171_2]) ).
cnf(f_171_11,plain,
( ~ c_Orderings_Oord__class_Oless(U_504,c_Groups_Ozero__class_Ozero(U_504),U_507)
| ~ c_Orderings_Oord__class_Oless__eq(U_504,hAPP(c_Groups_Otimes__class_Otimes(U_504,U_505),U_507),U_506)
| c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Rings_Oinverse__class_Odivide(U_504,U_506,U_507))
| ~ class_Fields_Olinordered__field__inverse__zero(U_504) ),
inference(clausify,[status(thm)],[f_171_2]) ).
cnf(f_171_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_504,U_507,c_Groups_Ozero__class_Ozero(U_504))
| c_Orderings_Oord__class_Oless(U_504,U_507,c_Groups_Ozero__class_Ozero(U_504))
| ~ c_Orderings_Oord__class_Oless__eq(U_504,hAPP(c_Groups_Otimes__class_Otimes(U_504,U_505),U_507),U_506)
| c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Rings_Oinverse__class_Odivide(U_504,U_506,U_507))
| ~ class_Fields_Olinordered__field__inverse__zero(U_504) ),
inference(clausify,[status(thm)],[f_171_2]) ).
cnf(f_171_13,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Groups_Ozero__class_Ozero(U_504))
| c_Orderings_Oord__class_Oless(U_504,U_507,c_Groups_Ozero__class_Ozero(U_504))
| ~ c_Orderings_Oord__class_Oless__eq(U_504,hAPP(c_Groups_Otimes__class_Otimes(U_504,U_505),U_507),U_506)
| c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Rings_Oinverse__class_Odivide(U_504,U_506,U_507))
| ~ class_Fields_Olinordered__field__inverse__zero(U_504) ),
inference(clausify,[status(thm)],[f_171_2]) ).
cnf(f_171_14,plain,
( ~ c_Orderings_Oord__class_Oless(U_504,U_507,c_Groups_Ozero__class_Ozero(U_504))
| ~ c_Orderings_Oord__class_Oless__eq(U_504,U_506,hAPP(c_Groups_Otimes__class_Otimes(U_504,U_505),U_507))
| ~ c_Orderings_Oord__class_Oless__eq(U_504,hAPP(c_Groups_Otimes__class_Otimes(U_504,U_505),U_507),U_506)
| c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Rings_Oinverse__class_Odivide(U_504,U_506,U_507))
| ~ class_Fields_Olinordered__field__inverse__zero(U_504) ),
inference(clausify,[status(thm)],[f_171_2]) ).
cnf(f_171_15,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Groups_Ozero__class_Ozero(U_504))
| ~ c_Orderings_Oord__class_Oless__eq(U_504,U_506,hAPP(c_Groups_Otimes__class_Otimes(U_504,U_505),U_507))
| ~ c_Orderings_Oord__class_Oless__eq(U_504,hAPP(c_Groups_Otimes__class_Otimes(U_504,U_505),U_507),U_506)
| c_Orderings_Oord__class_Oless__eq(U_504,U_505,c_Rings_Oinverse__class_Odivide(U_504,U_506,U_507))
| ~ class_Fields_Olinordered__field__inverse__zero(U_504) ),
inference(clausify,[status(thm)],[f_171_2]) ).
fof(f_172_1,plain,
! [V_a_2,V_ca_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2)
| ( ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
& ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_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,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) )
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))
& 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,c_Groups_Ozero__class_Ozero(T_a),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__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_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,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))
| ~ 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,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__le__eq]) ).
fof(f_172_2,plain,
! [U_511,U_510,U_509,U_508] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_508,c_Rings_Oinverse__class_Odivide(U_508,U_509,U_510),U_511)
| ( ( ( ~ c_Orderings_Oord__class_Oless__eq(U_508,c_Groups_Ozero__class_Ozero(U_508),U_511)
& ~ c_Orderings_Oord__class_Oless(U_508,U_510,c_Groups_Ozero__class_Ozero(U_508)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_508,hAPP(c_Groups_Otimes__class_Otimes(U_508,U_511),U_510),U_509)
& c_Orderings_Oord__class_Oless(U_508,U_510,c_Groups_Ozero__class_Ozero(U_508)) ) )
& ~ c_Orderings_Oord__class_Oless(U_508,c_Groups_Ozero__class_Ozero(U_508),U_510) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_508,U_509,hAPP(c_Groups_Otimes__class_Otimes(U_508,U_511),U_510))
& c_Orderings_Oord__class_Oless(U_508,c_Groups_Ozero__class_Ozero(U_508),U_510) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless__eq(U_508,c_Groups_Ozero__class_Ozero(U_508),U_511)
| c_Orderings_Oord__class_Oless(U_508,U_510,c_Groups_Ozero__class_Ozero(U_508)) )
& ( c_Orderings_Oord__class_Oless__eq(U_508,hAPP(c_Groups_Otimes__class_Otimes(U_508,U_511),U_510),U_509)
| ~ c_Orderings_Oord__class_Oless(U_508,U_510,c_Groups_Ozero__class_Ozero(U_508)) ) )
| c_Orderings_Oord__class_Oless(U_508,c_Groups_Ozero__class_Ozero(U_508),U_510) )
& ( c_Orderings_Oord__class_Oless__eq(U_508,U_509,hAPP(c_Groups_Otimes__class_Otimes(U_508,U_511),U_510))
| ~ c_Orderings_Oord__class_Oless(U_508,c_Groups_Ozero__class_Ozero(U_508),U_510) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_508,c_Rings_Oinverse__class_Odivide(U_508,U_509,U_510),U_511) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_508) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
cnf(f_172_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_508,U_509,hAPP(c_Groups_Otimes__class_Otimes(U_508,U_511),U_510))
| ~ c_Orderings_Oord__class_Oless(U_508,c_Groups_Ozero__class_Ozero(U_508),U_510)
| ~ c_Orderings_Oord__class_Oless__eq(U_508,c_Rings_Oinverse__class_Odivide(U_508,U_509,U_510),U_511)
| ~ class_Fields_Olinordered__field__inverse__zero(U_508) ),
inference(clausify,[status(thm)],[f_172_2]) ).
cnf(f_172_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_508,hAPP(c_Groups_Otimes__class_Otimes(U_508,U_511),U_510),U_509)
| ~ c_Orderings_Oord__class_Oless(U_508,U_510,c_Groups_Ozero__class_Ozero(U_508))
| c_Orderings_Oord__class_Oless(U_508,c_Groups_Ozero__class_Ozero(U_508),U_510)
| ~ c_Orderings_Oord__class_Oless__eq(U_508,c_Rings_Oinverse__class_Odivide(U_508,U_509,U_510),U_511)
| ~ class_Fields_Olinordered__field__inverse__zero(U_508) ),
inference(clausify,[status(thm)],[f_172_2]) ).
cnf(f_172_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_508,c_Groups_Ozero__class_Ozero(U_508),U_511)
| c_Orderings_Oord__class_Oless(U_508,U_510,c_Groups_Ozero__class_Ozero(U_508))
| c_Orderings_Oord__class_Oless(U_508,c_Groups_Ozero__class_Ozero(U_508),U_510)
| ~ c_Orderings_Oord__class_Oless__eq(U_508,c_Rings_Oinverse__class_Odivide(U_508,U_509,U_510),U_511)
| ~ class_Fields_Olinordered__field__inverse__zero(U_508) ),
inference(clausify,[status(thm)],[f_172_2]) ).
cnf(f_172_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_508,c_Groups_Ozero__class_Ozero(U_508),U_510)
| c_Orderings_Oord__class_Oless(U_508,c_Groups_Ozero__class_Ozero(U_508),U_510)
| c_Orderings_Oord__class_Oless__eq(U_508,c_Rings_Oinverse__class_Odivide(U_508,U_509,U_510),U_511)
| ~ class_Fields_Olinordered__field__inverse__zero(U_508) ),
inference(clausify,[status(thm)],[f_172_2]) ).
cnf(f_172_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_508,U_510,c_Groups_Ozero__class_Ozero(U_508))
| c_Orderings_Oord__class_Oless(U_508,U_510,c_Groups_Ozero__class_Ozero(U_508))
| c_Orderings_Oord__class_Oless(U_508,c_Groups_Ozero__class_Ozero(U_508),U_510)
| c_Orderings_Oord__class_Oless__eq(U_508,c_Rings_Oinverse__class_Odivide(U_508,U_509,U_510),U_511)
| ~ class_Fields_Olinordered__field__inverse__zero(U_508) ),
inference(clausify,[status(thm)],[f_172_2]) ).
cnf(f_172_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_508,c_Groups_Ozero__class_Ozero(U_508),U_511)
| c_Orderings_Oord__class_Oless(U_508,U_510,c_Groups_Ozero__class_Ozero(U_508))
| c_Orderings_Oord__class_Oless(U_508,c_Groups_Ozero__class_Ozero(U_508),U_510)
| c_Orderings_Oord__class_Oless__eq(U_508,c_Rings_Oinverse__class_Odivide(U_508,U_509,U_510),U_511)
| ~ class_Fields_Olinordered__field__inverse__zero(U_508) ),
inference(clausify,[status(thm)],[f_172_2]) ).
cnf(f_172_9,plain,
( ~ c_Orderings_Oord__class_Oless(U_508,U_510,c_Groups_Ozero__class_Ozero(U_508))
| ~ c_Orderings_Oord__class_Oless__eq(U_508,hAPP(c_Groups_Otimes__class_Otimes(U_508,U_511),U_510),U_509)
| c_Orderings_Oord__class_Oless(U_508,c_Groups_Ozero__class_Ozero(U_508),U_510)
| c_Orderings_Oord__class_Oless__eq(U_508,c_Rings_Oinverse__class_Odivide(U_508,U_509,U_510),U_511)
| ~ class_Fields_Olinordered__field__inverse__zero(U_508) ),
inference(clausify,[status(thm)],[f_172_2]) ).
cnf(f_172_10,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_508,c_Groups_Ozero__class_Ozero(U_508),U_511)
| ~ c_Orderings_Oord__class_Oless__eq(U_508,hAPP(c_Groups_Otimes__class_Otimes(U_508,U_511),U_510),U_509)
| c_Orderings_Oord__class_Oless(U_508,c_Groups_Ozero__class_Ozero(U_508),U_510)
| c_Orderings_Oord__class_Oless__eq(U_508,c_Rings_Oinverse__class_Odivide(U_508,U_509,U_510),U_511)
| ~ class_Fields_Olinordered__field__inverse__zero(U_508) ),
inference(clausify,[status(thm)],[f_172_2]) ).
cnf(f_172_11,plain,
( ~ c_Orderings_Oord__class_Oless(U_508,c_Groups_Ozero__class_Ozero(U_508),U_510)
| ~ c_Orderings_Oord__class_Oless__eq(U_508,U_509,hAPP(c_Groups_Otimes__class_Otimes(U_508,U_511),U_510))
| c_Orderings_Oord__class_Oless__eq(U_508,c_Rings_Oinverse__class_Odivide(U_508,U_509,U_510),U_511)
| ~ class_Fields_Olinordered__field__inverse__zero(U_508) ),
inference(clausify,[status(thm)],[f_172_2]) ).
cnf(f_172_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_508,U_510,c_Groups_Ozero__class_Ozero(U_508))
| c_Orderings_Oord__class_Oless(U_508,U_510,c_Groups_Ozero__class_Ozero(U_508))
| ~ c_Orderings_Oord__class_Oless__eq(U_508,U_509,hAPP(c_Groups_Otimes__class_Otimes(U_508,U_511),U_510))
| c_Orderings_Oord__class_Oless__eq(U_508,c_Rings_Oinverse__class_Odivide(U_508,U_509,U_510),U_511)
| ~ class_Fields_Olinordered__field__inverse__zero(U_508) ),
inference(clausify,[status(thm)],[f_172_2]) ).
cnf(f_172_13,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_508,c_Groups_Ozero__class_Ozero(U_508),U_511)
| c_Orderings_Oord__class_Oless(U_508,U_510,c_Groups_Ozero__class_Ozero(U_508))
| ~ c_Orderings_Oord__class_Oless__eq(U_508,U_509,hAPP(c_Groups_Otimes__class_Otimes(U_508,U_511),U_510))
| c_Orderings_Oord__class_Oless__eq(U_508,c_Rings_Oinverse__class_Odivide(U_508,U_509,U_510),U_511)
| ~ class_Fields_Olinordered__field__inverse__zero(U_508) ),
inference(clausify,[status(thm)],[f_172_2]) ).
cnf(f_172_14,plain,
( ~ c_Orderings_Oord__class_Oless(U_508,U_510,c_Groups_Ozero__class_Ozero(U_508))
| ~ c_Orderings_Oord__class_Oless__eq(U_508,hAPP(c_Groups_Otimes__class_Otimes(U_508,U_511),U_510),U_509)
| ~ c_Orderings_Oord__class_Oless__eq(U_508,U_509,hAPP(c_Groups_Otimes__class_Otimes(U_508,U_511),U_510))
| c_Orderings_Oord__class_Oless__eq(U_508,c_Rings_Oinverse__class_Odivide(U_508,U_509,U_510),U_511)
| ~ class_Fields_Olinordered__field__inverse__zero(U_508) ),
inference(clausify,[status(thm)],[f_172_2]) ).
cnf(f_172_15,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_508,c_Groups_Ozero__class_Ozero(U_508),U_511)
| ~ c_Orderings_Oord__class_Oless__eq(U_508,hAPP(c_Groups_Otimes__class_Otimes(U_508,U_511),U_510),U_509)
| ~ c_Orderings_Oord__class_Oless__eq(U_508,U_509,hAPP(c_Groups_Otimes__class_Otimes(U_508,U_511),U_510))
| c_Orderings_Oord__class_Oless__eq(U_508,c_Rings_Oinverse__class_Odivide(U_508,U_509,U_510),U_511)
| ~ class_Fields_Olinordered__field__inverse__zero(U_508) ),
inference(clausify,[status(thm)],[f_172_2]) ).
fof(f_173_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__le__divide__eq]) ).
fof(f_173_2,plain,
! [U_515,U_514,U_513,U_512] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_512,U_514,c_Rings_Oinverse__class_Odivide(U_512,U_515,U_513))
| ~ c_Orderings_Oord__class_Oless__eq(U_512,hAPP(c_Groups_Otimes__class_Otimes(U_512,U_514),U_513),U_515) )
& ( c_Orderings_Oord__class_Oless__eq(U_512,hAPP(c_Groups_Otimes__class_Otimes(U_512,U_514),U_513),U_515)
| ~ c_Orderings_Oord__class_Oless__eq(U_512,U_514,c_Rings_Oinverse__class_Odivide(U_512,U_515,U_513)) ) )
| ~ c_Orderings_Oord__class_Oless(U_512,c_Groups_Ozero__class_Ozero(U_512),U_513)
| ~ class_Fields_Olinordered__field(U_512) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
cnf(f_173_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_512,hAPP(c_Groups_Otimes__class_Otimes(U_512,U_514),U_513),U_515)
| ~ c_Orderings_Oord__class_Oless__eq(U_512,U_514,c_Rings_Oinverse__class_Odivide(U_512,U_515,U_513))
| ~ c_Orderings_Oord__class_Oless(U_512,c_Groups_Ozero__class_Ozero(U_512),U_513)
| ~ class_Fields_Olinordered__field(U_512) ),
inference(clausify,[status(thm)],[f_173_2]) ).
cnf(f_173_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_512,U_514,c_Rings_Oinverse__class_Odivide(U_512,U_515,U_513))
| ~ c_Orderings_Oord__class_Oless__eq(U_512,hAPP(c_Groups_Otimes__class_Otimes(U_512,U_514),U_513),U_515)
| ~ c_Orderings_Oord__class_Oless(U_512,c_Groups_Ozero__class_Ozero(U_512),U_513)
| ~ class_Fields_Olinordered__field(U_512) ),
inference(clausify,[status(thm)],[f_173_2]) ).
fof(f_174_1,plain,
! [V_a_2,V_b_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__divide__le__eq]) ).
fof(f_174_2,plain,
! [U_519,U_518,U_517,U_516] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_516,c_Rings_Oinverse__class_Odivide(U_516,U_518,U_517),U_519)
| ~ c_Orderings_Oord__class_Oless__eq(U_516,U_518,hAPP(c_Groups_Otimes__class_Otimes(U_516,U_519),U_517)) )
& ( c_Orderings_Oord__class_Oless__eq(U_516,U_518,hAPP(c_Groups_Otimes__class_Otimes(U_516,U_519),U_517))
| ~ c_Orderings_Oord__class_Oless__eq(U_516,c_Rings_Oinverse__class_Odivide(U_516,U_518,U_517),U_519) ) )
| ~ c_Orderings_Oord__class_Oless(U_516,c_Groups_Ozero__class_Ozero(U_516),U_517)
| ~ class_Fields_Olinordered__field(U_516) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
cnf(f_174_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_516,U_518,hAPP(c_Groups_Otimes__class_Otimes(U_516,U_519),U_517))
| ~ c_Orderings_Oord__class_Oless__eq(U_516,c_Rings_Oinverse__class_Odivide(U_516,U_518,U_517),U_519)
| ~ c_Orderings_Oord__class_Oless(U_516,c_Groups_Ozero__class_Ozero(U_516),U_517)
| ~ class_Fields_Olinordered__field(U_516) ),
inference(clausify,[status(thm)],[f_174_2]) ).
cnf(f_174_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_516,c_Rings_Oinverse__class_Odivide(U_516,U_518,U_517),U_519)
| ~ c_Orderings_Oord__class_Oless__eq(U_516,U_518,hAPP(c_Groups_Otimes__class_Otimes(U_516,U_519),U_517))
| ~ c_Orderings_Oord__class_Oless(U_516,c_Groups_Ozero__class_Ozero(U_516),U_517)
| ~ class_Fields_Olinordered__field(U_516) ),
inference(clausify,[status(thm)],[f_174_2]) ).
fof(f_175_1,plain,
! [V_z,V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__le]) ).
fof(f_175_2,plain,
! [U_523,U_522,U_521,U_520] :
( c_Orderings_Oord__class_Oless__eq(U_520,c_Rings_Oinverse__class_Odivide(U_520,U_522,U_521),U_523)
| ~ c_Orderings_Oord__class_Oless__eq(U_520,U_522,hAPP(c_Groups_Otimes__class_Otimes(U_520,U_523),U_521))
| ~ c_Orderings_Oord__class_Oless(U_520,c_Groups_Ozero__class_Ozero(U_520),U_521)
| ~ class_Fields_Olinordered__field(U_520) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
cnf(f_175_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_520,c_Rings_Oinverse__class_Odivide(U_520,U_522,U_521),U_523)
| ~ c_Orderings_Oord__class_Oless__eq(U_520,U_522,hAPP(c_Groups_Otimes__class_Otimes(U_520,U_523),U_521))
| ~ c_Orderings_Oord__class_Oless(U_520,c_Groups_Ozero__class_Ozero(U_520),U_521)
| ~ class_Fields_Olinordered__field(U_520) ),
inference(clausify,[status(thm)],[f_175_2]) ).
fof(f_176_1,plain,
! [V_x,V_z,V_y,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y),V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__imp__le__div__pos]) ).
fof(f_176_2,plain,
! [U_527,U_526,U_525,U_524] :
( c_Orderings_Oord__class_Oless__eq(U_524,U_526,c_Rings_Oinverse__class_Odivide(U_524,U_527,U_525))
| ~ c_Orderings_Oord__class_Oless__eq(U_524,hAPP(c_Groups_Otimes__class_Otimes(U_524,U_526),U_525),U_527)
| ~ c_Orderings_Oord__class_Oless(U_524,c_Groups_Ozero__class_Ozero(U_524),U_525)
| ~ class_Fields_Olinordered__field(U_524) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
cnf(f_176_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_524,U_526,c_Rings_Oinverse__class_Odivide(U_524,U_527,U_525))
| ~ c_Orderings_Oord__class_Oless__eq(U_524,hAPP(c_Groups_Otimes__class_Otimes(U_524,U_526),U_525),U_527)
| ~ c_Orderings_Oord__class_Oless(U_524,c_Groups_Ozero__class_Ozero(U_524),U_525)
| ~ class_Fields_Olinordered__field(U_524) ),
inference(clausify,[status(thm)],[f_176_2]) ).
fof(f_177_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__le__divide__eq]) ).
fof(f_177_2,plain,
! [U_531,U_530,U_529,U_528] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_528,U_530,c_Rings_Oinverse__class_Odivide(U_528,U_531,U_529))
| ~ c_Orderings_Oord__class_Oless__eq(U_528,U_531,hAPP(c_Groups_Otimes__class_Otimes(U_528,U_530),U_529)) )
& ( c_Orderings_Oord__class_Oless__eq(U_528,U_531,hAPP(c_Groups_Otimes__class_Otimes(U_528,U_530),U_529))
| ~ c_Orderings_Oord__class_Oless__eq(U_528,U_530,c_Rings_Oinverse__class_Odivide(U_528,U_531,U_529)) ) )
| ~ c_Orderings_Oord__class_Oless(U_528,U_529,c_Groups_Ozero__class_Ozero(U_528))
| ~ class_Fields_Olinordered__field(U_528) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
cnf(f_177_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_528,U_531,hAPP(c_Groups_Otimes__class_Otimes(U_528,U_530),U_529))
| ~ c_Orderings_Oord__class_Oless__eq(U_528,U_530,c_Rings_Oinverse__class_Odivide(U_528,U_531,U_529))
| ~ c_Orderings_Oord__class_Oless(U_528,U_529,c_Groups_Ozero__class_Ozero(U_528))
| ~ class_Fields_Olinordered__field(U_528) ),
inference(clausify,[status(thm)],[f_177_2]) ).
cnf(f_177_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_528,U_530,c_Rings_Oinverse__class_Odivide(U_528,U_531,U_529))
| ~ c_Orderings_Oord__class_Oless__eq(U_528,U_531,hAPP(c_Groups_Otimes__class_Otimes(U_528,U_530),U_529))
| ~ c_Orderings_Oord__class_Oless(U_528,U_529,c_Groups_Ozero__class_Ozero(U_528))
| ~ class_Fields_Olinordered__field(U_528) ),
inference(clausify,[status(thm)],[f_177_2]) ).
fof(f_178_1,plain,
! [V_a_2,V_b_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),V_a_2) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__divide__le__eq]) ).
fof(f_178_2,plain,
! [U_535,U_534,U_533,U_532] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_532,c_Rings_Oinverse__class_Odivide(U_532,U_534,U_533),U_535)
| ~ c_Orderings_Oord__class_Oless__eq(U_532,hAPP(c_Groups_Otimes__class_Otimes(U_532,U_535),U_533),U_534) )
& ( c_Orderings_Oord__class_Oless__eq(U_532,hAPP(c_Groups_Otimes__class_Otimes(U_532,U_535),U_533),U_534)
| ~ c_Orderings_Oord__class_Oless__eq(U_532,c_Rings_Oinverse__class_Odivide(U_532,U_534,U_533),U_535) ) )
| ~ c_Orderings_Oord__class_Oless(U_532,U_533,c_Groups_Ozero__class_Ozero(U_532))
| ~ class_Fields_Olinordered__field(U_532) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
cnf(f_178_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_532,hAPP(c_Groups_Otimes__class_Otimes(U_532,U_535),U_533),U_534)
| ~ c_Orderings_Oord__class_Oless__eq(U_532,c_Rings_Oinverse__class_Odivide(U_532,U_534,U_533),U_535)
| ~ c_Orderings_Oord__class_Oless(U_532,U_533,c_Groups_Ozero__class_Ozero(U_532))
| ~ class_Fields_Olinordered__field(U_532) ),
inference(clausify,[status(thm)],[f_178_2]) ).
cnf(f_178_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_532,c_Rings_Oinverse__class_Odivide(U_532,U_534,U_533),U_535)
| ~ c_Orderings_Oord__class_Oless__eq(U_532,hAPP(c_Groups_Otimes__class_Otimes(U_532,U_535),U_533),U_534)
| ~ c_Orderings_Oord__class_Oless(U_532,U_533,c_Groups_Ozero__class_Ozero(U_532))
| ~ class_Fields_Olinordered__field(U_532) ),
inference(clausify,[status(thm)],[f_178_2]) ).
fof(f_179_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__left__mono]) ).
fof(f_179_2,plain,
! [U_539,U_538,U_537,U_536] :
( c_Orderings_Oord__class_Oless__eq(U_536,c_Rings_Oinverse__class_Odivide(U_536,U_539,U_538),c_Rings_Oinverse__class_Odivide(U_536,U_539,U_537))
| ~ c_Orderings_Oord__class_Oless(U_536,c_Groups_Ozero__class_Ozero(U_536),hAPP(c_Groups_Otimes__class_Otimes(U_536,U_538),U_537))
| ~ c_Orderings_Oord__class_Oless__eq(U_536,c_Groups_Ozero__class_Ozero(U_536),U_539)
| ~ c_Orderings_Oord__class_Oless__eq(U_536,U_537,U_538)
| ~ class_Fields_Olinordered__field(U_536) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
cnf(f_179_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_536,c_Rings_Oinverse__class_Odivide(U_536,U_539,U_538),c_Rings_Oinverse__class_Odivide(U_536,U_539,U_537))
| ~ c_Orderings_Oord__class_Oless(U_536,c_Groups_Ozero__class_Ozero(U_536),hAPP(c_Groups_Otimes__class_Otimes(U_536,U_538),U_537))
| ~ c_Orderings_Oord__class_Oless__eq(U_536,c_Groups_Ozero__class_Ozero(U_536),U_539)
| ~ c_Orderings_Oord__class_Oless__eq(U_536,U_537,U_538)
| ~ class_Fields_Olinordered__field(U_536) ),
inference(clausify,[status(thm)],[f_179_2]) ).
fof(f_180_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__left__mono__neg]) ).
fof(f_180_2,plain,
! [U_543,U_542,U_541,U_540] :
( c_Orderings_Oord__class_Oless__eq(U_540,c_Rings_Oinverse__class_Odivide(U_540,U_543,U_541),c_Rings_Oinverse__class_Odivide(U_540,U_543,U_542))
| ~ c_Orderings_Oord__class_Oless(U_540,c_Groups_Ozero__class_Ozero(U_540),hAPP(c_Groups_Otimes__class_Otimes(U_540,U_541),U_542))
| ~ c_Orderings_Oord__class_Oless__eq(U_540,U_543,c_Groups_Ozero__class_Ozero(U_540))
| ~ c_Orderings_Oord__class_Oless__eq(U_540,U_541,U_542)
| ~ class_Fields_Olinordered__field__inverse__zero(U_540) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
cnf(f_180_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_540,c_Rings_Oinverse__class_Odivide(U_540,U_543,U_541),c_Rings_Oinverse__class_Odivide(U_540,U_543,U_542))
| ~ c_Orderings_Oord__class_Oless(U_540,c_Groups_Ozero__class_Ozero(U_540),hAPP(c_Groups_Otimes__class_Otimes(U_540,U_541),U_542))
| ~ c_Orderings_Oord__class_Oless__eq(U_540,U_543,c_Groups_Ozero__class_Ozero(U_540))
| ~ c_Orderings_Oord__class_Oless__eq(U_540,U_541,U_542)
| ~ class_Fields_Olinordered__field__inverse__zero(U_540) ),
inference(clausify,[status(thm)],[f_180_2]) ).
fof(f_181_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_181_2,plain,
! [U_545,U_544] :
( c_Orderings_Oord__class_Oless__eq(U_544,U_545,U_545)
| ~ class_Orderings_Opreorder(U_544) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
cnf(f_181_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_544,U_545,U_545)
| ~ class_Orderings_Opreorder(U_544) ),
inference(clausify,[status(thm)],[f_181_2]) ).
fof(f_182_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_182_2,plain,
! [U_548,U_547,U_546] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_546,U_547,U_548)
| ~ c_Orderings_Oord__class_Oless__eq(U_546,U_548,U_547) )
& ( c_Orderings_Oord__class_Oless__eq(U_546,U_548,U_547)
| c_Orderings_Oord__class_Oless(U_546,U_547,U_548) ) )
| ~ class_Orderings_Olinorder(U_546) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
cnf(f_182_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_546,U_548,U_547)
| c_Orderings_Oord__class_Oless(U_546,U_547,U_548)
| ~ class_Orderings_Olinorder(U_546) ),
inference(clausify,[status(thm)],[f_182_2]) ).
cnf(f_182_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_546,U_547,U_548)
| ~ c_Orderings_Oord__class_Oless__eq(U_546,U_548,U_547)
| ~ class_Orderings_Olinorder(U_546) ),
inference(clausify,[status(thm)],[f_182_2]) ).
fof(f_183_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_183_2,plain,
! [U_551,U_550,U_549] :
( ( ( ~ c_Orderings_Oord__class_Oless__eq(U_549,U_550,U_551)
| ~ c_Orderings_Oord__class_Oless(U_549,U_551,U_550) )
& ( c_Orderings_Oord__class_Oless(U_549,U_551,U_550)
| c_Orderings_Oord__class_Oless__eq(U_549,U_550,U_551) ) )
| ~ class_Orderings_Olinorder(U_549) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
cnf(f_183_3,plain,
( c_Orderings_Oord__class_Oless(U_549,U_551,U_550)
| c_Orderings_Oord__class_Oless__eq(U_549,U_550,U_551)
| ~ class_Orderings_Olinorder(U_549) ),
inference(clausify,[status(thm)],[f_183_2]) ).
cnf(f_183_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_549,U_550,U_551)
| ~ c_Orderings_Oord__class_Oless(U_549,U_551,U_550)
| ~ class_Orderings_Olinorder(U_549) ),
inference(clausify,[status(thm)],[f_183_2]) ).
fof(f_184_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_184_2,plain,
! [U_554,U_553,U_552] :
( c_Orderings_Oord__class_Oless(U_552,U_554,U_553)
| c_Orderings_Oord__class_Oless__eq(U_552,U_553,U_554)
| ~ class_Orderings_Olinorder(U_552) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
cnf(f_184_3,plain,
( c_Orderings_Oord__class_Oless(U_552,U_554,U_553)
| c_Orderings_Oord__class_Oless__eq(U_552,U_553,U_554)
| ~ class_Orderings_Olinorder(U_552) ),
inference(clausify,[status(thm)],[f_184_2]) ).
fof(f_185_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_185_2,plain,
! [U_557,U_556,U_555] :
( ( ( c_Orderings_Oord__class_Oless(U_555,U_556,U_557)
| U_556 = U_557
| ~ c_Orderings_Oord__class_Oless__eq(U_555,U_556,U_557) )
& ( ( U_556 != U_557
& c_Orderings_Oord__class_Oless__eq(U_555,U_556,U_557) )
| ~ c_Orderings_Oord__class_Oless(U_555,U_556,U_557) ) )
| ~ class_Orderings_Oorder(U_555) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
cnf(f_185_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_555,U_556,U_557)
| ~ c_Orderings_Oord__class_Oless(U_555,U_556,U_557)
| ~ class_Orderings_Oorder(U_555) ),
inference(clausify,[status(thm)],[f_185_2]) ).
cnf(f_185_4,plain,
( U_556 != U_557
| ~ c_Orderings_Oord__class_Oless(U_555,U_556,U_557)
| ~ class_Orderings_Oorder(U_555) ),
inference(clausify,[status(thm)],[f_185_2]) ).
cnf(f_185_5,plain,
( c_Orderings_Oord__class_Oless(U_555,U_556,U_557)
| U_556 = U_557
| ~ c_Orderings_Oord__class_Oless__eq(U_555,U_556,U_557)
| ~ class_Orderings_Oorder(U_555) ),
inference(clausify,[status(thm)],[f_185_2]) ).
fof(f_186_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_186_2,plain,
! [U_560,U_559,U_558] :
( ( ( c_Orderings_Oord__class_Oless(U_558,U_559,U_560)
| c_Orderings_Oord__class_Oless__eq(U_558,U_560,U_559)
| ~ c_Orderings_Oord__class_Oless__eq(U_558,U_559,U_560) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(U_558,U_560,U_559)
& c_Orderings_Oord__class_Oless__eq(U_558,U_559,U_560) )
| ~ c_Orderings_Oord__class_Oless(U_558,U_559,U_560) ) )
| ~ class_Orderings_Opreorder(U_558) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
cnf(f_186_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_558,U_559,U_560)
| ~ c_Orderings_Oord__class_Oless(U_558,U_559,U_560)
| ~ class_Orderings_Opreorder(U_558) ),
inference(clausify,[status(thm)],[f_186_2]) ).
cnf(f_186_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_558,U_560,U_559)
| ~ c_Orderings_Oord__class_Oless(U_558,U_559,U_560)
| ~ class_Orderings_Opreorder(U_558) ),
inference(clausify,[status(thm)],[f_186_2]) ).
cnf(f_186_5,plain,
( c_Orderings_Oord__class_Oless(U_558,U_559,U_560)
| c_Orderings_Oord__class_Oless__eq(U_558,U_560,U_559)
| ~ c_Orderings_Oord__class_Oless__eq(U_558,U_559,U_560)
| ~ class_Orderings_Opreorder(U_558) ),
inference(clausify,[status(thm)],[f_186_2]) ).
fof(f_187_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_187_2,plain,
! [U_563,U_562,U_561] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_561,U_562,U_563)
| ( U_562 != U_563
& ~ c_Orderings_Oord__class_Oless(U_561,U_562,U_563) ) )
& ( U_562 = U_563
| c_Orderings_Oord__class_Oless(U_561,U_562,U_563)
| ~ c_Orderings_Oord__class_Oless__eq(U_561,U_562,U_563) ) )
| ~ class_Orderings_Oorder(U_561) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
cnf(f_187_3,plain,
( U_562 = U_563
| c_Orderings_Oord__class_Oless(U_561,U_562,U_563)
| ~ c_Orderings_Oord__class_Oless__eq(U_561,U_562,U_563)
| ~ class_Orderings_Oorder(U_561) ),
inference(clausify,[status(thm)],[f_187_2]) ).
cnf(f_187_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_561,U_562,U_563)
| c_Orderings_Oord__class_Oless__eq(U_561,U_562,U_563)
| ~ class_Orderings_Oorder(U_561) ),
inference(clausify,[status(thm)],[f_187_2]) ).
cnf(f_187_5,plain,
( U_562 != U_563
| c_Orderings_Oord__class_Oless__eq(U_561,U_562,U_563)
| ~ class_Orderings_Oorder(U_561) ),
inference(clausify,[status(thm)],[f_187_2]) ).
fof(f_188_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_188_2,plain,
! [U_566,U_565,U_564] :
( c_Orderings_Oord__class_Oless__eq(U_564,U_566,U_565)
| c_Orderings_Oord__class_Oless(U_564,U_565,U_566)
| ~ class_Orderings_Olinorder(U_564) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
cnf(f_188_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_564,U_566,U_565)
| c_Orderings_Oord__class_Oless(U_564,U_565,U_566)
| ~ class_Orderings_Olinorder(U_564) ),
inference(clausify,[status(thm)],[f_188_2]) ).
fof(f_189_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_189_2,plain,
! [U_569,U_568,U_567] :
( c_Orderings_Oord__class_Oless(U_567,U_569,U_568)
| c_Orderings_Oord__class_Oless__eq(U_567,U_568,U_569)
| ~ class_Orderings_Olinorder(U_567) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
cnf(f_189_3,plain,
( c_Orderings_Oord__class_Oless(U_567,U_569,U_568)
| c_Orderings_Oord__class_Oless__eq(U_567,U_568,U_569)
| ~ class_Orderings_Olinorder(U_567) ),
inference(clausify,[status(thm)],[f_189_2]) ).
fof(f_190_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_190_2,plain,
! [U_575,U_574,U_573,U_572] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_573,U_572),U_574,U_575)
| ? [U_571] : ~ c_Orderings_Oord__class_Oless__eq(U_572,hAPP(U_574,U_571),hAPP(U_575,U_571)) )
& ( ! [U_570] : c_Orderings_Oord__class_Oless__eq(U_572,hAPP(U_574,U_570),hAPP(U_575,U_570))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_573,U_572),U_574,U_575) ) )
| ~ class_Orderings_Oord(U_572) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
fof(f_190_3,plain,
! [U_575,U_574,U_573,U_572] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_573,U_572),U_574,U_575)
| ~ c_Orderings_Oord__class_Oless__eq(U_572,hAPP(U_574,sK4(U_575,U_574,U_573,U_572)),hAPP(U_575,sK4(U_575,U_574,U_573,U_572))) )
& ( ! [U_570] : c_Orderings_Oord__class_Oless__eq(U_572,hAPP(U_574,U_570),hAPP(U_575,U_570))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_573,U_572),U_574,U_575) ) )
| ~ class_Orderings_Oord(U_572) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_571,sK4(U_575,U_574,U_573,U_572))],[f_190_2]) ).
cnf(f_190_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_572,hAPP(U_574,U_570),hAPP(U_575,U_570))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_573,U_572),U_574,U_575)
| ~ class_Orderings_Oord(U_572) ),
inference(clausify,[status(thm)],[f_190_3]) ).
cnf(f_190_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_573,U_572),U_574,U_575)
| ~ c_Orderings_Oord__class_Oless__eq(U_572,hAPP(U_574,sK4(U_575,U_574,U_573,U_572)),hAPP(U_575,sK4(U_575,U_574,U_573,U_572)))
| ~ class_Orderings_Oord(U_572) ),
inference(clausify,[status(thm)],[f_190_3]) ).
fof(f_191_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_191_2,plain,
! [U_578,U_577,U_576] :
( c_Orderings_Oord__class_Oless__eq(U_576,U_578,U_577)
| c_Orderings_Oord__class_Oless__eq(U_576,U_577,U_578)
| ~ class_Orderings_Olinorder(U_576) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
cnf(f_191_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_576,U_578,U_577)
| c_Orderings_Oord__class_Oless__eq(U_576,U_577,U_578)
| ~ class_Orderings_Olinorder(U_576) ),
inference(clausify,[status(thm)],[f_191_2]) ).
fof(f_192_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_192_2,plain,
! [U_581,U_580,U_579] :
( ( ( U_580 = U_581
| ~ c_Orderings_Oord__class_Oless__eq(U_579,U_581,U_580)
| ~ c_Orderings_Oord__class_Oless__eq(U_579,U_580,U_581) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_579,U_581,U_580)
& c_Orderings_Oord__class_Oless__eq(U_579,U_580,U_581) )
| U_580 != U_581 ) )
| ~ class_Orderings_Oorder(U_579) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
cnf(f_192_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_579,U_580,U_581)
| U_580 != U_581
| ~ class_Orderings_Oorder(U_579) ),
inference(clausify,[status(thm)],[f_192_2]) ).
cnf(f_192_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_579,U_581,U_580)
| U_580 != U_581
| ~ class_Orderings_Oorder(U_579) ),
inference(clausify,[status(thm)],[f_192_2]) ).
cnf(f_192_5,plain,
( U_580 = U_581
| ~ c_Orderings_Oord__class_Oless__eq(U_579,U_581,U_580)
| ~ c_Orderings_Oord__class_Oless__eq(U_579,U_580,U_581)
| ~ class_Orderings_Oorder(U_579) ),
inference(clausify,[status(thm)],[f_192_2]) ).
fof(f_193_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_193_2,plain,
! [U_584,U_583,U_582] :
( c_Orderings_Oord__class_Oless__eq(U_582,U_583,U_584)
| U_583 != U_584
| ~ class_Orderings_Opreorder(U_582) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
cnf(f_193_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_582,U_583,U_584)
| U_583 != U_584
| ~ class_Orderings_Opreorder(U_582) ),
inference(clausify,[status(thm)],[f_193_2]) ).
fof(f_194_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_194_2,plain,
! [U_589,U_588,U_587,U_586,U_585] :
( c_Orderings_Oord__class_Oless__eq(U_585,hAPP(U_587,U_589),hAPP(U_588,U_589))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_586,U_585),U_587,U_588)
| ~ class_Orderings_Oord(U_585) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
cnf(f_194_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_585,hAPP(U_587,U_589),hAPP(U_588,U_589))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_586,U_585),U_587,U_588)
| ~ class_Orderings_Oord(U_585) ),
inference(clausify,[status(thm)],[f_194_2]) ).
fof(f_195_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_195_2,plain,
! [U_592,U_591,U_590] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_590,U_592,U_591)
| U_592 != U_591 )
& ( U_592 = U_591
| ~ c_Orderings_Oord__class_Oless__eq(U_590,U_592,U_591) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_590,U_591,U_592)
| ~ class_Orderings_Oorder(U_590) ),
inference(variable_rename,[status(thm)],[f_195_1]) ).
cnf(f_195_3,plain,
( U_592 = U_591
| ~ c_Orderings_Oord__class_Oless__eq(U_590,U_592,U_591)
| ~ c_Orderings_Oord__class_Oless__eq(U_590,U_591,U_592)
| ~ class_Orderings_Oorder(U_590) ),
inference(clausify,[status(thm)],[f_195_2]) ).
cnf(f_195_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_590,U_592,U_591)
| U_592 != U_591
| ~ c_Orderings_Oord__class_Oless__eq(U_590,U_591,U_592)
| ~ class_Orderings_Oorder(U_590) ),
inference(clausify,[status(thm)],[f_195_2]) ).
fof(f_196_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,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_196_2,plain,
! [U_596,U_595,U_594,U_593] :
( c_Orderings_Oord__class_Oless__eq(U_593,U_594,U_596)
| ~ c_Orderings_Oord__class_Oless__eq(U_593,U_595,U_596)
| U_594 != U_595
| ~ class_Orderings_Oord(U_593) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
cnf(f_196_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_593,U_594,U_596)
| ~ c_Orderings_Oord__class_Oless__eq(U_593,U_595,U_596)
| U_594 != U_595
| ~ class_Orderings_Oord(U_593) ),
inference(clausify,[status(thm)],[f_196_2]) ).
fof(f_197_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_197_2,plain,
! [U_600,U_599,U_598,U_597] :
( c_Orderings_Oord__class_Oless__eq(U_597,U_600,U_598)
| ~ c_Orderings_Oord__class_Oless__eq(U_597,U_600,U_599)
| U_598 != U_599
| ~ class_Orderings_Oorder(U_597) ),
inference(variable_rename,[status(thm)],[f_197_1]) ).
cnf(f_197_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_597,U_600,U_598)
| ~ c_Orderings_Oord__class_Oless__eq(U_597,U_600,U_599)
| U_598 != U_599
| ~ class_Orderings_Oorder(U_597) ),
inference(clausify,[status(thm)],[f_197_2]) ).
fof(f_198_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_198_2,plain,
! [U_604,U_603,U_602,U_601] :
( c_Orderings_Oord__class_Oless__eq(U_601,U_602,U_604)
| U_603 != U_604
| ~ c_Orderings_Oord__class_Oless__eq(U_601,U_602,U_603)
| ~ class_Orderings_Oord(U_601) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
cnf(f_198_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_601,U_602,U_604)
| U_603 != U_604
| ~ c_Orderings_Oord__class_Oless__eq(U_601,U_602,U_603)
| ~ class_Orderings_Oord(U_601) ),
inference(clausify,[status(thm)],[f_198_2]) ).
fof(f_199_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_199_2,plain,
! [U_608,U_607,U_606,U_605] :
( c_Orderings_Oord__class_Oless__eq(U_605,U_608,U_607)
| U_606 != U_608
| ~ c_Orderings_Oord__class_Oless__eq(U_605,U_606,U_607)
| ~ class_Orderings_Oorder(U_605) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
cnf(f_199_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_605,U_608,U_607)
| U_606 != U_608
| ~ c_Orderings_Oord__class_Oless__eq(U_605,U_606,U_607)
| ~ class_Orderings_Oorder(U_605) ),
inference(clausify,[status(thm)],[f_199_2]) ).
fof(f_200_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_200_2,plain,
! [U_611,U_610,U_609] :
( U_610 = U_611
| ~ c_Orderings_Oord__class_Oless__eq(U_609,U_611,U_610)
| ~ c_Orderings_Oord__class_Oless__eq(U_609,U_610,U_611)
| ~ class_Orderings_Oorder(U_609) ),
inference(variable_rename,[status(thm)],[f_200_1]) ).
cnf(f_200_3,plain,
( U_610 = U_611
| ~ c_Orderings_Oord__class_Oless__eq(U_609,U_611,U_610)
| ~ c_Orderings_Oord__class_Oless__eq(U_609,U_610,U_611)
| ~ class_Orderings_Oorder(U_609) ),
inference(clausify,[status(thm)],[f_200_2]) ).
fof(f_201_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_201_2,plain,
! [U_615,U_614,U_613,U_612] :
( c_Orderings_Oord__class_Oless__eq(U_612,U_613,U_615)
| ~ c_Orderings_Oord__class_Oless__eq(U_612,U_614,U_615)
| ~ c_Orderings_Oord__class_Oless__eq(U_612,U_613,U_614)
| ~ class_Orderings_Opreorder(U_612) ),
inference(variable_rename,[status(thm)],[f_201_1]) ).
cnf(f_201_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_612,U_613,U_615)
| ~ c_Orderings_Oord__class_Oless__eq(U_612,U_614,U_615)
| ~ c_Orderings_Oord__class_Oless__eq(U_612,U_613,U_614)
| ~ class_Orderings_Opreorder(U_612) ),
inference(clausify,[status(thm)],[f_201_2]) ).
fof(f_202_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_202_2,plain,
! [U_618,U_617,U_616] :
( U_618 = U_617
| ~ c_Orderings_Oord__class_Oless__eq(U_616,U_618,U_617)
| ~ c_Orderings_Oord__class_Oless__eq(U_616,U_617,U_618)
| ~ class_Orderings_Oorder(U_616) ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
cnf(f_202_3,plain,
( U_618 = U_617
| ~ c_Orderings_Oord__class_Oless__eq(U_616,U_618,U_617)
| ~ c_Orderings_Oord__class_Oless__eq(U_616,U_617,U_618)
| ~ class_Orderings_Oorder(U_616) ),
inference(clausify,[status(thm)],[f_202_2]) ).
fof(f_203_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_203_2,plain,
! [U_622,U_621,U_620,U_619] :
( c_Orderings_Oord__class_Oless__eq(U_619,U_622,U_621)
| ~ c_Orderings_Oord__class_Oless__eq(U_619,U_622,U_620)
| ~ c_Orderings_Oord__class_Oless__eq(U_619,U_620,U_621)
| ~ class_Orderings_Oorder(U_619) ),
inference(variable_rename,[status(thm)],[f_203_1]) ).
cnf(f_203_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_619,U_622,U_621)
| ~ c_Orderings_Oord__class_Oless__eq(U_619,U_622,U_620)
| ~ c_Orderings_Oord__class_Oless__eq(U_619,U_620,U_621)
| ~ class_Orderings_Oorder(U_619) ),
inference(clausify,[status(thm)],[f_203_2]) ).
fof(f_204_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_204_2,plain,
! [U_627,U_626,U_625,U_624,U_623] :
( c_Orderings_Oord__class_Oless__eq(U_623,hAPP(U_625,U_627),hAPP(U_626,U_627))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_624,U_623),U_625,U_626)
| ~ class_Orderings_Oord(U_623) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
cnf(f_204_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_623,hAPP(U_625,U_627),hAPP(U_626,U_627))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_624,U_623),U_625,U_626)
| ~ class_Orderings_Oord(U_623) ),
inference(clausify,[status(thm)],[f_204_2]) ).
fof(f_205_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_205_2,plain,
! [U_630,U_629,U_628] :
( c_Orderings_Oord__class_Oless__eq(U_628,U_630,U_629)
| c_Orderings_Oord__class_Oless__eq(U_628,U_629,U_630)
| ~ class_Orderings_Olinorder(U_628) ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
cnf(f_205_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_628,U_630,U_629)
| c_Orderings_Oord__class_Oless__eq(U_628,U_629,U_630)
| ~ class_Orderings_Olinorder(U_628) ),
inference(clausify,[status(thm)],[f_205_2]) ).
fof(f_206_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_206_2,plain,
! [U_633,U_632,U_631] :
( c_Orderings_Oord__class_Oless(U_631,U_633,U_632)
| U_632 = U_633
| c_Orderings_Oord__class_Oless(U_631,U_632,U_633)
| ~ class_Orderings_Olinorder(U_631) ),
inference(variable_rename,[status(thm)],[f_206_1]) ).
cnf(f_206_3,plain,
( c_Orderings_Oord__class_Oless(U_631,U_633,U_632)
| U_632 = U_633
| c_Orderings_Oord__class_Oless(U_631,U_632,U_633)
| ~ class_Orderings_Olinorder(U_631) ),
inference(clausify,[status(thm)],[f_206_2]) ).
fof(f_207_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_207_2,plain,
! [U_636,U_635,U_634] :
( ~ c_Orderings_Oord__class_Oless(U_634,U_636,U_635)
| ~ c_Orderings_Oord__class_Oless(U_634,U_635,U_636)
| ~ class_Orderings_Opreorder(U_634) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
cnf(f_207_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_634,U_636,U_635)
| ~ c_Orderings_Oord__class_Oless(U_634,U_635,U_636)
| ~ class_Orderings_Opreorder(U_634) ),
inference(clausify,[status(thm)],[f_207_2]) ).
fof(f_208_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_208_2,plain,
! [U_640,U_639,U_638,U_637] :
( c_Orderings_Oord__class_Oless(U_637,U_640,U_639)
| ~ c_Orderings_Oord__class_Oless(U_637,U_640,U_638)
| ~ c_Orderings_Oord__class_Oless(U_637,U_638,U_639)
| ~ class_Orderings_Oorder(U_637) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
cnf(f_208_3,plain,
( c_Orderings_Oord__class_Oless(U_637,U_640,U_639)
| ~ c_Orderings_Oord__class_Oless(U_637,U_640,U_638)
| ~ c_Orderings_Oord__class_Oless(U_637,U_638,U_639)
| ~ class_Orderings_Oorder(U_637) ),
inference(clausify,[status(thm)],[f_208_2]) ).
fof(f_209_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_209_2,plain,
! [U_644,U_643,U_642,U_641] :
( c_Orderings_Oord__class_Oless(U_641,U_642,U_644)
| ~ c_Orderings_Oord__class_Oless(U_641,U_643,U_644)
| ~ c_Orderings_Oord__class_Oless(U_641,U_642,U_643)
| ~ class_Orderings_Opreorder(U_641) ),
inference(variable_rename,[status(thm)],[f_209_1]) ).
cnf(f_209_3,plain,
( c_Orderings_Oord__class_Oless(U_641,U_642,U_644)
| ~ c_Orderings_Oord__class_Oless(U_641,U_643,U_644)
| ~ c_Orderings_Oord__class_Oless(U_641,U_642,U_643)
| ~ class_Orderings_Opreorder(U_641) ),
inference(clausify,[status(thm)],[f_209_2]) ).
fof(f_210_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_210_2,plain,
! [U_648,U_647,U_646,U_645] :
( c_Orderings_Oord__class_Oless(U_645,U_648,U_647)
| U_646 != U_648
| ~ c_Orderings_Oord__class_Oless(U_645,U_646,U_647)
| ~ class_Orderings_Oorder(U_645) ),
inference(variable_rename,[status(thm)],[f_210_1]) ).
cnf(f_210_3,plain,
( c_Orderings_Oord__class_Oless(U_645,U_648,U_647)
| U_646 != U_648
| ~ c_Orderings_Oord__class_Oless(U_645,U_646,U_647)
| ~ class_Orderings_Oorder(U_645) ),
inference(clausify,[status(thm)],[f_210_2]) ).
fof(f_211_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_211_2,plain,
! [U_652,U_651,U_650,U_649] :
( c_Orderings_Oord__class_Oless(U_649,U_650,U_652)
| U_651 != U_652
| ~ c_Orderings_Oord__class_Oless(U_649,U_650,U_651)
| ~ class_Orderings_Oord(U_649) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
cnf(f_211_3,plain,
( c_Orderings_Oord__class_Oless(U_649,U_650,U_652)
| U_651 != U_652
| ~ c_Orderings_Oord__class_Oless(U_649,U_650,U_651)
| ~ class_Orderings_Oord(U_649) ),
inference(clausify,[status(thm)],[f_211_2]) ).
fof(f_212_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_212_2,plain,
! [U_656,U_655,U_654,U_653] :
( c_Orderings_Oord__class_Oless(U_653,U_656,U_654)
| ~ c_Orderings_Oord__class_Oless(U_653,U_656,U_655)
| U_654 != U_655
| ~ class_Orderings_Oorder(U_653) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
cnf(f_212_3,plain,
( c_Orderings_Oord__class_Oless(U_653,U_656,U_654)
| ~ c_Orderings_Oord__class_Oless(U_653,U_656,U_655)
| U_654 != U_655
| ~ class_Orderings_Oorder(U_653) ),
inference(clausify,[status(thm)],[f_212_2]) ).
fof(f_213_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_213_2,plain,
! [U_660,U_659,U_658,U_657] :
( c_Orderings_Oord__class_Oless(U_657,U_658,U_660)
| ~ c_Orderings_Oord__class_Oless(U_657,U_659,U_660)
| U_658 != U_659
| ~ class_Orderings_Oord(U_657) ),
inference(variable_rename,[status(thm)],[f_213_1]) ).
cnf(f_213_3,plain,
( c_Orderings_Oord__class_Oless(U_657,U_658,U_660)
| ~ c_Orderings_Oord__class_Oless(U_657,U_659,U_660)
| U_658 != U_659
| ~ class_Orderings_Oord(U_657) ),
inference(clausify,[status(thm)],[f_213_2]) ).
fof(f_214_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_214_2,plain,
! [U_663,U_662,U_661] :
( ~ c_Orderings_Oord__class_Oless(U_661,U_663,U_662)
| ~ c_Orderings_Oord__class_Oless(U_661,U_662,U_663)
| ~ class_Orderings_Oorder(U_661) ),
inference(variable_rename,[status(thm)],[f_214_1]) ).
cnf(f_214_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_661,U_663,U_662)
| ~ c_Orderings_Oord__class_Oless(U_661,U_662,U_663)
| ~ class_Orderings_Oorder(U_661) ),
inference(clausify,[status(thm)],[f_214_2]) ).
fof(f_215_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_215_2,plain,
! [U_666,U_665,U_664] :
( ~ c_Orderings_Oord__class_Oless(U_664,U_666,U_665)
| ~ c_Orderings_Oord__class_Oless(U_664,U_665,U_666)
| ~ class_Orderings_Opreorder(U_664) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
cnf(f_215_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_664,U_666,U_665)
| ~ c_Orderings_Oord__class_Oless(U_664,U_665,U_666)
| ~ class_Orderings_Opreorder(U_664) ),
inference(clausify,[status(thm)],[f_215_2]) ).
fof(f_216_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_216_2,plain,
! [U_669,U_668,U_667] :
( U_669 != U_668
| ~ c_Orderings_Oord__class_Oless(U_667,U_668,U_669)
| ~ class_Orderings_Oorder(U_667) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
cnf(f_216_3,plain,
( U_669 != U_668
| ~ c_Orderings_Oord__class_Oless(U_667,U_668,U_669)
| ~ class_Orderings_Oorder(U_667) ),
inference(clausify,[status(thm)],[f_216_2]) ).
fof(f_217_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_217_2,plain,
! [U_672,U_671,U_670] :
( U_671 != U_672
| ~ c_Orderings_Oord__class_Oless(U_670,U_671,U_672)
| ~ class_Orderings_Oorder(U_670) ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
cnf(f_217_3,plain,
( U_671 != U_672
| ~ c_Orderings_Oord__class_Oless(U_670,U_671,U_672)
| ~ class_Orderings_Oorder(U_670) ),
inference(clausify,[status(thm)],[f_217_2]) ).
fof(f_218_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_218_2,plain,
! [U_675,U_674,U_673] :
( ~ c_Orderings_Oord__class_Oless(U_673,U_675,U_674)
| ~ c_Orderings_Oord__class_Oless(U_673,U_674,U_675)
| ~ class_Orderings_Opreorder(U_673) ),
inference(variable_rename,[status(thm)],[f_218_1]) ).
cnf(f_218_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_673,U_675,U_674)
| ~ c_Orderings_Oord__class_Oless(U_673,U_674,U_675)
| ~ class_Orderings_Opreorder(U_673) ),
inference(clausify,[status(thm)],[f_218_2]) ).
fof(f_219_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_219_2,plain,
! [U_678,U_677,U_676] :
( ~ c_Orderings_Oord__class_Oless(U_676,U_678,U_677)
| ~ c_Orderings_Oord__class_Oless(U_676,U_677,U_678)
| ~ class_Orderings_Opreorder(U_676) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
cnf(f_219_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_676,U_678,U_677)
| ~ c_Orderings_Oord__class_Oless(U_676,U_677,U_678)
| ~ class_Orderings_Opreorder(U_676) ),
inference(clausify,[status(thm)],[f_219_2]) ).
fof(f_220_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_220_2,plain,
! [U_681,U_680,U_679] :
( U_680 != U_681
| ~ c_Orderings_Oord__class_Oless(U_679,U_680,U_681)
| ~ class_Orderings_Oorder(U_679) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
cnf(f_220_3,plain,
( U_680 != U_681
| ~ c_Orderings_Oord__class_Oless(U_679,U_680,U_681)
| ~ class_Orderings_Oorder(U_679) ),
inference(clausify,[status(thm)],[f_220_2]) ).
fof(f_221_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_221_2,plain,
! [U_684,U_683,U_682] :
( c_Orderings_Oord__class_Oless(U_682,U_684,U_683)
| c_Orderings_Oord__class_Oless(U_682,U_683,U_684)
| U_683 = U_684
| ~ class_Orderings_Olinorder(U_682) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
cnf(f_221_3,plain,
( c_Orderings_Oord__class_Oless(U_682,U_684,U_683)
| c_Orderings_Oord__class_Oless(U_682,U_683,U_684)
| U_683 = U_684
| ~ class_Orderings_Olinorder(U_682) ),
inference(clausify,[status(thm)],[f_221_2]) ).
fof(f_222_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_222_2,plain,
! [U_687,U_686,U_685] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_685,U_687,U_686)
| U_687 != U_686 )
& ( U_687 = U_686
| c_Orderings_Oord__class_Oless(U_685,U_687,U_686) ) )
| c_Orderings_Oord__class_Oless(U_685,U_686,U_687)
| ~ class_Orderings_Olinorder(U_685) ),
inference(variable_rename,[status(thm)],[f_222_1]) ).
cnf(f_222_3,plain,
( U_687 = U_686
| c_Orderings_Oord__class_Oless(U_685,U_687,U_686)
| c_Orderings_Oord__class_Oless(U_685,U_686,U_687)
| ~ class_Orderings_Olinorder(U_685) ),
inference(clausify,[status(thm)],[f_222_2]) ).
cnf(f_222_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_685,U_687,U_686)
| U_687 != U_686
| c_Orderings_Oord__class_Oless(U_685,U_686,U_687)
| ~ class_Orderings_Olinorder(U_685) ),
inference(clausify,[status(thm)],[f_222_2]) ).
fof(f_223_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_223_2,plain,
! [U_690,U_689,U_688] :
( c_Orderings_Oord__class_Oless(U_688,U_690,U_689)
| U_689 = U_690
| c_Orderings_Oord__class_Oless(U_688,U_689,U_690)
| ~ class_Orderings_Olinorder(U_688) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
cnf(f_223_3,plain,
( c_Orderings_Oord__class_Oless(U_688,U_690,U_689)
| U_689 = U_690
| c_Orderings_Oord__class_Oless(U_688,U_689,U_690)
| ~ class_Orderings_Olinorder(U_688) ),
inference(clausify,[status(thm)],[f_223_2]) ).
fof(f_224_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_224_2,plain,
! [U_693,U_692,U_691] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_691,U_692,U_693)
| ( U_692 != U_693
& ~ c_Orderings_Oord__class_Oless(U_691,U_693,U_692) ) )
& ( U_692 = U_693
| c_Orderings_Oord__class_Oless(U_691,U_693,U_692)
| c_Orderings_Oord__class_Oless(U_691,U_692,U_693) ) )
| ~ class_Orderings_Olinorder(U_691) ),
inference(variable_rename,[status(thm)],[f_224_1]) ).
cnf(f_224_3,plain,
( U_692 = U_693
| c_Orderings_Oord__class_Oless(U_691,U_693,U_692)
| c_Orderings_Oord__class_Oless(U_691,U_692,U_693)
| ~ class_Orderings_Olinorder(U_691) ),
inference(clausify,[status(thm)],[f_224_2]) ).
cnf(f_224_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_691,U_693,U_692)
| ~ c_Orderings_Oord__class_Oless(U_691,U_692,U_693)
| ~ class_Orderings_Olinorder(U_691) ),
inference(clausify,[status(thm)],[f_224_2]) ).
cnf(f_224_5,plain,
( U_692 != U_693
| ~ c_Orderings_Oord__class_Oless(U_691,U_692,U_693)
| ~ class_Orderings_Olinorder(U_691) ),
inference(clausify,[status(thm)],[f_224_2]) ).
fof(f_225_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_225_2,plain,
! [U_696,U_695,U_694] :
( ( ( U_695 != U_696
| ( ~ c_Orderings_Oord__class_Oless(U_694,U_696,U_695)
& ~ c_Orderings_Oord__class_Oless(U_694,U_695,U_696) ) )
& ( c_Orderings_Oord__class_Oless(U_694,U_696,U_695)
| c_Orderings_Oord__class_Oless(U_694,U_695,U_696)
| U_695 = U_696 ) )
| ~ class_Orderings_Olinorder(U_694) ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
cnf(f_225_3,plain,
( c_Orderings_Oord__class_Oless(U_694,U_696,U_695)
| c_Orderings_Oord__class_Oless(U_694,U_695,U_696)
| U_695 = U_696
| ~ class_Orderings_Olinorder(U_694) ),
inference(clausify,[status(thm)],[f_225_2]) ).
cnf(f_225_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_694,U_695,U_696)
| U_695 != U_696
| ~ class_Orderings_Olinorder(U_694) ),
inference(clausify,[status(thm)],[f_225_2]) ).
cnf(f_225_5,plain,
( ~ c_Orderings_Oord__class_Oless(U_694,U_696,U_695)
| U_695 != U_696
| ~ class_Orderings_Olinorder(U_694) ),
inference(clausify,[status(thm)],[f_225_2]) ).
fof(f_226_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_226_2,plain,
! [U_698,U_697] :
( ~ c_Orderings_Oord__class_Oless(U_697,U_698,U_698)
| ~ class_Orderings_Opreorder(U_697) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
cnf(f_226_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_697,U_698,U_698)
| ~ class_Orderings_Opreorder(U_697) ),
inference(clausify,[status(thm)],[f_226_2]) ).
fof(f_227_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_227_2,plain,
! [U_702,U_701,U_700,U_699] :
( c_Orderings_Oord__class_Oless(U_699,U_702,U_701)
| ~ c_Orderings_Oord__class_Oless(U_699,U_702,U_700)
| ~ c_Orderings_Oord__class_Oless__eq(U_699,U_700,U_701)
| ~ class_Orderings_Oorder(U_699) ),
inference(variable_rename,[status(thm)],[f_227_1]) ).
cnf(f_227_3,plain,
( c_Orderings_Oord__class_Oless(U_699,U_702,U_701)
| ~ c_Orderings_Oord__class_Oless(U_699,U_702,U_700)
| ~ c_Orderings_Oord__class_Oless__eq(U_699,U_700,U_701)
| ~ class_Orderings_Oorder(U_699) ),
inference(clausify,[status(thm)],[f_227_2]) ).
fof(f_228_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_228_2,plain,
! [U_706,U_705,U_704,U_703] :
( c_Orderings_Oord__class_Oless(U_703,U_704,U_706)
| ~ c_Orderings_Oord__class_Oless(U_703,U_705,U_706)
| ~ c_Orderings_Oord__class_Oless__eq(U_703,U_704,U_705)
| ~ class_Orderings_Opreorder(U_703) ),
inference(variable_rename,[status(thm)],[f_228_1]) ).
cnf(f_228_3,plain,
( c_Orderings_Oord__class_Oless(U_703,U_704,U_706)
| ~ c_Orderings_Oord__class_Oless(U_703,U_705,U_706)
| ~ c_Orderings_Oord__class_Oless__eq(U_703,U_704,U_705)
| ~ class_Orderings_Opreorder(U_703) ),
inference(clausify,[status(thm)],[f_228_2]) ).
fof(f_229_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_229_2,plain,
! [U_710,U_709,U_708,U_707] :
( c_Orderings_Oord__class_Oless(U_707,U_710,U_709)
| ~ c_Orderings_Oord__class_Oless__eq(U_707,U_710,U_708)
| ~ c_Orderings_Oord__class_Oless(U_707,U_708,U_709)
| ~ class_Orderings_Oorder(U_707) ),
inference(variable_rename,[status(thm)],[f_229_1]) ).
cnf(f_229_3,plain,
( c_Orderings_Oord__class_Oless(U_707,U_710,U_709)
| ~ c_Orderings_Oord__class_Oless__eq(U_707,U_710,U_708)
| ~ c_Orderings_Oord__class_Oless(U_707,U_708,U_709)
| ~ class_Orderings_Oorder(U_707) ),
inference(clausify,[status(thm)],[f_229_2]) ).
fof(f_230_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_230_2,plain,
! [U_714,U_713,U_712,U_711] :
( c_Orderings_Oord__class_Oless(U_711,U_712,U_714)
| ~ c_Orderings_Oord__class_Oless__eq(U_711,U_713,U_714)
| ~ c_Orderings_Oord__class_Oless(U_711,U_712,U_713)
| ~ class_Orderings_Opreorder(U_711) ),
inference(variable_rename,[status(thm)],[f_230_1]) ).
cnf(f_230_3,plain,
( c_Orderings_Oord__class_Oless(U_711,U_712,U_714)
| ~ c_Orderings_Oord__class_Oless__eq(U_711,U_713,U_714)
| ~ c_Orderings_Oord__class_Oless(U_711,U_712,U_713)
| ~ class_Orderings_Opreorder(U_711) ),
inference(clausify,[status(thm)],[f_230_2]) ).
fof(f_231_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_231_2,plain,
! [U_717,U_716,U_715] :
( c_Orderings_Oord__class_Oless(U_715,U_716,U_717)
| U_717 = U_716
| ~ c_Orderings_Oord__class_Oless__eq(U_715,U_716,U_717)
| ~ class_Orderings_Oorder(U_715) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
cnf(f_231_3,plain,
( c_Orderings_Oord__class_Oless(U_715,U_716,U_717)
| U_717 = U_716
| ~ c_Orderings_Oord__class_Oless__eq(U_715,U_716,U_717)
| ~ class_Orderings_Oorder(U_715) ),
inference(clausify,[status(thm)],[f_231_2]) ).
fof(f_232_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_232_2,plain,
! [U_720,U_719,U_718] :
( c_Orderings_Oord__class_Oless(U_718,U_719,U_720)
| U_719 = U_720
| ~ c_Orderings_Oord__class_Oless__eq(U_718,U_719,U_720)
| ~ class_Orderings_Oorder(U_718) ),
inference(variable_rename,[status(thm)],[f_232_1]) ).
cnf(f_232_3,plain,
( c_Orderings_Oord__class_Oless(U_718,U_719,U_720)
| U_719 = U_720
| ~ c_Orderings_Oord__class_Oless__eq(U_718,U_719,U_720)
| ~ class_Orderings_Oorder(U_718) ),
inference(clausify,[status(thm)],[f_232_2]) ).
fof(f_233_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_233_2,plain,
! [U_723,U_722,U_721] :
( U_722 = U_723
| c_Orderings_Oord__class_Oless(U_721,U_722,U_723)
| ~ c_Orderings_Oord__class_Oless__eq(U_721,U_722,U_723)
| ~ class_Orderings_Oorder(U_721) ),
inference(variable_rename,[status(thm)],[f_233_1]) ).
cnf(f_233_3,plain,
( U_722 = U_723
| c_Orderings_Oord__class_Oless(U_721,U_722,U_723)
| ~ c_Orderings_Oord__class_Oless__eq(U_721,U_722,U_723)
| ~ class_Orderings_Oorder(U_721) ),
inference(clausify,[status(thm)],[f_233_2]) ).
fof(f_234_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_234_2,plain,
! [U_726,U_725,U_724] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_724,U_725,U_726)
| U_725 != U_726 )
& ( U_725 = U_726
| c_Orderings_Oord__class_Oless(U_724,U_725,U_726) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_724,U_725,U_726)
| ~ class_Orderings_Olinorder(U_724) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
cnf(f_234_3,plain,
( U_725 = U_726
| c_Orderings_Oord__class_Oless(U_724,U_725,U_726)
| ~ c_Orderings_Oord__class_Oless__eq(U_724,U_725,U_726)
| ~ class_Orderings_Olinorder(U_724) ),
inference(clausify,[status(thm)],[f_234_2]) ).
cnf(f_234_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_724,U_725,U_726)
| U_725 != U_726
| ~ c_Orderings_Oord__class_Oless__eq(U_724,U_725,U_726)
| ~ class_Orderings_Olinorder(U_724) ),
inference(clausify,[status(thm)],[f_234_2]) ).
fof(f_235_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_235_2,plain,
! [U_729,U_728,U_727] :
( c_Orderings_Oord__class_Oless__eq(U_727,U_728,U_729)
| ~ c_Orderings_Oord__class_Oless(U_727,U_728,U_729)
| ~ class_Orderings_Opreorder(U_727) ),
inference(variable_rename,[status(thm)],[f_235_1]) ).
cnf(f_235_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_727,U_728,U_729)
| ~ c_Orderings_Oord__class_Oless(U_727,U_728,U_729)
| ~ class_Orderings_Opreorder(U_727) ),
inference(clausify,[status(thm)],[f_235_2]) ).
fof(f_236_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_236_2,plain,
! [U_732,U_731,U_730] :
( ~ c_Orderings_Oord__class_Oless(U_730,U_732,U_731)
| ~ c_Orderings_Oord__class_Oless__eq(U_730,U_731,U_732)
| ~ class_Orderings_Olinorder(U_730) ),
inference(variable_rename,[status(thm)],[f_236_1]) ).
cnf(f_236_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_730,U_732,U_731)
| ~ c_Orderings_Oord__class_Oless__eq(U_730,U_731,U_732)
| ~ class_Orderings_Olinorder(U_730) ),
inference(clausify,[status(thm)],[f_236_2]) ).
fof(f_237_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_237_2,plain,
! [U_735,U_734,U_733] :
( c_Orderings_Oord__class_Oless(U_733,U_735,U_734)
| ~ c_Orderings_Oord__class_Oless__eq(U_733,U_735,U_734)
| U_734 = U_735
| ~ class_Orderings_Oorder(U_733) ),
inference(variable_rename,[status(thm)],[f_237_1]) ).
cnf(f_237_3,plain,
( c_Orderings_Oord__class_Oless(U_733,U_735,U_734)
| ~ c_Orderings_Oord__class_Oless__eq(U_733,U_735,U_734)
| U_734 = U_735
| ~ class_Orderings_Oorder(U_733) ),
inference(clausify,[status(thm)],[f_237_2]) ).
fof(f_238_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_238_2,plain,
! [U_738,U_737,U_736] :
( c_Orderings_Oord__class_Oless(U_736,U_737,U_738)
| ~ c_Orderings_Oord__class_Oless__eq(U_736,U_737,U_738)
| U_737 = U_738
| ~ class_Orderings_Oorder(U_736) ),
inference(variable_rename,[status(thm)],[f_238_1]) ).
cnf(f_238_3,plain,
( c_Orderings_Oord__class_Oless(U_736,U_737,U_738)
| ~ c_Orderings_Oord__class_Oless__eq(U_736,U_737,U_738)
| U_737 = U_738
| ~ class_Orderings_Oorder(U_736) ),
inference(clausify,[status(thm)],[f_238_2]) ).
fof(f_239_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_239_2,plain,
! [U_741,U_740,U_739] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_739,U_740,U_741)
| U_740 != U_741 )
& ( U_740 = U_741
| ~ c_Orderings_Oord__class_Oless__eq(U_739,U_740,U_741) ) )
| c_Orderings_Oord__class_Oless(U_739,U_740,U_741)
| ~ class_Orderings_Olinorder(U_739) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
cnf(f_239_3,plain,
( U_740 = U_741
| ~ c_Orderings_Oord__class_Oless__eq(U_739,U_740,U_741)
| c_Orderings_Oord__class_Oless(U_739,U_740,U_741)
| ~ class_Orderings_Olinorder(U_739) ),
inference(clausify,[status(thm)],[f_239_2]) ).
cnf(f_239_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_739,U_740,U_741)
| U_740 != U_741
| c_Orderings_Oord__class_Oless(U_739,U_740,U_741)
| ~ class_Orderings_Olinorder(U_739) ),
inference(clausify,[status(thm)],[f_239_2]) ).
fof(f_240_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ? [B_z] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,B_z),V_x),V_y)
& c_Orderings_Oord__class_Oless(T_a,B_z,c_Groups_Oone__class_Oone(T_a))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),B_z) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_field__le__mult__one__interval]) ).
fof(f_240_2,plain,
! [U_745,U_744,U_743] :
( c_Orderings_Oord__class_Oless__eq(U_743,U_744,U_745)
| ? [U_742] :
( ~ c_Orderings_Oord__class_Oless__eq(U_743,hAPP(c_Groups_Otimes__class_Otimes(U_743,U_742),U_744),U_745)
& c_Orderings_Oord__class_Oless(U_743,U_742,c_Groups_Oone__class_Oone(U_743))
& c_Orderings_Oord__class_Oless(U_743,c_Groups_Ozero__class_Ozero(U_743),U_742) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_743) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
fof(f_240_3,plain,
! [U_745,U_744,U_743] :
( c_Orderings_Oord__class_Oless__eq(U_743,U_744,U_745)
| ( ~ c_Orderings_Oord__class_Oless__eq(U_743,hAPP(c_Groups_Otimes__class_Otimes(U_743,sK5(U_745,U_744,U_743)),U_744),U_745)
& c_Orderings_Oord__class_Oless(U_743,sK5(U_745,U_744,U_743),c_Groups_Oone__class_Oone(U_743))
& c_Orderings_Oord__class_Oless(U_743,c_Groups_Ozero__class_Ozero(U_743),sK5(U_745,U_744,U_743)) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_743) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_742,sK5(U_745,U_744,U_743))],[f_240_2]) ).
cnf(f_240_4,plain,
( c_Orderings_Oord__class_Oless(U_743,c_Groups_Ozero__class_Ozero(U_743),sK5(U_745,U_744,U_743))
| c_Orderings_Oord__class_Oless__eq(U_743,U_744,U_745)
| ~ class_Fields_Olinordered__field__inverse__zero(U_743) ),
inference(clausify,[status(thm)],[f_240_3]) ).
cnf(f_240_5,plain,
( c_Orderings_Oord__class_Oless(U_743,sK5(U_745,U_744,U_743),c_Groups_Oone__class_Oone(U_743))
| c_Orderings_Oord__class_Oless__eq(U_743,U_744,U_745)
| ~ class_Fields_Olinordered__field__inverse__zero(U_743) ),
inference(clausify,[status(thm)],[f_240_3]) ).
cnf(f_240_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_743,hAPP(c_Groups_Otimes__class_Otimes(U_743,sK5(U_745,U_744,U_743)),U_744),U_745)
| c_Orderings_Oord__class_Oless__eq(U_743,U_744,U_745)
| ~ class_Fields_Olinordered__field__inverse__zero(U_743) ),
inference(clausify,[status(thm)],[f_240_3]) ).
fof(f_241_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(c_Groups_Otimes__class_Otimes(T_a,V_u),V_x),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_241_2,plain,
! [U_751,U_750,U_749,U_748,U_747,U_746] :
( c_Orderings_Oord__class_Oless(U_746,c_Groups_Oplus__class_Oplus(U_746,hAPP(c_Groups_Otimes__class_Otimes(U_746,U_750),U_747),hAPP(c_Groups_Otimes__class_Otimes(U_746,U_751),U_749)),U_748)
| c_Groups_Oplus__class_Oplus(U_746,U_750,U_751) != c_Groups_Oone__class_Oone(U_746)
| ~ c_Orderings_Oord__class_Oless__eq(U_746,c_Groups_Ozero__class_Ozero(U_746),U_751)
| ~ c_Orderings_Oord__class_Oless__eq(U_746,c_Groups_Ozero__class_Ozero(U_746),U_750)
| ~ c_Orderings_Oord__class_Oless(U_746,U_749,U_748)
| ~ c_Orderings_Oord__class_Oless(U_746,U_747,U_748)
| ~ class_Rings_Olinordered__semiring__1__strict(U_746) ),
inference(variable_rename,[status(thm)],[f_241_1]) ).
cnf(f_241_3,plain,
( c_Orderings_Oord__class_Oless(U_746,c_Groups_Oplus__class_Oplus(U_746,hAPP(c_Groups_Otimes__class_Otimes(U_746,U_750),U_747),hAPP(c_Groups_Otimes__class_Otimes(U_746,U_751),U_749)),U_748)
| c_Groups_Oplus__class_Oplus(U_746,U_750,U_751) != c_Groups_Oone__class_Oone(U_746)
| ~ c_Orderings_Oord__class_Oless__eq(U_746,c_Groups_Ozero__class_Ozero(U_746),U_751)
| ~ c_Orderings_Oord__class_Oless__eq(U_746,c_Groups_Ozero__class_Ozero(U_746),U_750)
| ~ c_Orderings_Oord__class_Oless(U_746,U_749,U_748)
| ~ c_Orderings_Oord__class_Oless(U_746,U_747,U_748)
| ~ class_Rings_Olinordered__semiring__1__strict(U_746) ),
inference(clausify,[status(thm)],[f_241_2]) ).
fof(f_242_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(c_Groups_Otimes__class_Otimes(T_a,V_u),V_x),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_242_2,plain,
! [U_757,U_756,U_755,U_754,U_753,U_752] :
( c_Orderings_Oord__class_Oless__eq(U_752,c_Groups_Oplus__class_Oplus(U_752,hAPP(c_Groups_Otimes__class_Otimes(U_752,U_756),U_753),hAPP(c_Groups_Otimes__class_Otimes(U_752,U_757),U_755)),U_754)
| c_Groups_Oplus__class_Oplus(U_752,U_756,U_757) != c_Groups_Oone__class_Oone(U_752)
| ~ c_Orderings_Oord__class_Oless__eq(U_752,c_Groups_Ozero__class_Ozero(U_752),U_757)
| ~ c_Orderings_Oord__class_Oless__eq(U_752,c_Groups_Ozero__class_Ozero(U_752),U_756)
| ~ c_Orderings_Oord__class_Oless__eq(U_752,U_755,U_754)
| ~ c_Orderings_Oord__class_Oless__eq(U_752,U_753,U_754)
| ~ class_Rings_Olinordered__semiring__1(U_752) ),
inference(variable_rename,[status(thm)],[f_242_1]) ).
cnf(f_242_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_752,c_Groups_Oplus__class_Oplus(U_752,hAPP(c_Groups_Otimes__class_Otimes(U_752,U_756),U_753),hAPP(c_Groups_Otimes__class_Otimes(U_752,U_757),U_755)),U_754)
| c_Groups_Oplus__class_Oplus(U_752,U_756,U_757) != c_Groups_Oone__class_Oone(U_752)
| ~ c_Orderings_Oord__class_Oless__eq(U_752,c_Groups_Ozero__class_Ozero(U_752),U_757)
| ~ c_Orderings_Oord__class_Oless__eq(U_752,c_Groups_Ozero__class_Ozero(U_752),U_756)
| ~ c_Orderings_Oord__class_Oless__eq(U_752,U_755,U_754)
| ~ c_Orderings_Oord__class_Oless__eq(U_752,U_753,U_754)
| ~ class_Rings_Olinordered__semiring__1(U_752) ),
inference(clausify,[status(thm)],[f_242_2]) ).
fof(f_243_1,plain,
! [V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) )
& ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__le__inverse__iff]) ).
fof(f_243_2,plain,
! [U_759,U_758] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_758,c_Groups_Oone__class_Oone(U_758),c_Rings_Oinverse__class_Oinverse(U_758,U_759))
| ~ c_Orderings_Oord__class_Oless__eq(U_758,U_759,c_Groups_Oone__class_Oone(U_758))
| ~ c_Orderings_Oord__class_Oless(U_758,c_Groups_Ozero__class_Ozero(U_758),U_759) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_758,U_759,c_Groups_Oone__class_Oone(U_758))
& c_Orderings_Oord__class_Oless(U_758,c_Groups_Ozero__class_Ozero(U_758),U_759) )
| ~ c_Orderings_Oord__class_Oless__eq(U_758,c_Groups_Oone__class_Oone(U_758),c_Rings_Oinverse__class_Oinverse(U_758,U_759)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_758) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
cnf(f_243_3,plain,
( c_Orderings_Oord__class_Oless(U_758,c_Groups_Ozero__class_Ozero(U_758),U_759)
| ~ c_Orderings_Oord__class_Oless__eq(U_758,c_Groups_Oone__class_Oone(U_758),c_Rings_Oinverse__class_Oinverse(U_758,U_759))
| ~ class_Fields_Olinordered__field__inverse__zero(U_758) ),
inference(clausify,[status(thm)],[f_243_2]) ).
cnf(f_243_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_758,U_759,c_Groups_Oone__class_Oone(U_758))
| ~ c_Orderings_Oord__class_Oless__eq(U_758,c_Groups_Oone__class_Oone(U_758),c_Rings_Oinverse__class_Oinverse(U_758,U_759))
| ~ class_Fields_Olinordered__field__inverse__zero(U_758) ),
inference(clausify,[status(thm)],[f_243_2]) ).
cnf(f_243_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_758,c_Groups_Oone__class_Oone(U_758),c_Rings_Oinverse__class_Oinverse(U_758,U_759))
| ~ c_Orderings_Oord__class_Oless__eq(U_758,U_759,c_Groups_Oone__class_Oone(U_758))
| ~ c_Orderings_Oord__class_Oless(U_758,c_Groups_Ozero__class_Ozero(U_758),U_759)
| ~ class_Fields_Olinordered__field__inverse__zero(U_758) ),
inference(clausify,[status(thm)],[f_243_2]) ).
fof(f_244_1,plain,
! [V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
| ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2)
& ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)) ) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__less__1__iff]) ).
fof(f_244_2,plain,
! [U_761,U_760] :
( ( ( c_Orderings_Oord__class_Oless(U_760,c_Rings_Oinverse__class_Oinverse(U_760,U_761),c_Groups_Oone__class_Oone(U_760))
| ( ~ c_Orderings_Oord__class_Oless(U_760,c_Groups_Oone__class_Oone(U_760),U_761)
& ~ c_Orderings_Oord__class_Oless__eq(U_760,U_761,c_Groups_Ozero__class_Ozero(U_760)) ) )
& ( c_Orderings_Oord__class_Oless(U_760,c_Groups_Oone__class_Oone(U_760),U_761)
| c_Orderings_Oord__class_Oless__eq(U_760,U_761,c_Groups_Ozero__class_Ozero(U_760))
| ~ c_Orderings_Oord__class_Oless(U_760,c_Rings_Oinverse__class_Oinverse(U_760,U_761),c_Groups_Oone__class_Oone(U_760)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_760) ),
inference(variable_rename,[status(thm)],[f_244_1]) ).
cnf(f_244_3,plain,
( c_Orderings_Oord__class_Oless(U_760,c_Groups_Oone__class_Oone(U_760),U_761)
| c_Orderings_Oord__class_Oless__eq(U_760,U_761,c_Groups_Ozero__class_Ozero(U_760))
| ~ c_Orderings_Oord__class_Oless(U_760,c_Rings_Oinverse__class_Oinverse(U_760,U_761),c_Groups_Oone__class_Oone(U_760))
| ~ class_Fields_Olinordered__field__inverse__zero(U_760) ),
inference(clausify,[status(thm)],[f_244_2]) ).
cnf(f_244_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_760,U_761,c_Groups_Ozero__class_Ozero(U_760))
| c_Orderings_Oord__class_Oless(U_760,c_Rings_Oinverse__class_Oinverse(U_760,U_761),c_Groups_Oone__class_Oone(U_760))
| ~ class_Fields_Olinordered__field__inverse__zero(U_760) ),
inference(clausify,[status(thm)],[f_244_2]) ).
cnf(f_244_5,plain,
( ~ c_Orderings_Oord__class_Oless(U_760,c_Groups_Oone__class_Oone(U_760),U_761)
| c_Orderings_Oord__class_Oless(U_760,c_Rings_Oinverse__class_Oinverse(U_760,U_761),c_Groups_Oone__class_Oone(U_760))
| ~ class_Fields_Olinordered__field__inverse__zero(U_760) ),
inference(clausify,[status(thm)],[f_244_2]) ).
fof(f_245_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(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(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__le__inverse]) ).
fof(f_245_2,plain,
! [U_763,U_762] :
( c_Orderings_Oord__class_Oless__eq(U_762,c_Groups_Oone__class_Oone(U_762),c_Rings_Oinverse__class_Oinverse(U_762,U_763))
| ~ c_Orderings_Oord__class_Oless__eq(U_762,U_763,c_Groups_Oone__class_Oone(U_762))
| ~ c_Orderings_Oord__class_Oless(U_762,c_Groups_Ozero__class_Ozero(U_762),U_763)
| ~ class_Fields_Olinordered__field(U_762) ),
inference(variable_rename,[status(thm)],[f_245_1]) ).
cnf(f_245_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_762,c_Groups_Oone__class_Oone(U_762),c_Rings_Oinverse__class_Oinverse(U_762,U_763))
| ~ c_Orderings_Oord__class_Oless__eq(U_762,U_763,c_Groups_Oone__class_Oone(U_762))
| ~ c_Orderings_Oord__class_Oless(U_762,c_Groups_Ozero__class_Ozero(U_762),U_763)
| ~ class_Fields_Olinordered__field(U_762) ),
inference(clausify,[status(thm)],[f_245_2]) ).
fof(f_246_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_246_2,plain,
! [U_765,U_764] :
( ( ( c_Groups_Osgn__class_Osgn(U_764,U_765) = c_Groups_Oone__class_Oone(U_764)
| ~ c_Orderings_Oord__class_Oless(U_764,c_Groups_Ozero__class_Ozero(U_764),U_765) )
& ( c_Orderings_Oord__class_Oless(U_764,c_Groups_Ozero__class_Ozero(U_764),U_765)
| c_Groups_Osgn__class_Osgn(U_764,U_765) != c_Groups_Oone__class_Oone(U_764) ) )
| ~ class_Rings_Olinordered__idom(U_764) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
cnf(f_246_3,plain,
( c_Orderings_Oord__class_Oless(U_764,c_Groups_Ozero__class_Ozero(U_764),U_765)
| c_Groups_Osgn__class_Osgn(U_764,U_765) != c_Groups_Oone__class_Oone(U_764)
| ~ class_Rings_Olinordered__idom(U_764) ),
inference(clausify,[status(thm)],[f_246_2]) ).
cnf(f_246_4,plain,
( c_Groups_Osgn__class_Osgn(U_764,U_765) = c_Groups_Oone__class_Oone(U_764)
| ~ c_Orderings_Oord__class_Oless(U_764,c_Groups_Ozero__class_Ozero(U_764),U_765)
| ~ class_Rings_Olinordered__idom(U_764) ),
inference(clausify,[status(thm)],[f_246_2]) ).
fof(f_247_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_247_2,plain,
! [U_767,U_766] :
( c_Groups_Osgn__class_Osgn(U_766,U_767) = c_Groups_Oone__class_Oone(U_766)
| ~ c_Orderings_Oord__class_Oless(U_766,c_Groups_Ozero__class_Ozero(U_766),U_767)
| ~ class_Rings_Olinordered__idom(U_766) ),
inference(variable_rename,[status(thm)],[f_247_1]) ).
cnf(f_247_3,plain,
( c_Groups_Osgn__class_Osgn(U_766,U_767) = c_Groups_Oone__class_Oone(U_766)
| ~ c_Orderings_Oord__class_Oless(U_766,c_Groups_Ozero__class_Ozero(U_766),U_767)
| ~ class_Rings_Olinordered__idom(U_766) ),
inference(clausify,[status(thm)],[f_247_2]) ).
fof(f_248_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_248_2,plain,
! [U_771,U_770,U_769,U_768] :
( ( ( c_Orderings_Oord__class_Oless(tc_fun(U_769,U_768),U_770,U_771)
| c_Orderings_Oord__class_Oless__eq(tc_fun(U_769,U_768),U_771,U_770)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_769,U_768),U_770,U_771) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_769,U_768),U_771,U_770)
& c_Orderings_Oord__class_Oless__eq(tc_fun(U_769,U_768),U_770,U_771) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_769,U_768),U_770,U_771) ) )
| ~ class_Orderings_Oord(U_768) ),
inference(variable_rename,[status(thm)],[f_248_1]) ).
cnf(f_248_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_769,U_768),U_770,U_771)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_769,U_768),U_770,U_771)
| ~ class_Orderings_Oord(U_768) ),
inference(clausify,[status(thm)],[f_248_2]) ).
cnf(f_248_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_769,U_768),U_771,U_770)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_769,U_768),U_770,U_771)
| ~ class_Orderings_Oord(U_768) ),
inference(clausify,[status(thm)],[f_248_2]) ).
cnf(f_248_5,plain,
( c_Orderings_Oord__class_Oless(tc_fun(U_769,U_768),U_770,U_771)
| c_Orderings_Oord__class_Oless__eq(tc_fun(U_769,U_768),U_771,U_770)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_769,U_768),U_770,U_771)
| ~ class_Orderings_Oord(U_768) ),
inference(clausify,[status(thm)],[f_248_2]) ).
fof(f_249_1,plain,
! [V_a,T_a] :
( c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = V_a
| ~ class_Rings_Odivision__ring__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__inverse__eq]) ).
fof(f_249_2,plain,
! [U_773,U_772] :
( c_Rings_Oinverse__class_Oinverse(U_772,c_Rings_Oinverse__class_Oinverse(U_772,U_773)) = U_773
| ~ class_Rings_Odivision__ring__inverse__zero(U_772) ),
inference(variable_rename,[status(thm)],[f_249_1]) ).
cnf(f_249_3,plain,
( c_Rings_Oinverse__class_Oinverse(U_772,c_Rings_Oinverse__class_Oinverse(U_772,U_773)) = U_773
| ~ class_Rings_Odivision__ring__inverse__zero(U_772) ),
inference(clausify,[status(thm)],[f_249_2]) ).
fof(f_250_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_250_2,plain,
! [U_775,U_774] :
( c_Groups_Osgn__class_Osgn(U_774,c_Groups_Osgn__class_Osgn(U_774,U_775)) = c_Groups_Osgn__class_Osgn(U_774,U_775)
| ~ class_Rings_Olinordered__idom(U_774) ),
inference(variable_rename,[status(thm)],[f_250_1]) ).
cnf(f_250_3,plain,
( c_Groups_Osgn__class_Osgn(U_774,c_Groups_Osgn__class_Osgn(U_774,U_775)) = c_Groups_Osgn__class_Osgn(U_774,U_775)
| ~ class_Rings_Olinordered__idom(U_774) ),
inference(clausify,[status(thm)],[f_250_2]) ).
fof(f_251_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Rings_Oinverse__class_Oinverse(T_a,V_a_2) = c_Rings_Oinverse__class_Oinverse(T_a,V_b_2)
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| c_Rings_Oinverse__class_Oinverse(T_a,V_a_2) != c_Rings_Oinverse__class_Oinverse(T_a,V_b_2) ) )
| ~ class_Rings_Odivision__ring__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__eq__iff__eq]) ).
fof(f_251_2,plain,
! [U_778,U_777,U_776] :
( ( ( c_Rings_Oinverse__class_Oinverse(U_776,U_777) = c_Rings_Oinverse__class_Oinverse(U_776,U_778)
| U_777 != U_778 )
& ( U_777 = U_778
| c_Rings_Oinverse__class_Oinverse(U_776,U_777) != c_Rings_Oinverse__class_Oinverse(U_776,U_778) ) )
| ~ class_Rings_Odivision__ring__inverse__zero(U_776) ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
cnf(f_251_3,plain,
( U_777 = U_778
| c_Rings_Oinverse__class_Oinverse(U_776,U_777) != c_Rings_Oinverse__class_Oinverse(U_776,U_778)
| ~ class_Rings_Odivision__ring__inverse__zero(U_776) ),
inference(clausify,[status(thm)],[f_251_2]) ).
cnf(f_251_4,plain,
( c_Rings_Oinverse__class_Oinverse(U_776,U_777) = c_Rings_Oinverse__class_Oinverse(U_776,U_778)
| U_777 != U_778
| ~ class_Rings_Odivision__ring__inverse__zero(U_776) ),
inference(clausify,[status(thm)],[f_251_2]) ).
fof(f_252_1,plain,
! [V_b,V_a,T_a] :
( V_a = V_b
| c_Rings_Oinverse__class_Oinverse(T_a,V_a) != c_Rings_Oinverse__class_Oinverse(T_a,V_b)
| ~ class_Rings_Odivision__ring__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__eq__imp__eq]) ).
fof(f_252_2,plain,
! [U_781,U_780,U_779] :
( U_780 = U_781
| c_Rings_Oinverse__class_Oinverse(U_779,U_780) != c_Rings_Oinverse__class_Oinverse(U_779,U_781)
| ~ class_Rings_Odivision__ring__inverse__zero(U_779) ),
inference(variable_rename,[status(thm)],[f_252_1]) ).
cnf(f_252_3,plain,
( U_780 = U_781
| c_Rings_Oinverse__class_Oinverse(U_779,U_780) != c_Rings_Oinverse__class_Oinverse(U_779,U_781)
| ~ class_Rings_Odivision__ring__inverse__zero(U_779) ),
inference(clausify,[status(thm)],[f_252_2]) ).
fof(f_253_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_253_2,plain,
! [U_784,U_783,U_782] :
( c_Groups_Oplus__class_Oplus(U_782,U_783,U_784) = c_Groups_Oplus__class_Oplus(U_782,U_784,U_783)
| ~ class_Rings_Ocomm__semiring__1(U_782) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
cnf(f_253_3,plain,
( c_Groups_Oplus__class_Oplus(U_782,U_783,U_784) = c_Groups_Oplus__class_Oplus(U_782,U_784,U_783)
| ~ class_Rings_Ocomm__semiring__1(U_782) ),
inference(clausify,[status(thm)],[f_253_2]) ).
fof(f_254_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_254_2,plain,
! [U_788,U_787,U_786,U_785] :
( c_Groups_Oplus__class_Oplus(U_785,U_786,c_Groups_Oplus__class_Oplus(U_785,U_787,U_788)) = c_Groups_Oplus__class_Oplus(U_785,U_787,c_Groups_Oplus__class_Oplus(U_785,U_786,U_788))
| ~ class_Rings_Ocomm__semiring__1(U_785) ),
inference(variable_rename,[status(thm)],[f_254_1]) ).
cnf(f_254_3,plain,
( c_Groups_Oplus__class_Oplus(U_785,U_786,c_Groups_Oplus__class_Oplus(U_785,U_787,U_788)) = c_Groups_Oplus__class_Oplus(U_785,U_787,c_Groups_Oplus__class_Oplus(U_785,U_786,U_788))
| ~ class_Rings_Ocomm__semiring__1(U_785) ),
inference(clausify,[status(thm)],[f_254_2]) ).
fof(f_255_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_255_2,plain,
! [U_792,U_791,U_790,U_789] :
( c_Groups_Oplus__class_Oplus(U_789,U_790,c_Groups_Oplus__class_Oplus(U_789,U_791,U_792)) = c_Groups_Oplus__class_Oplus(U_789,c_Groups_Oplus__class_Oplus(U_789,U_790,U_791),U_792)
| ~ class_Rings_Ocomm__semiring__1(U_789) ),
inference(variable_rename,[status(thm)],[f_255_1]) ).
cnf(f_255_3,plain,
( c_Groups_Oplus__class_Oplus(U_789,U_790,c_Groups_Oplus__class_Oplus(U_789,U_791,U_792)) = c_Groups_Oplus__class_Oplus(U_789,c_Groups_Oplus__class_Oplus(U_789,U_790,U_791),U_792)
| ~ class_Rings_Ocomm__semiring__1(U_789) ),
inference(clausify,[status(thm)],[f_255_2]) ).
fof(f_256_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_256_2,plain,
! [U_796,U_795,U_794,U_793] :
( c_Groups_Oplus__class_Oplus(U_793,c_Groups_Oplus__class_Oplus(U_793,U_794,U_795),U_796) = c_Groups_Oplus__class_Oplus(U_793,U_794,c_Groups_Oplus__class_Oplus(U_793,U_795,U_796))
| ~ class_Rings_Ocomm__semiring__1(U_793) ),
inference(variable_rename,[status(thm)],[f_256_1]) ).
cnf(f_256_3,plain,
( c_Groups_Oplus__class_Oplus(U_793,c_Groups_Oplus__class_Oplus(U_793,U_794,U_795),U_796) = c_Groups_Oplus__class_Oplus(U_793,U_794,c_Groups_Oplus__class_Oplus(U_793,U_795,U_796))
| ~ class_Rings_Ocomm__semiring__1(U_793) ),
inference(clausify,[status(thm)],[f_256_2]) ).
fof(f_257_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_257_2,plain,
! [U_800,U_799,U_798,U_797] :
( c_Groups_Oplus__class_Oplus(U_797,c_Groups_Oplus__class_Oplus(U_797,U_798,U_799),U_800) = c_Groups_Oplus__class_Oplus(U_797,c_Groups_Oplus__class_Oplus(U_797,U_798,U_800),U_799)
| ~ class_Rings_Ocomm__semiring__1(U_797) ),
inference(variable_rename,[status(thm)],[f_257_1]) ).
cnf(f_257_3,plain,
( c_Groups_Oplus__class_Oplus(U_797,c_Groups_Oplus__class_Oplus(U_797,U_798,U_799),U_800) = c_Groups_Oplus__class_Oplus(U_797,c_Groups_Oplus__class_Oplus(U_797,U_798,U_800),U_799)
| ~ class_Rings_Ocomm__semiring__1(U_797) ),
inference(clausify,[status(thm)],[f_257_2]) ).
fof(f_258_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_258_2,plain,
! [U_805,U_804,U_803,U_802,U_801] :
( c_Groups_Oplus__class_Oplus(U_801,c_Groups_Oplus__class_Oplus(U_801,U_802,U_803),c_Groups_Oplus__class_Oplus(U_801,U_804,U_805)) = c_Groups_Oplus__class_Oplus(U_801,c_Groups_Oplus__class_Oplus(U_801,U_802,U_804),c_Groups_Oplus__class_Oplus(U_801,U_803,U_805))
| ~ class_Rings_Ocomm__semiring__1(U_801) ),
inference(variable_rename,[status(thm)],[f_258_1]) ).
cnf(f_258_3,plain,
( c_Groups_Oplus__class_Oplus(U_801,c_Groups_Oplus__class_Oplus(U_801,U_802,U_803),c_Groups_Oplus__class_Oplus(U_801,U_804,U_805)) = c_Groups_Oplus__class_Oplus(U_801,c_Groups_Oplus__class_Oplus(U_801,U_802,U_804),c_Groups_Oplus__class_Oplus(U_801,U_803,U_805))
| ~ class_Rings_Ocomm__semiring__1(U_801) ),
inference(clausify,[status(thm)],[f_258_2]) ).
fof(f_259_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_259_2,plain,
! [U_809,U_808,U_807,U_806] :
( c_Groups_Oplus__class_Oplus(U_806,c_Groups_Oplus__class_Oplus(U_806,U_807,U_808),U_809) = c_Groups_Oplus__class_Oplus(U_806,U_807,c_Groups_Oplus__class_Oplus(U_806,U_808,U_809))
| ~ class_Groups_Oab__semigroup__add(U_806) ),
inference(variable_rename,[status(thm)],[f_259_1]) ).
cnf(f_259_3,plain,
( c_Groups_Oplus__class_Oplus(U_806,c_Groups_Oplus__class_Oplus(U_806,U_807,U_808),U_809) = c_Groups_Oplus__class_Oplus(U_806,U_807,c_Groups_Oplus__class_Oplus(U_806,U_808,U_809))
| ~ class_Groups_Oab__semigroup__add(U_806) ),
inference(clausify,[status(thm)],[f_259_2]) ).
fof(f_260_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_260_2,plain,
! [U_813,U_812,U_811,U_810] :
( ( ( c_Groups_Oplus__class_Oplus(U_810,U_811,U_812) = c_Groups_Oplus__class_Oplus(U_810,U_811,U_813)
| U_812 != U_813 )
& ( U_812 = U_813
| c_Groups_Oplus__class_Oplus(U_810,U_811,U_812) != c_Groups_Oplus__class_Oplus(U_810,U_811,U_813) ) )
| ~ class_Groups_Ocancel__semigroup__add(U_810) ),
inference(variable_rename,[status(thm)],[f_260_1]) ).
cnf(f_260_3,plain,
( U_812 = U_813
| c_Groups_Oplus__class_Oplus(U_810,U_811,U_812) != c_Groups_Oplus__class_Oplus(U_810,U_811,U_813)
| ~ class_Groups_Ocancel__semigroup__add(U_810) ),
inference(clausify,[status(thm)],[f_260_2]) ).
cnf(f_260_4,plain,
( c_Groups_Oplus__class_Oplus(U_810,U_811,U_812) = c_Groups_Oplus__class_Oplus(U_810,U_811,U_813)
| U_812 != U_813
| ~ class_Groups_Ocancel__semigroup__add(U_810) ),
inference(clausify,[status(thm)],[f_260_2]) ).
fof(f_261_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_261_2,plain,
! [U_817,U_816,U_815,U_814] :
( ( ( c_Groups_Oplus__class_Oplus(U_814,U_815,U_816) = c_Groups_Oplus__class_Oplus(U_814,U_817,U_816)
| U_815 != U_817 )
& ( U_815 = U_817
| c_Groups_Oplus__class_Oplus(U_814,U_815,U_816) != c_Groups_Oplus__class_Oplus(U_814,U_817,U_816) ) )
| ~ class_Groups_Ocancel__semigroup__add(U_814) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
cnf(f_261_3,plain,
( U_815 = U_817
| c_Groups_Oplus__class_Oplus(U_814,U_815,U_816) != c_Groups_Oplus__class_Oplus(U_814,U_817,U_816)
| ~ class_Groups_Ocancel__semigroup__add(U_814) ),
inference(clausify,[status(thm)],[f_261_2]) ).
cnf(f_261_4,plain,
( c_Groups_Oplus__class_Oplus(U_814,U_815,U_816) = c_Groups_Oplus__class_Oplus(U_814,U_817,U_816)
| U_815 != U_817
| ~ class_Groups_Ocancel__semigroup__add(U_814) ),
inference(clausify,[status(thm)],[f_261_2]) ).
fof(f_262_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_262_2,plain,
! [U_821,U_820,U_819,U_818] :
( U_820 = U_821
| c_Groups_Oplus__class_Oplus(U_818,U_819,U_820) != c_Groups_Oplus__class_Oplus(U_818,U_819,U_821)
| ~ class_Groups_Ocancel__semigroup__add(U_818) ),
inference(variable_rename,[status(thm)],[f_262_1]) ).
cnf(f_262_3,plain,
( U_820 = U_821
| c_Groups_Oplus__class_Oplus(U_818,U_819,U_820) != c_Groups_Oplus__class_Oplus(U_818,U_819,U_821)
| ~ class_Groups_Ocancel__semigroup__add(U_818) ),
inference(clausify,[status(thm)],[f_262_2]) ).
fof(f_263_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_263_2,plain,
! [U_825,U_824,U_823,U_822] :
( U_824 = U_825
| c_Groups_Oplus__class_Oplus(U_822,U_823,U_824) != c_Groups_Oplus__class_Oplus(U_822,U_823,U_825)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_822) ),
inference(variable_rename,[status(thm)],[f_263_1]) ).
cnf(f_263_3,plain,
( U_824 = U_825
| c_Groups_Oplus__class_Oplus(U_822,U_823,U_824) != c_Groups_Oplus__class_Oplus(U_822,U_823,U_825)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_822) ),
inference(clausify,[status(thm)],[f_263_2]) ).
fof(f_264_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_264_2,plain,
! [U_829,U_828,U_827,U_826] :
( U_827 = U_829
| c_Groups_Oplus__class_Oplus(U_826,U_827,U_828) != c_Groups_Oplus__class_Oplus(U_826,U_829,U_828)
| ~ class_Groups_Ocancel__semigroup__add(U_826) ),
inference(variable_rename,[status(thm)],[f_264_1]) ).
cnf(f_264_3,plain,
( U_827 = U_829
| c_Groups_Oplus__class_Oplus(U_826,U_827,U_828) != c_Groups_Oplus__class_Oplus(U_826,U_829,U_828)
| ~ class_Groups_Ocancel__semigroup__add(U_826) ),
inference(clausify,[status(thm)],[f_264_2]) ).
fof(f_265_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_a))),c_Rings_Oinverse__class_Oinverse(T_a,V_b))
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__add]) ).
fof(f_265_2,plain,
! [U_832,U_831,U_830] :
( c_Groups_Oplus__class_Oplus(U_830,c_Rings_Oinverse__class_Oinverse(U_830,U_831),c_Rings_Oinverse__class_Oinverse(U_830,U_832)) = hAPP(c_Groups_Otimes__class_Otimes(U_830,hAPP(c_Groups_Otimes__class_Otimes(U_830,c_Groups_Oplus__class_Oplus(U_830,U_831,U_832)),c_Rings_Oinverse__class_Oinverse(U_830,U_831))),c_Rings_Oinverse__class_Oinverse(U_830,U_832))
| U_832 = c_Groups_Ozero__class_Ozero(U_830)
| U_831 = c_Groups_Ozero__class_Ozero(U_830)
| ~ class_Fields_Ofield(U_830) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
cnf(f_265_3,plain,
( c_Groups_Oplus__class_Oplus(U_830,c_Rings_Oinverse__class_Oinverse(U_830,U_831),c_Rings_Oinverse__class_Oinverse(U_830,U_832)) = hAPP(c_Groups_Otimes__class_Otimes(U_830,hAPP(c_Groups_Otimes__class_Otimes(U_830,c_Groups_Oplus__class_Oplus(U_830,U_831,U_832)),c_Rings_Oinverse__class_Oinverse(U_830,U_831))),c_Rings_Oinverse__class_Oinverse(U_830,U_832))
| U_832 = c_Groups_Ozero__class_Ozero(U_830)
| U_831 = c_Groups_Ozero__class_Ozero(U_830)
| ~ class_Fields_Ofield(U_830) ),
inference(clausify,[status(thm)],[f_265_2]) ).
fof(f_266_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))),c_Rings_Oinverse__class_Oinverse(T_a,V_b))
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_division__ring__inverse__add]) ).
fof(f_266_2,plain,
! [U_835,U_834,U_833] :
( c_Groups_Oplus__class_Oplus(U_833,c_Rings_Oinverse__class_Oinverse(U_833,U_834),c_Rings_Oinverse__class_Oinverse(U_833,U_835)) = hAPP(c_Groups_Otimes__class_Otimes(U_833,hAPP(c_Groups_Otimes__class_Otimes(U_833,c_Rings_Oinverse__class_Oinverse(U_833,U_834)),c_Groups_Oplus__class_Oplus(U_833,U_834,U_835))),c_Rings_Oinverse__class_Oinverse(U_833,U_835))
| U_835 = c_Groups_Ozero__class_Ozero(U_833)
| U_834 = c_Groups_Ozero__class_Ozero(U_833)
| ~ class_Rings_Odivision__ring(U_833) ),
inference(variable_rename,[status(thm)],[f_266_1]) ).
cnf(f_266_3,plain,
( c_Groups_Oplus__class_Oplus(U_833,c_Rings_Oinverse__class_Oinverse(U_833,U_834),c_Rings_Oinverse__class_Oinverse(U_833,U_835)) = hAPP(c_Groups_Otimes__class_Otimes(U_833,hAPP(c_Groups_Otimes__class_Otimes(U_833,c_Rings_Oinverse__class_Oinverse(U_833,U_834)),c_Groups_Oplus__class_Oplus(U_833,U_834,U_835))),c_Rings_Oinverse__class_Oinverse(U_833,U_835))
| U_835 = c_Groups_Ozero__class_Ozero(U_833)
| U_834 = c_Groups_Ozero__class_Ozero(U_833)
| ~ class_Rings_Odivision__ring(U_833) ),
inference(clausify,[status(thm)],[f_266_2]) ).
fof(f_267_1,plain,
! [T_a] :
( c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_field__inverse__zero]) ).
fof(f_267_2,plain,
! [U_836] :
( c_Rings_Oinverse__class_Oinverse(U_836,c_Groups_Ozero__class_Ozero(U_836)) = c_Groups_Ozero__class_Ozero(U_836)
| ~ class_Fields_Ofield__inverse__zero(U_836) ),
inference(variable_rename,[status(thm)],[f_267_1]) ).
cnf(f_267_3,plain,
( c_Rings_Oinverse__class_Oinverse(U_836,c_Groups_Ozero__class_Ozero(U_836)) = c_Groups_Ozero__class_Ozero(U_836)
| ~ class_Fields_Ofield__inverse__zero(U_836) ),
inference(clausify,[status(thm)],[f_267_2]) ).
fof(f_268_1,plain,
! [V_b,V_a,T_a] :
( V_a = V_b
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| c_Rings_Oinverse__class_Oinverse(T_a,V_a) != c_Rings_Oinverse__class_Oinverse(T_a,V_b)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__eq__imp__eq]) ).
fof(f_268_2,plain,
! [U_839,U_838,U_837] :
( U_838 = U_839
| U_839 = c_Groups_Ozero__class_Ozero(U_837)
| U_838 = c_Groups_Ozero__class_Ozero(U_837)
| c_Rings_Oinverse__class_Oinverse(U_837,U_838) != c_Rings_Oinverse__class_Oinverse(U_837,U_839)
| ~ class_Rings_Odivision__ring(U_837) ),
inference(variable_rename,[status(thm)],[f_268_1]) ).
cnf(f_268_3,plain,
( U_838 = U_839
| U_839 = c_Groups_Ozero__class_Ozero(U_837)
| U_838 = c_Groups_Ozero__class_Ozero(U_837)
| c_Rings_Oinverse__class_Oinverse(U_837,U_838) != c_Rings_Oinverse__class_Oinverse(U_837,U_839)
| ~ class_Rings_Odivision__ring(U_837) ),
inference(clausify,[status(thm)],[f_268_2]) ).
fof(f_269_1,plain,
! [V_a,T_a] :
( V_a = c_Groups_Ozero__class_Ozero(T_a)
| c_Rings_Oinverse__class_Oinverse(T_a,V_a) != c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__zero__imp__zero]) ).
fof(f_269_2,plain,
! [U_841,U_840] :
( U_841 = c_Groups_Ozero__class_Ozero(U_840)
| c_Rings_Oinverse__class_Oinverse(U_840,U_841) != c_Groups_Ozero__class_Ozero(U_840)
| ~ class_Rings_Odivision__ring(U_840) ),
inference(variable_rename,[status(thm)],[f_269_1]) ).
cnf(f_269_3,plain,
( U_841 = c_Groups_Ozero__class_Ozero(U_840)
| c_Rings_Oinverse__class_Oinverse(U_840,U_841) != c_Groups_Ozero__class_Ozero(U_840)
| ~ class_Rings_Odivision__ring(U_840) ),
inference(clausify,[status(thm)],[f_269_2]) ).
fof(f_270_1,plain,
! [V_a,T_a] :
( c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = V_a
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__inverse__eq]) ).
fof(f_270_2,plain,
! [U_843,U_842] :
( c_Rings_Oinverse__class_Oinverse(U_842,c_Rings_Oinverse__class_Oinverse(U_842,U_843)) = U_843
| U_843 = c_Groups_Ozero__class_Ozero(U_842)
| ~ class_Rings_Odivision__ring(U_842) ),
inference(variable_rename,[status(thm)],[f_270_1]) ).
cnf(f_270_3,plain,
( c_Rings_Oinverse__class_Oinverse(U_842,c_Rings_Oinverse__class_Oinverse(U_842,U_843)) = U_843
| U_843 = c_Groups_Ozero__class_Ozero(U_842)
| ~ class_Rings_Odivision__ring(U_842) ),
inference(clausify,[status(thm)],[f_270_2]) ).
fof(f_271_1,plain,
! [V_a,T_a] :
( c_Rings_Oinverse__class_Oinverse(T_a,V_a) != c_Groups_Ozero__class_Ozero(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__imp__inverse__nonzero]) ).
fof(f_271_2,plain,
! [U_845,U_844] :
( c_Rings_Oinverse__class_Oinverse(U_844,U_845) != c_Groups_Ozero__class_Ozero(U_844)
| U_845 = c_Groups_Ozero__class_Ozero(U_844)
| ~ class_Rings_Odivision__ring(U_844) ),
inference(variable_rename,[status(thm)],[f_271_1]) ).
cnf(f_271_3,plain,
( c_Rings_Oinverse__class_Oinverse(U_844,U_845) != c_Groups_Ozero__class_Ozero(U_844)
| U_845 = c_Groups_Ozero__class_Ozero(U_844)
| ~ class_Rings_Odivision__ring(U_844) ),
inference(clausify,[status(thm)],[f_271_2]) ).
fof(f_272_1,plain,
! [V_a_2,T_a] :
( ( ( c_Rings_Oinverse__class_Oinverse(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_Rings_Oinverse__class_Oinverse(T_a,V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Odivision__ring__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__nonzero__iff__nonzero]) ).
fof(f_272_2,plain,
! [U_847,U_846] :
( ( ( c_Rings_Oinverse__class_Oinverse(U_846,U_847) = c_Groups_Ozero__class_Ozero(U_846)
| U_847 != c_Groups_Ozero__class_Ozero(U_846) )
& ( U_847 = c_Groups_Ozero__class_Ozero(U_846)
| c_Rings_Oinverse__class_Oinverse(U_846,U_847) != c_Groups_Ozero__class_Ozero(U_846) ) )
| ~ class_Rings_Odivision__ring__inverse__zero(U_846) ),
inference(variable_rename,[status(thm)],[f_272_1]) ).
cnf(f_272_3,plain,
( U_847 = c_Groups_Ozero__class_Ozero(U_846)
| c_Rings_Oinverse__class_Oinverse(U_846,U_847) != c_Groups_Ozero__class_Ozero(U_846)
| ~ class_Rings_Odivision__ring__inverse__zero(U_846) ),
inference(clausify,[status(thm)],[f_272_2]) ).
cnf(f_272_4,plain,
( c_Rings_Oinverse__class_Oinverse(U_846,U_847) = c_Groups_Ozero__class_Ozero(U_846)
| U_847 != c_Groups_Ozero__class_Ozero(U_846)
| ~ class_Rings_Odivision__ring__inverse__zero(U_846) ),
inference(clausify,[status(thm)],[f_272_2]) ).
fof(f_273_1,plain,
! [T_a] :
( c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__zero]) ).
fof(f_273_2,plain,
! [U_848] :
( c_Rings_Oinverse__class_Oinverse(U_848,c_Groups_Ozero__class_Ozero(U_848)) = c_Groups_Ozero__class_Ozero(U_848)
| ~ class_Rings_Odivision__ring__inverse__zero(U_848) ),
inference(variable_rename,[status(thm)],[f_273_1]) ).
cnf(f_273_3,plain,
( c_Rings_Oinverse__class_Oinverse(U_848,c_Groups_Ozero__class_Ozero(U_848)) = c_Groups_Ozero__class_Ozero(U_848)
| ~ class_Rings_Odivision__ring__inverse__zero(U_848) ),
inference(clausify,[status(thm)],[f_273_2]) ).
fof(f_274_1,plain,
! [V_b,V_a,T_a] :
( c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_b))
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__mult__distrib]) ).
fof(f_274_2,plain,
! [U_851,U_850,U_849] :
( c_Rings_Oinverse__class_Oinverse(U_849,hAPP(c_Groups_Otimes__class_Otimes(U_849,U_850),U_851)) = hAPP(c_Groups_Otimes__class_Otimes(U_849,c_Rings_Oinverse__class_Oinverse(U_849,U_850)),c_Rings_Oinverse__class_Oinverse(U_849,U_851))
| ~ class_Fields_Ofield__inverse__zero(U_849) ),
inference(variable_rename,[status(thm)],[f_274_1]) ).
cnf(f_274_3,plain,
( c_Rings_Oinverse__class_Oinverse(U_849,hAPP(c_Groups_Otimes__class_Otimes(U_849,U_850),U_851)) = hAPP(c_Groups_Otimes__class_Otimes(U_849,c_Rings_Oinverse__class_Oinverse(U_849,U_850)),c_Rings_Oinverse__class_Oinverse(U_849,U_851))
| ~ class_Fields_Ofield__inverse__zero(U_849) ),
inference(clausify,[status(thm)],[f_274_2]) ).
fof(f_275_1,plain,
! [V_x_2,T_a] :
( ( ( c_Rings_Oinverse__class_Oinverse(T_a,V_x_2) = c_Groups_Oone__class_Oone(T_a)
| V_x_2 != c_Groups_Oone__class_Oone(T_a) )
& ( V_x_2 = c_Groups_Oone__class_Oone(T_a)
| c_Rings_Oinverse__class_Oinverse(T_a,V_x_2) != c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__eq__1__iff]) ).
fof(f_275_2,plain,
! [U_853,U_852] :
( ( ( c_Rings_Oinverse__class_Oinverse(U_852,U_853) = c_Groups_Oone__class_Oone(U_852)
| U_853 != c_Groups_Oone__class_Oone(U_852) )
& ( U_853 = c_Groups_Oone__class_Oone(U_852)
| c_Rings_Oinverse__class_Oinverse(U_852,U_853) != c_Groups_Oone__class_Oone(U_852) ) )
| ~ class_Fields_Ofield__inverse__zero(U_852) ),
inference(variable_rename,[status(thm)],[f_275_1]) ).
cnf(f_275_3,plain,
( U_853 = c_Groups_Oone__class_Oone(U_852)
| c_Rings_Oinverse__class_Oinverse(U_852,U_853) != c_Groups_Oone__class_Oone(U_852)
| ~ class_Fields_Ofield__inverse__zero(U_852) ),
inference(clausify,[status(thm)],[f_275_2]) ).
cnf(f_275_4,plain,
( c_Rings_Oinverse__class_Oinverse(U_852,U_853) = c_Groups_Oone__class_Oone(U_852)
| U_853 != c_Groups_Oone__class_Oone(U_852)
| ~ class_Fields_Ofield__inverse__zero(U_852) ),
inference(clausify,[status(thm)],[f_275_2]) ).
fof(f_276_1,plain,
! [T_a] :
( c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__1]) ).
fof(f_276_2,plain,
! [U_854] :
( c_Rings_Oinverse__class_Oinverse(U_854,c_Groups_Oone__class_Oone(U_854)) = c_Groups_Oone__class_Oone(U_854)
| ~ class_Rings_Odivision__ring(U_854) ),
inference(variable_rename,[status(thm)],[f_276_1]) ).
cnf(f_276_3,plain,
( c_Rings_Oinverse__class_Oinverse(U_854,c_Groups_Oone__class_Oone(U_854)) = c_Groups_Oone__class_Oone(U_854)
| ~ class_Rings_Odivision__ring(U_854) ),
inference(clausify,[status(thm)],[f_276_2]) ).
fof(f_277_1,plain,
! [V_b,V_a,T_a] :
( c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_b,V_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__divide]) ).
fof(f_277_2,plain,
! [U_857,U_856,U_855] :
( c_Rings_Oinverse__class_Oinverse(U_855,c_Rings_Oinverse__class_Odivide(U_855,U_856,U_857)) = c_Rings_Oinverse__class_Odivide(U_855,U_857,U_856)
| ~ class_Fields_Ofield__inverse__zero(U_855) ),
inference(variable_rename,[status(thm)],[f_277_1]) ).
cnf(f_277_3,plain,
( c_Rings_Oinverse__class_Oinverse(U_855,c_Rings_Oinverse__class_Odivide(U_855,U_856,U_857)) = c_Rings_Oinverse__class_Odivide(U_855,U_857,U_856)
| ~ class_Fields_Ofield__inverse__zero(U_855) ),
inference(clausify,[status(thm)],[f_277_2]) ).
fof(f_278_1,plain,
c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_INVERSE__ZERO]) ).
cnf(f_278_2,plain,
c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_278_1]) ).
fof(f_279_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_279_2,plain,
! [U_859,U_858] :
( c_Groups_Oplus__class_Oplus(U_858,U_859,c_Groups_Ozero__class_Ozero(U_858)) = U_859
| ~ class_Groups_Ocomm__monoid__add(U_858) ),
inference(variable_rename,[status(thm)],[f_279_1]) ).
cnf(f_279_3,plain,
( c_Groups_Oplus__class_Oplus(U_858,U_859,c_Groups_Ozero__class_Ozero(U_858)) = U_859
| ~ class_Groups_Ocomm__monoid__add(U_858) ),
inference(clausify,[status(thm)],[f_279_2]) ).
fof(f_280_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_280_2,plain,
! [U_861,U_860] :
( c_Groups_Oplus__class_Oplus(U_860,U_861,c_Groups_Ozero__class_Ozero(U_860)) = U_861
| ~ class_Groups_Omonoid__add(U_860) ),
inference(variable_rename,[status(thm)],[f_280_1]) ).
cnf(f_280_3,plain,
( c_Groups_Oplus__class_Oplus(U_860,U_861,c_Groups_Ozero__class_Ozero(U_860)) = U_861
| ~ class_Groups_Omonoid__add(U_860) ),
inference(clausify,[status(thm)],[f_280_2]) ).
fof(f_281_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_281_2,plain,
! [U_863,U_862] :
( ( ( c_Groups_Ozero__class_Ozero(U_862) = c_Groups_Oplus__class_Oplus(U_862,U_863,U_863)
| U_863 != c_Groups_Ozero__class_Ozero(U_862) )
& ( U_863 = c_Groups_Ozero__class_Ozero(U_862)
| c_Groups_Ozero__class_Ozero(U_862) != c_Groups_Oplus__class_Oplus(U_862,U_863,U_863) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_862) ),
inference(variable_rename,[status(thm)],[f_281_1]) ).
cnf(f_281_3,plain,
( U_863 = c_Groups_Ozero__class_Ozero(U_862)
| c_Groups_Ozero__class_Ozero(U_862) != c_Groups_Oplus__class_Oplus(U_862,U_863,U_863)
| ~ class_Groups_Olinordered__ab__group__add(U_862) ),
inference(clausify,[status(thm)],[f_281_2]) ).
cnf(f_281_4,plain,
( c_Groups_Ozero__class_Ozero(U_862) = c_Groups_Oplus__class_Oplus(U_862,U_863,U_863)
| U_863 != c_Groups_Ozero__class_Ozero(U_862)
| ~ class_Groups_Olinordered__ab__group__add(U_862) ),
inference(clausify,[status(thm)],[f_281_2]) ).
fof(f_282_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_282_2,plain,
! [U_865,U_864] :
( c_Groups_Oplus__class_Oplus(U_864,c_Groups_Ozero__class_Ozero(U_864),U_865) = U_865
| ~ class_Groups_Ocomm__monoid__add(U_864) ),
inference(variable_rename,[status(thm)],[f_282_1]) ).
cnf(f_282_3,plain,
( c_Groups_Oplus__class_Oplus(U_864,c_Groups_Ozero__class_Ozero(U_864),U_865) = U_865
| ~ class_Groups_Ocomm__monoid__add(U_864) ),
inference(clausify,[status(thm)],[f_282_2]) ).
fof(f_283_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_283_2,plain,
! [U_867,U_866] :
( c_Groups_Oplus__class_Oplus(U_866,c_Groups_Ozero__class_Ozero(U_866),U_867) = U_867
| ~ class_Groups_Omonoid__add(U_866) ),
inference(variable_rename,[status(thm)],[f_283_1]) ).
cnf(f_283_3,plain,
( c_Groups_Oplus__class_Oplus(U_866,c_Groups_Ozero__class_Ozero(U_866),U_867) = U_867
| ~ class_Groups_Omonoid__add(U_866) ),
inference(clausify,[status(thm)],[f_283_2]) ).
fof(f_284_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_284_2,plain,
! [U_870,U_869,U_868] :
( ( ( U_869 = c_Groups_Oplus__class_Oplus(U_868,U_869,U_870)
| U_870 != c_Groups_Ozero__class_Ozero(U_868) )
& ( U_870 = c_Groups_Ozero__class_Ozero(U_868)
| U_869 != c_Groups_Oplus__class_Oplus(U_868,U_869,U_870) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_868) ),
inference(variable_rename,[status(thm)],[f_284_1]) ).
cnf(f_284_3,plain,
( U_870 = c_Groups_Ozero__class_Ozero(U_868)
| U_869 != c_Groups_Oplus__class_Oplus(U_868,U_869,U_870)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_868) ),
inference(clausify,[status(thm)],[f_284_2]) ).
cnf(f_284_4,plain,
( U_869 = c_Groups_Oplus__class_Oplus(U_868,U_869,U_870)
| U_870 != c_Groups_Ozero__class_Ozero(U_868)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_868) ),
inference(clausify,[status(thm)],[f_284_2]) ).
fof(f_285_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_285_2,plain,
! [U_872,U_871] :
( c_Groups_Oplus__class_Oplus(U_871,U_872,c_Groups_Ozero__class_Ozero(U_871)) = U_872
| ~ class_Rings_Ocomm__semiring__1(U_871) ),
inference(variable_rename,[status(thm)],[f_285_1]) ).
cnf(f_285_3,plain,
( c_Groups_Oplus__class_Oplus(U_871,U_872,c_Groups_Ozero__class_Ozero(U_871)) = U_872
| ~ class_Rings_Ocomm__semiring__1(U_871) ),
inference(clausify,[status(thm)],[f_285_2]) ).
fof(f_286_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_286_2,plain,
! [U_874,U_873] :
( c_Groups_Oplus__class_Oplus(U_873,c_Groups_Ozero__class_Ozero(U_873),U_874) = U_874
| ~ class_Rings_Ocomm__semiring__1(U_873) ),
inference(variable_rename,[status(thm)],[f_286_1]) ).
cnf(f_286_3,plain,
( c_Groups_Oplus__class_Oplus(U_873,c_Groups_Ozero__class_Ozero(U_873),U_874) = U_874
| ~ class_Rings_Ocomm__semiring__1(U_873) ),
inference(clausify,[status(thm)],[f_286_2]) ).
fof(f_287_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_287_2,plain,
! [U_878,U_877,U_876,U_875] :
( c_Orderings_Oord__class_Oless__eq(U_875,U_877,U_878)
| ~ c_Orderings_Oord__class_Oless__eq(U_875,c_Groups_Oplus__class_Oplus(U_875,U_876,U_877),c_Groups_Oplus__class_Oplus(U_875,U_876,U_878))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_875) ),
inference(variable_rename,[status(thm)],[f_287_1]) ).
cnf(f_287_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_875,U_877,U_878)
| ~ c_Orderings_Oord__class_Oless__eq(U_875,c_Groups_Oplus__class_Oplus(U_875,U_876,U_877),c_Groups_Oplus__class_Oplus(U_875,U_876,U_878))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_875) ),
inference(clausify,[status(thm)],[f_287_2]) ).
fof(f_288_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_288_2,plain,
! [U_882,U_881,U_880,U_879] :
( c_Orderings_Oord__class_Oless__eq(U_879,U_880,U_882)
| ~ c_Orderings_Oord__class_Oless__eq(U_879,c_Groups_Oplus__class_Oplus(U_879,U_880,U_881),c_Groups_Oplus__class_Oplus(U_879,U_882,U_881))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_879) ),
inference(variable_rename,[status(thm)],[f_288_1]) ).
cnf(f_288_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_879,U_880,U_882)
| ~ c_Orderings_Oord__class_Oless__eq(U_879,c_Groups_Oplus__class_Oplus(U_879,U_880,U_881),c_Groups_Oplus__class_Oplus(U_879,U_882,U_881))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_879) ),
inference(clausify,[status(thm)],[f_288_2]) ).
fof(f_289_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_289_2,plain,
! [U_887,U_886,U_885,U_884,U_883] :
( c_Orderings_Oord__class_Oless__eq(U_883,c_Groups_Oplus__class_Oplus(U_883,U_884,U_886),c_Groups_Oplus__class_Oplus(U_883,U_885,U_887))
| ~ c_Orderings_Oord__class_Oless__eq(U_883,U_886,U_887)
| ~ c_Orderings_Oord__class_Oless__eq(U_883,U_884,U_885)
| ~ class_Groups_Oordered__ab__semigroup__add(U_883) ),
inference(variable_rename,[status(thm)],[f_289_1]) ).
cnf(f_289_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_883,c_Groups_Oplus__class_Oplus(U_883,U_884,U_886),c_Groups_Oplus__class_Oplus(U_883,U_885,U_887))
| ~ c_Orderings_Oord__class_Oless__eq(U_883,U_886,U_887)
| ~ c_Orderings_Oord__class_Oless__eq(U_883,U_884,U_885)
| ~ class_Groups_Oordered__ab__semigroup__add(U_883) ),
inference(clausify,[status(thm)],[f_289_2]) ).
fof(f_290_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_290_2,plain,
! [U_891,U_890,U_889,U_888] :
( c_Orderings_Oord__class_Oless__eq(U_888,c_Groups_Oplus__class_Oplus(U_888,U_891,U_889),c_Groups_Oplus__class_Oplus(U_888,U_891,U_890))
| ~ c_Orderings_Oord__class_Oless__eq(U_888,U_889,U_890)
| ~ class_Groups_Oordered__ab__semigroup__add(U_888) ),
inference(variable_rename,[status(thm)],[f_290_1]) ).
cnf(f_290_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_888,c_Groups_Oplus__class_Oplus(U_888,U_891,U_889),c_Groups_Oplus__class_Oplus(U_888,U_891,U_890))
| ~ c_Orderings_Oord__class_Oless__eq(U_888,U_889,U_890)
| ~ class_Groups_Oordered__ab__semigroup__add(U_888) ),
inference(clausify,[status(thm)],[f_290_2]) ).
fof(f_291_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_291_2,plain,
! [U_895,U_894,U_893,U_892] :
( c_Orderings_Oord__class_Oless__eq(U_892,c_Groups_Oplus__class_Oplus(U_892,U_893,U_895),c_Groups_Oplus__class_Oplus(U_892,U_894,U_895))
| ~ c_Orderings_Oord__class_Oless__eq(U_892,U_893,U_894)
| ~ class_Groups_Oordered__ab__semigroup__add(U_892) ),
inference(variable_rename,[status(thm)],[f_291_1]) ).
cnf(f_291_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_892,c_Groups_Oplus__class_Oplus(U_892,U_893,U_895),c_Groups_Oplus__class_Oplus(U_892,U_894,U_895))
| ~ c_Orderings_Oord__class_Oless__eq(U_892,U_893,U_894)
| ~ class_Groups_Oordered__ab__semigroup__add(U_892) ),
inference(clausify,[status(thm)],[f_291_2]) ).
fof(f_292_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_292_2,plain,
! [U_899,U_898,U_897,U_896] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_896,c_Groups_Oplus__class_Oplus(U_896,U_897,U_898),c_Groups_Oplus__class_Oplus(U_896,U_897,U_899))
| ~ c_Orderings_Oord__class_Oless__eq(U_896,U_898,U_899) )
& ( c_Orderings_Oord__class_Oless__eq(U_896,U_898,U_899)
| ~ c_Orderings_Oord__class_Oless__eq(U_896,c_Groups_Oplus__class_Oplus(U_896,U_897,U_898),c_Groups_Oplus__class_Oplus(U_896,U_897,U_899)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_896) ),
inference(variable_rename,[status(thm)],[f_292_1]) ).
cnf(f_292_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_896,U_898,U_899)
| ~ c_Orderings_Oord__class_Oless__eq(U_896,c_Groups_Oplus__class_Oplus(U_896,U_897,U_898),c_Groups_Oplus__class_Oplus(U_896,U_897,U_899))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_896) ),
inference(clausify,[status(thm)],[f_292_2]) ).
cnf(f_292_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_896,c_Groups_Oplus__class_Oplus(U_896,U_897,U_898),c_Groups_Oplus__class_Oplus(U_896,U_897,U_899))
| ~ c_Orderings_Oord__class_Oless__eq(U_896,U_898,U_899)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_896) ),
inference(clausify,[status(thm)],[f_292_2]) ).
fof(f_293_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_293_2,plain,
! [U_903,U_902,U_901,U_900] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_900,c_Groups_Oplus__class_Oplus(U_900,U_901,U_902),c_Groups_Oplus__class_Oplus(U_900,U_903,U_902))
| ~ c_Orderings_Oord__class_Oless__eq(U_900,U_901,U_903) )
& ( c_Orderings_Oord__class_Oless__eq(U_900,U_901,U_903)
| ~ c_Orderings_Oord__class_Oless__eq(U_900,c_Groups_Oplus__class_Oplus(U_900,U_901,U_902),c_Groups_Oplus__class_Oplus(U_900,U_903,U_902)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_900) ),
inference(variable_rename,[status(thm)],[f_293_1]) ).
cnf(f_293_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_900,U_901,U_903)
| ~ c_Orderings_Oord__class_Oless__eq(U_900,c_Groups_Oplus__class_Oplus(U_900,U_901,U_902),c_Groups_Oplus__class_Oplus(U_900,U_903,U_902))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_900) ),
inference(clausify,[status(thm)],[f_293_2]) ).
cnf(f_293_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_900,c_Groups_Oplus__class_Oplus(U_900,U_901,U_902),c_Groups_Oplus__class_Oplus(U_900,U_903,U_902))
| ~ c_Orderings_Oord__class_Oless__eq(U_900,U_901,U_903)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_900) ),
inference(clausify,[status(thm)],[f_293_2]) ).
fof(f_294_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_294_2,plain,
! [U_907,U_906,U_905,U_904] :
( ( ( c_Orderings_Oord__class_Oless(U_904,c_Groups_Oplus__class_Oplus(U_904,U_905,U_906),c_Groups_Oplus__class_Oplus(U_904,U_907,U_906))
| ~ c_Orderings_Oord__class_Oless(U_904,U_905,U_907) )
& ( c_Orderings_Oord__class_Oless(U_904,U_905,U_907)
| ~ c_Orderings_Oord__class_Oless(U_904,c_Groups_Oplus__class_Oplus(U_904,U_905,U_906),c_Groups_Oplus__class_Oplus(U_904,U_907,U_906)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_904) ),
inference(variable_rename,[status(thm)],[f_294_1]) ).
cnf(f_294_3,plain,
( c_Orderings_Oord__class_Oless(U_904,U_905,U_907)
| ~ c_Orderings_Oord__class_Oless(U_904,c_Groups_Oplus__class_Oplus(U_904,U_905,U_906),c_Groups_Oplus__class_Oplus(U_904,U_907,U_906))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_904) ),
inference(clausify,[status(thm)],[f_294_2]) ).
cnf(f_294_4,plain,
( c_Orderings_Oord__class_Oless(U_904,c_Groups_Oplus__class_Oplus(U_904,U_905,U_906),c_Groups_Oplus__class_Oplus(U_904,U_907,U_906))
| ~ c_Orderings_Oord__class_Oless(U_904,U_905,U_907)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_904) ),
inference(clausify,[status(thm)],[f_294_2]) ).
fof(f_295_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_295_2,plain,
! [U_911,U_910,U_909,U_908] :
( ( ( c_Orderings_Oord__class_Oless(U_908,c_Groups_Oplus__class_Oplus(U_908,U_909,U_910),c_Groups_Oplus__class_Oplus(U_908,U_909,U_911))
| ~ c_Orderings_Oord__class_Oless(U_908,U_910,U_911) )
& ( c_Orderings_Oord__class_Oless(U_908,U_910,U_911)
| ~ c_Orderings_Oord__class_Oless(U_908,c_Groups_Oplus__class_Oplus(U_908,U_909,U_910),c_Groups_Oplus__class_Oplus(U_908,U_909,U_911)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_908) ),
inference(variable_rename,[status(thm)],[f_295_1]) ).
cnf(f_295_3,plain,
( c_Orderings_Oord__class_Oless(U_908,U_910,U_911)
| ~ c_Orderings_Oord__class_Oless(U_908,c_Groups_Oplus__class_Oplus(U_908,U_909,U_910),c_Groups_Oplus__class_Oplus(U_908,U_909,U_911))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_908) ),
inference(clausify,[status(thm)],[f_295_2]) ).
cnf(f_295_4,plain,
( c_Orderings_Oord__class_Oless(U_908,c_Groups_Oplus__class_Oplus(U_908,U_909,U_910),c_Groups_Oplus__class_Oplus(U_908,U_909,U_911))
| ~ c_Orderings_Oord__class_Oless(U_908,U_910,U_911)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_908) ),
inference(clausify,[status(thm)],[f_295_2]) ).
fof(f_296_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_296_2,plain,
! [U_915,U_914,U_913,U_912] :
( c_Orderings_Oord__class_Oless(U_912,c_Groups_Oplus__class_Oplus(U_912,U_913,U_915),c_Groups_Oplus__class_Oplus(U_912,U_914,U_915))
| ~ c_Orderings_Oord__class_Oless(U_912,U_913,U_914)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_912) ),
inference(variable_rename,[status(thm)],[f_296_1]) ).
cnf(f_296_3,plain,
( c_Orderings_Oord__class_Oless(U_912,c_Groups_Oplus__class_Oplus(U_912,U_913,U_915),c_Groups_Oplus__class_Oplus(U_912,U_914,U_915))
| ~ c_Orderings_Oord__class_Oless(U_912,U_913,U_914)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_912) ),
inference(clausify,[status(thm)],[f_296_2]) ).
fof(f_297_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_297_2,plain,
! [U_919,U_918,U_917,U_916] :
( c_Orderings_Oord__class_Oless(U_916,c_Groups_Oplus__class_Oplus(U_916,U_919,U_917),c_Groups_Oplus__class_Oplus(U_916,U_919,U_918))
| ~ c_Orderings_Oord__class_Oless(U_916,U_917,U_918)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_916) ),
inference(variable_rename,[status(thm)],[f_297_1]) ).
cnf(f_297_3,plain,
( c_Orderings_Oord__class_Oless(U_916,c_Groups_Oplus__class_Oplus(U_916,U_919,U_917),c_Groups_Oplus__class_Oplus(U_916,U_919,U_918))
| ~ c_Orderings_Oord__class_Oless(U_916,U_917,U_918)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_916) ),
inference(clausify,[status(thm)],[f_297_2]) ).
fof(f_298_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_298_2,plain,
! [U_924,U_923,U_922,U_921,U_920] :
( c_Orderings_Oord__class_Oless(U_920,c_Groups_Oplus__class_Oplus(U_920,U_921,U_923),c_Groups_Oplus__class_Oplus(U_920,U_922,U_924))
| ~ c_Orderings_Oord__class_Oless(U_920,U_923,U_924)
| ~ c_Orderings_Oord__class_Oless(U_920,U_921,U_922)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_920) ),
inference(variable_rename,[status(thm)],[f_298_1]) ).
cnf(f_298_3,plain,
( c_Orderings_Oord__class_Oless(U_920,c_Groups_Oplus__class_Oplus(U_920,U_921,U_923),c_Groups_Oplus__class_Oplus(U_920,U_922,U_924))
| ~ c_Orderings_Oord__class_Oless(U_920,U_923,U_924)
| ~ c_Orderings_Oord__class_Oless(U_920,U_921,U_922)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_920) ),
inference(clausify,[status(thm)],[f_298_2]) ).
fof(f_299_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_299_2,plain,
! [U_928,U_927,U_926,U_925] :
( c_Orderings_Oord__class_Oless(U_925,U_926,U_928)
| ~ c_Orderings_Oord__class_Oless(U_925,c_Groups_Oplus__class_Oplus(U_925,U_926,U_927),c_Groups_Oplus__class_Oplus(U_925,U_928,U_927))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_925) ),
inference(variable_rename,[status(thm)],[f_299_1]) ).
cnf(f_299_3,plain,
( c_Orderings_Oord__class_Oless(U_925,U_926,U_928)
| ~ c_Orderings_Oord__class_Oless(U_925,c_Groups_Oplus__class_Oplus(U_925,U_926,U_927),c_Groups_Oplus__class_Oplus(U_925,U_928,U_927))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_925) ),
inference(clausify,[status(thm)],[f_299_2]) ).
fof(f_300_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_300_2,plain,
! [U_932,U_931,U_930,U_929] :
( c_Orderings_Oord__class_Oless(U_929,U_931,U_932)
| ~ c_Orderings_Oord__class_Oless(U_929,c_Groups_Oplus__class_Oplus(U_929,U_930,U_931),c_Groups_Oplus__class_Oplus(U_929,U_930,U_932))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_929) ),
inference(variable_rename,[status(thm)],[f_300_1]) ).
cnf(f_300_3,plain,
( c_Orderings_Oord__class_Oless(U_929,U_931,U_932)
| ~ c_Orderings_Oord__class_Oless(U_929,c_Groups_Oplus__class_Oplus(U_929,U_930,U_931),c_Groups_Oplus__class_Oplus(U_929,U_930,U_932))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_929) ),
inference(clausify,[status(thm)],[f_300_2]) ).
fof(f_301_1,plain,
! [V_b_H,V_b,V_a,T_a] :
( 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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),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_301_2,plain,
! [U_936,U_935,U_934,U_933] :
( hAPP(c_Groups_Otimes__class_Otimes(U_933,U_934),c_Groups_Oplus__class_Oplus(U_933,U_935,U_936)) = c_Groups_Oplus__class_Oplus(U_933,hAPP(c_Groups_Otimes__class_Otimes(U_933,U_934),U_935),hAPP(c_Groups_Otimes__class_Otimes(U_933,U_934),U_936))
| ~ class_RealVector_Oreal__normed__algebra(U_933) ),
inference(variable_rename,[status(thm)],[f_301_1]) ).
cnf(f_301_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_933,U_934),c_Groups_Oplus__class_Oplus(U_933,U_935,U_936)) = c_Groups_Oplus__class_Oplus(U_933,hAPP(c_Groups_Otimes__class_Otimes(U_933,U_934),U_935),hAPP(c_Groups_Otimes__class_Otimes(U_933,U_934),U_936))
| ~ class_RealVector_Oreal__normed__algebra(U_933) ),
inference(clausify,[status(thm)],[f_301_2]) ).
fof(f_302_1,plain,
! [V_y,V_x,V_xa,T_a] :
( 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(c_Groups_Otimes__class_Otimes(T_a,V_xa),V_x),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_302_2,plain,
! [U_940,U_939,U_938,U_937] :
( hAPP(c_Groups_Otimes__class_Otimes(U_937,U_938),c_Groups_Oplus__class_Oplus(U_937,U_939,U_940)) = c_Groups_Oplus__class_Oplus(U_937,hAPP(c_Groups_Otimes__class_Otimes(U_937,U_938),U_939),hAPP(c_Groups_Otimes__class_Otimes(U_937,U_938),U_940))
| ~ class_RealVector_Oreal__normed__algebra(U_937) ),
inference(variable_rename,[status(thm)],[f_302_1]) ).
cnf(f_302_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_937,U_938),c_Groups_Oplus__class_Oplus(U_937,U_939,U_940)) = c_Groups_Oplus__class_Oplus(U_937,hAPP(c_Groups_Otimes__class_Otimes(U_937,U_938),U_939),hAPP(c_Groups_Otimes__class_Otimes(U_937,U_938),U_940))
| ~ class_RealVector_Oreal__normed__algebra(U_937) ),
inference(clausify,[status(thm)],[f_302_2]) ).
fof(f_303_1,plain,
! [V_b,V_a_H,V_a,T_a] :
( 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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),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_303_2,plain,
! [U_944,U_943,U_942,U_941] :
( hAPP(c_Groups_Otimes__class_Otimes(U_941,c_Groups_Oplus__class_Oplus(U_941,U_942,U_943)),U_944) = c_Groups_Oplus__class_Oplus(U_941,hAPP(c_Groups_Otimes__class_Otimes(U_941,U_942),U_944),hAPP(c_Groups_Otimes__class_Otimes(U_941,U_943),U_944))
| ~ class_RealVector_Oreal__normed__algebra(U_941) ),
inference(variable_rename,[status(thm)],[f_303_1]) ).
cnf(f_303_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_941,c_Groups_Oplus__class_Oplus(U_941,U_942,U_943)),U_944) = c_Groups_Oplus__class_Oplus(U_941,hAPP(c_Groups_Otimes__class_Otimes(U_941,U_942),U_944),hAPP(c_Groups_Otimes__class_Otimes(U_941,U_943),U_944))
| ~ class_RealVector_Oreal__normed__algebra(U_941) ),
inference(clausify,[status(thm)],[f_303_2]) ).
fof(f_304_1,plain,
! [V_ya,V_y,V_x,T_a] :
( 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(c_Groups_Otimes__class_Otimes(T_a,V_x),V_ya),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_304_2,plain,
! [U_948,U_947,U_946,U_945] :
( hAPP(c_Groups_Otimes__class_Otimes(U_945,c_Groups_Oplus__class_Oplus(U_945,U_946,U_947)),U_948) = c_Groups_Oplus__class_Oplus(U_945,hAPP(c_Groups_Otimes__class_Otimes(U_945,U_946),U_948),hAPP(c_Groups_Otimes__class_Otimes(U_945,U_947),U_948))
| ~ class_RealVector_Oreal__normed__algebra(U_945) ),
inference(variable_rename,[status(thm)],[f_304_1]) ).
cnf(f_304_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_945,c_Groups_Oplus__class_Oplus(U_945,U_946,U_947)),U_948) = c_Groups_Oplus__class_Oplus(U_945,hAPP(c_Groups_Otimes__class_Otimes(U_945,U_946),U_948),hAPP(c_Groups_Otimes__class_Otimes(U_945,U_947),U_948))
| ~ class_RealVector_Oreal__normed__algebra(U_945) ),
inference(clausify,[status(thm)],[f_304_2]) ).
fof(f_305_1,plain,
! [V_z,V_y,V_x,T_a] :
( 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(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y),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_305_2,plain,
! [U_952,U_951,U_950,U_949] :
( hAPP(c_Groups_Otimes__class_Otimes(U_949,U_950),c_Groups_Oplus__class_Oplus(U_949,U_951,U_952)) = c_Groups_Oplus__class_Oplus(U_949,hAPP(c_Groups_Otimes__class_Otimes(U_949,U_950),U_951),hAPP(c_Groups_Otimes__class_Otimes(U_949,U_950),U_952))
| ~ class_Rings_Ocomm__semiring__1(U_949) ),
inference(variable_rename,[status(thm)],[f_305_1]) ).
cnf(f_305_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_949,U_950),c_Groups_Oplus__class_Oplus(U_949,U_951,U_952)) = c_Groups_Oplus__class_Oplus(U_949,hAPP(c_Groups_Otimes__class_Otimes(U_949,U_950),U_951),hAPP(c_Groups_Otimes__class_Otimes(U_949,U_950),U_952))
| ~ class_Rings_Ocomm__semiring__1(U_949) ),
inference(clausify,[status(thm)],[f_305_2]) ).
fof(f_306_1,plain,
! [V_db_2,V_ca_2,V_b_2,V_a_2,T_a] :
( ( ( ( V_ca_2 != V_db_2
& V_a_2 != V_b_2 )
| c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_db_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_db_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_ca_2)) )
& ( c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_ca_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_db_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_db_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b_2),V_ca_2))
| V_ca_2 = V_db_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_306_2,plain,
! [U_957,U_956,U_955,U_954,U_953] :
( ( ( ( U_956 != U_957
& U_954 != U_955 )
| c_Groups_Oplus__class_Oplus(U_953,hAPP(c_Groups_Otimes__class_Otimes(U_953,U_954),U_956),hAPP(c_Groups_Otimes__class_Otimes(U_953,U_955),U_957)) = c_Groups_Oplus__class_Oplus(U_953,hAPP(c_Groups_Otimes__class_Otimes(U_953,U_954),U_957),hAPP(c_Groups_Otimes__class_Otimes(U_953,U_955),U_956)) )
& ( c_Groups_Oplus__class_Oplus(U_953,hAPP(c_Groups_Otimes__class_Otimes(U_953,U_954),U_956),hAPP(c_Groups_Otimes__class_Otimes(U_953,U_955),U_957)) != c_Groups_Oplus__class_Oplus(U_953,hAPP(c_Groups_Otimes__class_Otimes(U_953,U_954),U_957),hAPP(c_Groups_Otimes__class_Otimes(U_953,U_955),U_956))
| U_956 = U_957
| U_954 = U_955 ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_953) ),
inference(variable_rename,[status(thm)],[f_306_1]) ).
cnf(f_306_3,plain,
( c_Groups_Oplus__class_Oplus(U_953,hAPP(c_Groups_Otimes__class_Otimes(U_953,U_954),U_956),hAPP(c_Groups_Otimes__class_Otimes(U_953,U_955),U_957)) != c_Groups_Oplus__class_Oplus(U_953,hAPP(c_Groups_Otimes__class_Otimes(U_953,U_954),U_957),hAPP(c_Groups_Otimes__class_Otimes(U_953,U_955),U_956))
| U_956 = U_957
| U_954 = U_955
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_953) ),
inference(clausify,[status(thm)],[f_306_2]) ).
cnf(f_306_4,plain,
( U_954 != U_955
| c_Groups_Oplus__class_Oplus(U_953,hAPP(c_Groups_Otimes__class_Otimes(U_953,U_954),U_956),hAPP(c_Groups_Otimes__class_Otimes(U_953,U_955),U_957)) = c_Groups_Oplus__class_Oplus(U_953,hAPP(c_Groups_Otimes__class_Otimes(U_953,U_954),U_957),hAPP(c_Groups_Otimes__class_Otimes(U_953,U_955),U_956))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_953) ),
inference(clausify,[status(thm)],[f_306_2]) ).
cnf(f_306_5,plain,
( U_956 != U_957
| c_Groups_Oplus__class_Oplus(U_953,hAPP(c_Groups_Otimes__class_Otimes(U_953,U_954),U_956),hAPP(c_Groups_Otimes__class_Otimes(U_953,U_955),U_957)) = c_Groups_Oplus__class_Oplus(U_953,hAPP(c_Groups_Otimes__class_Otimes(U_953,U_954),U_957),hAPP(c_Groups_Otimes__class_Otimes(U_953,U_955),U_956))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_953) ),
inference(clausify,[status(thm)],[f_306_2]) ).
fof(f_307_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),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_307_2,plain,
! [U_961,U_960,U_959,U_958] :
( hAPP(c_Groups_Otimes__class_Otimes(U_958,c_Groups_Oplus__class_Oplus(U_958,U_959,U_960)),U_961) = c_Groups_Oplus__class_Oplus(U_958,hAPP(c_Groups_Otimes__class_Otimes(U_958,U_959),U_961),hAPP(c_Groups_Otimes__class_Otimes(U_958,U_960),U_961))
| ~ class_Rings_Ocomm__semiring__1(U_958) ),
inference(variable_rename,[status(thm)],[f_307_1]) ).
cnf(f_307_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_958,c_Groups_Oplus__class_Oplus(U_958,U_959,U_960)),U_961) = c_Groups_Oplus__class_Oplus(U_958,hAPP(c_Groups_Otimes__class_Otimes(U_958,U_959),U_961),hAPP(c_Groups_Otimes__class_Otimes(U_958,U_960),U_961))
| ~ class_Rings_Ocomm__semiring__1(U_958) ),
inference(clausify,[status(thm)],[f_307_2]) ).
fof(f_308_1,plain,
! [V_b,V_m,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_m),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_m)) = 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_308_2,plain,
! [U_965,U_964,U_963,U_962] :
( c_Groups_Oplus__class_Oplus(U_962,hAPP(c_Groups_Otimes__class_Otimes(U_962,U_963),U_964),hAPP(c_Groups_Otimes__class_Otimes(U_962,U_965),U_964)) = hAPP(c_Groups_Otimes__class_Otimes(U_962,c_Groups_Oplus__class_Oplus(U_962,U_963,U_965)),U_964)
| ~ class_Rings_Ocomm__semiring__1(U_962) ),
inference(variable_rename,[status(thm)],[f_308_1]) ).
cnf(f_308_3,plain,
( c_Groups_Oplus__class_Oplus(U_962,hAPP(c_Groups_Otimes__class_Otimes(U_962,U_963),U_964),hAPP(c_Groups_Otimes__class_Otimes(U_962,U_965),U_964)) = hAPP(c_Groups_Otimes__class_Otimes(U_962,c_Groups_Oplus__class_Oplus(U_962,U_963,U_965)),U_964)
| ~ class_Rings_Ocomm__semiring__1(U_962) ),
inference(clausify,[status(thm)],[f_308_2]) ).
fof(f_309_1,plain,
! [V_za_2,V_x_2,V_y_2,V_wa_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_y_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_za_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_za_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_y_2))
| ( V_y_2 != V_za_2
& V_wa_2 != V_x_2 ) )
& ( V_y_2 = V_za_2
| V_wa_2 = V_x_2
| c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_y_2),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_za_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_wa_2),V_za_2),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_309_2,plain,
! [U_970,U_969,U_968,U_967,U_966] :
( ( ( c_Groups_Oplus__class_Oplus(U_966,hAPP(c_Groups_Otimes__class_Otimes(U_966,U_967),U_968),hAPP(c_Groups_Otimes__class_Otimes(U_966,U_969),U_970)) = c_Groups_Oplus__class_Oplus(U_966,hAPP(c_Groups_Otimes__class_Otimes(U_966,U_967),U_970),hAPP(c_Groups_Otimes__class_Otimes(U_966,U_969),U_968))
| ( U_968 != U_970
& U_967 != U_969 ) )
& ( U_968 = U_970
| U_967 = U_969
| c_Groups_Oplus__class_Oplus(U_966,hAPP(c_Groups_Otimes__class_Otimes(U_966,U_967),U_968),hAPP(c_Groups_Otimes__class_Otimes(U_966,U_969),U_970)) != c_Groups_Oplus__class_Oplus(U_966,hAPP(c_Groups_Otimes__class_Otimes(U_966,U_967),U_970),hAPP(c_Groups_Otimes__class_Otimes(U_966,U_969),U_968)) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_966) ),
inference(variable_rename,[status(thm)],[f_309_1]) ).
cnf(f_309_3,plain,
( U_968 = U_970
| U_967 = U_969
| c_Groups_Oplus__class_Oplus(U_966,hAPP(c_Groups_Otimes__class_Otimes(U_966,U_967),U_968),hAPP(c_Groups_Otimes__class_Otimes(U_966,U_969),U_970)) != c_Groups_Oplus__class_Oplus(U_966,hAPP(c_Groups_Otimes__class_Otimes(U_966,U_967),U_970),hAPP(c_Groups_Otimes__class_Otimes(U_966,U_969),U_968))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_966) ),
inference(clausify,[status(thm)],[f_309_2]) ).
cnf(f_309_4,plain,
( U_967 != U_969
| c_Groups_Oplus__class_Oplus(U_966,hAPP(c_Groups_Otimes__class_Otimes(U_966,U_967),U_968),hAPP(c_Groups_Otimes__class_Otimes(U_966,U_969),U_970)) = c_Groups_Oplus__class_Oplus(U_966,hAPP(c_Groups_Otimes__class_Otimes(U_966,U_967),U_970),hAPP(c_Groups_Otimes__class_Otimes(U_966,U_969),U_968))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_966) ),
inference(clausify,[status(thm)],[f_309_2]) ).
cnf(f_309_5,plain,
( U_968 != U_970
| c_Groups_Oplus__class_Oplus(U_966,hAPP(c_Groups_Otimes__class_Otimes(U_966,U_967),U_968),hAPP(c_Groups_Otimes__class_Otimes(U_966,U_969),U_970)) = c_Groups_Oplus__class_Oplus(U_966,hAPP(c_Groups_Otimes__class_Otimes(U_966,U_967),U_970),hAPP(c_Groups_Otimes__class_Otimes(U_966,U_969),U_968))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_966) ),
inference(clausify,[status(thm)],[f_309_2]) ).
fof(f_310_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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(c_Groups_Otimes__class_Otimes(T_a,V_a),V_c),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_310_2,plain,
! [U_974,U_973,U_972,U_971] :
( 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(c_Groups_Otimes__class_Otimes(U_971,U_972),U_974),hAPP(c_Groups_Otimes__class_Otimes(U_971,U_973),U_974))
| ~ class_Rings_Ocomm__semiring(U_971) ),
inference(variable_rename,[status(thm)],[f_310_1]) ).
cnf(f_310_3,plain,
( 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(c_Groups_Otimes__class_Otimes(U_971,U_972),U_974),hAPP(c_Groups_Otimes__class_Otimes(U_971,U_973),U_974))
| ~ class_Rings_Ocomm__semiring(U_971) ),
inference(clausify,[status(thm)],[f_310_2]) ).
fof(f_311_1,plain,
! [V_c,V_b,V_e,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_b),V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,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_311_2,plain,
! [U_979,U_978,U_977,U_976,U_975] :
( c_Groups_Oplus__class_Oplus(U_975,hAPP(c_Groups_Otimes__class_Otimes(U_975,U_976),U_977),c_Groups_Oplus__class_Oplus(U_975,hAPP(c_Groups_Otimes__class_Otimes(U_975,U_978),U_977),U_979)) = c_Groups_Oplus__class_Oplus(U_975,hAPP(c_Groups_Otimes__class_Otimes(U_975,c_Groups_Oplus__class_Oplus(U_975,U_976,U_978)),U_977),U_979)
| ~ class_Rings_Osemiring(U_975) ),
inference(variable_rename,[status(thm)],[f_311_1]) ).
cnf(f_311_3,plain,
( c_Groups_Oplus__class_Oplus(U_975,hAPP(c_Groups_Otimes__class_Otimes(U_975,U_976),U_977),c_Groups_Oplus__class_Oplus(U_975,hAPP(c_Groups_Otimes__class_Otimes(U_975,U_978),U_977),U_979)) = c_Groups_Oplus__class_Oplus(U_975,hAPP(c_Groups_Otimes__class_Otimes(U_975,c_Groups_Oplus__class_Oplus(U_975,U_976,U_978)),U_977),U_979)
| ~ class_Rings_Osemiring(U_975) ),
inference(clausify,[status(thm)],[f_311_2]) ).
fof(f_312_1,plain,
! [V_ya,V_y,V_x,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya))
| ~ class_RealVector_Oreal__normed__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide_Oadd]) ).
fof(f_312_2,plain,
! [U_983,U_982,U_981,U_980] :
( c_Rings_Oinverse__class_Odivide(U_980,c_Groups_Oplus__class_Oplus(U_980,U_981,U_982),U_983) = c_Groups_Oplus__class_Oplus(U_980,c_Rings_Oinverse__class_Odivide(U_980,U_981,U_983),c_Rings_Oinverse__class_Odivide(U_980,U_982,U_983))
| ~ class_RealVector_Oreal__normed__field(U_980) ),
inference(variable_rename,[status(thm)],[f_312_1]) ).
cnf(f_312_3,plain,
( c_Rings_Oinverse__class_Odivide(U_980,c_Groups_Oplus__class_Oplus(U_980,U_981,U_982),U_983) = c_Groups_Oplus__class_Oplus(U_980,c_Rings_Oinverse__class_Odivide(U_980,U_981,U_983),c_Rings_Oinverse__class_Odivide(U_980,U_982,U_983))
| ~ class_RealVector_Oreal__normed__field(U_980) ),
inference(clausify,[status(thm)],[f_312_2]) ).
fof(f_313_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__divide__distrib]) ).
fof(f_313_2,plain,
! [U_987,U_986,U_985,U_984] :
( c_Rings_Oinverse__class_Odivide(U_984,c_Groups_Oplus__class_Oplus(U_984,U_985,U_986),U_987) = c_Groups_Oplus__class_Oplus(U_984,c_Rings_Oinverse__class_Odivide(U_984,U_985,U_987),c_Rings_Oinverse__class_Odivide(U_984,U_986,U_987))
| ~ class_Rings_Odivision__ring(U_984) ),
inference(variable_rename,[status(thm)],[f_313_1]) ).
cnf(f_313_3,plain,
( c_Rings_Oinverse__class_Odivide(U_984,c_Groups_Oplus__class_Oplus(U_984,U_985,U_986),U_987) = c_Groups_Oplus__class_Oplus(U_984,c_Rings_Oinverse__class_Odivide(U_984,U_985,U_987),c_Rings_Oinverse__class_Odivide(U_984,U_986,U_987))
| ~ class_Rings_Odivision__ring(U_984) ),
inference(clausify,[status(thm)],[f_313_2]) ).
fof(f_314_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_314_2,plain,
! [U_990,U_989,U_988] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_990,U_988),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_990,U_989))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_988,U_989) ),
inference(variable_rename,[status(thm)],[f_314_1]) ).
cnf(f_314_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_990,U_988),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_990,U_989))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_988,U_989) ),
inference(clausify,[status(thm)],[f_314_2]) ).
fof(f_315_1,plain,
! [V_w,V_z2,V_z1] : 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(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_z1),V_w),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_315_2,plain,
! [U_993,U_992,U_991] : hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_991,U_992)),U_993) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_991),U_993),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_992),U_993)),
inference(variable_rename,[status(thm)],[f_315_1]) ).
cnf(f_315_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_991,U_992)),U_993) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_991),U_993),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_992),U_993)),
inference(clausify,[status(thm)],[f_315_2]) ).
fof(f_316_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_316_2,plain,
! [U_995,U_994] :
( ( ( c_Groups_Osgn__class_Osgn(U_994,U_995) = c_Groups_Ozero__class_Ozero(U_994)
| U_995 != c_Groups_Ozero__class_Ozero(U_994) )
& ( U_995 = c_Groups_Ozero__class_Ozero(U_994)
| c_Groups_Osgn__class_Osgn(U_994,U_995) != c_Groups_Ozero__class_Ozero(U_994) ) )
| ~ class_RealVector_Oreal__normed__vector(U_994) ),
inference(variable_rename,[status(thm)],[f_316_1]) ).
cnf(f_316_3,plain,
( U_995 = c_Groups_Ozero__class_Ozero(U_994)
| c_Groups_Osgn__class_Osgn(U_994,U_995) != c_Groups_Ozero__class_Ozero(U_994)
| ~ class_RealVector_Oreal__normed__vector(U_994) ),
inference(clausify,[status(thm)],[f_316_2]) ).
cnf(f_316_4,plain,
( c_Groups_Osgn__class_Osgn(U_994,U_995) = c_Groups_Ozero__class_Ozero(U_994)
| U_995 != c_Groups_Ozero__class_Ozero(U_994)
| ~ class_RealVector_Oreal__normed__vector(U_994) ),
inference(clausify,[status(thm)],[f_316_2]) ).
fof(f_317_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_317_2,plain,
! [U_996] :
( c_Groups_Osgn__class_Osgn(U_996,c_Groups_Ozero__class_Ozero(U_996)) = c_Groups_Ozero__class_Ozero(U_996)
| ~ class_RealVector_Oreal__normed__vector(U_996) ),
inference(variable_rename,[status(thm)],[f_317_1]) ).
cnf(f_317_3,plain,
( c_Groups_Osgn__class_Osgn(U_996,c_Groups_Ozero__class_Ozero(U_996)) = c_Groups_Ozero__class_Ozero(U_996)
| ~ class_RealVector_Oreal__normed__vector(U_996) ),
inference(clausify,[status(thm)],[f_317_2]) ).
fof(f_318_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_318_2,plain,
! [U_997] :
( c_Groups_Osgn__class_Osgn(U_997,c_Groups_Ozero__class_Ozero(U_997)) = c_Groups_Ozero__class_Ozero(U_997)
| ~ class_Groups_Osgn__if(U_997) ),
inference(variable_rename,[status(thm)],[f_318_1]) ).
cnf(f_318_3,plain,
( c_Groups_Osgn__class_Osgn(U_997,c_Groups_Ozero__class_Ozero(U_997)) = c_Groups_Ozero__class_Ozero(U_997)
| ~ class_Groups_Osgn__if(U_997) ),
inference(clausify,[status(thm)],[f_318_2]) ).
fof(f_319_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_319_2,plain,
! [U_999,U_998] :
( ( ( c_Groups_Osgn__class_Osgn(U_998,U_999) = c_Groups_Ozero__class_Ozero(U_998)
| U_999 != c_Groups_Ozero__class_Ozero(U_998) )
& ( U_999 = c_Groups_Ozero__class_Ozero(U_998)
| c_Groups_Osgn__class_Osgn(U_998,U_999) != c_Groups_Ozero__class_Ozero(U_998) ) )
| ~ class_Rings_Olinordered__idom(U_998) ),
inference(variable_rename,[status(thm)],[f_319_1]) ).
cnf(f_319_3,plain,
( U_999 = c_Groups_Ozero__class_Ozero(U_998)
| c_Groups_Osgn__class_Osgn(U_998,U_999) != c_Groups_Ozero__class_Ozero(U_998)
| ~ class_Rings_Olinordered__idom(U_998) ),
inference(clausify,[status(thm)],[f_319_2]) ).
cnf(f_319_4,plain,
( c_Groups_Osgn__class_Osgn(U_998,U_999) = c_Groups_Ozero__class_Ozero(U_998)
| U_999 != c_Groups_Ozero__class_Ozero(U_998)
| ~ class_Rings_Olinordered__idom(U_998) ),
inference(clausify,[status(thm)],[f_319_2]) ).
fof(f_320_1,plain,
! [V_y,V_x,T_a] :
( c_Groups_Osgn__class_Osgn(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y)) = 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_320_2,plain,
! [U_1002,U_1001,U_1000] :
( c_Groups_Osgn__class_Osgn(U_1000,hAPP(c_Groups_Otimes__class_Otimes(U_1000,U_1001),U_1002)) = hAPP(c_Groups_Otimes__class_Otimes(U_1000,c_Groups_Osgn__class_Osgn(U_1000,U_1001)),c_Groups_Osgn__class_Osgn(U_1000,U_1002))
| ~ class_RealVector_Oreal__normed__div__algebra(U_1000) ),
inference(variable_rename,[status(thm)],[f_320_1]) ).
cnf(f_320_3,plain,
( c_Groups_Osgn__class_Osgn(U_1000,hAPP(c_Groups_Otimes__class_Otimes(U_1000,U_1001),U_1002)) = hAPP(c_Groups_Otimes__class_Otimes(U_1000,c_Groups_Osgn__class_Osgn(U_1000,U_1001)),c_Groups_Osgn__class_Osgn(U_1000,U_1002))
| ~ class_RealVector_Oreal__normed__div__algebra(U_1000) ),
inference(clausify,[status(thm)],[f_320_2]) ).
fof(f_321_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Osgn__class_Osgn(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = 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_321_2,plain,
! [U_1005,U_1004,U_1003] :
( c_Groups_Osgn__class_Osgn(U_1003,hAPP(c_Groups_Otimes__class_Otimes(U_1003,U_1004),U_1005)) = hAPP(c_Groups_Otimes__class_Otimes(U_1003,c_Groups_Osgn__class_Osgn(U_1003,U_1004)),c_Groups_Osgn__class_Osgn(U_1003,U_1005))
| ~ class_Rings_Olinordered__idom(U_1003) ),
inference(variable_rename,[status(thm)],[f_321_1]) ).
cnf(f_321_3,plain,
( c_Groups_Osgn__class_Osgn(U_1003,hAPP(c_Groups_Otimes__class_Otimes(U_1003,U_1004),U_1005)) = hAPP(c_Groups_Otimes__class_Otimes(U_1003,c_Groups_Osgn__class_Osgn(U_1003,U_1004)),c_Groups_Osgn__class_Osgn(U_1003,U_1005))
| ~ class_Rings_Olinordered__idom(U_1003) ),
inference(clausify,[status(thm)],[f_321_2]) ).
fof(f_322_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_322_2,plain,
! [U_1006] :
( c_Groups_Osgn__class_Osgn(U_1006,c_Groups_Oone__class_Oone(U_1006)) = c_Groups_Oone__class_Oone(U_1006)
| ~ class_RealVector_Oreal__normed__algebra__1(U_1006) ),
inference(variable_rename,[status(thm)],[f_322_1]) ).
cnf(f_322_3,plain,
( c_Groups_Osgn__class_Osgn(U_1006,c_Groups_Oone__class_Oone(U_1006)) = c_Groups_Oone__class_Oone(U_1006)
| ~ class_RealVector_Oreal__normed__algebra__1(U_1006) ),
inference(clausify,[status(thm)],[f_322_2]) ).
fof(f_323_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(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_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__nonpositive__iff__nonpositive]) ).
fof(f_323_2,plain,
! [U_1008,U_1007] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1007,c_Rings_Oinverse__class_Oinverse(U_1007,U_1008),c_Groups_Ozero__class_Ozero(U_1007))
| ~ c_Orderings_Oord__class_Oless__eq(U_1007,U_1008,c_Groups_Ozero__class_Ozero(U_1007)) )
& ( c_Orderings_Oord__class_Oless__eq(U_1007,U_1008,c_Groups_Ozero__class_Ozero(U_1007))
| ~ c_Orderings_Oord__class_Oless__eq(U_1007,c_Rings_Oinverse__class_Oinverse(U_1007,U_1008),c_Groups_Ozero__class_Ozero(U_1007)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_1007) ),
inference(variable_rename,[status(thm)],[f_323_1]) ).
cnf(f_323_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1007,U_1008,c_Groups_Ozero__class_Ozero(U_1007))
| ~ c_Orderings_Oord__class_Oless__eq(U_1007,c_Rings_Oinverse__class_Oinverse(U_1007,U_1008),c_Groups_Ozero__class_Ozero(U_1007))
| ~ class_Fields_Olinordered__field__inverse__zero(U_1007) ),
inference(clausify,[status(thm)],[f_323_2]) ).
cnf(f_323_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1007,c_Rings_Oinverse__class_Oinverse(U_1007,U_1008),c_Groups_Ozero__class_Ozero(U_1007))
| ~ c_Orderings_Oord__class_Oless__eq(U_1007,U_1008,c_Groups_Ozero__class_Ozero(U_1007))
| ~ class_Fields_Olinordered__field__inverse__zero(U_1007) ),
inference(clausify,[status(thm)],[f_323_2]) ).
fof(f_324_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(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),V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__nonnegative__iff__nonnegative]) ).
fof(f_324_2,plain,
! [U_1010,U_1009] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1009,c_Groups_Ozero__class_Ozero(U_1009),c_Rings_Oinverse__class_Oinverse(U_1009,U_1010))
| ~ c_Orderings_Oord__class_Oless__eq(U_1009,c_Groups_Ozero__class_Ozero(U_1009),U_1010) )
& ( c_Orderings_Oord__class_Oless__eq(U_1009,c_Groups_Ozero__class_Ozero(U_1009),U_1010)
| ~ c_Orderings_Oord__class_Oless__eq(U_1009,c_Groups_Ozero__class_Ozero(U_1009),c_Rings_Oinverse__class_Oinverse(U_1009,U_1010)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_1009) ),
inference(variable_rename,[status(thm)],[f_324_1]) ).
cnf(f_324_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1009,c_Groups_Ozero__class_Ozero(U_1009),U_1010)
| ~ c_Orderings_Oord__class_Oless__eq(U_1009,c_Groups_Ozero__class_Ozero(U_1009),c_Rings_Oinverse__class_Oinverse(U_1009,U_1010))
| ~ class_Fields_Olinordered__field__inverse__zero(U_1009) ),
inference(clausify,[status(thm)],[f_324_2]) ).
cnf(f_324_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1009,c_Groups_Ozero__class_Ozero(U_1009),c_Rings_Oinverse__class_Oinverse(U_1009,U_1010))
| ~ c_Orderings_Oord__class_Oless__eq(U_1009,c_Groups_Ozero__class_Ozero(U_1009),U_1010)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1009) ),
inference(clausify,[status(thm)],[f_324_2]) ).
fof(f_325_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_b,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__less__imp__less__neg]) ).
fof(f_325_2,plain,
! [U_1013,U_1012,U_1011] :
( c_Orderings_Oord__class_Oless(U_1011,U_1013,U_1012)
| ~ c_Orderings_Oord__class_Oless(U_1011,U_1013,c_Groups_Ozero__class_Ozero(U_1011))
| ~ c_Orderings_Oord__class_Oless(U_1011,c_Rings_Oinverse__class_Oinverse(U_1011,U_1012),c_Rings_Oinverse__class_Oinverse(U_1011,U_1013))
| ~ class_Fields_Olinordered__field(U_1011) ),
inference(variable_rename,[status(thm)],[f_325_1]) ).
cnf(f_325_3,plain,
( c_Orderings_Oord__class_Oless(U_1011,U_1013,U_1012)
| ~ c_Orderings_Oord__class_Oless(U_1011,U_1013,c_Groups_Ozero__class_Ozero(U_1011))
| ~ c_Orderings_Oord__class_Oless(U_1011,c_Rings_Oinverse__class_Oinverse(U_1011,U_1012),c_Rings_Oinverse__class_Oinverse(U_1011,U_1013))
| ~ class_Fields_Olinordered__field(U_1011) ),
inference(clausify,[status(thm)],[f_325_2]) ).
fof(f_326_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,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__less__imp__less]) ).
fof(f_326_2,plain,
! [U_1016,U_1015,U_1014] :
( c_Orderings_Oord__class_Oless(U_1014,U_1016,U_1015)
| ~ c_Orderings_Oord__class_Oless(U_1014,c_Groups_Ozero__class_Ozero(U_1014),U_1015)
| ~ c_Orderings_Oord__class_Oless(U_1014,c_Rings_Oinverse__class_Oinverse(U_1014,U_1015),c_Rings_Oinverse__class_Oinverse(U_1014,U_1016))
| ~ class_Fields_Olinordered__field(U_1014) ),
inference(variable_rename,[status(thm)],[f_326_1]) ).
cnf(f_326_3,plain,
( c_Orderings_Oord__class_Oless(U_1014,U_1016,U_1015)
| ~ c_Orderings_Oord__class_Oless(U_1014,c_Groups_Ozero__class_Ozero(U_1014),U_1015)
| ~ c_Orderings_Oord__class_Oless(U_1014,c_Rings_Oinverse__class_Oinverse(U_1014,U_1015),c_Rings_Oinverse__class_Oinverse(U_1014,U_1016))
| ~ class_Fields_Olinordered__field(U_1014) ),
inference(clausify,[status(thm)],[f_326_2]) ).
fof(f_327_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__negative__imp__negative]) ).
fof(f_327_2,plain,
! [U_1018,U_1017] :
( c_Orderings_Oord__class_Oless(U_1017,U_1018,c_Groups_Ozero__class_Ozero(U_1017))
| U_1018 = c_Groups_Ozero__class_Ozero(U_1017)
| ~ c_Orderings_Oord__class_Oless(U_1017,c_Rings_Oinverse__class_Oinverse(U_1017,U_1018),c_Groups_Ozero__class_Ozero(U_1017))
| ~ class_Fields_Olinordered__field(U_1017) ),
inference(variable_rename,[status(thm)],[f_327_1]) ).
cnf(f_327_3,plain,
( c_Orderings_Oord__class_Oless(U_1017,U_1018,c_Groups_Ozero__class_Ozero(U_1017))
| U_1018 = c_Groups_Ozero__class_Ozero(U_1017)
| ~ c_Orderings_Oord__class_Oless(U_1017,c_Rings_Oinverse__class_Oinverse(U_1017,U_1018),c_Groups_Ozero__class_Ozero(U_1017))
| ~ class_Fields_Olinordered__field(U_1017) ),
inference(clausify,[status(thm)],[f_327_2]) ).
fof(f_328_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(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,V_a,V_b)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__imp__inverse__less__neg]) ).
fof(f_328_2,plain,
! [U_1021,U_1020,U_1019] :
( c_Orderings_Oord__class_Oless(U_1019,c_Rings_Oinverse__class_Oinverse(U_1019,U_1021),c_Rings_Oinverse__class_Oinverse(U_1019,U_1020))
| ~ c_Orderings_Oord__class_Oless(U_1019,U_1021,c_Groups_Ozero__class_Ozero(U_1019))
| ~ c_Orderings_Oord__class_Oless(U_1019,U_1020,U_1021)
| ~ class_Fields_Olinordered__field(U_1019) ),
inference(variable_rename,[status(thm)],[f_328_1]) ).
cnf(f_328_3,plain,
( c_Orderings_Oord__class_Oless(U_1019,c_Rings_Oinverse__class_Oinverse(U_1019,U_1021),c_Rings_Oinverse__class_Oinverse(U_1019,U_1020))
| ~ c_Orderings_Oord__class_Oless(U_1019,U_1021,c_Groups_Ozero__class_Ozero(U_1019))
| ~ c_Orderings_Oord__class_Oless(U_1019,U_1020,U_1021)
| ~ class_Fields_Olinordered__field(U_1019) ),
inference(clausify,[status(thm)],[f_328_2]) ).
fof(f_329_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,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,V_a,V_b)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__imp__inverse__less]) ).
fof(f_329_2,plain,
! [U_1024,U_1023,U_1022] :
( c_Orderings_Oord__class_Oless(U_1022,c_Rings_Oinverse__class_Oinverse(U_1022,U_1024),c_Rings_Oinverse__class_Oinverse(U_1022,U_1023))
| ~ c_Orderings_Oord__class_Oless(U_1022,c_Groups_Ozero__class_Ozero(U_1022),U_1023)
| ~ c_Orderings_Oord__class_Oless(U_1022,U_1023,U_1024)
| ~ class_Fields_Olinordered__field(U_1022) ),
inference(variable_rename,[status(thm)],[f_329_1]) ).
cnf(f_329_3,plain,
( c_Orderings_Oord__class_Oless(U_1022,c_Rings_Oinverse__class_Oinverse(U_1022,U_1024),c_Rings_Oinverse__class_Oinverse(U_1022,U_1023))
| ~ c_Orderings_Oord__class_Oless(U_1022,c_Groups_Ozero__class_Ozero(U_1022),U_1023)
| ~ c_Orderings_Oord__class_Oless(U_1022,U_1023,U_1024)
| ~ class_Fields_Olinordered__field(U_1022) ),
inference(clausify,[status(thm)],[f_329_2]) ).
fof(f_330_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_negative__imp__inverse__negative]) ).
fof(f_330_2,plain,
! [U_1026,U_1025] :
( c_Orderings_Oord__class_Oless(U_1025,c_Rings_Oinverse__class_Oinverse(U_1025,U_1026),c_Groups_Ozero__class_Ozero(U_1025))
| ~ c_Orderings_Oord__class_Oless(U_1025,U_1026,c_Groups_Ozero__class_Ozero(U_1025))
| ~ class_Fields_Olinordered__field(U_1025) ),
inference(variable_rename,[status(thm)],[f_330_1]) ).
cnf(f_330_3,plain,
( c_Orderings_Oord__class_Oless(U_1025,c_Rings_Oinverse__class_Oinverse(U_1025,U_1026),c_Groups_Ozero__class_Ozero(U_1025))
| ~ c_Orderings_Oord__class_Oless(U_1025,U_1026,c_Groups_Ozero__class_Ozero(U_1025))
| ~ class_Fields_Olinordered__field(U_1025) ),
inference(clausify,[status(thm)],[f_330_2]) ).
fof(f_331_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__positive__imp__positive]) ).
fof(f_331_2,plain,
! [U_1028,U_1027] :
( c_Orderings_Oord__class_Oless(U_1027,c_Groups_Ozero__class_Ozero(U_1027),U_1028)
| U_1028 = c_Groups_Ozero__class_Ozero(U_1027)
| ~ c_Orderings_Oord__class_Oless(U_1027,c_Groups_Ozero__class_Ozero(U_1027),c_Rings_Oinverse__class_Oinverse(U_1027,U_1028))
| ~ class_Fields_Olinordered__field(U_1027) ),
inference(variable_rename,[status(thm)],[f_331_1]) ).
cnf(f_331_3,plain,
( c_Orderings_Oord__class_Oless(U_1027,c_Groups_Ozero__class_Ozero(U_1027),U_1028)
| U_1028 = c_Groups_Ozero__class_Ozero(U_1027)
| ~ c_Orderings_Oord__class_Oless(U_1027,c_Groups_Ozero__class_Ozero(U_1027),c_Rings_Oinverse__class_Oinverse(U_1027,U_1028))
| ~ class_Fields_Olinordered__field(U_1027) ),
inference(clausify,[status(thm)],[f_331_2]) ).
fof(f_332_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_positive__imp__inverse__positive]) ).
fof(f_332_2,plain,
! [U_1030,U_1029] :
( c_Orderings_Oord__class_Oless(U_1029,c_Groups_Ozero__class_Ozero(U_1029),c_Rings_Oinverse__class_Oinverse(U_1029,U_1030))
| ~ c_Orderings_Oord__class_Oless(U_1029,c_Groups_Ozero__class_Ozero(U_1029),U_1030)
| ~ class_Fields_Olinordered__field(U_1029) ),
inference(variable_rename,[status(thm)],[f_332_1]) ).
cnf(f_332_3,plain,
( c_Orderings_Oord__class_Oless(U_1029,c_Groups_Ozero__class_Ozero(U_1029),c_Rings_Oinverse__class_Oinverse(U_1029,U_1030))
| ~ c_Orderings_Oord__class_Oless(U_1029,c_Groups_Ozero__class_Ozero(U_1029),U_1030)
| ~ class_Fields_Olinordered__field(U_1029) ),
inference(clausify,[status(thm)],[f_332_2]) ).
fof(f_333_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(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_Rings_Oinverse__class_Oinverse(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__negative__iff__negative]) ).
fof(f_333_2,plain,
! [U_1032,U_1031] :
( ( ( c_Orderings_Oord__class_Oless(U_1031,c_Rings_Oinverse__class_Oinverse(U_1031,U_1032),c_Groups_Ozero__class_Ozero(U_1031))
| ~ c_Orderings_Oord__class_Oless(U_1031,U_1032,c_Groups_Ozero__class_Ozero(U_1031)) )
& ( c_Orderings_Oord__class_Oless(U_1031,U_1032,c_Groups_Ozero__class_Ozero(U_1031))
| ~ c_Orderings_Oord__class_Oless(U_1031,c_Rings_Oinverse__class_Oinverse(U_1031,U_1032),c_Groups_Ozero__class_Ozero(U_1031)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_1031) ),
inference(variable_rename,[status(thm)],[f_333_1]) ).
cnf(f_333_3,plain,
( c_Orderings_Oord__class_Oless(U_1031,U_1032,c_Groups_Ozero__class_Ozero(U_1031))
| ~ c_Orderings_Oord__class_Oless(U_1031,c_Rings_Oinverse__class_Oinverse(U_1031,U_1032),c_Groups_Ozero__class_Ozero(U_1031))
| ~ class_Fields_Olinordered__field__inverse__zero(U_1031) ),
inference(clausify,[status(thm)],[f_333_2]) ).
cnf(f_333_4,plain,
( c_Orderings_Oord__class_Oless(U_1031,c_Rings_Oinverse__class_Oinverse(U_1031,U_1032),c_Groups_Ozero__class_Ozero(U_1031))
| ~ c_Orderings_Oord__class_Oless(U_1031,U_1032,c_Groups_Ozero__class_Ozero(U_1031))
| ~ class_Fields_Olinordered__field__inverse__zero(U_1031) ),
inference(clausify,[status(thm)],[f_333_2]) ).
fof(f_334_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(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_Rings_Oinverse__class_Oinverse(T_a,V_a_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__positive__iff__positive]) ).
fof(f_334_2,plain,
! [U_1034,U_1033] :
( ( ( c_Orderings_Oord__class_Oless(U_1033,c_Groups_Ozero__class_Ozero(U_1033),c_Rings_Oinverse__class_Oinverse(U_1033,U_1034))
| ~ c_Orderings_Oord__class_Oless(U_1033,c_Groups_Ozero__class_Ozero(U_1033),U_1034) )
& ( c_Orderings_Oord__class_Oless(U_1033,c_Groups_Ozero__class_Ozero(U_1033),U_1034)
| ~ c_Orderings_Oord__class_Oless(U_1033,c_Groups_Ozero__class_Ozero(U_1033),c_Rings_Oinverse__class_Oinverse(U_1033,U_1034)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_1033) ),
inference(variable_rename,[status(thm)],[f_334_1]) ).
cnf(f_334_3,plain,
( c_Orderings_Oord__class_Oless(U_1033,c_Groups_Ozero__class_Ozero(U_1033),U_1034)
| ~ c_Orderings_Oord__class_Oless(U_1033,c_Groups_Ozero__class_Ozero(U_1033),c_Rings_Oinverse__class_Oinverse(U_1033,U_1034))
| ~ class_Fields_Olinordered__field__inverse__zero(U_1033) ),
inference(clausify,[status(thm)],[f_334_2]) ).
cnf(f_334_4,plain,
( c_Orderings_Oord__class_Oless(U_1033,c_Groups_Ozero__class_Ozero(U_1033),c_Rings_Oinverse__class_Oinverse(U_1033,U_1034))
| ~ c_Orderings_Oord__class_Oless(U_1033,c_Groups_Ozero__class_Ozero(U_1033),U_1034)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1033) ),
inference(clausify,[status(thm)],[f_334_2]) ).
fof(f_335_1,plain,
! [V_b,V_a,T_a] :
( c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__mult__distrib]) ).
fof(f_335_2,plain,
! [U_1037,U_1036,U_1035] :
( c_Rings_Oinverse__class_Oinverse(U_1035,hAPP(c_Groups_Otimes__class_Otimes(U_1035,U_1036),U_1037)) = hAPP(c_Groups_Otimes__class_Otimes(U_1035,c_Rings_Oinverse__class_Oinverse(U_1035,U_1037)),c_Rings_Oinverse__class_Oinverse(U_1035,U_1036))
| U_1037 = c_Groups_Ozero__class_Ozero(U_1035)
| U_1036 = c_Groups_Ozero__class_Ozero(U_1035)
| ~ class_Rings_Odivision__ring(U_1035) ),
inference(variable_rename,[status(thm)],[f_335_1]) ).
cnf(f_335_3,plain,
( c_Rings_Oinverse__class_Oinverse(U_1035,hAPP(c_Groups_Otimes__class_Otimes(U_1035,U_1036),U_1037)) = hAPP(c_Groups_Otimes__class_Otimes(U_1035,c_Rings_Oinverse__class_Oinverse(U_1035,U_1037)),c_Rings_Oinverse__class_Oinverse(U_1035,U_1036))
| U_1037 = c_Groups_Ozero__class_Ozero(U_1035)
| U_1036 = c_Groups_Ozero__class_Ozero(U_1035)
| ~ class_Rings_Odivision__ring(U_1035) ),
inference(clausify,[status(thm)],[f_335_2]) ).
fof(f_336_1,plain,
! [V_b,V_a,T_a] :
( c_Rings_Oinverse__class_Oinverse(T_a,V_a) = V_b
| hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b) != c_Groups_Oone__class_Oone(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__unique]) ).
fof(f_336_2,plain,
! [U_1040,U_1039,U_1038] :
( c_Rings_Oinverse__class_Oinverse(U_1038,U_1039) = U_1040
| hAPP(c_Groups_Otimes__class_Otimes(U_1038,U_1039),U_1040) != c_Groups_Oone__class_Oone(U_1038)
| ~ class_Rings_Odivision__ring(U_1038) ),
inference(variable_rename,[status(thm)],[f_336_1]) ).
cnf(f_336_3,plain,
( c_Rings_Oinverse__class_Oinverse(U_1038,U_1039) = U_1040
| hAPP(c_Groups_Otimes__class_Otimes(U_1038,U_1039),U_1040) != c_Groups_Oone__class_Oone(U_1038)
| ~ class_Rings_Odivision__ring(U_1038) ),
inference(clausify,[status(thm)],[f_336_2]) ).
fof(f_337_1,plain,
! [V_b,V_a,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_field__divide__inverse]) ).
fof(f_337_2,plain,
! [U_1043,U_1042,U_1041] :
( c_Rings_Oinverse__class_Odivide(U_1041,U_1042,U_1043) = hAPP(c_Groups_Otimes__class_Otimes(U_1041,U_1042),c_Rings_Oinverse__class_Oinverse(U_1041,U_1043))
| ~ class_Fields_Ofield(U_1041) ),
inference(variable_rename,[status(thm)],[f_337_1]) ).
cnf(f_337_3,plain,
( c_Rings_Oinverse__class_Odivide(U_1041,U_1042,U_1043) = hAPP(c_Groups_Otimes__class_Otimes(U_1041,U_1042),c_Rings_Oinverse__class_Oinverse(U_1041,U_1043))
| ~ class_Fields_Ofield(U_1041) ),
inference(clausify,[status(thm)],[f_337_2]) ).
fof(f_338_1,plain,
! [V_b,V_a,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__inverse]) ).
fof(f_338_2,plain,
! [U_1046,U_1045,U_1044] :
( c_Rings_Oinverse__class_Odivide(U_1044,U_1045,U_1046) = hAPP(c_Groups_Otimes__class_Otimes(U_1044,U_1045),c_Rings_Oinverse__class_Oinverse(U_1044,U_1046))
| ~ class_Rings_Odivision__ring(U_1044) ),
inference(variable_rename,[status(thm)],[f_338_1]) ).
cnf(f_338_3,plain,
( c_Rings_Oinverse__class_Odivide(U_1044,U_1045,U_1046) = hAPP(c_Groups_Otimes__class_Otimes(U_1044,U_1045),c_Rings_Oinverse__class_Oinverse(U_1044,U_1046))
| ~ class_Rings_Odivision__ring(U_1044) ),
inference(clausify,[status(thm)],[f_338_2]) ).
fof(f_339_1,plain,
! [V_a,T_a] :
( c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_field__class_Onormalizing__field__rules_I2_J]) ).
fof(f_339_2,plain,
! [U_1048,U_1047] :
( c_Rings_Oinverse__class_Oinverse(U_1047,U_1048) = c_Rings_Oinverse__class_Odivide(U_1047,c_Groups_Oone__class_Oone(U_1047),U_1048)
| ~ class_Fields_Ofield(U_1047) ),
inference(variable_rename,[status(thm)],[f_339_1]) ).
cnf(f_339_3,plain,
( c_Rings_Oinverse__class_Oinverse(U_1047,U_1048) = c_Rings_Oinverse__class_Odivide(U_1047,c_Groups_Oone__class_Oone(U_1047),U_1048)
| ~ class_Fields_Ofield(U_1047) ),
inference(clausify,[status(thm)],[f_339_2]) ).
fof(f_340_1,plain,
! [V_a,T_a] :
( c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__eq__divide]) ).
fof(f_340_2,plain,
! [U_1050,U_1049] :
( c_Rings_Oinverse__class_Oinverse(U_1049,U_1050) = c_Rings_Oinverse__class_Odivide(U_1049,c_Groups_Oone__class_Oone(U_1049),U_1050)
| ~ class_Rings_Odivision__ring(U_1049) ),
inference(variable_rename,[status(thm)],[f_340_1]) ).
cnf(f_340_3,plain,
( c_Rings_Oinverse__class_Oinverse(U_1049,U_1050) = c_Rings_Oinverse__class_Odivide(U_1049,c_Groups_Oone__class_Oone(U_1049),U_1050)
| ~ class_Rings_Odivision__ring(U_1049) ),
inference(clausify,[status(thm)],[f_340_2]) ).
fof(f_341_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_341_2,plain,
! [U_1053,U_1052,U_1051] :
( c_Orderings_Oord__class_Oless__eq(U_1051,c_Groups_Oplus__class_Oplus(U_1051,U_1052,U_1053),c_Groups_Ozero__class_Ozero(U_1051))
| ~ c_Orderings_Oord__class_Oless__eq(U_1051,U_1053,c_Groups_Ozero__class_Ozero(U_1051))
| ~ c_Orderings_Oord__class_Oless__eq(U_1051,U_1052,c_Groups_Ozero__class_Ozero(U_1051))
| ~ class_Groups_Oordered__comm__monoid__add(U_1051) ),
inference(variable_rename,[status(thm)],[f_341_1]) ).
cnf(f_341_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1051,c_Groups_Oplus__class_Oplus(U_1051,U_1052,U_1053),c_Groups_Ozero__class_Ozero(U_1051))
| ~ c_Orderings_Oord__class_Oless__eq(U_1051,U_1053,c_Groups_Ozero__class_Ozero(U_1051))
| ~ c_Orderings_Oord__class_Oless__eq(U_1051,U_1052,c_Groups_Ozero__class_Ozero(U_1051))
| ~ class_Groups_Oordered__comm__monoid__add(U_1051) ),
inference(clausify,[status(thm)],[f_341_2]) ).
fof(f_342_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_342_2,plain,
! [U_1057,U_1056,U_1055,U_1054] :
( c_Orderings_Oord__class_Oless__eq(U_1054,U_1056,c_Groups_Oplus__class_Oplus(U_1054,U_1057,U_1055))
| ~ c_Orderings_Oord__class_Oless__eq(U_1054,U_1056,U_1057)
| ~ c_Orderings_Oord__class_Oless__eq(U_1054,c_Groups_Ozero__class_Ozero(U_1054),U_1055)
| ~ class_Groups_Oordered__comm__monoid__add(U_1054) ),
inference(variable_rename,[status(thm)],[f_342_1]) ).
cnf(f_342_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1054,U_1056,c_Groups_Oplus__class_Oplus(U_1054,U_1057,U_1055))
| ~ c_Orderings_Oord__class_Oless__eq(U_1054,U_1056,U_1057)
| ~ c_Orderings_Oord__class_Oless__eq(U_1054,c_Groups_Ozero__class_Ozero(U_1054),U_1055)
| ~ class_Groups_Oordered__comm__monoid__add(U_1054) ),
inference(clausify,[status(thm)],[f_342_2]) ).
fof(f_343_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_343_2,plain,
! [U_1061,U_1060,U_1059,U_1058] :
( c_Orderings_Oord__class_Oless__eq(U_1058,U_1060,c_Groups_Oplus__class_Oplus(U_1058,U_1059,U_1061))
| ~ c_Orderings_Oord__class_Oless__eq(U_1058,U_1060,U_1061)
| ~ c_Orderings_Oord__class_Oless__eq(U_1058,c_Groups_Ozero__class_Ozero(U_1058),U_1059)
| ~ class_Groups_Oordered__comm__monoid__add(U_1058) ),
inference(variable_rename,[status(thm)],[f_343_1]) ).
cnf(f_343_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1058,U_1060,c_Groups_Oplus__class_Oplus(U_1058,U_1059,U_1061))
| ~ c_Orderings_Oord__class_Oless__eq(U_1058,U_1060,U_1061)
| ~ c_Orderings_Oord__class_Oless__eq(U_1058,c_Groups_Ozero__class_Ozero(U_1058),U_1059)
| ~ class_Groups_Oordered__comm__monoid__add(U_1058) ),
inference(clausify,[status(thm)],[f_343_2]) ).
fof(f_344_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_344_2,plain,
! [U_1064,U_1063,U_1062] :
( ( ( c_Groups_Oplus__class_Oplus(U_1062,U_1063,U_1064) = c_Groups_Ozero__class_Ozero(U_1062)
| U_1064 != c_Groups_Ozero__class_Ozero(U_1062)
| U_1063 != c_Groups_Ozero__class_Ozero(U_1062) )
& ( ( U_1064 = c_Groups_Ozero__class_Ozero(U_1062)
& U_1063 = c_Groups_Ozero__class_Ozero(U_1062) )
| c_Groups_Oplus__class_Oplus(U_1062,U_1063,U_1064) != c_Groups_Ozero__class_Ozero(U_1062) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_1062,c_Groups_Ozero__class_Ozero(U_1062),U_1064)
| ~ c_Orderings_Oord__class_Oless__eq(U_1062,c_Groups_Ozero__class_Ozero(U_1062),U_1063)
| ~ class_Groups_Oordered__comm__monoid__add(U_1062) ),
inference(variable_rename,[status(thm)],[f_344_1]) ).
cnf(f_344_3,plain,
( U_1063 = c_Groups_Ozero__class_Ozero(U_1062)
| c_Groups_Oplus__class_Oplus(U_1062,U_1063,U_1064) != c_Groups_Ozero__class_Ozero(U_1062)
| ~ c_Orderings_Oord__class_Oless__eq(U_1062,c_Groups_Ozero__class_Ozero(U_1062),U_1064)
| ~ c_Orderings_Oord__class_Oless__eq(U_1062,c_Groups_Ozero__class_Ozero(U_1062),U_1063)
| ~ class_Groups_Oordered__comm__monoid__add(U_1062) ),
inference(clausify,[status(thm)],[f_344_2]) ).
cnf(f_344_4,plain,
( U_1064 = c_Groups_Ozero__class_Ozero(U_1062)
| c_Groups_Oplus__class_Oplus(U_1062,U_1063,U_1064) != c_Groups_Ozero__class_Ozero(U_1062)
| ~ c_Orderings_Oord__class_Oless__eq(U_1062,c_Groups_Ozero__class_Ozero(U_1062),U_1064)
| ~ c_Orderings_Oord__class_Oless__eq(U_1062,c_Groups_Ozero__class_Ozero(U_1062),U_1063)
| ~ class_Groups_Oordered__comm__monoid__add(U_1062) ),
inference(clausify,[status(thm)],[f_344_2]) ).
cnf(f_344_5,plain,
( c_Groups_Oplus__class_Oplus(U_1062,U_1063,U_1064) = c_Groups_Ozero__class_Ozero(U_1062)
| U_1064 != c_Groups_Ozero__class_Ozero(U_1062)
| U_1063 != c_Groups_Ozero__class_Ozero(U_1062)
| ~ c_Orderings_Oord__class_Oless__eq(U_1062,c_Groups_Ozero__class_Ozero(U_1062),U_1064)
| ~ c_Orderings_Oord__class_Oless__eq(U_1062,c_Groups_Ozero__class_Ozero(U_1062),U_1063)
| ~ class_Groups_Oordered__comm__monoid__add(U_1062) ),
inference(clausify,[status(thm)],[f_344_2]) ).
fof(f_345_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_345_2,plain,
! [U_1067,U_1066,U_1065] :
( c_Orderings_Oord__class_Oless__eq(U_1065,c_Groups_Ozero__class_Ozero(U_1065),c_Groups_Oplus__class_Oplus(U_1065,U_1066,U_1067))
| ~ c_Orderings_Oord__class_Oless__eq(U_1065,c_Groups_Ozero__class_Ozero(U_1065),U_1067)
| ~ c_Orderings_Oord__class_Oless__eq(U_1065,c_Groups_Ozero__class_Ozero(U_1065),U_1066)
| ~ class_Groups_Oordered__comm__monoid__add(U_1065) ),
inference(variable_rename,[status(thm)],[f_345_1]) ).
cnf(f_345_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1065,c_Groups_Ozero__class_Ozero(U_1065),c_Groups_Oplus__class_Oplus(U_1065,U_1066,U_1067))
| ~ c_Orderings_Oord__class_Oless__eq(U_1065,c_Groups_Ozero__class_Ozero(U_1065),U_1067)
| ~ c_Orderings_Oord__class_Oless__eq(U_1065,c_Groups_Ozero__class_Ozero(U_1065),U_1066)
| ~ class_Groups_Oordered__comm__monoid__add(U_1065) ),
inference(clausify,[status(thm)],[f_345_2]) ).
fof(f_346_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_346_2,plain,
! [U_1069,U_1068] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1068,c_Groups_Oplus__class_Oplus(U_1068,U_1069,U_1069),c_Groups_Ozero__class_Ozero(U_1068))
| ~ c_Orderings_Oord__class_Oless__eq(U_1068,U_1069,c_Groups_Ozero__class_Ozero(U_1068)) )
& ( c_Orderings_Oord__class_Oless__eq(U_1068,U_1069,c_Groups_Ozero__class_Ozero(U_1068))
| ~ c_Orderings_Oord__class_Oless__eq(U_1068,c_Groups_Oplus__class_Oplus(U_1068,U_1069,U_1069),c_Groups_Ozero__class_Ozero(U_1068)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1068) ),
inference(variable_rename,[status(thm)],[f_346_1]) ).
cnf(f_346_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1068,U_1069,c_Groups_Ozero__class_Ozero(U_1068))
| ~ c_Orderings_Oord__class_Oless__eq(U_1068,c_Groups_Oplus__class_Oplus(U_1068,U_1069,U_1069),c_Groups_Ozero__class_Ozero(U_1068))
| ~ class_Groups_Olinordered__ab__group__add(U_1068) ),
inference(clausify,[status(thm)],[f_346_2]) ).
cnf(f_346_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1068,c_Groups_Oplus__class_Oplus(U_1068,U_1069,U_1069),c_Groups_Ozero__class_Ozero(U_1068))
| ~ c_Orderings_Oord__class_Oless__eq(U_1068,U_1069,c_Groups_Ozero__class_Ozero(U_1068))
| ~ class_Groups_Olinordered__ab__group__add(U_1068) ),
inference(clausify,[status(thm)],[f_346_2]) ).
fof(f_347_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_347_2,plain,
! [U_1071,U_1070] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1070,c_Groups_Ozero__class_Ozero(U_1070),c_Groups_Oplus__class_Oplus(U_1070,U_1071,U_1071))
| ~ c_Orderings_Oord__class_Oless__eq(U_1070,c_Groups_Ozero__class_Ozero(U_1070),U_1071) )
& ( c_Orderings_Oord__class_Oless__eq(U_1070,c_Groups_Ozero__class_Ozero(U_1070),U_1071)
| ~ c_Orderings_Oord__class_Oless__eq(U_1070,c_Groups_Ozero__class_Ozero(U_1070),c_Groups_Oplus__class_Oplus(U_1070,U_1071,U_1071)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1070) ),
inference(variable_rename,[status(thm)],[f_347_1]) ).
cnf(f_347_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1070,c_Groups_Ozero__class_Ozero(U_1070),U_1071)
| ~ c_Orderings_Oord__class_Oless__eq(U_1070,c_Groups_Ozero__class_Ozero(U_1070),c_Groups_Oplus__class_Oplus(U_1070,U_1071,U_1071))
| ~ class_Groups_Olinordered__ab__group__add(U_1070) ),
inference(clausify,[status(thm)],[f_347_2]) ).
cnf(f_347_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1070,c_Groups_Ozero__class_Ozero(U_1070),c_Groups_Oplus__class_Oplus(U_1070,U_1071,U_1071))
| ~ c_Orderings_Oord__class_Oless__eq(U_1070,c_Groups_Ozero__class_Ozero(U_1070),U_1071)
| ~ class_Groups_Olinordered__ab__group__add(U_1070) ),
inference(clausify,[status(thm)],[f_347_2]) ).
fof(f_348_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_348_2,plain,
! [U_1074,U_1073,U_1072] :
( c_Orderings_Oord__class_Oless(U_1072,c_Groups_Oplus__class_Oplus(U_1072,U_1073,U_1074),c_Groups_Ozero__class_Ozero(U_1072))
| ~ c_Orderings_Oord__class_Oless(U_1072,U_1074,c_Groups_Ozero__class_Ozero(U_1072))
| ~ c_Orderings_Oord__class_Oless(U_1072,U_1073,c_Groups_Ozero__class_Ozero(U_1072))
| ~ class_Groups_Oordered__comm__monoid__add(U_1072) ),
inference(variable_rename,[status(thm)],[f_348_1]) ).
cnf(f_348_3,plain,
( c_Orderings_Oord__class_Oless(U_1072,c_Groups_Oplus__class_Oplus(U_1072,U_1073,U_1074),c_Groups_Ozero__class_Ozero(U_1072))
| ~ c_Orderings_Oord__class_Oless(U_1072,U_1074,c_Groups_Ozero__class_Ozero(U_1072))
| ~ c_Orderings_Oord__class_Oless(U_1072,U_1073,c_Groups_Ozero__class_Ozero(U_1072))
| ~ class_Groups_Oordered__comm__monoid__add(U_1072) ),
inference(clausify,[status(thm)],[f_348_2]) ).
fof(f_349_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_349_2,plain,
! [U_1077,U_1076,U_1075] :
( c_Orderings_Oord__class_Oless(U_1075,c_Groups_Ozero__class_Ozero(U_1075),c_Groups_Oplus__class_Oplus(U_1075,U_1076,U_1077))
| ~ c_Orderings_Oord__class_Oless(U_1075,c_Groups_Ozero__class_Ozero(U_1075),U_1077)
| ~ c_Orderings_Oord__class_Oless(U_1075,c_Groups_Ozero__class_Ozero(U_1075),U_1076)
| ~ class_Groups_Oordered__comm__monoid__add(U_1075) ),
inference(variable_rename,[status(thm)],[f_349_1]) ).
cnf(f_349_3,plain,
( c_Orderings_Oord__class_Oless(U_1075,c_Groups_Ozero__class_Ozero(U_1075),c_Groups_Oplus__class_Oplus(U_1075,U_1076,U_1077))
| ~ c_Orderings_Oord__class_Oless(U_1075,c_Groups_Ozero__class_Ozero(U_1075),U_1077)
| ~ c_Orderings_Oord__class_Oless(U_1075,c_Groups_Ozero__class_Ozero(U_1075),U_1076)
| ~ class_Groups_Oordered__comm__monoid__add(U_1075) ),
inference(clausify,[status(thm)],[f_349_2]) ).
fof(f_350_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_350_2,plain,
! [U_1079,U_1078] :
( ( ( c_Orderings_Oord__class_Oless(U_1078,c_Groups_Oplus__class_Oplus(U_1078,U_1079,U_1079),c_Groups_Ozero__class_Ozero(U_1078))
| ~ c_Orderings_Oord__class_Oless(U_1078,U_1079,c_Groups_Ozero__class_Ozero(U_1078)) )
& ( c_Orderings_Oord__class_Oless(U_1078,U_1079,c_Groups_Ozero__class_Ozero(U_1078))
| ~ c_Orderings_Oord__class_Oless(U_1078,c_Groups_Oplus__class_Oplus(U_1078,U_1079,U_1079),c_Groups_Ozero__class_Ozero(U_1078)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1078) ),
inference(variable_rename,[status(thm)],[f_350_1]) ).
cnf(f_350_3,plain,
( c_Orderings_Oord__class_Oless(U_1078,U_1079,c_Groups_Ozero__class_Ozero(U_1078))
| ~ c_Orderings_Oord__class_Oless(U_1078,c_Groups_Oplus__class_Oplus(U_1078,U_1079,U_1079),c_Groups_Ozero__class_Ozero(U_1078))
| ~ class_Groups_Olinordered__ab__group__add(U_1078) ),
inference(clausify,[status(thm)],[f_350_2]) ).
cnf(f_350_4,plain,
( c_Orderings_Oord__class_Oless(U_1078,c_Groups_Oplus__class_Oplus(U_1078,U_1079,U_1079),c_Groups_Ozero__class_Ozero(U_1078))
| ~ c_Orderings_Oord__class_Oless(U_1078,U_1079,c_Groups_Ozero__class_Ozero(U_1078))
| ~ class_Groups_Olinordered__ab__group__add(U_1078) ),
inference(clausify,[status(thm)],[f_350_2]) ).
fof(f_351_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_351_2,plain,
! [U_1081,U_1080] :
( ( ( c_Orderings_Oord__class_Oless(U_1080,c_Groups_Ozero__class_Ozero(U_1080),c_Groups_Oplus__class_Oplus(U_1080,U_1081,U_1081))
| ~ c_Orderings_Oord__class_Oless(U_1080,c_Groups_Ozero__class_Ozero(U_1080),U_1081) )
& ( c_Orderings_Oord__class_Oless(U_1080,c_Groups_Ozero__class_Ozero(U_1080),U_1081)
| ~ c_Orderings_Oord__class_Oless(U_1080,c_Groups_Ozero__class_Ozero(U_1080),c_Groups_Oplus__class_Oplus(U_1080,U_1081,U_1081)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1080) ),
inference(variable_rename,[status(thm)],[f_351_1]) ).
cnf(f_351_3,plain,
( c_Orderings_Oord__class_Oless(U_1080,c_Groups_Ozero__class_Ozero(U_1080),U_1081)
| ~ c_Orderings_Oord__class_Oless(U_1080,c_Groups_Ozero__class_Ozero(U_1080),c_Groups_Oplus__class_Oplus(U_1080,U_1081,U_1081))
| ~ class_Groups_Olinordered__ab__group__add(U_1080) ),
inference(clausify,[status(thm)],[f_351_2]) ).
cnf(f_351_4,plain,
( c_Orderings_Oord__class_Oless(U_1080,c_Groups_Ozero__class_Ozero(U_1080),c_Groups_Oplus__class_Oplus(U_1080,U_1081,U_1081))
| ~ c_Orderings_Oord__class_Oless(U_1080,c_Groups_Ozero__class_Ozero(U_1080),U_1081)
| ~ class_Groups_Olinordered__ab__group__add(U_1080) ),
inference(clausify,[status(thm)],[f_351_2]) ).
fof(f_352_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_352_2,plain,
! [U_1085,U_1084,U_1083,U_1082] :
( c_Orderings_Oord__class_Oless(U_1082,U_1084,c_Groups_Oplus__class_Oplus(U_1082,U_1083,U_1085))
| ~ c_Orderings_Oord__class_Oless(U_1082,U_1084,U_1085)
| ~ c_Orderings_Oord__class_Oless(U_1082,c_Groups_Ozero__class_Ozero(U_1082),U_1083)
| ~ class_Rings_Olinordered__semidom(U_1082) ),
inference(variable_rename,[status(thm)],[f_352_1]) ).
cnf(f_352_3,plain,
( c_Orderings_Oord__class_Oless(U_1082,U_1084,c_Groups_Oplus__class_Oplus(U_1082,U_1083,U_1085))
| ~ c_Orderings_Oord__class_Oless(U_1082,U_1084,U_1085)
| ~ c_Orderings_Oord__class_Oless(U_1082,c_Groups_Ozero__class_Ozero(U_1082),U_1083)
| ~ class_Rings_Olinordered__semidom(U_1082) ),
inference(clausify,[status(thm)],[f_352_2]) ).
fof(f_353_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_353_2,plain,
! [U_1090,U_1089,U_1088,U_1087,U_1086] :
( c_Orderings_Oord__class_Oless(U_1086,c_Groups_Oplus__class_Oplus(U_1086,U_1087,U_1089),c_Groups_Oplus__class_Oplus(U_1086,U_1088,U_1090))
| ~ c_Orderings_Oord__class_Oless__eq(U_1086,U_1089,U_1090)
| ~ c_Orderings_Oord__class_Oless(U_1086,U_1087,U_1088)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1086) ),
inference(variable_rename,[status(thm)],[f_353_1]) ).
cnf(f_353_3,plain,
( c_Orderings_Oord__class_Oless(U_1086,c_Groups_Oplus__class_Oplus(U_1086,U_1087,U_1089),c_Groups_Oplus__class_Oplus(U_1086,U_1088,U_1090))
| ~ c_Orderings_Oord__class_Oless__eq(U_1086,U_1089,U_1090)
| ~ c_Orderings_Oord__class_Oless(U_1086,U_1087,U_1088)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1086) ),
inference(clausify,[status(thm)],[f_353_2]) ).
fof(f_354_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_354_2,plain,
! [U_1095,U_1094,U_1093,U_1092,U_1091] :
( c_Orderings_Oord__class_Oless(U_1091,c_Groups_Oplus__class_Oplus(U_1091,U_1092,U_1094),c_Groups_Oplus__class_Oplus(U_1091,U_1093,U_1095))
| ~ c_Orderings_Oord__class_Oless(U_1091,U_1094,U_1095)
| ~ c_Orderings_Oord__class_Oless__eq(U_1091,U_1092,U_1093)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1091) ),
inference(variable_rename,[status(thm)],[f_354_1]) ).
cnf(f_354_3,plain,
( c_Orderings_Oord__class_Oless(U_1091,c_Groups_Oplus__class_Oplus(U_1091,U_1092,U_1094),c_Groups_Oplus__class_Oplus(U_1091,U_1093,U_1095))
| ~ c_Orderings_Oord__class_Oless(U_1091,U_1094,U_1095)
| ~ c_Orderings_Oord__class_Oless__eq(U_1091,U_1092,U_1093)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1091) ),
inference(clausify,[status(thm)],[f_354_2]) ).
fof(f_355_1,plain,
! [V_d,V_c,V_b,V_a,V_r,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_r),V_c)) != c_Groups_Oplus__class_Oplus(T_a,V_b,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_355_2,plain,
! [U_1101,U_1100,U_1099,U_1098,U_1097,U_1096] :
( c_Groups_Oplus__class_Oplus(U_1096,U_1098,hAPP(c_Groups_Otimes__class_Otimes(U_1096,U_1097),U_1100)) != c_Groups_Oplus__class_Oplus(U_1096,U_1099,hAPP(c_Groups_Otimes__class_Otimes(U_1096,U_1097),U_1101))
| U_1100 = U_1101
| U_1098 != U_1099
| U_1097 = c_Groups_Ozero__class_Ozero(U_1096)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1096) ),
inference(variable_rename,[status(thm)],[f_355_1]) ).
cnf(f_355_3,plain,
( c_Groups_Oplus__class_Oplus(U_1096,U_1098,hAPP(c_Groups_Otimes__class_Otimes(U_1096,U_1097),U_1100)) != c_Groups_Oplus__class_Oplus(U_1096,U_1099,hAPP(c_Groups_Otimes__class_Otimes(U_1096,U_1097),U_1101))
| U_1100 = U_1101
| U_1098 != U_1099
| U_1097 = c_Groups_Ozero__class_Ozero(U_1096)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1096) ),
inference(clausify,[status(thm)],[f_355_2]) ).
fof(f_356_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_356_2,plain,
! [U_1103,U_1102] :
( c_Orderings_Oord__class_Oless(U_1102,U_1103,c_Groups_Oplus__class_Oplus(U_1102,U_1103,c_Groups_Oone__class_Oone(U_1102)))
| ~ class_Rings_Olinordered__semidom(U_1102) ),
inference(variable_rename,[status(thm)],[f_356_1]) ).
cnf(f_356_3,plain,
( c_Orderings_Oord__class_Oless(U_1102,U_1103,c_Groups_Oplus__class_Oplus(U_1102,U_1103,c_Groups_Oone__class_Oone(U_1102)))
| ~ class_Rings_Olinordered__semidom(U_1102) ),
inference(clausify,[status(thm)],[f_356_2]) ).
fof(f_357_1,plain,
! [V_m,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_m),V_m) = 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_357_2,plain,
! [U_1106,U_1105,U_1104] :
( c_Groups_Oplus__class_Oplus(U_1104,hAPP(c_Groups_Otimes__class_Otimes(U_1104,U_1105),U_1106),U_1106) = hAPP(c_Groups_Otimes__class_Otimes(U_1104,c_Groups_Oplus__class_Oplus(U_1104,U_1105,c_Groups_Oone__class_Oone(U_1104))),U_1106)
| ~ class_Rings_Ocomm__semiring__1(U_1104) ),
inference(variable_rename,[status(thm)],[f_357_1]) ).
cnf(f_357_3,plain,
( c_Groups_Oplus__class_Oplus(U_1104,hAPP(c_Groups_Otimes__class_Otimes(U_1104,U_1105),U_1106),U_1106) = hAPP(c_Groups_Otimes__class_Otimes(U_1104,c_Groups_Oplus__class_Oplus(U_1104,U_1105,c_Groups_Oone__class_Oone(U_1104))),U_1106)
| ~ class_Rings_Ocomm__semiring__1(U_1104) ),
inference(clausify,[status(thm)],[f_357_2]) ).
fof(f_358_1,plain,
! [V_a,V_m,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_m)) = 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_358_2,plain,
! [U_1109,U_1108,U_1107] :
( c_Groups_Oplus__class_Oplus(U_1107,U_1108,hAPP(c_Groups_Otimes__class_Otimes(U_1107,U_1109),U_1108)) = hAPP(c_Groups_Otimes__class_Otimes(U_1107,c_Groups_Oplus__class_Oplus(U_1107,U_1109,c_Groups_Oone__class_Oone(U_1107))),U_1108)
| ~ class_Rings_Ocomm__semiring__1(U_1107) ),
inference(variable_rename,[status(thm)],[f_358_1]) ).
cnf(f_358_3,plain,
( c_Groups_Oplus__class_Oplus(U_1107,U_1108,hAPP(c_Groups_Otimes__class_Otimes(U_1107,U_1109),U_1108)) = hAPP(c_Groups_Otimes__class_Otimes(U_1107,c_Groups_Oplus__class_Oplus(U_1107,U_1109,c_Groups_Oone__class_Oone(U_1107))),U_1108)
| ~ class_Rings_Ocomm__semiring__1(U_1107) ),
inference(clausify,[status(thm)],[f_358_2]) ).
fof(f_359_1,plain,
! [V_m,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_m,V_m) = 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_359_2,plain,
! [U_1111,U_1110] :
( c_Groups_Oplus__class_Oplus(U_1110,U_1111,U_1111) = hAPP(c_Groups_Otimes__class_Otimes(U_1110,c_Groups_Oplus__class_Oplus(U_1110,c_Groups_Oone__class_Oone(U_1110),c_Groups_Oone__class_Oone(U_1110))),U_1111)
| ~ class_Rings_Ocomm__semiring__1(U_1110) ),
inference(variable_rename,[status(thm)],[f_359_1]) ).
cnf(f_359_3,plain,
( c_Groups_Oplus__class_Oplus(U_1110,U_1111,U_1111) = hAPP(c_Groups_Otimes__class_Otimes(U_1110,c_Groups_Oplus__class_Oplus(U_1110,c_Groups_Oone__class_Oone(U_1110),c_Groups_Oone__class_Oone(U_1110))),U_1111)
| ~ class_Rings_Ocomm__semiring__1(U_1110) ),
inference(clausify,[status(thm)],[f_359_2]) ).
fof(f_360_1,plain,
! [V_y,V_x] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,V_y) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_y)),
inference(fof_nnf,[status(thm)],[fact_divide__real__def]) ).
fof(f_360_2,plain,
! [U_1113,U_1112] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1112,U_1113) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1112),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,U_1113)),
inference(variable_rename,[status(thm)],[f_360_1]) ).
cnf(f_360_3,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1112,U_1113) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1112),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,U_1113)),
inference(clausify,[status(thm)],[f_360_2]) ).
fof(f_361_1,plain,
! [V_S,V_R] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_R,V_S) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_R),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_S)),
inference(fof_nnf,[status(thm)],[fact_real__divide__def]) ).
fof(f_361_2,plain,
! [U_1115,U_1114] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1114,U_1115) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1114),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,U_1115)),
inference(variable_rename,[status(thm)],[f_361_1]) ).
cnf(f_361_3,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1114,U_1115) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1114),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,U_1115)),
inference(clausify,[status(thm)],[f_361_2]) ).
fof(f_362_1,plain,
! [V_y_2,V_x_2] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_x_2),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(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x_2),V_x_2),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_362_2,plain,
! [U_1117,U_1116] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1116),U_1116),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1117),U_1117)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1117 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1116 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( U_1117 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_1116 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1116),U_1116),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1117),U_1117)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_362_1]) ).
fof(f_362_3,plain,
( ! [U_1121,U_1119] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1119),U_1119),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1121),U_1121)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1121 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1119 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_1120,U_1118] :
( ( U_1120 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_1118 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1118),U_1118),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1120),U_1120)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_362_2]) ).
cnf(f_362_4,plain,
( U_1118 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1118),U_1118),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1120),U_1120)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_362_3]) ).
cnf(f_362_5,plain,
( U_1120 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1118),U_1118),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1120),U_1120)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_362_3]) ).
cnf(f_362_6,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1119),U_1119),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1121),U_1121)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1121 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1119 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_362_3]) ).
fof(f_363_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_363_2,plain,
! [U_1123,U_1122] :
( ( ( c_Orderings_Oord__class_Oless(U_1122,c_Groups_Osgn__class_Osgn(U_1122,U_1123),c_Groups_Ozero__class_Ozero(U_1122))
| ~ c_Orderings_Oord__class_Oless(U_1122,U_1123,c_Groups_Ozero__class_Ozero(U_1122)) )
& ( c_Orderings_Oord__class_Oless(U_1122,U_1123,c_Groups_Ozero__class_Ozero(U_1122))
| ~ c_Orderings_Oord__class_Oless(U_1122,c_Groups_Osgn__class_Osgn(U_1122,U_1123),c_Groups_Ozero__class_Ozero(U_1122)) ) )
| ~ class_Rings_Olinordered__idom(U_1122) ),
inference(variable_rename,[status(thm)],[f_363_1]) ).
cnf(f_363_3,plain,
( c_Orderings_Oord__class_Oless(U_1122,U_1123,c_Groups_Ozero__class_Ozero(U_1122))
| ~ c_Orderings_Oord__class_Oless(U_1122,c_Groups_Osgn__class_Osgn(U_1122,U_1123),c_Groups_Ozero__class_Ozero(U_1122))
| ~ class_Rings_Olinordered__idom(U_1122) ),
inference(clausify,[status(thm)],[f_363_2]) ).
cnf(f_363_4,plain,
( c_Orderings_Oord__class_Oless(U_1122,c_Groups_Osgn__class_Osgn(U_1122,U_1123),c_Groups_Ozero__class_Ozero(U_1122))
| ~ c_Orderings_Oord__class_Oless(U_1122,U_1123,c_Groups_Ozero__class_Ozero(U_1122))
| ~ class_Rings_Olinordered__idom(U_1122) ),
inference(clausify,[status(thm)],[f_363_2]) ).
fof(f_364_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_364_2,plain,
! [U_1125,U_1124] :
( ( ( c_Orderings_Oord__class_Oless(U_1124,c_Groups_Ozero__class_Ozero(U_1124),c_Groups_Osgn__class_Osgn(U_1124,U_1125))
| ~ c_Orderings_Oord__class_Oless(U_1124,c_Groups_Ozero__class_Ozero(U_1124),U_1125) )
& ( c_Orderings_Oord__class_Oless(U_1124,c_Groups_Ozero__class_Ozero(U_1124),U_1125)
| ~ c_Orderings_Oord__class_Oless(U_1124,c_Groups_Ozero__class_Ozero(U_1124),c_Groups_Osgn__class_Osgn(U_1124,U_1125)) ) )
| ~ class_Rings_Olinordered__idom(U_1124) ),
inference(variable_rename,[status(thm)],[f_364_1]) ).
cnf(f_364_3,plain,
( c_Orderings_Oord__class_Oless(U_1124,c_Groups_Ozero__class_Ozero(U_1124),U_1125)
| ~ c_Orderings_Oord__class_Oless(U_1124,c_Groups_Ozero__class_Ozero(U_1124),c_Groups_Osgn__class_Osgn(U_1124,U_1125))
| ~ class_Rings_Olinordered__idom(U_1124) ),
inference(clausify,[status(thm)],[f_364_2]) ).
cnf(f_364_4,plain,
( c_Orderings_Oord__class_Oless(U_1124,c_Groups_Ozero__class_Ozero(U_1124),c_Groups_Osgn__class_Osgn(U_1124,U_1125))
| ~ c_Orderings_Oord__class_Oless(U_1124,c_Groups_Ozero__class_Ozero(U_1124),U_1125)
| ~ class_Rings_Olinordered__idom(U_1124) ),
inference(clausify,[status(thm)],[f_364_2]) ).
fof(f_365_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_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,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__le__imp__le__neg]) ).
fof(f_365_2,plain,
! [U_1128,U_1127,U_1126] :
( c_Orderings_Oord__class_Oless__eq(U_1126,U_1128,U_1127)
| ~ c_Orderings_Oord__class_Oless(U_1126,U_1128,c_Groups_Ozero__class_Ozero(U_1126))
| ~ c_Orderings_Oord__class_Oless__eq(U_1126,c_Rings_Oinverse__class_Oinverse(U_1126,U_1127),c_Rings_Oinverse__class_Oinverse(U_1126,U_1128))
| ~ class_Fields_Olinordered__field(U_1126) ),
inference(variable_rename,[status(thm)],[f_365_1]) ).
cnf(f_365_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1126,U_1128,U_1127)
| ~ c_Orderings_Oord__class_Oless(U_1126,U_1128,c_Groups_Ozero__class_Ozero(U_1126))
| ~ c_Orderings_Oord__class_Oless__eq(U_1126,c_Rings_Oinverse__class_Oinverse(U_1126,U_1127),c_Rings_Oinverse__class_Oinverse(U_1126,U_1128))
| ~ class_Fields_Olinordered__field(U_1126) ),
inference(clausify,[status(thm)],[f_365_2]) ).
fof(f_366_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(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__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__le__imp__le]) ).
fof(f_366_2,plain,
! [U_1131,U_1130,U_1129] :
( c_Orderings_Oord__class_Oless__eq(U_1129,U_1131,U_1130)
| ~ c_Orderings_Oord__class_Oless(U_1129,c_Groups_Ozero__class_Ozero(U_1129),U_1130)
| ~ c_Orderings_Oord__class_Oless__eq(U_1129,c_Rings_Oinverse__class_Oinverse(U_1129,U_1130),c_Rings_Oinverse__class_Oinverse(U_1129,U_1131))
| ~ class_Fields_Olinordered__field(U_1129) ),
inference(variable_rename,[status(thm)],[f_366_1]) ).
cnf(f_366_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1129,U_1131,U_1130)
| ~ c_Orderings_Oord__class_Oless(U_1129,c_Groups_Ozero__class_Ozero(U_1129),U_1130)
| ~ c_Orderings_Oord__class_Oless__eq(U_1129,c_Rings_Oinverse__class_Oinverse(U_1129,U_1130),c_Rings_Oinverse__class_Oinverse(U_1129,U_1131))
| ~ class_Fields_Olinordered__field(U_1129) ),
inference(clausify,[status(thm)],[f_366_2]) ).
fof(f_367_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(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__eq(T_a,V_a,V_b)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__imp__inverse__le__neg]) ).
fof(f_367_2,plain,
! [U_1134,U_1133,U_1132] :
( c_Orderings_Oord__class_Oless__eq(U_1132,c_Rings_Oinverse__class_Oinverse(U_1132,U_1134),c_Rings_Oinverse__class_Oinverse(U_1132,U_1133))
| ~ c_Orderings_Oord__class_Oless(U_1132,U_1134,c_Groups_Ozero__class_Ozero(U_1132))
| ~ c_Orderings_Oord__class_Oless__eq(U_1132,U_1133,U_1134)
| ~ class_Fields_Olinordered__field(U_1132) ),
inference(variable_rename,[status(thm)],[f_367_1]) ).
cnf(f_367_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1132,c_Rings_Oinverse__class_Oinverse(U_1132,U_1134),c_Rings_Oinverse__class_Oinverse(U_1132,U_1133))
| ~ c_Orderings_Oord__class_Oless(U_1132,U_1134,c_Groups_Ozero__class_Ozero(U_1132))
| ~ c_Orderings_Oord__class_Oless__eq(U_1132,U_1133,U_1134)
| ~ class_Fields_Olinordered__field(U_1132) ),
inference(clausify,[status(thm)],[f_367_2]) ).
fof(f_368_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_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_a,V_b)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__imp__inverse__le]) ).
fof(f_368_2,plain,
! [U_1137,U_1136,U_1135] :
( c_Orderings_Oord__class_Oless__eq(U_1135,c_Rings_Oinverse__class_Oinverse(U_1135,U_1137),c_Rings_Oinverse__class_Oinverse(U_1135,U_1136))
| ~ c_Orderings_Oord__class_Oless(U_1135,c_Groups_Ozero__class_Ozero(U_1135),U_1136)
| ~ c_Orderings_Oord__class_Oless__eq(U_1135,U_1136,U_1137)
| ~ class_Fields_Olinordered__field(U_1135) ),
inference(variable_rename,[status(thm)],[f_368_1]) ).
cnf(f_368_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1135,c_Rings_Oinverse__class_Oinverse(U_1135,U_1137),c_Rings_Oinverse__class_Oinverse(U_1135,U_1136))
| ~ c_Orderings_Oord__class_Oless(U_1135,c_Groups_Ozero__class_Ozero(U_1135),U_1136)
| ~ c_Orderings_Oord__class_Oless__eq(U_1135,U_1136,U_1137)
| ~ class_Fields_Olinordered__field(U_1135) ),
inference(clausify,[status(thm)],[f_368_2]) ).
fof(f_369_1,plain,
! [V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2)
& ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)) ) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__le__1__iff]) ).
fof(f_369_2,plain,
! [U_1139,U_1138] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1138,c_Rings_Oinverse__class_Oinverse(U_1138,U_1139),c_Groups_Oone__class_Oone(U_1138))
| ( ~ c_Orderings_Oord__class_Oless__eq(U_1138,c_Groups_Oone__class_Oone(U_1138),U_1139)
& ~ c_Orderings_Oord__class_Oless__eq(U_1138,U_1139,c_Groups_Ozero__class_Ozero(U_1138)) ) )
& ( c_Orderings_Oord__class_Oless__eq(U_1138,c_Groups_Oone__class_Oone(U_1138),U_1139)
| c_Orderings_Oord__class_Oless__eq(U_1138,U_1139,c_Groups_Ozero__class_Ozero(U_1138))
| ~ c_Orderings_Oord__class_Oless__eq(U_1138,c_Rings_Oinverse__class_Oinverse(U_1138,U_1139),c_Groups_Oone__class_Oone(U_1138)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_1138) ),
inference(variable_rename,[status(thm)],[f_369_1]) ).
cnf(f_369_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1138,c_Groups_Oone__class_Oone(U_1138),U_1139)
| c_Orderings_Oord__class_Oless__eq(U_1138,U_1139,c_Groups_Ozero__class_Ozero(U_1138))
| ~ c_Orderings_Oord__class_Oless__eq(U_1138,c_Rings_Oinverse__class_Oinverse(U_1138,U_1139),c_Groups_Oone__class_Oone(U_1138))
| ~ class_Fields_Olinordered__field__inverse__zero(U_1138) ),
inference(clausify,[status(thm)],[f_369_2]) ).
cnf(f_369_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1138,U_1139,c_Groups_Ozero__class_Ozero(U_1138))
| c_Orderings_Oord__class_Oless__eq(U_1138,c_Rings_Oinverse__class_Oinverse(U_1138,U_1139),c_Groups_Oone__class_Oone(U_1138))
| ~ class_Fields_Olinordered__field__inverse__zero(U_1138) ),
inference(clausify,[status(thm)],[f_369_2]) ).
cnf(f_369_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1138,c_Groups_Oone__class_Oone(U_1138),U_1139)
| c_Orderings_Oord__class_Oless__eq(U_1138,c_Rings_Oinverse__class_Oinverse(U_1138,U_1139),c_Groups_Oone__class_Oone(U_1138))
| ~ class_Fields_Olinordered__field__inverse__zero(U_1138) ),
inference(clausify,[status(thm)],[f_369_2]) ).
fof(f_370_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__less__inverse]) ).
fof(f_370_2,plain,
! [U_1141,U_1140] :
( c_Orderings_Oord__class_Oless(U_1140,c_Groups_Oone__class_Oone(U_1140),c_Rings_Oinverse__class_Oinverse(U_1140,U_1141))
| ~ c_Orderings_Oord__class_Oless(U_1140,U_1141,c_Groups_Oone__class_Oone(U_1140))
| ~ c_Orderings_Oord__class_Oless(U_1140,c_Groups_Ozero__class_Ozero(U_1140),U_1141)
| ~ class_Fields_Olinordered__field(U_1140) ),
inference(variable_rename,[status(thm)],[f_370_1]) ).
cnf(f_370_3,plain,
( c_Orderings_Oord__class_Oless(U_1140,c_Groups_Oone__class_Oone(U_1140),c_Rings_Oinverse__class_Oinverse(U_1140,U_1141))
| ~ c_Orderings_Oord__class_Oless(U_1140,U_1141,c_Groups_Oone__class_Oone(U_1140))
| ~ c_Orderings_Oord__class_Oless(U_1140,c_Groups_Ozero__class_Ozero(U_1140),U_1141)
| ~ class_Fields_Olinordered__field(U_1140) ),
inference(clausify,[status(thm)],[f_370_2]) ).
fof(f_371_1,plain,
! [V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) )
& ( ( c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__less__inverse__iff]) ).
fof(f_371_2,plain,
! [U_1143,U_1142] :
( ( ( c_Orderings_Oord__class_Oless(U_1142,c_Groups_Oone__class_Oone(U_1142),c_Rings_Oinverse__class_Oinverse(U_1142,U_1143))
| ~ c_Orderings_Oord__class_Oless(U_1142,U_1143,c_Groups_Oone__class_Oone(U_1142))
| ~ c_Orderings_Oord__class_Oless(U_1142,c_Groups_Ozero__class_Ozero(U_1142),U_1143) )
& ( ( c_Orderings_Oord__class_Oless(U_1142,U_1143,c_Groups_Oone__class_Oone(U_1142))
& c_Orderings_Oord__class_Oless(U_1142,c_Groups_Ozero__class_Ozero(U_1142),U_1143) )
| ~ c_Orderings_Oord__class_Oless(U_1142,c_Groups_Oone__class_Oone(U_1142),c_Rings_Oinverse__class_Oinverse(U_1142,U_1143)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_1142) ),
inference(variable_rename,[status(thm)],[f_371_1]) ).
cnf(f_371_3,plain,
( c_Orderings_Oord__class_Oless(U_1142,c_Groups_Ozero__class_Ozero(U_1142),U_1143)
| ~ c_Orderings_Oord__class_Oless(U_1142,c_Groups_Oone__class_Oone(U_1142),c_Rings_Oinverse__class_Oinverse(U_1142,U_1143))
| ~ class_Fields_Olinordered__field__inverse__zero(U_1142) ),
inference(clausify,[status(thm)],[f_371_2]) ).
cnf(f_371_4,plain,
( c_Orderings_Oord__class_Oless(U_1142,U_1143,c_Groups_Oone__class_Oone(U_1142))
| ~ c_Orderings_Oord__class_Oless(U_1142,c_Groups_Oone__class_Oone(U_1142),c_Rings_Oinverse__class_Oinverse(U_1142,U_1143))
| ~ class_Fields_Olinordered__field__inverse__zero(U_1142) ),
inference(clausify,[status(thm)],[f_371_2]) ).
cnf(f_371_5,plain,
( c_Orderings_Oord__class_Oless(U_1142,c_Groups_Oone__class_Oone(U_1142),c_Rings_Oinverse__class_Oinverse(U_1142,U_1143))
| ~ c_Orderings_Oord__class_Oless(U_1142,U_1143,c_Groups_Oone__class_Oone(U_1142))
| ~ c_Orderings_Oord__class_Oless(U_1142,c_Groups_Ozero__class_Ozero(U_1142),U_1143)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1142) ),
inference(clausify,[status(thm)],[f_371_2]) ).
fof(f_372_1,plain,
! [V_a,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_a) = c_Groups_Oone__class_Oone(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_field__inverse]) ).
fof(f_372_2,plain,
! [U_1145,U_1144] :
( hAPP(c_Groups_Otimes__class_Otimes(U_1144,c_Rings_Oinverse__class_Oinverse(U_1144,U_1145)),U_1145) = c_Groups_Oone__class_Oone(U_1144)
| U_1145 = c_Groups_Ozero__class_Ozero(U_1144)
| ~ class_Fields_Ofield(U_1144) ),
inference(variable_rename,[status(thm)],[f_372_1]) ).
cnf(f_372_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_1144,c_Rings_Oinverse__class_Oinverse(U_1144,U_1145)),U_1145) = c_Groups_Oone__class_Oone(U_1144)
| U_1145 = c_Groups_Ozero__class_Ozero(U_1144)
| ~ class_Fields_Ofield(U_1144) ),
inference(clausify,[status(thm)],[f_372_2]) ).
fof(f_373_1,plain,
! [V_a,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)),V_a) = c_Groups_Oone__class_Oone(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_left__inverse]) ).
fof(f_373_2,plain,
! [U_1147,U_1146] :
( hAPP(c_Groups_Otimes__class_Otimes(U_1146,c_Rings_Oinverse__class_Oinverse(U_1146,U_1147)),U_1147) = c_Groups_Oone__class_Oone(U_1146)
| U_1147 = c_Groups_Ozero__class_Ozero(U_1146)
| ~ class_Rings_Odivision__ring(U_1146) ),
inference(variable_rename,[status(thm)],[f_373_1]) ).
cnf(f_373_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_1146,c_Rings_Oinverse__class_Oinverse(U_1146,U_1147)),U_1147) = c_Groups_Oone__class_Oone(U_1146)
| U_1147 = c_Groups_Ozero__class_Ozero(U_1146)
| ~ class_Rings_Odivision__ring(U_1146) ),
inference(clausify,[status(thm)],[f_373_2]) ).
fof(f_374_1,plain,
! [V_a,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)) = c_Groups_Oone__class_Oone(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_right__inverse]) ).
fof(f_374_2,plain,
! [U_1149,U_1148] :
( hAPP(c_Groups_Otimes__class_Otimes(U_1148,U_1149),c_Rings_Oinverse__class_Oinverse(U_1148,U_1149)) = c_Groups_Oone__class_Oone(U_1148)
| U_1149 = c_Groups_Ozero__class_Ozero(U_1148)
| ~ class_Rings_Odivision__ring(U_1148) ),
inference(variable_rename,[status(thm)],[f_374_1]) ).
cnf(f_374_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_1148,U_1149),c_Rings_Oinverse__class_Oinverse(U_1148,U_1149)) = c_Groups_Oone__class_Oone(U_1148)
| U_1149 = c_Groups_Ozero__class_Ozero(U_1148)
| ~ class_Rings_Odivision__ring(U_1148) ),
inference(clausify,[status(thm)],[f_374_2]) ).
fof(f_375_1,plain,
! [V_a,T_a] :
( c_Rings_Oinverse__class_Oinverse(T_a,V_a) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__eq__divide]) ).
fof(f_375_2,plain,
! [U_1151,U_1150] :
( c_Rings_Oinverse__class_Oinverse(U_1150,U_1151) = c_Rings_Oinverse__class_Odivide(U_1150,c_Groups_Oone__class_Oone(U_1150),U_1151)
| U_1151 = c_Groups_Ozero__class_Ozero(U_1150)
| ~ class_Rings_Odivision__ring(U_1150) ),
inference(variable_rename,[status(thm)],[f_375_1]) ).
cnf(f_375_3,plain,
( c_Rings_Oinverse__class_Oinverse(U_1150,U_1151) = c_Rings_Oinverse__class_Odivide(U_1150,c_Groups_Oone__class_Oone(U_1150),U_1151)
| U_1151 = c_Groups_Ozero__class_Ozero(U_1150)
| ~ class_Rings_Odivision__ring(U_1150) ),
inference(clausify,[status(thm)],[f_375_2]) ).
fof(f_376_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_376_2,plain,
! [U_1154,U_1153,U_1152] :
( c_Orderings_Oord__class_Oless(U_1152,c_Groups_Oplus__class_Oplus(U_1152,U_1153,U_1154),c_Groups_Ozero__class_Ozero(U_1152))
| ~ c_Orderings_Oord__class_Oless(U_1152,U_1154,c_Groups_Ozero__class_Ozero(U_1152))
| ~ c_Orderings_Oord__class_Oless__eq(U_1152,U_1153,c_Groups_Ozero__class_Ozero(U_1152))
| ~ class_Groups_Oordered__comm__monoid__add(U_1152) ),
inference(variable_rename,[status(thm)],[f_376_1]) ).
cnf(f_376_3,plain,
( c_Orderings_Oord__class_Oless(U_1152,c_Groups_Oplus__class_Oplus(U_1152,U_1153,U_1154),c_Groups_Ozero__class_Ozero(U_1152))
| ~ c_Orderings_Oord__class_Oless(U_1152,U_1154,c_Groups_Ozero__class_Ozero(U_1152))
| ~ c_Orderings_Oord__class_Oless__eq(U_1152,U_1153,c_Groups_Ozero__class_Ozero(U_1152))
| ~ class_Groups_Oordered__comm__monoid__add(U_1152) ),
inference(clausify,[status(thm)],[f_376_2]) ).
fof(f_377_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_377_2,plain,
! [U_1157,U_1156,U_1155] :
( c_Orderings_Oord__class_Oless(U_1155,c_Groups_Oplus__class_Oplus(U_1155,U_1156,U_1157),c_Groups_Ozero__class_Ozero(U_1155))
| ~ c_Orderings_Oord__class_Oless__eq(U_1155,U_1157,c_Groups_Ozero__class_Ozero(U_1155))
| ~ c_Orderings_Oord__class_Oless(U_1155,U_1156,c_Groups_Ozero__class_Ozero(U_1155))
| ~ class_Groups_Oordered__comm__monoid__add(U_1155) ),
inference(variable_rename,[status(thm)],[f_377_1]) ).
cnf(f_377_3,plain,
( c_Orderings_Oord__class_Oless(U_1155,c_Groups_Oplus__class_Oplus(U_1155,U_1156,U_1157),c_Groups_Ozero__class_Ozero(U_1155))
| ~ c_Orderings_Oord__class_Oless__eq(U_1155,U_1157,c_Groups_Ozero__class_Ozero(U_1155))
| ~ c_Orderings_Oord__class_Oless(U_1155,U_1156,c_Groups_Ozero__class_Ozero(U_1155))
| ~ class_Groups_Oordered__comm__monoid__add(U_1155) ),
inference(clausify,[status(thm)],[f_377_2]) ).
fof(f_378_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_378_2,plain,
! [U_1161,U_1160,U_1159,U_1158] :
( c_Orderings_Oord__class_Oless(U_1158,U_1160,c_Groups_Oplus__class_Oplus(U_1158,U_1159,U_1161))
| ~ c_Orderings_Oord__class_Oless(U_1158,U_1160,U_1161)
| ~ c_Orderings_Oord__class_Oless__eq(U_1158,c_Groups_Ozero__class_Ozero(U_1158),U_1159)
| ~ class_Groups_Oordered__comm__monoid__add(U_1158) ),
inference(variable_rename,[status(thm)],[f_378_1]) ).
cnf(f_378_3,plain,
( c_Orderings_Oord__class_Oless(U_1158,U_1160,c_Groups_Oplus__class_Oplus(U_1158,U_1159,U_1161))
| ~ c_Orderings_Oord__class_Oless(U_1158,U_1160,U_1161)
| ~ c_Orderings_Oord__class_Oless__eq(U_1158,c_Groups_Ozero__class_Ozero(U_1158),U_1159)
| ~ class_Groups_Oordered__comm__monoid__add(U_1158) ),
inference(clausify,[status(thm)],[f_378_2]) ).
fof(f_379_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_379_2,plain,
! [U_1165,U_1164,U_1163,U_1162] :
( c_Orderings_Oord__class_Oless(U_1162,U_1164,c_Groups_Oplus__class_Oplus(U_1162,U_1163,U_1165))
| ~ c_Orderings_Oord__class_Oless__eq(U_1162,U_1164,U_1165)
| ~ c_Orderings_Oord__class_Oless(U_1162,c_Groups_Ozero__class_Ozero(U_1162),U_1163)
| ~ class_Groups_Oordered__comm__monoid__add(U_1162) ),
inference(variable_rename,[status(thm)],[f_379_1]) ).
cnf(f_379_3,plain,
( c_Orderings_Oord__class_Oless(U_1162,U_1164,c_Groups_Oplus__class_Oplus(U_1162,U_1163,U_1165))
| ~ c_Orderings_Oord__class_Oless__eq(U_1162,U_1164,U_1165)
| ~ c_Orderings_Oord__class_Oless(U_1162,c_Groups_Ozero__class_Ozero(U_1162),U_1163)
| ~ class_Groups_Oordered__comm__monoid__add(U_1162) ),
inference(clausify,[status(thm)],[f_379_2]) ).
fof(f_380_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_380_2,plain,
! [U_1168,U_1167,U_1166] :
( c_Orderings_Oord__class_Oless(U_1166,c_Groups_Ozero__class_Ozero(U_1166),c_Groups_Oplus__class_Oplus(U_1166,U_1167,U_1168))
| ~ c_Orderings_Oord__class_Oless(U_1166,c_Groups_Ozero__class_Ozero(U_1166),U_1168)
| ~ c_Orderings_Oord__class_Oless__eq(U_1166,c_Groups_Ozero__class_Ozero(U_1166),U_1167)
| ~ class_Groups_Oordered__comm__monoid__add(U_1166) ),
inference(variable_rename,[status(thm)],[f_380_1]) ).
cnf(f_380_3,plain,
( c_Orderings_Oord__class_Oless(U_1166,c_Groups_Ozero__class_Ozero(U_1166),c_Groups_Oplus__class_Oplus(U_1166,U_1167,U_1168))
| ~ c_Orderings_Oord__class_Oless(U_1166,c_Groups_Ozero__class_Ozero(U_1166),U_1168)
| ~ c_Orderings_Oord__class_Oless__eq(U_1166,c_Groups_Ozero__class_Ozero(U_1166),U_1167)
| ~ class_Groups_Oordered__comm__monoid__add(U_1166) ),
inference(clausify,[status(thm)],[f_380_2]) ).
fof(f_381_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_381_2,plain,
! [U_1171,U_1170,U_1169] :
( c_Orderings_Oord__class_Oless(U_1169,c_Groups_Ozero__class_Ozero(U_1169),c_Groups_Oplus__class_Oplus(U_1169,U_1170,U_1171))
| ~ c_Orderings_Oord__class_Oless__eq(U_1169,c_Groups_Ozero__class_Ozero(U_1169),U_1171)
| ~ c_Orderings_Oord__class_Oless(U_1169,c_Groups_Ozero__class_Ozero(U_1169),U_1170)
| ~ class_Groups_Oordered__comm__monoid__add(U_1169) ),
inference(variable_rename,[status(thm)],[f_381_1]) ).
cnf(f_381_3,plain,
( c_Orderings_Oord__class_Oless(U_1169,c_Groups_Ozero__class_Ozero(U_1169),c_Groups_Oplus__class_Oplus(U_1169,U_1170,U_1171))
| ~ c_Orderings_Oord__class_Oless__eq(U_1169,c_Groups_Ozero__class_Ozero(U_1169),U_1171)
| ~ c_Orderings_Oord__class_Oless(U_1169,c_Groups_Ozero__class_Ozero(U_1169),U_1170)
| ~ class_Groups_Oordered__comm__monoid__add(U_1169) ),
inference(clausify,[status(thm)],[f_381_2]) ).
fof(f_382_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_382_2,plain,
! [U_1172] :
( c_Orderings_Oord__class_Oless(U_1172,c_Groups_Ozero__class_Ozero(U_1172),c_Groups_Oplus__class_Oplus(U_1172,c_Groups_Oone__class_Oone(U_1172),c_Groups_Oone__class_Oone(U_1172)))
| ~ class_Rings_Olinordered__semidom(U_1172) ),
inference(variable_rename,[status(thm)],[f_382_1]) ).
cnf(f_382_3,plain,
( c_Orderings_Oord__class_Oless(U_1172,c_Groups_Ozero__class_Ozero(U_1172),c_Groups_Oplus__class_Oplus(U_1172,c_Groups_Oone__class_Oone(U_1172),c_Groups_Oone__class_Oone(U_1172)))
| ~ class_Rings_Olinordered__semidom(U_1172) ),
inference(clausify,[status(thm)],[f_382_2]) ).
fof(f_383_1,plain,
! [V_w,V_x,V_z,V_y,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_w,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_z),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_w),V_y)),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_y),V_z))
| V_z = c_Groups_Ozero__class_Ozero(T_a)
| V_y = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__frac__eq]) ).
fof(f_383_2,plain,
! [U_1177,U_1176,U_1175,U_1174,U_1173] :
( c_Groups_Oplus__class_Oplus(U_1173,c_Rings_Oinverse__class_Odivide(U_1173,U_1176,U_1174),c_Rings_Oinverse__class_Odivide(U_1173,U_1177,U_1175)) = c_Rings_Oinverse__class_Odivide(U_1173,c_Groups_Oplus__class_Oplus(U_1173,hAPP(c_Groups_Otimes__class_Otimes(U_1173,U_1176),U_1175),hAPP(c_Groups_Otimes__class_Otimes(U_1173,U_1177),U_1174)),hAPP(c_Groups_Otimes__class_Otimes(U_1173,U_1174),U_1175))
| U_1175 = c_Groups_Ozero__class_Ozero(U_1173)
| U_1174 = c_Groups_Ozero__class_Ozero(U_1173)
| ~ class_Fields_Ofield(U_1173) ),
inference(variable_rename,[status(thm)],[f_383_1]) ).
cnf(f_383_3,plain,
( c_Groups_Oplus__class_Oplus(U_1173,c_Rings_Oinverse__class_Odivide(U_1173,U_1176,U_1174),c_Rings_Oinverse__class_Odivide(U_1173,U_1177,U_1175)) = c_Rings_Oinverse__class_Odivide(U_1173,c_Groups_Oplus__class_Oplus(U_1173,hAPP(c_Groups_Otimes__class_Otimes(U_1173,U_1176),U_1175),hAPP(c_Groups_Otimes__class_Otimes(U_1173,U_1177),U_1174)),hAPP(c_Groups_Otimes__class_Otimes(U_1173,U_1174),U_1175))
| U_1175 = c_Groups_Ozero__class_Ozero(U_1173)
| U_1174 = c_Groups_Ozero__class_Ozero(U_1173)
| ~ class_Fields_Ofield(U_1173) ),
inference(clausify,[status(thm)],[f_383_2]) ).
fof(f_384_1,plain,
! [V_y,V_x,V_z,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y)),V_z)
| V_z = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__add__eq__iff]) ).
fof(f_384_2,plain,
! [U_1181,U_1180,U_1179,U_1178] :
( c_Groups_Oplus__class_Oplus(U_1178,c_Rings_Oinverse__class_Odivide(U_1178,U_1180,U_1179),U_1181) = c_Rings_Oinverse__class_Odivide(U_1178,c_Groups_Oplus__class_Oplus(U_1178,U_1180,hAPP(c_Groups_Otimes__class_Otimes(U_1178,U_1179),U_1181)),U_1179)
| U_1179 = c_Groups_Ozero__class_Ozero(U_1178)
| ~ class_Fields_Ofield(U_1178) ),
inference(variable_rename,[status(thm)],[f_384_1]) ).
cnf(f_384_3,plain,
( c_Groups_Oplus__class_Oplus(U_1178,c_Rings_Oinverse__class_Odivide(U_1178,U_1180,U_1179),U_1181) = c_Rings_Oinverse__class_Odivide(U_1178,c_Groups_Oplus__class_Oplus(U_1178,U_1180,hAPP(c_Groups_Otimes__class_Otimes(U_1178,U_1179),U_1181)),U_1179)
| U_1179 = c_Groups_Ozero__class_Ozero(U_1178)
| ~ class_Fields_Ofield(U_1178) ),
inference(clausify,[status(thm)],[f_384_2]) ).
fof(f_385_1,plain,
! [V_z,V_x,V_y,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y)),V_y)
| V_y = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__frac__num]) ).
fof(f_385_2,plain,
! [U_1185,U_1184,U_1183,U_1182] :
( c_Groups_Oplus__class_Oplus(U_1182,c_Rings_Oinverse__class_Odivide(U_1182,U_1184,U_1183),U_1185) = c_Rings_Oinverse__class_Odivide(U_1182,c_Groups_Oplus__class_Oplus(U_1182,U_1184,hAPP(c_Groups_Otimes__class_Otimes(U_1182,U_1185),U_1183)),U_1183)
| U_1183 = c_Groups_Ozero__class_Ozero(U_1182)
| ~ class_Fields_Ofield__inverse__zero(U_1182) ),
inference(variable_rename,[status(thm)],[f_385_1]) ).
cnf(f_385_3,plain,
( c_Groups_Oplus__class_Oplus(U_1182,c_Rings_Oinverse__class_Odivide(U_1182,U_1184,U_1183),U_1185) = c_Rings_Oinverse__class_Odivide(U_1182,c_Groups_Oplus__class_Oplus(U_1182,U_1184,hAPP(c_Groups_Otimes__class_Otimes(U_1182,U_1185),U_1183)),U_1183)
| U_1183 = c_Groups_Ozero__class_Ozero(U_1182)
| ~ class_Fields_Ofield__inverse__zero(U_1182) ),
inference(clausify,[status(thm)],[f_385_2]) ).
fof(f_386_1,plain,
! [V_y,V_x,V_z,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_x),V_y),V_z)
| V_z = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__divide__eq__iff]) ).
fof(f_386_2,plain,
! [U_1189,U_1188,U_1187,U_1186] :
( c_Groups_Oplus__class_Oplus(U_1186,U_1188,c_Rings_Oinverse__class_Odivide(U_1186,U_1189,U_1187)) = c_Rings_Oinverse__class_Odivide(U_1186,c_Groups_Oplus__class_Oplus(U_1186,hAPP(c_Groups_Otimes__class_Otimes(U_1186,U_1187),U_1188),U_1189),U_1187)
| U_1187 = c_Groups_Ozero__class_Ozero(U_1186)
| ~ class_Fields_Ofield(U_1186) ),
inference(variable_rename,[status(thm)],[f_386_1]) ).
cnf(f_386_3,plain,
( c_Groups_Oplus__class_Oplus(U_1186,U_1188,c_Rings_Oinverse__class_Odivide(U_1186,U_1189,U_1187)) = c_Rings_Oinverse__class_Odivide(U_1186,c_Groups_Oplus__class_Oplus(U_1186,hAPP(c_Groups_Otimes__class_Otimes(U_1186,U_1187),U_1188),U_1189),U_1187)
| U_1187 = c_Groups_Ozero__class_Ozero(U_1186)
| ~ class_Fields_Ofield(U_1186) ),
inference(clausify,[status(thm)],[f_386_2]) ).
fof(f_387_1,plain,
! [V_x,V_z,V_y,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),V_y)),V_y)
| V_y = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__num__frac]) ).
fof(f_387_2,plain,
! [U_1193,U_1192,U_1191,U_1190] :
( c_Groups_Oplus__class_Oplus(U_1190,U_1192,c_Rings_Oinverse__class_Odivide(U_1190,U_1193,U_1191)) = c_Rings_Oinverse__class_Odivide(U_1190,c_Groups_Oplus__class_Oplus(U_1190,U_1193,hAPP(c_Groups_Otimes__class_Otimes(U_1190,U_1192),U_1191)),U_1191)
| U_1191 = c_Groups_Ozero__class_Ozero(U_1190)
| ~ class_Fields_Ofield__inverse__zero(U_1190) ),
inference(variable_rename,[status(thm)],[f_387_1]) ).
cnf(f_387_3,plain,
( c_Groups_Oplus__class_Oplus(U_1190,U_1192,c_Rings_Oinverse__class_Odivide(U_1190,U_1193,U_1191)) = c_Rings_Oinverse__class_Odivide(U_1190,c_Groups_Oplus__class_Oplus(U_1190,U_1193,hAPP(c_Groups_Otimes__class_Otimes(U_1190,U_1192),U_1191)),U_1191)
| U_1191 = c_Groups_Ozero__class_Ozero(U_1190)
| ~ class_Fields_Ofield__inverse__zero(U_1190) ),
inference(clausify,[status(thm)],[f_387_2]) ).
fof(f_388_1,plain,
! [V_x] :
( hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_nnf,[status(thm)],[fact_real__mult__inverse__left]) ).
fof(f_388_2,plain,
! [U_1194] :
( hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,U_1194)),U_1194) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_1194 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[f_388_1]) ).
cnf(f_388_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,U_1194)),U_1194) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_1194 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_388_2]) ).
fof(f_389_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_gt__half__sum]) ).
fof(f_389_2,plain,
! [U_1197,U_1196,U_1195] :
( c_Orderings_Oord__class_Oless(U_1195,c_Rings_Oinverse__class_Odivide(U_1195,c_Groups_Oplus__class_Oplus(U_1195,U_1196,U_1197),c_Groups_Oplus__class_Oplus(U_1195,c_Groups_Oone__class_Oone(U_1195),c_Groups_Oone__class_Oone(U_1195))),U_1197)
| ~ c_Orderings_Oord__class_Oless(U_1195,U_1196,U_1197)
| ~ class_Fields_Olinordered__field(U_1195) ),
inference(variable_rename,[status(thm)],[f_389_1]) ).
cnf(f_389_3,plain,
( c_Orderings_Oord__class_Oless(U_1195,c_Rings_Oinverse__class_Odivide(U_1195,c_Groups_Oplus__class_Oplus(U_1195,U_1196,U_1197),c_Groups_Oplus__class_Oplus(U_1195,c_Groups_Oone__class_Oone(U_1195),c_Groups_Oone__class_Oone(U_1195))),U_1197)
| ~ c_Orderings_Oord__class_Oless(U_1195,U_1196,U_1197)
| ~ class_Fields_Olinordered__field(U_1195) ),
inference(clausify,[status(thm)],[f_389_2]) ).
fof(f_390_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__half__sum]) ).
fof(f_390_2,plain,
! [U_1200,U_1199,U_1198] :
( c_Orderings_Oord__class_Oless(U_1198,U_1199,c_Rings_Oinverse__class_Odivide(U_1198,c_Groups_Oplus__class_Oplus(U_1198,U_1199,U_1200),c_Groups_Oplus__class_Oplus(U_1198,c_Groups_Oone__class_Oone(U_1198),c_Groups_Oone__class_Oone(U_1198))))
| ~ c_Orderings_Oord__class_Oless(U_1198,U_1199,U_1200)
| ~ class_Fields_Olinordered__field(U_1198) ),
inference(variable_rename,[status(thm)],[f_390_1]) ).
cnf(f_390_3,plain,
( c_Orderings_Oord__class_Oless(U_1198,U_1199,c_Rings_Oinverse__class_Odivide(U_1198,c_Groups_Oplus__class_Oplus(U_1198,U_1199,U_1200),c_Groups_Oplus__class_Oplus(U_1198,c_Groups_Oone__class_Oone(U_1198),c_Groups_Oone__class_Oone(U_1198))))
| ~ c_Orderings_Oord__class_Oless(U_1198,U_1199,U_1200)
| ~ class_Fields_Olinordered__field(U_1198) ),
inference(clausify,[status(thm)],[f_390_2]) ).
fof(f_391_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_391_2,plain,
! [U_1201] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1201) = 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_1201) ),
inference(variable_rename,[status(thm)],[f_391_1]) ).
cnf(f_391_3,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1201) = 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_1201) ),
inference(clausify,[status(thm)],[f_391_2]) ).
fof(f_392_1,plain,
! [V_y,V_x,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_x),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_392_2,plain,
! [U_1204,U_1203,U_1202] :
( ~ c_Orderings_Oord__class_Oless(U_1202,c_Groups_Oplus__class_Oplus(U_1202,hAPP(c_Groups_Otimes__class_Otimes(U_1202,U_1203),U_1203),hAPP(c_Groups_Otimes__class_Otimes(U_1202,U_1204),U_1204)),c_Groups_Ozero__class_Ozero(U_1202))
| ~ class_Rings_Olinordered__ring(U_1202) ),
inference(variable_rename,[status(thm)],[f_392_1]) ).
cnf(f_392_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_1202,c_Groups_Oplus__class_Oplus(U_1202,hAPP(c_Groups_Otimes__class_Otimes(U_1202,U_1203),U_1203),hAPP(c_Groups_Otimes__class_Otimes(U_1202,U_1204),U_1204)),c_Groups_Ozero__class_Ozero(U_1202))
| ~ class_Rings_Olinordered__ring(U_1202) ),
inference(clausify,[status(thm)],[f_392_2]) ).
fof(f_393_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(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),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(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),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_393_2,plain,
! [U_1207,U_1206,U_1205] :
( ( ( c_Orderings_Oord__class_Oless(U_1205,c_Groups_Ozero__class_Ozero(U_1205),c_Groups_Oplus__class_Oplus(U_1205,hAPP(c_Groups_Otimes__class_Otimes(U_1205,U_1206),U_1206),hAPP(c_Groups_Otimes__class_Otimes(U_1205,U_1207),U_1207)))
| ( U_1207 = c_Groups_Ozero__class_Ozero(U_1205)
& U_1206 = c_Groups_Ozero__class_Ozero(U_1205) ) )
& ( U_1207 != c_Groups_Ozero__class_Ozero(U_1205)
| U_1206 != c_Groups_Ozero__class_Ozero(U_1205)
| ~ c_Orderings_Oord__class_Oless(U_1205,c_Groups_Ozero__class_Ozero(U_1205),c_Groups_Oplus__class_Oplus(U_1205,hAPP(c_Groups_Otimes__class_Otimes(U_1205,U_1206),U_1206),hAPP(c_Groups_Otimes__class_Otimes(U_1205,U_1207),U_1207))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_1205) ),
inference(variable_rename,[status(thm)],[f_393_1]) ).
cnf(f_393_3,plain,
( U_1207 != c_Groups_Ozero__class_Ozero(U_1205)
| U_1206 != c_Groups_Ozero__class_Ozero(U_1205)
| ~ c_Orderings_Oord__class_Oless(U_1205,c_Groups_Ozero__class_Ozero(U_1205),c_Groups_Oplus__class_Oplus(U_1205,hAPP(c_Groups_Otimes__class_Otimes(U_1205,U_1206),U_1206),hAPP(c_Groups_Otimes__class_Otimes(U_1205,U_1207),U_1207)))
| ~ class_Rings_Olinordered__ring__strict(U_1205) ),
inference(clausify,[status(thm)],[f_393_2]) ).
cnf(f_393_4,plain,
( U_1206 = c_Groups_Ozero__class_Ozero(U_1205)
| c_Orderings_Oord__class_Oless(U_1205,c_Groups_Ozero__class_Ozero(U_1205),c_Groups_Oplus__class_Oplus(U_1205,hAPP(c_Groups_Otimes__class_Otimes(U_1205,U_1206),U_1206),hAPP(c_Groups_Otimes__class_Otimes(U_1205,U_1207),U_1207)))
| ~ class_Rings_Olinordered__ring__strict(U_1205) ),
inference(clausify,[status(thm)],[f_393_2]) ).
cnf(f_393_5,plain,
( U_1207 = c_Groups_Ozero__class_Ozero(U_1205)
| c_Orderings_Oord__class_Oless(U_1205,c_Groups_Ozero__class_Ozero(U_1205),c_Groups_Oplus__class_Oplus(U_1205,hAPP(c_Groups_Otimes__class_Otimes(U_1205,U_1206),U_1206),hAPP(c_Groups_Otimes__class_Otimes(U_1205,U_1207),U_1207)))
| ~ class_Rings_Olinordered__ring__strict(U_1205) ),
inference(clausify,[status(thm)],[f_393_2]) ).
fof(f_394_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(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),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(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),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_394_2,plain,
! [U_1210,U_1209,U_1208] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1208,c_Groups_Oplus__class_Oplus(U_1208,hAPP(c_Groups_Otimes__class_Otimes(U_1208,U_1209),U_1209),hAPP(c_Groups_Otimes__class_Otimes(U_1208,U_1210),U_1210)),c_Groups_Ozero__class_Ozero(U_1208))
| U_1210 != c_Groups_Ozero__class_Ozero(U_1208)
| U_1209 != c_Groups_Ozero__class_Ozero(U_1208) )
& ( ( U_1210 = c_Groups_Ozero__class_Ozero(U_1208)
& U_1209 = c_Groups_Ozero__class_Ozero(U_1208) )
| ~ c_Orderings_Oord__class_Oless__eq(U_1208,c_Groups_Oplus__class_Oplus(U_1208,hAPP(c_Groups_Otimes__class_Otimes(U_1208,U_1209),U_1209),hAPP(c_Groups_Otimes__class_Otimes(U_1208,U_1210),U_1210)),c_Groups_Ozero__class_Ozero(U_1208)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_1208) ),
inference(variable_rename,[status(thm)],[f_394_1]) ).
cnf(f_394_3,plain,
( U_1209 = c_Groups_Ozero__class_Ozero(U_1208)
| ~ c_Orderings_Oord__class_Oless__eq(U_1208,c_Groups_Oplus__class_Oplus(U_1208,hAPP(c_Groups_Otimes__class_Otimes(U_1208,U_1209),U_1209),hAPP(c_Groups_Otimes__class_Otimes(U_1208,U_1210),U_1210)),c_Groups_Ozero__class_Ozero(U_1208))
| ~ class_Rings_Olinordered__ring__strict(U_1208) ),
inference(clausify,[status(thm)],[f_394_2]) ).
cnf(f_394_4,plain,
( U_1210 = c_Groups_Ozero__class_Ozero(U_1208)
| ~ c_Orderings_Oord__class_Oless__eq(U_1208,c_Groups_Oplus__class_Oplus(U_1208,hAPP(c_Groups_Otimes__class_Otimes(U_1208,U_1209),U_1209),hAPP(c_Groups_Otimes__class_Otimes(U_1208,U_1210),U_1210)),c_Groups_Ozero__class_Ozero(U_1208))
| ~ class_Rings_Olinordered__ring__strict(U_1208) ),
inference(clausify,[status(thm)],[f_394_2]) ).
cnf(f_394_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1208,c_Groups_Oplus__class_Oplus(U_1208,hAPP(c_Groups_Otimes__class_Otimes(U_1208,U_1209),U_1209),hAPP(c_Groups_Otimes__class_Otimes(U_1208,U_1210),U_1210)),c_Groups_Ozero__class_Ozero(U_1208))
| U_1210 != c_Groups_Ozero__class_Ozero(U_1208)
| U_1209 != c_Groups_Ozero__class_Ozero(U_1208)
| ~ class_Rings_Olinordered__ring__strict(U_1208) ),
inference(clausify,[status(thm)],[f_394_2]) ).
fof(f_395_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(c_Groups_Otimes__class_Otimes(T_a,V_x),V_x),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_395_2,plain,
! [U_1213,U_1212,U_1211] :
( c_Orderings_Oord__class_Oless__eq(U_1211,c_Groups_Ozero__class_Ozero(U_1211),c_Groups_Oplus__class_Oplus(U_1211,hAPP(c_Groups_Otimes__class_Otimes(U_1211,U_1212),U_1212),hAPP(c_Groups_Otimes__class_Otimes(U_1211,U_1213),U_1213)))
| ~ class_Rings_Olinordered__ring(U_1211) ),
inference(variable_rename,[status(thm)],[f_395_1]) ).
cnf(f_395_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1211,c_Groups_Ozero__class_Ozero(U_1211),c_Groups_Oplus__class_Oplus(U_1211,hAPP(c_Groups_Otimes__class_Otimes(U_1211,U_1212),U_1212),hAPP(c_Groups_Otimes__class_Otimes(U_1211,U_1213),U_1213)))
| ~ class_Rings_Olinordered__ring(U_1211) ),
inference(clausify,[status(thm)],[f_395_2]) ).
fof(f_396_1,plain,
! [V_u,V_y,V_x1,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_u),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x1)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x1),V_y),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_u))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x1)
| ~ 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__inverse__cancel2]) ).
fof(f_396_2,plain,
! [U_1217,U_1216,U_1215,U_1214] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1216),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,U_1214)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1217),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,U_1215)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1215),U_1216),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1214),U_1217))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1215)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1214) ),
inference(variable_rename,[status(thm)],[f_396_1]) ).
cnf(f_396_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1216),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,U_1214)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1217),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,U_1215)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1215),U_1216),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1214),U_1217))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1215)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1214) ),
inference(clausify,[status(thm)],[f_396_2]) ).
fof(f_397_1,plain,
! [V_u,V_y,V_x1,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)),V_y),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x1)),V_u))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x1),V_y),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_u))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x1)
| ~ 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__inverse__cancel]) ).
fof(f_397_2,plain,
! [U_1221,U_1220,U_1219,U_1218] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,U_1218)),U_1220),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,U_1219)),U_1221))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1219),U_1220),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1218),U_1221))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1219)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1218) ),
inference(variable_rename,[status(thm)],[f_397_1]) ).
cnf(f_397_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,U_1218)),U_1220),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,U_1219)),U_1221))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1219),U_1220),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1218),U_1221))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1219)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1218) ),
inference(clausify,[status(thm)],[f_397_2]) ).
fof(f_398_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),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(c_Groups_Otimes__class_Otimes(T_a,V_x_2),V_x_2),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_398_2,plain,
! [U_1224,U_1223,U_1222] :
( ( ( c_Groups_Oplus__class_Oplus(U_1222,hAPP(c_Groups_Otimes__class_Otimes(U_1222,U_1223),U_1223),hAPP(c_Groups_Otimes__class_Otimes(U_1222,U_1224),U_1224)) = c_Groups_Ozero__class_Ozero(U_1222)
| U_1224 != c_Groups_Ozero__class_Ozero(U_1222)
| U_1223 != c_Groups_Ozero__class_Ozero(U_1222) )
& ( ( U_1224 = c_Groups_Ozero__class_Ozero(U_1222)
& U_1223 = c_Groups_Ozero__class_Ozero(U_1222) )
| c_Groups_Oplus__class_Oplus(U_1222,hAPP(c_Groups_Otimes__class_Otimes(U_1222,U_1223),U_1223),hAPP(c_Groups_Otimes__class_Otimes(U_1222,U_1224),U_1224)) != c_Groups_Ozero__class_Ozero(U_1222) ) )
| ~ class_Rings_Olinordered__ring__strict(U_1222) ),
inference(variable_rename,[status(thm)],[f_398_1]) ).
cnf(f_398_3,plain,
( U_1223 = c_Groups_Ozero__class_Ozero(U_1222)
| c_Groups_Oplus__class_Oplus(U_1222,hAPP(c_Groups_Otimes__class_Otimes(U_1222,U_1223),U_1223),hAPP(c_Groups_Otimes__class_Otimes(U_1222,U_1224),U_1224)) != c_Groups_Ozero__class_Ozero(U_1222)
| ~ class_Rings_Olinordered__ring__strict(U_1222) ),
inference(clausify,[status(thm)],[f_398_2]) ).
cnf(f_398_4,plain,
( U_1224 = c_Groups_Ozero__class_Ozero(U_1222)
| c_Groups_Oplus__class_Oplus(U_1222,hAPP(c_Groups_Otimes__class_Otimes(U_1222,U_1223),U_1223),hAPP(c_Groups_Otimes__class_Otimes(U_1222,U_1224),U_1224)) != c_Groups_Ozero__class_Ozero(U_1222)
| ~ class_Rings_Olinordered__ring__strict(U_1222) ),
inference(clausify,[status(thm)],[f_398_2]) ).
cnf(f_398_5,plain,
( c_Groups_Oplus__class_Oplus(U_1222,hAPP(c_Groups_Otimes__class_Otimes(U_1222,U_1223),U_1223),hAPP(c_Groups_Otimes__class_Otimes(U_1222,U_1224),U_1224)) = c_Groups_Ozero__class_Ozero(U_1222)
| U_1224 != c_Groups_Ozero__class_Ozero(U_1222)
| U_1223 != c_Groups_Ozero__class_Ozero(U_1222)
| ~ class_Rings_Olinordered__ring__strict(U_1222) ),
inference(clausify,[status(thm)],[f_398_2]) ).
fof(f_399_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_399_2,plain,
! [U_1226,U_1225] :
( ( ( c_Orderings_Oord__class_Oless(U_1225,c_Groups_Oplus__class_Oplus(U_1225,U_1226,U_1226),c_Groups_Ozero__class_Ozero(U_1225))
| ~ c_Orderings_Oord__class_Oless(U_1225,U_1226,c_Groups_Ozero__class_Ozero(U_1225)) )
& ( c_Orderings_Oord__class_Oless(U_1225,U_1226,c_Groups_Ozero__class_Ozero(U_1225))
| ~ c_Orderings_Oord__class_Oless(U_1225,c_Groups_Oplus__class_Oplus(U_1225,U_1226,U_1226),c_Groups_Ozero__class_Ozero(U_1225)) ) )
| ~ class_Rings_Olinordered__idom(U_1225) ),
inference(variable_rename,[status(thm)],[f_399_1]) ).
cnf(f_399_3,plain,
( c_Orderings_Oord__class_Oless(U_1225,U_1226,c_Groups_Ozero__class_Ozero(U_1225))
| ~ c_Orderings_Oord__class_Oless(U_1225,c_Groups_Oplus__class_Oplus(U_1225,U_1226,U_1226),c_Groups_Ozero__class_Ozero(U_1225))
| ~ class_Rings_Olinordered__idom(U_1225) ),
inference(clausify,[status(thm)],[f_399_2]) ).
cnf(f_399_4,plain,
( c_Orderings_Oord__class_Oless(U_1225,c_Groups_Oplus__class_Oplus(U_1225,U_1226,U_1226),c_Groups_Ozero__class_Ozero(U_1225))
| ~ c_Orderings_Oord__class_Oless(U_1225,U_1226,c_Groups_Ozero__class_Ozero(U_1225))
| ~ class_Rings_Olinordered__idom(U_1225) ),
inference(clausify,[status(thm)],[f_399_2]) ).
fof(f_400_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_400_2,plain,
! [U_1228,U_1227] :
( ( ( c_Groups_Oplus__class_Oplus(U_1227,U_1228,U_1228) = c_Groups_Ozero__class_Ozero(U_1227)
| U_1228 != c_Groups_Ozero__class_Ozero(U_1227) )
& ( U_1228 = c_Groups_Ozero__class_Ozero(U_1227)
| c_Groups_Oplus__class_Oplus(U_1227,U_1228,U_1228) != c_Groups_Ozero__class_Ozero(U_1227) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1227) ),
inference(variable_rename,[status(thm)],[f_400_1]) ).
cnf(f_400_3,plain,
( U_1228 = c_Groups_Ozero__class_Ozero(U_1227)
| c_Groups_Oplus__class_Oplus(U_1227,U_1228,U_1228) != c_Groups_Ozero__class_Ozero(U_1227)
| ~ class_Groups_Olinordered__ab__group__add(U_1227) ),
inference(clausify,[status(thm)],[f_400_2]) ).
cnf(f_400_4,plain,
( c_Groups_Oplus__class_Oplus(U_1227,U_1228,U_1228) = c_Groups_Ozero__class_Ozero(U_1227)
| U_1228 != c_Groups_Ozero__class_Ozero(U_1227)
| ~ class_Groups_Olinordered__ab__group__add(U_1227) ),
inference(clausify,[status(thm)],[f_400_2]) ).
fof(f_401_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ? [B_e] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Groups_Oplus__class_Oplus(T_a,V_y,B_e))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),B_e) )
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_field__le__epsilon]) ).
fof(f_401_2,plain,
! [U_1232,U_1231,U_1230] :
( c_Orderings_Oord__class_Oless__eq(U_1230,U_1231,U_1232)
| ? [U_1229] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1230,U_1231,c_Groups_Oplus__class_Oplus(U_1230,U_1232,U_1229))
& c_Orderings_Oord__class_Oless(U_1230,c_Groups_Ozero__class_Ozero(U_1230),U_1229) )
| ~ class_Fields_Olinordered__field(U_1230) ),
inference(variable_rename,[status(thm)],[f_401_1]) ).
fof(f_401_3,plain,
! [U_1232,U_1231,U_1230] :
( c_Orderings_Oord__class_Oless__eq(U_1230,U_1231,U_1232)
| ( ~ c_Orderings_Oord__class_Oless__eq(U_1230,U_1231,c_Groups_Oplus__class_Oplus(U_1230,U_1232,sK6(U_1232,U_1231,U_1230)))
& c_Orderings_Oord__class_Oless(U_1230,c_Groups_Ozero__class_Ozero(U_1230),sK6(U_1232,U_1231,U_1230)) )
| ~ class_Fields_Olinordered__field(U_1230) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_1229,sK6(U_1232,U_1231,U_1230))],[f_401_2]) ).
cnf(f_401_4,plain,
( c_Orderings_Oord__class_Oless(U_1230,c_Groups_Ozero__class_Ozero(U_1230),sK6(U_1232,U_1231,U_1230))
| c_Orderings_Oord__class_Oless__eq(U_1230,U_1231,U_1232)
| ~ class_Fields_Olinordered__field(U_1230) ),
inference(clausify,[status(thm)],[f_401_3]) ).
cnf(f_401_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1230,U_1231,c_Groups_Oplus__class_Oplus(U_1230,U_1232,sK6(U_1232,U_1231,U_1230)))
| c_Orderings_Oord__class_Oless__eq(U_1230,U_1231,U_1232)
| ~ class_Fields_Olinordered__field(U_1230) ),
inference(clausify,[status(thm)],[f_401_3]) ).
fof(f_402_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),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_ln__add__one__self__le__self]) ).
fof(f_402_2,plain,
! [U_1233] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1233)),U_1233)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1233) ),
inference(variable_rename,[status(thm)],[f_402_1]) ).
cnf(f_402_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1233)),U_1233)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1233) ),
inference(clausify,[status(thm)],[f_402_2]) ).
fof(f_403_1,plain,
! [V_y,V_x] :
( hAPP(c_Transcendental_Oln,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_y)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x),hAPP(c_Transcendental_Oln,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_ln__mult]) ).
fof(f_403_2,plain,
! [U_1235,U_1234] :
( hAPP(c_Transcendental_Oln,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1234),U_1235)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,U_1234),hAPP(c_Transcendental_Oln,U_1235))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1235)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1234) ),
inference(variable_rename,[status(thm)],[f_403_1]) ).
cnf(f_403_3,plain,
( hAPP(c_Transcendental_Oln,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1234),U_1235)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,U_1234),hAPP(c_Transcendental_Oln,U_1235))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1235)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1234) ),
inference(clausify,[status(thm)],[f_403_2]) ).
fof(f_404_1,plain,
! [V_y_2,V_x_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x_2),hAPP(c_Transcendental_Oln,V_y_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x_2),hAPP(c_Transcendental_Oln,V_y_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_ln__less__cancel__iff]) ).
fof(f_404_2,plain,
! [U_1237,U_1236] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,U_1236),hAPP(c_Transcendental_Oln,U_1237))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1236,U_1237) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1236,U_1237)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,U_1236),hAPP(c_Transcendental_Oln,U_1237)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1237)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1236) ),
inference(variable_rename,[status(thm)],[f_404_1]) ).
cnf(f_404_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1236,U_1237)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,U_1236),hAPP(c_Transcendental_Oln,U_1237))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1237)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1236) ),
inference(clausify,[status(thm)],[f_404_2]) ).
cnf(f_404_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,U_1236),hAPP(c_Transcendental_Oln,U_1237))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1236,U_1237)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1237)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1236) ),
inference(clausify,[status(thm)],[f_404_2]) ).
fof(f_405_1,plain,
! [V_y_2,V_x_2] :
( ( ( hAPP(c_Transcendental_Oln,V_x_2) = hAPP(c_Transcendental_Oln,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_Transcendental_Oln,V_x_2) != hAPP(c_Transcendental_Oln,V_y_2) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_ln__inj__iff]) ).
fof(f_405_2,plain,
! [U_1239,U_1238] :
( ( ( hAPP(c_Transcendental_Oln,U_1238) = hAPP(c_Transcendental_Oln,U_1239)
| U_1238 != U_1239 )
& ( U_1238 = U_1239
| hAPP(c_Transcendental_Oln,U_1238) != hAPP(c_Transcendental_Oln,U_1239) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1239)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1238) ),
inference(variable_rename,[status(thm)],[f_405_1]) ).
cnf(f_405_3,plain,
( U_1238 = U_1239
| hAPP(c_Transcendental_Oln,U_1238) != hAPP(c_Transcendental_Oln,U_1239)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1239)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1238) ),
inference(clausify,[status(thm)],[f_405_2]) ).
cnf(f_405_4,plain,
( hAPP(c_Transcendental_Oln,U_1238) = hAPP(c_Transcendental_Oln,U_1239)
| U_1238 != U_1239
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1239)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1238) ),
inference(clausify,[status(thm)],[f_405_2]) ).
fof(f_406_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x),V_x)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_ln__less__self]) ).
fof(f_406_2,plain,
! [U_1240] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,U_1240),U_1240)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1240) ),
inference(variable_rename,[status(thm)],[f_406_1]) ).
cnf(f_406_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,U_1240),U_1240)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1240) ),
inference(clausify,[status(thm)],[f_406_2]) ).
fof(f_407_1,plain,
hAPP(c_Transcendental_Oln,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_ln__one]) ).
cnf(f_407_2,plain,
hAPP(c_Transcendental_Oln,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_407_1]) ).
fof(f_408_1,plain,
! [V_y_2,V_x_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x_2),hAPP(c_Transcendental_Oln,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(c_Transcendental_Oln,V_x_2),hAPP(c_Transcendental_Oln,V_y_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_ln__le__cancel__iff]) ).
fof(f_408_2,plain,
! [U_1242,U_1241] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,U_1241),hAPP(c_Transcendental_Oln,U_1242))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1241,U_1242) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1241,U_1242)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,U_1241),hAPP(c_Transcendental_Oln,U_1242)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1242)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1241) ),
inference(variable_rename,[status(thm)],[f_408_1]) ).
cnf(f_408_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1241,U_1242)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,U_1241),hAPP(c_Transcendental_Oln,U_1242))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1242)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1241) ),
inference(clausify,[status(thm)],[f_408_2]) ).
cnf(f_408_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,U_1241),hAPP(c_Transcendental_Oln,U_1242))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1241,U_1242)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1242)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1241) ),
inference(clausify,[status(thm)],[f_408_2]) ).
fof(f_409_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_ln__ge__zero]) ).
fof(f_409_2,plain,
! [U_1243] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1243))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1243) ),
inference(variable_rename,[status(thm)],[f_409_1]) ).
cnf(f_409_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1243))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1243) ),
inference(clausify,[status(thm)],[f_409_2]) ).
fof(f_410_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x)) ),
inference(fof_nnf,[status(thm)],[fact_ln__gt__zero__imp__gt__one]) ).
fof(f_410_2,plain,
! [U_1244] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1244)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1244)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1244)) ),
inference(variable_rename,[status(thm)],[f_410_1]) ).
cnf(f_410_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1244)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1244)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1244)) ),
inference(clausify,[status(thm)],[f_410_2]) ).
fof(f_411_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(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_ln__less__zero]) ).
fof(f_411_2,plain,
! [U_1245] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,U_1245),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1245,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_1245) ),
inference(variable_rename,[status(thm)],[f_411_1]) ).
cnf(f_411_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,U_1245),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1245,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_1245) ),
inference(clausify,[status(thm)],[f_411_2]) ).
fof(f_412_1,plain,
! [V_x_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,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),V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_ln__less__zero__iff]) ).
fof(f_412_2,plain,
! [U_1246] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,U_1246),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1246,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1246,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,U_1246),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1246) ),
inference(variable_rename,[status(thm)],[f_412_1]) ).
cnf(f_412_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1246,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,U_1246),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1246) ),
inference(clausify,[status(thm)],[f_412_2]) ).
cnf(f_412_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,U_1246),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1246,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_1246) ),
inference(clausify,[status(thm)],[f_412_2]) ).
fof(f_413_1,plain,
! [V_x_2] :
( ( ( hAPP(c_Transcendental_Oln,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_x_2 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( V_x_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| hAPP(c_Transcendental_Oln,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),V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_ln__eq__zero__iff]) ).
fof(f_413_2,plain,
! [U_1247] :
( ( ( hAPP(c_Transcendental_Oln,U_1247) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1247 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( U_1247 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| hAPP(c_Transcendental_Oln,U_1247) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1247) ),
inference(variable_rename,[status(thm)],[f_413_1]) ).
cnf(f_413_3,plain,
( U_1247 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| hAPP(c_Transcendental_Oln,U_1247) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1247) ),
inference(clausify,[status(thm)],[f_413_2]) ).
cnf(f_413_4,plain,
( hAPP(c_Transcendental_Oln,U_1247) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1247 != 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_1247) ),
inference(clausify,[status(thm)],[f_413_2]) ).
fof(f_414_1,plain,
! [V_x_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_ln__gt__zero__iff]) ).
fof(f_414_2,plain,
! [U_1248] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1248))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1248) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1248)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1248)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1248) ),
inference(variable_rename,[status(thm)],[f_414_1]) ).
cnf(f_414_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1248)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1248))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1248) ),
inference(clausify,[status(thm)],[f_414_2]) ).
cnf(f_414_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1248))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1248)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1248) ),
inference(clausify,[status(thm)],[f_414_2]) ).
fof(f_415_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_ln__gt__zero]) ).
fof(f_415_2,plain,
! [U_1249] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1249))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1249) ),
inference(variable_rename,[status(thm)],[f_415_1]) ).
cnf(f_415_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1249))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1249) ),
inference(clausify,[status(thm)],[f_415_2]) ).
fof(f_416_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x)) ),
inference(fof_nnf,[status(thm)],[fact_ln__ge__zero__imp__ge__one]) ).
fof(f_416_2,plain,
! [U_1250] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1250)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1250)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1250)) ),
inference(variable_rename,[status(thm)],[f_416_1]) ).
cnf(f_416_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1250)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1250)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1250)) ),
inference(clausify,[status(thm)],[f_416_2]) ).
fof(f_417_1,plain,
! [V_x_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,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_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_ln__ge__zero__iff]) ).
fof(f_417_2,plain,
! [U_1251] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1251))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1251) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1251)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1251)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1251) ),
inference(variable_rename,[status(thm)],[f_417_1]) ).
cnf(f_417_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1251)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1251))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1251) ),
inference(clausify,[status(thm)],[f_417_2]) ).
cnf(f_417_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1251))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1251)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1251) ),
inference(clausify,[status(thm)],[f_417_2]) ).
fof(f_418_1,plain,
! [V_a_2,V_wa_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)
| ( ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
& ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)
& c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
& ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
| c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2) ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__le__eq__number__of1]) ).
fof(f_418_2,plain,
! [U_1255,U_1254,U_1253,U_1252] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1252,c_Rings_Oinverse__class_Odivide(U_1252,U_1253,c_Int_Onumber__class_Onumber__of(U_1252,U_1254)),U_1255)
| ( ( ( ~ c_Orderings_Oord__class_Oless__eq(U_1252,c_Groups_Ozero__class_Ozero(U_1252),U_1255)
& ~ c_Orderings_Oord__class_Oless(U_1252,c_Int_Onumber__class_Onumber__of(U_1252,U_1254),c_Groups_Ozero__class_Ozero(U_1252)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_1252,hAPP(c_Groups_Otimes__class_Otimes(U_1252,U_1255),c_Int_Onumber__class_Onumber__of(U_1252,U_1254)),U_1253)
& c_Orderings_Oord__class_Oless(U_1252,c_Int_Onumber__class_Onumber__of(U_1252,U_1254),c_Groups_Ozero__class_Ozero(U_1252)) ) )
& ~ c_Orderings_Oord__class_Oless(U_1252,c_Groups_Ozero__class_Ozero(U_1252),c_Int_Onumber__class_Onumber__of(U_1252,U_1254)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_1252,U_1253,hAPP(c_Groups_Otimes__class_Otimes(U_1252,U_1255),c_Int_Onumber__class_Onumber__of(U_1252,U_1254)))
& c_Orderings_Oord__class_Oless(U_1252,c_Groups_Ozero__class_Ozero(U_1252),c_Int_Onumber__class_Onumber__of(U_1252,U_1254)) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless__eq(U_1252,c_Groups_Ozero__class_Ozero(U_1252),U_1255)
| c_Orderings_Oord__class_Oless(U_1252,c_Int_Onumber__class_Onumber__of(U_1252,U_1254),c_Groups_Ozero__class_Ozero(U_1252)) )
& ( c_Orderings_Oord__class_Oless__eq(U_1252,hAPP(c_Groups_Otimes__class_Otimes(U_1252,U_1255),c_Int_Onumber__class_Onumber__of(U_1252,U_1254)),U_1253)
| ~ c_Orderings_Oord__class_Oless(U_1252,c_Int_Onumber__class_Onumber__of(U_1252,U_1254),c_Groups_Ozero__class_Ozero(U_1252)) ) )
| c_Orderings_Oord__class_Oless(U_1252,c_Groups_Ozero__class_Ozero(U_1252),c_Int_Onumber__class_Onumber__of(U_1252,U_1254)) )
& ( c_Orderings_Oord__class_Oless__eq(U_1252,U_1253,hAPP(c_Groups_Otimes__class_Otimes(U_1252,U_1255),c_Int_Onumber__class_Onumber__of(U_1252,U_1254)))
| ~ c_Orderings_Oord__class_Oless(U_1252,c_Groups_Ozero__class_Ozero(U_1252),c_Int_Onumber__class_Onumber__of(U_1252,U_1254)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_1252,c_Rings_Oinverse__class_Odivide(U_1252,U_1253,c_Int_Onumber__class_Onumber__of(U_1252,U_1254)),U_1255) ) )
| ~ class_Int_Onumber(U_1252)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1252) ),
inference(variable_rename,[status(thm)],[f_418_1]) ).
cnf(f_418_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1252,U_1253,hAPP(c_Groups_Otimes__class_Otimes(U_1252,U_1255),c_Int_Onumber__class_Onumber__of(U_1252,U_1254)))
| ~ c_Orderings_Oord__class_Oless(U_1252,c_Groups_Ozero__class_Ozero(U_1252),c_Int_Onumber__class_Onumber__of(U_1252,U_1254))
| ~ c_Orderings_Oord__class_Oless__eq(U_1252,c_Rings_Oinverse__class_Odivide(U_1252,U_1253,c_Int_Onumber__class_Onumber__of(U_1252,U_1254)),U_1255)
| ~ class_Int_Onumber(U_1252)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1252) ),
inference(clausify,[status(thm)],[f_418_2]) ).
cnf(f_418_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1252,hAPP(c_Groups_Otimes__class_Otimes(U_1252,U_1255),c_Int_Onumber__class_Onumber__of(U_1252,U_1254)),U_1253)
| ~ c_Orderings_Oord__class_Oless(U_1252,c_Int_Onumber__class_Onumber__of(U_1252,U_1254),c_Groups_Ozero__class_Ozero(U_1252))
| c_Orderings_Oord__class_Oless(U_1252,c_Groups_Ozero__class_Ozero(U_1252),c_Int_Onumber__class_Onumber__of(U_1252,U_1254))
| ~ c_Orderings_Oord__class_Oless__eq(U_1252,c_Rings_Oinverse__class_Odivide(U_1252,U_1253,c_Int_Onumber__class_Onumber__of(U_1252,U_1254)),U_1255)
| ~ class_Int_Onumber(U_1252)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1252) ),
inference(clausify,[status(thm)],[f_418_2]) ).
cnf(f_418_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1252,c_Groups_Ozero__class_Ozero(U_1252),U_1255)
| c_Orderings_Oord__class_Oless(U_1252,c_Int_Onumber__class_Onumber__of(U_1252,U_1254),c_Groups_Ozero__class_Ozero(U_1252))
| c_Orderings_Oord__class_Oless(U_1252,c_Groups_Ozero__class_Ozero(U_1252),c_Int_Onumber__class_Onumber__of(U_1252,U_1254))
| ~ c_Orderings_Oord__class_Oless__eq(U_1252,c_Rings_Oinverse__class_Odivide(U_1252,U_1253,c_Int_Onumber__class_Onumber__of(U_1252,U_1254)),U_1255)
| ~ class_Int_Onumber(U_1252)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1252) ),
inference(clausify,[status(thm)],[f_418_2]) ).
cnf(f_418_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_1252,c_Groups_Ozero__class_Ozero(U_1252),c_Int_Onumber__class_Onumber__of(U_1252,U_1254))
| c_Orderings_Oord__class_Oless(U_1252,c_Groups_Ozero__class_Ozero(U_1252),c_Int_Onumber__class_Onumber__of(U_1252,U_1254))
| c_Orderings_Oord__class_Oless__eq(U_1252,c_Rings_Oinverse__class_Odivide(U_1252,U_1253,c_Int_Onumber__class_Onumber__of(U_1252,U_1254)),U_1255)
| ~ class_Int_Onumber(U_1252)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1252) ),
inference(clausify,[status(thm)],[f_418_2]) ).
cnf(f_418_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_1252,c_Int_Onumber__class_Onumber__of(U_1252,U_1254),c_Groups_Ozero__class_Ozero(U_1252))
| c_Orderings_Oord__class_Oless(U_1252,c_Int_Onumber__class_Onumber__of(U_1252,U_1254),c_Groups_Ozero__class_Ozero(U_1252))
| c_Orderings_Oord__class_Oless(U_1252,c_Groups_Ozero__class_Ozero(U_1252),c_Int_Onumber__class_Onumber__of(U_1252,U_1254))
| c_Orderings_Oord__class_Oless__eq(U_1252,c_Rings_Oinverse__class_Odivide(U_1252,U_1253,c_Int_Onumber__class_Onumber__of(U_1252,U_1254)),U_1255)
| ~ class_Int_Onumber(U_1252)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1252) ),
inference(clausify,[status(thm)],[f_418_2]) ).
cnf(f_418_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1252,c_Groups_Ozero__class_Ozero(U_1252),U_1255)
| c_Orderings_Oord__class_Oless(U_1252,c_Int_Onumber__class_Onumber__of(U_1252,U_1254),c_Groups_Ozero__class_Ozero(U_1252))
| c_Orderings_Oord__class_Oless(U_1252,c_Groups_Ozero__class_Ozero(U_1252),c_Int_Onumber__class_Onumber__of(U_1252,U_1254))
| c_Orderings_Oord__class_Oless__eq(U_1252,c_Rings_Oinverse__class_Odivide(U_1252,U_1253,c_Int_Onumber__class_Onumber__of(U_1252,U_1254)),U_1255)
| ~ class_Int_Onumber(U_1252)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1252) ),
inference(clausify,[status(thm)],[f_418_2]) ).
cnf(f_418_9,plain,
( ~ c_Orderings_Oord__class_Oless(U_1252,c_Int_Onumber__class_Onumber__of(U_1252,U_1254),c_Groups_Ozero__class_Ozero(U_1252))
| ~ c_Orderings_Oord__class_Oless__eq(U_1252,hAPP(c_Groups_Otimes__class_Otimes(U_1252,U_1255),c_Int_Onumber__class_Onumber__of(U_1252,U_1254)),U_1253)
| c_Orderings_Oord__class_Oless(U_1252,c_Groups_Ozero__class_Ozero(U_1252),c_Int_Onumber__class_Onumber__of(U_1252,U_1254))
| c_Orderings_Oord__class_Oless__eq(U_1252,c_Rings_Oinverse__class_Odivide(U_1252,U_1253,c_Int_Onumber__class_Onumber__of(U_1252,U_1254)),U_1255)
| ~ class_Int_Onumber(U_1252)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1252) ),
inference(clausify,[status(thm)],[f_418_2]) ).
cnf(f_418_10,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1252,c_Groups_Ozero__class_Ozero(U_1252),U_1255)
| ~ c_Orderings_Oord__class_Oless__eq(U_1252,hAPP(c_Groups_Otimes__class_Otimes(U_1252,U_1255),c_Int_Onumber__class_Onumber__of(U_1252,U_1254)),U_1253)
| c_Orderings_Oord__class_Oless(U_1252,c_Groups_Ozero__class_Ozero(U_1252),c_Int_Onumber__class_Onumber__of(U_1252,U_1254))
| c_Orderings_Oord__class_Oless__eq(U_1252,c_Rings_Oinverse__class_Odivide(U_1252,U_1253,c_Int_Onumber__class_Onumber__of(U_1252,U_1254)),U_1255)
| ~ class_Int_Onumber(U_1252)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1252) ),
inference(clausify,[status(thm)],[f_418_2]) ).
cnf(f_418_11,plain,
( ~ c_Orderings_Oord__class_Oless(U_1252,c_Groups_Ozero__class_Ozero(U_1252),c_Int_Onumber__class_Onumber__of(U_1252,U_1254))
| ~ c_Orderings_Oord__class_Oless__eq(U_1252,U_1253,hAPP(c_Groups_Otimes__class_Otimes(U_1252,U_1255),c_Int_Onumber__class_Onumber__of(U_1252,U_1254)))
| c_Orderings_Oord__class_Oless__eq(U_1252,c_Rings_Oinverse__class_Odivide(U_1252,U_1253,c_Int_Onumber__class_Onumber__of(U_1252,U_1254)),U_1255)
| ~ class_Int_Onumber(U_1252)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1252) ),
inference(clausify,[status(thm)],[f_418_2]) ).
cnf(f_418_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_1252,c_Int_Onumber__class_Onumber__of(U_1252,U_1254),c_Groups_Ozero__class_Ozero(U_1252))
| c_Orderings_Oord__class_Oless(U_1252,c_Int_Onumber__class_Onumber__of(U_1252,U_1254),c_Groups_Ozero__class_Ozero(U_1252))
| ~ c_Orderings_Oord__class_Oless__eq(U_1252,U_1253,hAPP(c_Groups_Otimes__class_Otimes(U_1252,U_1255),c_Int_Onumber__class_Onumber__of(U_1252,U_1254)))
| c_Orderings_Oord__class_Oless__eq(U_1252,c_Rings_Oinverse__class_Odivide(U_1252,U_1253,c_Int_Onumber__class_Onumber__of(U_1252,U_1254)),U_1255)
| ~ class_Int_Onumber(U_1252)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1252) ),
inference(clausify,[status(thm)],[f_418_2]) ).
cnf(f_418_13,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1252,c_Groups_Ozero__class_Ozero(U_1252),U_1255)
| c_Orderings_Oord__class_Oless(U_1252,c_Int_Onumber__class_Onumber__of(U_1252,U_1254),c_Groups_Ozero__class_Ozero(U_1252))
| ~ c_Orderings_Oord__class_Oless__eq(U_1252,U_1253,hAPP(c_Groups_Otimes__class_Otimes(U_1252,U_1255),c_Int_Onumber__class_Onumber__of(U_1252,U_1254)))
| c_Orderings_Oord__class_Oless__eq(U_1252,c_Rings_Oinverse__class_Odivide(U_1252,U_1253,c_Int_Onumber__class_Onumber__of(U_1252,U_1254)),U_1255)
| ~ class_Int_Onumber(U_1252)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1252) ),
inference(clausify,[status(thm)],[f_418_2]) ).
cnf(f_418_14,plain,
( ~ c_Orderings_Oord__class_Oless(U_1252,c_Int_Onumber__class_Onumber__of(U_1252,U_1254),c_Groups_Ozero__class_Ozero(U_1252))
| ~ c_Orderings_Oord__class_Oless__eq(U_1252,hAPP(c_Groups_Otimes__class_Otimes(U_1252,U_1255),c_Int_Onumber__class_Onumber__of(U_1252,U_1254)),U_1253)
| ~ c_Orderings_Oord__class_Oless__eq(U_1252,U_1253,hAPP(c_Groups_Otimes__class_Otimes(U_1252,U_1255),c_Int_Onumber__class_Onumber__of(U_1252,U_1254)))
| c_Orderings_Oord__class_Oless__eq(U_1252,c_Rings_Oinverse__class_Odivide(U_1252,U_1253,c_Int_Onumber__class_Onumber__of(U_1252,U_1254)),U_1255)
| ~ class_Int_Onumber(U_1252)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1252) ),
inference(clausify,[status(thm)],[f_418_2]) ).
cnf(f_418_15,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1252,c_Groups_Ozero__class_Ozero(U_1252),U_1255)
| ~ c_Orderings_Oord__class_Oless__eq(U_1252,hAPP(c_Groups_Otimes__class_Otimes(U_1252,U_1255),c_Int_Onumber__class_Onumber__of(U_1252,U_1254)),U_1253)
| ~ c_Orderings_Oord__class_Oless__eq(U_1252,U_1253,hAPP(c_Groups_Otimes__class_Otimes(U_1252,U_1255),c_Int_Onumber__class_Onumber__of(U_1252,U_1254)))
| c_Orderings_Oord__class_Oless__eq(U_1252,c_Rings_Oinverse__class_Odivide(U_1252,U_1253,c_Int_Onumber__class_Onumber__of(U_1252,U_1254)),U_1255)
| ~ class_Int_Onumber(U_1252)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1252) ),
inference(clausify,[status(thm)],[f_418_2]) ).
fof(f_419_1,plain,
! [V_wa_2,V_ca_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
| ( ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
& ~ 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(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_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,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) )
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2))
& 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,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
| 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(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_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,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2))
| ~ 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,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__le__eq__number__of]) ).
fof(f_419_2,plain,
! [U_1259,U_1258,U_1257,U_1256] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1256,c_Rings_Oinverse__class_Odivide(U_1256,U_1257,U_1258),c_Int_Onumber__class_Onumber__of(U_1256,U_1259))
| ( ( ( ~ c_Orderings_Oord__class_Oless__eq(U_1256,c_Groups_Ozero__class_Ozero(U_1256),c_Int_Onumber__class_Onumber__of(U_1256,U_1259))
& ~ c_Orderings_Oord__class_Oless(U_1256,U_1258,c_Groups_Ozero__class_Ozero(U_1256)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_1256,hAPP(c_Groups_Otimes__class_Otimes(U_1256,c_Int_Onumber__class_Onumber__of(U_1256,U_1259)),U_1258),U_1257)
& c_Orderings_Oord__class_Oless(U_1256,U_1258,c_Groups_Ozero__class_Ozero(U_1256)) ) )
& ~ c_Orderings_Oord__class_Oless(U_1256,c_Groups_Ozero__class_Ozero(U_1256),U_1258) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_1256,U_1257,hAPP(c_Groups_Otimes__class_Otimes(U_1256,c_Int_Onumber__class_Onumber__of(U_1256,U_1259)),U_1258))
& c_Orderings_Oord__class_Oless(U_1256,c_Groups_Ozero__class_Ozero(U_1256),U_1258) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless__eq(U_1256,c_Groups_Ozero__class_Ozero(U_1256),c_Int_Onumber__class_Onumber__of(U_1256,U_1259))
| c_Orderings_Oord__class_Oless(U_1256,U_1258,c_Groups_Ozero__class_Ozero(U_1256)) )
& ( c_Orderings_Oord__class_Oless__eq(U_1256,hAPP(c_Groups_Otimes__class_Otimes(U_1256,c_Int_Onumber__class_Onumber__of(U_1256,U_1259)),U_1258),U_1257)
| ~ c_Orderings_Oord__class_Oless(U_1256,U_1258,c_Groups_Ozero__class_Ozero(U_1256)) ) )
| c_Orderings_Oord__class_Oless(U_1256,c_Groups_Ozero__class_Ozero(U_1256),U_1258) )
& ( c_Orderings_Oord__class_Oless__eq(U_1256,U_1257,hAPP(c_Groups_Otimes__class_Otimes(U_1256,c_Int_Onumber__class_Onumber__of(U_1256,U_1259)),U_1258))
| ~ c_Orderings_Oord__class_Oless(U_1256,c_Groups_Ozero__class_Ozero(U_1256),U_1258) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_1256,c_Rings_Oinverse__class_Odivide(U_1256,U_1257,U_1258),c_Int_Onumber__class_Onumber__of(U_1256,U_1259)) ) )
| ~ class_Int_Onumber(U_1256)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1256) ),
inference(variable_rename,[status(thm)],[f_419_1]) ).
cnf(f_419_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1256,U_1257,hAPP(c_Groups_Otimes__class_Otimes(U_1256,c_Int_Onumber__class_Onumber__of(U_1256,U_1259)),U_1258))
| ~ c_Orderings_Oord__class_Oless(U_1256,c_Groups_Ozero__class_Ozero(U_1256),U_1258)
| ~ c_Orderings_Oord__class_Oless__eq(U_1256,c_Rings_Oinverse__class_Odivide(U_1256,U_1257,U_1258),c_Int_Onumber__class_Onumber__of(U_1256,U_1259))
| ~ class_Int_Onumber(U_1256)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1256) ),
inference(clausify,[status(thm)],[f_419_2]) ).
cnf(f_419_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1256,hAPP(c_Groups_Otimes__class_Otimes(U_1256,c_Int_Onumber__class_Onumber__of(U_1256,U_1259)),U_1258),U_1257)
| ~ c_Orderings_Oord__class_Oless(U_1256,U_1258,c_Groups_Ozero__class_Ozero(U_1256))
| c_Orderings_Oord__class_Oless(U_1256,c_Groups_Ozero__class_Ozero(U_1256),U_1258)
| ~ c_Orderings_Oord__class_Oless__eq(U_1256,c_Rings_Oinverse__class_Odivide(U_1256,U_1257,U_1258),c_Int_Onumber__class_Onumber__of(U_1256,U_1259))
| ~ class_Int_Onumber(U_1256)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1256) ),
inference(clausify,[status(thm)],[f_419_2]) ).
cnf(f_419_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1256,c_Groups_Ozero__class_Ozero(U_1256),c_Int_Onumber__class_Onumber__of(U_1256,U_1259))
| c_Orderings_Oord__class_Oless(U_1256,U_1258,c_Groups_Ozero__class_Ozero(U_1256))
| c_Orderings_Oord__class_Oless(U_1256,c_Groups_Ozero__class_Ozero(U_1256),U_1258)
| ~ c_Orderings_Oord__class_Oless__eq(U_1256,c_Rings_Oinverse__class_Odivide(U_1256,U_1257,U_1258),c_Int_Onumber__class_Onumber__of(U_1256,U_1259))
| ~ class_Int_Onumber(U_1256)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1256) ),
inference(clausify,[status(thm)],[f_419_2]) ).
cnf(f_419_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_1256,c_Groups_Ozero__class_Ozero(U_1256),U_1258)
| c_Orderings_Oord__class_Oless(U_1256,c_Groups_Ozero__class_Ozero(U_1256),U_1258)
| c_Orderings_Oord__class_Oless__eq(U_1256,c_Rings_Oinverse__class_Odivide(U_1256,U_1257,U_1258),c_Int_Onumber__class_Onumber__of(U_1256,U_1259))
| ~ class_Int_Onumber(U_1256)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1256) ),
inference(clausify,[status(thm)],[f_419_2]) ).
cnf(f_419_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_1256,U_1258,c_Groups_Ozero__class_Ozero(U_1256))
| c_Orderings_Oord__class_Oless(U_1256,U_1258,c_Groups_Ozero__class_Ozero(U_1256))
| c_Orderings_Oord__class_Oless(U_1256,c_Groups_Ozero__class_Ozero(U_1256),U_1258)
| c_Orderings_Oord__class_Oless__eq(U_1256,c_Rings_Oinverse__class_Odivide(U_1256,U_1257,U_1258),c_Int_Onumber__class_Onumber__of(U_1256,U_1259))
| ~ class_Int_Onumber(U_1256)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1256) ),
inference(clausify,[status(thm)],[f_419_2]) ).
cnf(f_419_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1256,c_Groups_Ozero__class_Ozero(U_1256),c_Int_Onumber__class_Onumber__of(U_1256,U_1259))
| c_Orderings_Oord__class_Oless(U_1256,U_1258,c_Groups_Ozero__class_Ozero(U_1256))
| c_Orderings_Oord__class_Oless(U_1256,c_Groups_Ozero__class_Ozero(U_1256),U_1258)
| c_Orderings_Oord__class_Oless__eq(U_1256,c_Rings_Oinverse__class_Odivide(U_1256,U_1257,U_1258),c_Int_Onumber__class_Onumber__of(U_1256,U_1259))
| ~ class_Int_Onumber(U_1256)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1256) ),
inference(clausify,[status(thm)],[f_419_2]) ).
cnf(f_419_9,plain,
( ~ c_Orderings_Oord__class_Oless(U_1256,U_1258,c_Groups_Ozero__class_Ozero(U_1256))
| ~ c_Orderings_Oord__class_Oless__eq(U_1256,hAPP(c_Groups_Otimes__class_Otimes(U_1256,c_Int_Onumber__class_Onumber__of(U_1256,U_1259)),U_1258),U_1257)
| c_Orderings_Oord__class_Oless(U_1256,c_Groups_Ozero__class_Ozero(U_1256),U_1258)
| c_Orderings_Oord__class_Oless__eq(U_1256,c_Rings_Oinverse__class_Odivide(U_1256,U_1257,U_1258),c_Int_Onumber__class_Onumber__of(U_1256,U_1259))
| ~ class_Int_Onumber(U_1256)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1256) ),
inference(clausify,[status(thm)],[f_419_2]) ).
cnf(f_419_10,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1256,c_Groups_Ozero__class_Ozero(U_1256),c_Int_Onumber__class_Onumber__of(U_1256,U_1259))
| ~ c_Orderings_Oord__class_Oless__eq(U_1256,hAPP(c_Groups_Otimes__class_Otimes(U_1256,c_Int_Onumber__class_Onumber__of(U_1256,U_1259)),U_1258),U_1257)
| c_Orderings_Oord__class_Oless(U_1256,c_Groups_Ozero__class_Ozero(U_1256),U_1258)
| c_Orderings_Oord__class_Oless__eq(U_1256,c_Rings_Oinverse__class_Odivide(U_1256,U_1257,U_1258),c_Int_Onumber__class_Onumber__of(U_1256,U_1259))
| ~ class_Int_Onumber(U_1256)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1256) ),
inference(clausify,[status(thm)],[f_419_2]) ).
cnf(f_419_11,plain,
( ~ c_Orderings_Oord__class_Oless(U_1256,c_Groups_Ozero__class_Ozero(U_1256),U_1258)
| ~ c_Orderings_Oord__class_Oless__eq(U_1256,U_1257,hAPP(c_Groups_Otimes__class_Otimes(U_1256,c_Int_Onumber__class_Onumber__of(U_1256,U_1259)),U_1258))
| c_Orderings_Oord__class_Oless__eq(U_1256,c_Rings_Oinverse__class_Odivide(U_1256,U_1257,U_1258),c_Int_Onumber__class_Onumber__of(U_1256,U_1259))
| ~ class_Int_Onumber(U_1256)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1256) ),
inference(clausify,[status(thm)],[f_419_2]) ).
cnf(f_419_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_1256,U_1258,c_Groups_Ozero__class_Ozero(U_1256))
| c_Orderings_Oord__class_Oless(U_1256,U_1258,c_Groups_Ozero__class_Ozero(U_1256))
| ~ c_Orderings_Oord__class_Oless__eq(U_1256,U_1257,hAPP(c_Groups_Otimes__class_Otimes(U_1256,c_Int_Onumber__class_Onumber__of(U_1256,U_1259)),U_1258))
| c_Orderings_Oord__class_Oless__eq(U_1256,c_Rings_Oinverse__class_Odivide(U_1256,U_1257,U_1258),c_Int_Onumber__class_Onumber__of(U_1256,U_1259))
| ~ class_Int_Onumber(U_1256)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1256) ),
inference(clausify,[status(thm)],[f_419_2]) ).
cnf(f_419_13,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1256,c_Groups_Ozero__class_Ozero(U_1256),c_Int_Onumber__class_Onumber__of(U_1256,U_1259))
| c_Orderings_Oord__class_Oless(U_1256,U_1258,c_Groups_Ozero__class_Ozero(U_1256))
| ~ c_Orderings_Oord__class_Oless__eq(U_1256,U_1257,hAPP(c_Groups_Otimes__class_Otimes(U_1256,c_Int_Onumber__class_Onumber__of(U_1256,U_1259)),U_1258))
| c_Orderings_Oord__class_Oless__eq(U_1256,c_Rings_Oinverse__class_Odivide(U_1256,U_1257,U_1258),c_Int_Onumber__class_Onumber__of(U_1256,U_1259))
| ~ class_Int_Onumber(U_1256)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1256) ),
inference(clausify,[status(thm)],[f_419_2]) ).
cnf(f_419_14,plain,
( ~ c_Orderings_Oord__class_Oless(U_1256,U_1258,c_Groups_Ozero__class_Ozero(U_1256))
| ~ c_Orderings_Oord__class_Oless__eq(U_1256,hAPP(c_Groups_Otimes__class_Otimes(U_1256,c_Int_Onumber__class_Onumber__of(U_1256,U_1259)),U_1258),U_1257)
| ~ c_Orderings_Oord__class_Oless__eq(U_1256,U_1257,hAPP(c_Groups_Otimes__class_Otimes(U_1256,c_Int_Onumber__class_Onumber__of(U_1256,U_1259)),U_1258))
| c_Orderings_Oord__class_Oless__eq(U_1256,c_Rings_Oinverse__class_Odivide(U_1256,U_1257,U_1258),c_Int_Onumber__class_Onumber__of(U_1256,U_1259))
| ~ class_Int_Onumber(U_1256)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1256) ),
inference(clausify,[status(thm)],[f_419_2]) ).
cnf(f_419_15,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1256,c_Groups_Ozero__class_Ozero(U_1256),c_Int_Onumber__class_Onumber__of(U_1256,U_1259))
| ~ c_Orderings_Oord__class_Oless__eq(U_1256,hAPP(c_Groups_Otimes__class_Otimes(U_1256,c_Int_Onumber__class_Onumber__of(U_1256,U_1259)),U_1258),U_1257)
| ~ c_Orderings_Oord__class_Oless__eq(U_1256,U_1257,hAPP(c_Groups_Otimes__class_Otimes(U_1256,c_Int_Onumber__class_Onumber__of(U_1256,U_1259)),U_1258))
| c_Orderings_Oord__class_Oless__eq(U_1256,c_Rings_Oinverse__class_Odivide(U_1256,U_1257,U_1258),c_Int_Onumber__class_Onumber__of(U_1256,U_1259))
| ~ class_Int_Onumber(U_1256)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1256) ),
inference(clausify,[status(thm)],[f_419_2]) ).
fof(f_420_1,plain,
! [V_ca_2,V_b_2,V_wa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
| ( ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(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,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_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,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) )
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_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__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(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,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_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,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_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__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__divide__eq__number__of]) ).
fof(f_420_2,plain,
! [U_1263,U_1262,U_1261,U_1260] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261),c_Rings_Oinverse__class_Odivide(U_1260,U_1262,U_1263))
| ( ( ( ~ c_Orderings_Oord__class_Oless__eq(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261),c_Groups_Ozero__class_Ozero(U_1260))
& ~ c_Orderings_Oord__class_Oless(U_1260,U_1263,c_Groups_Ozero__class_Ozero(U_1260)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_1260,U_1262,hAPP(c_Groups_Otimes__class_Otimes(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261)),U_1263))
& c_Orderings_Oord__class_Oless(U_1260,U_1263,c_Groups_Ozero__class_Ozero(U_1260)) ) )
& ~ c_Orderings_Oord__class_Oless(U_1260,c_Groups_Ozero__class_Ozero(U_1260),U_1263) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_1260,hAPP(c_Groups_Otimes__class_Otimes(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261)),U_1263),U_1262)
& c_Orderings_Oord__class_Oless(U_1260,c_Groups_Ozero__class_Ozero(U_1260),U_1263) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless__eq(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261),c_Groups_Ozero__class_Ozero(U_1260))
| c_Orderings_Oord__class_Oless(U_1260,U_1263,c_Groups_Ozero__class_Ozero(U_1260)) )
& ( c_Orderings_Oord__class_Oless__eq(U_1260,U_1262,hAPP(c_Groups_Otimes__class_Otimes(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261)),U_1263))
| ~ c_Orderings_Oord__class_Oless(U_1260,U_1263,c_Groups_Ozero__class_Ozero(U_1260)) ) )
| c_Orderings_Oord__class_Oless(U_1260,c_Groups_Ozero__class_Ozero(U_1260),U_1263) )
& ( c_Orderings_Oord__class_Oless__eq(U_1260,hAPP(c_Groups_Otimes__class_Otimes(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261)),U_1263),U_1262)
| ~ c_Orderings_Oord__class_Oless(U_1260,c_Groups_Ozero__class_Ozero(U_1260),U_1263) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261),c_Rings_Oinverse__class_Odivide(U_1260,U_1262,U_1263)) ) )
| ~ class_Int_Onumber(U_1260)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1260) ),
inference(variable_rename,[status(thm)],[f_420_1]) ).
cnf(f_420_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1260,hAPP(c_Groups_Otimes__class_Otimes(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261)),U_1263),U_1262)
| ~ c_Orderings_Oord__class_Oless(U_1260,c_Groups_Ozero__class_Ozero(U_1260),U_1263)
| ~ c_Orderings_Oord__class_Oless__eq(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261),c_Rings_Oinverse__class_Odivide(U_1260,U_1262,U_1263))
| ~ class_Int_Onumber(U_1260)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1260) ),
inference(clausify,[status(thm)],[f_420_2]) ).
cnf(f_420_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1260,U_1262,hAPP(c_Groups_Otimes__class_Otimes(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261)),U_1263))
| ~ c_Orderings_Oord__class_Oless(U_1260,U_1263,c_Groups_Ozero__class_Ozero(U_1260))
| c_Orderings_Oord__class_Oless(U_1260,c_Groups_Ozero__class_Ozero(U_1260),U_1263)
| ~ c_Orderings_Oord__class_Oless__eq(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261),c_Rings_Oinverse__class_Odivide(U_1260,U_1262,U_1263))
| ~ class_Int_Onumber(U_1260)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1260) ),
inference(clausify,[status(thm)],[f_420_2]) ).
cnf(f_420_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261),c_Groups_Ozero__class_Ozero(U_1260))
| c_Orderings_Oord__class_Oless(U_1260,U_1263,c_Groups_Ozero__class_Ozero(U_1260))
| c_Orderings_Oord__class_Oless(U_1260,c_Groups_Ozero__class_Ozero(U_1260),U_1263)
| ~ c_Orderings_Oord__class_Oless__eq(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261),c_Rings_Oinverse__class_Odivide(U_1260,U_1262,U_1263))
| ~ class_Int_Onumber(U_1260)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1260) ),
inference(clausify,[status(thm)],[f_420_2]) ).
cnf(f_420_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_1260,c_Groups_Ozero__class_Ozero(U_1260),U_1263)
| c_Orderings_Oord__class_Oless(U_1260,c_Groups_Ozero__class_Ozero(U_1260),U_1263)
| c_Orderings_Oord__class_Oless__eq(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261),c_Rings_Oinverse__class_Odivide(U_1260,U_1262,U_1263))
| ~ class_Int_Onumber(U_1260)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1260) ),
inference(clausify,[status(thm)],[f_420_2]) ).
cnf(f_420_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_1260,U_1263,c_Groups_Ozero__class_Ozero(U_1260))
| c_Orderings_Oord__class_Oless(U_1260,U_1263,c_Groups_Ozero__class_Ozero(U_1260))
| c_Orderings_Oord__class_Oless(U_1260,c_Groups_Ozero__class_Ozero(U_1260),U_1263)
| c_Orderings_Oord__class_Oless__eq(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261),c_Rings_Oinverse__class_Odivide(U_1260,U_1262,U_1263))
| ~ class_Int_Onumber(U_1260)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1260) ),
inference(clausify,[status(thm)],[f_420_2]) ).
cnf(f_420_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261),c_Groups_Ozero__class_Ozero(U_1260))
| c_Orderings_Oord__class_Oless(U_1260,U_1263,c_Groups_Ozero__class_Ozero(U_1260))
| c_Orderings_Oord__class_Oless(U_1260,c_Groups_Ozero__class_Ozero(U_1260),U_1263)
| c_Orderings_Oord__class_Oless__eq(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261),c_Rings_Oinverse__class_Odivide(U_1260,U_1262,U_1263))
| ~ class_Int_Onumber(U_1260)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1260) ),
inference(clausify,[status(thm)],[f_420_2]) ).
cnf(f_420_9,plain,
( ~ c_Orderings_Oord__class_Oless(U_1260,U_1263,c_Groups_Ozero__class_Ozero(U_1260))
| ~ c_Orderings_Oord__class_Oless__eq(U_1260,U_1262,hAPP(c_Groups_Otimes__class_Otimes(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261)),U_1263))
| c_Orderings_Oord__class_Oless(U_1260,c_Groups_Ozero__class_Ozero(U_1260),U_1263)
| c_Orderings_Oord__class_Oless__eq(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261),c_Rings_Oinverse__class_Odivide(U_1260,U_1262,U_1263))
| ~ class_Int_Onumber(U_1260)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1260) ),
inference(clausify,[status(thm)],[f_420_2]) ).
cnf(f_420_10,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261),c_Groups_Ozero__class_Ozero(U_1260))
| ~ c_Orderings_Oord__class_Oless__eq(U_1260,U_1262,hAPP(c_Groups_Otimes__class_Otimes(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261)),U_1263))
| c_Orderings_Oord__class_Oless(U_1260,c_Groups_Ozero__class_Ozero(U_1260),U_1263)
| c_Orderings_Oord__class_Oless__eq(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261),c_Rings_Oinverse__class_Odivide(U_1260,U_1262,U_1263))
| ~ class_Int_Onumber(U_1260)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1260) ),
inference(clausify,[status(thm)],[f_420_2]) ).
cnf(f_420_11,plain,
( ~ c_Orderings_Oord__class_Oless(U_1260,c_Groups_Ozero__class_Ozero(U_1260),U_1263)
| ~ c_Orderings_Oord__class_Oless__eq(U_1260,hAPP(c_Groups_Otimes__class_Otimes(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261)),U_1263),U_1262)
| c_Orderings_Oord__class_Oless__eq(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261),c_Rings_Oinverse__class_Odivide(U_1260,U_1262,U_1263))
| ~ class_Int_Onumber(U_1260)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1260) ),
inference(clausify,[status(thm)],[f_420_2]) ).
cnf(f_420_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_1260,U_1263,c_Groups_Ozero__class_Ozero(U_1260))
| c_Orderings_Oord__class_Oless(U_1260,U_1263,c_Groups_Ozero__class_Ozero(U_1260))
| ~ c_Orderings_Oord__class_Oless__eq(U_1260,hAPP(c_Groups_Otimes__class_Otimes(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261)),U_1263),U_1262)
| c_Orderings_Oord__class_Oless__eq(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261),c_Rings_Oinverse__class_Odivide(U_1260,U_1262,U_1263))
| ~ class_Int_Onumber(U_1260)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1260) ),
inference(clausify,[status(thm)],[f_420_2]) ).
cnf(f_420_13,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261),c_Groups_Ozero__class_Ozero(U_1260))
| c_Orderings_Oord__class_Oless(U_1260,U_1263,c_Groups_Ozero__class_Ozero(U_1260))
| ~ c_Orderings_Oord__class_Oless__eq(U_1260,hAPP(c_Groups_Otimes__class_Otimes(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261)),U_1263),U_1262)
| c_Orderings_Oord__class_Oless__eq(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261),c_Rings_Oinverse__class_Odivide(U_1260,U_1262,U_1263))
| ~ class_Int_Onumber(U_1260)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1260) ),
inference(clausify,[status(thm)],[f_420_2]) ).
cnf(f_420_14,plain,
( ~ c_Orderings_Oord__class_Oless(U_1260,U_1263,c_Groups_Ozero__class_Ozero(U_1260))
| ~ c_Orderings_Oord__class_Oless__eq(U_1260,U_1262,hAPP(c_Groups_Otimes__class_Otimes(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261)),U_1263))
| ~ c_Orderings_Oord__class_Oless__eq(U_1260,hAPP(c_Groups_Otimes__class_Otimes(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261)),U_1263),U_1262)
| c_Orderings_Oord__class_Oless__eq(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261),c_Rings_Oinverse__class_Odivide(U_1260,U_1262,U_1263))
| ~ class_Int_Onumber(U_1260)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1260) ),
inference(clausify,[status(thm)],[f_420_2]) ).
cnf(f_420_15,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261),c_Groups_Ozero__class_Ozero(U_1260))
| ~ c_Orderings_Oord__class_Oless__eq(U_1260,U_1262,hAPP(c_Groups_Otimes__class_Otimes(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261)),U_1263))
| ~ c_Orderings_Oord__class_Oless__eq(U_1260,hAPP(c_Groups_Otimes__class_Otimes(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261)),U_1263),U_1262)
| c_Orderings_Oord__class_Oless__eq(U_1260,c_Int_Onumber__class_Onumber__of(U_1260,U_1261),c_Rings_Oinverse__class_Odivide(U_1260,U_1262,U_1263))
| ~ class_Int_Onumber(U_1260)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1260) ),
inference(clausify,[status(thm)],[f_420_2]) ).
fof(f_421_1,plain,
! [V_wa_2,V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))
| ( ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
& ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))
& c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
& ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))) ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__divide__eq__number__of1]) ).
fof(f_421_2,plain,
! [U_1267,U_1266,U_1265,U_1264] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1264,U_1265,c_Rings_Oinverse__class_Odivide(U_1264,U_1266,c_Int_Onumber__class_Onumber__of(U_1264,U_1267)))
| ( ( ( ~ c_Orderings_Oord__class_Oless__eq(U_1264,U_1265,c_Groups_Ozero__class_Ozero(U_1264))
& ~ c_Orderings_Oord__class_Oless(U_1264,c_Int_Onumber__class_Onumber__of(U_1264,U_1267),c_Groups_Ozero__class_Ozero(U_1264)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_1264,U_1266,hAPP(c_Groups_Otimes__class_Otimes(U_1264,U_1265),c_Int_Onumber__class_Onumber__of(U_1264,U_1267)))
& c_Orderings_Oord__class_Oless(U_1264,c_Int_Onumber__class_Onumber__of(U_1264,U_1267),c_Groups_Ozero__class_Ozero(U_1264)) ) )
& ~ c_Orderings_Oord__class_Oless(U_1264,c_Groups_Ozero__class_Ozero(U_1264),c_Int_Onumber__class_Onumber__of(U_1264,U_1267)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_1264,hAPP(c_Groups_Otimes__class_Otimes(U_1264,U_1265),c_Int_Onumber__class_Onumber__of(U_1264,U_1267)),U_1266)
& c_Orderings_Oord__class_Oless(U_1264,c_Groups_Ozero__class_Ozero(U_1264),c_Int_Onumber__class_Onumber__of(U_1264,U_1267)) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless__eq(U_1264,U_1265,c_Groups_Ozero__class_Ozero(U_1264))
| c_Orderings_Oord__class_Oless(U_1264,c_Int_Onumber__class_Onumber__of(U_1264,U_1267),c_Groups_Ozero__class_Ozero(U_1264)) )
& ( c_Orderings_Oord__class_Oless__eq(U_1264,U_1266,hAPP(c_Groups_Otimes__class_Otimes(U_1264,U_1265),c_Int_Onumber__class_Onumber__of(U_1264,U_1267)))
| ~ c_Orderings_Oord__class_Oless(U_1264,c_Int_Onumber__class_Onumber__of(U_1264,U_1267),c_Groups_Ozero__class_Ozero(U_1264)) ) )
| c_Orderings_Oord__class_Oless(U_1264,c_Groups_Ozero__class_Ozero(U_1264),c_Int_Onumber__class_Onumber__of(U_1264,U_1267)) )
& ( c_Orderings_Oord__class_Oless__eq(U_1264,hAPP(c_Groups_Otimes__class_Otimes(U_1264,U_1265),c_Int_Onumber__class_Onumber__of(U_1264,U_1267)),U_1266)
| ~ c_Orderings_Oord__class_Oless(U_1264,c_Groups_Ozero__class_Ozero(U_1264),c_Int_Onumber__class_Onumber__of(U_1264,U_1267)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_1264,U_1265,c_Rings_Oinverse__class_Odivide(U_1264,U_1266,c_Int_Onumber__class_Onumber__of(U_1264,U_1267))) ) )
| ~ class_Int_Onumber(U_1264)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1264) ),
inference(variable_rename,[status(thm)],[f_421_1]) ).
cnf(f_421_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1264,hAPP(c_Groups_Otimes__class_Otimes(U_1264,U_1265),c_Int_Onumber__class_Onumber__of(U_1264,U_1267)),U_1266)
| ~ c_Orderings_Oord__class_Oless(U_1264,c_Groups_Ozero__class_Ozero(U_1264),c_Int_Onumber__class_Onumber__of(U_1264,U_1267))
| ~ c_Orderings_Oord__class_Oless__eq(U_1264,U_1265,c_Rings_Oinverse__class_Odivide(U_1264,U_1266,c_Int_Onumber__class_Onumber__of(U_1264,U_1267)))
| ~ class_Int_Onumber(U_1264)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1264) ),
inference(clausify,[status(thm)],[f_421_2]) ).
cnf(f_421_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1264,U_1266,hAPP(c_Groups_Otimes__class_Otimes(U_1264,U_1265),c_Int_Onumber__class_Onumber__of(U_1264,U_1267)))
| ~ c_Orderings_Oord__class_Oless(U_1264,c_Int_Onumber__class_Onumber__of(U_1264,U_1267),c_Groups_Ozero__class_Ozero(U_1264))
| c_Orderings_Oord__class_Oless(U_1264,c_Groups_Ozero__class_Ozero(U_1264),c_Int_Onumber__class_Onumber__of(U_1264,U_1267))
| ~ c_Orderings_Oord__class_Oless__eq(U_1264,U_1265,c_Rings_Oinverse__class_Odivide(U_1264,U_1266,c_Int_Onumber__class_Onumber__of(U_1264,U_1267)))
| ~ class_Int_Onumber(U_1264)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1264) ),
inference(clausify,[status(thm)],[f_421_2]) ).
cnf(f_421_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1264,U_1265,c_Groups_Ozero__class_Ozero(U_1264))
| c_Orderings_Oord__class_Oless(U_1264,c_Int_Onumber__class_Onumber__of(U_1264,U_1267),c_Groups_Ozero__class_Ozero(U_1264))
| c_Orderings_Oord__class_Oless(U_1264,c_Groups_Ozero__class_Ozero(U_1264),c_Int_Onumber__class_Onumber__of(U_1264,U_1267))
| ~ c_Orderings_Oord__class_Oless__eq(U_1264,U_1265,c_Rings_Oinverse__class_Odivide(U_1264,U_1266,c_Int_Onumber__class_Onumber__of(U_1264,U_1267)))
| ~ class_Int_Onumber(U_1264)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1264) ),
inference(clausify,[status(thm)],[f_421_2]) ).
cnf(f_421_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_1264,c_Groups_Ozero__class_Ozero(U_1264),c_Int_Onumber__class_Onumber__of(U_1264,U_1267))
| c_Orderings_Oord__class_Oless(U_1264,c_Groups_Ozero__class_Ozero(U_1264),c_Int_Onumber__class_Onumber__of(U_1264,U_1267))
| c_Orderings_Oord__class_Oless__eq(U_1264,U_1265,c_Rings_Oinverse__class_Odivide(U_1264,U_1266,c_Int_Onumber__class_Onumber__of(U_1264,U_1267)))
| ~ class_Int_Onumber(U_1264)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1264) ),
inference(clausify,[status(thm)],[f_421_2]) ).
cnf(f_421_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_1264,c_Int_Onumber__class_Onumber__of(U_1264,U_1267),c_Groups_Ozero__class_Ozero(U_1264))
| c_Orderings_Oord__class_Oless(U_1264,c_Int_Onumber__class_Onumber__of(U_1264,U_1267),c_Groups_Ozero__class_Ozero(U_1264))
| c_Orderings_Oord__class_Oless(U_1264,c_Groups_Ozero__class_Ozero(U_1264),c_Int_Onumber__class_Onumber__of(U_1264,U_1267))
| c_Orderings_Oord__class_Oless__eq(U_1264,U_1265,c_Rings_Oinverse__class_Odivide(U_1264,U_1266,c_Int_Onumber__class_Onumber__of(U_1264,U_1267)))
| ~ class_Int_Onumber(U_1264)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1264) ),
inference(clausify,[status(thm)],[f_421_2]) ).
cnf(f_421_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1264,U_1265,c_Groups_Ozero__class_Ozero(U_1264))
| c_Orderings_Oord__class_Oless(U_1264,c_Int_Onumber__class_Onumber__of(U_1264,U_1267),c_Groups_Ozero__class_Ozero(U_1264))
| c_Orderings_Oord__class_Oless(U_1264,c_Groups_Ozero__class_Ozero(U_1264),c_Int_Onumber__class_Onumber__of(U_1264,U_1267))
| c_Orderings_Oord__class_Oless__eq(U_1264,U_1265,c_Rings_Oinverse__class_Odivide(U_1264,U_1266,c_Int_Onumber__class_Onumber__of(U_1264,U_1267)))
| ~ class_Int_Onumber(U_1264)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1264) ),
inference(clausify,[status(thm)],[f_421_2]) ).
cnf(f_421_9,plain,
( ~ c_Orderings_Oord__class_Oless(U_1264,c_Int_Onumber__class_Onumber__of(U_1264,U_1267),c_Groups_Ozero__class_Ozero(U_1264))
| ~ c_Orderings_Oord__class_Oless__eq(U_1264,U_1266,hAPP(c_Groups_Otimes__class_Otimes(U_1264,U_1265),c_Int_Onumber__class_Onumber__of(U_1264,U_1267)))
| c_Orderings_Oord__class_Oless(U_1264,c_Groups_Ozero__class_Ozero(U_1264),c_Int_Onumber__class_Onumber__of(U_1264,U_1267))
| c_Orderings_Oord__class_Oless__eq(U_1264,U_1265,c_Rings_Oinverse__class_Odivide(U_1264,U_1266,c_Int_Onumber__class_Onumber__of(U_1264,U_1267)))
| ~ class_Int_Onumber(U_1264)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1264) ),
inference(clausify,[status(thm)],[f_421_2]) ).
cnf(f_421_10,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1264,U_1265,c_Groups_Ozero__class_Ozero(U_1264))
| ~ c_Orderings_Oord__class_Oless__eq(U_1264,U_1266,hAPP(c_Groups_Otimes__class_Otimes(U_1264,U_1265),c_Int_Onumber__class_Onumber__of(U_1264,U_1267)))
| c_Orderings_Oord__class_Oless(U_1264,c_Groups_Ozero__class_Ozero(U_1264),c_Int_Onumber__class_Onumber__of(U_1264,U_1267))
| c_Orderings_Oord__class_Oless__eq(U_1264,U_1265,c_Rings_Oinverse__class_Odivide(U_1264,U_1266,c_Int_Onumber__class_Onumber__of(U_1264,U_1267)))
| ~ class_Int_Onumber(U_1264)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1264) ),
inference(clausify,[status(thm)],[f_421_2]) ).
cnf(f_421_11,plain,
( ~ c_Orderings_Oord__class_Oless(U_1264,c_Groups_Ozero__class_Ozero(U_1264),c_Int_Onumber__class_Onumber__of(U_1264,U_1267))
| ~ c_Orderings_Oord__class_Oless__eq(U_1264,hAPP(c_Groups_Otimes__class_Otimes(U_1264,U_1265),c_Int_Onumber__class_Onumber__of(U_1264,U_1267)),U_1266)
| c_Orderings_Oord__class_Oless__eq(U_1264,U_1265,c_Rings_Oinverse__class_Odivide(U_1264,U_1266,c_Int_Onumber__class_Onumber__of(U_1264,U_1267)))
| ~ class_Int_Onumber(U_1264)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1264) ),
inference(clausify,[status(thm)],[f_421_2]) ).
cnf(f_421_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_1264,c_Int_Onumber__class_Onumber__of(U_1264,U_1267),c_Groups_Ozero__class_Ozero(U_1264))
| c_Orderings_Oord__class_Oless(U_1264,c_Int_Onumber__class_Onumber__of(U_1264,U_1267),c_Groups_Ozero__class_Ozero(U_1264))
| ~ c_Orderings_Oord__class_Oless__eq(U_1264,hAPP(c_Groups_Otimes__class_Otimes(U_1264,U_1265),c_Int_Onumber__class_Onumber__of(U_1264,U_1267)),U_1266)
| c_Orderings_Oord__class_Oless__eq(U_1264,U_1265,c_Rings_Oinverse__class_Odivide(U_1264,U_1266,c_Int_Onumber__class_Onumber__of(U_1264,U_1267)))
| ~ class_Int_Onumber(U_1264)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1264) ),
inference(clausify,[status(thm)],[f_421_2]) ).
cnf(f_421_13,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1264,U_1265,c_Groups_Ozero__class_Ozero(U_1264))
| c_Orderings_Oord__class_Oless(U_1264,c_Int_Onumber__class_Onumber__of(U_1264,U_1267),c_Groups_Ozero__class_Ozero(U_1264))
| ~ c_Orderings_Oord__class_Oless__eq(U_1264,hAPP(c_Groups_Otimes__class_Otimes(U_1264,U_1265),c_Int_Onumber__class_Onumber__of(U_1264,U_1267)),U_1266)
| c_Orderings_Oord__class_Oless__eq(U_1264,U_1265,c_Rings_Oinverse__class_Odivide(U_1264,U_1266,c_Int_Onumber__class_Onumber__of(U_1264,U_1267)))
| ~ class_Int_Onumber(U_1264)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1264) ),
inference(clausify,[status(thm)],[f_421_2]) ).
cnf(f_421_14,plain,
( ~ c_Orderings_Oord__class_Oless(U_1264,c_Int_Onumber__class_Onumber__of(U_1264,U_1267),c_Groups_Ozero__class_Ozero(U_1264))
| ~ c_Orderings_Oord__class_Oless__eq(U_1264,U_1266,hAPP(c_Groups_Otimes__class_Otimes(U_1264,U_1265),c_Int_Onumber__class_Onumber__of(U_1264,U_1267)))
| ~ c_Orderings_Oord__class_Oless__eq(U_1264,hAPP(c_Groups_Otimes__class_Otimes(U_1264,U_1265),c_Int_Onumber__class_Onumber__of(U_1264,U_1267)),U_1266)
| c_Orderings_Oord__class_Oless__eq(U_1264,U_1265,c_Rings_Oinverse__class_Odivide(U_1264,U_1266,c_Int_Onumber__class_Onumber__of(U_1264,U_1267)))
| ~ class_Int_Onumber(U_1264)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1264) ),
inference(clausify,[status(thm)],[f_421_2]) ).
cnf(f_421_15,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1264,U_1265,c_Groups_Ozero__class_Ozero(U_1264))
| ~ c_Orderings_Oord__class_Oless__eq(U_1264,U_1266,hAPP(c_Groups_Otimes__class_Otimes(U_1264,U_1265),c_Int_Onumber__class_Onumber__of(U_1264,U_1267)))
| ~ c_Orderings_Oord__class_Oless__eq(U_1264,hAPP(c_Groups_Otimes__class_Otimes(U_1264,U_1265),c_Int_Onumber__class_Onumber__of(U_1264,U_1267)),U_1266)
| c_Orderings_Oord__class_Oless__eq(U_1264,U_1265,c_Rings_Oinverse__class_Odivide(U_1264,U_1266,c_Int_Onumber__class_Onumber__of(U_1264,U_1267)))
| ~ class_Int_Onumber(U_1264)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1264) ),
inference(clausify,[status(thm)],[f_421_2]) ).
fof(f_422_1,plain,
! [V_x_2] :
( c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,V_x_2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_DERIV__ln__divide]) ).
fof(f_422_2,plain,
! [U_1268] :
( c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,U_1268,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1268))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1268) ),
inference(variable_rename,[status(thm)],[f_422_1]) ).
cnf(f_422_3,plain,
( c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,U_1268,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1268))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1268) ),
inference(clausify,[status(thm)],[f_422_2]) ).
fof(f_423_1,plain,
! [V_z,V_w,V_v,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w),V_z)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),V_z)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__number__of__left]) ).
fof(f_423_2,plain,
! [U_1272,U_1271,U_1270,U_1269] :
( c_Groups_Oplus__class_Oplus(U_1269,c_Int_Onumber__class_Onumber__of(U_1269,U_1270),c_Groups_Oplus__class_Oplus(U_1269,c_Int_Onumber__class_Onumber__of(U_1269,U_1271),U_1272)) = c_Groups_Oplus__class_Oplus(U_1269,c_Int_Onumber__class_Onumber__of(U_1269,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1270,U_1271)),U_1272)
| ~ class_Int_Onumber__ring(U_1269) ),
inference(variable_rename,[status(thm)],[f_423_1]) ).
cnf(f_423_3,plain,
( c_Groups_Oplus__class_Oplus(U_1269,c_Int_Onumber__class_Onumber__of(U_1269,U_1270),c_Groups_Oplus__class_Oplus(U_1269,c_Int_Onumber__class_Onumber__of(U_1269,U_1271),U_1272)) = c_Groups_Oplus__class_Oplus(U_1269,c_Int_Onumber__class_Onumber__of(U_1269,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1270,U_1271)),U_1272)
| ~ class_Int_Onumber__ring(U_1269) ),
inference(clausify,[status(thm)],[f_423_2]) ).
fof(f_424_1,plain,
! [V_w,V_v,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__number__of__eq]) ).
fof(f_424_2,plain,
! [U_1275,U_1274,U_1273] :
( c_Groups_Oplus__class_Oplus(U_1273,c_Int_Onumber__class_Onumber__of(U_1273,U_1274),c_Int_Onumber__class_Onumber__of(U_1273,U_1275)) = c_Int_Onumber__class_Onumber__of(U_1273,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1274,U_1275))
| ~ class_Int_Onumber__ring(U_1273) ),
inference(variable_rename,[status(thm)],[f_424_1]) ).
cnf(f_424_3,plain,
( c_Groups_Oplus__class_Oplus(U_1273,c_Int_Onumber__class_Onumber__of(U_1273,U_1274),c_Int_Onumber__class_Onumber__of(U_1273,U_1275)) = c_Int_Onumber__class_Onumber__of(U_1273,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1274,U_1275))
| ~ class_Int_Onumber__ring(U_1273) ),
inference(clausify,[status(thm)],[f_424_2]) ).
fof(f_425_1,plain,
! [V_w,V_v,T_a] :
( c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Int_Onumber__class_Onumber__of(T_a,V_w))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__add]) ).
fof(f_425_2,plain,
! [U_1278,U_1277,U_1276] :
( c_Int_Onumber__class_Onumber__of(U_1276,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1277,U_1278)) = c_Groups_Oplus__class_Oplus(U_1276,c_Int_Onumber__class_Onumber__of(U_1276,U_1277),c_Int_Onumber__class_Onumber__of(U_1276,U_1278))
| ~ class_Int_Onumber__ring(U_1276) ),
inference(variable_rename,[status(thm)],[f_425_1]) ).
cnf(f_425_3,plain,
( c_Int_Onumber__class_Onumber__of(U_1276,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1277,U_1278)) = c_Groups_Oplus__class_Oplus(U_1276,c_Int_Onumber__class_Onumber__of(U_1276,U_1277),c_Int_Onumber__class_Onumber__of(U_1276,U_1278))
| ~ class_Int_Onumber__ring(U_1276) ),
inference(clausify,[status(thm)],[f_425_2]) ).
fof(f_426_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__number__of]) ).
fof(f_426_2,plain,
! [U_1281,U_1280,U_1279] :
( ( ( c_Orderings_Oord__class_Oless(U_1279,c_Int_Onumber__class_Onumber__of(U_1279,U_1280),c_Int_Onumber__class_Onumber__of(U_1279,U_1281))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1280,U_1281) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1280,U_1281)
| ~ c_Orderings_Oord__class_Oless(U_1279,c_Int_Onumber__class_Onumber__of(U_1279,U_1280),c_Int_Onumber__class_Onumber__of(U_1279,U_1281)) ) )
| ~ class_Rings_Olinordered__idom(U_1279)
| ~ class_Int_Onumber__ring(U_1279) ),
inference(variable_rename,[status(thm)],[f_426_1]) ).
cnf(f_426_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1280,U_1281)
| ~ c_Orderings_Oord__class_Oless(U_1279,c_Int_Onumber__class_Onumber__of(U_1279,U_1280),c_Int_Onumber__class_Onumber__of(U_1279,U_1281))
| ~ class_Rings_Olinordered__idom(U_1279)
| ~ class_Int_Onumber__ring(U_1279) ),
inference(clausify,[status(thm)],[f_426_2]) ).
cnf(f_426_4,plain,
( c_Orderings_Oord__class_Oless(U_1279,c_Int_Onumber__class_Onumber__of(U_1279,U_1280),c_Int_Onumber__class_Onumber__of(U_1279,U_1281))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1280,U_1281)
| ~ class_Rings_Olinordered__idom(U_1279)
| ~ class_Int_Onumber__ring(U_1279) ),
inference(clausify,[status(thm)],[f_426_2]) ).
fof(f_427_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| c_Int_Onumber__class_Onumber__of(T_a,V_x_2) != c_Int_Onumber__class_Onumber__of(T_a,V_y_2) ) )
| ~ class_Int_Oring__char__0(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__number__of]) ).
fof(f_427_2,plain,
! [U_1284,U_1283,U_1282] :
( ( ( c_Int_Onumber__class_Onumber__of(U_1282,U_1283) = c_Int_Onumber__class_Onumber__of(U_1282,U_1284)
| U_1283 != U_1284 )
& ( U_1283 = U_1284
| c_Int_Onumber__class_Onumber__of(U_1282,U_1283) != c_Int_Onumber__class_Onumber__of(U_1282,U_1284) ) )
| ~ class_Int_Oring__char__0(U_1282)
| ~ class_Int_Onumber__ring(U_1282) ),
inference(variable_rename,[status(thm)],[f_427_1]) ).
cnf(f_427_3,plain,
( U_1283 = U_1284
| c_Int_Onumber__class_Onumber__of(U_1282,U_1283) != c_Int_Onumber__class_Onumber__of(U_1282,U_1284)
| ~ class_Int_Oring__char__0(U_1282)
| ~ class_Int_Onumber__ring(U_1282) ),
inference(clausify,[status(thm)],[f_427_2]) ).
cnf(f_427_4,plain,
( c_Int_Onumber__class_Onumber__of(U_1282,U_1283) = c_Int_Onumber__class_Onumber__of(U_1282,U_1284)
| U_1283 != U_1284
| ~ class_Int_Oring__char__0(U_1282)
| ~ class_Int_Onumber__ring(U_1282) ),
inference(clausify,[status(thm)],[f_427_2]) ).
fof(f_428_1,plain,
! [V_x_2,V_wa_2,T_a] :
( ( ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = V_x_2
| V_x_2 != c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) )
& ( V_x_2 = c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)
| c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) != V_x_2 ) )
| ~ class_Int_Onumber(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__reorient]) ).
fof(f_428_2,plain,
! [U_1287,U_1286,U_1285] :
( ( ( c_Int_Onumber__class_Onumber__of(U_1285,U_1286) = U_1287
| U_1287 != c_Int_Onumber__class_Onumber__of(U_1285,U_1286) )
& ( U_1287 = c_Int_Onumber__class_Onumber__of(U_1285,U_1286)
| c_Int_Onumber__class_Onumber__of(U_1285,U_1286) != U_1287 ) )
| ~ class_Int_Onumber(U_1285) ),
inference(variable_rename,[status(thm)],[f_428_1]) ).
cnf(f_428_3,plain,
( U_1287 = c_Int_Onumber__class_Onumber__of(U_1285,U_1286)
| c_Int_Onumber__class_Onumber__of(U_1285,U_1286) != U_1287
| ~ class_Int_Onumber(U_1285) ),
inference(clausify,[status(thm)],[f_428_2]) ).
cnf(f_428_4,plain,
( c_Int_Onumber__class_Onumber__of(U_1285,U_1286) = U_1287
| U_1287 != c_Int_Onumber__class_Onumber__of(U_1285,U_1286)
| ~ class_Int_Onumber(U_1285) ),
inference(clausify,[status(thm)],[f_428_2]) ).
fof(f_429_1,plain,
! [V_z,V_w,V_v,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v)),hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)),V_z)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_w))),V_z)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__number__of__left]) ).
fof(f_429_2,plain,
! [U_1291,U_1290,U_1289,U_1288] :
( hAPP(c_Groups_Otimes__class_Otimes(U_1288,c_Int_Onumber__class_Onumber__of(U_1288,U_1289)),hAPP(c_Groups_Otimes__class_Otimes(U_1288,c_Int_Onumber__class_Onumber__of(U_1288,U_1290)),U_1291)) = hAPP(c_Groups_Otimes__class_Otimes(U_1288,c_Int_Onumber__class_Onumber__of(U_1288,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1289),U_1290))),U_1291)
| ~ class_Int_Onumber__ring(U_1288) ),
inference(variable_rename,[status(thm)],[f_429_1]) ).
cnf(f_429_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_1288,c_Int_Onumber__class_Onumber__of(U_1288,U_1289)),hAPP(c_Groups_Otimes__class_Otimes(U_1288,c_Int_Onumber__class_Onumber__of(U_1288,U_1290)),U_1291)) = hAPP(c_Groups_Otimes__class_Otimes(U_1288,c_Int_Onumber__class_Onumber__of(U_1288,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1289),U_1290))),U_1291)
| ~ class_Int_Onumber__ring(U_1288) ),
inference(clausify,[status(thm)],[f_429_2]) ).
fof(f_430_1,plain,
! [V_w,V_v,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v)),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_w))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_arith__simps_I32_J]) ).
fof(f_430_2,plain,
! [U_1294,U_1293,U_1292] :
( hAPP(c_Groups_Otimes__class_Otimes(U_1292,c_Int_Onumber__class_Onumber__of(U_1292,U_1293)),c_Int_Onumber__class_Onumber__of(U_1292,U_1294)) = c_Int_Onumber__class_Onumber__of(U_1292,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1293),U_1294))
| ~ class_Int_Onumber__ring(U_1292) ),
inference(variable_rename,[status(thm)],[f_430_1]) ).
cnf(f_430_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_1292,c_Int_Onumber__class_Onumber__of(U_1292,U_1293)),c_Int_Onumber__class_Onumber__of(U_1292,U_1294)) = c_Int_Onumber__class_Onumber__of(U_1292,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1293),U_1294))
| ~ class_Int_Onumber__ring(U_1292) ),
inference(clausify,[status(thm)],[f_430_2]) ).
fof(f_431_1,plain,
! [V_w,V_v,T_a] :
( c_Int_Onumber__class_Onumber__of(T_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_w)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v)),c_Int_Onumber__class_Onumber__of(T_a,V_w))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__mult]) ).
fof(f_431_2,plain,
! [U_1297,U_1296,U_1295] :
( c_Int_Onumber__class_Onumber__of(U_1295,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1296),U_1297)) = hAPP(c_Groups_Otimes__class_Otimes(U_1295,c_Int_Onumber__class_Onumber__of(U_1295,U_1296)),c_Int_Onumber__class_Onumber__of(U_1295,U_1297))
| ~ class_Int_Onumber__ring(U_1295) ),
inference(variable_rename,[status(thm)],[f_431_1]) ).
cnf(f_431_3,plain,
( c_Int_Onumber__class_Onumber__of(U_1295,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1296),U_1297)) = hAPP(c_Groups_Otimes__class_Otimes(U_1295,c_Int_Onumber__class_Onumber__of(U_1295,U_1296)),c_Int_Onumber__class_Onumber__of(U_1295,U_1297))
| ~ class_Int_Onumber__ring(U_1295) ),
inference(clausify,[status(thm)],[f_431_2]) ).
fof(f_432_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__number__of]) ).
fof(f_432_2,plain,
! [U_1300,U_1299,U_1298] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1298,c_Int_Onumber__class_Onumber__of(U_1298,U_1299),c_Int_Onumber__class_Onumber__of(U_1298,U_1300))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1299,U_1300) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1299,U_1300)
| ~ c_Orderings_Oord__class_Oless__eq(U_1298,c_Int_Onumber__class_Onumber__of(U_1298,U_1299),c_Int_Onumber__class_Onumber__of(U_1298,U_1300)) ) )
| ~ class_Rings_Olinordered__idom(U_1298)
| ~ class_Int_Onumber__ring(U_1298) ),
inference(variable_rename,[status(thm)],[f_432_1]) ).
cnf(f_432_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1299,U_1300)
| ~ c_Orderings_Oord__class_Oless__eq(U_1298,c_Int_Onumber__class_Onumber__of(U_1298,U_1299),c_Int_Onumber__class_Onumber__of(U_1298,U_1300))
| ~ class_Rings_Olinordered__idom(U_1298)
| ~ class_Int_Onumber__ring(U_1298) ),
inference(clausify,[status(thm)],[f_432_2]) ).
cnf(f_432_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1298,c_Int_Onumber__class_Onumber__of(U_1298,U_1299),c_Int_Onumber__class_Onumber__of(U_1298,U_1300))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1299,U_1300)
| ~ class_Rings_Olinordered__idom(U_1298)
| ~ class_Int_Onumber__ring(U_1298) ),
inference(clausify,[status(thm)],[f_432_2]) ).
fof(f_433_1,plain,
! [V_wa_2,V_v_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
| c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2)) )
& ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) ) )
| ~ class_Orderings_Olinorder(T_a)
| ~ class_Int_Onumber(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__number__of__eq__not__less]) ).
fof(f_433_2,plain,
! [U_1303,U_1302,U_1301] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1301,c_Int_Onumber__class_Onumber__of(U_1301,U_1302),c_Int_Onumber__class_Onumber__of(U_1301,U_1303))
| c_Orderings_Oord__class_Oless(U_1301,c_Int_Onumber__class_Onumber__of(U_1301,U_1303),c_Int_Onumber__class_Onumber__of(U_1301,U_1302)) )
& ( ~ c_Orderings_Oord__class_Oless(U_1301,c_Int_Onumber__class_Onumber__of(U_1301,U_1303),c_Int_Onumber__class_Onumber__of(U_1301,U_1302))
| ~ c_Orderings_Oord__class_Oless__eq(U_1301,c_Int_Onumber__class_Onumber__of(U_1301,U_1302),c_Int_Onumber__class_Onumber__of(U_1301,U_1303)) ) )
| ~ class_Orderings_Olinorder(U_1301)
| ~ class_Int_Onumber(U_1301) ),
inference(variable_rename,[status(thm)],[f_433_1]) ).
cnf(f_433_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_1301,c_Int_Onumber__class_Onumber__of(U_1301,U_1303),c_Int_Onumber__class_Onumber__of(U_1301,U_1302))
| ~ c_Orderings_Oord__class_Oless__eq(U_1301,c_Int_Onumber__class_Onumber__of(U_1301,U_1302),c_Int_Onumber__class_Onumber__of(U_1301,U_1303))
| ~ class_Orderings_Olinorder(U_1301)
| ~ class_Int_Onumber(U_1301) ),
inference(clausify,[status(thm)],[f_433_2]) ).
cnf(f_433_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1301,c_Int_Onumber__class_Onumber__of(U_1301,U_1302),c_Int_Onumber__class_Onumber__of(U_1301,U_1303))
| c_Orderings_Oord__class_Oless(U_1301,c_Int_Onumber__class_Onumber__of(U_1301,U_1303),c_Int_Onumber__class_Onumber__of(U_1301,U_1302))
| ~ class_Orderings_Olinorder(U_1301)
| ~ class_Int_Onumber(U_1301) ),
inference(clausify,[status(thm)],[f_433_2]) ).
fof(f_434_1,plain,
! [V_v,V_b,V_a,T_b] :
( hAPP(c_Groups_Otimes__class_Otimes(T_b,c_Groups_Oplus__class_Oplus(T_b,V_a,V_b)),c_Int_Onumber__class_Onumber__of(T_b,V_v)) = c_Groups_Oplus__class_Oplus(T_b,hAPP(c_Groups_Otimes__class_Otimes(T_b,V_a),c_Int_Onumber__class_Onumber__of(T_b,V_v)),hAPP(c_Groups_Otimes__class_Otimes(T_b,V_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)))
| ~ class_Rings_Osemiring(T_b)
| ~ class_Int_Onumber(T_b) ),
inference(fof_nnf,[status(thm)],[fact_left__distrib__number__of]) ).
fof(f_434_2,plain,
! [U_1307,U_1306,U_1305,U_1304] :
( hAPP(c_Groups_Otimes__class_Otimes(U_1304,c_Groups_Oplus__class_Oplus(U_1304,U_1305,U_1306)),c_Int_Onumber__class_Onumber__of(U_1304,U_1307)) = c_Groups_Oplus__class_Oplus(U_1304,hAPP(c_Groups_Otimes__class_Otimes(U_1304,U_1305),c_Int_Onumber__class_Onumber__of(U_1304,U_1307)),hAPP(c_Groups_Otimes__class_Otimes(U_1304,U_1306),c_Int_Onumber__class_Onumber__of(U_1304,U_1307)))
| ~ class_Rings_Osemiring(U_1304)
| ~ class_Int_Onumber(U_1304) ),
inference(variable_rename,[status(thm)],[f_434_1]) ).
cnf(f_434_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_1304,c_Groups_Oplus__class_Oplus(U_1304,U_1305,U_1306)),c_Int_Onumber__class_Onumber__of(U_1304,U_1307)) = c_Groups_Oplus__class_Oplus(U_1304,hAPP(c_Groups_Otimes__class_Otimes(U_1304,U_1305),c_Int_Onumber__class_Onumber__of(U_1304,U_1307)),hAPP(c_Groups_Otimes__class_Otimes(U_1304,U_1306),c_Int_Onumber__class_Onumber__of(U_1304,U_1307)))
| ~ class_Rings_Osemiring(U_1304)
| ~ class_Int_Onumber(U_1304) ),
inference(clausify,[status(thm)],[f_434_2]) ).
fof(f_435_1,plain,
! [V_c,V_b,V_v,T_b] :
( hAPP(c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v)),c_Groups_Oplus__class_Oplus(T_b,V_b,V_c)) = c_Groups_Oplus__class_Oplus(T_b,hAPP(c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_b),hAPP(c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_c))
| ~ class_Rings_Osemiring(T_b)
| ~ class_Int_Onumber(T_b) ),
inference(fof_nnf,[status(thm)],[fact_right__distrib__number__of]) ).
fof(f_435_2,plain,
! [U_1311,U_1310,U_1309,U_1308] :
( hAPP(c_Groups_Otimes__class_Otimes(U_1308,c_Int_Onumber__class_Onumber__of(U_1308,U_1309)),c_Groups_Oplus__class_Oplus(U_1308,U_1310,U_1311)) = c_Groups_Oplus__class_Oplus(U_1308,hAPP(c_Groups_Otimes__class_Otimes(U_1308,c_Int_Onumber__class_Onumber__of(U_1308,U_1309)),U_1310),hAPP(c_Groups_Otimes__class_Otimes(U_1308,c_Int_Onumber__class_Onumber__of(U_1308,U_1309)),U_1311))
| ~ class_Rings_Osemiring(U_1308)
| ~ class_Int_Onumber(U_1308) ),
inference(variable_rename,[status(thm)],[f_435_1]) ).
cnf(f_435_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_1308,c_Int_Onumber__class_Onumber__of(U_1308,U_1309)),c_Groups_Oplus__class_Oplus(U_1308,U_1310,U_1311)) = c_Groups_Oplus__class_Oplus(U_1308,hAPP(c_Groups_Otimes__class_Otimes(U_1308,c_Int_Onumber__class_Onumber__of(U_1308,U_1309)),U_1310),hAPP(c_Groups_Otimes__class_Otimes(U_1308,c_Int_Onumber__class_Onumber__of(U_1308,U_1309)),U_1311))
| ~ class_Rings_Osemiring(U_1308)
| ~ class_Int_Onumber(U_1308) ),
inference(clausify,[status(thm)],[f_435_2]) ).
fof(f_436_1,plain,
! [V_wa_2,V_b_2,V_a_2,T_a] :
( ( ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
| ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)
& c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Groups_Ozero__class_Ozero(T_a) )
| ( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) != V_b_2
& c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
& ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) != c_Groups_Ozero__class_Ozero(T_a) )
& ( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) = V_b_2
| c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Groups_Ozero__class_Ozero(T_a) ) )
| V_a_2 != c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of1]) ).
fof(f_436_2,plain,
! [U_1315,U_1314,U_1313,U_1312] :
( ( ( U_1313 = c_Rings_Oinverse__class_Odivide(U_1312,U_1314,c_Int_Onumber__class_Onumber__of(U_1312,U_1315))
| ( U_1313 != c_Groups_Ozero__class_Ozero(U_1312)
& c_Int_Onumber__class_Onumber__of(U_1312,U_1315) = c_Groups_Ozero__class_Ozero(U_1312) )
| ( hAPP(c_Groups_Otimes__class_Otimes(U_1312,U_1313),c_Int_Onumber__class_Onumber__of(U_1312,U_1315)) != U_1314
& c_Int_Onumber__class_Onumber__of(U_1312,U_1315) != c_Groups_Ozero__class_Ozero(U_1312) ) )
& ( ( ( U_1313 = c_Groups_Ozero__class_Ozero(U_1312)
| c_Int_Onumber__class_Onumber__of(U_1312,U_1315) != c_Groups_Ozero__class_Ozero(U_1312) )
& ( hAPP(c_Groups_Otimes__class_Otimes(U_1312,U_1313),c_Int_Onumber__class_Onumber__of(U_1312,U_1315)) = U_1314
| c_Int_Onumber__class_Onumber__of(U_1312,U_1315) = c_Groups_Ozero__class_Ozero(U_1312) ) )
| U_1313 != c_Rings_Oinverse__class_Odivide(U_1312,U_1314,c_Int_Onumber__class_Onumber__of(U_1312,U_1315)) ) )
| ~ class_Int_Onumber(U_1312)
| ~ class_Fields_Ofield__inverse__zero(U_1312) ),
inference(variable_rename,[status(thm)],[f_436_1]) ).
cnf(f_436_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_1312,U_1313),c_Int_Onumber__class_Onumber__of(U_1312,U_1315)) = U_1314
| c_Int_Onumber__class_Onumber__of(U_1312,U_1315) = c_Groups_Ozero__class_Ozero(U_1312)
| U_1313 != c_Rings_Oinverse__class_Odivide(U_1312,U_1314,c_Int_Onumber__class_Onumber__of(U_1312,U_1315))
| ~ class_Int_Onumber(U_1312)
| ~ class_Fields_Ofield__inverse__zero(U_1312) ),
inference(clausify,[status(thm)],[f_436_2]) ).
cnf(f_436_4,plain,
( U_1313 = c_Groups_Ozero__class_Ozero(U_1312)
| c_Int_Onumber__class_Onumber__of(U_1312,U_1315) != c_Groups_Ozero__class_Ozero(U_1312)
| U_1313 != c_Rings_Oinverse__class_Odivide(U_1312,U_1314,c_Int_Onumber__class_Onumber__of(U_1312,U_1315))
| ~ class_Int_Onumber(U_1312)
| ~ class_Fields_Ofield__inverse__zero(U_1312) ),
inference(clausify,[status(thm)],[f_436_2]) ).
cnf(f_436_5,plain,
( c_Int_Onumber__class_Onumber__of(U_1312,U_1315) = c_Groups_Ozero__class_Ozero(U_1312)
| c_Int_Onumber__class_Onumber__of(U_1312,U_1315) != c_Groups_Ozero__class_Ozero(U_1312)
| U_1313 = c_Rings_Oinverse__class_Odivide(U_1312,U_1314,c_Int_Onumber__class_Onumber__of(U_1312,U_1315))
| ~ class_Int_Onumber(U_1312)
| ~ class_Fields_Ofield__inverse__zero(U_1312) ),
inference(clausify,[status(thm)],[f_436_2]) ).
cnf(f_436_6,plain,
( U_1313 != c_Groups_Ozero__class_Ozero(U_1312)
| c_Int_Onumber__class_Onumber__of(U_1312,U_1315) != c_Groups_Ozero__class_Ozero(U_1312)
| U_1313 = c_Rings_Oinverse__class_Odivide(U_1312,U_1314,c_Int_Onumber__class_Onumber__of(U_1312,U_1315))
| ~ class_Int_Onumber(U_1312)
| ~ class_Fields_Ofield__inverse__zero(U_1312) ),
inference(clausify,[status(thm)],[f_436_2]) ).
cnf(f_436_7,plain,
( c_Int_Onumber__class_Onumber__of(U_1312,U_1315) = c_Groups_Ozero__class_Ozero(U_1312)
| hAPP(c_Groups_Otimes__class_Otimes(U_1312,U_1313),c_Int_Onumber__class_Onumber__of(U_1312,U_1315)) != U_1314
| U_1313 = c_Rings_Oinverse__class_Odivide(U_1312,U_1314,c_Int_Onumber__class_Onumber__of(U_1312,U_1315))
| ~ class_Int_Onumber(U_1312)
| ~ class_Fields_Ofield__inverse__zero(U_1312) ),
inference(clausify,[status(thm)],[f_436_2]) ).
cnf(f_436_8,plain,
( U_1313 != c_Groups_Ozero__class_Ozero(U_1312)
| hAPP(c_Groups_Otimes__class_Otimes(U_1312,U_1313),c_Int_Onumber__class_Onumber__of(U_1312,U_1315)) != U_1314
| U_1313 = c_Rings_Oinverse__class_Odivide(U_1312,U_1314,c_Int_Onumber__class_Onumber__of(U_1312,U_1315))
| ~ class_Int_Onumber(U_1312)
| ~ class_Fields_Ofield__inverse__zero(U_1312) ),
inference(clausify,[status(thm)],[f_436_2]) ).
fof(f_437_1,plain,
! [V_ca_2,V_b_2,V_wa_2,T_a] :
( ( ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)
| ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) != c_Groups_Ozero__class_Ozero(T_a)
& V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2) != V_b_2
& V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
& ( ( ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2) = V_b_2
| V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) ) )
| c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) != c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2) ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of]) ).
fof(f_437_2,plain,
! [U_1319,U_1318,U_1317,U_1316] :
( ( ( c_Int_Onumber__class_Onumber__of(U_1316,U_1317) = c_Rings_Oinverse__class_Odivide(U_1316,U_1318,U_1319)
| ( c_Int_Onumber__class_Onumber__of(U_1316,U_1317) != c_Groups_Ozero__class_Ozero(U_1316)
& U_1319 = c_Groups_Ozero__class_Ozero(U_1316) )
| ( hAPP(c_Groups_Otimes__class_Otimes(U_1316,c_Int_Onumber__class_Onumber__of(U_1316,U_1317)),U_1319) != U_1318
& U_1319 != c_Groups_Ozero__class_Ozero(U_1316) ) )
& ( ( ( c_Int_Onumber__class_Onumber__of(U_1316,U_1317) = c_Groups_Ozero__class_Ozero(U_1316)
| U_1319 != c_Groups_Ozero__class_Ozero(U_1316) )
& ( hAPP(c_Groups_Otimes__class_Otimes(U_1316,c_Int_Onumber__class_Onumber__of(U_1316,U_1317)),U_1319) = U_1318
| U_1319 = c_Groups_Ozero__class_Ozero(U_1316) ) )
| c_Int_Onumber__class_Onumber__of(U_1316,U_1317) != c_Rings_Oinverse__class_Odivide(U_1316,U_1318,U_1319) ) )
| ~ class_Int_Onumber(U_1316)
| ~ class_Fields_Ofield__inverse__zero(U_1316) ),
inference(variable_rename,[status(thm)],[f_437_1]) ).
cnf(f_437_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_1316,c_Int_Onumber__class_Onumber__of(U_1316,U_1317)),U_1319) = U_1318
| U_1319 = c_Groups_Ozero__class_Ozero(U_1316)
| c_Int_Onumber__class_Onumber__of(U_1316,U_1317) != c_Rings_Oinverse__class_Odivide(U_1316,U_1318,U_1319)
| ~ class_Int_Onumber(U_1316)
| ~ class_Fields_Ofield__inverse__zero(U_1316) ),
inference(clausify,[status(thm)],[f_437_2]) ).
cnf(f_437_4,plain,
( c_Int_Onumber__class_Onumber__of(U_1316,U_1317) = c_Groups_Ozero__class_Ozero(U_1316)
| U_1319 != c_Groups_Ozero__class_Ozero(U_1316)
| c_Int_Onumber__class_Onumber__of(U_1316,U_1317) != c_Rings_Oinverse__class_Odivide(U_1316,U_1318,U_1319)
| ~ class_Int_Onumber(U_1316)
| ~ class_Fields_Ofield__inverse__zero(U_1316) ),
inference(clausify,[status(thm)],[f_437_2]) ).
cnf(f_437_5,plain,
( U_1319 = c_Groups_Ozero__class_Ozero(U_1316)
| U_1319 != c_Groups_Ozero__class_Ozero(U_1316)
| c_Int_Onumber__class_Onumber__of(U_1316,U_1317) = c_Rings_Oinverse__class_Odivide(U_1316,U_1318,U_1319)
| ~ class_Int_Onumber(U_1316)
| ~ class_Fields_Ofield__inverse__zero(U_1316) ),
inference(clausify,[status(thm)],[f_437_2]) ).
cnf(f_437_6,plain,
( c_Int_Onumber__class_Onumber__of(U_1316,U_1317) != c_Groups_Ozero__class_Ozero(U_1316)
| U_1319 != c_Groups_Ozero__class_Ozero(U_1316)
| c_Int_Onumber__class_Onumber__of(U_1316,U_1317) = c_Rings_Oinverse__class_Odivide(U_1316,U_1318,U_1319)
| ~ class_Int_Onumber(U_1316)
| ~ class_Fields_Ofield__inverse__zero(U_1316) ),
inference(clausify,[status(thm)],[f_437_2]) ).
cnf(f_437_7,plain,
( U_1319 = c_Groups_Ozero__class_Ozero(U_1316)
| hAPP(c_Groups_Otimes__class_Otimes(U_1316,c_Int_Onumber__class_Onumber__of(U_1316,U_1317)),U_1319) != U_1318
| c_Int_Onumber__class_Onumber__of(U_1316,U_1317) = c_Rings_Oinverse__class_Odivide(U_1316,U_1318,U_1319)
| ~ class_Int_Onumber(U_1316)
| ~ class_Fields_Ofield__inverse__zero(U_1316) ),
inference(clausify,[status(thm)],[f_437_2]) ).
cnf(f_437_8,plain,
( c_Int_Onumber__class_Onumber__of(U_1316,U_1317) != c_Groups_Ozero__class_Ozero(U_1316)
| hAPP(c_Groups_Otimes__class_Otimes(U_1316,c_Int_Onumber__class_Onumber__of(U_1316,U_1317)),U_1319) != U_1318
| c_Int_Onumber__class_Onumber__of(U_1316,U_1317) = c_Rings_Oinverse__class_Odivide(U_1316,U_1318,U_1319)
| ~ class_Int_Onumber(U_1316)
| ~ class_Fields_Ofield__inverse__zero(U_1316) ),
inference(clausify,[status(thm)],[f_437_2]) ).
fof(f_438_1,plain,
! [V_wa_2,V_ca_2,V_b_2,T_a] :
( ( ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2) = c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)
| ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) != c_Groups_Ozero__class_Ozero(T_a)
& V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 != hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)
& V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
& ( ( ( c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_b_2 = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2)
| V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) ) )
| c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2) != c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of]) ).
fof(f_438_2,plain,
! [U_1323,U_1322,U_1321,U_1320] :
( ( ( c_Rings_Oinverse__class_Odivide(U_1320,U_1321,U_1322) = c_Int_Onumber__class_Onumber__of(U_1320,U_1323)
| ( c_Int_Onumber__class_Onumber__of(U_1320,U_1323) != c_Groups_Ozero__class_Ozero(U_1320)
& U_1322 = c_Groups_Ozero__class_Ozero(U_1320) )
| ( U_1321 != hAPP(c_Groups_Otimes__class_Otimes(U_1320,c_Int_Onumber__class_Onumber__of(U_1320,U_1323)),U_1322)
& U_1322 != c_Groups_Ozero__class_Ozero(U_1320) ) )
& ( ( ( c_Int_Onumber__class_Onumber__of(U_1320,U_1323) = c_Groups_Ozero__class_Ozero(U_1320)
| U_1322 != c_Groups_Ozero__class_Ozero(U_1320) )
& ( U_1321 = hAPP(c_Groups_Otimes__class_Otimes(U_1320,c_Int_Onumber__class_Onumber__of(U_1320,U_1323)),U_1322)
| U_1322 = c_Groups_Ozero__class_Ozero(U_1320) ) )
| c_Rings_Oinverse__class_Odivide(U_1320,U_1321,U_1322) != c_Int_Onumber__class_Onumber__of(U_1320,U_1323) ) )
| ~ class_Int_Onumber(U_1320)
| ~ class_Fields_Ofield__inverse__zero(U_1320) ),
inference(variable_rename,[status(thm)],[f_438_1]) ).
cnf(f_438_3,plain,
( U_1321 = hAPP(c_Groups_Otimes__class_Otimes(U_1320,c_Int_Onumber__class_Onumber__of(U_1320,U_1323)),U_1322)
| U_1322 = c_Groups_Ozero__class_Ozero(U_1320)
| c_Rings_Oinverse__class_Odivide(U_1320,U_1321,U_1322) != c_Int_Onumber__class_Onumber__of(U_1320,U_1323)
| ~ class_Int_Onumber(U_1320)
| ~ class_Fields_Ofield__inverse__zero(U_1320) ),
inference(clausify,[status(thm)],[f_438_2]) ).
cnf(f_438_4,plain,
( c_Int_Onumber__class_Onumber__of(U_1320,U_1323) = c_Groups_Ozero__class_Ozero(U_1320)
| U_1322 != c_Groups_Ozero__class_Ozero(U_1320)
| c_Rings_Oinverse__class_Odivide(U_1320,U_1321,U_1322) != c_Int_Onumber__class_Onumber__of(U_1320,U_1323)
| ~ class_Int_Onumber(U_1320)
| ~ class_Fields_Ofield__inverse__zero(U_1320) ),
inference(clausify,[status(thm)],[f_438_2]) ).
cnf(f_438_5,plain,
( U_1322 = c_Groups_Ozero__class_Ozero(U_1320)
| U_1322 != c_Groups_Ozero__class_Ozero(U_1320)
| c_Rings_Oinverse__class_Odivide(U_1320,U_1321,U_1322) = c_Int_Onumber__class_Onumber__of(U_1320,U_1323)
| ~ class_Int_Onumber(U_1320)
| ~ class_Fields_Ofield__inverse__zero(U_1320) ),
inference(clausify,[status(thm)],[f_438_2]) ).
cnf(f_438_6,plain,
( c_Int_Onumber__class_Onumber__of(U_1320,U_1323) != c_Groups_Ozero__class_Ozero(U_1320)
| U_1322 != c_Groups_Ozero__class_Ozero(U_1320)
| c_Rings_Oinverse__class_Odivide(U_1320,U_1321,U_1322) = c_Int_Onumber__class_Onumber__of(U_1320,U_1323)
| ~ class_Int_Onumber(U_1320)
| ~ class_Fields_Ofield__inverse__zero(U_1320) ),
inference(clausify,[status(thm)],[f_438_2]) ).
cnf(f_438_7,plain,
( U_1322 = c_Groups_Ozero__class_Ozero(U_1320)
| U_1321 != hAPP(c_Groups_Otimes__class_Otimes(U_1320,c_Int_Onumber__class_Onumber__of(U_1320,U_1323)),U_1322)
| c_Rings_Oinverse__class_Odivide(U_1320,U_1321,U_1322) = c_Int_Onumber__class_Onumber__of(U_1320,U_1323)
| ~ class_Int_Onumber(U_1320)
| ~ class_Fields_Ofield__inverse__zero(U_1320) ),
inference(clausify,[status(thm)],[f_438_2]) ).
cnf(f_438_8,plain,
( c_Int_Onumber__class_Onumber__of(U_1320,U_1323) != c_Groups_Ozero__class_Ozero(U_1320)
| U_1321 != hAPP(c_Groups_Otimes__class_Otimes(U_1320,c_Int_Onumber__class_Onumber__of(U_1320,U_1323)),U_1322)
| c_Rings_Oinverse__class_Odivide(U_1320,U_1321,U_1322) = c_Int_Onumber__class_Onumber__of(U_1320,U_1323)
| ~ class_Int_Onumber(U_1320)
| ~ class_Fields_Ofield__inverse__zero(U_1320) ),
inference(clausify,[status(thm)],[f_438_2]) ).
fof(f_439_1,plain,
! [V_a_2,V_wa_2,V_b_2,T_a] :
( ( ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) = V_a_2
| ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)
& c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 != hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
& c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
& ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_b_2 = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
| c_Int_Onumber__class_Onumber__of(T_a,V_wa_2) = c_Groups_Ozero__class_Ozero(T_a) ) )
| c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) != V_a_2 ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of1]) ).
fof(f_439_2,plain,
! [U_1327,U_1326,U_1325,U_1324] :
( ( ( c_Rings_Oinverse__class_Odivide(U_1324,U_1325,c_Int_Onumber__class_Onumber__of(U_1324,U_1326)) = U_1327
| ( U_1327 != c_Groups_Ozero__class_Ozero(U_1324)
& c_Int_Onumber__class_Onumber__of(U_1324,U_1326) = c_Groups_Ozero__class_Ozero(U_1324) )
| ( U_1325 != hAPP(c_Groups_Otimes__class_Otimes(U_1324,U_1327),c_Int_Onumber__class_Onumber__of(U_1324,U_1326))
& c_Int_Onumber__class_Onumber__of(U_1324,U_1326) != c_Groups_Ozero__class_Ozero(U_1324) ) )
& ( ( ( U_1327 = c_Groups_Ozero__class_Ozero(U_1324)
| c_Int_Onumber__class_Onumber__of(U_1324,U_1326) != c_Groups_Ozero__class_Ozero(U_1324) )
& ( U_1325 = hAPP(c_Groups_Otimes__class_Otimes(U_1324,U_1327),c_Int_Onumber__class_Onumber__of(U_1324,U_1326))
| c_Int_Onumber__class_Onumber__of(U_1324,U_1326) = c_Groups_Ozero__class_Ozero(U_1324) ) )
| c_Rings_Oinverse__class_Odivide(U_1324,U_1325,c_Int_Onumber__class_Onumber__of(U_1324,U_1326)) != U_1327 ) )
| ~ class_Int_Onumber(U_1324)
| ~ class_Fields_Ofield__inverse__zero(U_1324) ),
inference(variable_rename,[status(thm)],[f_439_1]) ).
cnf(f_439_3,plain,
( U_1325 = hAPP(c_Groups_Otimes__class_Otimes(U_1324,U_1327),c_Int_Onumber__class_Onumber__of(U_1324,U_1326))
| c_Int_Onumber__class_Onumber__of(U_1324,U_1326) = c_Groups_Ozero__class_Ozero(U_1324)
| c_Rings_Oinverse__class_Odivide(U_1324,U_1325,c_Int_Onumber__class_Onumber__of(U_1324,U_1326)) != U_1327
| ~ class_Int_Onumber(U_1324)
| ~ class_Fields_Ofield__inverse__zero(U_1324) ),
inference(clausify,[status(thm)],[f_439_2]) ).
cnf(f_439_4,plain,
( U_1327 = c_Groups_Ozero__class_Ozero(U_1324)
| c_Int_Onumber__class_Onumber__of(U_1324,U_1326) != c_Groups_Ozero__class_Ozero(U_1324)
| c_Rings_Oinverse__class_Odivide(U_1324,U_1325,c_Int_Onumber__class_Onumber__of(U_1324,U_1326)) != U_1327
| ~ class_Int_Onumber(U_1324)
| ~ class_Fields_Ofield__inverse__zero(U_1324) ),
inference(clausify,[status(thm)],[f_439_2]) ).
cnf(f_439_5,plain,
( c_Int_Onumber__class_Onumber__of(U_1324,U_1326) = c_Groups_Ozero__class_Ozero(U_1324)
| c_Int_Onumber__class_Onumber__of(U_1324,U_1326) != c_Groups_Ozero__class_Ozero(U_1324)
| c_Rings_Oinverse__class_Odivide(U_1324,U_1325,c_Int_Onumber__class_Onumber__of(U_1324,U_1326)) = U_1327
| ~ class_Int_Onumber(U_1324)
| ~ class_Fields_Ofield__inverse__zero(U_1324) ),
inference(clausify,[status(thm)],[f_439_2]) ).
cnf(f_439_6,plain,
( U_1327 != c_Groups_Ozero__class_Ozero(U_1324)
| c_Int_Onumber__class_Onumber__of(U_1324,U_1326) != c_Groups_Ozero__class_Ozero(U_1324)
| c_Rings_Oinverse__class_Odivide(U_1324,U_1325,c_Int_Onumber__class_Onumber__of(U_1324,U_1326)) = U_1327
| ~ class_Int_Onumber(U_1324)
| ~ class_Fields_Ofield__inverse__zero(U_1324) ),
inference(clausify,[status(thm)],[f_439_2]) ).
cnf(f_439_7,plain,
( c_Int_Onumber__class_Onumber__of(U_1324,U_1326) = c_Groups_Ozero__class_Ozero(U_1324)
| U_1325 != hAPP(c_Groups_Otimes__class_Otimes(U_1324,U_1327),c_Int_Onumber__class_Onumber__of(U_1324,U_1326))
| c_Rings_Oinverse__class_Odivide(U_1324,U_1325,c_Int_Onumber__class_Onumber__of(U_1324,U_1326)) = U_1327
| ~ class_Int_Onumber(U_1324)
| ~ class_Fields_Ofield__inverse__zero(U_1324) ),
inference(clausify,[status(thm)],[f_439_2]) ).
cnf(f_439_8,plain,
( U_1327 != c_Groups_Ozero__class_Ozero(U_1324)
| U_1325 != hAPP(c_Groups_Otimes__class_Otimes(U_1324,U_1327),c_Int_Onumber__class_Onumber__of(U_1324,U_1326))
| c_Rings_Oinverse__class_Odivide(U_1324,U_1325,c_Int_Onumber__class_Onumber__of(U_1324,U_1326)) = U_1327
| ~ class_Int_Onumber(U_1324)
| ~ class_Fields_Ofield__inverse__zero(U_1324) ),
inference(clausify,[status(thm)],[f_439_2]) ).
fof(f_440_1,plain,
! [V_w,T_b] :
( c_Rings_Oinverse__class_Oinverse(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_w)) = c_Rings_Oinverse__class_Odivide(T_b,c_Groups_Oone__class_Oone(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w))
| ~ class_Rings_Odivision__ring(T_b)
| ~ class_Int_Onumber(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inverse__eq__divide__number__of]) ).
fof(f_440_2,plain,
! [U_1329,U_1328] :
( c_Rings_Oinverse__class_Oinverse(U_1328,c_Int_Onumber__class_Onumber__of(U_1328,U_1329)) = c_Rings_Oinverse__class_Odivide(U_1328,c_Groups_Oone__class_Oone(U_1328),c_Int_Onumber__class_Onumber__of(U_1328,U_1329))
| ~ class_Rings_Odivision__ring(U_1328)
| ~ class_Int_Onumber(U_1328) ),
inference(variable_rename,[status(thm)],[f_440_1]) ).
cnf(f_440_3,plain,
( c_Rings_Oinverse__class_Oinverse(U_1328,c_Int_Onumber__class_Onumber__of(U_1328,U_1329)) = c_Rings_Oinverse__class_Odivide(U_1328,c_Groups_Oone__class_Oone(U_1328),c_Int_Onumber__class_Onumber__of(U_1328,U_1329))
| ~ class_Rings_Odivision__ring(U_1328)
| ~ class_Int_Onumber(U_1328) ),
inference(clausify,[status(thm)],[f_440_2]) ).
fof(f_441_1,plain,
! [V_a_2,V_wa_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2)
| ( ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
& ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) )
| ( ~ c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)
& c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
& ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) )
| ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
| c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_a_2) ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__less__eq__number__of1]) ).
fof(f_441_2,plain,
! [U_1333,U_1332,U_1331,U_1330] :
( ( ( c_Orderings_Oord__class_Oless(U_1330,c_Rings_Oinverse__class_Odivide(U_1330,U_1331,c_Int_Onumber__class_Onumber__of(U_1330,U_1332)),U_1333)
| ( ( ( ~ c_Orderings_Oord__class_Oless(U_1330,c_Groups_Ozero__class_Ozero(U_1330),U_1333)
& ~ c_Orderings_Oord__class_Oless(U_1330,c_Int_Onumber__class_Onumber__of(U_1330,U_1332),c_Groups_Ozero__class_Ozero(U_1330)) )
| ( ~ c_Orderings_Oord__class_Oless(U_1330,hAPP(c_Groups_Otimes__class_Otimes(U_1330,U_1333),c_Int_Onumber__class_Onumber__of(U_1330,U_1332)),U_1331)
& c_Orderings_Oord__class_Oless(U_1330,c_Int_Onumber__class_Onumber__of(U_1330,U_1332),c_Groups_Ozero__class_Ozero(U_1330)) ) )
& ~ c_Orderings_Oord__class_Oless(U_1330,c_Groups_Ozero__class_Ozero(U_1330),c_Int_Onumber__class_Onumber__of(U_1330,U_1332)) )
| ( ~ c_Orderings_Oord__class_Oless(U_1330,U_1331,hAPP(c_Groups_Otimes__class_Otimes(U_1330,U_1333),c_Int_Onumber__class_Onumber__of(U_1330,U_1332)))
& c_Orderings_Oord__class_Oless(U_1330,c_Groups_Ozero__class_Ozero(U_1330),c_Int_Onumber__class_Onumber__of(U_1330,U_1332)) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless(U_1330,c_Groups_Ozero__class_Ozero(U_1330),U_1333)
| c_Orderings_Oord__class_Oless(U_1330,c_Int_Onumber__class_Onumber__of(U_1330,U_1332),c_Groups_Ozero__class_Ozero(U_1330)) )
& ( c_Orderings_Oord__class_Oless(U_1330,hAPP(c_Groups_Otimes__class_Otimes(U_1330,U_1333),c_Int_Onumber__class_Onumber__of(U_1330,U_1332)),U_1331)
| ~ c_Orderings_Oord__class_Oless(U_1330,c_Int_Onumber__class_Onumber__of(U_1330,U_1332),c_Groups_Ozero__class_Ozero(U_1330)) ) )
| c_Orderings_Oord__class_Oless(U_1330,c_Groups_Ozero__class_Ozero(U_1330),c_Int_Onumber__class_Onumber__of(U_1330,U_1332)) )
& ( c_Orderings_Oord__class_Oless(U_1330,U_1331,hAPP(c_Groups_Otimes__class_Otimes(U_1330,U_1333),c_Int_Onumber__class_Onumber__of(U_1330,U_1332)))
| ~ c_Orderings_Oord__class_Oless(U_1330,c_Groups_Ozero__class_Ozero(U_1330),c_Int_Onumber__class_Onumber__of(U_1330,U_1332)) ) )
| ~ c_Orderings_Oord__class_Oless(U_1330,c_Rings_Oinverse__class_Odivide(U_1330,U_1331,c_Int_Onumber__class_Onumber__of(U_1330,U_1332)),U_1333) ) )
| ~ class_Int_Onumber(U_1330)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1330) ),
inference(variable_rename,[status(thm)],[f_441_1]) ).
cnf(f_441_3,plain,
( c_Orderings_Oord__class_Oless(U_1330,U_1331,hAPP(c_Groups_Otimes__class_Otimes(U_1330,U_1333),c_Int_Onumber__class_Onumber__of(U_1330,U_1332)))
| ~ c_Orderings_Oord__class_Oless(U_1330,c_Groups_Ozero__class_Ozero(U_1330),c_Int_Onumber__class_Onumber__of(U_1330,U_1332))
| ~ c_Orderings_Oord__class_Oless(U_1330,c_Rings_Oinverse__class_Odivide(U_1330,U_1331,c_Int_Onumber__class_Onumber__of(U_1330,U_1332)),U_1333)
| ~ class_Int_Onumber(U_1330)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1330) ),
inference(clausify,[status(thm)],[f_441_2]) ).
cnf(f_441_4,plain,
( c_Orderings_Oord__class_Oless(U_1330,hAPP(c_Groups_Otimes__class_Otimes(U_1330,U_1333),c_Int_Onumber__class_Onumber__of(U_1330,U_1332)),U_1331)
| ~ c_Orderings_Oord__class_Oless(U_1330,c_Int_Onumber__class_Onumber__of(U_1330,U_1332),c_Groups_Ozero__class_Ozero(U_1330))
| c_Orderings_Oord__class_Oless(U_1330,c_Groups_Ozero__class_Ozero(U_1330),c_Int_Onumber__class_Onumber__of(U_1330,U_1332))
| ~ c_Orderings_Oord__class_Oless(U_1330,c_Rings_Oinverse__class_Odivide(U_1330,U_1331,c_Int_Onumber__class_Onumber__of(U_1330,U_1332)),U_1333)
| ~ class_Int_Onumber(U_1330)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1330) ),
inference(clausify,[status(thm)],[f_441_2]) ).
cnf(f_441_5,plain,
( c_Orderings_Oord__class_Oless(U_1330,c_Groups_Ozero__class_Ozero(U_1330),U_1333)
| c_Orderings_Oord__class_Oless(U_1330,c_Int_Onumber__class_Onumber__of(U_1330,U_1332),c_Groups_Ozero__class_Ozero(U_1330))
| c_Orderings_Oord__class_Oless(U_1330,c_Groups_Ozero__class_Ozero(U_1330),c_Int_Onumber__class_Onumber__of(U_1330,U_1332))
| ~ c_Orderings_Oord__class_Oless(U_1330,c_Rings_Oinverse__class_Odivide(U_1330,U_1331,c_Int_Onumber__class_Onumber__of(U_1330,U_1332)),U_1333)
| ~ class_Int_Onumber(U_1330)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1330) ),
inference(clausify,[status(thm)],[f_441_2]) ).
cnf(f_441_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_1330,c_Groups_Ozero__class_Ozero(U_1330),c_Int_Onumber__class_Onumber__of(U_1330,U_1332))
| c_Orderings_Oord__class_Oless(U_1330,c_Groups_Ozero__class_Ozero(U_1330),c_Int_Onumber__class_Onumber__of(U_1330,U_1332))
| c_Orderings_Oord__class_Oless(U_1330,c_Rings_Oinverse__class_Odivide(U_1330,U_1331,c_Int_Onumber__class_Onumber__of(U_1330,U_1332)),U_1333)
| ~ class_Int_Onumber(U_1330)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1330) ),
inference(clausify,[status(thm)],[f_441_2]) ).
cnf(f_441_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_1330,c_Int_Onumber__class_Onumber__of(U_1330,U_1332),c_Groups_Ozero__class_Ozero(U_1330))
| c_Orderings_Oord__class_Oless(U_1330,c_Int_Onumber__class_Onumber__of(U_1330,U_1332),c_Groups_Ozero__class_Ozero(U_1330))
| c_Orderings_Oord__class_Oless(U_1330,c_Groups_Ozero__class_Ozero(U_1330),c_Int_Onumber__class_Onumber__of(U_1330,U_1332))
| c_Orderings_Oord__class_Oless(U_1330,c_Rings_Oinverse__class_Odivide(U_1330,U_1331,c_Int_Onumber__class_Onumber__of(U_1330,U_1332)),U_1333)
| ~ class_Int_Onumber(U_1330)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1330) ),
inference(clausify,[status(thm)],[f_441_2]) ).
cnf(f_441_8,plain,
( ~ c_Orderings_Oord__class_Oless(U_1330,c_Groups_Ozero__class_Ozero(U_1330),U_1333)
| c_Orderings_Oord__class_Oless(U_1330,c_Int_Onumber__class_Onumber__of(U_1330,U_1332),c_Groups_Ozero__class_Ozero(U_1330))
| c_Orderings_Oord__class_Oless(U_1330,c_Groups_Ozero__class_Ozero(U_1330),c_Int_Onumber__class_Onumber__of(U_1330,U_1332))
| c_Orderings_Oord__class_Oless(U_1330,c_Rings_Oinverse__class_Odivide(U_1330,U_1331,c_Int_Onumber__class_Onumber__of(U_1330,U_1332)),U_1333)
| ~ class_Int_Onumber(U_1330)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1330) ),
inference(clausify,[status(thm)],[f_441_2]) ).
cnf(f_441_9,plain,
( ~ c_Orderings_Oord__class_Oless(U_1330,c_Int_Onumber__class_Onumber__of(U_1330,U_1332),c_Groups_Ozero__class_Ozero(U_1330))
| ~ c_Orderings_Oord__class_Oless(U_1330,hAPP(c_Groups_Otimes__class_Otimes(U_1330,U_1333),c_Int_Onumber__class_Onumber__of(U_1330,U_1332)),U_1331)
| c_Orderings_Oord__class_Oless(U_1330,c_Groups_Ozero__class_Ozero(U_1330),c_Int_Onumber__class_Onumber__of(U_1330,U_1332))
| c_Orderings_Oord__class_Oless(U_1330,c_Rings_Oinverse__class_Odivide(U_1330,U_1331,c_Int_Onumber__class_Onumber__of(U_1330,U_1332)),U_1333)
| ~ class_Int_Onumber(U_1330)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1330) ),
inference(clausify,[status(thm)],[f_441_2]) ).
cnf(f_441_10,plain,
( ~ c_Orderings_Oord__class_Oless(U_1330,c_Groups_Ozero__class_Ozero(U_1330),U_1333)
| ~ c_Orderings_Oord__class_Oless(U_1330,hAPP(c_Groups_Otimes__class_Otimes(U_1330,U_1333),c_Int_Onumber__class_Onumber__of(U_1330,U_1332)),U_1331)
| c_Orderings_Oord__class_Oless(U_1330,c_Groups_Ozero__class_Ozero(U_1330),c_Int_Onumber__class_Onumber__of(U_1330,U_1332))
| c_Orderings_Oord__class_Oless(U_1330,c_Rings_Oinverse__class_Odivide(U_1330,U_1331,c_Int_Onumber__class_Onumber__of(U_1330,U_1332)),U_1333)
| ~ class_Int_Onumber(U_1330)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1330) ),
inference(clausify,[status(thm)],[f_441_2]) ).
cnf(f_441_11,plain,
( ~ c_Orderings_Oord__class_Oless(U_1330,c_Groups_Ozero__class_Ozero(U_1330),c_Int_Onumber__class_Onumber__of(U_1330,U_1332))
| ~ c_Orderings_Oord__class_Oless(U_1330,U_1331,hAPP(c_Groups_Otimes__class_Otimes(U_1330,U_1333),c_Int_Onumber__class_Onumber__of(U_1330,U_1332)))
| c_Orderings_Oord__class_Oless(U_1330,c_Rings_Oinverse__class_Odivide(U_1330,U_1331,c_Int_Onumber__class_Onumber__of(U_1330,U_1332)),U_1333)
| ~ class_Int_Onumber(U_1330)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1330) ),
inference(clausify,[status(thm)],[f_441_2]) ).
cnf(f_441_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_1330,c_Int_Onumber__class_Onumber__of(U_1330,U_1332),c_Groups_Ozero__class_Ozero(U_1330))
| c_Orderings_Oord__class_Oless(U_1330,c_Int_Onumber__class_Onumber__of(U_1330,U_1332),c_Groups_Ozero__class_Ozero(U_1330))
| ~ c_Orderings_Oord__class_Oless(U_1330,U_1331,hAPP(c_Groups_Otimes__class_Otimes(U_1330,U_1333),c_Int_Onumber__class_Onumber__of(U_1330,U_1332)))
| c_Orderings_Oord__class_Oless(U_1330,c_Rings_Oinverse__class_Odivide(U_1330,U_1331,c_Int_Onumber__class_Onumber__of(U_1330,U_1332)),U_1333)
| ~ class_Int_Onumber(U_1330)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1330) ),
inference(clausify,[status(thm)],[f_441_2]) ).
cnf(f_441_13,plain,
( ~ c_Orderings_Oord__class_Oless(U_1330,c_Groups_Ozero__class_Ozero(U_1330),U_1333)
| c_Orderings_Oord__class_Oless(U_1330,c_Int_Onumber__class_Onumber__of(U_1330,U_1332),c_Groups_Ozero__class_Ozero(U_1330))
| ~ c_Orderings_Oord__class_Oless(U_1330,U_1331,hAPP(c_Groups_Otimes__class_Otimes(U_1330,U_1333),c_Int_Onumber__class_Onumber__of(U_1330,U_1332)))
| c_Orderings_Oord__class_Oless(U_1330,c_Rings_Oinverse__class_Odivide(U_1330,U_1331,c_Int_Onumber__class_Onumber__of(U_1330,U_1332)),U_1333)
| ~ class_Int_Onumber(U_1330)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1330) ),
inference(clausify,[status(thm)],[f_441_2]) ).
cnf(f_441_14,plain,
( ~ c_Orderings_Oord__class_Oless(U_1330,c_Int_Onumber__class_Onumber__of(U_1330,U_1332),c_Groups_Ozero__class_Ozero(U_1330))
| ~ c_Orderings_Oord__class_Oless(U_1330,hAPP(c_Groups_Otimes__class_Otimes(U_1330,U_1333),c_Int_Onumber__class_Onumber__of(U_1330,U_1332)),U_1331)
| ~ c_Orderings_Oord__class_Oless(U_1330,U_1331,hAPP(c_Groups_Otimes__class_Otimes(U_1330,U_1333),c_Int_Onumber__class_Onumber__of(U_1330,U_1332)))
| c_Orderings_Oord__class_Oless(U_1330,c_Rings_Oinverse__class_Odivide(U_1330,U_1331,c_Int_Onumber__class_Onumber__of(U_1330,U_1332)),U_1333)
| ~ class_Int_Onumber(U_1330)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1330) ),
inference(clausify,[status(thm)],[f_441_2]) ).
cnf(f_441_15,plain,
( ~ c_Orderings_Oord__class_Oless(U_1330,c_Groups_Ozero__class_Ozero(U_1330),U_1333)
| ~ c_Orderings_Oord__class_Oless(U_1330,hAPP(c_Groups_Otimes__class_Otimes(U_1330,U_1333),c_Int_Onumber__class_Onumber__of(U_1330,U_1332)),U_1331)
| ~ c_Orderings_Oord__class_Oless(U_1330,U_1331,hAPP(c_Groups_Otimes__class_Otimes(U_1330,U_1333),c_Int_Onumber__class_Onumber__of(U_1330,U_1332)))
| c_Orderings_Oord__class_Oless(U_1330,c_Rings_Oinverse__class_Odivide(U_1330,U_1331,c_Int_Onumber__class_Onumber__of(U_1330,U_1332)),U_1333)
| ~ class_Int_Onumber(U_1330)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1330) ),
inference(clausify,[status(thm)],[f_441_2]) ).
fof(f_442_1,plain,
! [V_wa_2,V_ca_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
| ( ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_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,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_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,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) )
| ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_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,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_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,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_2),V_b_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,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_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,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__less__eq__number__of]) ).
fof(f_442_2,plain,
! [U_1337,U_1336,U_1335,U_1334] :
( ( ( c_Orderings_Oord__class_Oless(U_1334,c_Rings_Oinverse__class_Odivide(U_1334,U_1335,U_1336),c_Int_Onumber__class_Onumber__of(U_1334,U_1337))
| ( ( ( ~ c_Orderings_Oord__class_Oless(U_1334,c_Groups_Ozero__class_Ozero(U_1334),c_Int_Onumber__class_Onumber__of(U_1334,U_1337))
& ~ c_Orderings_Oord__class_Oless(U_1334,U_1336,c_Groups_Ozero__class_Ozero(U_1334)) )
| ( ~ c_Orderings_Oord__class_Oless(U_1334,hAPP(c_Groups_Otimes__class_Otimes(U_1334,c_Int_Onumber__class_Onumber__of(U_1334,U_1337)),U_1336),U_1335)
& c_Orderings_Oord__class_Oless(U_1334,U_1336,c_Groups_Ozero__class_Ozero(U_1334)) ) )
& ~ c_Orderings_Oord__class_Oless(U_1334,c_Groups_Ozero__class_Ozero(U_1334),U_1336) )
| ( ~ c_Orderings_Oord__class_Oless(U_1334,U_1335,hAPP(c_Groups_Otimes__class_Otimes(U_1334,c_Int_Onumber__class_Onumber__of(U_1334,U_1337)),U_1336))
& c_Orderings_Oord__class_Oless(U_1334,c_Groups_Ozero__class_Ozero(U_1334),U_1336) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless(U_1334,c_Groups_Ozero__class_Ozero(U_1334),c_Int_Onumber__class_Onumber__of(U_1334,U_1337))
| c_Orderings_Oord__class_Oless(U_1334,U_1336,c_Groups_Ozero__class_Ozero(U_1334)) )
& ( c_Orderings_Oord__class_Oless(U_1334,hAPP(c_Groups_Otimes__class_Otimes(U_1334,c_Int_Onumber__class_Onumber__of(U_1334,U_1337)),U_1336),U_1335)
| ~ c_Orderings_Oord__class_Oless(U_1334,U_1336,c_Groups_Ozero__class_Ozero(U_1334)) ) )
| c_Orderings_Oord__class_Oless(U_1334,c_Groups_Ozero__class_Ozero(U_1334),U_1336) )
& ( c_Orderings_Oord__class_Oless(U_1334,U_1335,hAPP(c_Groups_Otimes__class_Otimes(U_1334,c_Int_Onumber__class_Onumber__of(U_1334,U_1337)),U_1336))
| ~ c_Orderings_Oord__class_Oless(U_1334,c_Groups_Ozero__class_Ozero(U_1334),U_1336) ) )
| ~ c_Orderings_Oord__class_Oless(U_1334,c_Rings_Oinverse__class_Odivide(U_1334,U_1335,U_1336),c_Int_Onumber__class_Onumber__of(U_1334,U_1337)) ) )
| ~ class_Int_Onumber(U_1334)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1334) ),
inference(variable_rename,[status(thm)],[f_442_1]) ).
cnf(f_442_3,plain,
( c_Orderings_Oord__class_Oless(U_1334,U_1335,hAPP(c_Groups_Otimes__class_Otimes(U_1334,c_Int_Onumber__class_Onumber__of(U_1334,U_1337)),U_1336))
| ~ c_Orderings_Oord__class_Oless(U_1334,c_Groups_Ozero__class_Ozero(U_1334),U_1336)
| ~ c_Orderings_Oord__class_Oless(U_1334,c_Rings_Oinverse__class_Odivide(U_1334,U_1335,U_1336),c_Int_Onumber__class_Onumber__of(U_1334,U_1337))
| ~ class_Int_Onumber(U_1334)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1334) ),
inference(clausify,[status(thm)],[f_442_2]) ).
cnf(f_442_4,plain,
( c_Orderings_Oord__class_Oless(U_1334,hAPP(c_Groups_Otimes__class_Otimes(U_1334,c_Int_Onumber__class_Onumber__of(U_1334,U_1337)),U_1336),U_1335)
| ~ c_Orderings_Oord__class_Oless(U_1334,U_1336,c_Groups_Ozero__class_Ozero(U_1334))
| c_Orderings_Oord__class_Oless(U_1334,c_Groups_Ozero__class_Ozero(U_1334),U_1336)
| ~ c_Orderings_Oord__class_Oless(U_1334,c_Rings_Oinverse__class_Odivide(U_1334,U_1335,U_1336),c_Int_Onumber__class_Onumber__of(U_1334,U_1337))
| ~ class_Int_Onumber(U_1334)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1334) ),
inference(clausify,[status(thm)],[f_442_2]) ).
cnf(f_442_5,plain,
( c_Orderings_Oord__class_Oless(U_1334,c_Groups_Ozero__class_Ozero(U_1334),c_Int_Onumber__class_Onumber__of(U_1334,U_1337))
| c_Orderings_Oord__class_Oless(U_1334,U_1336,c_Groups_Ozero__class_Ozero(U_1334))
| c_Orderings_Oord__class_Oless(U_1334,c_Groups_Ozero__class_Ozero(U_1334),U_1336)
| ~ c_Orderings_Oord__class_Oless(U_1334,c_Rings_Oinverse__class_Odivide(U_1334,U_1335,U_1336),c_Int_Onumber__class_Onumber__of(U_1334,U_1337))
| ~ class_Int_Onumber(U_1334)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1334) ),
inference(clausify,[status(thm)],[f_442_2]) ).
cnf(f_442_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_1334,c_Groups_Ozero__class_Ozero(U_1334),U_1336)
| c_Orderings_Oord__class_Oless(U_1334,c_Groups_Ozero__class_Ozero(U_1334),U_1336)
| c_Orderings_Oord__class_Oless(U_1334,c_Rings_Oinverse__class_Odivide(U_1334,U_1335,U_1336),c_Int_Onumber__class_Onumber__of(U_1334,U_1337))
| ~ class_Int_Onumber(U_1334)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1334) ),
inference(clausify,[status(thm)],[f_442_2]) ).
cnf(f_442_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_1334,U_1336,c_Groups_Ozero__class_Ozero(U_1334))
| c_Orderings_Oord__class_Oless(U_1334,U_1336,c_Groups_Ozero__class_Ozero(U_1334))
| c_Orderings_Oord__class_Oless(U_1334,c_Groups_Ozero__class_Ozero(U_1334),U_1336)
| c_Orderings_Oord__class_Oless(U_1334,c_Rings_Oinverse__class_Odivide(U_1334,U_1335,U_1336),c_Int_Onumber__class_Onumber__of(U_1334,U_1337))
| ~ class_Int_Onumber(U_1334)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1334) ),
inference(clausify,[status(thm)],[f_442_2]) ).
cnf(f_442_8,plain,
( ~ c_Orderings_Oord__class_Oless(U_1334,c_Groups_Ozero__class_Ozero(U_1334),c_Int_Onumber__class_Onumber__of(U_1334,U_1337))
| c_Orderings_Oord__class_Oless(U_1334,U_1336,c_Groups_Ozero__class_Ozero(U_1334))
| c_Orderings_Oord__class_Oless(U_1334,c_Groups_Ozero__class_Ozero(U_1334),U_1336)
| c_Orderings_Oord__class_Oless(U_1334,c_Rings_Oinverse__class_Odivide(U_1334,U_1335,U_1336),c_Int_Onumber__class_Onumber__of(U_1334,U_1337))
| ~ class_Int_Onumber(U_1334)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1334) ),
inference(clausify,[status(thm)],[f_442_2]) ).
cnf(f_442_9,plain,
( ~ c_Orderings_Oord__class_Oless(U_1334,U_1336,c_Groups_Ozero__class_Ozero(U_1334))
| ~ c_Orderings_Oord__class_Oless(U_1334,hAPP(c_Groups_Otimes__class_Otimes(U_1334,c_Int_Onumber__class_Onumber__of(U_1334,U_1337)),U_1336),U_1335)
| c_Orderings_Oord__class_Oless(U_1334,c_Groups_Ozero__class_Ozero(U_1334),U_1336)
| c_Orderings_Oord__class_Oless(U_1334,c_Rings_Oinverse__class_Odivide(U_1334,U_1335,U_1336),c_Int_Onumber__class_Onumber__of(U_1334,U_1337))
| ~ class_Int_Onumber(U_1334)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1334) ),
inference(clausify,[status(thm)],[f_442_2]) ).
cnf(f_442_10,plain,
( ~ c_Orderings_Oord__class_Oless(U_1334,c_Groups_Ozero__class_Ozero(U_1334),c_Int_Onumber__class_Onumber__of(U_1334,U_1337))
| ~ c_Orderings_Oord__class_Oless(U_1334,hAPP(c_Groups_Otimes__class_Otimes(U_1334,c_Int_Onumber__class_Onumber__of(U_1334,U_1337)),U_1336),U_1335)
| c_Orderings_Oord__class_Oless(U_1334,c_Groups_Ozero__class_Ozero(U_1334),U_1336)
| c_Orderings_Oord__class_Oless(U_1334,c_Rings_Oinverse__class_Odivide(U_1334,U_1335,U_1336),c_Int_Onumber__class_Onumber__of(U_1334,U_1337))
| ~ class_Int_Onumber(U_1334)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1334) ),
inference(clausify,[status(thm)],[f_442_2]) ).
cnf(f_442_11,plain,
( ~ c_Orderings_Oord__class_Oless(U_1334,c_Groups_Ozero__class_Ozero(U_1334),U_1336)
| ~ c_Orderings_Oord__class_Oless(U_1334,U_1335,hAPP(c_Groups_Otimes__class_Otimes(U_1334,c_Int_Onumber__class_Onumber__of(U_1334,U_1337)),U_1336))
| c_Orderings_Oord__class_Oless(U_1334,c_Rings_Oinverse__class_Odivide(U_1334,U_1335,U_1336),c_Int_Onumber__class_Onumber__of(U_1334,U_1337))
| ~ class_Int_Onumber(U_1334)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1334) ),
inference(clausify,[status(thm)],[f_442_2]) ).
cnf(f_442_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_1334,U_1336,c_Groups_Ozero__class_Ozero(U_1334))
| c_Orderings_Oord__class_Oless(U_1334,U_1336,c_Groups_Ozero__class_Ozero(U_1334))
| ~ c_Orderings_Oord__class_Oless(U_1334,U_1335,hAPP(c_Groups_Otimes__class_Otimes(U_1334,c_Int_Onumber__class_Onumber__of(U_1334,U_1337)),U_1336))
| c_Orderings_Oord__class_Oless(U_1334,c_Rings_Oinverse__class_Odivide(U_1334,U_1335,U_1336),c_Int_Onumber__class_Onumber__of(U_1334,U_1337))
| ~ class_Int_Onumber(U_1334)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1334) ),
inference(clausify,[status(thm)],[f_442_2]) ).
cnf(f_442_13,plain,
( ~ c_Orderings_Oord__class_Oless(U_1334,c_Groups_Ozero__class_Ozero(U_1334),c_Int_Onumber__class_Onumber__of(U_1334,U_1337))
| c_Orderings_Oord__class_Oless(U_1334,U_1336,c_Groups_Ozero__class_Ozero(U_1334))
| ~ c_Orderings_Oord__class_Oless(U_1334,U_1335,hAPP(c_Groups_Otimes__class_Otimes(U_1334,c_Int_Onumber__class_Onumber__of(U_1334,U_1337)),U_1336))
| c_Orderings_Oord__class_Oless(U_1334,c_Rings_Oinverse__class_Odivide(U_1334,U_1335,U_1336),c_Int_Onumber__class_Onumber__of(U_1334,U_1337))
| ~ class_Int_Onumber(U_1334)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1334) ),
inference(clausify,[status(thm)],[f_442_2]) ).
cnf(f_442_14,plain,
( ~ c_Orderings_Oord__class_Oless(U_1334,U_1336,c_Groups_Ozero__class_Ozero(U_1334))
| ~ c_Orderings_Oord__class_Oless(U_1334,hAPP(c_Groups_Otimes__class_Otimes(U_1334,c_Int_Onumber__class_Onumber__of(U_1334,U_1337)),U_1336),U_1335)
| ~ c_Orderings_Oord__class_Oless(U_1334,U_1335,hAPP(c_Groups_Otimes__class_Otimes(U_1334,c_Int_Onumber__class_Onumber__of(U_1334,U_1337)),U_1336))
| c_Orderings_Oord__class_Oless(U_1334,c_Rings_Oinverse__class_Odivide(U_1334,U_1335,U_1336),c_Int_Onumber__class_Onumber__of(U_1334,U_1337))
| ~ class_Int_Onumber(U_1334)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1334) ),
inference(clausify,[status(thm)],[f_442_2]) ).
cnf(f_442_15,plain,
( ~ c_Orderings_Oord__class_Oless(U_1334,c_Groups_Ozero__class_Ozero(U_1334),c_Int_Onumber__class_Onumber__of(U_1334,U_1337))
| ~ c_Orderings_Oord__class_Oless(U_1334,hAPP(c_Groups_Otimes__class_Otimes(U_1334,c_Int_Onumber__class_Onumber__of(U_1334,U_1337)),U_1336),U_1335)
| ~ c_Orderings_Oord__class_Oless(U_1334,U_1335,hAPP(c_Groups_Otimes__class_Otimes(U_1334,c_Int_Onumber__class_Onumber__of(U_1334,U_1337)),U_1336))
| c_Orderings_Oord__class_Oless(U_1334,c_Rings_Oinverse__class_Odivide(U_1334,U_1335,U_1336),c_Int_Onumber__class_Onumber__of(U_1334,U_1337))
| ~ class_Int_Onumber(U_1334)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1334) ),
inference(clausify,[status(thm)],[f_442_2]) ).
fof(f_443_1,plain,
! [V_ca_2,V_b_2,V_wa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2))
| ( ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(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,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_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,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) )
| ( ~ c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_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,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(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,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_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,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) )
& ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_ca_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,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_ca_2)) ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__divide__eq__number__of]) ).
fof(f_443_2,plain,
! [U_1341,U_1340,U_1339,U_1338] :
( ( ( c_Orderings_Oord__class_Oless(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339),c_Rings_Oinverse__class_Odivide(U_1338,U_1340,U_1341))
| ( ( ( ~ c_Orderings_Oord__class_Oless(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339),c_Groups_Ozero__class_Ozero(U_1338))
& ~ c_Orderings_Oord__class_Oless(U_1338,U_1341,c_Groups_Ozero__class_Ozero(U_1338)) )
| ( ~ c_Orderings_Oord__class_Oless(U_1338,U_1340,hAPP(c_Groups_Otimes__class_Otimes(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339)),U_1341))
& c_Orderings_Oord__class_Oless(U_1338,U_1341,c_Groups_Ozero__class_Ozero(U_1338)) ) )
& ~ c_Orderings_Oord__class_Oless(U_1338,c_Groups_Ozero__class_Ozero(U_1338),U_1341) )
| ( ~ c_Orderings_Oord__class_Oless(U_1338,hAPP(c_Groups_Otimes__class_Otimes(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339)),U_1341),U_1340)
& c_Orderings_Oord__class_Oless(U_1338,c_Groups_Ozero__class_Ozero(U_1338),U_1341) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339),c_Groups_Ozero__class_Ozero(U_1338))
| c_Orderings_Oord__class_Oless(U_1338,U_1341,c_Groups_Ozero__class_Ozero(U_1338)) )
& ( c_Orderings_Oord__class_Oless(U_1338,U_1340,hAPP(c_Groups_Otimes__class_Otimes(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339)),U_1341))
| ~ c_Orderings_Oord__class_Oless(U_1338,U_1341,c_Groups_Ozero__class_Ozero(U_1338)) ) )
| c_Orderings_Oord__class_Oless(U_1338,c_Groups_Ozero__class_Ozero(U_1338),U_1341) )
& ( c_Orderings_Oord__class_Oless(U_1338,hAPP(c_Groups_Otimes__class_Otimes(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339)),U_1341),U_1340)
| ~ c_Orderings_Oord__class_Oless(U_1338,c_Groups_Ozero__class_Ozero(U_1338),U_1341) ) )
| ~ c_Orderings_Oord__class_Oless(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339),c_Rings_Oinverse__class_Odivide(U_1338,U_1340,U_1341)) ) )
| ~ class_Int_Onumber(U_1338)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1338) ),
inference(variable_rename,[status(thm)],[f_443_1]) ).
cnf(f_443_3,plain,
( c_Orderings_Oord__class_Oless(U_1338,hAPP(c_Groups_Otimes__class_Otimes(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339)),U_1341),U_1340)
| ~ c_Orderings_Oord__class_Oless(U_1338,c_Groups_Ozero__class_Ozero(U_1338),U_1341)
| ~ c_Orderings_Oord__class_Oless(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339),c_Rings_Oinverse__class_Odivide(U_1338,U_1340,U_1341))
| ~ class_Int_Onumber(U_1338)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1338) ),
inference(clausify,[status(thm)],[f_443_2]) ).
cnf(f_443_4,plain,
( c_Orderings_Oord__class_Oless(U_1338,U_1340,hAPP(c_Groups_Otimes__class_Otimes(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339)),U_1341))
| ~ c_Orderings_Oord__class_Oless(U_1338,U_1341,c_Groups_Ozero__class_Ozero(U_1338))
| c_Orderings_Oord__class_Oless(U_1338,c_Groups_Ozero__class_Ozero(U_1338),U_1341)
| ~ c_Orderings_Oord__class_Oless(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339),c_Rings_Oinverse__class_Odivide(U_1338,U_1340,U_1341))
| ~ class_Int_Onumber(U_1338)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1338) ),
inference(clausify,[status(thm)],[f_443_2]) ).
cnf(f_443_5,plain,
( c_Orderings_Oord__class_Oless(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339),c_Groups_Ozero__class_Ozero(U_1338))
| c_Orderings_Oord__class_Oless(U_1338,U_1341,c_Groups_Ozero__class_Ozero(U_1338))
| c_Orderings_Oord__class_Oless(U_1338,c_Groups_Ozero__class_Ozero(U_1338),U_1341)
| ~ c_Orderings_Oord__class_Oless(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339),c_Rings_Oinverse__class_Odivide(U_1338,U_1340,U_1341))
| ~ class_Int_Onumber(U_1338)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1338) ),
inference(clausify,[status(thm)],[f_443_2]) ).
cnf(f_443_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_1338,c_Groups_Ozero__class_Ozero(U_1338),U_1341)
| c_Orderings_Oord__class_Oless(U_1338,c_Groups_Ozero__class_Ozero(U_1338),U_1341)
| c_Orderings_Oord__class_Oless(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339),c_Rings_Oinverse__class_Odivide(U_1338,U_1340,U_1341))
| ~ class_Int_Onumber(U_1338)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1338) ),
inference(clausify,[status(thm)],[f_443_2]) ).
cnf(f_443_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_1338,U_1341,c_Groups_Ozero__class_Ozero(U_1338))
| c_Orderings_Oord__class_Oless(U_1338,U_1341,c_Groups_Ozero__class_Ozero(U_1338))
| c_Orderings_Oord__class_Oless(U_1338,c_Groups_Ozero__class_Ozero(U_1338),U_1341)
| c_Orderings_Oord__class_Oless(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339),c_Rings_Oinverse__class_Odivide(U_1338,U_1340,U_1341))
| ~ class_Int_Onumber(U_1338)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1338) ),
inference(clausify,[status(thm)],[f_443_2]) ).
cnf(f_443_8,plain,
( ~ c_Orderings_Oord__class_Oless(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339),c_Groups_Ozero__class_Ozero(U_1338))
| c_Orderings_Oord__class_Oless(U_1338,U_1341,c_Groups_Ozero__class_Ozero(U_1338))
| c_Orderings_Oord__class_Oless(U_1338,c_Groups_Ozero__class_Ozero(U_1338),U_1341)
| c_Orderings_Oord__class_Oless(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339),c_Rings_Oinverse__class_Odivide(U_1338,U_1340,U_1341))
| ~ class_Int_Onumber(U_1338)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1338) ),
inference(clausify,[status(thm)],[f_443_2]) ).
cnf(f_443_9,plain,
( ~ c_Orderings_Oord__class_Oless(U_1338,U_1341,c_Groups_Ozero__class_Ozero(U_1338))
| ~ c_Orderings_Oord__class_Oless(U_1338,U_1340,hAPP(c_Groups_Otimes__class_Otimes(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339)),U_1341))
| c_Orderings_Oord__class_Oless(U_1338,c_Groups_Ozero__class_Ozero(U_1338),U_1341)
| c_Orderings_Oord__class_Oless(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339),c_Rings_Oinverse__class_Odivide(U_1338,U_1340,U_1341))
| ~ class_Int_Onumber(U_1338)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1338) ),
inference(clausify,[status(thm)],[f_443_2]) ).
cnf(f_443_10,plain,
( ~ c_Orderings_Oord__class_Oless(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339),c_Groups_Ozero__class_Ozero(U_1338))
| ~ c_Orderings_Oord__class_Oless(U_1338,U_1340,hAPP(c_Groups_Otimes__class_Otimes(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339)),U_1341))
| c_Orderings_Oord__class_Oless(U_1338,c_Groups_Ozero__class_Ozero(U_1338),U_1341)
| c_Orderings_Oord__class_Oless(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339),c_Rings_Oinverse__class_Odivide(U_1338,U_1340,U_1341))
| ~ class_Int_Onumber(U_1338)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1338) ),
inference(clausify,[status(thm)],[f_443_2]) ).
cnf(f_443_11,plain,
( ~ c_Orderings_Oord__class_Oless(U_1338,c_Groups_Ozero__class_Ozero(U_1338),U_1341)
| ~ c_Orderings_Oord__class_Oless(U_1338,hAPP(c_Groups_Otimes__class_Otimes(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339)),U_1341),U_1340)
| c_Orderings_Oord__class_Oless(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339),c_Rings_Oinverse__class_Odivide(U_1338,U_1340,U_1341))
| ~ class_Int_Onumber(U_1338)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1338) ),
inference(clausify,[status(thm)],[f_443_2]) ).
cnf(f_443_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_1338,U_1341,c_Groups_Ozero__class_Ozero(U_1338))
| c_Orderings_Oord__class_Oless(U_1338,U_1341,c_Groups_Ozero__class_Ozero(U_1338))
| ~ c_Orderings_Oord__class_Oless(U_1338,hAPP(c_Groups_Otimes__class_Otimes(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339)),U_1341),U_1340)
| c_Orderings_Oord__class_Oless(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339),c_Rings_Oinverse__class_Odivide(U_1338,U_1340,U_1341))
| ~ class_Int_Onumber(U_1338)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1338) ),
inference(clausify,[status(thm)],[f_443_2]) ).
cnf(f_443_13,plain,
( ~ c_Orderings_Oord__class_Oless(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339),c_Groups_Ozero__class_Ozero(U_1338))
| c_Orderings_Oord__class_Oless(U_1338,U_1341,c_Groups_Ozero__class_Ozero(U_1338))
| ~ c_Orderings_Oord__class_Oless(U_1338,hAPP(c_Groups_Otimes__class_Otimes(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339)),U_1341),U_1340)
| c_Orderings_Oord__class_Oless(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339),c_Rings_Oinverse__class_Odivide(U_1338,U_1340,U_1341))
| ~ class_Int_Onumber(U_1338)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1338) ),
inference(clausify,[status(thm)],[f_443_2]) ).
cnf(f_443_14,plain,
( ~ c_Orderings_Oord__class_Oless(U_1338,U_1341,c_Groups_Ozero__class_Ozero(U_1338))
| ~ c_Orderings_Oord__class_Oless(U_1338,U_1340,hAPP(c_Groups_Otimes__class_Otimes(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339)),U_1341))
| ~ c_Orderings_Oord__class_Oless(U_1338,hAPP(c_Groups_Otimes__class_Otimes(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339)),U_1341),U_1340)
| c_Orderings_Oord__class_Oless(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339),c_Rings_Oinverse__class_Odivide(U_1338,U_1340,U_1341))
| ~ class_Int_Onumber(U_1338)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1338) ),
inference(clausify,[status(thm)],[f_443_2]) ).
cnf(f_443_15,plain,
( ~ c_Orderings_Oord__class_Oless(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339),c_Groups_Ozero__class_Ozero(U_1338))
| ~ c_Orderings_Oord__class_Oless(U_1338,U_1340,hAPP(c_Groups_Otimes__class_Otimes(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339)),U_1341))
| ~ c_Orderings_Oord__class_Oless(U_1338,hAPP(c_Groups_Otimes__class_Otimes(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339)),U_1341),U_1340)
| c_Orderings_Oord__class_Oless(U_1338,c_Int_Onumber__class_Onumber__of(U_1338,U_1339),c_Rings_Oinverse__class_Odivide(U_1338,U_1340,U_1341))
| ~ class_Int_Onumber(U_1338)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1338) ),
inference(clausify,[status(thm)],[f_443_2]) ).
fof(f_444_1,plain,
! [V_wa_2,V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))
| ( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
& ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) )
| ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))
& c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
& ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) )
| ( ~ c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))) ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__divide__eq__number__of1]) ).
fof(f_444_2,plain,
! [U_1345,U_1344,U_1343,U_1342] :
( ( ( c_Orderings_Oord__class_Oless(U_1342,U_1343,c_Rings_Oinverse__class_Odivide(U_1342,U_1344,c_Int_Onumber__class_Onumber__of(U_1342,U_1345)))
| ( ( ( ~ c_Orderings_Oord__class_Oless(U_1342,U_1343,c_Groups_Ozero__class_Ozero(U_1342))
& ~ c_Orderings_Oord__class_Oless(U_1342,c_Int_Onumber__class_Onumber__of(U_1342,U_1345),c_Groups_Ozero__class_Ozero(U_1342)) )
| ( ~ c_Orderings_Oord__class_Oless(U_1342,U_1344,hAPP(c_Groups_Otimes__class_Otimes(U_1342,U_1343),c_Int_Onumber__class_Onumber__of(U_1342,U_1345)))
& c_Orderings_Oord__class_Oless(U_1342,c_Int_Onumber__class_Onumber__of(U_1342,U_1345),c_Groups_Ozero__class_Ozero(U_1342)) ) )
& ~ c_Orderings_Oord__class_Oless(U_1342,c_Groups_Ozero__class_Ozero(U_1342),c_Int_Onumber__class_Onumber__of(U_1342,U_1345)) )
| ( ~ c_Orderings_Oord__class_Oless(U_1342,hAPP(c_Groups_Otimes__class_Otimes(U_1342,U_1343),c_Int_Onumber__class_Onumber__of(U_1342,U_1345)),U_1344)
& c_Orderings_Oord__class_Oless(U_1342,c_Groups_Ozero__class_Ozero(U_1342),c_Int_Onumber__class_Onumber__of(U_1342,U_1345)) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless(U_1342,U_1343,c_Groups_Ozero__class_Ozero(U_1342))
| c_Orderings_Oord__class_Oless(U_1342,c_Int_Onumber__class_Onumber__of(U_1342,U_1345),c_Groups_Ozero__class_Ozero(U_1342)) )
& ( c_Orderings_Oord__class_Oless(U_1342,U_1344,hAPP(c_Groups_Otimes__class_Otimes(U_1342,U_1343),c_Int_Onumber__class_Onumber__of(U_1342,U_1345)))
| ~ c_Orderings_Oord__class_Oless(U_1342,c_Int_Onumber__class_Onumber__of(U_1342,U_1345),c_Groups_Ozero__class_Ozero(U_1342)) ) )
| c_Orderings_Oord__class_Oless(U_1342,c_Groups_Ozero__class_Ozero(U_1342),c_Int_Onumber__class_Onumber__of(U_1342,U_1345)) )
& ( c_Orderings_Oord__class_Oless(U_1342,hAPP(c_Groups_Otimes__class_Otimes(U_1342,U_1343),c_Int_Onumber__class_Onumber__of(U_1342,U_1345)),U_1344)
| ~ c_Orderings_Oord__class_Oless(U_1342,c_Groups_Ozero__class_Ozero(U_1342),c_Int_Onumber__class_Onumber__of(U_1342,U_1345)) ) )
| ~ c_Orderings_Oord__class_Oless(U_1342,U_1343,c_Rings_Oinverse__class_Odivide(U_1342,U_1344,c_Int_Onumber__class_Onumber__of(U_1342,U_1345))) ) )
| ~ class_Int_Onumber(U_1342)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1342) ),
inference(variable_rename,[status(thm)],[f_444_1]) ).
cnf(f_444_3,plain,
( c_Orderings_Oord__class_Oless(U_1342,hAPP(c_Groups_Otimes__class_Otimes(U_1342,U_1343),c_Int_Onumber__class_Onumber__of(U_1342,U_1345)),U_1344)
| ~ c_Orderings_Oord__class_Oless(U_1342,c_Groups_Ozero__class_Ozero(U_1342),c_Int_Onumber__class_Onumber__of(U_1342,U_1345))
| ~ c_Orderings_Oord__class_Oless(U_1342,U_1343,c_Rings_Oinverse__class_Odivide(U_1342,U_1344,c_Int_Onumber__class_Onumber__of(U_1342,U_1345)))
| ~ class_Int_Onumber(U_1342)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1342) ),
inference(clausify,[status(thm)],[f_444_2]) ).
cnf(f_444_4,plain,
( c_Orderings_Oord__class_Oless(U_1342,U_1344,hAPP(c_Groups_Otimes__class_Otimes(U_1342,U_1343),c_Int_Onumber__class_Onumber__of(U_1342,U_1345)))
| ~ c_Orderings_Oord__class_Oless(U_1342,c_Int_Onumber__class_Onumber__of(U_1342,U_1345),c_Groups_Ozero__class_Ozero(U_1342))
| c_Orderings_Oord__class_Oless(U_1342,c_Groups_Ozero__class_Ozero(U_1342),c_Int_Onumber__class_Onumber__of(U_1342,U_1345))
| ~ c_Orderings_Oord__class_Oless(U_1342,U_1343,c_Rings_Oinverse__class_Odivide(U_1342,U_1344,c_Int_Onumber__class_Onumber__of(U_1342,U_1345)))
| ~ class_Int_Onumber(U_1342)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1342) ),
inference(clausify,[status(thm)],[f_444_2]) ).
cnf(f_444_5,plain,
( c_Orderings_Oord__class_Oless(U_1342,U_1343,c_Groups_Ozero__class_Ozero(U_1342))
| c_Orderings_Oord__class_Oless(U_1342,c_Int_Onumber__class_Onumber__of(U_1342,U_1345),c_Groups_Ozero__class_Ozero(U_1342))
| c_Orderings_Oord__class_Oless(U_1342,c_Groups_Ozero__class_Ozero(U_1342),c_Int_Onumber__class_Onumber__of(U_1342,U_1345))
| ~ c_Orderings_Oord__class_Oless(U_1342,U_1343,c_Rings_Oinverse__class_Odivide(U_1342,U_1344,c_Int_Onumber__class_Onumber__of(U_1342,U_1345)))
| ~ class_Int_Onumber(U_1342)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1342) ),
inference(clausify,[status(thm)],[f_444_2]) ).
cnf(f_444_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_1342,c_Groups_Ozero__class_Ozero(U_1342),c_Int_Onumber__class_Onumber__of(U_1342,U_1345))
| c_Orderings_Oord__class_Oless(U_1342,c_Groups_Ozero__class_Ozero(U_1342),c_Int_Onumber__class_Onumber__of(U_1342,U_1345))
| c_Orderings_Oord__class_Oless(U_1342,U_1343,c_Rings_Oinverse__class_Odivide(U_1342,U_1344,c_Int_Onumber__class_Onumber__of(U_1342,U_1345)))
| ~ class_Int_Onumber(U_1342)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1342) ),
inference(clausify,[status(thm)],[f_444_2]) ).
cnf(f_444_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_1342,c_Int_Onumber__class_Onumber__of(U_1342,U_1345),c_Groups_Ozero__class_Ozero(U_1342))
| c_Orderings_Oord__class_Oless(U_1342,c_Int_Onumber__class_Onumber__of(U_1342,U_1345),c_Groups_Ozero__class_Ozero(U_1342))
| c_Orderings_Oord__class_Oless(U_1342,c_Groups_Ozero__class_Ozero(U_1342),c_Int_Onumber__class_Onumber__of(U_1342,U_1345))
| c_Orderings_Oord__class_Oless(U_1342,U_1343,c_Rings_Oinverse__class_Odivide(U_1342,U_1344,c_Int_Onumber__class_Onumber__of(U_1342,U_1345)))
| ~ class_Int_Onumber(U_1342)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1342) ),
inference(clausify,[status(thm)],[f_444_2]) ).
cnf(f_444_8,plain,
( ~ c_Orderings_Oord__class_Oless(U_1342,U_1343,c_Groups_Ozero__class_Ozero(U_1342))
| c_Orderings_Oord__class_Oless(U_1342,c_Int_Onumber__class_Onumber__of(U_1342,U_1345),c_Groups_Ozero__class_Ozero(U_1342))
| c_Orderings_Oord__class_Oless(U_1342,c_Groups_Ozero__class_Ozero(U_1342),c_Int_Onumber__class_Onumber__of(U_1342,U_1345))
| c_Orderings_Oord__class_Oless(U_1342,U_1343,c_Rings_Oinverse__class_Odivide(U_1342,U_1344,c_Int_Onumber__class_Onumber__of(U_1342,U_1345)))
| ~ class_Int_Onumber(U_1342)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1342) ),
inference(clausify,[status(thm)],[f_444_2]) ).
cnf(f_444_9,plain,
( ~ c_Orderings_Oord__class_Oless(U_1342,c_Int_Onumber__class_Onumber__of(U_1342,U_1345),c_Groups_Ozero__class_Ozero(U_1342))
| ~ c_Orderings_Oord__class_Oless(U_1342,U_1344,hAPP(c_Groups_Otimes__class_Otimes(U_1342,U_1343),c_Int_Onumber__class_Onumber__of(U_1342,U_1345)))
| c_Orderings_Oord__class_Oless(U_1342,c_Groups_Ozero__class_Ozero(U_1342),c_Int_Onumber__class_Onumber__of(U_1342,U_1345))
| c_Orderings_Oord__class_Oless(U_1342,U_1343,c_Rings_Oinverse__class_Odivide(U_1342,U_1344,c_Int_Onumber__class_Onumber__of(U_1342,U_1345)))
| ~ class_Int_Onumber(U_1342)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1342) ),
inference(clausify,[status(thm)],[f_444_2]) ).
cnf(f_444_10,plain,
( ~ c_Orderings_Oord__class_Oless(U_1342,U_1343,c_Groups_Ozero__class_Ozero(U_1342))
| ~ c_Orderings_Oord__class_Oless(U_1342,U_1344,hAPP(c_Groups_Otimes__class_Otimes(U_1342,U_1343),c_Int_Onumber__class_Onumber__of(U_1342,U_1345)))
| c_Orderings_Oord__class_Oless(U_1342,c_Groups_Ozero__class_Ozero(U_1342),c_Int_Onumber__class_Onumber__of(U_1342,U_1345))
| c_Orderings_Oord__class_Oless(U_1342,U_1343,c_Rings_Oinverse__class_Odivide(U_1342,U_1344,c_Int_Onumber__class_Onumber__of(U_1342,U_1345)))
| ~ class_Int_Onumber(U_1342)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1342) ),
inference(clausify,[status(thm)],[f_444_2]) ).
cnf(f_444_11,plain,
( ~ c_Orderings_Oord__class_Oless(U_1342,c_Groups_Ozero__class_Ozero(U_1342),c_Int_Onumber__class_Onumber__of(U_1342,U_1345))
| ~ c_Orderings_Oord__class_Oless(U_1342,hAPP(c_Groups_Otimes__class_Otimes(U_1342,U_1343),c_Int_Onumber__class_Onumber__of(U_1342,U_1345)),U_1344)
| c_Orderings_Oord__class_Oless(U_1342,U_1343,c_Rings_Oinverse__class_Odivide(U_1342,U_1344,c_Int_Onumber__class_Onumber__of(U_1342,U_1345)))
| ~ class_Int_Onumber(U_1342)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1342) ),
inference(clausify,[status(thm)],[f_444_2]) ).
cnf(f_444_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_1342,c_Int_Onumber__class_Onumber__of(U_1342,U_1345),c_Groups_Ozero__class_Ozero(U_1342))
| c_Orderings_Oord__class_Oless(U_1342,c_Int_Onumber__class_Onumber__of(U_1342,U_1345),c_Groups_Ozero__class_Ozero(U_1342))
| ~ c_Orderings_Oord__class_Oless(U_1342,hAPP(c_Groups_Otimes__class_Otimes(U_1342,U_1343),c_Int_Onumber__class_Onumber__of(U_1342,U_1345)),U_1344)
| c_Orderings_Oord__class_Oless(U_1342,U_1343,c_Rings_Oinverse__class_Odivide(U_1342,U_1344,c_Int_Onumber__class_Onumber__of(U_1342,U_1345)))
| ~ class_Int_Onumber(U_1342)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1342) ),
inference(clausify,[status(thm)],[f_444_2]) ).
cnf(f_444_13,plain,
( ~ c_Orderings_Oord__class_Oless(U_1342,U_1343,c_Groups_Ozero__class_Ozero(U_1342))
| c_Orderings_Oord__class_Oless(U_1342,c_Int_Onumber__class_Onumber__of(U_1342,U_1345),c_Groups_Ozero__class_Ozero(U_1342))
| ~ c_Orderings_Oord__class_Oless(U_1342,hAPP(c_Groups_Otimes__class_Otimes(U_1342,U_1343),c_Int_Onumber__class_Onumber__of(U_1342,U_1345)),U_1344)
| c_Orderings_Oord__class_Oless(U_1342,U_1343,c_Rings_Oinverse__class_Odivide(U_1342,U_1344,c_Int_Onumber__class_Onumber__of(U_1342,U_1345)))
| ~ class_Int_Onumber(U_1342)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1342) ),
inference(clausify,[status(thm)],[f_444_2]) ).
cnf(f_444_14,plain,
( ~ c_Orderings_Oord__class_Oless(U_1342,c_Int_Onumber__class_Onumber__of(U_1342,U_1345),c_Groups_Ozero__class_Ozero(U_1342))
| ~ c_Orderings_Oord__class_Oless(U_1342,U_1344,hAPP(c_Groups_Otimes__class_Otimes(U_1342,U_1343),c_Int_Onumber__class_Onumber__of(U_1342,U_1345)))
| ~ c_Orderings_Oord__class_Oless(U_1342,hAPP(c_Groups_Otimes__class_Otimes(U_1342,U_1343),c_Int_Onumber__class_Onumber__of(U_1342,U_1345)),U_1344)
| c_Orderings_Oord__class_Oless(U_1342,U_1343,c_Rings_Oinverse__class_Odivide(U_1342,U_1344,c_Int_Onumber__class_Onumber__of(U_1342,U_1345)))
| ~ class_Int_Onumber(U_1342)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1342) ),
inference(clausify,[status(thm)],[f_444_2]) ).
cnf(f_444_15,plain,
( ~ c_Orderings_Oord__class_Oless(U_1342,U_1343,c_Groups_Ozero__class_Ozero(U_1342))
| ~ c_Orderings_Oord__class_Oless(U_1342,U_1344,hAPP(c_Groups_Otimes__class_Otimes(U_1342,U_1343),c_Int_Onumber__class_Onumber__of(U_1342,U_1345)))
| ~ c_Orderings_Oord__class_Oless(U_1342,hAPP(c_Groups_Otimes__class_Otimes(U_1342,U_1343),c_Int_Onumber__class_Onumber__of(U_1342,U_1345)),U_1344)
| c_Orderings_Oord__class_Oless(U_1342,U_1343,c_Rings_Oinverse__class_Odivide(U_1342,U_1344,c_Int_Onumber__class_Onumber__of(U_1342,U_1345)))
| ~ class_Int_Onumber(U_1342)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1342) ),
inference(clausify,[status(thm)],[f_444_2]) ).
fof(f_445_1,plain,
! [V_x_2] :
( c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,V_x_2,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_DERIV__ln]) ).
fof(f_445_2,plain,
! [U_1346] :
( c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,U_1346,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,U_1346))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1346) ),
inference(variable_rename,[status(thm)],[f_445_1]) ).
cnf(f_445_3,plain,
( c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oln,U_1346,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,U_1346))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1346) ),
inference(clausify,[status(thm)],[f_445_2]) ).
fof(f_446_1,plain,
! [V_x_2,V_ca_2,T_a] :
( c_Deriv_Oderiv(T_a,c_Groups_Otimes__class_Otimes(T_a,V_ca_2),V_x_2,V_ca_2)
| ~ class_RealVector_Oreal__normed__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_DERIV__cmult__Id]) ).
fof(f_446_2,plain,
! [U_1349,U_1348,U_1347] :
( c_Deriv_Oderiv(U_1347,c_Groups_Otimes__class_Otimes(U_1347,U_1348),U_1349,U_1348)
| ~ class_RealVector_Oreal__normed__field(U_1347) ),
inference(variable_rename,[status(thm)],[f_446_1]) ).
cnf(f_446_3,plain,
( c_Deriv_Oderiv(U_1347,c_Groups_Otimes__class_Otimes(U_1347,U_1348),U_1349,U_1348)
| ~ class_RealVector_Oreal__normed__field(U_1347) ),
inference(clausify,[status(thm)],[f_446_2]) ).
fof(f_447_1,plain,
! [V_k,T_a] :
( c_Int_Onumber__class_Onumber__of(T_a,c_Int_Osucc(V_k)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_k))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__succ]) ).
fof(f_447_2,plain,
! [U_1351,U_1350] :
( c_Int_Onumber__class_Onumber__of(U_1350,c_Int_Osucc(U_1351)) = c_Groups_Oplus__class_Oplus(U_1350,c_Groups_Oone__class_Oone(U_1350),c_Int_Onumber__class_Onumber__of(U_1350,U_1351))
| ~ class_Int_Onumber__ring(U_1350) ),
inference(variable_rename,[status(thm)],[f_447_1]) ).
cnf(f_447_3,plain,
( c_Int_Onumber__class_Onumber__of(U_1350,c_Int_Osucc(U_1351)) = c_Groups_Oplus__class_Oplus(U_1350,c_Groups_Oone__class_Oone(U_1350),c_Int_Onumber__class_Onumber__of(U_1350,U_1351))
| ~ class_Int_Onumber__ring(U_1350) ),
inference(clausify,[status(thm)],[f_447_2]) ).
fof(f_448_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_448_2,plain,
! [U_1352] :
( ( ( ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1352) = 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_1352) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1352) = 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_1352) ) )
| U_1352 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1352) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1352 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_448_1]) ).
fof(f_448_3,plain,
( ! [U_1354] :
( ( ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1354) = 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_1354) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1354) = 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_1354) ) )
| U_1354 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_1353] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1353) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1353 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_448_2]) ).
cnf(f_448_4,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1353) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1353 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_448_3]) ).
cnf(f_448_5,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1354) = 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_1354)
| U_1354 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_448_3]) ).
cnf(f_448_6,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1354) = 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_1354)
| U_1354 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_448_3]) ).
fof(f_449_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_449_2,plain,
! [U_1355] :
( ( ( ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1355) = 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_1355) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1355) = 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_1355) ) )
| U_1355 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1355) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1355 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_449_1]) ).
fof(f_449_3,plain,
( ! [U_1357] :
( ( ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1357) = 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_1357) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1357) = 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_1357) ) )
| U_1357 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_1356] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1356) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1356 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_449_2]) ).
cnf(f_449_4,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1356) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1356 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_449_3]) ).
cnf(f_449_5,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1357) = 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_1357)
| U_1357 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_449_3]) ).
cnf(f_449_6,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1357) = 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_1357)
| U_1357 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_449_3]) ).
fof(f_450_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),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_exp__ge__add__one__self__aux]) ).
fof(f_450_2,plain,
! [U_1358] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1358),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1358))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1358) ),
inference(variable_rename,[status(thm)],[f_450_1]) ).
cnf(f_450_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_1358),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1358))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1358) ),
inference(clausify,[status(thm)],[f_450_2]) ).
fof(f_451_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_exp__less__mono]) ).
fof(f_451_2,plain,
! [U_1360,U_1359] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1359),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1360))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1359,U_1360) ),
inference(variable_rename,[status(thm)],[f_451_1]) ).
cnf(f_451_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1359),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1360))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1359,U_1360) ),
inference(clausify,[status(thm)],[f_451_2]) ).
fof(f_452_1,plain,
! [V_w,V_v] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_w)),
inference(fof_nnf,[status(thm)],[fact_plus__numeral__code_I9_J]) ).
fof(f_452_2,plain,
! [U_1362,U_1361] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1361),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1362)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1361,U_1362)),
inference(variable_rename,[status(thm)],[f_452_1]) ).
cnf(f_452_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1361),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1362)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1361,U_1362)),
inference(clausify,[status(thm)],[f_452_2]) ).
fof(f_453_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__number__of__int__code]) ).
fof(f_453_2,plain,
! [U_1364,U_1363] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1363),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1364))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1363,U_1364) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1363,U_1364)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1363),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1364)) ) ),
inference(variable_rename,[status(thm)],[f_453_1]) ).
fof(f_453_3,plain,
( ! [U_1368,U_1366] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1366),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1368))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1366,U_1368) )
& ! [U_1367,U_1365] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1365,U_1367)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1365),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1367)) ) ),
inference(miniscope,[status(thm)],[f_453_2]) ).
cnf(f_453_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1365,U_1367)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1365),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1367)) ),
inference(clausify,[status(thm)],[f_453_3]) ).
cnf(f_453_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1366),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1368))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1366,U_1368) ),
inference(clausify,[status(thm)],[f_453_3]) ).
fof(f_454_1,plain,
! [V_w,V_v] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_v)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_w)),
inference(fof_nnf,[status(thm)],[fact_times__numeral__code_I5_J]) ).
fof(f_454_2,plain,
! [U_1370,U_1369] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1369)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1370)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1369),U_1370)),
inference(variable_rename,[status(thm)],[f_454_1]) ).
cnf(f_454_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1369)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1370)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1369),U_1370)),
inference(clausify,[status(thm)],[f_454_2]) ).
fof(f_455_1,plain,
! [V_z,V_w,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w))),V_z) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))),V_z)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__number__of__mult]) ).
fof(f_455_2,plain,
! [U_1373,U_1372,U_1371] :
( hAPP(c_Groups_Otimes__class_Otimes(U_1371,c_Groups_Ouminus__class_Ouminus(U_1371,c_Int_Onumber__class_Onumber__of(U_1371,U_1372))),U_1373) = hAPP(c_Groups_Otimes__class_Otimes(U_1371,c_Int_Onumber__class_Onumber__of(U_1371,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1372))),U_1373)
| ~ class_Int_Onumber__ring(U_1371) ),
inference(variable_rename,[status(thm)],[f_455_1]) ).
cnf(f_455_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_1371,c_Groups_Ouminus__class_Ouminus(U_1371,c_Int_Onumber__class_Onumber__of(U_1371,U_1372))),U_1373) = hAPP(c_Groups_Otimes__class_Otimes(U_1371,c_Int_Onumber__class_Onumber__of(U_1371,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1372))),U_1373)
| ~ class_Int_Onumber__ring(U_1371) ),
inference(clausify,[status(thm)],[f_455_2]) ).
fof(f_456_1,plain,
! [V_w,T_a] :
( c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__minus]) ).
fof(f_456_2,plain,
! [U_1375,U_1374] :
( c_Int_Onumber__class_Onumber__of(U_1374,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1375)) = c_Groups_Ouminus__class_Ouminus(U_1374,c_Int_Onumber__class_Onumber__of(U_1374,U_1375))
| ~ class_Int_Onumber__ring(U_1374) ),
inference(variable_rename,[status(thm)],[f_456_1]) ).
cnf(f_456_3,plain,
( c_Int_Onumber__class_Onumber__of(U_1374,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1375)) = c_Groups_Ouminus__class_Ouminus(U_1374,c_Int_Onumber__class_Onumber__of(U_1374,U_1375))
| ~ class_Int_Onumber__ring(U_1374) ),
inference(clausify,[status(thm)],[f_456_2]) ).
fof(f_457_1,plain,
! [V_w,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_arith__simps_I30_J]) ).
fof(f_457_2,plain,
! [U_1377,U_1376] :
( c_Groups_Ouminus__class_Ouminus(U_1376,c_Int_Onumber__class_Onumber__of(U_1376,U_1377)) = c_Int_Onumber__class_Onumber__of(U_1376,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1377))
| ~ class_Int_Onumber__ring(U_1376) ),
inference(variable_rename,[status(thm)],[f_457_1]) ).
cnf(f_457_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_1376,c_Int_Onumber__class_Onumber__of(U_1376,U_1377)) = c_Int_Onumber__class_Onumber__of(U_1376,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1377))
| ~ class_Int_Onumber__ring(U_1376) ),
inference(clausify,[status(thm)],[f_457_2]) ).
fof(f_458_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k_2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__number__of__int__code]) ).
fof(f_458_2,plain,
! [U_1379,U_1378] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1378),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1379))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1378,U_1379) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1378,U_1379)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1378),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1379)) ) ),
inference(variable_rename,[status(thm)],[f_458_1]) ).
fof(f_458_3,plain,
( ! [U_1383,U_1381] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1381),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1383))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1381,U_1383) )
& ! [U_1382,U_1380] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1380,U_1382)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1380),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1382)) ) ),
inference(miniscope,[status(thm)],[f_458_2]) ).
cnf(f_458_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1380,U_1382)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1380),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1382)) ),
inference(clausify,[status(thm)],[f_458_3]) ).
cnf(f_458_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1381),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1383))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1381,U_1383) ),
inference(clausify,[status(thm)],[f_458_3]) ).
fof(f_459_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_459_2,plain,
! [U_1385,U_1384] :
( c_Groups_Osgn__class_Osgn(U_1384,c_Groups_Ouminus__class_Ouminus(U_1384,U_1385)) = c_Groups_Ouminus__class_Ouminus(U_1384,c_Groups_Osgn__class_Osgn(U_1384,U_1385))
| ~ class_RealVector_Oreal__normed__vector(U_1384) ),
inference(variable_rename,[status(thm)],[f_459_1]) ).
cnf(f_459_3,plain,
( c_Groups_Osgn__class_Osgn(U_1384,c_Groups_Ouminus__class_Ouminus(U_1384,U_1385)) = c_Groups_Ouminus__class_Ouminus(U_1384,c_Groups_Osgn__class_Osgn(U_1384,U_1385))
| ~ class_RealVector_Oreal__normed__vector(U_1384) ),
inference(clausify,[status(thm)],[f_459_2]) ).
fof(f_460_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),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(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_exp__le__cancel__iff]) ).
fof(f_460_2,plain,
! [U_1387,U_1386] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1386),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1387))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1386,U_1387) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1386,U_1387)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1386),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1387)) ) ),
inference(variable_rename,[status(thm)],[f_460_1]) ).
fof(f_460_3,plain,
( ! [U_1391,U_1389] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1389),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1391))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1389,U_1391) )
& ! [U_1390,U_1388] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1388,U_1390)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1388),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1390)) ) ),
inference(miniscope,[status(thm)],[f_460_2]) ).
cnf(f_460_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1388,U_1390)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1388),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1390)) ),
inference(clausify,[status(thm)],[f_460_3]) ).
cnf(f_460_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1389),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1391))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1389,U_1391) ),
inference(clausify,[status(thm)],[f_460_3]) ).
fof(f_461_1,plain,
! [V_x,T_a] :
( hAPP(c_Transcendental_Oexp(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Transcendental_Oexp(T_a),V_x))
| ~ class_SEQ_Obanach(T_a)
| ~ class_RealVector_Oreal__normed__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_exp__minus]) ).
fof(f_461_2,plain,
! [U_1393,U_1392] :
( hAPP(c_Transcendental_Oexp(U_1392),c_Groups_Ouminus__class_Ouminus(U_1392,U_1393)) = c_Rings_Oinverse__class_Oinverse(U_1392,hAPP(c_Transcendental_Oexp(U_1392),U_1393))
| ~ class_SEQ_Obanach(U_1392)
| ~ class_RealVector_Oreal__normed__field(U_1392) ),
inference(variable_rename,[status(thm)],[f_461_1]) ).
cnf(f_461_3,plain,
( hAPP(c_Transcendental_Oexp(U_1392),c_Groups_Ouminus__class_Ouminus(U_1392,U_1393)) = c_Rings_Oinverse__class_Oinverse(U_1392,hAPP(c_Transcendental_Oexp(U_1392),U_1393))
| ~ class_SEQ_Obanach(U_1392)
| ~ class_RealVector_Oreal__normed__field(U_1392) ),
inference(clausify,[status(thm)],[f_461_2]) ).
fof(f_462_1,plain,
! [V_y_2,V_x_2] :
( ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2) = hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2) != hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y_2) ) ),
inference(fof_nnf,[status(thm)],[fact_exp__inj__iff]) ).
fof(f_462_2,plain,
! [U_1395,U_1394] :
( ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1394) = hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1395)
| U_1394 != U_1395 )
& ( U_1394 = U_1395
| hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1394) != hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1395) ) ),
inference(variable_rename,[status(thm)],[f_462_1]) ).
fof(f_462_3,plain,
( ! [U_1399,U_1397] :
( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1397) = hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1399)
| U_1397 != U_1399 )
& ! [U_1398,U_1396] :
( U_1396 = U_1398
| hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1396) != hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1398) ) ),
inference(miniscope,[status(thm)],[f_462_2]) ).
cnf(f_462_4,plain,
( U_1396 = U_1398
| hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1396) != hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1398) ),
inference(clausify,[status(thm)],[f_462_3]) ).
cnf(f_462_5,plain,
( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1397) = hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1399)
| U_1397 != U_1399 ),
inference(clausify,[status(thm)],[f_462_3]) ).
fof(f_463_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_463_2,plain,
! [U_1400] :
( c_Groups_Ouminus__class_Ouminus(U_1400,c_Groups_Ozero__class_Ozero(U_1400)) = c_Groups_Ozero__class_Ozero(U_1400)
| ~ class_Groups_Ogroup__add(U_1400) ),
inference(variable_rename,[status(thm)],[f_463_1]) ).
cnf(f_463_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_1400,c_Groups_Ozero__class_Ozero(U_1400)) = c_Groups_Ozero__class_Ozero(U_1400)
| ~ class_Groups_Ogroup__add(U_1400) ),
inference(clausify,[status(thm)],[f_463_2]) ).
fof(f_464_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_464_2,plain,
! [U_1402,U_1401] :
( ( ( c_Groups_Ozero__class_Ozero(U_1401) = c_Groups_Ouminus__class_Ouminus(U_1401,U_1402)
| c_Groups_Ozero__class_Ozero(U_1401) != U_1402 )
& ( c_Groups_Ozero__class_Ozero(U_1401) = U_1402
| c_Groups_Ozero__class_Ozero(U_1401) != c_Groups_Ouminus__class_Ouminus(U_1401,U_1402) ) )
| ~ class_Groups_Ogroup__add(U_1401) ),
inference(variable_rename,[status(thm)],[f_464_1]) ).
cnf(f_464_3,plain,
( c_Groups_Ozero__class_Ozero(U_1401) = U_1402
| c_Groups_Ozero__class_Ozero(U_1401) != c_Groups_Ouminus__class_Ouminus(U_1401,U_1402)
| ~ class_Groups_Ogroup__add(U_1401) ),
inference(clausify,[status(thm)],[f_464_2]) ).
cnf(f_464_4,plain,
( c_Groups_Ozero__class_Ozero(U_1401) = c_Groups_Ouminus__class_Ouminus(U_1401,U_1402)
| c_Groups_Ozero__class_Ozero(U_1401) != U_1402
| ~ class_Groups_Ogroup__add(U_1401) ),
inference(clausify,[status(thm)],[f_464_2]) ).
fof(f_465_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_465_2,plain,
! [U_1404,U_1403] :
( ( ( U_1404 = c_Groups_Ouminus__class_Ouminus(U_1403,U_1404)
| U_1404 != c_Groups_Ozero__class_Ozero(U_1403) )
& ( U_1404 = c_Groups_Ozero__class_Ozero(U_1403)
| U_1404 != c_Groups_Ouminus__class_Ouminus(U_1403,U_1404) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1403) ),
inference(variable_rename,[status(thm)],[f_465_1]) ).
cnf(f_465_3,plain,
( U_1404 = c_Groups_Ozero__class_Ozero(U_1403)
| U_1404 != c_Groups_Ouminus__class_Ouminus(U_1403,U_1404)
| ~ class_Groups_Olinordered__ab__group__add(U_1403) ),
inference(clausify,[status(thm)],[f_465_2]) ).
cnf(f_465_4,plain,
( U_1404 = c_Groups_Ouminus__class_Ouminus(U_1403,U_1404)
| U_1404 != c_Groups_Ozero__class_Ozero(U_1403)
| ~ class_Groups_Olinordered__ab__group__add(U_1403) ),
inference(clausify,[status(thm)],[f_465_2]) ).
fof(f_466_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_466_2,plain,
! [U_1406,U_1405] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_1405,U_1406) = c_Groups_Ozero__class_Ozero(U_1405)
| U_1406 != c_Groups_Ozero__class_Ozero(U_1405) )
& ( U_1406 = c_Groups_Ozero__class_Ozero(U_1405)
| c_Groups_Ouminus__class_Ouminus(U_1405,U_1406) != c_Groups_Ozero__class_Ozero(U_1405) ) )
| ~ class_Groups_Ogroup__add(U_1405) ),
inference(variable_rename,[status(thm)],[f_466_1]) ).
cnf(f_466_3,plain,
( U_1406 = c_Groups_Ozero__class_Ozero(U_1405)
| c_Groups_Ouminus__class_Ouminus(U_1405,U_1406) != c_Groups_Ozero__class_Ozero(U_1405)
| ~ class_Groups_Ogroup__add(U_1405) ),
inference(clausify,[status(thm)],[f_466_2]) ).
cnf(f_466_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1405,U_1406) = c_Groups_Ozero__class_Ozero(U_1405)
| U_1406 != c_Groups_Ozero__class_Ozero(U_1405)
| ~ class_Groups_Ogroup__add(U_1405) ),
inference(clausify,[status(thm)],[f_466_2]) ).
fof(f_467_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_467_2,plain,
! [U_1408,U_1407] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_1407,U_1408) = U_1408
| U_1408 != c_Groups_Ozero__class_Ozero(U_1407) )
& ( U_1408 = c_Groups_Ozero__class_Ozero(U_1407)
| c_Groups_Ouminus__class_Ouminus(U_1407,U_1408) != U_1408 ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1407) ),
inference(variable_rename,[status(thm)],[f_467_1]) ).
cnf(f_467_3,plain,
( U_1408 = c_Groups_Ozero__class_Ozero(U_1407)
| c_Groups_Ouminus__class_Ouminus(U_1407,U_1408) != U_1408
| ~ class_Groups_Olinordered__ab__group__add(U_1407) ),
inference(clausify,[status(thm)],[f_467_2]) ).
cnf(f_467_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1407,U_1408) = U_1408
| U_1408 != c_Groups_Ozero__class_Ozero(U_1407)
| ~ class_Groups_Olinordered__ab__group__add(U_1407) ),
inference(clausify,[status(thm)],[f_467_2]) ).
fof(f_468_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_468_2,plain,
! [U_1411,U_1410,U_1409] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1409,U_1410,c_Groups_Ouminus__class_Ouminus(U_1409,U_1411))
| ~ c_Orderings_Oord__class_Oless__eq(U_1409,U_1411,c_Groups_Ouminus__class_Ouminus(U_1409,U_1410)) )
& ( c_Orderings_Oord__class_Oless__eq(U_1409,U_1411,c_Groups_Ouminus__class_Ouminus(U_1409,U_1410))
| ~ c_Orderings_Oord__class_Oless__eq(U_1409,U_1410,c_Groups_Ouminus__class_Ouminus(U_1409,U_1411)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1409) ),
inference(variable_rename,[status(thm)],[f_468_1]) ).
cnf(f_468_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1409,U_1411,c_Groups_Ouminus__class_Ouminus(U_1409,U_1410))
| ~ c_Orderings_Oord__class_Oless__eq(U_1409,U_1410,c_Groups_Ouminus__class_Ouminus(U_1409,U_1411))
| ~ class_Groups_Oordered__ab__group__add(U_1409) ),
inference(clausify,[status(thm)],[f_468_2]) ).
cnf(f_468_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1409,U_1410,c_Groups_Ouminus__class_Ouminus(U_1409,U_1411))
| ~ c_Orderings_Oord__class_Oless__eq(U_1409,U_1411,c_Groups_Ouminus__class_Ouminus(U_1409,U_1410))
| ~ class_Groups_Oordered__ab__group__add(U_1409) ),
inference(clausify,[status(thm)],[f_468_2]) ).
fof(f_469_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_469_2,plain,
! [U_1414,U_1413,U_1412] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1412,c_Groups_Ouminus__class_Ouminus(U_1412,U_1413),U_1414)
| ~ c_Orderings_Oord__class_Oless__eq(U_1412,c_Groups_Ouminus__class_Ouminus(U_1412,U_1414),U_1413) )
& ( c_Orderings_Oord__class_Oless__eq(U_1412,c_Groups_Ouminus__class_Ouminus(U_1412,U_1414),U_1413)
| ~ c_Orderings_Oord__class_Oless__eq(U_1412,c_Groups_Ouminus__class_Ouminus(U_1412,U_1413),U_1414) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1412) ),
inference(variable_rename,[status(thm)],[f_469_1]) ).
cnf(f_469_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1412,c_Groups_Ouminus__class_Ouminus(U_1412,U_1414),U_1413)
| ~ c_Orderings_Oord__class_Oless__eq(U_1412,c_Groups_Ouminus__class_Ouminus(U_1412,U_1413),U_1414)
| ~ class_Groups_Oordered__ab__group__add(U_1412) ),
inference(clausify,[status(thm)],[f_469_2]) ).
cnf(f_469_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1412,c_Groups_Ouminus__class_Ouminus(U_1412,U_1413),U_1414)
| ~ c_Orderings_Oord__class_Oless__eq(U_1412,c_Groups_Ouminus__class_Ouminus(U_1412,U_1414),U_1413)
| ~ class_Groups_Oordered__ab__group__add(U_1412) ),
inference(clausify,[status(thm)],[f_469_2]) ).
fof(f_470_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_470_2,plain,
! [U_1417,U_1416,U_1415] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1415,c_Groups_Ouminus__class_Ouminus(U_1415,U_1416),c_Groups_Ouminus__class_Ouminus(U_1415,U_1417))
| ~ c_Orderings_Oord__class_Oless__eq(U_1415,U_1417,U_1416) )
& ( c_Orderings_Oord__class_Oless__eq(U_1415,U_1417,U_1416)
| ~ c_Orderings_Oord__class_Oless__eq(U_1415,c_Groups_Ouminus__class_Ouminus(U_1415,U_1416),c_Groups_Ouminus__class_Ouminus(U_1415,U_1417)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1415) ),
inference(variable_rename,[status(thm)],[f_470_1]) ).
cnf(f_470_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1415,U_1417,U_1416)
| ~ c_Orderings_Oord__class_Oless__eq(U_1415,c_Groups_Ouminus__class_Ouminus(U_1415,U_1416),c_Groups_Ouminus__class_Ouminus(U_1415,U_1417))
| ~ class_Groups_Oordered__ab__group__add(U_1415) ),
inference(clausify,[status(thm)],[f_470_2]) ).
cnf(f_470_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1415,c_Groups_Ouminus__class_Ouminus(U_1415,U_1416),c_Groups_Ouminus__class_Ouminus(U_1415,U_1417))
| ~ c_Orderings_Oord__class_Oless__eq(U_1415,U_1417,U_1416)
| ~ class_Groups_Oordered__ab__group__add(U_1415) ),
inference(clausify,[status(thm)],[f_470_2]) ).
fof(f_471_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_471_2,plain,
! [U_1420,U_1419,U_1418] :
( c_Orderings_Oord__class_Oless__eq(U_1418,c_Groups_Ouminus__class_Ouminus(U_1418,U_1420),c_Groups_Ouminus__class_Ouminus(U_1418,U_1419))
| ~ c_Orderings_Oord__class_Oless__eq(U_1418,U_1419,U_1420)
| ~ class_Groups_Oordered__ab__group__add(U_1418) ),
inference(variable_rename,[status(thm)],[f_471_1]) ).
cnf(f_471_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1418,c_Groups_Ouminus__class_Ouminus(U_1418,U_1420),c_Groups_Ouminus__class_Ouminus(U_1418,U_1419))
| ~ c_Orderings_Oord__class_Oless__eq(U_1418,U_1419,U_1420)
| ~ class_Groups_Oordered__ab__group__add(U_1418) ),
inference(clausify,[status(thm)],[f_471_2]) ).
fof(f_472_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_472_2,plain,
! [U_1423,U_1422,U_1421] :
( c_Orderings_Oord__class_Oless__eq(U_1421,c_Groups_Ouminus__class_Ouminus(U_1421,U_1423),c_Groups_Ouminus__class_Ouminus(U_1421,U_1422))
| ~ c_Orderings_Oord__class_Oless__eq(U_1421,U_1422,U_1423)
| ~ class_Lattices_Oboolean__algebra(U_1421) ),
inference(variable_rename,[status(thm)],[f_472_1]) ).
cnf(f_472_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1421,c_Groups_Ouminus__class_Ouminus(U_1421,U_1423),c_Groups_Ouminus__class_Ouminus(U_1421,U_1422))
| ~ c_Orderings_Oord__class_Oless__eq(U_1421,U_1422,U_1423)
| ~ class_Lattices_Oboolean__algebra(U_1421) ),
inference(clausify,[status(thm)],[f_472_2]) ).
fof(f_473_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_473_2,plain,
! [U_1426,U_1425,U_1424] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1424,c_Groups_Ouminus__class_Ouminus(U_1424,U_1425),c_Groups_Ouminus__class_Ouminus(U_1424,U_1426))
| ~ c_Orderings_Oord__class_Oless__eq(U_1424,U_1426,U_1425) )
& ( c_Orderings_Oord__class_Oless__eq(U_1424,U_1426,U_1425)
| ~ c_Orderings_Oord__class_Oless__eq(U_1424,c_Groups_Ouminus__class_Ouminus(U_1424,U_1425),c_Groups_Ouminus__class_Ouminus(U_1424,U_1426)) ) )
| ~ class_Lattices_Oboolean__algebra(U_1424) ),
inference(variable_rename,[status(thm)],[f_473_1]) ).
cnf(f_473_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1424,U_1426,U_1425)
| ~ c_Orderings_Oord__class_Oless__eq(U_1424,c_Groups_Ouminus__class_Ouminus(U_1424,U_1425),c_Groups_Ouminus__class_Ouminus(U_1424,U_1426))
| ~ class_Lattices_Oboolean__algebra(U_1424) ),
inference(clausify,[status(thm)],[f_473_2]) ).
cnf(f_473_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1424,c_Groups_Ouminus__class_Ouminus(U_1424,U_1425),c_Groups_Ouminus__class_Ouminus(U_1424,U_1426))
| ~ c_Orderings_Oord__class_Oless__eq(U_1424,U_1426,U_1425)
| ~ class_Lattices_Oboolean__algebra(U_1424) ),
inference(clausify,[status(thm)],[f_473_2]) ).
fof(f_474_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_474_2,plain,
! [U_1429,U_1428,U_1427] :
( ( ( c_Orderings_Oord__class_Oless(U_1427,c_Groups_Ouminus__class_Ouminus(U_1427,U_1428),c_Groups_Ouminus__class_Ouminus(U_1427,U_1429))
| ~ c_Orderings_Oord__class_Oless(U_1427,U_1429,U_1428) )
& ( c_Orderings_Oord__class_Oless(U_1427,U_1429,U_1428)
| ~ c_Orderings_Oord__class_Oless(U_1427,c_Groups_Ouminus__class_Ouminus(U_1427,U_1428),c_Groups_Ouminus__class_Ouminus(U_1427,U_1429)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1427) ),
inference(variable_rename,[status(thm)],[f_474_1]) ).
cnf(f_474_3,plain,
( c_Orderings_Oord__class_Oless(U_1427,U_1429,U_1428)
| ~ c_Orderings_Oord__class_Oless(U_1427,c_Groups_Ouminus__class_Ouminus(U_1427,U_1428),c_Groups_Ouminus__class_Ouminus(U_1427,U_1429))
| ~ class_Groups_Oordered__ab__group__add(U_1427) ),
inference(clausify,[status(thm)],[f_474_2]) ).
cnf(f_474_4,plain,
( c_Orderings_Oord__class_Oless(U_1427,c_Groups_Ouminus__class_Ouminus(U_1427,U_1428),c_Groups_Ouminus__class_Ouminus(U_1427,U_1429))
| ~ c_Orderings_Oord__class_Oless(U_1427,U_1429,U_1428)
| ~ class_Groups_Oordered__ab__group__add(U_1427) ),
inference(clausify,[status(thm)],[f_474_2]) ).
fof(f_475_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_475_2,plain,
! [U_1432,U_1431,U_1430] :
( ( ( c_Orderings_Oord__class_Oless(U_1430,c_Groups_Ouminus__class_Ouminus(U_1430,U_1431),U_1432)
| ~ c_Orderings_Oord__class_Oless(U_1430,c_Groups_Ouminus__class_Ouminus(U_1430,U_1432),U_1431) )
& ( c_Orderings_Oord__class_Oless(U_1430,c_Groups_Ouminus__class_Ouminus(U_1430,U_1432),U_1431)
| ~ c_Orderings_Oord__class_Oless(U_1430,c_Groups_Ouminus__class_Ouminus(U_1430,U_1431),U_1432) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1430) ),
inference(variable_rename,[status(thm)],[f_475_1]) ).
cnf(f_475_3,plain,
( c_Orderings_Oord__class_Oless(U_1430,c_Groups_Ouminus__class_Ouminus(U_1430,U_1432),U_1431)
| ~ c_Orderings_Oord__class_Oless(U_1430,c_Groups_Ouminus__class_Ouminus(U_1430,U_1431),U_1432)
| ~ class_Groups_Oordered__ab__group__add(U_1430) ),
inference(clausify,[status(thm)],[f_475_2]) ).
cnf(f_475_4,plain,
( c_Orderings_Oord__class_Oless(U_1430,c_Groups_Ouminus__class_Ouminus(U_1430,U_1431),U_1432)
| ~ c_Orderings_Oord__class_Oless(U_1430,c_Groups_Ouminus__class_Ouminus(U_1430,U_1432),U_1431)
| ~ class_Groups_Oordered__ab__group__add(U_1430) ),
inference(clausify,[status(thm)],[f_475_2]) ).
fof(f_476_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_476_2,plain,
! [U_1435,U_1434,U_1433] :
( ( ( c_Orderings_Oord__class_Oless(U_1433,U_1434,c_Groups_Ouminus__class_Ouminus(U_1433,U_1435))
| ~ c_Orderings_Oord__class_Oless(U_1433,U_1435,c_Groups_Ouminus__class_Ouminus(U_1433,U_1434)) )
& ( c_Orderings_Oord__class_Oless(U_1433,U_1435,c_Groups_Ouminus__class_Ouminus(U_1433,U_1434))
| ~ c_Orderings_Oord__class_Oless(U_1433,U_1434,c_Groups_Ouminus__class_Ouminus(U_1433,U_1435)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1433) ),
inference(variable_rename,[status(thm)],[f_476_1]) ).
cnf(f_476_3,plain,
( c_Orderings_Oord__class_Oless(U_1433,U_1435,c_Groups_Ouminus__class_Ouminus(U_1433,U_1434))
| ~ c_Orderings_Oord__class_Oless(U_1433,U_1434,c_Groups_Ouminus__class_Ouminus(U_1433,U_1435))
| ~ class_Groups_Oordered__ab__group__add(U_1433) ),
inference(clausify,[status(thm)],[f_476_2]) ).
cnf(f_476_4,plain,
( c_Orderings_Oord__class_Oless(U_1433,U_1434,c_Groups_Ouminus__class_Ouminus(U_1433,U_1435))
| ~ c_Orderings_Oord__class_Oless(U_1433,U_1435,c_Groups_Ouminus__class_Ouminus(U_1433,U_1434))
| ~ class_Groups_Oordered__ab__group__add(U_1433) ),
inference(clausify,[status(thm)],[f_476_2]) ).
fof(f_477_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_a_2) = 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(c_Groups_Otimes__class_Otimes(T_a,V_a_2),V_a_2) != 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_477_2,plain,
! [U_1438,U_1437,U_1436] :
( ( ( hAPP(c_Groups_Otimes__class_Otimes(U_1436,U_1437),U_1437) = hAPP(c_Groups_Otimes__class_Otimes(U_1436,U_1438),U_1438)
| ( U_1437 != c_Groups_Ouminus__class_Ouminus(U_1436,U_1438)
& U_1437 != U_1438 ) )
& ( U_1437 = c_Groups_Ouminus__class_Ouminus(U_1436,U_1438)
| U_1437 = U_1438
| hAPP(c_Groups_Otimes__class_Otimes(U_1436,U_1437),U_1437) != hAPP(c_Groups_Otimes__class_Otimes(U_1436,U_1438),U_1438) ) )
| ~ class_Rings_Oidom(U_1436) ),
inference(variable_rename,[status(thm)],[f_477_1]) ).
cnf(f_477_3,plain,
( U_1437 = c_Groups_Ouminus__class_Ouminus(U_1436,U_1438)
| U_1437 = U_1438
| hAPP(c_Groups_Otimes__class_Otimes(U_1436,U_1437),U_1437) != hAPP(c_Groups_Otimes__class_Otimes(U_1436,U_1438),U_1438)
| ~ class_Rings_Oidom(U_1436) ),
inference(clausify,[status(thm)],[f_477_2]) ).
cnf(f_477_4,plain,
( U_1437 != U_1438
| hAPP(c_Groups_Otimes__class_Otimes(U_1436,U_1437),U_1437) = hAPP(c_Groups_Otimes__class_Otimes(U_1436,U_1438),U_1438)
| ~ class_Rings_Oidom(U_1436) ),
inference(clausify,[status(thm)],[f_477_2]) ).
cnf(f_477_5,plain,
( U_1437 != c_Groups_Ouminus__class_Ouminus(U_1436,U_1438)
| hAPP(c_Groups_Otimes__class_Otimes(U_1436,U_1437),U_1437) = hAPP(c_Groups_Otimes__class_Otimes(U_1436,U_1438),U_1438)
| ~ class_Rings_Oidom(U_1436) ),
inference(clausify,[status(thm)],[f_477_2]) ).
fof(f_478_1,plain,
! [V_b,V_a,T_a] :
( 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(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_478_2,plain,
! [U_1441,U_1440,U_1439] :
( hAPP(c_Groups_Otimes__class_Otimes(U_1439,c_Groups_Ouminus__class_Ouminus(U_1439,U_1440)),c_Groups_Ouminus__class_Ouminus(U_1439,U_1441)) = hAPP(c_Groups_Otimes__class_Otimes(U_1439,U_1440),U_1441)
| ~ class_Rings_Oring(U_1439) ),
inference(variable_rename,[status(thm)],[f_478_1]) ).
cnf(f_478_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_1439,c_Groups_Ouminus__class_Ouminus(U_1439,U_1440)),c_Groups_Ouminus__class_Ouminus(U_1439,U_1441)) = hAPP(c_Groups_Otimes__class_Otimes(U_1439,U_1440),U_1441)
| ~ class_Rings_Oring(U_1439) ),
inference(clausify,[status(thm)],[f_478_2]) ).
fof(f_479_1,plain,
! [V_b,V_a,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = 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_479_2,plain,
! [U_1444,U_1443,U_1442] :
( hAPP(c_Groups_Otimes__class_Otimes(U_1442,c_Groups_Ouminus__class_Ouminus(U_1442,U_1443)),U_1444) = hAPP(c_Groups_Otimes__class_Otimes(U_1442,U_1443),c_Groups_Ouminus__class_Ouminus(U_1442,U_1444))
| ~ class_Rings_Oring(U_1442) ),
inference(variable_rename,[status(thm)],[f_479_1]) ).
cnf(f_479_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_1442,c_Groups_Ouminus__class_Ouminus(U_1442,U_1443)),U_1444) = hAPP(c_Groups_Otimes__class_Otimes(U_1442,U_1443),c_Groups_Ouminus__class_Ouminus(U_1442,U_1444))
| ~ class_Rings_Oring(U_1442) ),
inference(clausify,[status(thm)],[f_479_2]) ).
fof(f_480_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = 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_480_2,plain,
! [U_1447,U_1446,U_1445] :
( c_Groups_Ouminus__class_Ouminus(U_1445,hAPP(c_Groups_Otimes__class_Otimes(U_1445,U_1446),U_1447)) = hAPP(c_Groups_Otimes__class_Otimes(U_1445,c_Groups_Ouminus__class_Ouminus(U_1445,U_1446)),U_1447)
| ~ class_Rings_Oring(U_1445) ),
inference(variable_rename,[status(thm)],[f_480_1]) ).
cnf(f_480_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_1445,hAPP(c_Groups_Otimes__class_Otimes(U_1445,U_1446),U_1447)) = hAPP(c_Groups_Otimes__class_Otimes(U_1445,c_Groups_Ouminus__class_Ouminus(U_1445,U_1446)),U_1447)
| ~ class_Rings_Oring(U_1445) ),
inference(clausify,[status(thm)],[f_480_2]) ).
fof(f_481_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = 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_481_2,plain,
! [U_1450,U_1449,U_1448] :
( c_Groups_Ouminus__class_Ouminus(U_1448,hAPP(c_Groups_Otimes__class_Otimes(U_1448,U_1449),U_1450)) = hAPP(c_Groups_Otimes__class_Otimes(U_1448,U_1449),c_Groups_Ouminus__class_Ouminus(U_1448,U_1450))
| ~ class_Rings_Oring(U_1448) ),
inference(variable_rename,[status(thm)],[f_481_1]) ).
cnf(f_481_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_1448,hAPP(c_Groups_Otimes__class_Otimes(U_1448,U_1449),U_1450)) = hAPP(c_Groups_Otimes__class_Otimes(U_1448,U_1449),c_Groups_Ouminus__class_Ouminus(U_1448,U_1450))
| ~ class_Rings_Oring(U_1448) ),
inference(clausify,[status(thm)],[f_481_2]) ).
fof(f_482_1,plain,
! [V_y,V_x,T_a] :
( 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(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_482_2,plain,
! [U_1453,U_1452,U_1451] :
( hAPP(c_Groups_Otimes__class_Otimes(U_1451,c_Groups_Ouminus__class_Ouminus(U_1451,U_1452)),U_1453) = c_Groups_Ouminus__class_Ouminus(U_1451,hAPP(c_Groups_Otimes__class_Otimes(U_1451,U_1452),U_1453))
| ~ class_RealVector_Oreal__normed__algebra(U_1451) ),
inference(variable_rename,[status(thm)],[f_482_1]) ).
cnf(f_482_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_1451,c_Groups_Ouminus__class_Ouminus(U_1451,U_1452)),U_1453) = c_Groups_Ouminus__class_Ouminus(U_1451,hAPP(c_Groups_Otimes__class_Otimes(U_1451,U_1452),U_1453))
| ~ class_RealVector_Oreal__normed__algebra(U_1451) ),
inference(clausify,[status(thm)],[f_482_2]) ).
fof(f_483_1,plain,
! [V_b,V_a,T_a] :
( 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(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_483_2,plain,
! [U_1456,U_1455,U_1454] :
( hAPP(c_Groups_Otimes__class_Otimes(U_1454,c_Groups_Ouminus__class_Ouminus(U_1454,U_1455)),U_1456) = c_Groups_Ouminus__class_Ouminus(U_1454,hAPP(c_Groups_Otimes__class_Otimes(U_1454,U_1455),U_1456))
| ~ class_RealVector_Oreal__normed__algebra(U_1454) ),
inference(variable_rename,[status(thm)],[f_483_1]) ).
cnf(f_483_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_1454,c_Groups_Ouminus__class_Ouminus(U_1454,U_1455)),U_1456) = c_Groups_Ouminus__class_Ouminus(U_1454,hAPP(c_Groups_Otimes__class_Otimes(U_1454,U_1455),U_1456))
| ~ class_RealVector_Oreal__normed__algebra(U_1454) ),
inference(clausify,[status(thm)],[f_483_2]) ).
fof(f_484_1,plain,
! [V_x,V_xa,T_a] :
( 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(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_484_2,plain,
! [U_1459,U_1458,U_1457] :
( hAPP(c_Groups_Otimes__class_Otimes(U_1457,U_1458),c_Groups_Ouminus__class_Ouminus(U_1457,U_1459)) = c_Groups_Ouminus__class_Ouminus(U_1457,hAPP(c_Groups_Otimes__class_Otimes(U_1457,U_1458),U_1459))
| ~ class_RealVector_Oreal__normed__algebra(U_1457) ),
inference(variable_rename,[status(thm)],[f_484_1]) ).
cnf(f_484_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_1457,U_1458),c_Groups_Ouminus__class_Ouminus(U_1457,U_1459)) = c_Groups_Ouminus__class_Ouminus(U_1457,hAPP(c_Groups_Otimes__class_Otimes(U_1457,U_1458),U_1459))
| ~ class_RealVector_Oreal__normed__algebra(U_1457) ),
inference(clausify,[status(thm)],[f_484_2]) ).
fof(f_485_1,plain,
! [V_b,V_a,T_a] :
( 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(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_485_2,plain,
! [U_1462,U_1461,U_1460] :
( hAPP(c_Groups_Otimes__class_Otimes(U_1460,U_1461),c_Groups_Ouminus__class_Ouminus(U_1460,U_1462)) = c_Groups_Ouminus__class_Ouminus(U_1460,hAPP(c_Groups_Otimes__class_Otimes(U_1460,U_1461),U_1462))
| ~ class_RealVector_Oreal__normed__algebra(U_1460) ),
inference(variable_rename,[status(thm)],[f_485_1]) ).
cnf(f_485_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_1460,U_1461),c_Groups_Ouminus__class_Ouminus(U_1460,U_1462)) = c_Groups_Ouminus__class_Ouminus(U_1460,hAPP(c_Groups_Otimes__class_Otimes(U_1460,U_1461),U_1462))
| ~ class_RealVector_Oreal__normed__algebra(U_1460) ),
inference(clausify,[status(thm)],[f_485_2]) ).
fof(f_486_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_486_2,plain,
! [U_1465,U_1464,U_1463] :
( c_Groups_Oplus__class_Oplus(U_1463,c_Groups_Ouminus__class_Ouminus(U_1463,U_1464),c_Groups_Oplus__class_Oplus(U_1463,U_1464,U_1465)) = U_1465
| ~ class_Groups_Ogroup__add(U_1463) ),
inference(variable_rename,[status(thm)],[f_486_1]) ).
cnf(f_486_3,plain,
( c_Groups_Oplus__class_Oplus(U_1463,c_Groups_Ouminus__class_Ouminus(U_1463,U_1464),c_Groups_Oplus__class_Oplus(U_1463,U_1464,U_1465)) = U_1465
| ~ class_Groups_Ogroup__add(U_1463) ),
inference(clausify,[status(thm)],[f_486_2]) ).
fof(f_487_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_487_2,plain,
! [U_1468,U_1467,U_1466] :
( c_Groups_Oplus__class_Oplus(U_1466,U_1467,c_Groups_Oplus__class_Oplus(U_1466,c_Groups_Ouminus__class_Ouminus(U_1466,U_1467),U_1468)) = U_1468
| ~ class_Groups_Ogroup__add(U_1466) ),
inference(variable_rename,[status(thm)],[f_487_1]) ).
cnf(f_487_3,plain,
( c_Groups_Oplus__class_Oplus(U_1466,U_1467,c_Groups_Oplus__class_Oplus(U_1466,c_Groups_Ouminus__class_Ouminus(U_1466,U_1467),U_1468)) = U_1468
| ~ class_Groups_Ogroup__add(U_1466) ),
inference(clausify,[status(thm)],[f_487_2]) ).
fof(f_488_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_488_2,plain,
! [U_1471,U_1470,U_1469] :
( c_Groups_Ouminus__class_Ouminus(U_1469,c_Groups_Oplus__class_Oplus(U_1469,U_1470,U_1471)) = c_Groups_Oplus__class_Oplus(U_1469,c_Groups_Ouminus__class_Ouminus(U_1469,U_1471),c_Groups_Ouminus__class_Ouminus(U_1469,U_1470))
| ~ class_Groups_Ogroup__add(U_1469) ),
inference(variable_rename,[status(thm)],[f_488_1]) ).
cnf(f_488_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_1469,c_Groups_Oplus__class_Oplus(U_1469,U_1470,U_1471)) = c_Groups_Oplus__class_Oplus(U_1469,c_Groups_Ouminus__class_Ouminus(U_1469,U_1471),c_Groups_Ouminus__class_Ouminus(U_1469,U_1470))
| ~ class_Groups_Ogroup__add(U_1469) ),
inference(clausify,[status(thm)],[f_488_2]) ).
fof(f_489_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_489_2,plain,
! [U_1474,U_1473,U_1472] :
( c_Groups_Ouminus__class_Ouminus(U_1472,c_Groups_Oplus__class_Oplus(U_1472,U_1473,U_1474)) = c_Groups_Oplus__class_Oplus(U_1472,c_Groups_Ouminus__class_Ouminus(U_1472,U_1473),c_Groups_Ouminus__class_Ouminus(U_1472,U_1474))
| ~ class_Groups_Oab__group__add(U_1472) ),
inference(variable_rename,[status(thm)],[f_489_1]) ).
cnf(f_489_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_1472,c_Groups_Oplus__class_Oplus(U_1472,U_1473,U_1474)) = c_Groups_Oplus__class_Oplus(U_1472,c_Groups_Ouminus__class_Ouminus(U_1472,U_1473),c_Groups_Ouminus__class_Ouminus(U_1472,U_1474))
| ~ class_Groups_Oab__group__add(U_1472) ),
inference(clausify,[status(thm)],[f_489_2]) ).
fof(f_490_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__divide__left]) ).
fof(f_490_2,plain,
! [U_1477,U_1476,U_1475] :
( c_Groups_Ouminus__class_Ouminus(U_1475,c_Rings_Oinverse__class_Odivide(U_1475,U_1476,U_1477)) = c_Rings_Oinverse__class_Odivide(U_1475,c_Groups_Ouminus__class_Ouminus(U_1475,U_1476),U_1477)
| ~ class_Rings_Odivision__ring(U_1475) ),
inference(variable_rename,[status(thm)],[f_490_1]) ).
cnf(f_490_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_1475,c_Rings_Oinverse__class_Odivide(U_1475,U_1476,U_1477)) = c_Rings_Oinverse__class_Odivide(U_1475,c_Groups_Ouminus__class_Ouminus(U_1475,U_1476),U_1477)
| ~ class_Rings_Odivision__ring(U_1475) ),
inference(clausify,[status(thm)],[f_490_2]) ).
fof(f_491_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__divide__right]) ).
fof(f_491_2,plain,
! [U_1480,U_1479,U_1478] :
( c_Groups_Ouminus__class_Ouminus(U_1478,c_Rings_Oinverse__class_Odivide(U_1478,U_1479,U_1480)) = c_Rings_Oinverse__class_Odivide(U_1478,U_1479,c_Groups_Ouminus__class_Ouminus(U_1478,U_1480))
| ~ class_Fields_Ofield__inverse__zero(U_1478) ),
inference(variable_rename,[status(thm)],[f_491_1]) ).
cnf(f_491_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_1478,c_Rings_Oinverse__class_Odivide(U_1478,U_1479,U_1480)) = c_Rings_Oinverse__class_Odivide(U_1478,U_1479,c_Groups_Ouminus__class_Ouminus(U_1478,U_1480))
| ~ class_Fields_Ofield__inverse__zero(U_1478) ),
inference(clausify,[status(thm)],[f_491_2]) ).
fof(f_492_1,plain,
! [V_b,V_a,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__divide__divide]) ).
fof(f_492_2,plain,
! [U_1483,U_1482,U_1481] :
( c_Rings_Oinverse__class_Odivide(U_1481,c_Groups_Ouminus__class_Ouminus(U_1481,U_1482),c_Groups_Ouminus__class_Ouminus(U_1481,U_1483)) = c_Rings_Oinverse__class_Odivide(U_1481,U_1482,U_1483)
| ~ class_Fields_Ofield__inverse__zero(U_1481) ),
inference(variable_rename,[status(thm)],[f_492_1]) ).
cnf(f_492_3,plain,
( c_Rings_Oinverse__class_Odivide(U_1481,c_Groups_Ouminus__class_Ouminus(U_1481,U_1482),c_Groups_Ouminus__class_Ouminus(U_1481,U_1483)) = c_Rings_Oinverse__class_Odivide(U_1481,U_1482,U_1483)
| ~ class_Fields_Ofield__inverse__zero(U_1481) ),
inference(clausify,[status(thm)],[f_492_2]) ).
fof(f_493_1,plain,
! [V_y,V_x,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))
| ~ class_RealVector_Oreal__normed__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide_Ominus]) ).
fof(f_493_2,plain,
! [U_1486,U_1485,U_1484] :
( c_Rings_Oinverse__class_Odivide(U_1484,c_Groups_Ouminus__class_Ouminus(U_1484,U_1485),U_1486) = c_Groups_Ouminus__class_Ouminus(U_1484,c_Rings_Oinverse__class_Odivide(U_1484,U_1485,U_1486))
| ~ class_RealVector_Oreal__normed__field(U_1484) ),
inference(variable_rename,[status(thm)],[f_493_1]) ).
cnf(f_493_3,plain,
( c_Rings_Oinverse__class_Odivide(U_1484,c_Groups_Ouminus__class_Ouminus(U_1484,U_1485),U_1486) = c_Groups_Ouminus__class_Ouminus(U_1484,c_Rings_Oinverse__class_Odivide(U_1484,U_1485,U_1486))
| ~ class_RealVector_Oreal__normed__field(U_1484) ),
inference(clausify,[status(thm)],[f_493_2]) ).
fof(f_494_1,plain,
! [V_a,T_a] :
( c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))
| ~ class_Rings_Odivision__ring__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__minus__eq]) ).
fof(f_494_2,plain,
! [U_1488,U_1487] :
( c_Rings_Oinverse__class_Oinverse(U_1487,c_Groups_Ouminus__class_Ouminus(U_1487,U_1488)) = c_Groups_Ouminus__class_Ouminus(U_1487,c_Rings_Oinverse__class_Oinverse(U_1487,U_1488))
| ~ class_Rings_Odivision__ring__inverse__zero(U_1487) ),
inference(variable_rename,[status(thm)],[f_494_1]) ).
cnf(f_494_3,plain,
( c_Rings_Oinverse__class_Oinverse(U_1487,c_Groups_Ouminus__class_Ouminus(U_1487,U_1488)) = c_Groups_Ouminus__class_Ouminus(U_1487,c_Rings_Oinverse__class_Oinverse(U_1487,U_1488))
| ~ class_Rings_Odivision__ring__inverse__zero(U_1487) ),
inference(clausify,[status(thm)],[f_494_2]) ).
fof(f_495_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_495_2,plain,
! [U_1490,U_1489] :
( c_Groups_Ouminus__class_Ouminus(U_1489,c_Groups_Ouminus__class_Ouminus(U_1489,U_1490)) = U_1490
| ~ class_Lattices_Oboolean__algebra(U_1489) ),
inference(variable_rename,[status(thm)],[f_495_1]) ).
cnf(f_495_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_1489,c_Groups_Ouminus__class_Ouminus(U_1489,U_1490)) = U_1490
| ~ class_Lattices_Oboolean__algebra(U_1489) ),
inference(clausify,[status(thm)],[f_495_2]) ).
fof(f_496_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_496_2,plain,
! [U_1494,U_1493,U_1492,U_1491] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1492,U_1491),U_1493),U_1494) = c_Groups_Ouminus__class_Ouminus(U_1491,hAPP(U_1493,U_1494))
| ~ class_Groups_Ouminus(U_1491) ),
inference(variable_rename,[status(thm)],[f_496_1]) ).
cnf(f_496_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1492,U_1491),U_1493),U_1494) = c_Groups_Ouminus__class_Ouminus(U_1491,hAPP(U_1493,U_1494))
| ~ class_Groups_Ouminus(U_1491) ),
inference(clausify,[status(thm)],[f_496_2]) ).
fof(f_497_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_497_2,plain,
! [U_1497,U_1496,U_1495] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_1495,U_1496) = c_Groups_Ouminus__class_Ouminus(U_1495,U_1497)
| U_1496 != U_1497 )
& ( U_1496 = U_1497
| c_Groups_Ouminus__class_Ouminus(U_1495,U_1496) != c_Groups_Ouminus__class_Ouminus(U_1495,U_1497) ) )
| ~ class_Lattices_Oboolean__algebra(U_1495) ),
inference(variable_rename,[status(thm)],[f_497_1]) ).
cnf(f_497_3,plain,
( U_1496 = U_1497
| c_Groups_Ouminus__class_Ouminus(U_1495,U_1496) != c_Groups_Ouminus__class_Ouminus(U_1495,U_1497)
| ~ class_Lattices_Oboolean__algebra(U_1495) ),
inference(clausify,[status(thm)],[f_497_2]) ).
cnf(f_497_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1495,U_1496) = c_Groups_Ouminus__class_Ouminus(U_1495,U_1497)
| U_1496 != U_1497
| ~ class_Lattices_Oboolean__algebra(U_1495) ),
inference(clausify,[status(thm)],[f_497_2]) ).
fof(f_498_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_498_2,plain,
! [U_1499,U_1498] :
( c_Groups_Ouminus__class_Ouminus(U_1498,c_Groups_Ouminus__class_Ouminus(U_1498,U_1499)) = U_1499
| ~ class_Groups_Ogroup__add(U_1498) ),
inference(variable_rename,[status(thm)],[f_498_1]) ).
cnf(f_498_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_1498,c_Groups_Ouminus__class_Ouminus(U_1498,U_1499)) = U_1499
| ~ class_Groups_Ogroup__add(U_1498) ),
inference(clausify,[status(thm)],[f_498_2]) ).
fof(f_499_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_499_2,plain,
! [U_1502,U_1501,U_1500] :
( ( ( U_1501 = c_Groups_Ouminus__class_Ouminus(U_1500,U_1502)
| U_1502 != c_Groups_Ouminus__class_Ouminus(U_1500,U_1501) )
& ( U_1502 = c_Groups_Ouminus__class_Ouminus(U_1500,U_1501)
| U_1501 != c_Groups_Ouminus__class_Ouminus(U_1500,U_1502) ) )
| ~ class_Groups_Ogroup__add(U_1500) ),
inference(variable_rename,[status(thm)],[f_499_1]) ).
cnf(f_499_3,plain,
( U_1502 = c_Groups_Ouminus__class_Ouminus(U_1500,U_1501)
| U_1501 != c_Groups_Ouminus__class_Ouminus(U_1500,U_1502)
| ~ class_Groups_Ogroup__add(U_1500) ),
inference(clausify,[status(thm)],[f_499_2]) ).
cnf(f_499_4,plain,
( U_1501 = c_Groups_Ouminus__class_Ouminus(U_1500,U_1502)
| U_1502 != c_Groups_Ouminus__class_Ouminus(U_1500,U_1501)
| ~ class_Groups_Ogroup__add(U_1500) ),
inference(clausify,[status(thm)],[f_499_2]) ).
fof(f_500_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_500_2,plain,
! [U_1505,U_1504,U_1503] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_1503,U_1504) = U_1505
| c_Groups_Ouminus__class_Ouminus(U_1503,U_1505) != U_1504 )
& ( c_Groups_Ouminus__class_Ouminus(U_1503,U_1505) = U_1504
| c_Groups_Ouminus__class_Ouminus(U_1503,U_1504) != U_1505 ) )
| ~ class_Groups_Ogroup__add(U_1503) ),
inference(variable_rename,[status(thm)],[f_500_1]) ).
cnf(f_500_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_1503,U_1505) = U_1504
| c_Groups_Ouminus__class_Ouminus(U_1503,U_1504) != U_1505
| ~ class_Groups_Ogroup__add(U_1503) ),
inference(clausify,[status(thm)],[f_500_2]) ).
cnf(f_500_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1503,U_1504) = U_1505
| c_Groups_Ouminus__class_Ouminus(U_1503,U_1505) != U_1504
| ~ class_Groups_Ogroup__add(U_1503) ),
inference(clausify,[status(thm)],[f_500_2]) ).
fof(f_501_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_501_2,plain,
! [U_1508,U_1507,U_1506] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_1506,U_1507) = c_Groups_Ouminus__class_Ouminus(U_1506,U_1508)
| U_1507 != U_1508 )
& ( U_1507 = U_1508
| c_Groups_Ouminus__class_Ouminus(U_1506,U_1507) != c_Groups_Ouminus__class_Ouminus(U_1506,U_1508) ) )
| ~ class_Groups_Ogroup__add(U_1506) ),
inference(variable_rename,[status(thm)],[f_501_1]) ).
cnf(f_501_3,plain,
( U_1507 = U_1508
| c_Groups_Ouminus__class_Ouminus(U_1506,U_1507) != c_Groups_Ouminus__class_Ouminus(U_1506,U_1508)
| ~ class_Groups_Ogroup__add(U_1506) ),
inference(clausify,[status(thm)],[f_501_2]) ).
cnf(f_501_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1506,U_1507) = c_Groups_Ouminus__class_Ouminus(U_1506,U_1508)
| U_1507 != U_1508
| ~ class_Groups_Ogroup__add(U_1506) ),
inference(clausify,[status(thm)],[f_501_2]) ).
fof(f_502_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_exp__less__cancel__iff]) ).
fof(f_502_2,plain,
! [U_1510,U_1509] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1509),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1510))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1509,U_1510) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1509,U_1510)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1509),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1510)) ) ),
inference(variable_rename,[status(thm)],[f_502_1]) ).
fof(f_502_3,plain,
( ! [U_1514,U_1512] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1512),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1514))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1512,U_1514) )
& ! [U_1513,U_1511] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1511,U_1513)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1511),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1513)) ) ),
inference(miniscope,[status(thm)],[f_502_2]) ).
cnf(f_502_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1511,U_1513)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1511),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1513)) ),
inference(clausify,[status(thm)],[f_502_3]) ).
cnf(f_502_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1512),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1514))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1512,U_1514) ),
inference(clausify,[status(thm)],[f_502_3]) ).
fof(f_503_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_exp__less__cancel]) ).
fof(f_503_2,plain,
! [U_1516,U_1515] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1515,U_1516)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1515),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1516)) ),
inference(variable_rename,[status(thm)],[f_503_1]) ).
cnf(f_503_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1515,U_1516)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1515),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1516)) ),
inference(clausify,[status(thm)],[f_503_2]) ).
fof(f_504_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_504_2,plain,
! [U_1518,U_1517] :
( U_1517 = U_1518
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1518,U_1517)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1517,U_1518) ),
inference(variable_rename,[status(thm)],[f_504_1]) ).
cnf(f_504_3,plain,
( U_1517 = U_1518
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1518,U_1517)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1517,U_1518) ),
inference(clausify,[status(thm)],[f_504_2]) ).
fof(f_505_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_505_2,plain,
! [U_1521,U_1520,U_1519] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1519,U_1521)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1520,U_1521)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1519,U_1520) ),
inference(variable_rename,[status(thm)],[f_505_1]) ).
cnf(f_505_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1519,U_1521)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1520,U_1521)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1519,U_1520) ),
inference(clausify,[status(thm)],[f_505_2]) ).
fof(f_506_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_506_2,plain,
! [U_1523,U_1522] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1523,U_1522)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1522,U_1523) ),
inference(variable_rename,[status(thm)],[f_506_1]) ).
cnf(f_506_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1523,U_1522)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1522,U_1523) ),
inference(clausify,[status(thm)],[f_506_2]) ).
fof(f_507_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_507_2,plain,
! [U_1524] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1524,U_1524),
inference(variable_rename,[status(thm)],[f_507_1]) ).
cnf(f_507_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1524,U_1524),
inference(clausify,[status(thm)],[f_507_2]) ).
fof(f_508_1,plain,
! [V_z] : 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_508_2,plain,
! [U_1525] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1525) = U_1525,
inference(variable_rename,[status(thm)],[f_508_1]) ).
cnf(f_508_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1525) = U_1525,
inference(clausify,[status(thm)],[f_508_2]) ).
fof(f_509_1,plain,
! [V_z] : 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_509_2,plain,
! [U_1526] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1526),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_1526,
inference(variable_rename,[status(thm)],[f_509_1]) ).
cnf(f_509_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1526),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_1526,
inference(clausify,[status(thm)],[f_509_2]) ).
fof(f_510_1,plain,
! [V_z3,V_z2,V_z1] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1),V_z2)),V_z3) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2),V_z3)),
inference(fof_nnf,[status(thm)],[fact_zmult__assoc]) ).
fof(f_510_2,plain,
! [U_1529,U_1528,U_1527] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1527),U_1528)),U_1529) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1527),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1528),U_1529)),
inference(variable_rename,[status(thm)],[f_510_1]) ).
cnf(f_510_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1527),U_1528)),U_1529) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1527),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1528),U_1529)),
inference(clausify,[status(thm)],[f_510_2]) ).
fof(f_511_1,plain,
! [V_w,V_z] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z),V_w) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w),V_z),
inference(fof_nnf,[status(thm)],[fact_zmult__commute]) ).
fof(f_511_2,plain,
! [U_1531,U_1530] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1530),U_1531) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1531),U_1530),
inference(variable_rename,[status(thm)],[f_511_1]) ).
cnf(f_511_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1530),U_1531) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1531),U_1530),
inference(clausify,[status(thm)],[f_511_2]) ).
fof(f_512_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_512_2,plain,
! [U_1533,U_1532] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1533,U_1532)
| U_1532 = U_1533
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1532,U_1533) ),
inference(variable_rename,[status(thm)],[f_512_1]) ).
cnf(f_512_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1533,U_1532)
| U_1532 = U_1533
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1532,U_1533) ),
inference(clausify,[status(thm)],[f_512_2]) ).
fof(f_513_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k),V_i),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_513_2,plain,
! [U_1536,U_1535,U_1534] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1536),U_1534),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1536),U_1535))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1536)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1534,U_1535) ),
inference(variable_rename,[status(thm)],[f_513_1]) ).
cnf(f_513_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1536),U_1534),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1536),U_1535))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1536)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1534,U_1535) ),
inference(clausify,[status(thm)],[f_513_2]) ).
fof(f_514_1,plain,
! [V_n_2,V_ma_2] :
( ( ( 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(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_514_2,plain,
! [U_1538,U_1537] :
( ( ( hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1537),U_1538) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_1538 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_1537 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( ( U_1538 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& U_1537 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1537),U_1538) != 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_1537) ),
inference(variable_rename,[status(thm)],[f_514_1]) ).
cnf(f_514_3,plain,
( U_1537 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1537),U_1538) != 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_1537) ),
inference(clausify,[status(thm)],[f_514_2]) ).
cnf(f_514_4,plain,
( U_1538 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1537),U_1538) != 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_1537) ),
inference(clausify,[status(thm)],[f_514_2]) ).
cnf(f_514_5,plain,
( hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1537),U_1538) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_1538 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_1537 != 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_1537) ),
inference(clausify,[status(thm)],[f_514_2]) ).
fof(f_515_1,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(fof_nnf,[status(thm)],[fact_int__0__less__1]) ).
cnf(f_515_2,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_515_1]) ).
fof(f_516_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_516_2,plain,
! [U_1539] : 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_1539),U_1539) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_516_1]) ).
cnf(f_516_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1539),U_1539) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_516_2]) ).
fof(f_517_1,plain,
! [V_k] : c_Int_Osucc(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(fof_nnf,[status(thm)],[fact_succ__def]) ).
fof(f_517_2,plain,
! [U_1540] : c_Int_Osucc(U_1540) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1540,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[f_517_1]) ).
cnf(f_517_3,plain,
c_Int_Osucc(U_1540) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1540,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_517_2]) ).
fof(f_518_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_518_2,plain,
! [U_1541] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1541) = U_1541,
inference(variable_rename,[status(thm)],[f_518_1]) ).
cnf(f_518_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1541) = U_1541,
inference(clausify,[status(thm)],[f_518_2]) ).
fof(f_519_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_519_2,plain,
! [U_1542] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1542,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_1542,
inference(variable_rename,[status(thm)],[f_519_1]) ).
cnf(f_519_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1542,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_1542,
inference(clausify,[status(thm)],[f_519_2]) ).
fof(f_520_1,plain,
! [V_za_2,V_wa_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ( V_wa_2 != V_za_2
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) ) )
& ( V_wa_2 = V_za_2
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(fof_nnf,[status(thm)],[fact_zless__add1__eq]) ).
fof(f_520_2,plain,
! [U_1544,U_1543] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1543,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1544,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ( U_1543 != U_1544
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1543,U_1544) ) )
& ( U_1543 = U_1544
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1543,U_1544)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1543,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1544,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_520_1]) ).
fof(f_520_3,plain,
( ! [U_1548,U_1546] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1546,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1548,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ( U_1546 != U_1548
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1546,U_1548) ) )
& ! [U_1547,U_1545] :
( U_1545 = U_1547
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1545,U_1547)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1545,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1547,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_520_2]) ).
cnf(f_520_4,plain,
( U_1545 = U_1547
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1545,U_1547)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1545,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1547,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_520_3]) ).
cnf(f_520_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1546,U_1548)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1546,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1548,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_520_3]) ).
cnf(f_520_6,plain,
( U_1546 != U_1548
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1546,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1548,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_520_3]) ).
fof(f_521_1,plain,
! [V_za_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2),V_za_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2),V_za_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(fof_nnf,[status(thm)],[fact_odd__less__0]) ).
fof(f_521_2,plain,
! [U_1549] :
( ( 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_1549),U_1549),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1549,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1549,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_1549),U_1549),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[f_521_1]) ).
fof(f_521_3,plain,
( ! [U_1551] :
( 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_1551),U_1551),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1551,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_1550] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1550,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_1550),U_1550),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(miniscope,[status(thm)],[f_521_2]) ).
cnf(f_521_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1550,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_1550),U_1550),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_521_3]) ).
cnf(f_521_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1551),U_1551),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1551,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_521_3]) ).
fof(f_522_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_522_2,plain,
! [U_1554,U_1553,U_1552] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1552,U_1554),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1553,U_1554))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1552,U_1553) ),
inference(variable_rename,[status(thm)],[f_522_1]) ).
cnf(f_522_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1552,U_1554),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1553,U_1554))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1552,U_1553) ),
inference(clausify,[status(thm)],[f_522_2]) ).
fof(f_523_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_523_2,plain,
! [U_1556,U_1555] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1555,U_1556) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1556,U_1555),
inference(variable_rename,[status(thm)],[f_523_1]) ).
cnf(f_523_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1555,U_1556) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1556,U_1555),
inference(clausify,[status(thm)],[f_523_2]) ).
fof(f_524_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_524_2,plain,
! [U_1559,U_1558,U_1557] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1557,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1558,U_1559)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1558,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1557,U_1559)),
inference(variable_rename,[status(thm)],[f_524_1]) ).
cnf(f_524_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1557,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1558,U_1559)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1558,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1557,U_1559)),
inference(clausify,[status(thm)],[f_524_2]) ).
fof(f_525_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_525_2,plain,
! [U_1562,U_1561,U_1560] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1560,U_1561),U_1562) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1560,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1561,U_1562)),
inference(variable_rename,[status(thm)],[f_525_1]) ).
cnf(f_525_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1560,U_1561),U_1562) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1560,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1561,U_1562)),
inference(clausify,[status(thm)],[f_525_2]) ).
fof(f_526_1,plain,
! [V_w,V_z2,V_z1] : 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(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z1),V_w),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z2),V_w)),
inference(fof_nnf,[status(thm)],[fact_zadd__zmult__distrib]) ).
fof(f_526_2,plain,
! [U_1565,U_1564,U_1563] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1563,U_1564)),U_1565) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1563),U_1565),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1564),U_1565)),
inference(variable_rename,[status(thm)],[f_526_1]) ).
cnf(f_526_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1563,U_1564)),U_1565) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1563),U_1565),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1564),U_1565)),
inference(clausify,[status(thm)],[f_526_2]) ).
fof(f_527_1,plain,
! [V_z2,V_z1,V_w] : 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(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w),V_z1),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_w),V_z2)),
inference(fof_nnf,[status(thm)],[fact_zadd__zmult__distrib2]) ).
fof(f_527_2,plain,
! [U_1568,U_1567,U_1566] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1566),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1567,U_1568)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1566),U_1567),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1566),U_1568)),
inference(variable_rename,[status(thm)],[f_527_1]) ).
cnf(f_527_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1566),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1567,U_1568)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1566),U_1567),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1566),U_1568)),
inference(clausify,[status(thm)],[f_527_2]) ).
fof(f_528_1,plain,
! [V_za_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_za_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_za_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2) ) ),
inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less]) ).
fof(f_528_2,plain,
! [U_1569] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1569)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1569) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1569)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1569) ) ),
inference(variable_rename,[status(thm)],[f_528_1]) ).
fof(f_528_3,plain,
( ! [U_1571] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1571)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1571) )
& ! [U_1570] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1570)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1570) ) ),
inference(miniscope,[status(thm)],[f_528_2]) ).
cnf(f_528_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1570)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1570) ),
inference(clausify,[status(thm)],[f_528_3]) ).
cnf(f_528_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1571)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1571) ),
inference(clausify,[status(thm)],[f_528_3]) ).
fof(f_529_1,plain,
! [V_za_2,V_wa_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,V_za_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_wa_2,V_za_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(fof_nnf,[status(thm)],[fact_zle__add1__eq__le]) ).
fof(f_529_2,plain,
! [U_1573,U_1572] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1572,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1573,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1572,U_1573) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1572,U_1573)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1572,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1573,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_529_1]) ).
fof(f_529_3,plain,
( ! [U_1577,U_1575] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1575,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1577,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1575,U_1577) )
& ! [U_1576,U_1574] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1574,U_1576)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1574,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1576,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_529_2]) ).
cnf(f_529_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1574,U_1576)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1574,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1576,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_529_3]) ).
cnf(f_529_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1575,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1577,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1575,U_1577) ),
inference(clausify,[status(thm)],[f_529_3]) ).
fof(f_530_1,plain,
! [V_za_2,V_wa_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_za_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,V_za_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_wa_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_za_2) ) ),
inference(fof_nnf,[status(thm)],[fact_add1__zle__eq]) ).
fof(f_530_2,plain,
! [U_1579,U_1578] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1578,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1579)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1578,U_1579) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1578,U_1579)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1578,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1579) ) ),
inference(variable_rename,[status(thm)],[f_530_1]) ).
fof(f_530_3,plain,
( ! [U_1583,U_1581] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1581,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1583)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1581,U_1583) )
& ! [U_1582,U_1580] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1580,U_1582)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1580,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1582) ) ),
inference(miniscope,[status(thm)],[f_530_2]) ).
cnf(f_530_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1580,U_1582)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1580,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1582) ),
inference(clausify,[status(thm)],[f_530_3]) ).
cnf(f_530_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1581,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1583)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1581,U_1583) ),
inference(clausify,[status(thm)],[f_530_3]) ).
fof(f_531_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_531_2,plain,
! [U_1584] :
( 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_1584))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1584) ),
inference(variable_rename,[status(thm)],[f_531_1]) ).
cnf(f_531_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1584))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1584) ),
inference(clausify,[status(thm)],[f_531_2]) ).
fof(f_532_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_532_2,plain,
! [U_1586,U_1585] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1585,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1586)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1585,U_1586) ),
inference(variable_rename,[status(thm)],[f_532_1]) ).
cnf(f_532_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1585,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1586)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1585,U_1586) ),
inference(clausify,[status(thm)],[f_532_2]) ).
fof(f_533_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_533_2,plain,
! [U_1590,U_1589,U_1588,U_1587] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1587,U_1589),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1588,U_1590))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1589,U_1590)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1587,U_1588) ),
inference(variable_rename,[status(thm)],[f_533_1]) ).
cnf(f_533_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1587,U_1589),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1588,U_1590))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1589,U_1590)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1587,U_1588) ),
inference(clausify,[status(thm)],[f_533_2]) ).
fof(f_534_1,plain,
! [V_wa_2,V_za_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_wa_2)
| V_za_2 = V_wa_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_za_2,V_wa_2) )
& ( ( V_za_2 != V_wa_2
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_za_2,V_wa_2) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_wa_2) ) ),
inference(fof_nnf,[status(thm)],[fact_zless__le]) ).
fof(f_534_2,plain,
! [U_1592,U_1591] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1591,U_1592)
| U_1591 = U_1592
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1591,U_1592) )
& ( ( U_1591 != U_1592
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1591,U_1592) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1591,U_1592) ) ),
inference(variable_rename,[status(thm)],[f_534_1]) ).
fof(f_534_3,plain,
( ! [U_1596,U_1594] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1594,U_1596)
| U_1594 = U_1596
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1594,U_1596) )
& ! [U_1595,U_1593] :
( ( U_1593 != U_1595
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1593,U_1595) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1593,U_1595) ) ),
inference(miniscope,[status(thm)],[f_534_2]) ).
cnf(f_534_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1593,U_1595)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1593,U_1595) ),
inference(clausify,[status(thm)],[f_534_3]) ).
cnf(f_534_5,plain,
( U_1593 != U_1595
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1593,U_1595) ),
inference(clausify,[status(thm)],[f_534_3]) ).
cnf(f_534_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1594,U_1596)
| U_1594 = U_1596
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1594,U_1596) ),
inference(clausify,[status(thm)],[f_534_3]) ).
fof(f_535_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_535_2,plain,
! [U_1599,U_1598,U_1597] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1599,U_1597),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1599,U_1598))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1597,U_1598) ),
inference(variable_rename,[status(thm)],[f_535_1]) ).
cnf(f_535_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1599,U_1597),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1599,U_1598))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1597,U_1598) ),
inference(clausify,[status(thm)],[f_535_2]) ).
fof(f_536_1,plain,
! [V_x] : hAPP(c_Transcendental_Oln,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x)) = V_x,
inference(fof_nnf,[status(thm)],[fact_ln__exp]) ).
fof(f_536_2,plain,
! [U_1600] : hAPP(c_Transcendental_Oln,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1600)) = U_1600,
inference(variable_rename,[status(thm)],[f_536_1]) ).
cnf(f_536_3,plain,
hAPP(c_Transcendental_Oln,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1600)) = U_1600,
inference(clausify,[status(thm)],[f_536_2]) ).
fof(f_537_1,plain,
! [V_x,V_u] :
( hAPP(c_Transcendental_Oln,V_x) = V_u
| hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_u) != V_x ),
inference(fof_nnf,[status(thm)],[fact_exp__ln__eq]) ).
fof(f_537_2,plain,
! [U_1602,U_1601] :
( hAPP(c_Transcendental_Oln,U_1602) = U_1601
| hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1601) != U_1602 ),
inference(variable_rename,[status(thm)],[f_537_1]) ).
cnf(f_537_3,plain,
( hAPP(c_Transcendental_Oln,U_1602) = U_1601
| hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1601) != U_1602 ),
inference(clausify,[status(thm)],[f_537_2]) ).
fof(f_538_1,plain,
! [V_x,V_y] :
( hAPP(c_Transcendental_Oln,V_x) = V_y
| hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_y) != V_x ),
inference(fof_nnf,[status(thm)],[fact_ln__unique]) ).
fof(f_538_2,plain,
! [U_1604,U_1603] :
( hAPP(c_Transcendental_Oln,U_1604) = U_1603
| hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1603) != U_1604 ),
inference(variable_rename,[status(thm)],[f_538_1]) ).
cnf(f_538_3,plain,
( hAPP(c_Transcendental_Oln,U_1604) = U_1603
| hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1603) != U_1604 ),
inference(clausify,[status(thm)],[f_538_2]) ).
fof(f_539_1,plain,
! [V_x,T_a] :
( hAPP(c_Transcendental_Oexp(T_a),V_x) != c_Groups_Ozero__class_Ozero(T_a)
| ~ class_SEQ_Obanach(T_a)
| ~ class_RealVector_Oreal__normed__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_exp__not__eq__zero]) ).
fof(f_539_2,plain,
! [U_1606,U_1605] :
( hAPP(c_Transcendental_Oexp(U_1605),U_1606) != c_Groups_Ozero__class_Ozero(U_1605)
| ~ class_SEQ_Obanach(U_1605)
| ~ class_RealVector_Oreal__normed__field(U_1605) ),
inference(variable_rename,[status(thm)],[f_539_1]) ).
cnf(f_539_3,plain,
( hAPP(c_Transcendental_Oexp(U_1605),U_1606) != c_Groups_Ozero__class_Ozero(U_1605)
| ~ class_SEQ_Obanach(U_1605)
| ~ class_RealVector_Oreal__normed__field(U_1605) ),
inference(clausify,[status(thm)],[f_539_2]) ).
fof(f_540_1,plain,
! [V_x_2,T_a] :
( c_Deriv_Oderiv(T_a,c_Transcendental_Oexp(T_a),V_x_2,hAPP(c_Transcendental_Oexp(T_a),V_x_2))
| ~ class_SEQ_Obanach(T_a)
| ~ class_RealVector_Oreal__normed__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_DERIV__exp]) ).
fof(f_540_2,plain,
! [U_1608,U_1607] :
( c_Deriv_Oderiv(U_1607,c_Transcendental_Oexp(U_1607),U_1608,hAPP(c_Transcendental_Oexp(U_1607),U_1608))
| ~ class_SEQ_Obanach(U_1607)
| ~ class_RealVector_Oreal__normed__field(U_1607) ),
inference(variable_rename,[status(thm)],[f_540_1]) ).
cnf(f_540_3,plain,
( c_Deriv_Oderiv(U_1607,c_Transcendental_Oexp(U_1607),U_1608,hAPP(c_Transcendental_Oexp(U_1607),U_1608))
| ~ class_SEQ_Obanach(U_1607)
| ~ class_RealVector_Oreal__normed__field(U_1607) ),
inference(clausify,[status(thm)],[f_540_2]) ).
fof(f_541_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_541_2,plain,
! [U_1610,U_1609] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1609,c_Groups_Ouminus__class_Ouminus(U_1609,U_1610),U_1610)
| ~ c_Orderings_Oord__class_Oless__eq(U_1609,c_Groups_Ozero__class_Ozero(U_1609),U_1610) )
& ( c_Orderings_Oord__class_Oless__eq(U_1609,c_Groups_Ozero__class_Ozero(U_1609),U_1610)
| ~ c_Orderings_Oord__class_Oless__eq(U_1609,c_Groups_Ouminus__class_Ouminus(U_1609,U_1610),U_1610) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1609) ),
inference(variable_rename,[status(thm)],[f_541_1]) ).
cnf(f_541_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1609,c_Groups_Ozero__class_Ozero(U_1609),U_1610)
| ~ c_Orderings_Oord__class_Oless__eq(U_1609,c_Groups_Ouminus__class_Ouminus(U_1609,U_1610),U_1610)
| ~ class_Groups_Olinordered__ab__group__add(U_1609) ),
inference(clausify,[status(thm)],[f_541_2]) ).
cnf(f_541_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1609,c_Groups_Ouminus__class_Ouminus(U_1609,U_1610),U_1610)
| ~ c_Orderings_Oord__class_Oless__eq(U_1609,c_Groups_Ozero__class_Ozero(U_1609),U_1610)
| ~ class_Groups_Olinordered__ab__group__add(U_1609) ),
inference(clausify,[status(thm)],[f_541_2]) ).
fof(f_542_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_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_542_2,plain,
! [U_1612,U_1611] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1611,c_Groups_Ouminus__class_Ouminus(U_1611,U_1612),c_Groups_Ozero__class_Ozero(U_1611))
| ~ c_Orderings_Oord__class_Oless__eq(U_1611,c_Groups_Ozero__class_Ozero(U_1611),U_1612) )
& ( c_Orderings_Oord__class_Oless__eq(U_1611,c_Groups_Ozero__class_Ozero(U_1611),U_1612)
| ~ c_Orderings_Oord__class_Oless__eq(U_1611,c_Groups_Ouminus__class_Ouminus(U_1611,U_1612),c_Groups_Ozero__class_Ozero(U_1611)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1611) ),
inference(variable_rename,[status(thm)],[f_542_1]) ).
cnf(f_542_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1611,c_Groups_Ozero__class_Ozero(U_1611),U_1612)
| ~ c_Orderings_Oord__class_Oless__eq(U_1611,c_Groups_Ouminus__class_Ouminus(U_1611,U_1612),c_Groups_Ozero__class_Ozero(U_1611))
| ~ class_Groups_Oordered__ab__group__add(U_1611) ),
inference(clausify,[status(thm)],[f_542_2]) ).
cnf(f_542_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1611,c_Groups_Ouminus__class_Ouminus(U_1611,U_1612),c_Groups_Ozero__class_Ozero(U_1611))
| ~ c_Orderings_Oord__class_Oless__eq(U_1611,c_Groups_Ozero__class_Ozero(U_1611),U_1612)
| ~ class_Groups_Oordered__ab__group__add(U_1611) ),
inference(clausify,[status(thm)],[f_542_2]) ).
fof(f_543_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,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_543_2,plain,
! [U_1614,U_1613] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1613,U_1614,c_Groups_Ouminus__class_Ouminus(U_1613,U_1614))
| ~ c_Orderings_Oord__class_Oless__eq(U_1613,U_1614,c_Groups_Ozero__class_Ozero(U_1613)) )
& ( c_Orderings_Oord__class_Oless__eq(U_1613,U_1614,c_Groups_Ozero__class_Ozero(U_1613))
| ~ c_Orderings_Oord__class_Oless__eq(U_1613,U_1614,c_Groups_Ouminus__class_Ouminus(U_1613,U_1614)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1613) ),
inference(variable_rename,[status(thm)],[f_543_1]) ).
cnf(f_543_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1613,U_1614,c_Groups_Ozero__class_Ozero(U_1613))
| ~ c_Orderings_Oord__class_Oless__eq(U_1613,U_1614,c_Groups_Ouminus__class_Ouminus(U_1613,U_1614))
| ~ class_Groups_Olinordered__ab__group__add(U_1613) ),
inference(clausify,[status(thm)],[f_543_2]) ).
cnf(f_543_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1613,U_1614,c_Groups_Ouminus__class_Ouminus(U_1613,U_1614))
| ~ c_Orderings_Oord__class_Oless__eq(U_1613,U_1614,c_Groups_Ozero__class_Ozero(U_1613))
| ~ class_Groups_Olinordered__ab__group__add(U_1613) ),
inference(clausify,[status(thm)],[f_543_2]) ).
fof(f_544_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_544_2,plain,
! [U_1616,U_1615] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1615,c_Groups_Ozero__class_Ozero(U_1615),c_Groups_Ouminus__class_Ouminus(U_1615,U_1616))
| ~ c_Orderings_Oord__class_Oless__eq(U_1615,U_1616,c_Groups_Ozero__class_Ozero(U_1615)) )
& ( c_Orderings_Oord__class_Oless__eq(U_1615,U_1616,c_Groups_Ozero__class_Ozero(U_1615))
| ~ c_Orderings_Oord__class_Oless__eq(U_1615,c_Groups_Ozero__class_Ozero(U_1615),c_Groups_Ouminus__class_Ouminus(U_1615,U_1616)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1615) ),
inference(variable_rename,[status(thm)],[f_544_1]) ).
cnf(f_544_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_1615,U_1616,c_Groups_Ozero__class_Ozero(U_1615))
| ~ c_Orderings_Oord__class_Oless__eq(U_1615,c_Groups_Ozero__class_Ozero(U_1615),c_Groups_Ouminus__class_Ouminus(U_1615,U_1616))
| ~ class_Groups_Oordered__ab__group__add(U_1615) ),
inference(clausify,[status(thm)],[f_544_2]) ).
cnf(f_544_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1615,c_Groups_Ozero__class_Ozero(U_1615),c_Groups_Ouminus__class_Ouminus(U_1615,U_1616))
| ~ c_Orderings_Oord__class_Oless__eq(U_1615,U_1616,c_Groups_Ozero__class_Ozero(U_1615))
| ~ class_Groups_Oordered__ab__group__add(U_1615) ),
inference(clausify,[status(thm)],[f_544_2]) ).
fof(f_545_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_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_545_2,plain,
! [U_1618,U_1617] :
( ( ( c_Orderings_Oord__class_Oless(U_1617,c_Groups_Ouminus__class_Ouminus(U_1617,U_1618),U_1618)
| ~ c_Orderings_Oord__class_Oless(U_1617,c_Groups_Ozero__class_Ozero(U_1617),U_1618) )
& ( c_Orderings_Oord__class_Oless(U_1617,c_Groups_Ozero__class_Ozero(U_1617),U_1618)
| ~ c_Orderings_Oord__class_Oless(U_1617,c_Groups_Ouminus__class_Ouminus(U_1617,U_1618),U_1618) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1617) ),
inference(variable_rename,[status(thm)],[f_545_1]) ).
cnf(f_545_3,plain,
( c_Orderings_Oord__class_Oless(U_1617,c_Groups_Ozero__class_Ozero(U_1617),U_1618)
| ~ c_Orderings_Oord__class_Oless(U_1617,c_Groups_Ouminus__class_Ouminus(U_1617,U_1618),U_1618)
| ~ class_Groups_Olinordered__ab__group__add(U_1617) ),
inference(clausify,[status(thm)],[f_545_2]) ).
cnf(f_545_4,plain,
( c_Orderings_Oord__class_Oless(U_1617,c_Groups_Ouminus__class_Ouminus(U_1617,U_1618),U_1618)
| ~ c_Orderings_Oord__class_Oless(U_1617,c_Groups_Ozero__class_Ozero(U_1617),U_1618)
| ~ class_Groups_Olinordered__ab__group__add(U_1617) ),
inference(clausify,[status(thm)],[f_545_2]) ).
fof(f_546_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_546_2,plain,
! [U_1620,U_1619] :
( ( ( c_Orderings_Oord__class_Oless(U_1619,c_Groups_Ouminus__class_Ouminus(U_1619,U_1620),c_Groups_Ozero__class_Ozero(U_1619))
| ~ c_Orderings_Oord__class_Oless(U_1619,c_Groups_Ozero__class_Ozero(U_1619),U_1620) )
& ( c_Orderings_Oord__class_Oless(U_1619,c_Groups_Ozero__class_Ozero(U_1619),U_1620)
| ~ c_Orderings_Oord__class_Oless(U_1619,c_Groups_Ouminus__class_Ouminus(U_1619,U_1620),c_Groups_Ozero__class_Ozero(U_1619)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1619) ),
inference(variable_rename,[status(thm)],[f_546_1]) ).
cnf(f_546_3,plain,
( c_Orderings_Oord__class_Oless(U_1619,c_Groups_Ozero__class_Ozero(U_1619),U_1620)
| ~ c_Orderings_Oord__class_Oless(U_1619,c_Groups_Ouminus__class_Ouminus(U_1619,U_1620),c_Groups_Ozero__class_Ozero(U_1619))
| ~ class_Groups_Oordered__ab__group__add(U_1619) ),
inference(clausify,[status(thm)],[f_546_2]) ).
cnf(f_546_4,plain,
( c_Orderings_Oord__class_Oless(U_1619,c_Groups_Ouminus__class_Ouminus(U_1619,U_1620),c_Groups_Ozero__class_Ozero(U_1619))
| ~ c_Orderings_Oord__class_Oless(U_1619,c_Groups_Ozero__class_Ozero(U_1619),U_1620)
| ~ class_Groups_Oordered__ab__group__add(U_1619) ),
inference(clausify,[status(thm)],[f_546_2]) ).
fof(f_547_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_547_2,plain,
! [U_1622,U_1621] :
( ( ( c_Orderings_Oord__class_Oless(U_1621,c_Groups_Ozero__class_Ozero(U_1621),c_Groups_Ouminus__class_Ouminus(U_1621,U_1622))
| ~ c_Orderings_Oord__class_Oless(U_1621,U_1622,c_Groups_Ozero__class_Ozero(U_1621)) )
& ( c_Orderings_Oord__class_Oless(U_1621,U_1622,c_Groups_Ozero__class_Ozero(U_1621))
| ~ c_Orderings_Oord__class_Oless(U_1621,c_Groups_Ozero__class_Ozero(U_1621),c_Groups_Ouminus__class_Ouminus(U_1621,U_1622)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1621) ),
inference(variable_rename,[status(thm)],[f_547_1]) ).
cnf(f_547_3,plain,
( c_Orderings_Oord__class_Oless(U_1621,U_1622,c_Groups_Ozero__class_Ozero(U_1621))
| ~ c_Orderings_Oord__class_Oless(U_1621,c_Groups_Ozero__class_Ozero(U_1621),c_Groups_Ouminus__class_Ouminus(U_1621,U_1622))
| ~ class_Groups_Oordered__ab__group__add(U_1621) ),
inference(clausify,[status(thm)],[f_547_2]) ).
cnf(f_547_4,plain,
( c_Orderings_Oord__class_Oless(U_1621,c_Groups_Ozero__class_Ozero(U_1621),c_Groups_Ouminus__class_Ouminus(U_1621,U_1622))
| ~ c_Orderings_Oord__class_Oless(U_1621,U_1622,c_Groups_Ozero__class_Ozero(U_1621))
| ~ class_Groups_Oordered__ab__group__add(U_1621) ),
inference(clausify,[status(thm)],[f_547_2]) ).
fof(f_548_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_548_2,plain,
! [U_1624,U_1623] :
( ( ( c_Orderings_Oord__class_Oless(U_1623,U_1624,c_Groups_Ouminus__class_Ouminus(U_1623,U_1624))
| ~ c_Orderings_Oord__class_Oless(U_1623,U_1624,c_Groups_Ozero__class_Ozero(U_1623)) )
& ( c_Orderings_Oord__class_Oless(U_1623,U_1624,c_Groups_Ozero__class_Ozero(U_1623))
| ~ c_Orderings_Oord__class_Oless(U_1623,U_1624,c_Groups_Ouminus__class_Ouminus(U_1623,U_1624)) ) )
| ~ class_Rings_Olinordered__idom(U_1623) ),
inference(variable_rename,[status(thm)],[f_548_1]) ).
cnf(f_548_3,plain,
( c_Orderings_Oord__class_Oless(U_1623,U_1624,c_Groups_Ozero__class_Ozero(U_1623))
| ~ c_Orderings_Oord__class_Oless(U_1623,U_1624,c_Groups_Ouminus__class_Ouminus(U_1623,U_1624))
| ~ class_Rings_Olinordered__idom(U_1623) ),
inference(clausify,[status(thm)],[f_548_2]) ).
cnf(f_548_4,plain,
( c_Orderings_Oord__class_Oless(U_1623,U_1624,c_Groups_Ouminus__class_Ouminus(U_1623,U_1624))
| ~ c_Orderings_Oord__class_Oless(U_1623,U_1624,c_Groups_Ozero__class_Ozero(U_1623))
| ~ class_Rings_Olinordered__idom(U_1623) ),
inference(clausify,[status(thm)],[f_548_2]) ).
fof(f_549_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_549_2,plain,
! [U_1627,U_1626,U_1625] :
( ( ( c_Groups_Oplus__class_Oplus(U_1625,U_1626,U_1627) = c_Groups_Ozero__class_Ozero(U_1625)
| U_1627 != c_Groups_Ouminus__class_Ouminus(U_1625,U_1626) )
& ( U_1627 = c_Groups_Ouminus__class_Ouminus(U_1625,U_1626)
| c_Groups_Oplus__class_Oplus(U_1625,U_1626,U_1627) != c_Groups_Ozero__class_Ozero(U_1625) ) )
| ~ class_Groups_Ogroup__add(U_1625) ),
inference(variable_rename,[status(thm)],[f_549_1]) ).
cnf(f_549_3,plain,
( U_1627 = c_Groups_Ouminus__class_Ouminus(U_1625,U_1626)
| c_Groups_Oplus__class_Oplus(U_1625,U_1626,U_1627) != c_Groups_Ozero__class_Ozero(U_1625)
| ~ class_Groups_Ogroup__add(U_1625) ),
inference(clausify,[status(thm)],[f_549_2]) ).
cnf(f_549_4,plain,
( c_Groups_Oplus__class_Oplus(U_1625,U_1626,U_1627) = c_Groups_Ozero__class_Ozero(U_1625)
| U_1627 != c_Groups_Ouminus__class_Ouminus(U_1625,U_1626)
| ~ class_Groups_Ogroup__add(U_1625) ),
inference(clausify,[status(thm)],[f_549_2]) ).
fof(f_550_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_550_2,plain,
! [U_1629,U_1628] :
( c_Groups_Oplus__class_Oplus(U_1628,U_1629,c_Groups_Ouminus__class_Ouminus(U_1628,U_1629)) = c_Groups_Ozero__class_Ozero(U_1628)
| ~ class_Groups_Ogroup__add(U_1628) ),
inference(variable_rename,[status(thm)],[f_550_1]) ).
cnf(f_550_3,plain,
( c_Groups_Oplus__class_Oplus(U_1628,U_1629,c_Groups_Ouminus__class_Ouminus(U_1628,U_1629)) = c_Groups_Ozero__class_Ozero(U_1628)
| ~ class_Groups_Ogroup__add(U_1628) ),
inference(clausify,[status(thm)],[f_550_2]) ).
fof(f_551_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_551_2,plain,
! [U_1632,U_1631,U_1630] :
( ( ( U_1631 = c_Groups_Ouminus__class_Ouminus(U_1630,U_1632)
| c_Groups_Oplus__class_Oplus(U_1630,U_1631,U_1632) != c_Groups_Ozero__class_Ozero(U_1630) )
& ( c_Groups_Oplus__class_Oplus(U_1630,U_1631,U_1632) = c_Groups_Ozero__class_Ozero(U_1630)
| U_1631 != c_Groups_Ouminus__class_Ouminus(U_1630,U_1632) ) )
| ~ class_Groups_Ogroup__add(U_1630) ),
inference(variable_rename,[status(thm)],[f_551_1]) ).
cnf(f_551_3,plain,
( c_Groups_Oplus__class_Oplus(U_1630,U_1631,U_1632) = c_Groups_Ozero__class_Ozero(U_1630)
| U_1631 != c_Groups_Ouminus__class_Ouminus(U_1630,U_1632)
| ~ class_Groups_Ogroup__add(U_1630) ),
inference(clausify,[status(thm)],[f_551_2]) ).
cnf(f_551_4,plain,
( U_1631 = c_Groups_Ouminus__class_Ouminus(U_1630,U_1632)
| c_Groups_Oplus__class_Oplus(U_1630,U_1631,U_1632) != c_Groups_Ozero__class_Ozero(U_1630)
| ~ class_Groups_Ogroup__add(U_1630) ),
inference(clausify,[status(thm)],[f_551_2]) ).
fof(f_552_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_552_2,plain,
! [U_1634,U_1633] :
( c_Groups_Oplus__class_Oplus(U_1633,c_Groups_Ouminus__class_Ouminus(U_1633,U_1634),U_1634) = c_Groups_Ozero__class_Ozero(U_1633)
| ~ class_Groups_Ogroup__add(U_1633) ),
inference(variable_rename,[status(thm)],[f_552_1]) ).
cnf(f_552_3,plain,
( c_Groups_Oplus__class_Oplus(U_1633,c_Groups_Ouminus__class_Ouminus(U_1633,U_1634),U_1634) = c_Groups_Ozero__class_Ozero(U_1633)
| ~ class_Groups_Ogroup__add(U_1633) ),
inference(clausify,[status(thm)],[f_552_2]) ).
fof(f_553_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_553_2,plain,
! [U_1636,U_1635] :
( c_Groups_Oplus__class_Oplus(U_1635,c_Groups_Ouminus__class_Ouminus(U_1635,U_1636),U_1636) = c_Groups_Ozero__class_Ozero(U_1635)
| ~ class_Groups_Oab__group__add(U_1635) ),
inference(variable_rename,[status(thm)],[f_553_1]) ).
cnf(f_553_3,plain,
( c_Groups_Oplus__class_Oplus(U_1635,c_Groups_Ouminus__class_Ouminus(U_1635,U_1636),U_1636) = c_Groups_Ozero__class_Ozero(U_1635)
| ~ class_Groups_Oab__group__add(U_1635) ),
inference(clausify,[status(thm)],[f_553_2]) ).
fof(f_554_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_554_2,plain,
! [U_1639,U_1638,U_1637] :
( c_Groups_Ouminus__class_Ouminus(U_1637,U_1638) = U_1639
| c_Groups_Oplus__class_Oplus(U_1637,U_1638,U_1639) != c_Groups_Ozero__class_Ozero(U_1637)
| ~ class_Groups_Ogroup__add(U_1637) ),
inference(variable_rename,[status(thm)],[f_554_1]) ).
cnf(f_554_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_1637,U_1638) = U_1639
| c_Groups_Oplus__class_Oplus(U_1637,U_1638,U_1639) != c_Groups_Ozero__class_Ozero(U_1637)
| ~ class_Groups_Ogroup__add(U_1637) ),
inference(clausify,[status(thm)],[f_554_2]) ).
fof(f_555_1,plain,
! [V_x,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = 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_555_2,plain,
! [U_1641,U_1640] :
( c_Groups_Ouminus__class_Ouminus(U_1640,U_1641) = hAPP(c_Groups_Otimes__class_Otimes(U_1640,c_Groups_Ouminus__class_Ouminus(U_1640,c_Groups_Oone__class_Oone(U_1640))),U_1641)
| ~ class_Rings_Ocomm__ring__1(U_1640) ),
inference(variable_rename,[status(thm)],[f_555_1]) ).
cnf(f_555_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_1640,U_1641) = hAPP(c_Groups_Otimes__class_Otimes(U_1640,c_Groups_Ouminus__class_Ouminus(U_1640,c_Groups_Oone__class_Oone(U_1640))),U_1641)
| ~ class_Rings_Ocomm__ring__1(U_1640) ),
inference(clausify,[status(thm)],[f_555_2]) ).
fof(f_556_1,plain,
! [V_x_2,T_a] :
( ( ( 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(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_556_2,plain,
! [U_1643,U_1642] :
( ( ( hAPP(c_Groups_Otimes__class_Otimes(U_1642,U_1643),U_1643) = c_Groups_Oone__class_Oone(U_1642)
| ( U_1643 != c_Groups_Ouminus__class_Ouminus(U_1642,c_Groups_Oone__class_Oone(U_1642))
& U_1643 != c_Groups_Oone__class_Oone(U_1642) ) )
& ( U_1643 = c_Groups_Ouminus__class_Ouminus(U_1642,c_Groups_Oone__class_Oone(U_1642))
| U_1643 = c_Groups_Oone__class_Oone(U_1642)
| hAPP(c_Groups_Otimes__class_Otimes(U_1642,U_1643),U_1643) != c_Groups_Oone__class_Oone(U_1642) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(U_1642) ),
inference(variable_rename,[status(thm)],[f_556_1]) ).
cnf(f_556_3,plain,
( U_1643 = c_Groups_Ouminus__class_Ouminus(U_1642,c_Groups_Oone__class_Oone(U_1642))
| U_1643 = c_Groups_Oone__class_Oone(U_1642)
| hAPP(c_Groups_Otimes__class_Otimes(U_1642,U_1643),U_1643) != c_Groups_Oone__class_Oone(U_1642)
| ~ class_Rings_Oring__1__no__zero__divisors(U_1642) ),
inference(clausify,[status(thm)],[f_556_2]) ).
cnf(f_556_4,plain,
( U_1643 != c_Groups_Oone__class_Oone(U_1642)
| hAPP(c_Groups_Otimes__class_Otimes(U_1642,U_1643),U_1643) = c_Groups_Oone__class_Oone(U_1642)
| ~ class_Rings_Oring__1__no__zero__divisors(U_1642) ),
inference(clausify,[status(thm)],[f_556_2]) ).
cnf(f_556_5,plain,
( U_1643 != c_Groups_Ouminus__class_Ouminus(U_1642,c_Groups_Oone__class_Oone(U_1642))
| hAPP(c_Groups_Otimes__class_Otimes(U_1642,U_1643),U_1643) = c_Groups_Oone__class_Oone(U_1642)
| ~ class_Rings_Oring__1__no__zero__divisors(U_1642) ),
inference(clausify,[status(thm)],[f_556_2]) ).
fof(f_557_1,plain,
! [V_a,V_b,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__divide]) ).
fof(f_557_2,plain,
! [U_1646,U_1645,U_1644] :
( c_Rings_Oinverse__class_Odivide(U_1644,c_Groups_Ouminus__class_Ouminus(U_1644,U_1646),c_Groups_Ouminus__class_Ouminus(U_1644,U_1645)) = c_Rings_Oinverse__class_Odivide(U_1644,U_1646,U_1645)
| U_1645 = c_Groups_Ozero__class_Ozero(U_1644)
| ~ class_Rings_Odivision__ring(U_1644) ),
inference(variable_rename,[status(thm)],[f_557_1]) ).
cnf(f_557_3,plain,
( c_Rings_Oinverse__class_Odivide(U_1644,c_Groups_Ouminus__class_Ouminus(U_1644,U_1646),c_Groups_Ouminus__class_Ouminus(U_1644,U_1645)) = c_Rings_Oinverse__class_Odivide(U_1644,U_1646,U_1645)
| U_1645 = c_Groups_Ozero__class_Ozero(U_1644)
| ~ class_Rings_Odivision__ring(U_1644) ),
inference(clausify,[status(thm)],[f_557_2]) ).
fof(f_558_1,plain,
! [V_a,V_b,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)) = c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__right]) ).
fof(f_558_2,plain,
! [U_1649,U_1648,U_1647] :
( c_Groups_Ouminus__class_Ouminus(U_1647,c_Rings_Oinverse__class_Odivide(U_1647,U_1649,U_1648)) = c_Rings_Oinverse__class_Odivide(U_1647,U_1649,c_Groups_Ouminus__class_Ouminus(U_1647,U_1648))
| U_1648 = c_Groups_Ozero__class_Ozero(U_1647)
| ~ class_Rings_Odivision__ring(U_1647) ),
inference(variable_rename,[status(thm)],[f_558_1]) ).
cnf(f_558_3,plain,
( c_Groups_Ouminus__class_Ouminus(U_1647,c_Rings_Oinverse__class_Odivide(U_1647,U_1649,U_1648)) = c_Rings_Oinverse__class_Odivide(U_1647,U_1649,c_Groups_Ouminus__class_Ouminus(U_1647,U_1648))
| U_1648 = c_Groups_Ozero__class_Ozero(U_1647)
| ~ class_Rings_Odivision__ring(U_1647) ),
inference(clausify,[status(thm)],[f_558_2]) ).
fof(f_559_1,plain,
! [V_a,T_a] :
( c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__minus__eq]) ).
fof(f_559_2,plain,
! [U_1651,U_1650] :
( c_Rings_Oinverse__class_Oinverse(U_1650,c_Groups_Ouminus__class_Ouminus(U_1650,U_1651)) = c_Groups_Ouminus__class_Ouminus(U_1650,c_Rings_Oinverse__class_Oinverse(U_1650,U_1651))
| U_1651 = c_Groups_Ozero__class_Ozero(U_1650)
| ~ class_Rings_Odivision__ring(U_1650) ),
inference(variable_rename,[status(thm)],[f_559_1]) ).
cnf(f_559_3,plain,
( c_Rings_Oinverse__class_Oinverse(U_1650,c_Groups_Ouminus__class_Ouminus(U_1650,U_1651)) = c_Groups_Ouminus__class_Ouminus(U_1650,c_Rings_Oinverse__class_Oinverse(U_1650,U_1651))
| U_1651 = c_Groups_Ozero__class_Ozero(U_1650)
| ~ class_Rings_Odivision__ring(U_1650) ),
inference(clausify,[status(thm)],[f_559_2]) ).
fof(f_560_1,plain,
! [V_x,V_u] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_u),V_u)),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_560_2,plain,
! [U_1653,U_1652] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1652),U_1652)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1653),U_1653)),
inference(variable_rename,[status(thm)],[f_560_1]) ).
cnf(f_560_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1652),U_1652)),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_1653),U_1653)),
inference(clausify,[status(thm)],[f_560_2]) ).
fof(f_561_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_561_2,plain,
! [U_1655,U_1654] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1654,U_1655) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1655 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1654) )
& ( U_1655 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1654)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1654,U_1655) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_561_1]) ).
fof(f_561_3,plain,
( ! [U_1659,U_1657] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1657,U_1659) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1659 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1657) )
& ! [U_1658,U_1656] :
( U_1658 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1656)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1656,U_1658) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_561_2]) ).
cnf(f_561_4,plain,
( U_1658 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1656)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1656,U_1658) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_561_3]) ).
cnf(f_561_5,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1657,U_1659) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1659 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1657) ),
inference(clausify,[status(thm)],[f_561_3]) ).
fof(f_562_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_562_2,plain,
! [U_1661,U_1660] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1660,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1661)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1660 != U_1661 )
& ( U_1660 = U_1661
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1660,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1661)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_562_1]) ).
fof(f_562_3,plain,
( ! [U_1665,U_1663] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1663,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1665)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1663 != U_1665 )
& ! [U_1664,U_1662] :
( U_1662 = U_1664
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1662,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1664)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_562_2]) ).
cnf(f_562_4,plain,
( U_1662 = U_1664
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1662,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1664)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_562_3]) ).
cnf(f_562_5,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1663,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1665)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1663 != U_1665 ),
inference(clausify,[status(thm)],[f_562_3]) ).
fof(f_563_1,plain,
! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x)),
inference(fof_nnf,[status(thm)],[fact_exp__ge__zero]) ).
fof(f_563_2,plain,
! [U_1666] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1666)),
inference(variable_rename,[status(thm)],[f_563_1]) ).
cnf(f_563_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1666)),
inference(clausify,[status(thm)],[f_563_2]) ).
fof(f_564_1,plain,
! [V_x] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact_not__exp__le__zero]) ).
fof(f_564_2,plain,
! [U_1667] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1667),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[f_564_1]) ).
cnf(f_564_3,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1667),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_564_2]) ).
fof(f_565_1,plain,
! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x)),
inference(fof_nnf,[status(thm)],[fact_exp__gt__zero]) ).
fof(f_565_2,plain,
! [U_1668] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1668)),
inference(variable_rename,[status(thm)],[f_565_1]) ).
cnf(f_565_3,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1668)),
inference(clausify,[status(thm)],[f_565_2]) ).
fof(f_566_1,plain,
! [V_x] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact_not__exp__less__zero]) ).
fof(f_566_2,plain,
! [U_1669] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1669),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[f_566_1]) ).
cnf(f_566_3,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1669),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_566_2]) ).
fof(f_567_1,plain,
! [V_x_2] :
( ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_exp__eq__one__iff]) ).
fof(f_567_2,plain,
! [U_1670] :
( ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1670) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_1670 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( U_1670 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1670) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_567_1]) ).
fof(f_567_3,plain,
( ! [U_1672] :
( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1672) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_1672 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_1671] :
( U_1671 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1671) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_567_2]) ).
cnf(f_567_4,plain,
( U_1671 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1671) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_567_3]) ).
cnf(f_567_5,plain,
( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1672) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_1672 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_567_3]) ).
fof(f_568_1,plain,
! [T_a] :
( hAPP(c_Transcendental_Oexp(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Oone__class_Oone(T_a)
| ~ class_SEQ_Obanach(T_a)
| ~ class_RealVector_Oreal__normed__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_exp__zero]) ).
fof(f_568_2,plain,
! [U_1673] :
( hAPP(c_Transcendental_Oexp(U_1673),c_Groups_Ozero__class_Ozero(U_1673)) = c_Groups_Oone__class_Oone(U_1673)
| ~ class_SEQ_Obanach(U_1673)
| ~ class_RealVector_Oreal__normed__field(U_1673) ),
inference(variable_rename,[status(thm)],[f_568_1]) ).
cnf(f_568_3,plain,
( hAPP(c_Transcendental_Oexp(U_1673),c_Groups_Ozero__class_Ozero(U_1673)) = c_Groups_Oone__class_Oone(U_1673)
| ~ class_SEQ_Obanach(U_1673)
| ~ class_RealVector_Oreal__normed__field(U_1673) ),
inference(clausify,[status(thm)],[f_568_2]) ).
fof(f_569_1,plain,
! [V_y,V_x,T_a] :
( hAPP(c_Transcendental_Oexp(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Transcendental_Oexp(T_a),V_x)),hAPP(c_Transcendental_Oexp(T_a),V_y))
| ~ class_SEQ_Obanach(T_a)
| ~ class_RealVector_Oreal__normed__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_exp__add]) ).
fof(f_569_2,plain,
! [U_1676,U_1675,U_1674] :
( hAPP(c_Transcendental_Oexp(U_1674),c_Groups_Oplus__class_Oplus(U_1674,U_1675,U_1676)) = hAPP(c_Groups_Otimes__class_Otimes(U_1674,hAPP(c_Transcendental_Oexp(U_1674),U_1675)),hAPP(c_Transcendental_Oexp(U_1674),U_1676))
| ~ class_SEQ_Obanach(U_1674)
| ~ class_RealVector_Oreal__normed__field(U_1674) ),
inference(variable_rename,[status(thm)],[f_569_1]) ).
cnf(f_569_3,plain,
( hAPP(c_Transcendental_Oexp(U_1674),c_Groups_Oplus__class_Oplus(U_1674,U_1675,U_1676)) = hAPP(c_Groups_Otimes__class_Otimes(U_1674,hAPP(c_Transcendental_Oexp(U_1674),U_1675)),hAPP(c_Transcendental_Oexp(U_1674),U_1676))
| ~ class_SEQ_Obanach(U_1674)
| ~ class_RealVector_Oreal__normed__field(U_1674) ),
inference(clausify,[status(thm)],[f_569_2]) ).
fof(f_570_1,plain,
! [V_y,V_x,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Transcendental_Oexp(T_a),V_x)),hAPP(c_Transcendental_Oexp(T_a),V_y)) = hAPP(c_Transcendental_Oexp(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y))
| ~ class_SEQ_Obanach(T_a)
| ~ class_RealVector_Oreal__normed__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__exp__exp]) ).
fof(f_570_2,plain,
! [U_1679,U_1678,U_1677] :
( hAPP(c_Groups_Otimes__class_Otimes(U_1677,hAPP(c_Transcendental_Oexp(U_1677),U_1678)),hAPP(c_Transcendental_Oexp(U_1677),U_1679)) = hAPP(c_Transcendental_Oexp(U_1677),c_Groups_Oplus__class_Oplus(U_1677,U_1678,U_1679))
| ~ class_SEQ_Obanach(U_1677)
| ~ class_RealVector_Oreal__normed__field(U_1677) ),
inference(variable_rename,[status(thm)],[f_570_1]) ).
cnf(f_570_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_1677,hAPP(c_Transcendental_Oexp(U_1677),U_1678)),hAPP(c_Transcendental_Oexp(U_1677),U_1679)) = hAPP(c_Transcendental_Oexp(U_1677),c_Groups_Oplus__class_Oplus(U_1677,U_1678,U_1679))
| ~ class_SEQ_Obanach(U_1677)
| ~ class_RealVector_Oreal__normed__field(U_1677) ),
inference(clausify,[status(thm)],[f_570_2]) ).
fof(f_571_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_571_2,plain,
! [U_1681,U_1680] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1680,U_1681),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1681,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1680)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1681,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1680))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1680,U_1681),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_571_1]) ).
fof(f_571_3,plain,
( ! [U_1685,U_1683] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1683,U_1685),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1685,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1683)) )
& ! [U_1684,U_1682] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1684,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1682))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1682,U_1684),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_571_2]) ).
cnf(f_571_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1684,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1682))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1682,U_1684),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_571_3]) ).
cnf(f_571_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1683,U_1685),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1685,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1683)) ),
inference(clausify,[status(thm)],[f_571_3]) ).
fof(f_572_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_572_2,plain,
! [U_1687,U_1686] :
( ( 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_1686,U_1687))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1686),U_1687) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1686),U_1687)
| ~ 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_1686,U_1687)) ) ),
inference(variable_rename,[status(thm)],[f_572_1]) ).
fof(f_572_3,plain,
( ! [U_1691,U_1689] :
( 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_1689,U_1691))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1689),U_1691) )
& ! [U_1690,U_1688] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1688),U_1690)
| ~ 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_1688,U_1690)) ) ),
inference(miniscope,[status(thm)],[f_572_2]) ).
cnf(f_572_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1688),U_1690)
| ~ 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_1688,U_1690)) ),
inference(clausify,[status(thm)],[f_572_3]) ).
cnf(f_572_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1689,U_1691))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1689),U_1691) ),
inference(clausify,[status(thm)],[f_572_3]) ).
fof(f_573_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_573_2,plain,
! [U_1693,U_1692] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1692,U_1693),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1693,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1692)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1693,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1692))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1692,U_1693),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_573_1]) ).
fof(f_573_3,plain,
( ! [U_1697,U_1695] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1695,U_1697),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1697,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1695)) )
& ! [U_1696,U_1694] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1696,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1694))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1694,U_1696),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_573_2]) ).
cnf(f_573_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1696,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1694))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1694,U_1696),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_573_3]) ).
cnf(f_573_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1695,U_1697),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1697,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1695)) ),
inference(clausify,[status(thm)],[f_573_3]) ).
fof(f_574_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_574_2,plain,
! [U_1699,U_1698] :
( ( 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_1698,U_1699))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1698),U_1699) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1698),U_1699)
| ~ 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_1698,U_1699)) ) ),
inference(variable_rename,[status(thm)],[f_574_1]) ).
fof(f_574_3,plain,
( ! [U_1703,U_1701] :
( 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_1701,U_1703))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1701),U_1703) )
& ! [U_1702,U_1700] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1700),U_1702)
| ~ 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_1700,U_1702)) ) ),
inference(miniscope,[status(thm)],[f_574_2]) ).
cnf(f_574_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1700),U_1702)
| ~ 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_1700,U_1702)) ),
inference(clausify,[status(thm)],[f_574_3]) ).
cnf(f_574_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1701,U_1703))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1701),U_1703) ),
inference(clausify,[status(thm)],[f_574_3]) ).
fof(f_575_1,plain,
! [V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(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_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_exp__le__one__iff]) ).
fof(f_575_2,plain,
! [U_1704] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1704),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1704,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1704,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1704),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_575_1]) ).
fof(f_575_3,plain,
( ! [U_1706] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1706),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1706,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_1705] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1705,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1705),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_575_2]) ).
cnf(f_575_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1705,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1705),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_575_3]) ).
cnf(f_575_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1706),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1706,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_575_3]) ).
fof(f_576_1,plain,
! [V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_one__le__exp__iff]) ).
fof(f_576_2,plain,
! [U_1707] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1707))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1707) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1707)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1707)) ) ),
inference(variable_rename,[status(thm)],[f_576_1]) ).
fof(f_576_3,plain,
( ! [U_1709] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1709))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1709) )
& ! [U_1708] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1708)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1708)) ) ),
inference(miniscope,[status(thm)],[f_576_2]) ).
cnf(f_576_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1708)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1708)) ),
inference(clausify,[status(thm)],[f_576_3]) ).
cnf(f_576_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1709))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1709) ),
inference(clausify,[status(thm)],[f_576_3]) ).
fof(f_577_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_exp__gt__one]) ).
fof(f_577_2,plain,
! [U_1710] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1710))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1710) ),
inference(variable_rename,[status(thm)],[f_577_1]) ).
cnf(f_577_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1710))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1710) ),
inference(clausify,[status(thm)],[f_577_2]) ).
fof(f_578_1,plain,
! [V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_exp__less__one__iff]) ).
fof(f_578_2,plain,
! [U_1711] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1711),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1711,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1711,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1711),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_578_1]) ).
fof(f_578_3,plain,
( ! [U_1713] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1713),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1713,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_1712] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1712,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1712),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_578_2]) ).
cnf(f_578_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1712,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1712),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_578_3]) ).
cnf(f_578_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1713),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1713,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_578_3]) ).
fof(f_579_1,plain,
! [V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_one__less__exp__iff]) ).
fof(f_579_2,plain,
! [U_1714] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1714))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1714) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1714)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1714)) ) ),
inference(variable_rename,[status(thm)],[f_579_1]) ).
fof(f_579_3,plain,
( ! [U_1716] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1716))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1716) )
& ! [U_1715] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1715)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1715)) ) ),
inference(miniscope,[status(thm)],[f_579_2]) ).
cnf(f_579_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1715)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1715)) ),
inference(clausify,[status(thm)],[f_579_3]) ).
cnf(f_579_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),U_1716))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1716) ),
inference(clausify,[status(thm)],[f_579_3]) ).
fof(f_580_1,plain,
! [V_x] :
( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x)) = V_x
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_exp__ln]) ).
fof(f_580_2,plain,
! [U_1717] :
( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1717)) = U_1717
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1717) ),
inference(variable_rename,[status(thm)],[f_580_1]) ).
cnf(f_580_3,plain,
( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1717)) = U_1717
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1717) ),
inference(clausify,[status(thm)],[f_580_2]) ).
fof(f_581_1,plain,
! [V_x_2] :
( ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x_2)) = V_x_2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
| hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,V_x_2)) != V_x_2 ) ),
inference(fof_nnf,[status(thm)],[fact_exp__ln__iff]) ).
fof(f_581_2,plain,
! [U_1718] :
( ( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1718)) = U_1718
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1718) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1718)
| hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1718)) != U_1718 ) ),
inference(variable_rename,[status(thm)],[f_581_1]) ).
fof(f_581_3,plain,
( ! [U_1720] :
( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1720)) = U_1720
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1720) )
& ! [U_1719] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1719)
| hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1719)) != U_1719 ) ),
inference(miniscope,[status(thm)],[f_581_2]) ).
cnf(f_581_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1719)
| hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1719)) != U_1719 ),
inference(clausify,[status(thm)],[f_581_3]) ).
cnf(f_581_5,plain,
( hAPP(c_Transcendental_Oexp(tc_RealDef_Oreal),hAPP(c_Transcendental_Oln,U_1720)) = U_1720
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1720) ),
inference(clausify,[status(thm)],[f_581_3]) ).
fof(f_582_1,plain,
! [V_E_2,V_D_2,V_x_2,V_f_2,T_a] :
( V_D_2 = V_E_2
| ~ c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_E_2)
| ~ c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_D_2)
| ~ class_RealVector_Oreal__normed__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_DERIV__unique]) ).
fof(f_582_2,plain,
! [U_1725,U_1724,U_1723,U_1722,U_1721] :
( U_1724 = U_1725
| ~ c_Deriv_Oderiv(U_1721,U_1722,U_1723,U_1725)
| ~ c_Deriv_Oderiv(U_1721,U_1722,U_1723,U_1724)
| ~ class_RealVector_Oreal__normed__field(U_1721) ),
inference(variable_rename,[status(thm)],[f_582_1]) ).
cnf(f_582_3,plain,
( U_1724 = U_1725
| ~ c_Deriv_Oderiv(U_1721,U_1722,U_1723,U_1725)
| ~ c_Deriv_Oderiv(U_1721,U_1722,U_1723,U_1724)
| ~ class_RealVector_Oreal__normed__field(U_1721) ),
inference(clausify,[status(thm)],[f_582_2]) ).
fof(f_583_1,plain,
! [V_Y_2,V_X_2,V_x_2,V_f_2,T_a] :
( c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_Y_2)
| V_X_2 != V_Y_2
| ~ c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_X_2)
| ~ class_RealVector_Oreal__normed__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_DERIV__cong]) ).
fof(f_583_2,plain,
! [U_1730,U_1729,U_1728,U_1727,U_1726] :
( c_Deriv_Oderiv(U_1726,U_1727,U_1728,U_1730)
| U_1729 != U_1730
| ~ c_Deriv_Oderiv(U_1726,U_1727,U_1728,U_1729)
| ~ class_RealVector_Oreal__normed__field(U_1726) ),
inference(variable_rename,[status(thm)],[f_583_1]) ).
cnf(f_583_3,plain,
( c_Deriv_Oderiv(U_1726,U_1727,U_1728,U_1730)
| U_1729 != U_1730
| ~ c_Deriv_Oderiv(U_1726,U_1727,U_1728,U_1729)
| ~ class_RealVector_Oreal__normed__field(U_1726) ),
inference(clausify,[status(thm)],[f_583_2]) ).
fof(f_584_1,plain,
! [V_E_2,V_D_2,V_x_2,V_f_2,T_a] :
( c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_E_2)
| V_D_2 != V_E_2
| ~ c_Deriv_Oderiv(T_a,V_f_2,V_x_2,V_D_2)
| ~ class_RealVector_Oreal__normed__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Deriv_Olemma__DERIV__subst]) ).
fof(f_584_2,plain,
! [U_1735,U_1734,U_1733,U_1732,U_1731] :
( c_Deriv_Oderiv(U_1731,U_1732,U_1733,U_1735)
| U_1734 != U_1735
| ~ c_Deriv_Oderiv(U_1731,U_1732,U_1733,U_1734)
| ~ class_RealVector_Oreal__normed__field(U_1731) ),
inference(variable_rename,[status(thm)],[f_584_1]) ).
cnf(f_584_3,plain,
( c_Deriv_Oderiv(U_1731,U_1732,U_1733,U_1735)
| U_1734 != U_1735
| ~ c_Deriv_Oderiv(U_1731,U_1732,U_1733,U_1734)
| ~ class_RealVector_Oreal__normed__field(U_1731) ),
inference(clausify,[status(thm)],[f_584_2]) ).
fof(f_585_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_585_2,plain,
! [U_1737,U_1736] :
( ( ( ( ( c_Groups_Osgn__class_Osgn(U_1736,U_1737) = c_Groups_Ouminus__class_Ouminus(U_1736,c_Groups_Oone__class_Oone(U_1736))
| c_Orderings_Oord__class_Oless(U_1736,c_Groups_Ozero__class_Ozero(U_1736),U_1737) )
& ( c_Groups_Osgn__class_Osgn(U_1736,U_1737) = c_Groups_Oone__class_Oone(U_1736)
| ~ c_Orderings_Oord__class_Oless(U_1736,c_Groups_Ozero__class_Ozero(U_1736),U_1737) ) )
| U_1737 = c_Groups_Ozero__class_Ozero(U_1736) )
& ( c_Groups_Osgn__class_Osgn(U_1736,U_1737) = c_Groups_Ozero__class_Ozero(U_1736)
| U_1737 != c_Groups_Ozero__class_Ozero(U_1736) ) )
| ~ class_Groups_Osgn__if(U_1736) ),
inference(variable_rename,[status(thm)],[f_585_1]) ).
cnf(f_585_3,plain,
( c_Groups_Osgn__class_Osgn(U_1736,U_1737) = c_Groups_Ozero__class_Ozero(U_1736)
| U_1737 != c_Groups_Ozero__class_Ozero(U_1736)
| ~ class_Groups_Osgn__if(U_1736) ),
inference(clausify,[status(thm)],[f_585_2]) ).
cnf(f_585_4,plain,
( c_Groups_Osgn__class_Osgn(U_1736,U_1737) = c_Groups_Oone__class_Oone(U_1736)
| ~ c_Orderings_Oord__class_Oless(U_1736,c_Groups_Ozero__class_Ozero(U_1736),U_1737)
| U_1737 = c_Groups_Ozero__class_Ozero(U_1736)
| ~ class_Groups_Osgn__if(U_1736) ),
inference(clausify,[status(thm)],[f_585_2]) ).
cnf(f_585_5,plain,
( c_Groups_Osgn__class_Osgn(U_1736,U_1737) = c_Groups_Ouminus__class_Ouminus(U_1736,c_Groups_Oone__class_Oone(U_1736))
| c_Orderings_Oord__class_Oless(U_1736,c_Groups_Ozero__class_Ozero(U_1736),U_1737)
| U_1737 = c_Groups_Ozero__class_Ozero(U_1736)
| ~ class_Groups_Osgn__if(U_1736) ),
inference(clausify,[status(thm)],[f_585_2]) ).
fof(f_586_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_586_2,plain,
! [U_1739,U_1738] :
( c_Groups_Osgn__class_Osgn(U_1738,U_1739) = c_Groups_Ouminus__class_Ouminus(U_1738,c_Groups_Oone__class_Oone(U_1738))
| ~ c_Orderings_Oord__class_Oless(U_1738,U_1739,c_Groups_Ozero__class_Ozero(U_1738))
| ~ class_Rings_Olinordered__idom(U_1738) ),
inference(variable_rename,[status(thm)],[f_586_1]) ).
cnf(f_586_3,plain,
( c_Groups_Osgn__class_Osgn(U_1738,U_1739) = c_Groups_Ouminus__class_Ouminus(U_1738,c_Groups_Oone__class_Oone(U_1738))
| ~ c_Orderings_Oord__class_Oless(U_1738,U_1739,c_Groups_Ozero__class_Ozero(U_1738))
| ~ class_Rings_Olinordered__idom(U_1738) ),
inference(clausify,[status(thm)],[f_586_2]) ).
fof(f_587_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_587_2,plain,
! [U_1741,U_1740] :
( ( ( c_Groups_Osgn__class_Osgn(U_1740,U_1741) = c_Groups_Ouminus__class_Ouminus(U_1740,c_Groups_Oone__class_Oone(U_1740))
| ~ c_Orderings_Oord__class_Oless(U_1740,U_1741,c_Groups_Ozero__class_Ozero(U_1740)) )
& ( c_Orderings_Oord__class_Oless(U_1740,U_1741,c_Groups_Ozero__class_Ozero(U_1740))
| c_Groups_Osgn__class_Osgn(U_1740,U_1741) != c_Groups_Ouminus__class_Ouminus(U_1740,c_Groups_Oone__class_Oone(U_1740)) ) )
| ~ class_Rings_Olinordered__idom(U_1740) ),
inference(variable_rename,[status(thm)],[f_587_1]) ).
cnf(f_587_3,plain,
( c_Orderings_Oord__class_Oless(U_1740,U_1741,c_Groups_Ozero__class_Ozero(U_1740))
| c_Groups_Osgn__class_Osgn(U_1740,U_1741) != c_Groups_Ouminus__class_Ouminus(U_1740,c_Groups_Oone__class_Oone(U_1740))
| ~ class_Rings_Olinordered__idom(U_1740) ),
inference(clausify,[status(thm)],[f_587_2]) ).
cnf(f_587_4,plain,
( c_Groups_Osgn__class_Osgn(U_1740,U_1741) = c_Groups_Ouminus__class_Ouminus(U_1740,c_Groups_Oone__class_Oone(U_1740))
| ~ c_Orderings_Oord__class_Oless(U_1740,U_1741,c_Groups_Ozero__class_Ozero(U_1740))
| ~ class_Rings_Olinordered__idom(U_1740) ),
inference(clausify,[status(thm)],[f_587_2]) ).
fof(f_588_1,plain,
! [V_x] :
( hAPP(c_Transcendental_Oln,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,V_x))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_ln__inverse]) ).
fof(f_588_2,plain,
! [U_1742] :
( hAPP(c_Transcendental_Oln,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,U_1742)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,U_1742))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1742) ),
inference(variable_rename,[status(thm)],[f_588_1]) ).
cnf(f_588_3,plain,
( hAPP(c_Transcendental_Oln,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,U_1742)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oln,U_1742))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1742) ),
inference(clausify,[status(thm)],[f_588_2]) ).
fof(f_589_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(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(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q),V_r) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,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_589_2,plain,
! [U_1748,U_1747,U_1746,U_1745,U_1744,U_1743] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1747,U_1744)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1746,U_1743)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1746)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1748)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1745,U_1743)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1746),U_1747),U_1748),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1743),U_1744),U_1745) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1746),U_1747),U_1748) ),
inference(variable_rename,[status(thm)],[f_589_1]) ).
cnf(f_589_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1747,U_1744)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1746,U_1743)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1746)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1748)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1745,U_1743)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1746),U_1747),U_1748),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1743),U_1744),U_1745) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1746),U_1747),U_1748) ),
inference(clausify,[status(thm)],[f_589_2]) ).
fof(f_590_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(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(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_590_2,plain,
! [U_1753,U_1752,U_1751,U_1750,U_1749] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1752,U_1750)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1749,U_1751)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1749,U_1753)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1753,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(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1749),U_1750),U_1751),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1749),U_1752),U_1753)) ),
inference(variable_rename,[status(thm)],[f_590_1]) ).
cnf(f_590_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1752,U_1750)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1749,U_1751)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1749,U_1753)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1753,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(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1749),U_1750),U_1751),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1749),U_1752),U_1753)) ),
inference(clausify,[status(thm)],[f_590_2]) ).
fof(f_591_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(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(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_b),V_q),V_r) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,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_591_2,plain,
! [U_1759,U_1758,U_1757,U_1756,U_1755,U_1754] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1755,U_1758)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1757,U_1754)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1757)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1756)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1759,U_1757)
| ~ 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(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1757),U_1758),U_1759))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1754),U_1755),U_1756) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1757),U_1758),U_1759) ),
inference(variable_rename,[status(thm)],[f_591_1]) ).
cnf(f_591_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1755,U_1758)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1757,U_1754)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1757)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1756)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1759,U_1757)
| ~ 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(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1757),U_1758),U_1759))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1754),U_1755),U_1756) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1757),U_1758),U_1759) ),
inference(clausify,[status(thm)],[f_591_2]) ).
fof(f_592_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(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(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_592_2,plain,
! [U_1764,U_1763,U_1762,U_1761,U_1760] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1761,U_1763)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1764,U_1760)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1762,U_1760)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1762)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1760),U_1761),U_1762),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1760),U_1763),U_1764)) ),
inference(variable_rename,[status(thm)],[f_592_1]) ).
cnf(f_592_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1761,U_1763)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1764,U_1760)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1762,U_1760)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1762)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1760),U_1761),U_1762),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1760),U_1763),U_1764)) ),
inference(clausify,[status(thm)],[f_592_2]) ).
fof(f_593_1,plain,
! [V_w] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_w)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),
inference(fof_nnf,[status(thm)],[fact_minus__numeral__code_I5_J]) ).
fof(f_593_2,plain,
! [U_1765] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1765)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1765)),
inference(variable_rename,[status(thm)],[f_593_1]) ).
cnf(f_593_3,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1765)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1765)),
inference(clausify,[status(thm)],[f_593_2]) ).
fof(f_594_1,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_zminus__0]) ).
cnf(f_594_2,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_594_1]) ).
fof(f_595_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_595_2,plain,
! [U_1766] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1766)) = U_1766,
inference(variable_rename,[status(thm)],[f_595_1]) ).
cnf(f_595_3,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1766)) = U_1766,
inference(clausify,[status(thm)],[f_595_2]) ).
fof(f_596_1,plain,
! [V_w,V_z] : 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(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_z),V_w)),
inference(fof_nnf,[status(thm)],[fact_zmult__zminus]) ).
fof(f_596_2,plain,
! [U_1768,U_1767] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1767)),U_1768) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1767),U_1768)),
inference(variable_rename,[status(thm)],[f_596_1]) ).
cnf(f_596_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1767)),U_1768) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1767),U_1768)),
inference(clausify,[status(thm)],[f_596_2]) ).
fof(f_597_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_597_2,plain,
! [U_1769] :
( ( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_1769) = 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_1769) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_1769) = 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_1769) ) )
| U_1769 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_1769) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_1769 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_597_1]) ).
fof(f_597_3,plain,
( ! [U_1771] :
( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_1771) = 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_1771) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_1771) = 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_1771) ) )
| U_1771 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_1770] :
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_1770) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_1770 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_597_2]) ).
cnf(f_597_4,plain,
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_1770) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_1770 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_597_3]) ).
cnf(f_597_5,plain,
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_1771) = 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_1771)
| U_1771 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_597_3]) ).
cnf(f_597_6,plain,
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_1771) = 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_1771)
| U_1771 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_597_3]) ).
fof(f_598_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_598_2,plain,
! [U_1772] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1772),U_1772) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_598_1]) ).
cnf(f_598_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1772),U_1772) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_598_2]) ).
fof(f_599_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_599_2,plain,
! [U_1774,U_1773] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1773,U_1774)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1773),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1774)),
inference(variable_rename,[status(thm)],[f_599_1]) ).
cnf(f_599_3,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1773,U_1774)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1773),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1774)),
inference(clausify,[status(thm)],[f_599_2]) ).
fof(f_600_1,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_int__0__neq__1]) ).
cnf(f_600_2,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(clausify,[status(thm)],[f_600_1]) ).
fof(f_601_1,plain,
! [V_k] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_k) = V_k,
inference(fof_nnf,[status(thm)],[fact_number__of__is__id]) ).
fof(f_601_2,plain,
! [U_1775] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1775) = U_1775,
inference(variable_rename,[status(thm)],[f_601_1]) ).
cnf(f_601_3,plain,
c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_1775) = U_1775,
inference(clausify,[status(thm)],[f_601_2]) ).
fof(f_602_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(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_602_2,plain,
! [U_1778,U_1777,U_1776] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1778,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_1777)
| U_1776 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1777,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1776),U_1778))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1776) ),
inference(variable_rename,[status(thm)],[f_602_1]) ).
cnf(f_602_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1778,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_1777)
| U_1776 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1777,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1776),U_1778))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1776) ),
inference(clausify,[status(thm)],[f_602_2]) ).
fof(f_603_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(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_603_2,plain,
! [U_1781,U_1780,U_1779] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1781)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1780,U_1779)
| U_1779 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1780,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1779),U_1781))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1779) ),
inference(variable_rename,[status(thm)],[f_603_1]) ).
cnf(f_603_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_1781)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1780,U_1779)
| U_1779 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1780,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1779),U_1781))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1779) ),
inference(clausify,[status(thm)],[f_603_2]) ).
fof(f_604_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(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_604_2,plain,
! [U_1784,U_1783,U_1782] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1783)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1782)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1784,U_1782)
| ~ 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(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1782),U_1783),U_1784)) ),
inference(variable_rename,[status(thm)],[f_604_1]) ).
cnf(f_604_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1783)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1782)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1784,U_1782)
| ~ 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(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1782),U_1783),U_1784)) ),
inference(clausify,[status(thm)],[f_604_2]) ).
fof(f_605_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(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_605_2,plain,
! [U_1787,U_1786,U_1785] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1786,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_1785)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1787)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1785),U_1786),U_1787),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[f_605_1]) ).
cnf(f_605_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1786,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_1785)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1787)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1785),U_1786),U_1787),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_605_2]) ).
fof(f_606_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),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_606_2,plain,
! [U_1789,U_1788] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1788),U_1789))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1789)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1788) ),
inference(variable_rename,[status(thm)],[f_606_1]) ).
cnf(f_606_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1788),U_1789))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1789)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1788) ),
inference(clausify,[status(thm)],[f_606_2]) ).
fof(f_607_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_607_2,plain,
! [U_1791,U_1790] :
( 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_1790,U_1791))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1791)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1790) ),
inference(variable_rename,[status(thm)],[f_607_1]) ).
cnf(f_607_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1790,U_1791))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1791)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1790) ),
inference(clausify,[status(thm)],[f_607_2]) ).
fof(f_608_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]) ).
cnf(f_608_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_608_1]) ).
fof(f_609_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J]) ).
cnf(f_609_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_609_1]) ).
fof(f_610_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
| ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))) )
& ( c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2))))
| c_Int_Onumber__class_Onumber__of(T_a,V_x_2) != c_Int_Onumber__class_Onumber__of(T_a,V_y_2) ) )
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__number__of__eq]) ).
fof(f_610_2,plain,
! [U_1794,U_1793,U_1792] :
( ( ( c_Int_Onumber__class_Onumber__of(U_1792,U_1793) = c_Int_Onumber__class_Onumber__of(U_1792,U_1794)
| ~ c_Int_Oiszero(U_1792,c_Int_Onumber__class_Onumber__of(U_1792,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1793,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1794)))) )
& ( c_Int_Oiszero(U_1792,c_Int_Onumber__class_Onumber__of(U_1792,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1793,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1794))))
| c_Int_Onumber__class_Onumber__of(U_1792,U_1793) != c_Int_Onumber__class_Onumber__of(U_1792,U_1794) ) )
| ~ class_Int_Onumber__ring(U_1792) ),
inference(variable_rename,[status(thm)],[f_610_1]) ).
cnf(f_610_3,plain,
( c_Int_Oiszero(U_1792,c_Int_Onumber__class_Onumber__of(U_1792,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1793,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1794))))
| c_Int_Onumber__class_Onumber__of(U_1792,U_1793) != c_Int_Onumber__class_Onumber__of(U_1792,U_1794)
| ~ class_Int_Onumber__ring(U_1792) ),
inference(clausify,[status(thm)],[f_610_2]) ).
cnf(f_610_4,plain,
( c_Int_Onumber__class_Onumber__of(U_1792,U_1793) = c_Int_Onumber__class_Onumber__of(U_1792,U_1794)
| ~ c_Int_Oiszero(U_1792,c_Int_Onumber__class_Onumber__of(U_1792,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1793,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1794))))
| ~ class_Int_Onumber__ring(U_1792) ),
inference(clausify,[status(thm)],[f_610_2]) ).
fof(f_611_1,plain,
! [V_l_2,V_x_2,V_f_2] :
( ? [B_d] :
( ! [B_h] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(V_f_2,V_x_2),hAPP(V_f_2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,B_h)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_h,B_d)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_h) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_l_2)
| ~ c_Deriv_Oderiv(tc_RealDef_Oreal,V_f_2,V_x_2,V_l_2) ),
inference(fof_nnf,[status(thm)],[fact_DERIV__pos__inc__right]) ).
fof(f_611_2,plain,
! [U_1799,U_1798,U_1797] :
( ? [U_1796] :
( ! [U_1795] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(U_1797,U_1798),hAPP(U_1797,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1798,U_1795)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1795,U_1796)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1795) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1796) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1799)
| ~ c_Deriv_Oderiv(tc_RealDef_Oreal,U_1797,U_1798,U_1799) ),
inference(variable_rename,[status(thm)],[f_611_1]) ).
fof(f_611_3,plain,
! [U_1799,U_1798,U_1797] :
( ( ! [U_1795] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(U_1797,U_1798),hAPP(U_1797,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1798,U_1795)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1795,sK7(U_1799,U_1798,U_1797))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1795) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK7(U_1799,U_1798,U_1797)) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1799)
| ~ c_Deriv_Oderiv(tc_RealDef_Oreal,U_1797,U_1798,U_1799) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_1796,sK7(U_1799,U_1798,U_1797))],[f_611_2]) ).
cnf(f_611_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK7(U_1799,U_1798,U_1797))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1799)
| ~ c_Deriv_Oderiv(tc_RealDef_Oreal,U_1797,U_1798,U_1799) ),
inference(clausify,[status(thm)],[f_611_3]) ).
cnf(f_611_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(U_1797,U_1798),hAPP(U_1797,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1798,U_1795)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1795,sK7(U_1799,U_1798,U_1797))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1795)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1799)
| ~ c_Deriv_Oderiv(tc_RealDef_Oreal,U_1797,U_1798,U_1799) ),
inference(clausify,[status(thm)],[f_611_3]) ).
fof(f_612_1,plain,
! [V_l_2,V_x_2,V_f_2] :
( ? [B_d] :
( ! [B_h] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(V_f_2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,B_h)),hAPP(V_f_2,V_x_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_h,B_d)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_h) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_l_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Deriv_Oderiv(tc_RealDef_Oreal,V_f_2,V_x_2,V_l_2) ),
inference(fof_nnf,[status(thm)],[fact_DERIV__neg__dec__right]) ).
fof(f_612_2,plain,
! [U_1804,U_1803,U_1802] :
( ? [U_1801] :
( ! [U_1800] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(U_1802,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1803,U_1800)),hAPP(U_1802,U_1803))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1800,U_1801)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1800) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1801) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1804,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Deriv_Oderiv(tc_RealDef_Oreal,U_1802,U_1803,U_1804) ),
inference(variable_rename,[status(thm)],[f_612_1]) ).
fof(f_612_3,plain,
! [U_1804,U_1803,U_1802] :
( ( ! [U_1800] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(U_1802,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1803,U_1800)),hAPP(U_1802,U_1803))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1800,sK8(U_1804,U_1803,U_1802))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1800) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK8(U_1804,U_1803,U_1802)) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1804,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Deriv_Oderiv(tc_RealDef_Oreal,U_1802,U_1803,U_1804) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_1801,sK8(U_1804,U_1803,U_1802))],[f_612_2]) ).
cnf(f_612_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK8(U_1804,U_1803,U_1802))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1804,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Deriv_Oderiv(tc_RealDef_Oreal,U_1802,U_1803,U_1804) ),
inference(clausify,[status(thm)],[f_612_3]) ).
cnf(f_612_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(U_1802,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1803,U_1800)),hAPP(U_1802,U_1803))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1800,sK8(U_1804,U_1803,U_1802))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1800)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1804,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Deriv_Oderiv(tc_RealDef_Oreal,U_1802,U_1803,U_1804) ),
inference(clausify,[status(thm)],[f_612_3]) ).
fof(f_613_1,plain,
! [V_za_2,T_a] :
( ( ( c_Int_Oiszero(T_a,V_za_2)
| V_za_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_za_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Int_Oiszero(T_a,V_za_2) ) )
| ~ class_Rings_Osemiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_iszero__def]) ).
fof(f_613_2,plain,
! [U_1806,U_1805] :
( ( ( c_Int_Oiszero(U_1805,U_1806)
| U_1806 != c_Groups_Ozero__class_Ozero(U_1805) )
& ( U_1806 = c_Groups_Ozero__class_Ozero(U_1805)
| ~ c_Int_Oiszero(U_1805,U_1806) ) )
| ~ class_Rings_Osemiring__1(U_1805) ),
inference(variable_rename,[status(thm)],[f_613_1]) ).
cnf(f_613_3,plain,
( U_1806 = c_Groups_Ozero__class_Ozero(U_1805)
| ~ c_Int_Oiszero(U_1805,U_1806)
| ~ class_Rings_Osemiring__1(U_1805) ),
inference(clausify,[status(thm)],[f_613_2]) ).
cnf(f_613_4,plain,
( c_Int_Oiszero(U_1805,U_1806)
| U_1806 != c_Groups_Ozero__class_Ozero(U_1805)
| ~ class_Rings_Osemiring__1(U_1805) ),
inference(clausify,[status(thm)],[f_613_2]) ).
fof(f_614_1,plain,
! [T_a] :
( c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Osemiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_iszero__0]) ).
fof(f_614_2,plain,
! [U_1807] :
( c_Int_Oiszero(U_1807,c_Groups_Ozero__class_Ozero(U_1807))
| ~ class_Rings_Osemiring__1(U_1807) ),
inference(variable_rename,[status(thm)],[f_614_1]) ).
cnf(f_614_3,plain,
( c_Int_Oiszero(U_1807,c_Groups_Ozero__class_Ozero(U_1807))
| ~ class_Rings_Osemiring__1(U_1807) ),
inference(clausify,[status(thm)],[f_614_2]) ).
fof(f_615_1,plain,
! [T_a] :
( ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a))
| ~ class_Rings_Osemiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__iszero__1]) ).
fof(f_615_2,plain,
! [U_1808] :
( ~ c_Int_Oiszero(U_1808,c_Groups_Oone__class_Oone(U_1808))
| ~ class_Rings_Osemiring__1(U_1808) ),
inference(variable_rename,[status(thm)],[f_615_1]) ).
cnf(f_615_3,plain,
( ~ c_Int_Oiszero(U_1808,c_Groups_Oone__class_Oone(U_1808))
| ~ class_Rings_Osemiring__1(U_1808) ),
inference(clausify,[status(thm)],[f_615_2]) ).
fof(f_616_1,plain,
! [V_x_2,T_a] :
( ( ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls)))) )
& ( c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls))))
| c_Int_Onumber__class_Onumber__of(T_a,V_x_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__special_I3_J]) ).
fof(f_616_2,plain,
! [U_1810,U_1809] :
( ( ( c_Int_Onumber__class_Onumber__of(U_1809,U_1810) = c_Groups_Ozero__class_Ozero(U_1809)
| ~ c_Int_Oiszero(U_1809,c_Int_Onumber__class_Onumber__of(U_1809,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1810,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls)))) )
& ( c_Int_Oiszero(U_1809,c_Int_Onumber__class_Onumber__of(U_1809,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1810,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls))))
| c_Int_Onumber__class_Onumber__of(U_1809,U_1810) != c_Groups_Ozero__class_Ozero(U_1809) ) )
| ~ class_Int_Onumber__ring(U_1809) ),
inference(variable_rename,[status(thm)],[f_616_1]) ).
cnf(f_616_3,plain,
( c_Int_Oiszero(U_1809,c_Int_Onumber__class_Onumber__of(U_1809,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1810,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls))))
| c_Int_Onumber__class_Onumber__of(U_1809,U_1810) != c_Groups_Ozero__class_Ozero(U_1809)
| ~ class_Int_Onumber__ring(U_1809) ),
inference(clausify,[status(thm)],[f_616_2]) ).
cnf(f_616_4,plain,
( c_Int_Onumber__class_Onumber__of(U_1809,U_1810) = c_Groups_Ozero__class_Ozero(U_1809)
| ~ c_Int_Oiszero(U_1809,c_Int_Onumber__class_Onumber__of(U_1809,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1810,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls))))
| ~ class_Int_Onumber__ring(U_1809) ),
inference(clausify,[status(thm)],[f_616_2]) ).
fof(f_617_1,plain,
! [V_y_2,T_a] :
( ( ( c_Groups_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
| ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))) )
& ( c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2))))
| c_Groups_Ozero__class_Ozero(T_a) != c_Int_Onumber__class_Onumber__of(T_a,V_y_2) ) )
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__special_I1_J]) ).
fof(f_617_2,plain,
! [U_1812,U_1811] :
( ( ( c_Groups_Ozero__class_Ozero(U_1811) = c_Int_Onumber__class_Onumber__of(U_1811,U_1812)
| ~ c_Int_Oiszero(U_1811,c_Int_Onumber__class_Onumber__of(U_1811,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1812)))) )
& ( c_Int_Oiszero(U_1811,c_Int_Onumber__class_Onumber__of(U_1811,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1812))))
| c_Groups_Ozero__class_Ozero(U_1811) != c_Int_Onumber__class_Onumber__of(U_1811,U_1812) ) )
| ~ class_Int_Onumber__ring(U_1811) ),
inference(variable_rename,[status(thm)],[f_617_1]) ).
cnf(f_617_3,plain,
( c_Int_Oiszero(U_1811,c_Int_Onumber__class_Onumber__of(U_1811,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1812))))
| c_Groups_Ozero__class_Ozero(U_1811) != c_Int_Onumber__class_Onumber__of(U_1811,U_1812)
| ~ class_Int_Onumber__ring(U_1811) ),
inference(clausify,[status(thm)],[f_617_2]) ).
cnf(f_617_4,plain,
( c_Groups_Ozero__class_Ozero(U_1811) = c_Int_Onumber__class_Onumber__of(U_1811,U_1812)
| ~ c_Int_Oiszero(U_1811,c_Int_Onumber__class_Onumber__of(U_1811,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1812))))
| ~ class_Int_Onumber__ring(U_1811) ),
inference(clausify,[status(thm)],[f_617_2]) ).
fof(f_618_1,plain,
! [V_w,T_a] :
( c_Int_Onumber__class_Onumber__of(T_a,c_Int_Opred(V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),c_Int_Onumber__class_Onumber__of(T_a,V_w))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__pred]) ).
fof(f_618_2,plain,
! [U_1814,U_1813] :
( c_Int_Onumber__class_Onumber__of(U_1813,c_Int_Opred(U_1814)) = c_Groups_Oplus__class_Oplus(U_1813,c_Groups_Ouminus__class_Ouminus(U_1813,c_Groups_Oone__class_Oone(U_1813)),c_Int_Onumber__class_Onumber__of(U_1813,U_1814))
| ~ class_Int_Onumber__ring(U_1813) ),
inference(variable_rename,[status(thm)],[f_618_1]) ).
cnf(f_618_3,plain,
( c_Int_Onumber__class_Onumber__of(U_1813,c_Int_Opred(U_1814)) = c_Groups_Oplus__class_Oplus(U_1813,c_Groups_Ouminus__class_Ouminus(U_1813,c_Groups_Oone__class_Oone(U_1813)),c_Int_Onumber__class_Onumber__of(U_1813,U_1814))
| ~ class_Int_Onumber__ring(U_1813) ),
inference(clausify,[status(thm)],[f_618_2]) ).
fof(f_619_1,plain,
! [V_v_H_2,V_v_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2)
| ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_H_2)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2) ) )
& ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2)
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_H_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_2,V_v_H_2) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__nat__number__of]) ).
fof(f_619_2,plain,
! [U_1816,U_1815] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1815),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1816))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1815,U_1816)
| ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1816)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1815,U_1816) ) )
& ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1815,U_1816)
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1816)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1815,U_1816) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1815),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1816)) ) ),
inference(variable_rename,[status(thm)],[f_619_1]) ).
fof(f_619_3,plain,
( ! [U_1820,U_1818] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1818),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1820))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1818,U_1820)
| ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1820)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1818,U_1820) ) )
& ! [U_1819,U_1817] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1817,U_1819)
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1819)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1817,U_1819) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1817),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1819)) ) ),
inference(miniscope,[status(thm)],[f_619_2]) ).
cnf(f_619_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1819)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1817,U_1819)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1817),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1819)) ),
inference(clausify,[status(thm)],[f_619_3]) ).
cnf(f_619_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1817,U_1819)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1817),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1819)) ),
inference(clausify,[status(thm)],[f_619_3]) ).
cnf(f_619_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1818,U_1820)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1818,U_1820)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1818),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1820)) ),
inference(clausify,[status(thm)],[f_619_3]) ).
cnf(f_619_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1820)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1818,U_1820)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1818),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1820)) ),
inference(clausify,[status(thm)],[f_619_3]) ).
fof(f_620_1,plain,
! [V_v_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_v_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__0__number__of]) ).
fof(f_620_2,plain,
! [U_1821] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1821))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1821) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1821)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1821)) ) ),
inference(variable_rename,[status(thm)],[f_620_1]) ).
fof(f_620_3,plain,
( ! [U_1823] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1823))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1823) )
& ! [U_1822] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1822)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1822)) ) ),
inference(miniscope,[status(thm)],[f_620_2]) ).
cnf(f_620_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1822)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1822)) ),
inference(clausify,[status(thm)],[f_620_3]) ).
cnf(f_620_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1823))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1823) ),
inference(clausify,[status(thm)],[f_620_3]) ).
fof(f_621_1,plain,
! [V_v_2] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) ) ),
inference(fof_nnf,[status(thm)],[fact_eq__0__number__of]) ).
fof(f_621_2,plain,
! [U_1824] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1824)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1824,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1824,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1824) ) ),
inference(variable_rename,[status(thm)],[f_621_1]) ).
fof(f_621_3,plain,
( ! [U_1826] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1826)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1826,c_Int_OPls) )
& ! [U_1825] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1825,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1825) ) ),
inference(miniscope,[status(thm)],[f_621_2]) ).
cnf(f_621_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1825,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1825) ),
inference(clausify,[status(thm)],[f_621_3]) ).
cnf(f_621_5,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1826)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1826,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_621_3]) ).
fof(f_622_1,plain,
! [V_v_2] :
( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_eq__number__of__0]) ).
fof(f_622_2,plain,
! [U_1827] :
( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1827) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1827,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1827,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1827) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_622_1]) ).
fof(f_622_3,plain,
( ! [U_1829] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1829) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1829,c_Int_OPls) )
& ! [U_1828] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1828,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1828) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_622_2]) ).
cnf(f_622_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1828,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1828) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_622_3]) ).
cnf(f_622_5,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1829) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1829,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_622_3]) ).
fof(f_623_1,plain,
! [V_v_H_2,V_v_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,V_v_H_2) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_v_2,V_v_H_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_le__nat__number__of]) ).
fof(f_623_2,plain,
! [U_1831,U_1830] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1830),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1831))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1830,c_Int_OPls)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1830,U_1831) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1830,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1830,U_1831)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1830),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1831)) ) ),
inference(variable_rename,[status(thm)],[f_623_1]) ).
fof(f_623_3,plain,
( ! [U_1835,U_1833] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1833),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1835))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1833,c_Int_OPls)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1833,U_1835) ) )
& ! [U_1834,U_1832] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1832,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1832,U_1834)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1832),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1834)) ) ),
inference(miniscope,[status(thm)],[f_623_2]) ).
cnf(f_623_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1832,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1832,U_1834)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1832),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1834)) ),
inference(clausify,[status(thm)],[f_623_3]) ).
cnf(f_623_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1833,U_1835)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1833),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1835)) ),
inference(clausify,[status(thm)],[f_623_3]) ).
cnf(f_623_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1833,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1833),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1835)) ),
inference(clausify,[status(thm)],[f_623_3]) ).
fof(f_624_1,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls) = c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_minus__Pls]) ).
cnf(f_624_2,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OPls) = c_Int_OPls,
inference(clausify,[status(thm)],[f_624_1]) ).
fof(f_625_1,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_Pls__def]) ).
cnf(f_625_2,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_625_1]) ).
fof(f_626_1,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
inference(fof_nnf,[status(thm)],[fact_semiring__norm_I113_J]) ).
cnf(f_626_2,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
inference(clausify,[status(thm)],[f_626_1]) ).
fof(f_627_1,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_nat__number__of__Pls]) ).
cnf(f_627_2,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_627_1]) ).
fof(f_628_1,plain,
! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_OPls) = V_k,
inference(fof_nnf,[status(thm)],[fact_add__Pls__right]) ).
fof(f_628_2,plain,
! [U_1836] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1836,c_Int_OPls) = U_1836,
inference(variable_rename,[status(thm)],[f_628_1]) ).
cnf(f_628_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1836,c_Int_OPls) = U_1836,
inference(clausify,[status(thm)],[f_628_2]) ).
fof(f_629_1,plain,
! [V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,V_k) = V_k,
inference(fof_nnf,[status(thm)],[fact_add__Pls]) ).
fof(f_629_2,plain,
! [U_1837] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,U_1837) = U_1837,
inference(variable_rename,[status(thm)],[f_629_1]) ).
cnf(f_629_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,U_1837) = U_1837,
inference(clausify,[status(thm)],[f_629_2]) ).
fof(f_630_1,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I2_J]) ).
cnf(f_630_2,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(clausify,[status(thm)],[f_630_1]) ).
fof(f_631_1,plain,
! [V_w] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls),V_w) = c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_mult__Pls]) ).
fof(f_631_2,plain,
! [U_1838] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls),U_1838) = c_Int_OPls,
inference(variable_rename,[status(thm)],[f_631_1]) ).
cnf(f_631_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls),U_1838) = c_Int_OPls,
inference(clausify,[status(thm)],[f_631_2]) ).
fof(f_632_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I19_J]) ).
cnf(f_632_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(clausify,[status(thm)],[f_632_1]) ).
fof(f_633_1,plain,
! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x,
inference(fof_nnf,[status(thm)],[fact_succ__pred]) ).
fof(f_633_2,plain,
! [U_1839] : c_Int_Osucc(c_Int_Opred(U_1839)) = U_1839,
inference(variable_rename,[status(thm)],[f_633_1]) ).
cnf(f_633_3,plain,
c_Int_Osucc(c_Int_Opred(U_1839)) = U_1839,
inference(clausify,[status(thm)],[f_633_2]) ).
fof(f_634_1,plain,
! [T_a] :
( c_Groups_Ozero__class_Ozero(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_semiring__norm_I112_J]) ).
fof(f_634_2,plain,
! [U_1840] :
( c_Groups_Ozero__class_Ozero(U_1840) = c_Int_Onumber__class_Onumber__of(U_1840,c_Int_OPls)
| ~ class_Int_Onumber__ring(U_1840) ),
inference(variable_rename,[status(thm)],[f_634_1]) ).
cnf(f_634_3,plain,
( c_Groups_Ozero__class_Ozero(U_1840) = c_Int_Onumber__class_Onumber__of(U_1840,c_Int_OPls)
| ~ class_Int_Onumber__ring(U_1840) ),
inference(clausify,[status(thm)],[f_634_2]) ).
fof(f_635_1,plain,
! [T_a] :
( c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__Pls]) ).
fof(f_635_2,plain,
! [U_1841] :
( c_Int_Onumber__class_Onumber__of(U_1841,c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_1841)
| ~ class_Int_Onumber__ring(U_1841) ),
inference(variable_rename,[status(thm)],[f_635_1]) ).
cnf(f_635_3,plain,
( c_Int_Onumber__class_Onumber__of(U_1841,c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_1841)
| ~ class_Int_Onumber__ring(U_1841) ),
inference(clausify,[status(thm)],[f_635_2]) ).
fof(f_636_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) = V_a
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__numeral__0__right]) ).
fof(f_636_2,plain,
! [U_1843,U_1842] :
( c_Groups_Oplus__class_Oplus(U_1842,U_1843,c_Int_Onumber__class_Onumber__of(U_1842,c_Int_OPls)) = U_1843
| ~ class_Int_Onumber__ring(U_1842) ),
inference(variable_rename,[status(thm)],[f_636_1]) ).
cnf(f_636_3,plain,
( c_Groups_Oplus__class_Oplus(U_1842,U_1843,c_Int_Onumber__class_Onumber__of(U_1842,c_Int_OPls)) = U_1843
| ~ class_Int_Onumber__ring(U_1842) ),
inference(clausify,[status(thm)],[f_636_2]) ).
fof(f_637_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls),V_a) = V_a
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__numeral__0]) ).
fof(f_637_2,plain,
! [U_1845,U_1844] :
( c_Groups_Oplus__class_Oplus(U_1844,c_Int_Onumber__class_Onumber__of(U_1844,c_Int_OPls),U_1845) = U_1845
| ~ class_Int_Onumber__ring(U_1844) ),
inference(variable_rename,[status(thm)],[f_637_1]) ).
cnf(f_637_3,plain,
( c_Groups_Oplus__class_Oplus(U_1844,c_Int_Onumber__class_Onumber__of(U_1844,c_Int_OPls),U_1845) = U_1845
| ~ class_Int_Onumber__ring(U_1844) ),
inference(clausify,[status(thm)],[f_637_2]) ).
fof(f_638_1,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I1_J]) ).
cnf(f_638_2,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_638_1]) ).
fof(f_639_1,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),
inference(fof_nnf,[status(thm)],[fact_zero__is__num__zero]) ).
cnf(f_639_2,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),
inference(clausify,[status(thm)],[f_639_1]) ).
fof(f_640_1,plain,
! [V_v_H,V_v] :
( ( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,V_v_H))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v_H,c_Int_OPls) ) )
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) ) ),
inference(fof_nnf,[status(thm)],[fact_add__nat__number__of]) ).
fof(f_640_2,plain,
! [U_1847,U_1846] :
( ( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1846),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1847)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1846,U_1847))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1847,c_Int_OPls) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1846),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1847)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1846)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1847,c_Int_OPls) ) )
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1846,c_Int_OPls) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1846),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1847)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1847)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1846,c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[f_640_1]) ).
fof(f_640_3,plain,
( ! [U_1851,U_1849] :
( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1849),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1851)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1849,U_1851))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1851,c_Int_OPls) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1849),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1851)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1849)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1851,c_Int_OPls) ) )
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1849,c_Int_OPls) )
& ! [U_1850,U_1848] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1848),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1850)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1850)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1848,c_Int_OPls) ) ),
inference(miniscope,[status(thm)],[f_640_2]) ).
cnf(f_640_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1848),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1850)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1850)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1848,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_640_3]) ).
cnf(f_640_5,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1849),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1851)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1849)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1851,c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1849,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_640_3]) ).
cnf(f_640_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1849),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1851)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1849,U_1851))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1851,c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1849,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_640_3]) ).
fof(f_641_1,plain,
! [V_k,V_v_H,V_v] :
( ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)),V_k)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_v_H))),V_k)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) )
& ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)),V_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__number__of__mult__left]) ).
fof(f_641_2,plain,
! [U_1854,U_1853,U_1852] :
( ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1852)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1853)),U_1854)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1852),U_1853))),U_1854)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1852,c_Int_OPls) )
& ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1852)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1853)),U_1854)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1852,c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[f_641_1]) ).
fof(f_641_3,plain,
( ! [U_1860,U_1858,U_1856] :
( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1856)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1858)),U_1860)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1856),U_1858))),U_1860)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1856,c_Int_OPls) )
& ! [U_1859,U_1857,U_1855] :
( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1855)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1857)),U_1859)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1855,c_Int_OPls) ) ),
inference(miniscope,[status(thm)],[f_641_2]) ).
cnf(f_641_4,plain,
( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1855)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1857)),U_1859)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1855,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_641_3]) ).
cnf(f_641_5,plain,
( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1856)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1858)),U_1860)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1856),U_1858))),U_1860)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1856,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_641_3]) ).
fof(f_642_1,plain,
! [V_v_H,V_v] :
( ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_v),V_v_H))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) )
& ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__nat__number__of]) ).
fof(f_642_2,plain,
! [U_1862,U_1861] :
( ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1861)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1862)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1861),U_1862))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1861,c_Int_OPls) )
& ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1861)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1862)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1861,c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[f_642_1]) ).
fof(f_642_3,plain,
( ! [U_1866,U_1864] :
( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1864)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1866)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1864),U_1866))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1864,c_Int_OPls) )
& ! [U_1865,U_1863] :
( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1863)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1865)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1863,c_Int_OPls) ) ),
inference(miniscope,[status(thm)],[f_642_2]) ).
cnf(f_642_4,plain,
( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1863)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1865)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1863,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_642_3]) ).
cnf(f_642_5,plain,
( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1864)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1866)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_1864),U_1866))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1864,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_642_3]) ).
fof(f_643_1,plain,
! [T_a] :
( c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_iszero__Numeral0]) ).
fof(f_643_2,plain,
! [U_1867] :
( c_Int_Oiszero(U_1867,c_Int_Onumber__class_Onumber__of(U_1867,c_Int_OPls))
| ~ class_Int_Onumber__ring(U_1867) ),
inference(variable_rename,[status(thm)],[f_643_1]) ).
cnf(f_643_3,plain,
( c_Int_Oiszero(U_1867,c_Int_Onumber__class_Onumber__of(U_1867,c_Int_OPls))
| ~ class_Int_Onumber__ring(U_1867) ),
inference(clausify,[status(thm)],[f_643_2]) ).
fof(f_644_1,plain,
! [V_v] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__1__add__number__of]) ).
fof(f_644_2,plain,
! [U_1868] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1868)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(U_1868))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1868,c_Int_OPls) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1868)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1868,c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[f_644_1]) ).
fof(f_644_3,plain,
( ! [U_1870] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1870)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(U_1870))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1870,c_Int_OPls) )
& ! [U_1869] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1869)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1869,c_Int_OPls) ) ),
inference(miniscope,[status(thm)],[f_644_2]) ).
cnf(f_644_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1869)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1869,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_644_3]) ).
cnf(f_644_5,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1870)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(U_1870))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1870,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_644_3]) ).
fof(f_645_1,plain,
! [V_v] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(V_v))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_v),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_v,c_Int_OPls) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__number__of__add__1]) ).
fof(f_645_2,plain,
! [U_1871] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1871),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(U_1871))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1871,c_Int_OPls) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1871),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1871,c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[f_645_1]) ).
fof(f_645_3,plain,
( ! [U_1873] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1873),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(U_1873))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1873,c_Int_OPls) )
& ! [U_1872] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1872),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1872,c_Int_OPls) ) ),
inference(miniscope,[status(thm)],[f_645_2]) ).
cnf(f_645_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1872),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1872,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_645_3]) ).
cnf(f_645_5,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1873),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(U_1873))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1873,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_645_3]) ).
fof(f_646_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(V_k_2),V_l_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(V_k_2),V_l_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) ) ),
inference(fof_nnf,[status(thm)],[fact_le__iff__pred__less]) ).
fof(f_646_2,plain,
! [U_1875,U_1874] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1874,U_1875)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(U_1874),U_1875) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(U_1874),U_1875)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1874,U_1875) ) ),
inference(variable_rename,[status(thm)],[f_646_1]) ).
fof(f_646_3,plain,
( ! [U_1879,U_1877] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1877,U_1879)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(U_1877),U_1879) )
& ! [U_1878,U_1876] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(U_1876),U_1878)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1876,U_1878) ) ),
inference(miniscope,[status(thm)],[f_646_2]) ).
cnf(f_646_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(U_1876),U_1878)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1876,U_1878) ),
inference(clausify,[status(thm)],[f_646_3]) ).
cnf(f_646_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1877,U_1879)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(U_1877),U_1879) ),
inference(clausify,[status(thm)],[f_646_3]) ).
fof(f_647_1,plain,
! [V_x,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__Numeral0]) ).
fof(f_647_2,plain,
! [U_1881,U_1880] :
( c_Rings_Oinverse__class_Odivide(U_1880,U_1881,c_Int_Onumber__class_Onumber__of(U_1880,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_1880)
| ~ class_Int_Onumber__ring(U_1880)
| ~ class_Fields_Ofield__inverse__zero(U_1880) ),
inference(variable_rename,[status(thm)],[f_647_1]) ).
cnf(f_647_3,plain,
( c_Rings_Oinverse__class_Odivide(U_1880,U_1881,c_Int_Onumber__class_Onumber__of(U_1880,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_1880)
| ~ class_Int_Onumber__ring(U_1880)
| ~ class_Fields_Ofield__inverse__zero(U_1880) ),
inference(clausify,[status(thm)],[f_647_2]) ).
fof(f_648_1,plain,
! [V_y_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__special_I1_J]) ).
fof(f_648_2,plain,
! [U_1883,U_1882] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1882,c_Groups_Ozero__class_Ozero(U_1882),c_Int_Onumber__class_Onumber__of(U_1882,U_1883))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_1883) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_1883)
| ~ c_Orderings_Oord__class_Oless__eq(U_1882,c_Groups_Ozero__class_Ozero(U_1882),c_Int_Onumber__class_Onumber__of(U_1882,U_1883)) ) )
| ~ class_Rings_Olinordered__idom(U_1882)
| ~ class_Int_Onumber__ring(U_1882) ),
inference(variable_rename,[status(thm)],[f_648_1]) ).
cnf(f_648_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_1883)
| ~ c_Orderings_Oord__class_Oless__eq(U_1882,c_Groups_Ozero__class_Ozero(U_1882),c_Int_Onumber__class_Onumber__of(U_1882,U_1883))
| ~ class_Rings_Olinordered__idom(U_1882)
| ~ class_Int_Onumber__ring(U_1882) ),
inference(clausify,[status(thm)],[f_648_2]) ).
cnf(f_648_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1882,c_Groups_Ozero__class_Ozero(U_1882),c_Int_Onumber__class_Onumber__of(U_1882,U_1883))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_1883)
| ~ class_Rings_Olinordered__idom(U_1882)
| ~ class_Int_Onumber__ring(U_1882) ),
inference(clausify,[status(thm)],[f_648_2]) ).
fof(f_649_1,plain,
! [V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__special_I3_J]) ).
fof(f_649_2,plain,
! [U_1885,U_1884] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1884,c_Int_Onumber__class_Onumber__of(U_1884,U_1885),c_Groups_Ozero__class_Ozero(U_1884))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1885,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1885,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(U_1884,c_Int_Onumber__class_Onumber__of(U_1884,U_1885),c_Groups_Ozero__class_Ozero(U_1884)) ) )
| ~ class_Rings_Olinordered__idom(U_1884)
| ~ class_Int_Onumber__ring(U_1884) ),
inference(variable_rename,[status(thm)],[f_649_1]) ).
cnf(f_649_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1885,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(U_1884,c_Int_Onumber__class_Onumber__of(U_1884,U_1885),c_Groups_Ozero__class_Ozero(U_1884))
| ~ class_Rings_Olinordered__idom(U_1884)
| ~ class_Int_Onumber__ring(U_1884) ),
inference(clausify,[status(thm)],[f_649_2]) ).
cnf(f_649_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1884,c_Int_Onumber__class_Onumber__of(U_1884,U_1885),c_Groups_Ozero__class_Ozero(U_1884))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1885,c_Int_OPls)
| ~ class_Rings_Olinordered__idom(U_1884)
| ~ class_Int_Onumber__ring(U_1884) ),
inference(clausify,[status(thm)],[f_649_2]) ).
fof(f_650_1,plain,
! [V_y_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_y_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__special_I1_J]) ).
fof(f_650_2,plain,
! [U_1887,U_1886] :
( ( ( c_Orderings_Oord__class_Oless(U_1886,c_Groups_Ozero__class_Ozero(U_1886),c_Int_Onumber__class_Onumber__of(U_1886,U_1887))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1887) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1887)
| ~ c_Orderings_Oord__class_Oless(U_1886,c_Groups_Ozero__class_Ozero(U_1886),c_Int_Onumber__class_Onumber__of(U_1886,U_1887)) ) )
| ~ class_Rings_Olinordered__idom(U_1886)
| ~ class_Int_Onumber__ring(U_1886) ),
inference(variable_rename,[status(thm)],[f_650_1]) ).
cnf(f_650_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1887)
| ~ c_Orderings_Oord__class_Oless(U_1886,c_Groups_Ozero__class_Ozero(U_1886),c_Int_Onumber__class_Onumber__of(U_1886,U_1887))
| ~ class_Rings_Olinordered__idom(U_1886)
| ~ class_Int_Onumber__ring(U_1886) ),
inference(clausify,[status(thm)],[f_650_2]) ).
cnf(f_650_4,plain,
( c_Orderings_Oord__class_Oless(U_1886,c_Groups_Ozero__class_Ozero(U_1886),c_Int_Onumber__class_Onumber__of(U_1886,U_1887))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_1887)
| ~ class_Rings_Olinordered__idom(U_1886)
| ~ class_Int_Onumber__ring(U_1886) ),
inference(clausify,[status(thm)],[f_650_2]) ).
fof(f_651_1,plain,
! [V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__special_I3_J]) ).
fof(f_651_2,plain,
! [U_1889,U_1888] :
( ( ( c_Orderings_Oord__class_Oless(U_1888,c_Int_Onumber__class_Onumber__of(U_1888,U_1889),c_Groups_Ozero__class_Ozero(U_1888))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1889,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1889,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(U_1888,c_Int_Onumber__class_Onumber__of(U_1888,U_1889),c_Groups_Ozero__class_Ozero(U_1888)) ) )
| ~ class_Rings_Olinordered__idom(U_1888)
| ~ class_Int_Onumber__ring(U_1888) ),
inference(variable_rename,[status(thm)],[f_651_1]) ).
cnf(f_651_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1889,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(U_1888,c_Int_Onumber__class_Onumber__of(U_1888,U_1889),c_Groups_Ozero__class_Ozero(U_1888))
| ~ class_Rings_Olinordered__idom(U_1888)
| ~ class_Int_Onumber__ring(U_1888) ),
inference(clausify,[status(thm)],[f_651_2]) ).
cnf(f_651_4,plain,
( c_Orderings_Oord__class_Oless(U_1888,c_Int_Onumber__class_Onumber__of(U_1888,U_1889),c_Groups_Ozero__class_Ozero(U_1888))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1889,c_Int_OPls)
| ~ class_Rings_Olinordered__idom(U_1888)
| ~ class_Int_Onumber__ring(U_1888) ),
inference(clausify,[status(thm)],[f_651_2]) ).
fof(f_652_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
inference(fof_nnf,[status(thm)],[fact_number__of2]) ).
cnf(f_652_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
inference(clausify,[status(thm)],[f_652_1]) ).
fof(f_653_1,plain,
! [V_x_2,T_a] :
( ( ( c_Int_Onumber__class_Onumber__of(T_a,V_x_2) = c_Groups_Oone__class_Oone(T_a)
| ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))) )
& ( c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)))))
| c_Int_Onumber__class_Onumber__of(T_a,V_x_2) != c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__special_I4_J]) ).
fof(f_653_2,plain,
! [U_1891,U_1890] :
( ( ( c_Int_Onumber__class_Onumber__of(U_1890,U_1891) = c_Groups_Oone__class_Oone(U_1890)
| ~ c_Int_Oiszero(U_1890,c_Int_Onumber__class_Onumber__of(U_1890,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1891,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls))))) )
& ( c_Int_Oiszero(U_1890,c_Int_Onumber__class_Onumber__of(U_1890,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1891,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)))))
| c_Int_Onumber__class_Onumber__of(U_1890,U_1891) != c_Groups_Oone__class_Oone(U_1890) ) )
| ~ class_Int_Onumber__ring(U_1890) ),
inference(variable_rename,[status(thm)],[f_653_1]) ).
cnf(f_653_3,plain,
( c_Int_Oiszero(U_1890,c_Int_Onumber__class_Onumber__of(U_1890,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1891,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)))))
| c_Int_Onumber__class_Onumber__of(U_1890,U_1891) != c_Groups_Oone__class_Oone(U_1890)
| ~ class_Int_Onumber__ring(U_1890) ),
inference(clausify,[status(thm)],[f_653_2]) ).
cnf(f_653_4,plain,
( c_Int_Onumber__class_Onumber__of(U_1890,U_1891) = c_Groups_Oone__class_Oone(U_1890)
| ~ c_Int_Oiszero(U_1890,c_Int_Onumber__class_Onumber__of(U_1890,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1891,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)))))
| ~ class_Int_Onumber__ring(U_1890) ),
inference(clausify,[status(thm)],[f_653_2]) ).
fof(f_654_1,plain,
! [V_y_2,T_a] :
( ( ( c_Groups_Oone__class_Oone(T_a) = c_Int_Onumber__class_Onumber__of(T_a,V_y_2)
| ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2)))) )
& ( c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_y_2))))
| c_Groups_Oone__class_Oone(T_a) != c_Int_Onumber__class_Onumber__of(T_a,V_y_2) ) )
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__special_I2_J]) ).
fof(f_654_2,plain,
! [U_1893,U_1892] :
( ( ( c_Groups_Oone__class_Oone(U_1892) = c_Int_Onumber__class_Onumber__of(U_1892,U_1893)
| ~ c_Int_Oiszero(U_1892,c_Int_Onumber__class_Onumber__of(U_1892,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1893)))) )
& ( c_Int_Oiszero(U_1892,c_Int_Onumber__class_Onumber__of(U_1892,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1893))))
| c_Groups_Oone__class_Oone(U_1892) != c_Int_Onumber__class_Onumber__of(U_1892,U_1893) ) )
| ~ class_Int_Onumber__ring(U_1892) ),
inference(variable_rename,[status(thm)],[f_654_1]) ).
cnf(f_654_3,plain,
( c_Int_Oiszero(U_1892,c_Int_Onumber__class_Onumber__of(U_1892,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1893))))
| c_Groups_Oone__class_Oone(U_1892) != c_Int_Onumber__class_Onumber__of(U_1892,U_1893)
| ~ class_Int_Onumber__ring(U_1892) ),
inference(clausify,[status(thm)],[f_654_2]) ).
cnf(f_654_4,plain,
( c_Groups_Oone__class_Oone(U_1892) = c_Int_Onumber__class_Onumber__of(U_1892,U_1893)
| ~ c_Int_Oiszero(U_1892,c_Int_Onumber__class_Onumber__of(U_1892,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1893))))
| ~ class_Int_Onumber__ring(U_1892) ),
inference(clausify,[status(thm)],[f_654_2]) ).
fof(f_655_1,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)),
inference(fof_nnf,[status(thm)],[fact_Numeral1__eq1__nat]) ).
cnf(f_655_2,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)),
inference(clausify,[status(thm)],[f_655_1]) ).
fof(f_656_1,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_nat__numeral__1__eq__1]) ).
cnf(f_656_2,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_656_1]) ).
fof(f_657_1,plain,
! [V_l] : c_Int_OPls != c_Int_OBit1(V_l),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I39_J]) ).
fof(f_657_2,plain,
! [U_1894] : c_Int_OPls != c_Int_OBit1(U_1894),
inference(variable_rename,[status(thm)],[f_657_1]) ).
cnf(f_657_3,plain,
c_Int_OPls != c_Int_OBit1(U_1894),
inference(clausify,[status(thm)],[f_657_2]) ).
fof(f_658_1,plain,
! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_rel__simps_I46_J]) ).
fof(f_658_2,plain,
! [U_1895] : c_Int_OBit1(U_1895) != c_Int_OPls,
inference(variable_rename,[status(thm)],[f_658_1]) ).
cnf(f_658_3,plain,
c_Int_OBit1(U_1895) != c_Int_OPls,
inference(clausify,[status(thm)],[f_658_2]) ).
fof(f_659_1,plain,
! [V_k2_2,V_k1_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I16_J]) ).
fof(f_659_2,plain,
! [U_1897,U_1896] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_1896),c_Int_OBit1(U_1897))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1896,U_1897) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1896,U_1897)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_1896),c_Int_OBit1(U_1897)) ) ),
inference(variable_rename,[status(thm)],[f_659_1]) ).
fof(f_659_3,plain,
( ! [U_1901,U_1899] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_1899),c_Int_OBit1(U_1901))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1899,U_1901) )
& ! [U_1900,U_1898] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1898,U_1900)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_1898),c_Int_OBit1(U_1900)) ) ),
inference(miniscope,[status(thm)],[f_659_2]) ).
cnf(f_659_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1898,U_1900)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_1898),c_Int_OBit1(U_1900)) ),
inference(clausify,[status(thm)],[f_659_3]) ).
cnf(f_659_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_1899),c_Int_OBit1(U_1901))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1899,U_1901) ),
inference(clausify,[status(thm)],[f_659_3]) ).
fof(f_660_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I34_J]) ).
fof(f_660_2,plain,
! [U_1903,U_1902] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_1902),c_Int_OBit1(U_1903))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1902,U_1903) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1902,U_1903)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_1902),c_Int_OBit1(U_1903)) ) ),
inference(variable_rename,[status(thm)],[f_660_1]) ).
fof(f_660_3,plain,
( ! [U_1907,U_1905] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_1905),c_Int_OBit1(U_1907))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1905,U_1907) )
& ! [U_1906,U_1904] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1904,U_1906)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_1904),c_Int_OBit1(U_1906)) ) ),
inference(miniscope,[status(thm)],[f_660_2]) ).
cnf(f_660_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1904,U_1906)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_1904),c_Int_OBit1(U_1906)) ),
inference(clausify,[status(thm)],[f_660_3]) ).
cnf(f_660_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_1905),c_Int_OBit1(U_1907))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1905,U_1907) ),
inference(clausify,[status(thm)],[f_660_3]) ).
fof(f_661_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit1(V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I17_J]) ).
fof(f_661_2,plain,
! [U_1909,U_1908] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1908),c_Int_OBit1(U_1909))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1908,U_1909) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1908,U_1909)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1908),c_Int_OBit1(U_1909)) ) ),
inference(variable_rename,[status(thm)],[f_661_1]) ).
fof(f_661_3,plain,
( ! [U_1913,U_1911] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1911),c_Int_OBit1(U_1913))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1911,U_1913) )
& ! [U_1912,U_1910] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1910,U_1912)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1910),c_Int_OBit1(U_1912)) ) ),
inference(miniscope,[status(thm)],[f_661_2]) ).
cnf(f_661_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1910,U_1912)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1910),c_Int_OBit1(U_1912)) ),
inference(clausify,[status(thm)],[f_661_3]) ).
cnf(f_661_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1911),c_Int_OBit1(U_1913))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1911,U_1913) ),
inference(clausify,[status(thm)],[f_661_3]) ).
fof(f_662_1,plain,
! [V_k2_2,V_k1_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit1(V_k2_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__int__code_I16_J]) ).
fof(f_662_2,plain,
! [U_1915,U_1914] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1914),c_Int_OBit1(U_1915))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1914,U_1915) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1914,U_1915)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1914),c_Int_OBit1(U_1915)) ) ),
inference(variable_rename,[status(thm)],[f_662_1]) ).
fof(f_662_3,plain,
( ! [U_1919,U_1917] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1917),c_Int_OBit1(U_1919))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1917,U_1919) )
& ! [U_1918,U_1916] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1916,U_1918)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1916),c_Int_OBit1(U_1918)) ) ),
inference(miniscope,[status(thm)],[f_662_2]) ).
cnf(f_662_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1916,U_1918)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1916),c_Int_OBit1(U_1918)) ),
inference(clausify,[status(thm)],[f_662_3]) ).
cnf(f_662_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1917),c_Int_OBit1(U_1919))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1917,U_1919) ),
inference(clausify,[status(thm)],[f_662_3]) ).
fof(f_663_1,plain,
! [V_l_2,V_k_2] :
( ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
| V_k_2 != V_l_2 )
& ( V_k_2 = V_l_2
| c_Int_OBit1(V_k_2) != c_Int_OBit1(V_l_2) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I51_J]) ).
fof(f_663_2,plain,
! [U_1921,U_1920] :
( ( c_Int_OBit1(U_1920) = c_Int_OBit1(U_1921)
| U_1920 != U_1921 )
& ( U_1920 = U_1921
| c_Int_OBit1(U_1920) != c_Int_OBit1(U_1921) ) ),
inference(variable_rename,[status(thm)],[f_663_1]) ).
fof(f_663_3,plain,
( ! [U_1925,U_1923] :
( c_Int_OBit1(U_1923) = c_Int_OBit1(U_1925)
| U_1923 != U_1925 )
& ! [U_1924,U_1922] :
( U_1922 = U_1924
| c_Int_OBit1(U_1922) != c_Int_OBit1(U_1924) ) ),
inference(miniscope,[status(thm)],[f_663_2]) ).
cnf(f_663_4,plain,
( U_1922 = U_1924
| c_Int_OBit1(U_1922) != c_Int_OBit1(U_1924) ),
inference(clausify,[status(thm)],[f_663_3]) ).
cnf(f_663_5,plain,
( c_Int_OBit1(U_1923) = c_Int_OBit1(U_1925)
| U_1923 != U_1925 ),
inference(clausify,[status(thm)],[f_663_3]) ).
fof(f_664_1,plain,
! [V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I22_J]) ).
fof(f_664_2,plain,
! [U_1926] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_1926))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_1926) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_1926)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_1926)) ) ),
inference(variable_rename,[status(thm)],[f_664_1]) ).
fof(f_664_3,plain,
( ! [U_1928] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_1928))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_1928) )
& ! [U_1927] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_1927)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_1927)) ) ),
inference(miniscope,[status(thm)],[f_664_2]) ).
cnf(f_664_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_1927)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_1927)) ),
inference(clausify,[status(thm)],[f_664_3]) ).
cnf(f_664_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_1928))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_1928) ),
inference(clausify,[status(thm)],[f_664_3]) ).
fof(f_665_1,plain,
! [V_wa_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I4_J]) ).
fof(f_665_2,plain,
! [U_1929] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1929),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1929,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1929,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1929),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[f_665_1]) ).
fof(f_665_3,plain,
( ! [U_1931] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1931),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1931,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_1930] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1930,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1930),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(miniscope,[status(thm)],[f_665_2]) ).
cnf(f_665_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1930,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1930),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_665_3]) ).
cnf(f_665_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1931),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1931,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_665_3]) ).
fof(f_666_1,plain,
! [V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I12_J]) ).
fof(f_666_2,plain,
! [U_1932] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1932),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1932,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1932,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1932),c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[f_666_1]) ).
fof(f_666_3,plain,
( ! [U_1934] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1934),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1934,c_Int_OPls) )
& ! [U_1933] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1933,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1933),c_Int_OPls) ) ),
inference(miniscope,[status(thm)],[f_666_2]) ).
cnf(f_666_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1933,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1933),c_Int_OPls) ),
inference(clausify,[status(thm)],[f_666_3]) ).
cnf(f_666_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_1934),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1934,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_666_3]) ).
fof(f_667_1,plain,
! [V_k] : c_Int_OBit1(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k),V_k),
inference(fof_nnf,[status(thm)],[fact_Bit1__def]) ).
fof(f_667_2,plain,
! [U_1935] : c_Int_OBit1(U_1935) = 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_1935),U_1935),
inference(variable_rename,[status(thm)],[f_667_1]) ).
cnf(f_667_3,plain,
c_Int_OBit1(U_1935) = 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_1935),U_1935),
inference(clausify,[status(thm)],[f_667_2]) ).
fof(f_668_1,plain,
! [V_k] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(V_k)) = c_Int_OBit1(c_Int_Opred(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k))),
inference(fof_nnf,[status(thm)],[fact_minus__Bit1]) ).
fof(f_668_2,plain,
! [U_1936] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(U_1936)) = c_Int_OBit1(c_Int_Opred(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1936))),
inference(variable_rename,[status(thm)],[f_668_1]) ).
cnf(f_668_3,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit1(U_1936)) = c_Int_OBit1(c_Int_Opred(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_1936))),
inference(clausify,[status(thm)],[f_668_2]) ).
fof(f_669_1,plain,
! [V_w,T_a] :
( ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(V_w)))
| ~ class_Int_Oring__char__0(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_iszero__number__of__Bit1]) ).
fof(f_669_2,plain,
! [U_1938,U_1937] :
( ~ c_Int_Oiszero(U_1937,c_Int_Onumber__class_Onumber__of(U_1937,c_Int_OBit1(U_1938)))
| ~ class_Int_Oring__char__0(U_1937)
| ~ class_Int_Onumber__ring(U_1937) ),
inference(variable_rename,[status(thm)],[f_669_1]) ).
cnf(f_669_3,plain,
( ~ c_Int_Oiszero(U_1937,c_Int_Onumber__class_Onumber__of(U_1937,c_Int_OBit1(U_1938)))
| ~ class_Int_Oring__char__0(U_1937)
| ~ class_Int_Onumber__ring(U_1937) ),
inference(clausify,[status(thm)],[f_669_2]) ).
fof(f_670_1,plain,
c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
inference(fof_nnf,[status(thm)],[fact_succ__Pls]) ).
cnf(f_670_2,plain,
c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
inference(clausify,[status(thm)],[f_670_1]) ).
fof(f_671_1,plain,
! [V_w,T_a] :
( c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),c_Int_Onumber__class_Onumber__of(T_a,V_w))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__Bit1]) ).
fof(f_671_2,plain,
! [U_1940,U_1939] :
( c_Int_Onumber__class_Onumber__of(U_1939,c_Int_OBit1(U_1940)) = c_Groups_Oplus__class_Oplus(U_1939,c_Groups_Oplus__class_Oplus(U_1939,c_Groups_Oone__class_Oone(U_1939),c_Int_Onumber__class_Onumber__of(U_1939,U_1940)),c_Int_Onumber__class_Onumber__of(U_1939,U_1940))
| ~ class_Int_Onumber__ring(U_1939) ),
inference(variable_rename,[status(thm)],[f_671_1]) ).
cnf(f_671_3,plain,
( c_Int_Onumber__class_Onumber__of(U_1939,c_Int_OBit1(U_1940)) = c_Groups_Oplus__class_Oplus(U_1939,c_Groups_Oplus__class_Oplus(U_1939,c_Groups_Oone__class_Oone(U_1939),c_Int_Onumber__class_Onumber__of(U_1939,U_1940)),c_Int_Onumber__class_Onumber__of(U_1939,U_1940))
| ~ class_Int_Onumber__ring(U_1939) ),
inference(clausify,[status(thm)],[f_671_2]) ).
fof(f_672_1,plain,
! [V_a,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))),V_a) = V_a
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__numeral__1]) ).
fof(f_672_2,plain,
! [U_1942,U_1941] :
( hAPP(c_Groups_Otimes__class_Otimes(U_1941,c_Int_Onumber__class_Onumber__of(U_1941,c_Int_OBit1(c_Int_OPls))),U_1942) = U_1942
| ~ class_Int_Onumber__ring(U_1941) ),
inference(variable_rename,[status(thm)],[f_672_1]) ).
cnf(f_672_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_1941,c_Int_Onumber__class_Onumber__of(U_1941,c_Int_OBit1(c_Int_OPls))),U_1942) = U_1942
| ~ class_Int_Onumber__ring(U_1941) ),
inference(clausify,[status(thm)],[f_672_2]) ).
fof(f_673_1,plain,
! [V_a,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_a
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__numeral__1__right]) ).
fof(f_673_2,plain,
! [U_1944,U_1943] :
( hAPP(c_Groups_Otimes__class_Otimes(U_1943,U_1944),c_Int_Onumber__class_Onumber__of(U_1943,c_Int_OBit1(c_Int_OPls))) = U_1944
| ~ class_Int_Onumber__ring(U_1943) ),
inference(variable_rename,[status(thm)],[f_673_1]) ).
cnf(f_673_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_1943,U_1944),c_Int_Onumber__class_Onumber__of(U_1943,c_Int_OBit1(c_Int_OPls))) = U_1944
| ~ class_Int_Onumber__ring(U_1943) ),
inference(clausify,[status(thm)],[f_673_2]) ).
fof(f_674_1,plain,
! [T_a] :
( c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_numeral__1__eq__1]) ).
fof(f_674_2,plain,
! [U_1945] :
( c_Int_Onumber__class_Onumber__of(U_1945,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_1945)
| ~ class_Int_Onumber__ring(U_1945) ),
inference(variable_rename,[status(thm)],[f_674_1]) ).
cnf(f_674_3,plain,
( c_Int_Onumber__class_Onumber__of(U_1945,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_1945)
| ~ class_Int_Onumber__ring(U_1945) ),
inference(clausify,[status(thm)],[f_674_2]) ).
fof(f_675_1,plain,
! [T_a] :
( c_Groups_Oone__class_Oone(T_a) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_semiring__norm_I110_J]) ).
fof(f_675_2,plain,
! [U_1946] :
( c_Groups_Oone__class_Oone(U_1946) = c_Int_Onumber__class_Onumber__of(U_1946,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(U_1946) ),
inference(variable_rename,[status(thm)],[f_675_1]) ).
cnf(f_675_3,plain,
( c_Groups_Oone__class_Oone(U_1946) = c_Int_Onumber__class_Onumber__of(U_1946,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(U_1946) ),
inference(clausify,[status(thm)],[f_675_2]) ).
fof(f_676_1,plain,
! [V_x,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,V_x,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_x
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__Numeral1]) ).
fof(f_676_2,plain,
! [U_1948,U_1947] :
( c_Rings_Oinverse__class_Odivide(U_1947,U_1948,c_Int_Onumber__class_Onumber__of(U_1947,c_Int_OBit1(c_Int_OPls))) = U_1948
| ~ class_Int_Onumber__ring(U_1947)
| ~ class_Fields_Ofield(U_1947) ),
inference(variable_rename,[status(thm)],[f_676_1]) ).
cnf(f_676_3,plain,
( c_Rings_Oinverse__class_Odivide(U_1947,U_1948,c_Int_Onumber__class_Onumber__of(U_1947,c_Int_OBit1(c_Int_OPls))) = U_1948
| ~ class_Int_Onumber__ring(U_1947)
| ~ class_Fields_Ofield(U_1947) ),
inference(clausify,[status(thm)],[f_676_2]) ).
fof(f_677_1,plain,
! [V_a,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_a
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__numeral__1]) ).
fof(f_677_2,plain,
! [U_1950,U_1949] :
( c_Rings_Oinverse__class_Odivide(U_1949,U_1950,c_Int_Onumber__class_Onumber__of(U_1949,c_Int_OBit1(c_Int_OPls))) = U_1950
| ~ class_Int_Onumber__ring(U_1949)
| ~ class_Fields_Ofield(U_1949) ),
inference(variable_rename,[status(thm)],[f_677_1]) ).
cnf(f_677_3,plain,
( c_Rings_Oinverse__class_Odivide(U_1949,U_1950,c_Int_Onumber__class_Onumber__of(U_1949,c_Int_OBit1(c_Int_OPls))) = U_1950
| ~ class_Int_Onumber__ring(U_1949)
| ~ class_Fields_Ofield(U_1949) ),
inference(clausify,[status(thm)],[f_677_2]) ).
fof(f_678_1,plain,
! [T_a] :
( c_Rings_Oinverse__class_Oinverse(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inverse__numeral__1]) ).
fof(f_678_2,plain,
! [U_1951] :
( c_Rings_Oinverse__class_Oinverse(U_1951,c_Int_Onumber__class_Onumber__of(U_1951,c_Int_OBit1(c_Int_OPls))) = c_Int_Onumber__class_Onumber__of(U_1951,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(U_1951)
| ~ class_Fields_Ofield(U_1951) ),
inference(variable_rename,[status(thm)],[f_678_1]) ).
cnf(f_678_3,plain,
( c_Rings_Oinverse__class_Oinverse(U_1951,c_Int_Onumber__class_Onumber__of(U_1951,c_Int_OBit1(c_Int_OPls))) = c_Int_Onumber__class_Onumber__of(U_1951,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(U_1951)
| ~ class_Fields_Ofield(U_1951) ),
inference(clausify,[status(thm)],[f_678_2]) ).
fof(f_679_1,plain,
! [V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OPls) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I29_J]) ).
fof(f_679_2,plain,
! [U_1952] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_1952),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1952,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1952,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_1952),c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[f_679_1]) ).
fof(f_679_3,plain,
( ! [U_1954] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_1954),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1954,c_Int_OPls) )
& ! [U_1953] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1953,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_1953),c_Int_OPls) ) ),
inference(miniscope,[status(thm)],[f_679_2]) ).
cnf(f_679_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1953,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_1953),c_Int_OPls) ),
inference(clausify,[status(thm)],[f_679_3]) ).
cnf(f_679_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_1954),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1954,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_679_3]) ).
fof(f_680_1,plain,
! [V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_k_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I5_J]) ).
fof(f_680_2,plain,
! [U_1955] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_1955))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_1955) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_1955)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_1955)) ) ),
inference(variable_rename,[status(thm)],[f_680_1]) ).
fof(f_680_3,plain,
( ! [U_1957] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_1957))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_1957) )
& ! [U_1956] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_1956)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_1956)) ) ),
inference(miniscope,[status(thm)],[f_680_2]) ).
cnf(f_680_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_1956)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_1956)) ),
inference(clausify,[status(thm)],[f_680_3]) ).
cnf(f_680_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_1957))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_1957) ),
inference(clausify,[status(thm)],[f_680_3]) ).
fof(f_681_1,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)),
inference(fof_nnf,[status(thm)],[fact_one__is__num__one]) ).
cnf(f_681_2,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)),
inference(clausify,[status(thm)],[f_681_1]) ).
fof(f_682_1,plain,
! [T_a] :
( ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__iszero__Numeral1]) ).
fof(f_682_2,plain,
! [U_1958] :
( ~ c_Int_Oiszero(U_1958,c_Int_Onumber__class_Onumber__of(U_1958,c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_1958) ),
inference(variable_rename,[status(thm)],[f_682_1]) ).
cnf(f_682_3,plain,
( ~ c_Int_Oiszero(U_1958,c_Int_Onumber__class_Onumber__of(U_1958,c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_1958) ),
inference(clausify,[status(thm)],[f_682_2]) ).
fof(f_683_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J]) ).
cnf(f_683_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
inference(clausify,[status(thm)],[f_683_1]) ).
fof(f_684_1,plain,
! [V_y_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__special_I2_J]) ).
fof(f_684_2,plain,
! [U_1960,U_1959] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1959,c_Groups_Oone__class_Oone(U_1959),c_Int_Onumber__class_Onumber__of(U_1959,U_1960))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_1960) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_1960)
| ~ c_Orderings_Oord__class_Oless__eq(U_1959,c_Groups_Oone__class_Oone(U_1959),c_Int_Onumber__class_Onumber__of(U_1959,U_1960)) ) )
| ~ class_Rings_Olinordered__idom(U_1959)
| ~ class_Int_Onumber__ring(U_1959) ),
inference(variable_rename,[status(thm)],[f_684_1]) ).
cnf(f_684_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_1960)
| ~ c_Orderings_Oord__class_Oless__eq(U_1959,c_Groups_Oone__class_Oone(U_1959),c_Int_Onumber__class_Onumber__of(U_1959,U_1960))
| ~ class_Rings_Olinordered__idom(U_1959)
| ~ class_Int_Onumber__ring(U_1959) ),
inference(clausify,[status(thm)],[f_684_2]) ).
cnf(f_684_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1959,c_Groups_Oone__class_Oone(U_1959),c_Int_Onumber__class_Onumber__of(U_1959,U_1960))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_1960)
| ~ class_Rings_Olinordered__idom(U_1959)
| ~ class_Int_Onumber__ring(U_1959) ),
inference(clausify,[status(thm)],[f_684_2]) ).
fof(f_685_1,plain,
! [V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a)) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__special_I4_J]) ).
fof(f_685_2,plain,
! [U_1962,U_1961] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1961,c_Int_Onumber__class_Onumber__of(U_1961,U_1962),c_Groups_Oone__class_Oone(U_1961))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1962,c_Int_OBit1(c_Int_OPls)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1962,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless__eq(U_1961,c_Int_Onumber__class_Onumber__of(U_1961,U_1962),c_Groups_Oone__class_Oone(U_1961)) ) )
| ~ class_Rings_Olinordered__idom(U_1961)
| ~ class_Int_Onumber__ring(U_1961) ),
inference(variable_rename,[status(thm)],[f_685_1]) ).
cnf(f_685_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1962,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless__eq(U_1961,c_Int_Onumber__class_Onumber__of(U_1961,U_1962),c_Groups_Oone__class_Oone(U_1961))
| ~ class_Rings_Olinordered__idom(U_1961)
| ~ class_Int_Onumber__ring(U_1961) ),
inference(clausify,[status(thm)],[f_685_2]) ).
cnf(f_685_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1961,c_Int_Onumber__class_Onumber__of(U_1961,U_1962),c_Groups_Oone__class_Oone(U_1961))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_1962,c_Int_OBit1(c_Int_OPls))
| ~ class_Rings_Olinordered__idom(U_1961)
| ~ class_Int_Onumber__ring(U_1961) ),
inference(clausify,[status(thm)],[f_685_2]) ).
fof(f_686_1,plain,
! [V_y_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_y_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_y_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__special_I2_J]) ).
fof(f_686_2,plain,
! [U_1964,U_1963] :
( ( ( c_Orderings_Oord__class_Oless(U_1963,c_Groups_Oone__class_Oone(U_1963),c_Int_Onumber__class_Onumber__of(U_1963,U_1964))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_1964) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_1964)
| ~ c_Orderings_Oord__class_Oless(U_1963,c_Groups_Oone__class_Oone(U_1963),c_Int_Onumber__class_Onumber__of(U_1963,U_1964)) ) )
| ~ class_Rings_Olinordered__idom(U_1963)
| ~ class_Int_Onumber__ring(U_1963) ),
inference(variable_rename,[status(thm)],[f_686_1]) ).
cnf(f_686_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_1964)
| ~ c_Orderings_Oord__class_Oless(U_1963,c_Groups_Oone__class_Oone(U_1963),c_Int_Onumber__class_Onumber__of(U_1963,U_1964))
| ~ class_Rings_Olinordered__idom(U_1963)
| ~ class_Int_Onumber__ring(U_1963) ),
inference(clausify,[status(thm)],[f_686_2]) ).
cnf(f_686_4,plain,
( c_Orderings_Oord__class_Oless(U_1963,c_Groups_Oone__class_Oone(U_1963),c_Int_Onumber__class_Onumber__of(U_1963,U_1964))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_1964)
| ~ class_Rings_Olinordered__idom(U_1963)
| ~ class_Int_Onumber__ring(U_1963) ),
inference(clausify,[status(thm)],[f_686_2]) ).
fof(f_687_1,plain,
! [V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x_2,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a)) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__special_I4_J]) ).
fof(f_687_2,plain,
! [U_1966,U_1965] :
( ( ( c_Orderings_Oord__class_Oless(U_1965,c_Int_Onumber__class_Onumber__of(U_1965,U_1966),c_Groups_Oone__class_Oone(U_1965))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1966,c_Int_OBit1(c_Int_OPls)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1966,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless(U_1965,c_Int_Onumber__class_Onumber__of(U_1965,U_1966),c_Groups_Oone__class_Oone(U_1965)) ) )
| ~ class_Rings_Olinordered__idom(U_1965)
| ~ class_Int_Onumber__ring(U_1965) ),
inference(variable_rename,[status(thm)],[f_687_1]) ).
cnf(f_687_3,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1966,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless(U_1965,c_Int_Onumber__class_Onumber__of(U_1965,U_1966),c_Groups_Oone__class_Oone(U_1965))
| ~ class_Rings_Olinordered__idom(U_1965)
| ~ class_Int_Onumber__ring(U_1965) ),
inference(clausify,[status(thm)],[f_687_2]) ).
cnf(f_687_4,plain,
( c_Orderings_Oord__class_Oless(U_1965,c_Int_Onumber__class_Onumber__of(U_1965,U_1966),c_Groups_Oone__class_Oone(U_1965))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_1966,c_Int_OBit1(c_Int_OPls))
| ~ class_Rings_Olinordered__idom(U_1965)
| ~ class_Int_Onumber__ring(U_1965) ),
inference(clausify,[status(thm)],[f_687_2]) ).
fof(f_688_1,plain,
! [V_v,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_v),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_v,c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__special_I3_J]) ).
fof(f_688_2,plain,
! [U_1968,U_1967] :
( c_Groups_Oplus__class_Oplus(U_1967,c_Int_Onumber__class_Onumber__of(U_1967,U_1968),c_Groups_Oone__class_Oone(U_1967)) = c_Int_Onumber__class_Onumber__of(U_1967,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1968,c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_1967) ),
inference(variable_rename,[status(thm)],[f_688_1]) ).
cnf(f_688_3,plain,
( c_Groups_Oplus__class_Oplus(U_1967,c_Int_Onumber__class_Onumber__of(U_1967,U_1968),c_Groups_Oone__class_Oone(U_1967)) = c_Int_Onumber__class_Onumber__of(U_1967,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_1968,c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_1967) ),
inference(clausify,[status(thm)],[f_688_2]) ).
fof(f_689_1,plain,
! [V_w,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_w))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__special_I2_J]) ).
fof(f_689_2,plain,
! [U_1970,U_1969] :
( c_Groups_Oplus__class_Oplus(U_1969,c_Groups_Oone__class_Oone(U_1969),c_Int_Onumber__class_Onumber__of(U_1969,U_1970)) = c_Int_Onumber__class_Onumber__of(U_1969,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_1970))
| ~ class_Int_Onumber__ring(U_1969) ),
inference(variable_rename,[status(thm)],[f_689_1]) ).
cnf(f_689_3,plain,
( c_Groups_Oplus__class_Oplus(U_1969,c_Groups_Oone__class_Oone(U_1969),c_Int_Onumber__class_Onumber__of(U_1969,U_1970)) = c_Int_Onumber__class_Onumber__of(U_1969,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_1970))
| ~ class_Int_Onumber__ring(U_1969) ),
inference(clausify,[status(thm)],[f_689_2]) ).
fof(f_690_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_690_2,plain,
! [U_1971] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1971),
inference(variable_rename,[status(thm)],[f_690_1]) ).
cnf(f_690_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1971),
inference(clausify,[status(thm)],[f_690_2]) ).
fof(f_691_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_691_2,plain,
! [U_1972] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1972,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_691_1]) ).
cnf(f_691_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1972,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_691_2]) ).
fof(f_692_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),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(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),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_692_2,plain,
! [U_1975,U_1974,U_1973] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_1973),U_1974),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_1973),U_1975))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1974,U_1975)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1973) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1974,U_1975)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1973)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_1973),U_1974),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_1973),U_1975)) ) ),
inference(variable_rename,[status(thm)],[f_692_1]) ).
fof(f_692_3,plain,
( ! [U_1981,U_1979,U_1977] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_1977),U_1979),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_1977),U_1981))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1979,U_1981)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1977) ) )
& ! [U_1980,U_1978,U_1976] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1978,U_1980)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1976)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_1976),U_1978),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_1976),U_1980)) ) ),
inference(miniscope,[status(thm)],[f_692_2]) ).
cnf(f_692_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1978,U_1980)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1976)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_1976),U_1978),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_1976),U_1980)) ),
inference(clausify,[status(thm)],[f_692_3]) ).
cnf(f_692_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1977)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_1977),U_1979),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_1977),U_1981)) ),
inference(clausify,[status(thm)],[f_692_3]) ).
cnf(f_692_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1979,U_1981)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_1977),U_1979),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_1977),U_1981)) ),
inference(clausify,[status(thm)],[f_692_3]) ).
fof(f_693_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_693_2,plain,
! [U_1982] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1982,U_1982),
inference(variable_rename,[status(thm)],[f_693_1]) ).
cnf(f_693_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1982,U_1982),
inference(clausify,[status(thm)],[f_693_2]) ).
fof(f_694_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_694_2,plain,
! [U_1984,U_1983] :
( ( U_1983 != U_1984
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1984,U_1983)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1983,U_1984) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1984,U_1983)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1983,U_1984)
| U_1983 = U_1984 ) ),
inference(variable_rename,[status(thm)],[f_694_1]) ).
fof(f_694_3,plain,
( ! [U_1988,U_1986] :
( U_1986 != U_1988
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1988,U_1986)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1986,U_1988) ) )
& ! [U_1987,U_1985] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1987,U_1985)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1985,U_1987)
| U_1985 = U_1987 ) ),
inference(miniscope,[status(thm)],[f_694_2]) ).
cnf(f_694_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1987,U_1985)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1985,U_1987)
| U_1985 = U_1987 ),
inference(clausify,[status(thm)],[f_694_3]) ).
cnf(f_694_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1986,U_1988)
| U_1986 != U_1988 ),
inference(clausify,[status(thm)],[f_694_3]) ).
cnf(f_694_6,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1988,U_1986)
| U_1986 != U_1988 ),
inference(clausify,[status(thm)],[f_694_3]) ).
fof(f_695_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_695_2,plain,
! [U_1990,U_1989] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1990,U_1989)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1989,U_1990)
| U_1989 = U_1990 ),
inference(variable_rename,[status(thm)],[f_695_1]) ).
cnf(f_695_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1990,U_1989)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1989,U_1990)
| U_1989 = U_1990 ),
inference(clausify,[status(thm)],[f_695_2]) ).
fof(f_696_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_696_2,plain,
! [U_1991] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1991,U_1991),
inference(variable_rename,[status(thm)],[f_696_1]) ).
cnf(f_696_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1991,U_1991),
inference(clausify,[status(thm)],[f_696_2]) ).
fof(f_697_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_697_2,plain,
! [U_1993,U_1992] :
( U_1993 != U_1992
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1992,U_1993) ),
inference(variable_rename,[status(thm)],[f_697_1]) ).
cnf(f_697_3,plain,
( U_1993 != U_1992
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1992,U_1993) ),
inference(clausify,[status(thm)],[f_697_2]) ).
fof(f_698_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_698_2,plain,
! [U_1995,U_1994] :
( U_1994 != U_1995
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1994,U_1995) ),
inference(variable_rename,[status(thm)],[f_698_1]) ).
cnf(f_698_3,plain,
( U_1994 != U_1995
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1994,U_1995) ),
inference(clausify,[status(thm)],[f_698_2]) ).
fof(f_699_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_699_2,plain,
! [U_1998,U_1997,U_1996] :
( hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996))
| ( ~ hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1997,U_1996) )
| ( ~ hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996))
& U_1996 = U_1997 )
| ( ~ hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1996,U_1997) ) ),
inference(variable_rename,[status(thm)],[f_699_1]) ).
cnf(f_699_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1997,U_1996)
| hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996))
| U_1996 = U_1997
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1996,U_1997) ),
inference(clausify,[status(thm)],[f_699_2]) ).
cnf(f_699_4,plain,
( ~ hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996))
| hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996))
| U_1996 = U_1997
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1996,U_1997) ),
inference(clausify,[status(thm)],[f_699_2]) ).
cnf(f_699_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1997,U_1996)
| hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996))
| ~ hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1996,U_1997) ),
inference(clausify,[status(thm)],[f_699_2]) ).
cnf(f_699_6,plain,
( ~ hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996))
| hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996))
| ~ hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1996,U_1997) ),
inference(clausify,[status(thm)],[f_699_2]) ).
cnf(f_699_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1997,U_1996)
| hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996))
| U_1996 = U_1997
| ~ hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996)) ),
inference(clausify,[status(thm)],[f_699_2]) ).
cnf(f_699_8,plain,
( ~ hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996))
| hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996))
| U_1996 = U_1997
| ~ hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996)) ),
inference(clausify,[status(thm)],[f_699_2]) ).
cnf(f_699_9,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1997,U_1996)
| hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996))
| ~ hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996))
| ~ hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996)) ),
inference(clausify,[status(thm)],[f_699_2]) ).
cnf(f_699_10,plain,
( ~ hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996))
| hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996))
| ~ hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996))
| ~ hBOOL(hAPP(hAPP(U_1998,U_1997),U_1996)) ),
inference(clausify,[status(thm)],[f_699_2]) ).
fof(f_700_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_700_2,plain,
! [U_2000,U_1999] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1999,U_2000) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2000,U_1999),
inference(variable_rename,[status(thm)],[f_700_1]) ).
cnf(f_700_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1999,U_2000) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2000,U_1999),
inference(clausify,[status(thm)],[f_700_2]) ).
fof(f_701_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_701_2,plain,
! [U_2003,U_2002,U_2001] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2001,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2002,U_2003)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2002,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2001,U_2003)),
inference(variable_rename,[status(thm)],[f_701_1]) ).
cnf(f_701_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2001,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2002,U_2003)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2002,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2001,U_2003)),
inference(clausify,[status(thm)],[f_701_2]) ).
fof(f_702_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_702_2,plain,
! [U_2006,U_2005,U_2004] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2004,U_2005),U_2006) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2004,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2005,U_2006)),
inference(variable_rename,[status(thm)],[f_702_1]) ).
cnf(f_702_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2004,U_2005),U_2006) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2004,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2005,U_2006)),
inference(clausify,[status(thm)],[f_702_2]) ).
fof(f_703_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_703_2,plain,
! [U_2009,U_2008,U_2007] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2007,U_2008) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2007,U_2009)
| U_2008 != U_2009 )
& ( U_2008 = U_2009
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2007,U_2008) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2007,U_2009) ) ),
inference(variable_rename,[status(thm)],[f_703_1]) ).
fof(f_703_3,plain,
( ! [U_2015,U_2013] :
( ! [U_2011] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2011,U_2013) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2011,U_2015)
| U_2013 != U_2015 )
& ! [U_2014,U_2012] :
( ! [U_2010] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2010,U_2012) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2010,U_2014)
| U_2012 = U_2014 ) ),
inference(miniscope,[status(thm)],[f_703_2]) ).
cnf(f_703_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2010,U_2012) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2010,U_2014)
| U_2012 = U_2014 ),
inference(clausify,[status(thm)],[f_703_3]) ).
cnf(f_703_5,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2011,U_2013) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2011,U_2015)
| U_2013 != U_2015 ),
inference(clausify,[status(thm)],[f_703_3]) ).
fof(f_704_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_704_2,plain,
! [U_2018,U_2017,U_2016] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2016,U_2017) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2018,U_2017)
| U_2016 != U_2018 )
& ( U_2016 = U_2018
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2016,U_2017) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2018,U_2017) ) ),
inference(variable_rename,[status(thm)],[f_704_1]) ).
fof(f_704_3,plain,
( ! [U_2024,U_2022,U_2020] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2020,U_2022) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2024,U_2022)
| U_2020 != U_2024 )
& ! [U_2023,U_2021,U_2019] :
( U_2019 = U_2023
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2019,U_2021) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2023,U_2021) ) ),
inference(miniscope,[status(thm)],[f_704_2]) ).
cnf(f_704_4,plain,
( U_2019 = U_2023
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2019,U_2021) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2023,U_2021) ),
inference(clausify,[status(thm)],[f_704_3]) ).
cnf(f_704_5,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2020,U_2022) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2024,U_2022)
| U_2020 != U_2024 ),
inference(clausify,[status(thm)],[f_704_3]) ).
fof(f_705_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_705_2,plain,
! [U_2026,U_2025] :
( U_2025 = U_2026
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2026,U_2025)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2025,U_2026) ),
inference(variable_rename,[status(thm)],[f_705_1]) ).
cnf(f_705_3,plain,
( U_2025 = U_2026
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2026,U_2025)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2025,U_2026) ),
inference(clausify,[status(thm)],[f_705_2]) ).
fof(f_706_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_706_2,plain,
! [U_2029,U_2028,U_2027] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2027,U_2029)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2028,U_2029)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2027,U_2028) ),
inference(variable_rename,[status(thm)],[f_706_1]) ).
cnf(f_706_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2027,U_2029)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2028,U_2029)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2027,U_2028) ),
inference(clausify,[status(thm)],[f_706_2]) ).
fof(f_707_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_707_2,plain,
! [U_2031,U_2030] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2030,U_2031)
| U_2030 != U_2031 ),
inference(variable_rename,[status(thm)],[f_707_1]) ).
cnf(f_707_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2030,U_2031)
| U_2030 != U_2031 ),
inference(clausify,[status(thm)],[f_707_2]) ).
fof(f_708_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_708_2,plain,
! [U_2033,U_2032] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2033,U_2032)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2032,U_2033) ),
inference(variable_rename,[status(thm)],[f_708_1]) ).
cnf(f_708_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2033,U_2032)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2032,U_2033) ),
inference(clausify,[status(thm)],[f_708_2]) ).
fof(f_709_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_709_2,plain,
! [U_2034] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2034,U_2034),
inference(variable_rename,[status(thm)],[f_709_1]) ).
cnf(f_709_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2034,U_2034),
inference(clausify,[status(thm)],[f_709_2]) ).
fof(f_710_1,plain,
! [V_k,V_n,V_m] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_n)),V_k) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n),V_k)),
inference(fof_nnf,[status(thm)],[fact_nat__mult__assoc]) ).
fof(f_710_2,plain,
! [U_2037,U_2036,U_2035] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2035),U_2036)),U_2037) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2035),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2036),U_2037)),
inference(variable_rename,[status(thm)],[f_710_1]) ).
cnf(f_710_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2035),U_2036)),U_2037) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2035),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2036),U_2037)),
inference(clausify,[status(thm)],[f_710_2]) ).
fof(f_711_1,plain,
! [V_n,V_m] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_n) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n),V_m),
inference(fof_nnf,[status(thm)],[fact_nat__mult__commute]) ).
fof(f_711_2,plain,
! [U_2039,U_2038] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2038),U_2039) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2039),U_2038),
inference(variable_rename,[status(thm)],[f_711_1]) ).
cnf(f_711_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2038),U_2039) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2039),U_2038),
inference(clausify,[status(thm)],[f_711_2]) ).
fof(f_712_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_712_2,plain,
! [U_2040] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2040,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_712_1]) ).
cnf(f_712_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2040,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_712_2]) ).
fof(f_713_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_713_2,plain,
! [U_2041] :
( ( U_2041 != 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_2041) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2041)
| U_2041 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_713_1]) ).
fof(f_713_3,plain,
( ! [U_2043] :
( U_2043 != 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_2043) )
& ! [U_2042] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2042)
| U_2042 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_713_2]) ).
cnf(f_713_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2042)
| U_2042 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_713_3]) ).
cnf(f_713_5,plain,
( U_2043 != 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_2043) ),
inference(clausify,[status(thm)],[f_713_3]) ).
fof(f_714_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_714_2,plain,
! [U_2044] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2044,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_714_1]) ).
cnf(f_714_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2044,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_714_2]) ).
fof(f_715_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_715_2,plain,
! [U_2046,U_2045] :
( U_2046 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2045,U_2046) ),
inference(variable_rename,[status(thm)],[f_715_1]) ).
fof(f_715_3,plain,
! [U_2046] :
( ! [U_2045] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2045,U_2046)
| U_2046 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(miniscope,[status(thm)],[f_715_2]) ).
cnf(f_715_4,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2045,U_2046)
| U_2046 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_715_3]) ).
fof(f_716_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_716_2,plain,
! [U_2047] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2047)
| U_2047 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_716_1]) ).
cnf(f_716_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2047)
| U_2047 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_716_2]) ).
fof(f_717_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_717_2,plain,
! [U_2049,U_2048] :
( U_2049 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2048,U_2049) != U_2048 ),
inference(variable_rename,[status(thm)],[f_717_1]) ).
fof(f_717_3,plain,
! [U_2049] :
( ! [U_2048] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2048,U_2049) != U_2048
| U_2049 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(miniscope,[status(thm)],[f_717_2]) ).
cnf(f_717_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2048,U_2049) != U_2048
| U_2049 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_717_3]) ).
fof(f_718_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_718_2,plain,
! [U_2051,U_2050] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2050,U_2051) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2051 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2050 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( U_2051 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2050 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2050,U_2051) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_718_1]) ).
fof(f_718_3,plain,
( ! [U_2055,U_2053] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2053,U_2055) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2055 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2053 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2054,U_2052] :
( ( U_2054 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2052 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2052,U_2054) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_718_2]) ).
cnf(f_718_4,plain,
( U_2052 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2052,U_2054) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_718_3]) ).
cnf(f_718_5,plain,
( U_2054 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2052,U_2054) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_718_3]) ).
cnf(f_718_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2053,U_2055) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2055 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2053 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_718_3]) ).
fof(f_719_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_719_2,plain,
! [U_2056] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2056,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2056,
inference(variable_rename,[status(thm)],[f_719_1]) ).
cnf(f_719_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2056,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2056,
inference(clausify,[status(thm)],[f_719_2]) ).
fof(f_720_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_720_2,plain,
! [U_2057] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2057) = U_2057,
inference(variable_rename,[status(thm)],[f_720_1]) ).
cnf(f_720_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2057) = U_2057,
inference(clausify,[status(thm)],[f_720_2]) ).
fof(f_721_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_721_2,plain,
! [U_2058] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2058),
inference(variable_rename,[status(thm)],[f_721_1]) ).
cnf(f_721_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2058),
inference(clausify,[status(thm)],[f_721_2]) ).
fof(f_722_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_722_2,plain,
! [U_2059] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2059,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2059 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2059 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2059,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_722_1]) ).
fof(f_722_3,plain,
( ! [U_2061] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2061,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2061 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2060] :
( U_2060 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2060,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_722_2]) ).
cnf(f_722_4,plain,
( U_2060 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2060,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_722_3]) ).
cnf(f_722_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2061,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2061 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_722_3]) ).
fof(f_723_1,plain,
! [V_n_2,V_k_2,V_ma_2] :
( ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2) = 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(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2) != 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_723_2,plain,
! [U_2064,U_2063,U_2062] :
( ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2062),U_2063) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2064),U_2063)
| ( U_2063 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2062 != U_2064 ) )
& ( U_2063 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2062 = U_2064
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2062),U_2063) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2064),U_2063) ) ),
inference(variable_rename,[status(thm)],[f_723_1]) ).
fof(f_723_3,plain,
( ! [U_2070,U_2068,U_2066] :
( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2066),U_2068) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2070),U_2068)
| ( U_2068 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2066 != U_2070 ) )
& ! [U_2069,U_2067,U_2065] :
( U_2067 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2065 = U_2069
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2065),U_2067) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2069),U_2067) ) ),
inference(miniscope,[status(thm)],[f_723_2]) ).
cnf(f_723_4,plain,
( U_2067 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2065 = U_2069
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2065),U_2067) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2069),U_2067) ),
inference(clausify,[status(thm)],[f_723_3]) ).
cnf(f_723_5,plain,
( U_2066 != U_2070
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2066),U_2068) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2070),U_2068) ),
inference(clausify,[status(thm)],[f_723_3]) ).
cnf(f_723_6,plain,
( U_2068 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2066),U_2068) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2070),U_2068) ),
inference(clausify,[status(thm)],[f_723_3]) ).
fof(f_724_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2) = 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(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2) != 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_724_2,plain,
! [U_2073,U_2072,U_2071] :
( ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2071),U_2072) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2071),U_2073)
| ( U_2071 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2072 != U_2073 ) )
& ( U_2071 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2072 = U_2073
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2071),U_2072) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2071),U_2073) ) ),
inference(variable_rename,[status(thm)],[f_724_1]) ).
fof(f_724_3,plain,
( ! [U_2079,U_2077,U_2075] :
( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2075),U_2077) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2075),U_2079)
| ( U_2075 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2077 != U_2079 ) )
& ! [U_2078,U_2076,U_2074] :
( U_2074 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2076 = U_2078
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2074),U_2076) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2074),U_2078) ) ),
inference(miniscope,[status(thm)],[f_724_2]) ).
cnf(f_724_4,plain,
( U_2074 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2076 = U_2078
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2074),U_2076) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2074),U_2078) ),
inference(clausify,[status(thm)],[f_724_3]) ).
cnf(f_724_5,plain,
( U_2077 != U_2079
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2075),U_2077) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2075),U_2079) ),
inference(clausify,[status(thm)],[f_724_3]) ).
cnf(f_724_6,plain,
( U_2075 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2075),U_2077) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2075),U_2079) ),
inference(clausify,[status(thm)],[f_724_3]) ).
fof(f_725_1,plain,
! [V_n_2,V_ma_2] :
( ( 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(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_725_2,plain,
! [U_2081,U_2080] :
( ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2080),U_2081) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( U_2081 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2080 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_2081 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2080 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2080),U_2081) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_725_1]) ).
fof(f_725_3,plain,
( ! [U_2085,U_2083] :
( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2083),U_2085) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( U_2085 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2083 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_2084,U_2082] :
( U_2084 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2082 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2082),U_2084) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_725_2]) ).
cnf(f_725_4,plain,
( U_2084 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2082 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2082),U_2084) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_725_3]) ).
cnf(f_725_5,plain,
( U_2083 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2083),U_2085) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_725_3]) ).
cnf(f_725_6,plain,
( U_2085 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2083),U_2085) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_725_3]) ).
fof(f_726_1,plain,
! [V_m] : 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_726_2,plain,
! [U_2086] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2086),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_726_1]) ).
cnf(f_726_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2086),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_726_2]) ).
fof(f_727_1,plain,
! [V_n] : 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_727_2,plain,
! [U_2087] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2087) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_727_1]) ).
cnf(f_727_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2087) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_727_2]) ).
fof(f_728_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_728_2,plain,
! [U_2090,U_2089,U_2088] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2088,U_2090)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2088,U_2089),U_2090) ),
inference(variable_rename,[status(thm)],[f_728_1]) ).
cnf(f_728_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2088,U_2090)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2088,U_2089),U_2090) ),
inference(clausify,[status(thm)],[f_728_2]) ).
fof(f_729_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_729_2,plain,
! [U_2094,U_2093,U_2092,U_2091] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2093,U_2094)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2093,U_2092) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2091,U_2094)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2091,U_2092) ),
inference(variable_rename,[status(thm)],[f_729_1]) ).
cnf(f_729_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2093,U_2094)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2093,U_2092) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2091,U_2094)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2091,U_2092) ),
inference(clausify,[status(thm)],[f_729_2]) ).
fof(f_730_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_730_2,plain,
! [U_2098,U_2097,U_2096,U_2095] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2095,U_2097),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2096,U_2098))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2097,U_2098)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2095,U_2096) ),
inference(variable_rename,[status(thm)],[f_730_1]) ).
cnf(f_730_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2095,U_2097),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2096,U_2098))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2097,U_2098)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2095,U_2096) ),
inference(clausify,[status(thm)],[f_730_2]) ).
fof(f_731_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_731_2,plain,
! [U_2101,U_2100,U_2099] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2099,U_2101),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2100,U_2101))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2099,U_2100) ),
inference(variable_rename,[status(thm)],[f_731_1]) ).
cnf(f_731_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2099,U_2101),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2100,U_2101))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2099,U_2100) ),
inference(clausify,[status(thm)],[f_731_2]) ).
fof(f_732_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_732_2,plain,
! [U_2104,U_2103,U_2102] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2102,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2104,U_2103))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2102,U_2103) ),
inference(variable_rename,[status(thm)],[f_732_1]) ).
cnf(f_732_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2102,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2104,U_2103))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2102,U_2103) ),
inference(clausify,[status(thm)],[f_732_2]) ).
fof(f_733_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_733_2,plain,
! [U_2107,U_2106,U_2105] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2105,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2106,U_2107))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2105,U_2106) ),
inference(variable_rename,[status(thm)],[f_733_1]) ).
cnf(f_733_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2105,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2106,U_2107))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2105,U_2106) ),
inference(clausify,[status(thm)],[f_733_2]) ).
fof(f_734_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_734_2,plain,
! [U_2110,U_2109,U_2108] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2108,U_2109),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2108,U_2110))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2109,U_2110) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2109,U_2110)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2108,U_2109),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2108,U_2110)) ) ),
inference(variable_rename,[status(thm)],[f_734_1]) ).
fof(f_734_3,plain,
( ! [U_2116,U_2114] :
( ! [U_2112] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2112,U_2114),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2112,U_2116))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2114,U_2116) )
& ! [U_2115,U_2113] :
( ! [U_2111] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2111,U_2113),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2111,U_2115))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2113,U_2115) ) ),
inference(miniscope,[status(thm)],[f_734_2]) ).
cnf(f_734_4,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2111,U_2113),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2111,U_2115))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2113,U_2115) ),
inference(clausify,[status(thm)],[f_734_3]) ).
cnf(f_734_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2112,U_2114),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2112,U_2116))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2114,U_2116) ),
inference(clausify,[status(thm)],[f_734_3]) ).
fof(f_735_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_735_2,plain,
! [U_2118,U_2117] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2117,U_2118),U_2118),
inference(variable_rename,[status(thm)],[f_735_1]) ).
cnf(f_735_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2117,U_2118),U_2118),
inference(clausify,[status(thm)],[f_735_2]) ).
fof(f_736_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_736_2,plain,
! [U_2120,U_2119] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2119,U_2120),U_2119),
inference(variable_rename,[status(thm)],[f_736_1]) ).
cnf(f_736_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2119,U_2120),U_2119),
inference(clausify,[status(thm)],[f_736_2]) ).
fof(f_737_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_737_2,plain,
! [U_2122,U_2121] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2121,U_2122)
| ( U_2121 != U_2122
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2121,U_2122) ) ),
inference(variable_rename,[status(thm)],[f_737_1]) ).
cnf(f_737_3,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2121,U_2122)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2121,U_2122) ),
inference(clausify,[status(thm)],[f_737_2]) ).
cnf(f_737_4,plain,
( U_2121 != U_2122
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2121,U_2122) ),
inference(clausify,[status(thm)],[f_737_2]) ).
fof(f_738_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_738_2,plain,
! [U_2124,U_2123] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2123,U_2124)
| U_2123 = U_2124
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2123,U_2124) ),
inference(variable_rename,[status(thm)],[f_738_1]) ).
cnf(f_738_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2123,U_2124)
| U_2123 = U_2124
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2123,U_2124) ),
inference(clausify,[status(thm)],[f_738_2]) ).
fof(f_739_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_739_2,plain,
! [U_2126,U_2125] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2125,U_2126)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2125,U_2126) ),
inference(variable_rename,[status(thm)],[f_739_1]) ).
cnf(f_739_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2125,U_2126)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2125,U_2126) ),
inference(clausify,[status(thm)],[f_739_2]) ).
fof(f_740_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_740_2,plain,
! [U_2128,U_2127] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2127,U_2128)
| ( U_2127 != U_2128
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2127,U_2128) ) )
& ( U_2127 = U_2128
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2127,U_2128)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2127,U_2128) ) ),
inference(variable_rename,[status(thm)],[f_740_1]) ).
fof(f_740_3,plain,
( ! [U_2132,U_2130] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2130,U_2132)
| ( U_2130 != U_2132
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2130,U_2132) ) )
& ! [U_2131,U_2129] :
( U_2129 = U_2131
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2129,U_2131)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2129,U_2131) ) ),
inference(miniscope,[status(thm)],[f_740_2]) ).
cnf(f_740_4,plain,
( U_2129 = U_2131
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2129,U_2131)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2129,U_2131) ),
inference(clausify,[status(thm)],[f_740_3]) ).
cnf(f_740_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2130,U_2132)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2130,U_2132) ),
inference(clausify,[status(thm)],[f_740_3]) ).
cnf(f_740_6,plain,
( U_2130 != U_2132
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2130,U_2132) ),
inference(clausify,[status(thm)],[f_740_3]) ).
fof(f_741_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_741_2,plain,
! [U_2134,U_2133] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2133,U_2134)
| U_2133 = U_2134
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2133,U_2134) )
& ( ( U_2133 != U_2134
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2133,U_2134) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2133,U_2134) ) ),
inference(variable_rename,[status(thm)],[f_741_1]) ).
fof(f_741_3,plain,
( ! [U_2138,U_2136] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2136,U_2138)
| U_2136 = U_2138
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2136,U_2138) )
& ! [U_2137,U_2135] :
( ( U_2135 != U_2137
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2135,U_2137) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2135,U_2137) ) ),
inference(miniscope,[status(thm)],[f_741_2]) ).
cnf(f_741_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2135,U_2137)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2135,U_2137) ),
inference(clausify,[status(thm)],[f_741_3]) ).
cnf(f_741_5,plain,
( U_2135 != U_2137
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2135,U_2137) ),
inference(clausify,[status(thm)],[f_741_3]) ).
cnf(f_741_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2136,U_2138)
| U_2136 = U_2138
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2136,U_2138) ),
inference(clausify,[status(thm)],[f_741_3]) ).
fof(f_742_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_742_2,plain,
! [U_2140,U_2139] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2139,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2140,U_2139)),
inference(variable_rename,[status(thm)],[f_742_1]) ).
cnf(f_742_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2139,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2140,U_2139)),
inference(clausify,[status(thm)],[f_742_2]) ).
fof(f_743_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_743_2,plain,
! [U_2142,U_2141] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2141,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2141,U_2142)),
inference(variable_rename,[status(thm)],[f_743_1]) ).
cnf(f_743_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2141,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2141,U_2142)),
inference(clausify,[status(thm)],[f_743_2]) ).
fof(f_744_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_744_2,plain,
! [U_2146,U_2145] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2145,U_2146)
| ! [U_2144] : U_2146 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2145,U_2144) )
& ( ? [U_2143] : U_2146 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2145,U_2143)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2145,U_2146) ) ),
inference(variable_rename,[status(thm)],[f_744_1]) ).
fof(f_744_3,plain,
( ! [U_2150,U_2148] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2148,U_2150)
| ! [U_2144] : U_2150 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2148,U_2144) )
& ! [U_2149,U_2147] :
( ? [U_2143] : U_2149 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2147,U_2143)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2147,U_2149) ) ),
inference(miniscope,[status(thm)],[f_744_2]) ).
fof(f_744_4,plain,
( ! [U_2150,U_2148] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2148,U_2150)
| ! [U_2144] : U_2150 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2148,U_2144) )
& ! [U_2149,U_2147] :
( U_2149 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2147,sK9(U_2149,U_2147))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2147,U_2149) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_2143,sK9(U_2149,U_2147))],[f_744_3]) ).
cnf(f_744_5,plain,
( U_2149 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2147,sK9(U_2149,U_2147))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2147,U_2149) ),
inference(clausify,[status(thm)],[f_744_4]) ).
cnf(f_744_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2148,U_2150)
| U_2150 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2148,U_2144) ),
inference(clausify,[status(thm)],[f_744_4]) ).
fof(f_745_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_745_2,plain,
! [U_2153,U_2152,U_2151] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2151,U_2152),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2151,U_2153))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2152,U_2153) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2152,U_2153)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2151,U_2152),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2151,U_2153)) ) ),
inference(variable_rename,[status(thm)],[f_745_1]) ).
fof(f_745_3,plain,
( ! [U_2159,U_2157] :
( ! [U_2155] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2155,U_2157),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2155,U_2159))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2157,U_2159) )
& ! [U_2158,U_2156] :
( ! [U_2154] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2154,U_2156),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2154,U_2158))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2156,U_2158) ) ),
inference(miniscope,[status(thm)],[f_745_2]) ).
cnf(f_745_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2154,U_2156),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2154,U_2158))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2156,U_2158) ),
inference(clausify,[status(thm)],[f_745_3]) ).
cnf(f_745_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2155,U_2157),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2155,U_2159))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2157,U_2159) ),
inference(clausify,[status(thm)],[f_745_3]) ).
fof(f_746_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_746_2,plain,
! [U_2162,U_2161,U_2160] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2160,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2161,U_2162))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2160,U_2161) ),
inference(variable_rename,[status(thm)],[f_746_1]) ).
cnf(f_746_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2160,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2161,U_2162))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2160,U_2161) ),
inference(clausify,[status(thm)],[f_746_2]) ).
fof(f_747_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_747_2,plain,
! [U_2165,U_2164,U_2163] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2163,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2165,U_2164))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2163,U_2164) ),
inference(variable_rename,[status(thm)],[f_747_1]) ).
cnf(f_747_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2163,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2165,U_2164))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2163,U_2164) ),
inference(clausify,[status(thm)],[f_747_2]) ).
fof(f_748_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_748_2,plain,
! [U_2168,U_2167,U_2166] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2166,U_2168),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2167,U_2168))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2166,U_2167) ),
inference(variable_rename,[status(thm)],[f_748_1]) ).
cnf(f_748_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2166,U_2168),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2167,U_2168))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2166,U_2167) ),
inference(clausify,[status(thm)],[f_748_2]) ).
fof(f_749_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_749_2,plain,
! [U_2172,U_2171,U_2170,U_2169] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2169,U_2171),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2170,U_2172))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2171,U_2172)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2169,U_2170) ),
inference(variable_rename,[status(thm)],[f_749_1]) ).
cnf(f_749_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2169,U_2171),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2170,U_2172))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2171,U_2172)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2169,U_2170) ),
inference(clausify,[status(thm)],[f_749_2]) ).
fof(f_750_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_750_2,plain,
! [U_2175,U_2174,U_2173] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2174,U_2175)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2173,U_2174),U_2175) ),
inference(variable_rename,[status(thm)],[f_750_1]) ).
fof(f_750_3,plain,
! [U_2175,U_2174] :
( ! [U_2173] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2173,U_2174),U_2175)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2174,U_2175) ),
inference(miniscope,[status(thm)],[f_750_2]) ).
cnf(f_750_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2173,U_2174),U_2175)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2174,U_2175) ),
inference(clausify,[status(thm)],[f_750_3]) ).
fof(f_751_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_751_2,plain,
! [U_2178,U_2177,U_2176] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2176,U_2178)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2176,U_2177),U_2178) ),
inference(variable_rename,[status(thm)],[f_751_1]) ).
cnf(f_751_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2176,U_2178)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2176,U_2177),U_2178) ),
inference(clausify,[status(thm)],[f_751_2]) ).
fof(f_752_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_752_2,plain,
! [U_2181,U_2180,U_2179] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2180,U_2181)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2179,U_2181) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2179,U_2180),U_2181) ),
inference(variable_rename,[status(thm)],[f_752_1]) ).
cnf(f_752_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2179,U_2181)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2179,U_2180),U_2181) ),
inference(clausify,[status(thm)],[f_752_2]) ).
cnf(f_752_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2180,U_2181)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2179,U_2180),U_2181) ),
inference(clausify,[status(thm)],[f_752_2]) ).
fof(f_753_1,plain,
! [V_k,V_n,V_m] : 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(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_k),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n),V_k)),
inference(fof_nnf,[status(thm)],[fact_add__mult__distrib]) ).
fof(f_753_2,plain,
! [U_2184,U_2183,U_2182] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2182,U_2183)),U_2184) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2182),U_2184),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2183),U_2184)),
inference(variable_rename,[status(thm)],[f_753_1]) ).
cnf(f_753_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2182,U_2183)),U_2184) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2182),U_2184),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2183),U_2184)),
inference(clausify,[status(thm)],[f_753_2]) ).
fof(f_754_1,plain,
! [V_n,V_m,V_k] : 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(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_m),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_n)),
inference(fof_nnf,[status(thm)],[fact_add__mult__distrib2]) ).
fof(f_754_2,plain,
! [U_2187,U_2186,U_2185] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2185),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2186,U_2187)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2185),U_2186),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2185),U_2187)),
inference(variable_rename,[status(thm)],[f_754_1]) ).
cnf(f_754_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2185),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2186,U_2187)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2185),U_2186),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2185),U_2187)),
inference(clausify,[status(thm)],[f_754_2]) ).
fof(f_755_1,plain,
! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_m)),
inference(fof_nnf,[status(thm)],[fact_le__square]) ).
fof(f_755_2,plain,
! [U_2188] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2188,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2188),U_2188)),
inference(variable_rename,[status(thm)],[f_755_1]) ).
cnf(f_755_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2188,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2188),U_2188)),
inference(clausify,[status(thm)],[f_755_2]) ).
fof(f_756_1,plain,
! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_m))),
inference(fof_nnf,[status(thm)],[fact_le__cube]) ).
fof(f_756_2,plain,
! [U_2189] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2189,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2189),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2189),U_2189))),
inference(variable_rename,[status(thm)],[f_756_1]) ).
cnf(f_756_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2189,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2189),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2189),U_2189))),
inference(clausify,[status(thm)],[f_756_2]) ).
fof(f_757_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_k),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_757_2,plain,
! [U_2192,U_2191,U_2190] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2190),U_2192),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2191),U_2192))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2190,U_2191) ),
inference(variable_rename,[status(thm)],[f_757_1]) ).
cnf(f_757_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2190),U_2192),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2191),U_2192))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2190,U_2191) ),
inference(clausify,[status(thm)],[f_757_2]) ).
fof(f_758_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_i),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_758_2,plain,
! [U_2195,U_2194,U_2193] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2195),U_2193),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2195),U_2194))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2193,U_2194) ),
inference(variable_rename,[status(thm)],[f_758_1]) ).
cnf(f_758_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2195),U_2193),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2195),U_2194))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2193,U_2194) ),
inference(clausify,[status(thm)],[f_758_2]) ).
fof(f_759_1,plain,
! [V_l,V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_k),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_759_2,plain,
! [U_2199,U_2198,U_2197,U_2196] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2196),U_2198),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2197),U_2199))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2198,U_2199)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2196,U_2197) ),
inference(variable_rename,[status(thm)],[f_759_1]) ).
cnf(f_759_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2196),U_2198),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2197),U_2199))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2198,U_2199)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2196,U_2197) ),
inference(clausify,[status(thm)],[f_759_2]) ).
fof(f_760_1,plain,
! [V_n_2,V_ma_2] :
( ( 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(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_760_2,plain,
! [U_2201,U_2200] :
( ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2200),U_2201) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2201 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2200 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( U_2201 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_2200 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2200),U_2201) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_760_1]) ).
fof(f_760_3,plain,
( ! [U_2205,U_2203] :
( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2203),U_2205) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2205 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2203 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_2204,U_2202] :
( ( U_2204 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_2202 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2202),U_2204) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_760_2]) ).
cnf(f_760_4,plain,
( U_2202 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2202),U_2204) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_760_3]) ).
cnf(f_760_5,plain,
( U_2204 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2202),U_2204) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_760_3]) ).
cnf(f_760_6,plain,
( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2203),U_2205) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2205 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2203 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_760_3]) ).
fof(f_761_1,plain,
! [V_n] : 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_761_2,plain,
! [U_2206] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2206),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2206,
inference(variable_rename,[status(thm)],[f_761_1]) ).
cnf(f_761_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2206),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2206,
inference(clausify,[status(thm)],[f_761_2]) ).
fof(f_762_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = 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(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_762_2,plain,
! [U_2208,U_2207] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2207),U_2208)
| U_2208 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2207 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( U_2208 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_2207 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2207),U_2208) ) ),
inference(variable_rename,[status(thm)],[f_762_1]) ).
fof(f_762_3,plain,
( ! [U_2212,U_2210] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2210),U_2212)
| U_2212 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2210 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_2211,U_2209] :
( ( U_2211 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_2209 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2209),U_2211) ) ),
inference(miniscope,[status(thm)],[f_762_2]) ).
cnf(f_762_4,plain,
( U_2209 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2209),U_2211) ),
inference(clausify,[status(thm)],[f_762_3]) ).
cnf(f_762_5,plain,
( U_2211 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2209),U_2211) ),
inference(clausify,[status(thm)],[f_762_3]) ).
cnf(f_762_6,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2210),U_2212)
| U_2212 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2210 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_762_3]) ).
fof(f_763_1,plain,
! [V_n] : 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_763_2,plain,
! [U_2213] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2213) = U_2213,
inference(variable_rename,[status(thm)],[f_763_1]) ).
cnf(f_763_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2213) = U_2213,
inference(clausify,[status(thm)],[f_763_2]) ).
fof(f_764_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_764_2,plain,
! [U_2215,U_2214] :
( ( 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_2214,U_2215))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2215)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2214) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2215)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2214)
| ~ 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_2214,U_2215)) ) ),
inference(variable_rename,[status(thm)],[f_764_1]) ).
fof(f_764_3,plain,
( ! [U_2219,U_2217] :
( 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_2217,U_2219))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2219)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2217) ) )
& ! [U_2218,U_2216] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2218)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2216)
| ~ 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_2216,U_2218)) ) ),
inference(miniscope,[status(thm)],[f_764_2]) ).
cnf(f_764_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2218)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2216)
| ~ 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_2216,U_2218)) ),
inference(clausify,[status(thm)],[f_764_3]) ).
cnf(f_764_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2217)
| 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_2217,U_2219)) ),
inference(clausify,[status(thm)],[f_764_3]) ).
cnf(f_764_6,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2219)
| 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_2217,U_2219)) ),
inference(clausify,[status(thm)],[f_764_3]) ).
fof(f_765_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(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(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_765_2,plain,
! [U_2221,U_2220] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2220),U_2221))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2221)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2220) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2221)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2220) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2220),U_2221)) ) ),
inference(variable_rename,[status(thm)],[f_765_1]) ).
fof(f_765_3,plain,
( ! [U_2225,U_2223] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2223),U_2225))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2225)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2223) )
& ! [U_2224,U_2222] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2224)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2222) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2222),U_2224)) ) ),
inference(miniscope,[status(thm)],[f_765_2]) ).
cnf(f_765_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2222)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2222),U_2224)) ),
inference(clausify,[status(thm)],[f_765_3]) ).
cnf(f_765_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2224)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2222),U_2224)) ),
inference(clausify,[status(thm)],[f_765_3]) ).
cnf(f_765_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2223),U_2225))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2225)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2223) ),
inference(clausify,[status(thm)],[f_765_3]) ).
fof(f_766_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),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(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),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_766_2,plain,
! [U_2228,U_2227,U_2226] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2226),U_2227),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2226),U_2228))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2227,U_2228)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2226) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2227,U_2228)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2226) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2226),U_2227),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2226),U_2228)) ) ),
inference(variable_rename,[status(thm)],[f_766_1]) ).
fof(f_766_3,plain,
( ! [U_2234,U_2232,U_2230] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2230),U_2232),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2230),U_2234))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2232,U_2234)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2230) )
& ! [U_2233,U_2231,U_2229] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2231,U_2233)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2229) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2229),U_2231),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2229),U_2233)) ) ),
inference(miniscope,[status(thm)],[f_766_2]) ).
cnf(f_766_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2229)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2229),U_2231),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2229),U_2233)) ),
inference(clausify,[status(thm)],[f_766_3]) ).
cnf(f_766_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2231,U_2233)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2229),U_2231),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2229),U_2233)) ),
inference(clausify,[status(thm)],[f_766_3]) ).
cnf(f_766_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2230),U_2232),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2230),U_2234))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2232,U_2234)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2230) ),
inference(clausify,[status(thm)],[f_766_3]) ).
fof(f_767_1,plain,
! [V_n_2,V_k_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2),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(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2),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_767_2,plain,
! [U_2237,U_2236,U_2235] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2235),U_2236),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2237),U_2236))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2235,U_2237)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2236) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2235,U_2237)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2236) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2235),U_2236),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2237),U_2236)) ) ),
inference(variable_rename,[status(thm)],[f_767_1]) ).
fof(f_767_3,plain,
( ! [U_2243,U_2241,U_2239] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2239),U_2241),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2243),U_2241))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2239,U_2243)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2241) )
& ! [U_2242,U_2240,U_2238] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2238,U_2242)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2240) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2238),U_2240),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2242),U_2240)) ) ),
inference(miniscope,[status(thm)],[f_767_2]) ).
cnf(f_767_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2240)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2238),U_2240),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2242),U_2240)) ),
inference(clausify,[status(thm)],[f_767_3]) ).
cnf(f_767_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2238,U_2242)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2238),U_2240),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2242),U_2240)) ),
inference(clausify,[status(thm)],[f_767_3]) ).
cnf(f_767_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2239),U_2241),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2243),U_2241))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2239,U_2243)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2241) ),
inference(clausify,[status(thm)],[f_767_3]) ).
fof(f_768_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_k),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_768_2,plain,
! [U_2246,U_2245,U_2244] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2244),U_2246),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2245),U_2246))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2246)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2244,U_2245) ),
inference(variable_rename,[status(thm)],[f_768_1]) ).
cnf(f_768_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2244),U_2246),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2245),U_2246))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2246)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2244,U_2245) ),
inference(clausify,[status(thm)],[f_768_2]) ).
fof(f_769_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k),V_i),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_769_2,plain,
! [U_2249,U_2248,U_2247] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2249),U_2247),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2249),U_2248))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2249)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2247,U_2248) ),
inference(variable_rename,[status(thm)],[f_769_1]) ).
cnf(f_769_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2249),U_2247),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2249),U_2248))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2249)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2247,U_2248) ),
inference(clausify,[status(thm)],[f_769_2]) ).
fof(f_770_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(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_770_2,plain,
! [U_2251,U_2250] :
( U_2250 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2251 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2250 != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2250),U_2251) ),
inference(variable_rename,[status(thm)],[f_770_1]) ).
cnf(f_770_3,plain,
( U_2250 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2251 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2250 != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2250),U_2251) ),
inference(clausify,[status(thm)],[f_770_2]) ).
fof(f_771_1,plain,
! [V_n_2,V_k_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2),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(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_ma_2),V_k_2),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_771_2,plain,
! [U_2254,U_2253,U_2252] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2252),U_2253),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2254),U_2253))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2252,U_2254)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2253) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2252,U_2254)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2253)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2252),U_2253),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2254),U_2253)) ) ),
inference(variable_rename,[status(thm)],[f_771_1]) ).
fof(f_771_3,plain,
( ! [U_2260,U_2258,U_2256] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2256),U_2258),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2260),U_2258))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2256,U_2260)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2258) ) )
& ! [U_2259,U_2257,U_2255] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2255,U_2259)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2257)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2255),U_2257),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2259),U_2257)) ) ),
inference(miniscope,[status(thm)],[f_771_2]) ).
cnf(f_771_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2255,U_2259)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2257)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2255),U_2257),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2259),U_2257)) ),
inference(clausify,[status(thm)],[f_771_3]) ).
cnf(f_771_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2258)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2256),U_2258),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2260),U_2258)) ),
inference(clausify,[status(thm)],[f_771_3]) ).
cnf(f_771_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2256,U_2260)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2256),U_2258),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2260),U_2258)) ),
inference(clausify,[status(thm)],[f_771_3]) ).
fof(f_772_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),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(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),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_772_2,plain,
! [U_2263,U_2262,U_2261] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2261),U_2262),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2261),U_2263))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2262,U_2263) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2262,U_2263)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2261),U_2262),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2261),U_2263)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2261) ),
inference(variable_rename,[status(thm)],[f_772_1]) ).
cnf(f_772_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2262,U_2263)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2261),U_2262),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2261),U_2263))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2261) ),
inference(clausify,[status(thm)],[f_772_2]) ).
cnf(f_772_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2261),U_2262),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2261),U_2263))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2262,U_2263)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2261) ),
inference(clausify,[status(thm)],[f_772_2]) ).
fof(f_773_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2) = 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(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2) != 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_773_2,plain,
! [U_2266,U_2265,U_2264] :
( ( ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2264),U_2265) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2264),U_2266)
| U_2265 != U_2266 )
& ( U_2265 = U_2266
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2264),U_2265) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2264),U_2266) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2264) ),
inference(variable_rename,[status(thm)],[f_773_1]) ).
cnf(f_773_3,plain,
( U_2265 = U_2266
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2264),U_2265) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2264),U_2266)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2264) ),
inference(clausify,[status(thm)],[f_773_2]) ).
cnf(f_773_4,plain,
( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2264),U_2265) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2264),U_2266)
| U_2265 != U_2266
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2264) ),
inference(clausify,[status(thm)],[f_773_2]) ).
fof(f_774_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),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(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2),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_774_2,plain,
! [U_2269,U_2268,U_2267] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2267),U_2268),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2267),U_2269))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2268,U_2269) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2268,U_2269)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2267),U_2268),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2267),U_2269)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2267) ),
inference(variable_rename,[status(thm)],[f_774_1]) ).
cnf(f_774_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2268,U_2269)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2267),U_2268),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2267),U_2269))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2267) ),
inference(clausify,[status(thm)],[f_774_2]) ).
cnf(f_774_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2267),U_2268),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2267),U_2269))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2268,U_2269)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2267) ),
inference(clausify,[status(thm)],[f_774_2]) ).
fof(f_775_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2) = 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(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2),V_ma_2) != 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_775_2,plain,
! [U_2272,U_2271,U_2270] :
( ( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2270),U_2271) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2270),U_2272)
| ( U_2271 != U_2272
& U_2270 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_2271 = U_2272
| U_2270 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2270),U_2271) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2270),U_2272) ) ),
inference(variable_rename,[status(thm)],[f_775_1]) ).
fof(f_775_3,plain,
( ! [U_2278,U_2276,U_2274] :
( hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2274),U_2276) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2274),U_2278)
| ( U_2276 != U_2278
& U_2274 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_2277,U_2275,U_2273] :
( U_2275 = U_2277
| U_2273 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2273),U_2275) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2273),U_2277) ) ),
inference(miniscope,[status(thm)],[f_775_2]) ).
cnf(f_775_4,plain,
( U_2275 = U_2277
| U_2273 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2273),U_2275) != hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2273),U_2277) ),
inference(clausify,[status(thm)],[f_775_3]) ).
cnf(f_775_5,plain,
( U_2274 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2274),U_2276) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2274),U_2278) ),
inference(clausify,[status(thm)],[f_775_3]) ).
cnf(f_775_6,plain,
( U_2276 != U_2278
| hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2274),U_2276) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2274),U_2278) ),
inference(clausify,[status(thm)],[f_775_3]) ).
fof(f_776_1,plain,
! [V_k,V_j,V_u,V_i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j),V_u),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,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_776_2,plain,
! [U_2282,U_2281,U_2280,U_2279] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2279),U_2280),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2281),U_2280),U_2282)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2279,U_2281)),U_2280),U_2282),
inference(variable_rename,[status(thm)],[f_776_1]) ).
cnf(f_776_3,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2279),U_2280),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2281),U_2280),U_2282)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2279,U_2281)),U_2280),U_2282),
inference(clausify,[status(thm)],[f_776_2]) ).
fof(f_777_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_777_2,plain,
! [U_2285,U_2284,U_2283] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2283,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2285,U_2284))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2283,U_2284) ),
inference(variable_rename,[status(thm)],[f_777_1]) ).
cnf(f_777_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2283,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2285,U_2284))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2283,U_2284) ),
inference(clausify,[status(thm)],[f_777_2]) ).
fof(f_778_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_778_2,plain,
! [U_2288,U_2287,U_2286] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2286,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2287,U_2288))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2286,U_2287) ),
inference(variable_rename,[status(thm)],[f_778_1]) ).
cnf(f_778_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2286,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2287,U_2288))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2286,U_2287) ),
inference(clausify,[status(thm)],[f_778_2]) ).
fof(f_779_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_779_2,plain,
! [U_2291,U_2290,U_2289] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2289,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2291,U_2290))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2289,U_2290) ),
inference(variable_rename,[status(thm)],[f_779_1]) ).
cnf(f_779_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2289,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2291,U_2290))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2289,U_2290) ),
inference(clausify,[status(thm)],[f_779_2]) ).
fof(f_780_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_780_2,plain,
! [U_2294,U_2293,U_2292] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2292,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2293,U_2294))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2292,U_2293) ),
inference(variable_rename,[status(thm)],[f_780_1]) ).
cnf(f_780_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2292,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2293,U_2294))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2292,U_2293) ),
inference(clausify,[status(thm)],[f_780_2]) ).
fof(f_781_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_781_2,plain,
! [U_2296,U_2295] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2295,U_2296)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2295,U_2296) ),
inference(variable_rename,[status(thm)],[f_781_1]) ).
cnf(f_781_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2295,U_2296)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2295,U_2296) ),
inference(clausify,[status(thm)],[f_781_2]) ).
fof(f_782_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_782_2,plain,
! [U_2300,U_2299] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2299,U_2300)
| ! [U_2298] : U_2300 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2299,U_2298) )
& ( ? [U_2297] : U_2300 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2299,U_2297)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2299,U_2300) ) ),
inference(variable_rename,[status(thm)],[f_782_1]) ).
fof(f_782_3,plain,
( ! [U_2304,U_2302] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2302,U_2304)
| ! [U_2298] : U_2304 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2302,U_2298) )
& ! [U_2303,U_2301] :
( ? [U_2297] : U_2303 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2301,U_2297)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2301,U_2303) ) ),
inference(miniscope,[status(thm)],[f_782_2]) ).
fof(f_782_4,plain,
( ! [U_2304,U_2302] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2302,U_2304)
| ! [U_2298] : U_2304 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2302,U_2298) )
& ! [U_2303,U_2301] :
( U_2303 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2301,sK10(U_2303,U_2301))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2301,U_2303) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_2297,sK10(U_2303,U_2301))],[f_782_3]) ).
cnf(f_782_5,plain,
( U_2303 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2301,sK10(U_2303,U_2301))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2301,U_2303) ),
inference(clausify,[status(thm)],[f_782_4]) ).
cnf(f_782_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2302,U_2304)
| U_2304 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2302,U_2298) ),
inference(clausify,[status(thm)],[f_782_4]) ).
fof(f_783_1,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,c_Int_OBit1(c_Int_OPls)),
inference(fof_nnf,[status(thm)],[fact_one__code__numeral__code]) ).
cnf(f_783_2,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,c_Int_OBit1(c_Int_OPls)),
inference(clausify,[status(thm)],[f_783_1]) ).
fof(f_784_1,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,c_Int_OPls),
inference(fof_nnf,[status(thm)],[fact_zero__code__numeral__code]) ).
cnf(f_784_2,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral,c_Int_OPls),
inference(clausify,[status(thm)],[f_784_1]) ).
fof(f_785_1,plain,
! [T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_half]) ).
fof(f_785_2,plain,
! [U_2305] :
( c_Orderings_Oord__class_Oless(U_2305,c_Groups_Ozero__class_Ozero(U_2305),c_Rings_Oinverse__class_Odivide(U_2305,c_Groups_Oone__class_Oone(U_2305),c_Int_Onumber__class_Onumber__of(U_2305,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Int_Onumber__ring(U_2305)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2305) ),
inference(variable_rename,[status(thm)],[f_785_1]) ).
cnf(f_785_3,plain,
( c_Orderings_Oord__class_Oless(U_2305,c_Groups_Ozero__class_Ozero(U_2305),c_Rings_Oinverse__class_Odivide(U_2305,c_Groups_Oone__class_Oone(U_2305),c_Int_Onumber__class_Onumber__of(U_2305,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Int_Onumber__ring(U_2305)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2305) ),
inference(clausify,[status(thm)],[f_785_2]) ).
fof(f_786_1,plain,
! [V_k_2,V_P_2,V_db_2] :
( ! [B_x] :
( hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k_2),V_db_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_db_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_db_2) ),
inference(fof_nnf,[status(thm)],[fact_incr__mult__lemma]) ).
fof(f_786_2,plain,
! [U_2310,U_2309,U_2308] :
( ! [U_2307] :
( hBOOL(hAPP(U_2309,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2307,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_2310),U_2308))))
| ~ hBOOL(hAPP(U_2309,U_2307)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2310)
| ? [U_2306] :
( ~ hBOOL(hAPP(U_2309,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2306,U_2308)))
& hBOOL(hAPP(U_2309,U_2306)) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2308) ),
inference(variable_rename,[status(thm)],[f_786_1]) ).
fof(f_786_3,plain,
! [U_2310,U_2309,U_2308] :
( ! [U_2307] :
( hBOOL(hAPP(U_2309,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2307,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_2310),U_2308))))
| ~ hBOOL(hAPP(U_2309,U_2307)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2310)
| ( ~ hBOOL(hAPP(U_2309,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sK11(U_2310,U_2309,U_2308),U_2308)))
& hBOOL(hAPP(U_2309,sK11(U_2310,U_2309,U_2308))) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2308) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_2306,sK11(U_2310,U_2309,U_2308))],[f_786_2]) ).
cnf(f_786_4,plain,
( hBOOL(hAPP(U_2309,sK11(U_2310,U_2309,U_2308)))
| hBOOL(hAPP(U_2309,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2307,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_2310),U_2308))))
| ~ hBOOL(hAPP(U_2309,U_2307))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2310)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2308) ),
inference(clausify,[status(thm)],[f_786_3]) ).
cnf(f_786_5,plain,
( ~ hBOOL(hAPP(U_2309,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sK11(U_2310,U_2309,U_2308),U_2308)))
| hBOOL(hAPP(U_2309,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2307,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_2310),U_2308))))
| ~ hBOOL(hAPP(U_2309,U_2307))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2310)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2308) ),
inference(clausify,[status(thm)],[f_786_3]) ).
fof(f_787_1,plain,
! [V_wa_2,T_a] :
( ( ( c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_wa_2)))
| ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2)) )
& ( c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_wa_2))
| ~ c_Int_Oiszero(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_wa_2))) ) )
| ~ class_Int_Oring__char__0(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_iszero__number__of__Bit0]) ).
fof(f_787_2,plain,
! [U_2312,U_2311] :
( ( ( c_Int_Oiszero(U_2311,c_Int_Onumber__class_Onumber__of(U_2311,c_Int_OBit0(U_2312)))
| ~ c_Int_Oiszero(U_2311,c_Int_Onumber__class_Onumber__of(U_2311,U_2312)) )
& ( c_Int_Oiszero(U_2311,c_Int_Onumber__class_Onumber__of(U_2311,U_2312))
| ~ c_Int_Oiszero(U_2311,c_Int_Onumber__class_Onumber__of(U_2311,c_Int_OBit0(U_2312))) ) )
| ~ class_Int_Oring__char__0(U_2311)
| ~ class_Int_Onumber__ring(U_2311) ),
inference(variable_rename,[status(thm)],[f_787_1]) ).
cnf(f_787_3,plain,
( c_Int_Oiszero(U_2311,c_Int_Onumber__class_Onumber__of(U_2311,U_2312))
| ~ c_Int_Oiszero(U_2311,c_Int_Onumber__class_Onumber__of(U_2311,c_Int_OBit0(U_2312)))
| ~ class_Int_Oring__char__0(U_2311)
| ~ class_Int_Onumber__ring(U_2311) ),
inference(clausify,[status(thm)],[f_787_2]) ).
cnf(f_787_4,plain,
( c_Int_Oiszero(U_2311,c_Int_Onumber__class_Onumber__of(U_2311,c_Int_OBit0(U_2312)))
| ~ c_Int_Oiszero(U_2311,c_Int_Onumber__class_Onumber__of(U_2311,U_2312))
| ~ class_Int_Oring__char__0(U_2311)
| ~ class_Int_Onumber__ring(U_2311) ),
inference(clausify,[status(thm)],[f_787_2]) ).
fof(f_788_1,plain,
! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k),
inference(fof_nnf,[status(thm)],[fact_pred__Bit1]) ).
fof(f_788_2,plain,
! [U_2313] : c_Int_Opred(c_Int_OBit1(U_2313)) = c_Int_OBit0(U_2313),
inference(variable_rename,[status(thm)],[f_788_1]) ).
cnf(f_788_3,plain,
c_Int_Opred(c_Int_OBit1(U_2313)) = c_Int_OBit0(U_2313),
inference(clausify,[status(thm)],[f_788_2]) ).
fof(f_789_1,plain,
! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)),
inference(fof_nnf,[status(thm)],[fact_pred__Bit0]) ).
fof(f_789_2,plain,
! [U_2314] : c_Int_Opred(c_Int_OBit0(U_2314)) = c_Int_OBit1(c_Int_Opred(U_2314)),
inference(variable_rename,[status(thm)],[f_789_1]) ).
cnf(f_789_3,plain,
c_Int_Opred(c_Int_OBit0(U_2314)) = c_Int_OBit1(c_Int_Opred(U_2314)),
inference(clausify,[status(thm)],[f_789_2]) ).
fof(f_790_1,plain,
! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k),
inference(fof_nnf,[status(thm)],[fact_succ__Bit0]) ).
fof(f_790_2,plain,
! [U_2315] : c_Int_Osucc(c_Int_OBit0(U_2315)) = c_Int_OBit1(U_2315),
inference(variable_rename,[status(thm)],[f_790_1]) ).
cnf(f_790_3,plain,
c_Int_Osucc(c_Int_OBit0(U_2315)) = c_Int_OBit1(U_2315),
inference(clausify,[status(thm)],[f_790_2]) ).
fof(f_791_1,plain,
! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)),
inference(fof_nnf,[status(thm)],[fact_succ__Bit1]) ).
fof(f_791_2,plain,
! [U_2316] : c_Int_Osucc(c_Int_OBit1(U_2316)) = c_Int_OBit0(c_Int_Osucc(U_2316)),
inference(variable_rename,[status(thm)],[f_791_1]) ).
cnf(f_791_3,plain,
c_Int_Osucc(c_Int_OBit1(U_2316)) = c_Int_OBit0(c_Int_Osucc(U_2316)),
inference(clausify,[status(thm)],[f_791_2]) ).
fof(f_792_1,plain,
! [V_k2_2,V_k1_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I13_J]) ).
fof(f_792_2,plain,
! [U_2318,U_2317] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2317),c_Int_OBit0(U_2318))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2317,U_2318) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2317,U_2318)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2317),c_Int_OBit0(U_2318)) ) ),
inference(variable_rename,[status(thm)],[f_792_1]) ).
fof(f_792_3,plain,
( ! [U_2322,U_2320] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2320),c_Int_OBit0(U_2322))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2320,U_2322) )
& ! [U_2321,U_2319] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2319,U_2321)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2319),c_Int_OBit0(U_2321)) ) ),
inference(miniscope,[status(thm)],[f_792_2]) ).
cnf(f_792_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2319,U_2321)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2319),c_Int_OBit0(U_2321)) ),
inference(clausify,[status(thm)],[f_792_3]) ).
cnf(f_792_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2320),c_Int_OBit0(U_2322))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2320,U_2322) ),
inference(clausify,[status(thm)],[f_792_3]) ).
fof(f_793_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I31_J]) ).
fof(f_793_2,plain,
! [U_2324,U_2323] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2323),c_Int_OBit0(U_2324))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2323,U_2324) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2323,U_2324)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2323),c_Int_OBit0(U_2324)) ) ),
inference(variable_rename,[status(thm)],[f_793_1]) ).
fof(f_793_3,plain,
( ! [U_2328,U_2326] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2326),c_Int_OBit0(U_2328))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2326,U_2328) )
& ! [U_2327,U_2325] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2325,U_2327)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2325),c_Int_OBit0(U_2327)) ) ),
inference(miniscope,[status(thm)],[f_793_2]) ).
cnf(f_793_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2325,U_2327)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2325),c_Int_OBit0(U_2327)) ),
inference(clausify,[status(thm)],[f_793_3]) ).
cnf(f_793_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2326),c_Int_OBit0(U_2328))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2326,U_2328) ),
inference(clausify,[status(thm)],[f_793_3]) ).
fof(f_794_1,plain,
! [V_l,V_k] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k),V_l)),
inference(fof_nnf,[status(thm)],[fact_mult__Bit0]) ).
fof(f_794_2,plain,
! [U_2330,U_2329] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(U_2329)),U_2330) = c_Int_OBit0(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_2329),U_2330)),
inference(variable_rename,[status(thm)],[f_794_1]) ).
cnf(f_794_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(U_2329)),U_2330) = c_Int_OBit0(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_2329),U_2330)),
inference(clausify,[status(thm)],[f_794_2]) ).
fof(f_795_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit0(V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I14_J]) ).
fof(f_795_2,plain,
! [U_2332,U_2331] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2331),c_Int_OBit0(U_2332))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2331,U_2332) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2331,U_2332)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2331),c_Int_OBit0(U_2332)) ) ),
inference(variable_rename,[status(thm)],[f_795_1]) ).
fof(f_795_3,plain,
( ! [U_2336,U_2334] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2334),c_Int_OBit0(U_2336))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2334,U_2336) )
& ! [U_2335,U_2333] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2333,U_2335)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2333),c_Int_OBit0(U_2335)) ) ),
inference(miniscope,[status(thm)],[f_795_2]) ).
cnf(f_795_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2333,U_2335)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2333),c_Int_OBit0(U_2335)) ),
inference(clausify,[status(thm)],[f_795_3]) ).
cnf(f_795_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2334),c_Int_OBit0(U_2336))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2334,U_2336) ),
inference(clausify,[status(thm)],[f_795_3]) ).
fof(f_796_1,plain,
! [V_k2_2,V_k1_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit0(V_k2_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__int__code_I13_J]) ).
fof(f_796_2,plain,
! [U_2338,U_2337] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2337),c_Int_OBit0(U_2338))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2337,U_2338) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2337,U_2338)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2337),c_Int_OBit0(U_2338)) ) ),
inference(variable_rename,[status(thm)],[f_796_1]) ).
fof(f_796_3,plain,
( ! [U_2342,U_2340] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2340),c_Int_OBit0(U_2342))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2340,U_2342) )
& ! [U_2341,U_2339] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2339,U_2341)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2339),c_Int_OBit0(U_2341)) ) ),
inference(miniscope,[status(thm)],[f_796_2]) ).
cnf(f_796_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2339,U_2341)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2339),c_Int_OBit0(U_2341)) ),
inference(clausify,[status(thm)],[f_796_3]) ).
cnf(f_796_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2340),c_Int_OBit0(U_2342))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2340,U_2342) ),
inference(clausify,[status(thm)],[f_796_3]) ).
fof(f_797_1,plain,
! [V_k] : c_Int_OBit0(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_k),
inference(fof_nnf,[status(thm)],[fact_Bit0__def]) ).
fof(f_797_2,plain,
! [U_2343] : c_Int_OBit0(U_2343) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2343,U_2343),
inference(variable_rename,[status(thm)],[f_797_1]) ).
cnf(f_797_3,plain,
c_Int_OBit0(U_2343) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2343,U_2343),
inference(clausify,[status(thm)],[f_797_2]) ).
fof(f_798_1,plain,
! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit0(V_l)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)),
inference(fof_nnf,[status(thm)],[fact_add__Bit0__Bit0]) ).
fof(f_798_2,plain,
! [U_2345,U_2344] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(U_2344),c_Int_OBit0(U_2345)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2344,U_2345)),
inference(variable_rename,[status(thm)],[f_798_1]) ).
cnf(f_798_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(U_2344),c_Int_OBit0(U_2345)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2344,U_2345)),
inference(clausify,[status(thm)],[f_798_2]) ).
fof(f_799_1,plain,
! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I50_J]) ).
fof(f_799_2,plain,
! [U_2347,U_2346] : c_Int_OBit1(U_2346) != c_Int_OBit0(U_2347),
inference(variable_rename,[status(thm)],[f_799_1]) ).
cnf(f_799_3,plain,
c_Int_OBit1(U_2346) != c_Int_OBit0(U_2347),
inference(clausify,[status(thm)],[f_799_2]) ).
fof(f_800_1,plain,
! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I49_J]) ).
fof(f_800_2,plain,
! [U_2349,U_2348] : c_Int_OBit0(U_2348) != c_Int_OBit1(U_2349),
inference(variable_rename,[status(thm)],[f_800_1]) ).
cnf(f_800_3,plain,
c_Int_OBit0(U_2348) != c_Int_OBit1(U_2349),
inference(clausify,[status(thm)],[f_800_2]) ).
fof(f_801_1,plain,
! [V_k] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(V_k)) = c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_k)),
inference(fof_nnf,[status(thm)],[fact_minus__Bit0]) ).
fof(f_801_2,plain,
! [U_2350] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(U_2350)) = c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2350)),
inference(variable_rename,[status(thm)],[f_801_1]) ).
cnf(f_801_3,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Int_OBit0(U_2350)) = c_Int_OBit0(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2350)),
inference(clausify,[status(thm)],[f_801_2]) ).
fof(f_802_1,plain,
! [V_l_2,V_k_2] :
( ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
| V_k_2 != V_l_2 )
& ( V_k_2 = V_l_2
| c_Int_OBit0(V_k_2) != c_Int_OBit0(V_l_2) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I48_J]) ).
fof(f_802_2,plain,
! [U_2352,U_2351] :
( ( c_Int_OBit0(U_2351) = c_Int_OBit0(U_2352)
| U_2351 != U_2352 )
& ( U_2351 = U_2352
| c_Int_OBit0(U_2351) != c_Int_OBit0(U_2352) ) ),
inference(variable_rename,[status(thm)],[f_802_1]) ).
fof(f_802_3,plain,
( ! [U_2356,U_2354] :
( c_Int_OBit0(U_2354) = c_Int_OBit0(U_2356)
| U_2354 != U_2356 )
& ! [U_2355,U_2353] :
( U_2353 = U_2355
| c_Int_OBit0(U_2353) != c_Int_OBit0(U_2355) ) ),
inference(miniscope,[status(thm)],[f_802_2]) ).
cnf(f_802_4,plain,
( U_2353 = U_2355
| c_Int_OBit0(U_2353) != c_Int_OBit0(U_2355) ),
inference(clausify,[status(thm)],[f_802_3]) ).
cnf(f_802_5,plain,
( c_Int_OBit0(U_2354) = c_Int_OBit0(U_2356)
| U_2354 != U_2356 ),
inference(clausify,[status(thm)],[f_802_3]) ).
fof(f_803_1,plain,
! [V_k_2] :
( ( c_Int_OBit0(V_k_2) = c_Int_OPls
| V_k_2 != c_Int_OPls )
& ( V_k_2 = c_Int_OPls
| c_Int_OBit0(V_k_2) != c_Int_OPls ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I44_J]) ).
fof(f_803_2,plain,
! [U_2357] :
( ( c_Int_OBit0(U_2357) = c_Int_OPls
| U_2357 != c_Int_OPls )
& ( U_2357 = c_Int_OPls
| c_Int_OBit0(U_2357) != c_Int_OPls ) ),
inference(variable_rename,[status(thm)],[f_803_1]) ).
fof(f_803_3,plain,
( ! [U_2359] :
( c_Int_OBit0(U_2359) = c_Int_OPls
| U_2359 != c_Int_OPls )
& ! [U_2358] :
( U_2358 = c_Int_OPls
| c_Int_OBit0(U_2358) != c_Int_OPls ) ),
inference(miniscope,[status(thm)],[f_803_2]) ).
cnf(f_803_4,plain,
( U_2358 = c_Int_OPls
| c_Int_OBit0(U_2358) != c_Int_OPls ),
inference(clausify,[status(thm)],[f_803_3]) ).
cnf(f_803_5,plain,
( c_Int_OBit0(U_2359) = c_Int_OPls
| U_2359 != c_Int_OPls ),
inference(clausify,[status(thm)],[f_803_3]) ).
fof(f_804_1,plain,
! [V_l_2] :
( ( c_Int_OPls = c_Int_OBit0(V_l_2)
| c_Int_OPls != V_l_2 )
& ( c_Int_OPls = V_l_2
| c_Int_OPls != c_Int_OBit0(V_l_2) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I38_J]) ).
fof(f_804_2,plain,
! [U_2360] :
( ( c_Int_OPls = c_Int_OBit0(U_2360)
| c_Int_OPls != U_2360 )
& ( c_Int_OPls = U_2360
| c_Int_OPls != c_Int_OBit0(U_2360) ) ),
inference(variable_rename,[status(thm)],[f_804_1]) ).
fof(f_804_3,plain,
( ! [U_2362] :
( c_Int_OPls = c_Int_OBit0(U_2362)
| c_Int_OPls != U_2362 )
& ! [U_2361] :
( c_Int_OPls = U_2361
| c_Int_OPls != c_Int_OBit0(U_2361) ) ),
inference(miniscope,[status(thm)],[f_804_2]) ).
cnf(f_804_4,plain,
( c_Int_OPls = U_2361
| c_Int_OPls != c_Int_OBit0(U_2361) ),
inference(clausify,[status(thm)],[f_804_3]) ).
cnf(f_804_5,plain,
( c_Int_OPls = c_Int_OBit0(U_2362)
| c_Int_OPls != U_2362 ),
inference(clausify,[status(thm)],[f_804_3]) ).
fof(f_805_1,plain,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_Bit0__Pls]) ).
cnf(f_805_2,plain,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
inference(clausify,[status(thm)],[f_805_1]) ).
fof(f_806_1,plain,
! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(V_k),c_Int_OBit1(V_l)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)),
inference(fof_nnf,[status(thm)],[fact_add__Bit0__Bit1]) ).
fof(f_806_2,plain,
! [U_2364,U_2363] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(U_2363),c_Int_OBit1(U_2364)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2363,U_2364)),
inference(variable_rename,[status(thm)],[f_806_1]) ).
cnf(f_806_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(U_2363),c_Int_OBit1(U_2364)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2363,U_2364)),
inference(clausify,[status(thm)],[f_806_2]) ).
fof(f_807_1,plain,
! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit0(V_l)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_l)),
inference(fof_nnf,[status(thm)],[fact_add__Bit1__Bit0]) ).
fof(f_807_2,plain,
! [U_2366,U_2365] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(U_2365),c_Int_OBit0(U_2366)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2365,U_2366)),
inference(variable_rename,[status(thm)],[f_807_1]) ).
cnf(f_807_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(U_2365),c_Int_OBit0(U_2366)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2365,U_2366)),
inference(clausify,[status(thm)],[f_807_2]) ).
fof(f_808_1,plain,
! [V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_k_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_k_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I4_J]) ).
fof(f_808_2,plain,
! [U_2367] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_2367))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2367) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2367)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_2367)) ) ),
inference(variable_rename,[status(thm)],[f_808_1]) ).
fof(f_808_3,plain,
( ! [U_2369] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_2369))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2369) )
& ! [U_2368] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2368)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_2368)) ) ),
inference(miniscope,[status(thm)],[f_808_2]) ).
cnf(f_808_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2368)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_2368)) ),
inference(clausify,[status(thm)],[f_808_3]) ).
cnf(f_808_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_2369))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2369) ),
inference(clausify,[status(thm)],[f_808_3]) ).
fof(f_809_1,plain,
! [V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I10_J]) ).
fof(f_809_2,plain,
! [U_2370] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2370),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2370,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2370,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2370),c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[f_809_1]) ).
fof(f_809_3,plain,
( ! [U_2372] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2372),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2372,c_Int_OPls) )
& ! [U_2371] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2371,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2371),c_Int_OPls) ) ),
inference(miniscope,[status(thm)],[f_809_2]) ).
cnf(f_809_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2371,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2371),c_Int_OPls) ),
inference(clausify,[status(thm)],[f_809_3]) ).
cnf(f_809_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2372),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2372,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_809_3]) ).
fof(f_810_1,plain,
! [V_wa_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_wa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_wa_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I3_J]) ).
fof(f_810_2,plain,
! [U_2373] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2373),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2373,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2373,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2373),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[f_810_1]) ).
fof(f_810_3,plain,
( ! [U_2375] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2375),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2375,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_2374] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2374,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2374),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(miniscope,[status(thm)],[f_810_2]) ).
cnf(f_810_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2374,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2374),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_810_3]) ).
cnf(f_810_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2375),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2375,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_810_3]) ).
fof(f_811_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I16_J]) ).
fof(f_811_2,plain,
! [U_2377,U_2376] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2376),c_Int_OBit0(U_2377))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2376,U_2377) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2376,U_2377)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2376),c_Int_OBit0(U_2377)) ) ),
inference(variable_rename,[status(thm)],[f_811_1]) ).
fof(f_811_3,plain,
( ! [U_2381,U_2379] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2379),c_Int_OBit0(U_2381))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2379,U_2381) )
& ! [U_2380,U_2378] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2378,U_2380)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2378),c_Int_OBit0(U_2380)) ) ),
inference(miniscope,[status(thm)],[f_811_2]) ).
cnf(f_811_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2378,U_2380)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2378),c_Int_OBit0(U_2380)) ),
inference(clausify,[status(thm)],[f_811_3]) ).
cnf(f_811_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2379),c_Int_OBit0(U_2381))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2379,U_2381) ),
inference(clausify,[status(thm)],[f_811_3]) ).
fof(f_812_1,plain,
! [V_k2_2,V_k1_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__int__code_I15_J]) ).
fof(f_812_2,plain,
! [U_2383,U_2382] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2382),c_Int_OBit0(U_2383))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2382,U_2383) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2382,U_2383)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2382),c_Int_OBit0(U_2383)) ) ),
inference(variable_rename,[status(thm)],[f_812_1]) ).
fof(f_812_3,plain,
( ! [U_2387,U_2385] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2385),c_Int_OBit0(U_2387))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2385,U_2387) )
& ! [U_2386,U_2384] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2384,U_2386)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2384),c_Int_OBit0(U_2386)) ) ),
inference(miniscope,[status(thm)],[f_812_2]) ).
cnf(f_812_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2384,U_2386)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2384),c_Int_OBit0(U_2386)) ),
inference(clausify,[status(thm)],[f_812_3]) ).
cnf(f_812_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2385),c_Int_OBit0(U_2387))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2385,U_2387) ),
inference(clausify,[status(thm)],[f_812_3]) ).
fof(f_813_1,plain,
! [V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OPls) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I27_J]) ).
fof(f_813_2,plain,
! [U_2388] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2388),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2388,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2388,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2388),c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[f_813_1]) ).
fof(f_813_3,plain,
( ! [U_2390] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2390),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2390,c_Int_OPls) )
& ! [U_2389] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2389,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2389),c_Int_OPls) ) ),
inference(miniscope,[status(thm)],[f_813_2]) ).
cnf(f_813_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2389,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2389),c_Int_OPls) ),
inference(clausify,[status(thm)],[f_813_3]) ).
cnf(f_813_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2390),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2390,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_813_3]) ).
fof(f_814_1,plain,
! [V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_k_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(V_k_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I21_J]) ).
fof(f_814_2,plain,
! [U_2391] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_2391))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_2391) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_2391)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_2391)) ) ),
inference(variable_rename,[status(thm)],[f_814_1]) ).
fof(f_814_3,plain,
( ! [U_2393] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_2393))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_2393) )
& ! [U_2392] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_2392)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_2392)) ) ),
inference(miniscope,[status(thm)],[f_814_2]) ).
cnf(f_814_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_2392)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_2392)) ),
inference(clausify,[status(thm)],[f_814_3]) ).
cnf(f_814_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_2393))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_2393) ),
inference(clausify,[status(thm)],[f_814_3]) ).
fof(f_815_1,plain,
! [V_k2_2,V_k1_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I14_J]) ).
fof(f_815_2,plain,
! [U_2395,U_2394] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2394),c_Int_OBit1(U_2395))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2394,U_2395) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2394,U_2395)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2394),c_Int_OBit1(U_2395)) ) ),
inference(variable_rename,[status(thm)],[f_815_1]) ).
fof(f_815_3,plain,
( ! [U_2399,U_2397] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2397),c_Int_OBit1(U_2399))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2397,U_2399) )
& ! [U_2398,U_2396] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2396,U_2398)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2396),c_Int_OBit1(U_2398)) ) ),
inference(miniscope,[status(thm)],[f_815_2]) ).
cnf(f_815_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2396,U_2398)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2396),c_Int_OBit1(U_2398)) ),
inference(clausify,[status(thm)],[f_815_3]) ).
cnf(f_815_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2397),c_Int_OBit1(U_2399))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2397,U_2399) ),
inference(clausify,[status(thm)],[f_815_3]) ).
fof(f_816_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I32_J]) ).
fof(f_816_2,plain,
! [U_2401,U_2400] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2400),c_Int_OBit1(U_2401))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2400,U_2401) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2400,U_2401)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2400),c_Int_OBit1(U_2401)) ) ),
inference(variable_rename,[status(thm)],[f_816_1]) ).
fof(f_816_3,plain,
( ! [U_2405,U_2403] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2403),c_Int_OBit1(U_2405))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2403,U_2405) )
& ! [U_2404,U_2402] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2402,U_2404)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2402),c_Int_OBit1(U_2404)) ) ),
inference(miniscope,[status(thm)],[f_816_2]) ).
cnf(f_816_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2402,U_2404)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2402),c_Int_OBit1(U_2404)) ),
inference(clausify,[status(thm)],[f_816_3]) ).
cnf(f_816_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_2403),c_Int_OBit1(U_2405))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2403,U_2405) ),
inference(clausify,[status(thm)],[f_816_3]) ).
fof(f_817_1,plain,
! [V_w,T_a] :
( c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),c_Int_Onumber__class_Onumber__of(T_a,V_w))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__Bit0]) ).
fof(f_817_2,plain,
! [U_2407,U_2406] :
( c_Int_Onumber__class_Onumber__of(U_2406,c_Int_OBit0(U_2407)) = c_Groups_Oplus__class_Oplus(U_2406,c_Groups_Oplus__class_Oplus(U_2406,c_Groups_Ozero__class_Ozero(U_2406),c_Int_Onumber__class_Onumber__of(U_2406,U_2407)),c_Int_Onumber__class_Onumber__of(U_2406,U_2407))
| ~ class_Int_Onumber__ring(U_2406) ),
inference(variable_rename,[status(thm)],[f_817_1]) ).
cnf(f_817_3,plain,
( c_Int_Onumber__class_Onumber__of(U_2406,c_Int_OBit0(U_2407)) = c_Groups_Oplus__class_Oplus(U_2406,c_Groups_Oplus__class_Oplus(U_2406,c_Groups_Ozero__class_Ozero(U_2406),c_Int_Onumber__class_Onumber__of(U_2406,U_2407)),c_Int_Onumber__class_Onumber__of(U_2406,U_2407))
| ~ class_Int_Onumber__ring(U_2406) ),
inference(clausify,[status(thm)],[f_817_2]) ).
fof(f_818_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OBit1(V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I15_J]) ).
fof(f_818_2,plain,
! [U_2409,U_2408] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2408),c_Int_OBit1(U_2409))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2408,U_2409) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2408,U_2409)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2408),c_Int_OBit1(U_2409)) ) ),
inference(variable_rename,[status(thm)],[f_818_1]) ).
fof(f_818_3,plain,
( ! [U_2413,U_2411] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2411),c_Int_OBit1(U_2413))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2411,U_2413) )
& ! [U_2412,U_2410] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2410,U_2412)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2410),c_Int_OBit1(U_2412)) ) ),
inference(miniscope,[status(thm)],[f_818_2]) ).
cnf(f_818_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2410,U_2412)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2410),c_Int_OBit1(U_2412)) ),
inference(clausify,[status(thm)],[f_818_3]) ).
cnf(f_818_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2411),c_Int_OBit1(U_2413))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2411,U_2413) ),
inference(clausify,[status(thm)],[f_818_3]) ).
fof(f_819_1,plain,
! [V_k2_2,V_k1_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k1_2,V_k2_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_k1_2),c_Int_OBit1(V_k2_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__int__code_I14_J]) ).
fof(f_819_2,plain,
! [U_2415,U_2414] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2414),c_Int_OBit1(U_2415))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2414,U_2415) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2414,U_2415)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2414),c_Int_OBit1(U_2415)) ) ),
inference(variable_rename,[status(thm)],[f_819_1]) ).
fof(f_819_3,plain,
( ! [U_2419,U_2417] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2417),c_Int_OBit1(U_2419))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2417,U_2419) )
& ! [U_2418,U_2416] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2416,U_2418)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2416),c_Int_OBit1(U_2418)) ) ),
inference(miniscope,[status(thm)],[f_819_2]) ).
cnf(f_819_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2416,U_2418)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2416),c_Int_OBit1(U_2418)) ),
inference(clausify,[status(thm)],[f_819_3]) ).
cnf(f_819_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2417),c_Int_OBit1(U_2419))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2417,U_2419) ),
inference(clausify,[status(thm)],[f_819_3]) ).
fof(f_820_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OBit0(V_l_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I33_J]) ).
fof(f_820_2,plain,
! [U_2421,U_2420] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_2420),c_Int_OBit0(U_2421))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2420,U_2421) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2420,U_2421)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_2420),c_Int_OBit0(U_2421)) ) ),
inference(variable_rename,[status(thm)],[f_820_1]) ).
fof(f_820_3,plain,
( ! [U_2425,U_2423] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_2423),c_Int_OBit0(U_2425))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2423,U_2425) )
& ! [U_2424,U_2422] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2422,U_2424)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_2422),c_Int_OBit0(U_2424)) ) ),
inference(miniscope,[status(thm)],[f_820_2]) ).
cnf(f_820_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2422,U_2424)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_2422),c_Int_OBit0(U_2424)) ),
inference(clausify,[status(thm)],[f_820_3]) ).
cnf(f_820_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_2423),c_Int_OBit0(U_2425))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2423,U_2425) ),
inference(clausify,[status(thm)],[f_820_3]) ).
fof(f_821_1,plain,
! [V_k2_2,V_k1_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k1_2,V_k2_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k1_2),c_Int_OBit0(V_k2_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I15_J]) ).
fof(f_821_2,plain,
! [U_2427,U_2426] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_2426),c_Int_OBit0(U_2427))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2426,U_2427) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2426,U_2427)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_2426),c_Int_OBit0(U_2427)) ) ),
inference(variable_rename,[status(thm)],[f_821_1]) ).
fof(f_821_3,plain,
( ! [U_2431,U_2429] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_2429),c_Int_OBit0(U_2431))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2429,U_2431) )
& ! [U_2430,U_2428] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2428,U_2430)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_2428),c_Int_OBit0(U_2430)) ) ),
inference(miniscope,[status(thm)],[f_821_2]) ).
cnf(f_821_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2428,U_2430)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_2428),c_Int_OBit0(U_2430)) ),
inference(clausify,[status(thm)],[f_821_3]) ).
cnf(f_821_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_2429),c_Int_OBit0(U_2431))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2429,U_2431) ),
inference(clausify,[status(thm)],[f_821_3]) ).
fof(f_822_1,plain,
! [V_l,V_k] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit1(V_k)),V_l) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,V_k),V_l)),V_l),
inference(fof_nnf,[status(thm)],[fact_mult__Bit1]) ).
fof(f_822_2,plain,
! [U_2433,U_2432] : hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit1(U_2432)),U_2433) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_2432),U_2433)),U_2433),
inference(variable_rename,[status(thm)],[f_822_1]) ).
cnf(f_822_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit1(U_2432)),U_2433) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,U_2432),U_2433)),U_2433),
inference(clausify,[status(thm)],[f_822_2]) ).
fof(f_823_1,plain,
! [V_l,V_k] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(V_k),c_Int_OBit1(V_l)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,c_Int_Osucc(V_l))),
inference(fof_nnf,[status(thm)],[fact_add__Bit1__Bit1]) ).
fof(f_823_2,plain,
! [U_2435,U_2434] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(U_2434),c_Int_OBit1(U_2435)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2434,c_Int_Osucc(U_2435))),
inference(variable_rename,[status(thm)],[f_823_1]) ).
cnf(f_823_3,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(U_2434),c_Int_OBit1(U_2435)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2434,c_Int_Osucc(U_2435))),
inference(clausify,[status(thm)],[f_823_2]) ).
fof(f_824_1,plain,
! [V_w,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),c_Int_Onumber__class_Onumber__of(T_a,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_double__number__of__Bit0]) ).
fof(f_824_2,plain,
! [U_2437,U_2436] :
( hAPP(c_Groups_Otimes__class_Otimes(U_2436,c_Groups_Oplus__class_Oplus(U_2436,c_Groups_Oone__class_Oone(U_2436),c_Groups_Oone__class_Oone(U_2436))),c_Int_Onumber__class_Onumber__of(U_2436,U_2437)) = c_Int_Onumber__class_Onumber__of(U_2436,c_Int_OBit0(U_2437))
| ~ class_Int_Onumber__ring(U_2436) ),
inference(variable_rename,[status(thm)],[f_824_1]) ).
cnf(f_824_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_2436,c_Groups_Oplus__class_Oplus(U_2436,c_Groups_Oone__class_Oone(U_2436),c_Groups_Oone__class_Oone(U_2436))),c_Int_Onumber__class_Onumber__of(U_2436,U_2437)) = c_Int_Onumber__class_Onumber__of(U_2436,c_Int_OBit0(U_2437))
| ~ class_Int_Onumber__ring(U_2436) ),
inference(clausify,[status(thm)],[f_824_2]) ).
fof(f_825_1,plain,
! [V_n] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(V_n)))
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(V_n))) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,V_n)) ),
inference(fof_nnf,[status(thm)],[fact_number__of1]) ).
fof(f_825_2,plain,
! [U_2438] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(U_2438)))
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(U_2438))) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2438)) ),
inference(variable_rename,[status(thm)],[f_825_1]) ).
cnf(f_825_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(U_2438)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2438)) ),
inference(clausify,[status(thm)],[f_825_2]) ).
cnf(f_825_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(U_2438)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2438)) ),
inference(clausify,[status(thm)],[f_825_2]) ).
fof(f_826_1,plain,
! [V_za_2,V_y_2,V_x_2] :
( ( V_x_2 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_y_2,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_za_2))
| hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x_2) != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_y_2,V_za_2) )
& ( hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x_2) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_y_2,V_za_2)
| V_x_2 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_y_2,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_za_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_eq__divide__2__times__iff]) ).
fof(f_826_2,plain,
! [U_2441,U_2440,U_2439] :
( ( U_2439 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2440,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2441))
| hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2439) != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2440,U_2441) )
& ( hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2439) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2440,U_2441)
| U_2439 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2440,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2441)) ) ),
inference(variable_rename,[status(thm)],[f_826_1]) ).
fof(f_826_3,plain,
( ! [U_2447,U_2445,U_2443] :
( U_2443 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2445,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2447))
| hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2443) != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2445,U_2447) )
& ! [U_2446,U_2444,U_2442] :
( hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2442) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2444,U_2446)
| U_2442 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2444,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2446)) ) ),
inference(miniscope,[status(thm)],[f_826_2]) ).
cnf(f_826_4,plain,
( hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2442) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2444,U_2446)
| U_2442 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2444,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2446)) ),
inference(clausify,[status(thm)],[f_826_3]) ).
cnf(f_826_5,plain,
( U_2443 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2445,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2447))
| hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2443) != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2445,U_2447) ),
inference(clausify,[status(thm)],[f_826_3]) ).
fof(f_827_1,plain,
! [V_z,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_z),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__2__right]) ).
fof(f_827_2,plain,
! [U_2449,U_2448] :
( hAPP(c_Groups_Otimes__class_Otimes(U_2448,U_2449),c_Int_Onumber__class_Onumber__of(U_2448,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(U_2448,U_2449,U_2449)
| ~ class_Int_Onumber__ring(U_2448) ),
inference(variable_rename,[status(thm)],[f_827_1]) ).
cnf(f_827_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_2448,U_2449),c_Int_Onumber__class_Onumber__of(U_2448,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(U_2448,U_2449,U_2449)
| ~ class_Int_Onumber__ring(U_2448) ),
inference(clausify,[status(thm)],[f_827_2]) ).
fof(f_828_1,plain,
! [V_z,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__2]) ).
fof(f_828_2,plain,
! [U_2451,U_2450] :
( hAPP(c_Groups_Otimes__class_Otimes(U_2450,c_Int_Onumber__class_Onumber__of(U_2450,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2451) = c_Groups_Oplus__class_Oplus(U_2450,U_2451,U_2451)
| ~ class_Int_Onumber__ring(U_2450) ),
inference(variable_rename,[status(thm)],[f_828_1]) ).
cnf(f_828_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_2450,c_Int_Onumber__class_Onumber__of(U_2450,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2451) = c_Groups_Oplus__class_Oplus(U_2450,U_2451,U_2451)
| ~ class_Int_Onumber__ring(U_2450) ),
inference(clausify,[status(thm)],[f_828_2]) ).
fof(f_829_1,plain,
! [T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__add__one__is__two]) ).
fof(f_829_2,plain,
! [U_2452] :
( c_Groups_Oplus__class_Oplus(U_2452,c_Groups_Oone__class_Oone(U_2452),c_Groups_Oone__class_Oone(U_2452)) = c_Int_Onumber__class_Onumber__of(U_2452,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_2452) ),
inference(variable_rename,[status(thm)],[f_829_1]) ).
cnf(f_829_3,plain,
( c_Groups_Oplus__class_Oplus(U_2452,c_Groups_Oone__class_Oone(U_2452),c_Groups_Oone__class_Oone(U_2452)) = c_Int_Onumber__class_Onumber__of(U_2452,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_2452) ),
inference(clausify,[status(thm)],[f_829_2]) ).
fof(f_830_1,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(fof_nnf,[status(thm)],[fact_pos2]) ).
cnf(f_830_2,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(clausify,[status(thm)],[f_830_1]) ).
fof(f_831_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J]) ).
cnf(f_831_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(clausify,[status(thm)],[f_831_1]) ).
fof(f_832_1,plain,
! [V_z] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z),
inference(fof_nnf,[status(thm)],[fact_nat__mult__2__right]) ).
fof(f_832_2,plain,
! [U_2453] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2453),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2453,U_2453),
inference(variable_rename,[status(thm)],[f_832_1]) ).
cnf(f_832_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2453),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2453,U_2453),
inference(clausify,[status(thm)],[f_832_2]) ).
fof(f_833_1,plain,
! [V_z] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z),
inference(fof_nnf,[status(thm)],[fact_nat__mult__2]) ).
fof(f_833_2,plain,
! [U_2454] : hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2454) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2454,U_2454),
inference(variable_rename,[status(thm)],[f_833_1]) ).
cnf(f_833_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2454) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2454,U_2454),
inference(clausify,[status(thm)],[f_833_2]) ).
fof(f_834_1,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(fof_nnf,[status(thm)],[fact_nat__1__add__1]) ).
cnf(f_834_2,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(clausify,[status(thm)],[f_834_1]) ).
fof(f_835_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_real__less__half__sum]) ).
fof(f_835_2,plain,
! [U_2456,U_2455] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2455,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2455,U_2456),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2455,U_2456) ),
inference(variable_rename,[status(thm)],[f_835_1]) ).
cnf(f_835_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2455,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2455,U_2456),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2455,U_2456) ),
inference(clausify,[status(thm)],[f_835_2]) ).
fof(f_836_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_y)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_real__gt__half__sum]) ).
fof(f_836_2,plain,
! [U_2458,U_2457] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2457,U_2458),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2458)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2457,U_2458) ),
inference(variable_rename,[status(thm)],[f_836_1]) ).
cnf(f_836_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2457,U_2458),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2458)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2457,U_2458) ),
inference(clausify,[status(thm)],[f_836_2]) ).
fof(f_837_1,plain,
! [V_r,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_r,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_half__gt__zero]) ).
fof(f_837_2,plain,
! [U_2460,U_2459] :
( c_Orderings_Oord__class_Oless(U_2459,c_Groups_Ozero__class_Ozero(U_2459),c_Rings_Oinverse__class_Odivide(U_2459,U_2460,c_Int_Onumber__class_Onumber__of(U_2459,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(U_2459,c_Groups_Ozero__class_Ozero(U_2459),U_2460)
| ~ class_Int_Onumber__ring(U_2459)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2459) ),
inference(variable_rename,[status(thm)],[f_837_1]) ).
cnf(f_837_3,plain,
( c_Orderings_Oord__class_Oless(U_2459,c_Groups_Ozero__class_Ozero(U_2459),c_Rings_Oinverse__class_Odivide(U_2459,U_2460,c_Int_Onumber__class_Onumber__of(U_2459,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(U_2459,c_Groups_Ozero__class_Ozero(U_2459),U_2460)
| ~ class_Int_Onumber__ring(U_2459)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2459) ),
inference(clausify,[status(thm)],[f_837_2]) ).
fof(f_838_1,plain,
! [V_r_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_r_2,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_r_2,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) )
| ~ class_Int_Onumber__ring(T_a)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_half__gt__zero__iff]) ).
fof(f_838_2,plain,
! [U_2462,U_2461] :
( ( ( c_Orderings_Oord__class_Oless(U_2461,c_Groups_Ozero__class_Ozero(U_2461),c_Rings_Oinverse__class_Odivide(U_2461,U_2462,c_Int_Onumber__class_Onumber__of(U_2461,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(U_2461,c_Groups_Ozero__class_Ozero(U_2461),U_2462) )
& ( c_Orderings_Oord__class_Oless(U_2461,c_Groups_Ozero__class_Ozero(U_2461),U_2462)
| ~ c_Orderings_Oord__class_Oless(U_2461,c_Groups_Ozero__class_Ozero(U_2461),c_Rings_Oinverse__class_Odivide(U_2461,U_2462,c_Int_Onumber__class_Onumber__of(U_2461,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) )
| ~ class_Int_Onumber__ring(U_2461)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2461) ),
inference(variable_rename,[status(thm)],[f_838_1]) ).
cnf(f_838_3,plain,
( c_Orderings_Oord__class_Oless(U_2461,c_Groups_Ozero__class_Ozero(U_2461),U_2462)
| ~ c_Orderings_Oord__class_Oless(U_2461,c_Groups_Ozero__class_Ozero(U_2461),c_Rings_Oinverse__class_Odivide(U_2461,U_2462,c_Int_Onumber__class_Onumber__of(U_2461,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Int_Onumber__ring(U_2461)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2461) ),
inference(clausify,[status(thm)],[f_838_2]) ).
cnf(f_838_4,plain,
( c_Orderings_Oord__class_Oless(U_2461,c_Groups_Ozero__class_Ozero(U_2461),c_Rings_Oinverse__class_Odivide(U_2461,U_2462,c_Int_Onumber__class_Onumber__of(U_2461,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(U_2461,c_Groups_Ozero__class_Ozero(U_2461),U_2462)
| ~ class_Int_Onumber__ring(U_2461)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2461) ),
inference(clausify,[status(thm)],[f_838_2]) ).
fof(f_839_1,plain,
! [V_x] :
( V_x = c_Groups_Oone__class_Oone(tc_Int_Oint)
| V_x = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) ),
inference(fof_nnf,[status(thm)],[fact_int__pos__lt__two__imp__zero__or__one]) ).
fof(f_839_2,plain,
! [U_2463] :
( U_2463 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2463 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2463,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2463) ),
inference(variable_rename,[status(thm)],[f_839_1]) ).
cnf(f_839_3,plain,
( U_2463 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2463 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2463,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2463) ),
inference(clausify,[status(thm)],[f_839_2]) ).
fof(f_840_1,plain,
! [V_x] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = V_x,
inference(fof_nnf,[status(thm)],[fact_real__sum__of__halves]) ).
fof(f_840_2,plain,
! [U_2464] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2464,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2464,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = U_2464,
inference(variable_rename,[status(thm)],[f_840_1]) ).
cnf(f_840_3,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2464,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2464,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = U_2464,
inference(clausify,[status(thm)],[f_840_2]) ).
fof(f_841_1,plain,
! [V_D_2,V_x_2] :
( c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,V_x_2,V_D_2)
| ( V_D_2 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
| ( V_D_2 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) )
| V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_nnf,[status(thm)],[fact_DERIV__real__sqrt__generic]) ).
fof(f_841_2,plain,
! [U_2466,U_2465] :
( c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,U_2465,U_2466)
| ( U_2466 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2465))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2465,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
| ( U_2466 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2465)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2465) )
| U_2465 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[f_841_1]) ).
cnf(f_841_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2465,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,U_2465,U_2466)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2465)
| U_2465 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_841_2]) ).
cnf(f_841_4,plain,
( U_2466 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2465))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,U_2465,U_2466)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2465)
| U_2465 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_841_2]) ).
cnf(f_841_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2465,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,U_2465,U_2466)
| U_2466 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2465)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| U_2465 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_841_2]) ).
cnf(f_841_6,plain,
( U_2466 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2465))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,U_2465,U_2466)
| U_2466 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2465)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| U_2465 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_841_2]) ).
fof(f_842_1,plain,
! [V_k_2,V_v_2,V_b_2,V_a_2] :
( hAPP(V_v_2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a_2,V_b_2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(V_v_2,V_a_2),hAPP(V_v_2,V_b_2)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ? [B_x] : ~ c_Deriv_Oderiv(tc_RealDef_Oreal,V_v_2,B_x,V_k_2)
| V_a_2 = V_b_2 ),
inference(fof_nnf,[status(thm)],[fact_DERIV__const__average]) ).
fof(f_842_2,plain,
! [U_2471,U_2470,U_2469,U_2468] :
( hAPP(U_2470,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2468,U_2469),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(U_2470,U_2468),hAPP(U_2470,U_2469)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ? [U_2467] : ~ c_Deriv_Oderiv(tc_RealDef_Oreal,U_2470,U_2467,U_2471)
| U_2468 = U_2469 ),
inference(variable_rename,[status(thm)],[f_842_1]) ).
fof(f_842_3,plain,
! [U_2471,U_2470,U_2469,U_2468] :
( hAPP(U_2470,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2468,U_2469),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(U_2470,U_2468),hAPP(U_2470,U_2469)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ c_Deriv_Oderiv(tc_RealDef_Oreal,U_2470,sK12(U_2471,U_2470,U_2469,U_2468),U_2471)
| U_2468 = U_2469 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_2467,sK12(U_2471,U_2470,U_2469,U_2468))],[f_842_2]) ).
cnf(f_842_4,plain,
( hAPP(U_2470,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2468,U_2469),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(U_2470,U_2468),hAPP(U_2470,U_2469)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ c_Deriv_Oderiv(tc_RealDef_Oreal,U_2470,sK12(U_2471,U_2470,U_2469,U_2468),U_2471)
| U_2468 = U_2469 ),
inference(clausify,[status(thm)],[f_842_3]) ).
fof(f_843_1,plain,
! [V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__lt__1__iff]) ).
fof(f_843_2,plain,
! [U_2472] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2472),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2472,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2472,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2472),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_843_1]) ).
fof(f_843_3,plain,
( ! [U_2474] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2474),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2474,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ! [U_2473] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2473,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2473),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_843_2]) ).
cnf(f_843_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2473,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2473),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_843_3]) ).
cnf(f_843_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2474),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2474,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_843_3]) ).
fof(f_844_1,plain,
! [V_y_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__gt__1__iff]) ).
fof(f_844_2,plain,
! [U_2475] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2475))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2475) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2475)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2475)) ) ),
inference(variable_rename,[status(thm)],[f_844_1]) ).
fof(f_844_3,plain,
( ! [U_2477] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2477))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2477) )
& ! [U_2476] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2476)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2476)) ) ),
inference(miniscope,[status(thm)],[f_844_2]) ).
cnf(f_844_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2476)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2476)) ),
inference(clausify,[status(thm)],[f_844_3]) ).
cnf(f_844_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2477))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2477) ),
inference(clausify,[status(thm)],[f_844_3]) ).
fof(f_845_1,plain,
! [V_y_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__ge__1__iff]) ).
fof(f_845_2,plain,
! [U_2478] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2478))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2478) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2478)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2478)) ) ),
inference(variable_rename,[status(thm)],[f_845_1]) ).
fof(f_845_3,plain,
( ! [U_2480] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2480))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2480) )
& ! [U_2479] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2479)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2479)) ) ),
inference(miniscope,[status(thm)],[f_845_2]) ).
cnf(f_845_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2479)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2479)) ),
inference(clausify,[status(thm)],[f_845_3]) ).
cnf(f_845_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2480))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2480) ),
inference(clausify,[status(thm)],[f_845_3]) ).
fof(f_846_1,plain,
! [V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__le__1__iff]) ).
fof(f_846_2,plain,
! [U_2481] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2481),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2481,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2481,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2481),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_846_1]) ).
fof(f_846_3,plain,
( ! [U_2483] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2483),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2483,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ! [U_2482] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2482,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2482),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_846_2]) ).
cnf(f_846_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2482,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2482),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_846_3]) ).
cnf(f_846_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2483),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2483,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_846_3]) ).
fof(f_847_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_x))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__ge__one]) ).
fof(f_847_2,plain,
! [U_2484] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2484))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2484) ),
inference(variable_rename,[status(thm)],[f_847_1]) ).
cnf(f_847_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2484))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2484) ),
inference(clausify,[status(thm)],[f_847_2]) ).
fof(f_848_1,plain,
! [V_x_2] :
( ( hAPP(c_NthRoot_Osqrt,V_x_2) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| V_x_2 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( V_x_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| hAPP(c_NthRoot_Osqrt,V_x_2) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__eq__1__iff]) ).
fof(f_848_2,plain,
! [U_2485] :
( ( hAPP(c_NthRoot_Osqrt,U_2485) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_2485 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( U_2485 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| hAPP(c_NthRoot_Osqrt,U_2485) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_848_1]) ).
fof(f_848_3,plain,
( ! [U_2487] :
( hAPP(c_NthRoot_Osqrt,U_2487) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_2487 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ! [U_2486] :
( U_2486 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| hAPP(c_NthRoot_Osqrt,U_2486) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_848_2]) ).
cnf(f_848_4,plain,
( U_2486 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| hAPP(c_NthRoot_Osqrt,U_2486) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_848_3]) ).
cnf(f_848_5,plain,
( hAPP(c_NthRoot_Osqrt,U_2487) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_2487 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_848_3]) ).
fof(f_849_1,plain,
hAPP(c_NthRoot_Osqrt,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__one]) ).
cnf(f_849_2,plain,
hAPP(c_NthRoot_Osqrt,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_849_1]) ).
fof(f_850_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),hAPP(c_NthRoot_Osqrt,V_y))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__le__mono]) ).
fof(f_850_2,plain,
! [U_2489,U_2488] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2488),hAPP(c_NthRoot_Osqrt,U_2489))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2488,U_2489) ),
inference(variable_rename,[status(thm)],[f_850_1]) ).
cnf(f_850_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2488),hAPP(c_NthRoot_Osqrt,U_2489))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2488,U_2489) ),
inference(clausify,[status(thm)],[f_850_2]) ).
fof(f_851_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),hAPP(c_NthRoot_Osqrt,V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),hAPP(c_NthRoot_Osqrt,V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__le__iff]) ).
fof(f_851_2,plain,
! [U_2491,U_2490] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2490),hAPP(c_NthRoot_Osqrt,U_2491))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2490,U_2491) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2490,U_2491)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2490),hAPP(c_NthRoot_Osqrt,U_2491)) ) ),
inference(variable_rename,[status(thm)],[f_851_1]) ).
fof(f_851_3,plain,
( ! [U_2495,U_2493] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2493),hAPP(c_NthRoot_Osqrt,U_2495))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2493,U_2495) )
& ! [U_2494,U_2492] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2492,U_2494)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2492),hAPP(c_NthRoot_Osqrt,U_2494)) ) ),
inference(miniscope,[status(thm)],[f_851_2]) ).
cnf(f_851_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2492,U_2494)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2492),hAPP(c_NthRoot_Osqrt,U_2494)) ),
inference(clausify,[status(thm)],[f_851_3]) ).
cnf(f_851_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2493),hAPP(c_NthRoot_Osqrt,U_2495))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2493,U_2495) ),
inference(clausify,[status(thm)],[f_851_3]) ).
fof(f_852_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),hAPP(c_NthRoot_Osqrt,V_y))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__less__mono]) ).
fof(f_852_2,plain,
! [U_2497,U_2496] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2496),hAPP(c_NthRoot_Osqrt,U_2497))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2496,U_2497) ),
inference(variable_rename,[status(thm)],[f_852_1]) ).
cnf(f_852_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2496),hAPP(c_NthRoot_Osqrt,U_2497))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2496,U_2497) ),
inference(clausify,[status(thm)],[f_852_2]) ).
fof(f_853_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),hAPP(c_NthRoot_Osqrt,V_y_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),hAPP(c_NthRoot_Osqrt,V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__less__iff]) ).
fof(f_853_2,plain,
! [U_2499,U_2498] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2498),hAPP(c_NthRoot_Osqrt,U_2499))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2498,U_2499) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2498,U_2499)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2498),hAPP(c_NthRoot_Osqrt,U_2499)) ) ),
inference(variable_rename,[status(thm)],[f_853_1]) ).
fof(f_853_3,plain,
( ! [U_2503,U_2501] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2501),hAPP(c_NthRoot_Osqrt,U_2503))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2501,U_2503) )
& ! [U_2502,U_2500] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2500,U_2502)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2500),hAPP(c_NthRoot_Osqrt,U_2502)) ) ),
inference(miniscope,[status(thm)],[f_853_2]) ).
cnf(f_853_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2500,U_2502)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2500),hAPP(c_NthRoot_Osqrt,U_2502)) ),
inference(clausify,[status(thm)],[f_853_3]) ).
cnf(f_853_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2501),hAPP(c_NthRoot_Osqrt,U_2503))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2501,U_2503) ),
inference(clausify,[status(thm)],[f_853_3]) ).
fof(f_854_1,plain,
! [V_y,V_x] : hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_y)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)),hAPP(c_NthRoot_Osqrt,V_y)),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__mult]) ).
fof(f_854_2,plain,
! [U_2505,U_2504] : hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2504),U_2505)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2504)),hAPP(c_NthRoot_Osqrt,U_2505)),
inference(variable_rename,[status(thm)],[f_854_1]) ).
cnf(f_854_3,plain,
hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2504),U_2505)) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2504)),hAPP(c_NthRoot_Osqrt,U_2505)),
inference(clausify,[status(thm)],[f_854_2]) ).
fof(f_855_1,plain,
! [V_x] : hAPP(c_NthRoot_Osqrt,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__minus]) ).
fof(f_855_2,plain,
! [U_2506] : hAPP(c_NthRoot_Osqrt,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2506)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2506)),
inference(variable_rename,[status(thm)],[f_855_1]) ).
cnf(f_855_3,plain,
hAPP(c_NthRoot_Osqrt,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2506)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2506)),
inference(clausify,[status(thm)],[f_855_2]) ).
fof(f_856_1,plain,
! [V_x] : hAPP(c_NthRoot_Osqrt,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__inverse]) ).
fof(f_856_2,plain,
! [U_2507] : hAPP(c_NthRoot_Osqrt,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,U_2507)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2507)),
inference(variable_rename,[status(thm)],[f_856_1]) ).
cnf(f_856_3,plain,
hAPP(c_NthRoot_Osqrt,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,U_2507)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2507)),
inference(clausify,[status(thm)],[f_856_2]) ).
fof(f_857_1,plain,
! [V_y,V_x] : hAPP(c_NthRoot_Osqrt,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),hAPP(c_NthRoot_Osqrt,V_y)),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__divide]) ).
fof(f_857_2,plain,
! [U_2509,U_2508] : hAPP(c_NthRoot_Osqrt,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2508,U_2509)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2508),hAPP(c_NthRoot_Osqrt,U_2509)),
inference(variable_rename,[status(thm)],[f_857_1]) ).
cnf(f_857_3,plain,
hAPP(c_NthRoot_Osqrt,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2508,U_2509)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2508),hAPP(c_NthRoot_Osqrt,U_2509)),
inference(clausify,[status(thm)],[f_857_2]) ).
fof(f_858_1,plain,
! [V_y_2,V_x_2] :
( ( hAPP(c_NthRoot_Osqrt,V_x_2) = hAPP(c_NthRoot_Osqrt,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_NthRoot_Osqrt,V_x_2) != hAPP(c_NthRoot_Osqrt,V_y_2) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__eq__iff]) ).
fof(f_858_2,plain,
! [U_2511,U_2510] :
( ( hAPP(c_NthRoot_Osqrt,U_2510) = hAPP(c_NthRoot_Osqrt,U_2511)
| U_2510 != U_2511 )
& ( U_2510 = U_2511
| hAPP(c_NthRoot_Osqrt,U_2510) != hAPP(c_NthRoot_Osqrt,U_2511) ) ),
inference(variable_rename,[status(thm)],[f_858_1]) ).
fof(f_858_3,plain,
( ! [U_2515,U_2513] :
( hAPP(c_NthRoot_Osqrt,U_2513) = hAPP(c_NthRoot_Osqrt,U_2515)
| U_2513 != U_2515 )
& ! [U_2514,U_2512] :
( U_2512 = U_2514
| hAPP(c_NthRoot_Osqrt,U_2512) != hAPP(c_NthRoot_Osqrt,U_2514) ) ),
inference(miniscope,[status(thm)],[f_858_2]) ).
cnf(f_858_4,plain,
( U_2512 = U_2514
| hAPP(c_NthRoot_Osqrt,U_2512) != hAPP(c_NthRoot_Osqrt,U_2514) ),
inference(clausify,[status(thm)],[f_858_3]) ).
cnf(f_858_5,plain,
( hAPP(c_NthRoot_Osqrt,U_2513) = hAPP(c_NthRoot_Osqrt,U_2515)
| U_2513 != U_2515 ),
inference(clausify,[status(thm)],[f_858_3]) ).
fof(f_859_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_x))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__gt__zero]) ).
fof(f_859_2,plain,
! [U_2516] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2516))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2516) ),
inference(variable_rename,[status(thm)],[f_859_1]) ).
cnf(f_859_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2516))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2516) ),
inference(clausify,[status(thm)],[f_859_2]) ).
fof(f_860_1,plain,
! [V_x] :
( hAPP(c_NthRoot_Osqrt,V_x) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__not__eq__zero]) ).
fof(f_860_2,plain,
! [U_2517] :
( hAPP(c_NthRoot_Osqrt,U_2517) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2517) ),
inference(variable_rename,[status(thm)],[f_860_1]) ).
cnf(f_860_3,plain,
( hAPP(c_NthRoot_Osqrt,U_2517) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2517) ),
inference(clausify,[status(thm)],[f_860_2]) ).
fof(f_861_1,plain,
! [V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__lt__0__iff]) ).
fof(f_861_2,plain,
! [U_2518] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2518),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2518,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2518,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2518),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_861_1]) ).
fof(f_861_3,plain,
( ! [U_2520] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2520),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2520,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_2519] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2519,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2519),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_861_2]) ).
cnf(f_861_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2519,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2519),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_861_3]) ).
cnf(f_861_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2520),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2520,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_861_3]) ).
fof(f_862_1,plain,
! [V_y_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__gt__0__iff]) ).
fof(f_862_2,plain,
! [U_2521] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2521))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2521) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2521)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2521)) ) ),
inference(variable_rename,[status(thm)],[f_862_1]) ).
fof(f_862_3,plain,
( ! [U_2523] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2523))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2523) )
& ! [U_2522] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2522)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2522)) ) ),
inference(miniscope,[status(thm)],[f_862_2]) ).
cnf(f_862_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2522)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2522)) ),
inference(clausify,[status(thm)],[f_862_3]) ).
cnf(f_862_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2523))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2523) ),
inference(clausify,[status(thm)],[f_862_3]) ).
fof(f_863_1,plain,
! [V_y_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__ge__0__iff]) ).
fof(f_863_2,plain,
! [U_2524] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2524))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2524) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2524)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2524)) ) ),
inference(variable_rename,[status(thm)],[f_863_1]) ).
fof(f_863_3,plain,
( ! [U_2526] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2526))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2526) )
& ! [U_2525] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2525)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2525)) ) ),
inference(miniscope,[status(thm)],[f_863_2]) ).
cnf(f_863_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2525)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2525)) ),
inference(clausify,[status(thm)],[f_863_3]) ).
cnf(f_863_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2526))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2526) ),
inference(clausify,[status(thm)],[f_863_3]) ).
fof(f_864_1,plain,
! [V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__le__0__iff]) ).
fof(f_864_2,plain,
! [U_2527] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2527),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2527,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2527,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2527),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_864_1]) ).
fof(f_864_3,plain,
( ! [U_2529] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2529),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2529,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_2528] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2528,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2528),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_864_2]) ).
cnf(f_864_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2528,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2528),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_864_3]) ).
cnf(f_864_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2529),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2529,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_864_3]) ).
fof(f_865_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,V_x))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__ge__zero]) ).
fof(f_865_2,plain,
! [U_2530] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2530))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2530) ),
inference(variable_rename,[status(thm)],[f_865_1]) ).
cnf(f_865_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,U_2530))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2530) ),
inference(clausify,[status(thm)],[f_865_2]) ).
fof(f_866_1,plain,
! [V_x] :
( V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(c_NthRoot_Osqrt,V_x) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__eq__zero__cancel]) ).
fof(f_866_2,plain,
! [U_2531] :
( U_2531 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(c_NthRoot_Osqrt,U_2531) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2531) ),
inference(variable_rename,[status(thm)],[f_866_1]) ).
cnf(f_866_3,plain,
( U_2531 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(c_NthRoot_Osqrt,U_2531) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2531) ),
inference(clausify,[status(thm)],[f_866_2]) ).
fof(f_867_1,plain,
! [V_x_2] :
( ( hAPP(c_NthRoot_Osqrt,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(c_NthRoot_Osqrt,V_x_2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__eq__0__iff]) ).
fof(f_867_2,plain,
! [U_2532] :
( ( hAPP(c_NthRoot_Osqrt,U_2532) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2532 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( U_2532 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(c_NthRoot_Osqrt,U_2532) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_867_1]) ).
fof(f_867_3,plain,
( ! [U_2534] :
( hAPP(c_NthRoot_Osqrt,U_2534) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2534 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_2533] :
( U_2533 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(c_NthRoot_Osqrt,U_2533) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_867_2]) ).
cnf(f_867_4,plain,
( U_2533 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(c_NthRoot_Osqrt,U_2533) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_867_3]) ).
cnf(f_867_5,plain,
( hAPP(c_NthRoot_Osqrt,U_2534) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2534 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_867_3]) ).
fof(f_868_1,plain,
hAPP(c_NthRoot_Osqrt,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__zero]) ).
cnf(f_868_2,plain,
hAPP(c_NthRoot_Osqrt,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_868_1]) ).
fof(f_869_1,plain,
! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_x),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y),V_y)))),
inference(fof_nnf,[status(thm)],[fact_le__real__sqrt__sumsq]) ).
fof(f_869_2,plain,
! [U_2536,U_2535] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2535,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2535),U_2535),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2536),U_2536)))),
inference(variable_rename,[status(thm)],[f_869_1]) ).
cnf(f_869_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2535,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2535),U_2535),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2536),U_2536)))),
inference(clausify,[status(thm)],[f_869_2]) ).
fof(f_870_1,plain,
! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_x),V_x),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,V_y),V_y)))),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__mult__self__sum__ge__zero]) ).
fof(f_870_2,plain,
! [U_2538,U_2537] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2537),U_2537),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2538),U_2538)))),
inference(variable_rename,[status(thm)],[f_870_1]) ).
cnf(f_870_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2537),U_2537),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2538),U_2538)))),
inference(clausify,[status(thm)],[f_870_2]) ).
fof(f_871_1,plain,
! [V_x] :
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),V_x) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_sqrt__divide__self__eq]) ).
fof(f_871_2,plain,
! [U_2539] :
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2539),U_2539) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2539))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2539) ),
inference(variable_rename,[status(thm)],[f_871_1]) ).
cnf(f_871_3,plain,
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2539),U_2539) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2539))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2539) ),
inference(clausify,[status(thm)],[f_871_2]) ).
fof(f_872_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__two__ge__zero]) ).
cnf(f_872_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(clausify,[status(thm)],[f_872_1]) ).
fof(f_873_1,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__two__gt__zero]) ).
cnf(f_873_2,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(clausify,[status(thm)],[f_873_1]) ).
fof(f_874_1,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__two__gt__one]) ).
cnf(f_874_2,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(clausify,[status(thm)],[f_874_1]) ).
fof(f_875_1,plain,
! [V_u] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),V_u)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_u) ),
inference(fof_nnf,[status(thm)],[fact_lemma__real__divide__sqrt__less]) ).
fof(f_875_2,plain,
! [U_2540] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2540,hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),U_2540)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2540) ),
inference(variable_rename,[status(thm)],[f_875_1]) ).
cnf(f_875_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2540,hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),U_2540)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2540) ),
inference(clausify,[status(thm)],[f_875_2]) ).
fof(f_876_1,plain,
! [V_x_2] :
( c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,V_x_2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_DERIV__real__sqrt]) ).
fof(f_876_2,plain,
! [U_2541] :
( c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,U_2541,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2541)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2541) ),
inference(variable_rename,[status(thm)],[f_876_1]) ).
cnf(f_876_3,plain,
( c_Deriv_Oderiv(tc_RealDef_Oreal,c_NthRoot_Osqrt,U_2541,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2541)),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2541) ),
inference(clausify,[status(thm)],[f_876_2]) ).
fof(f_877_1,plain,
! [V_y,V_x,V_u] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),V_u)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_u) ),
inference(fof_nnf,[status(thm)],[fact_lemma__sqrt__hcomplex__capprox]) ).
fof(f_877_2,plain,
! [U_2544,U_2543,U_2542] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2543,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2544,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),U_2542)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2544)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2543)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2544,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2542,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2543,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2542,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2542) ),
inference(variable_rename,[status(thm)],[f_877_1]) ).
cnf(f_877_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2543,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2544,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),U_2542)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2544)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2543)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2544,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2542,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2543,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2542,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2542) ),
inference(clausify,[status(thm)],[f_877_2]) ).
fof(f_878_1,plain,
! [V_ya,V_xa,V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_xa,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_ya,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__sum__squares__mult__ge__zero]) ).
fof(f_878_2,plain,
! [U_2548,U_2547,U_2546,U_2545] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2545,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2546,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2547,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2548,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(variable_rename,[status(thm)],[f_878_1]) ).
cnf(f_878_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2545,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2546,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2547,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2548,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(clausify,[status(thm)],[f_878_2]) ).
fof(f_879_1,plain,
! [V_k,V_x] : hAPP(c_NthRoot_Osqrt,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,V_k)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),V_k),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__power]) ).
fof(f_879_2,plain,
! [U_2550,U_2549] : hAPP(c_NthRoot_Osqrt,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2549,U_2550)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2549),U_2550),
inference(variable_rename,[status(thm)],[f_879_1]) ).
cnf(f_879_3,plain,
hAPP(c_NthRoot_Osqrt,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2549,U_2550)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2549),U_2550),
inference(clausify,[status(thm)],[f_879_2]) ).
fof(f_880_1,plain,
! [V_x,T_a] :
( c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J]) ).
fof(f_880_2,plain,
! [U_2552,U_2551] :
( c_Power_Opower__class_Opower(U_2551,U_2552,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2551)
| ~ class_Rings_Ocomm__semiring__1(U_2551) ),
inference(variable_rename,[status(thm)],[f_880_1]) ).
cnf(f_880_3,plain,
( c_Power_Opower__class_Opower(U_2551,U_2552,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2551)
| ~ class_Rings_Ocomm__semiring__1(U_2551) ),
inference(clausify,[status(thm)],[f_880_2]) ).
fof(f_881_1,plain,
! [V_q,V_p,V_x,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_p)),c_Power_Opower__class_Opower(T_a,V_x,V_q)) = 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_881_2,plain,
! [U_2556,U_2555,U_2554,U_2553] :
( hAPP(c_Groups_Otimes__class_Otimes(U_2553,c_Power_Opower__class_Opower(U_2553,U_2554,U_2555)),c_Power_Opower__class_Opower(U_2553,U_2554,U_2556)) = c_Power_Opower__class_Opower(U_2553,U_2554,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2555,U_2556))
| ~ class_Rings_Ocomm__semiring__1(U_2553) ),
inference(variable_rename,[status(thm)],[f_881_1]) ).
cnf(f_881_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_2553,c_Power_Opower__class_Opower(U_2553,U_2554,U_2555)),c_Power_Opower__class_Opower(U_2553,U_2554,U_2556)) = c_Power_Opower__class_Opower(U_2553,U_2554,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2555,U_2556))
| ~ class_Rings_Ocomm__semiring__1(U_2553) ),
inference(clausify,[status(thm)],[f_881_2]) ).
fof(f_882_1,plain,
! [V_q,V_p,V_x,T_a] :
( c_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_p),V_q) = c_Power_Opower__class_Opower(T_a,V_x,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_882_2,plain,
! [U_2560,U_2559,U_2558,U_2557] :
( c_Power_Opower__class_Opower(U_2557,c_Power_Opower__class_Opower(U_2557,U_2558,U_2559),U_2560) = c_Power_Opower__class_Opower(U_2557,U_2558,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2559),U_2560))
| ~ class_Rings_Ocomm__semiring__1(U_2557) ),
inference(variable_rename,[status(thm)],[f_882_1]) ).
cnf(f_882_3,plain,
( c_Power_Opower__class_Opower(U_2557,c_Power_Opower__class_Opower(U_2557,U_2558,U_2559),U_2560) = c_Power_Opower__class_Opower(U_2557,U_2558,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2559),U_2560))
| ~ class_Rings_Ocomm__semiring__1(U_2557) ),
inference(clausify,[status(thm)],[f_882_2]) ).
fof(f_883_1,plain,
! [V_q,V_y,V_x,T_a] :
( c_Power_Opower__class_Opower(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_y),V_q) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_q)),c_Power_Opower__class_Opower(T_a,V_y,V_q))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J]) ).
fof(f_883_2,plain,
! [U_2564,U_2563,U_2562,U_2561] :
( c_Power_Opower__class_Opower(U_2561,hAPP(c_Groups_Otimes__class_Otimes(U_2561,U_2562),U_2563),U_2564) = hAPP(c_Groups_Otimes__class_Otimes(U_2561,c_Power_Opower__class_Opower(U_2561,U_2562,U_2564)),c_Power_Opower__class_Opower(U_2561,U_2563,U_2564))
| ~ class_Rings_Ocomm__semiring__1(U_2561) ),
inference(variable_rename,[status(thm)],[f_883_1]) ).
cnf(f_883_3,plain,
( c_Power_Opower__class_Opower(U_2561,hAPP(c_Groups_Otimes__class_Otimes(U_2561,U_2562),U_2563),U_2564) = hAPP(c_Groups_Otimes__class_Otimes(U_2561,c_Power_Opower__class_Opower(U_2561,U_2562,U_2564)),c_Power_Opower__class_Opower(U_2561,U_2563,U_2564))
| ~ class_Rings_Ocomm__semiring__1(U_2561) ),
inference(clausify,[status(thm)],[f_883_2]) ).
fof(f_884_1,plain,
! [V_x,T_a] :
( c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J]) ).
fof(f_884_2,plain,
! [U_2566,U_2565] :
( c_Power_Opower__class_Opower(U_2565,U_2566,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2566
| ~ class_Rings_Ocomm__semiring__1(U_2565) ),
inference(variable_rename,[status(thm)],[f_884_1]) ).
cnf(f_884_3,plain,
( c_Power_Opower__class_Opower(U_2565,U_2566,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2566
| ~ class_Rings_Ocomm__semiring__1(U_2565) ),
inference(clausify,[status(thm)],[f_884_2]) ).
fof(f_885_1,plain,
! [V_wa_2,V_a_2,T_a] :
( ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)) = c_Groups_Ozero__class_Ozero(T_a)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
| c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Power_Opower(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff__number__of]) ).
fof(f_885_2,plain,
! [U_2569,U_2568,U_2567] :
( ( ( c_Power_Opower__class_Opower(U_2567,U_2568,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2569)) = c_Groups_Ozero__class_Ozero(U_2567)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2569) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2568 != c_Groups_Ozero__class_Ozero(U_2567) )
& ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2569) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2568 = c_Groups_Ozero__class_Ozero(U_2567) )
| c_Power_Opower__class_Opower(U_2567,U_2568,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2569)) != c_Groups_Ozero__class_Ozero(U_2567) ) )
| ~ class_Rings_Ozero__neq__one(U_2567)
| ~ class_Rings_Ono__zero__divisors(U_2567)
| ~ class_Rings_Omult__zero(U_2567)
| ~ class_Power_Opower(U_2567) ),
inference(variable_rename,[status(thm)],[f_885_1]) ).
cnf(f_885_3,plain,
( U_2568 = c_Groups_Ozero__class_Ozero(U_2567)
| c_Power_Opower__class_Opower(U_2567,U_2568,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2569)) != c_Groups_Ozero__class_Ozero(U_2567)
| ~ class_Rings_Ozero__neq__one(U_2567)
| ~ class_Rings_Ono__zero__divisors(U_2567)
| ~ class_Rings_Omult__zero(U_2567)
| ~ class_Power_Opower(U_2567) ),
inference(clausify,[status(thm)],[f_885_2]) ).
cnf(f_885_4,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2569) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(U_2567,U_2568,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2569)) != c_Groups_Ozero__class_Ozero(U_2567)
| ~ class_Rings_Ozero__neq__one(U_2567)
| ~ class_Rings_Ono__zero__divisors(U_2567)
| ~ class_Rings_Omult__zero(U_2567)
| ~ class_Power_Opower(U_2567) ),
inference(clausify,[status(thm)],[f_885_2]) ).
cnf(f_885_5,plain,
( c_Power_Opower__class_Opower(U_2567,U_2568,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2569)) = c_Groups_Ozero__class_Ozero(U_2567)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2569) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2568 != c_Groups_Ozero__class_Ozero(U_2567)
| ~ class_Rings_Ozero__neq__one(U_2567)
| ~ class_Rings_Ono__zero__divisors(U_2567)
| ~ class_Rings_Omult__zero(U_2567)
| ~ class_Power_Opower(U_2567) ),
inference(clausify,[status(thm)],[f_885_2]) ).
fof(f_886_1,plain,
! [V_w,T_a] :
( ( ( c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)) = c_Groups_Ozero__class_Ozero(T_a)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w)) = c_Groups_Oone__class_Oone(T_a)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Osemiring__0(T_a)
| ~ class_Power_Opower(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__0__left__number__of]) ).
fof(f_886_2,plain,
! [U_2571,U_2570] :
( ( ( c_Power_Opower__class_Opower(U_2570,c_Groups_Ozero__class_Ozero(U_2570),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2571)) = c_Groups_Ozero__class_Ozero(U_2570)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2571) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Power_Opower__class_Opower(U_2570,c_Groups_Ozero__class_Ozero(U_2570),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2571)) = c_Groups_Oone__class_Oone(U_2570)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2571) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Osemiring__0(U_2570)
| ~ class_Power_Opower(U_2570) ),
inference(variable_rename,[status(thm)],[f_886_1]) ).
cnf(f_886_3,plain,
( c_Power_Opower__class_Opower(U_2570,c_Groups_Ozero__class_Ozero(U_2570),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2571)) = c_Groups_Oone__class_Oone(U_2570)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2571) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Osemiring__0(U_2570)
| ~ class_Power_Opower(U_2570) ),
inference(clausify,[status(thm)],[f_886_2]) ).
cnf(f_886_4,plain,
( c_Power_Opower__class_Opower(U_2570,c_Groups_Ozero__class_Ozero(U_2570),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2571)) = c_Groups_Ozero__class_Ozero(U_2570)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2571) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Osemiring__0(U_2570)
| ~ class_Power_Opower(U_2570) ),
inference(clausify,[status(thm)],[f_886_2]) ).
fof(f_887_1,plain,
! [V_a,T_a] :
( c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a)),V_a)
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power3__eq__cube]) ).
fof(f_887_2,plain,
! [U_2573,U_2572] :
( c_Power_Opower__class_Opower(U_2572,U_2573,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(U_2572,hAPP(c_Groups_Otimes__class_Otimes(U_2572,U_2573),U_2573)),U_2573)
| ~ class_Groups_Omonoid__mult(U_2572) ),
inference(variable_rename,[status(thm)],[f_887_1]) ).
cnf(f_887_3,plain,
( c_Power_Opower__class_Opower(U_2572,U_2573,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(U_2572,hAPP(c_Groups_Otimes__class_Otimes(U_2572,U_2573),U_2573)),U_2573)
| ~ class_Groups_Omonoid__mult(U_2572) ),
inference(clausify,[status(thm)],[f_887_2]) ).
fof(f_888_1,plain,
! [T_a] :
( c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Osemiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__power2]) ).
fof(f_888_2,plain,
! [U_2574] :
( c_Power_Opower__class_Opower(U_2574,c_Groups_Ozero__class_Ozero(U_2574),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_2574)
| ~ class_Rings_Osemiring__1(U_2574) ),
inference(variable_rename,[status(thm)],[f_888_1]) ).
cnf(f_888_3,plain,
( c_Power_Opower__class_Opower(U_2574,c_Groups_Ozero__class_Ozero(U_2574),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_2574)
| ~ class_Rings_Osemiring__1(U_2574) ),
inference(clausify,[status(thm)],[f_888_2]) ).
fof(f_889_1,plain,
! [V_a_2,T_a] :
( ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__eq__power2]) ).
fof(f_889_2,plain,
! [U_2576,U_2575] :
( ( ( c_Power_Opower__class_Opower(U_2575,U_2576,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_2575)
| U_2576 != c_Groups_Ozero__class_Ozero(U_2575) )
& ( U_2576 = c_Groups_Ozero__class_Ozero(U_2575)
| c_Power_Opower__class_Opower(U_2575,U_2576,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(U_2575) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(U_2575) ),
inference(variable_rename,[status(thm)],[f_889_1]) ).
cnf(f_889_3,plain,
( U_2576 = c_Groups_Ozero__class_Ozero(U_2575)
| c_Power_Opower__class_Opower(U_2575,U_2576,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(U_2575)
| ~ class_Rings_Oring__1__no__zero__divisors(U_2575) ),
inference(clausify,[status(thm)],[f_889_2]) ).
cnf(f_889_4,plain,
( c_Power_Opower__class_Opower(U_2575,U_2576,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_2575)
| U_2576 != c_Groups_Ozero__class_Ozero(U_2575)
| ~ class_Rings_Oring__1__no__zero__divisors(U_2575) ),
inference(clausify,[status(thm)],[f_889_2]) ).
fof(f_890_1,plain,
! [V_x,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,V_x),V_x) = c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J]) ).
fof(f_890_2,plain,
! [U_2578,U_2577] :
( hAPP(c_Groups_Otimes__class_Otimes(U_2577,U_2578),U_2578) = c_Power_Opower__class_Opower(U_2577,U_2578,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Ocomm__semiring__1(U_2577) ),
inference(variable_rename,[status(thm)],[f_890_1]) ).
cnf(f_890_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_2577,U_2578),U_2578) = c_Power_Opower__class_Opower(U_2577,U_2578,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Ocomm__semiring__1(U_2577) ),
inference(clausify,[status(thm)],[f_890_2]) ).
fof(f_891_1,plain,
! [V_a,T_a] :
( c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_a)
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__eq__square]) ).
fof(f_891_2,plain,
! [U_2580,U_2579] :
( c_Power_Opower__class_Opower(U_2579,U_2580,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(U_2579,U_2580),U_2580)
| ~ class_Groups_Omonoid__mult(U_2579) ),
inference(variable_rename,[status(thm)],[f_891_1]) ).
cnf(f_891_3,plain,
( c_Power_Opower__class_Opower(U_2579,U_2580,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(U_2579,U_2580),U_2580)
| ~ class_Groups_Omonoid__mult(U_2579) ),
inference(clausify,[status(thm)],[f_891_2]) ).
fof(f_892_1,plain,
! [T_a] :
( c_Power_Opower__class_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a)
| ~ class_Rings_Osemiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__power2]) ).
fof(f_892_2,plain,
! [U_2581] :
( c_Power_Opower__class_Opower(U_2581,c_Groups_Oone__class_Oone(U_2581),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_2581)
| ~ class_Rings_Osemiring__1(U_2581) ),
inference(variable_rename,[status(thm)],[f_892_1]) ).
cnf(f_892_3,plain,
( c_Power_Opower__class_Opower(U_2581,c_Groups_Oone__class_Oone(U_2581),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_2581)
| ~ class_Rings_Osemiring__1(U_2581) ),
inference(clausify,[status(thm)],[f_892_2]) ).
fof(f_893_1,plain,
! [V_a,T_a] :
( c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__minus]) ).
fof(f_893_2,plain,
! [U_2583,U_2582] :
( c_Power_Opower__class_Opower(U_2582,c_Groups_Ouminus__class_Ouminus(U_2582,U_2583),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(U_2582,U_2583,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Oring__1(U_2582) ),
inference(variable_rename,[status(thm)],[f_893_1]) ).
cnf(f_893_3,plain,
( c_Power_Opower__class_Opower(U_2582,c_Groups_Ouminus__class_Ouminus(U_2582,U_2583),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(U_2582,U_2583,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Oring__1(U_2582) ),
inference(clausify,[status(thm)],[f_893_2]) ).
fof(f_894_1,plain,
! [V_n,V_a,T_a] :
( c_Power_Opower__class_Opower(T_a,V_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__even__eq]) ).
fof(f_894_2,plain,
! [U_2586,U_2585,U_2584] :
( c_Power_Opower__class_Opower(U_2584,U_2585,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2586)) = c_Power_Opower__class_Opower(U_2584,c_Power_Opower__class_Opower(U_2584,U_2585,U_2586),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Groups_Omonoid__mult(U_2584) ),
inference(variable_rename,[status(thm)],[f_894_1]) ).
cnf(f_894_3,plain,
( c_Power_Opower__class_Opower(U_2584,U_2585,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2586)) = c_Power_Opower__class_Opower(U_2584,c_Power_Opower__class_Opower(U_2584,U_2585,U_2586),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Groups_Omonoid__mult(U_2584) ),
inference(clausify,[status(thm)],[f_894_2]) ).
fof(f_895_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__power2]) ).
fof(f_895_2,plain,
! [U_2588,U_2587] :
( c_Orderings_Oord__class_Oless__eq(U_2587,c_Groups_Ozero__class_Ozero(U_2587),c_Power_Opower__class_Opower(U_2587,U_2588,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__idom(U_2587) ),
inference(variable_rename,[status(thm)],[f_895_1]) ).
cnf(f_895_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2587,c_Groups_Ozero__class_Ozero(U_2587),c_Power_Opower__class_Opower(U_2587,U_2588,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__idom(U_2587) ),
inference(clausify,[status(thm)],[f_895_2]) ).
fof(f_896_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__le__imp__le]) ).
fof(f_896_2,plain,
! [U_2591,U_2590,U_2589] :
( c_Orderings_Oord__class_Oless__eq(U_2589,U_2590,U_2591)
| ~ c_Orderings_Oord__class_Oless__eq(U_2589,c_Groups_Ozero__class_Ozero(U_2589),U_2591)
| ~ c_Orderings_Oord__class_Oless__eq(U_2589,c_Power_Opower__class_Opower(U_2589,U_2590,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2589,U_2591,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__semidom(U_2589) ),
inference(variable_rename,[status(thm)],[f_896_1]) ).
cnf(f_896_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2589,U_2590,U_2591)
| ~ c_Orderings_Oord__class_Oless__eq(U_2589,c_Groups_Ozero__class_Ozero(U_2589),U_2591)
| ~ c_Orderings_Oord__class_Oless__eq(U_2589,c_Power_Opower__class_Opower(U_2589,U_2590,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2589,U_2591,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__semidom(U_2589) ),
inference(clausify,[status(thm)],[f_896_2]) ).
fof(f_897_1,plain,
! [V_y,V_x,T_a] :
( V_x = V_y
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__eq__imp__eq]) ).
fof(f_897_2,plain,
! [U_2594,U_2593,U_2592] :
( U_2593 = U_2594
| ~ c_Orderings_Oord__class_Oless__eq(U_2592,c_Groups_Ozero__class_Ozero(U_2592),U_2594)
| ~ c_Orderings_Oord__class_Oless__eq(U_2592,c_Groups_Ozero__class_Ozero(U_2592),U_2593)
| c_Power_Opower__class_Opower(U_2592,U_2593,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(U_2592,U_2594,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__semidom(U_2592) ),
inference(variable_rename,[status(thm)],[f_897_1]) ).
cnf(f_897_3,plain,
( U_2593 = U_2594
| ~ c_Orderings_Oord__class_Oless__eq(U_2592,c_Groups_Ozero__class_Ozero(U_2592),U_2594)
| ~ c_Orderings_Oord__class_Oless__eq(U_2592,c_Groups_Ozero__class_Ozero(U_2592),U_2593)
| c_Power_Opower__class_Opower(U_2592,U_2593,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(U_2592,U_2594,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__semidom(U_2592) ),
inference(clausify,[status(thm)],[f_897_2]) ).
fof(f_898_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__power2]) ).
fof(f_898_2,plain,
! [U_2596,U_2595] :
( ( ( c_Orderings_Oord__class_Oless(U_2595,c_Groups_Ozero__class_Ozero(U_2595),c_Power_Opower__class_Opower(U_2595,U_2596,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| U_2596 = c_Groups_Ozero__class_Ozero(U_2595) )
& ( U_2596 != c_Groups_Ozero__class_Ozero(U_2595)
| ~ c_Orderings_Oord__class_Oless(U_2595,c_Groups_Ozero__class_Ozero(U_2595),c_Power_Opower__class_Opower(U_2595,U_2596,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) )
| ~ class_Rings_Olinordered__idom(U_2595) ),
inference(variable_rename,[status(thm)],[f_898_1]) ).
cnf(f_898_3,plain,
( U_2596 != c_Groups_Ozero__class_Ozero(U_2595)
| ~ c_Orderings_Oord__class_Oless(U_2595,c_Groups_Ozero__class_Ozero(U_2595),c_Power_Opower__class_Opower(U_2595,U_2596,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__idom(U_2595) ),
inference(clausify,[status(thm)],[f_898_2]) ).
cnf(f_898_4,plain,
( c_Orderings_Oord__class_Oless(U_2595,c_Groups_Ozero__class_Ozero(U_2595),c_Power_Opower__class_Opower(U_2595,U_2596,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| U_2596 = c_Groups_Ozero__class_Ozero(U_2595)
| ~ class_Rings_Olinordered__idom(U_2595) ),
inference(clausify,[status(thm)],[f_898_2]) ).
fof(f_899_1,plain,
! [V_a,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__less__0]) ).
fof(f_899_2,plain,
! [U_2598,U_2597] :
( ~ c_Orderings_Oord__class_Oless(U_2597,c_Power_Opower__class_Opower(U_2597,U_2598,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(U_2597))
| ~ class_Rings_Olinordered__idom(U_2597) ),
inference(variable_rename,[status(thm)],[f_899_1]) ).
cnf(f_899_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_2597,c_Power_Opower__class_Opower(U_2597,U_2598,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(U_2597))
| ~ class_Rings_Olinordered__idom(U_2597) ),
inference(clausify,[status(thm)],[f_899_2]) ).
fof(f_900_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_a)
| V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
| c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__power2__eq__zero__iff]) ).
fof(f_900_2,plain,
! [U_2601,U_2600,U_2599] :
( ( ( c_Groups_Oplus__class_Oplus(U_2599,c_Power_Opower__class_Opower(U_2599,U_2600,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2599,U_2601,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(U_2599)
| U_2601 != c_Groups_Ozero__class_Ozero(U_2599)
| U_2600 != c_Groups_Ozero__class_Ozero(U_2599) )
& ( ( U_2601 = c_Groups_Ozero__class_Ozero(U_2599)
& U_2600 = c_Groups_Ozero__class_Ozero(U_2599) )
| c_Groups_Oplus__class_Oplus(U_2599,c_Power_Opower__class_Opower(U_2599,U_2600,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2599,U_2601,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(U_2599) ) )
| ~ class_Rings_Olinordered__idom(U_2599) ),
inference(variable_rename,[status(thm)],[f_900_1]) ).
cnf(f_900_3,plain,
( U_2600 = c_Groups_Ozero__class_Ozero(U_2599)
| c_Groups_Oplus__class_Oplus(U_2599,c_Power_Opower__class_Opower(U_2599,U_2600,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2599,U_2601,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(U_2599)
| ~ class_Rings_Olinordered__idom(U_2599) ),
inference(clausify,[status(thm)],[f_900_2]) ).
cnf(f_900_4,plain,
( U_2601 = c_Groups_Ozero__class_Ozero(U_2599)
| c_Groups_Oplus__class_Oplus(U_2599,c_Power_Opower__class_Opower(U_2599,U_2600,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2599,U_2601,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(U_2599)
| ~ class_Rings_Olinordered__idom(U_2599) ),
inference(clausify,[status(thm)],[f_900_2]) ).
cnf(f_900_5,plain,
( c_Groups_Oplus__class_Oplus(U_2599,c_Power_Opower__class_Opower(U_2599,U_2600,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2599,U_2601,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(U_2599)
| U_2601 != c_Groups_Ozero__class_Ozero(U_2599)
| U_2600 != c_Groups_Ozero__class_Ozero(U_2599)
| ~ class_Rings_Olinordered__idom(U_2599) ),
inference(clausify,[status(thm)],[f_900_2]) ).
fof(f_901_1,plain,
! [V_w,T_b] :
( c_Power_Opower__class_Opower(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_w),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(T_b,c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w))
| ~ class_Int_Onumber(T_b)
| ~ class_Groups_Omonoid__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_power2__eq__square__number__of]) ).
fof(f_901_2,plain,
! [U_2603,U_2602] :
( c_Power_Opower__class_Opower(U_2602,c_Int_Onumber__class_Onumber__of(U_2602,U_2603),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(U_2602,c_Int_Onumber__class_Onumber__of(U_2602,U_2603)),c_Int_Onumber__class_Onumber__of(U_2602,U_2603))
| ~ class_Int_Onumber(U_2602)
| ~ class_Groups_Omonoid__mult(U_2602) ),
inference(variable_rename,[status(thm)],[f_901_1]) ).
cnf(f_901_3,plain,
( c_Power_Opower__class_Opower(U_2602,c_Int_Onumber__class_Onumber__of(U_2602,U_2603),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(U_2602,c_Int_Onumber__class_Onumber__of(U_2602,U_2603)),c_Int_Onumber__class_Onumber__of(U_2602,U_2603))
| ~ class_Int_Onumber(U_2602)
| ~ class_Groups_Omonoid__mult(U_2602) ),
inference(clausify,[status(thm)],[f_901_2]) ).
fof(f_902_1,plain,
! [V_a_2,T_a] :
( ( ( c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a)
| ( V_a_2 != c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
& V_a_2 != c_Groups_Oone__class_Oone(T_a) ) )
& ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
| V_a_2 = c_Groups_Oone__class_Oone(T_a)
| c_Power_Opower__class_Opower(T_a,V_a_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__eq__1__iff]) ).
fof(f_902_2,plain,
! [U_2605,U_2604] :
( ( ( c_Power_Opower__class_Opower(U_2604,U_2605,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_2604)
| ( U_2605 != c_Groups_Ouminus__class_Ouminus(U_2604,c_Groups_Oone__class_Oone(U_2604))
& U_2605 != c_Groups_Oone__class_Oone(U_2604) ) )
& ( U_2605 = c_Groups_Ouminus__class_Ouminus(U_2604,c_Groups_Oone__class_Oone(U_2604))
| U_2605 = c_Groups_Oone__class_Oone(U_2604)
| c_Power_Opower__class_Opower(U_2604,U_2605,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(U_2604) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(U_2604) ),
inference(variable_rename,[status(thm)],[f_902_1]) ).
cnf(f_902_3,plain,
( U_2605 = c_Groups_Ouminus__class_Ouminus(U_2604,c_Groups_Oone__class_Oone(U_2604))
| U_2605 = c_Groups_Oone__class_Oone(U_2604)
| c_Power_Opower__class_Opower(U_2604,U_2605,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(U_2604)
| ~ class_Rings_Oring__1__no__zero__divisors(U_2604) ),
inference(clausify,[status(thm)],[f_902_2]) ).
cnf(f_902_4,plain,
( U_2605 != c_Groups_Oone__class_Oone(U_2604)
| c_Power_Opower__class_Opower(U_2604,U_2605,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_2604)
| ~ class_Rings_Oring__1__no__zero__divisors(U_2604) ),
inference(clausify,[status(thm)],[f_902_2]) ).
cnf(f_902_5,plain,
( U_2605 != c_Groups_Ouminus__class_Ouminus(U_2604,c_Groups_Oone__class_Oone(U_2604))
| c_Power_Opower__class_Opower(U_2604,U_2605,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_2604)
| ~ class_Rings_Oring__1__no__zero__divisors(U_2604) ),
inference(clausify,[status(thm)],[f_902_2]) ).
fof(f_903_1,plain,
! [V_n,V_x,T_a] :
( c_Power_Opower__class_Opower(T_a,V_x,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_n)),c_Power_Opower__class_Opower(T_a,V_x,V_n))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J]) ).
fof(f_903_2,plain,
! [U_2608,U_2607,U_2606] :
( c_Power_Opower__class_Opower(U_2606,U_2607,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2608)) = hAPP(c_Groups_Otimes__class_Otimes(U_2606,c_Power_Opower__class_Opower(U_2606,U_2607,U_2608)),c_Power_Opower__class_Opower(U_2606,U_2607,U_2608))
| ~ class_Rings_Ocomm__semiring__1(U_2606) ),
inference(variable_rename,[status(thm)],[f_903_1]) ).
cnf(f_903_3,plain,
( c_Power_Opower__class_Opower(U_2606,U_2607,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2608)) = hAPP(c_Groups_Otimes__class_Otimes(U_2606,c_Power_Opower__class_Opower(U_2606,U_2607,U_2608)),c_Power_Opower__class_Opower(U_2606,U_2607,U_2608))
| ~ class_Rings_Ocomm__semiring__1(U_2606) ),
inference(clausify,[status(thm)],[f_903_2]) ).
fof(f_904_1,plain,
! [V_n,V_a,T_a] :
( c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Power_Opower__class_Opower(T_a,V_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ring__1__class_Opower__minus__even]) ).
fof(f_904_2,plain,
! [U_2611,U_2610,U_2609] :
( c_Power_Opower__class_Opower(U_2609,c_Groups_Ouminus__class_Ouminus(U_2609,U_2610),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2611)) = c_Power_Opower__class_Opower(U_2609,U_2610,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2611))
| ~ class_Rings_Oring__1(U_2609) ),
inference(variable_rename,[status(thm)],[f_904_1]) ).
cnf(f_904_3,plain,
( c_Power_Opower__class_Opower(U_2609,c_Groups_Ouminus__class_Ouminus(U_2609,U_2610),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2611)) = c_Power_Opower__class_Opower(U_2609,U_2610,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2611))
| ~ class_Rings_Oring__1(U_2609) ),
inference(clausify,[status(thm)],[f_904_2]) ).
fof(f_905_1,plain,
! [V_y_2,V_x_2] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_y_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_realpow__two__sum__zero__iff]) ).
fof(f_905_2,plain,
! [U_2613,U_2612] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2612,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2613,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2613 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2612 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( U_2613 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_2612 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2612,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2613,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_905_1]) ).
fof(f_905_3,plain,
( ! [U_2617,U_2615] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2615,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2617,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2617 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2615 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_2616,U_2614] :
( ( U_2616 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_2614 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2614,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2616,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_905_2]) ).
cnf(f_905_4,plain,
( U_2614 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2614,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2616,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_905_3]) ).
cnf(f_905_5,plain,
( U_2616 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2614,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2616,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_905_3]) ).
cnf(f_905_6,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2615,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2617,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2617 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2615 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_905_3]) ).
fof(f_906_1,plain,
! [V_x] : hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(fof_nnf,[status(thm)],[fact_four__x__squared]) ).
fof(f_906_2,plain,
! [U_2618] : hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2618,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2618),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(variable_rename,[status(thm)],[f_906_1]) ).
cnf(f_906_3,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2618,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2618),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(clausify,[status(thm)],[f_906_2]) ).
fof(f_907_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),V_n)),
inference(fof_nnf,[status(thm)],[fact_two__realpow__ge__one]) ).
fof(f_907_2,plain,
! [U_2619] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),U_2619)),
inference(variable_rename,[status(thm)],[f_907_1]) ).
cnf(f_907_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),U_2619)),
inference(clausify,[status(thm)],[f_907_2]) ).
fof(f_908_1,plain,
! [V_x,V_u] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_u,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(fof_nnf,[status(thm)],[fact_realpow__square__minus__le]) ).
fof(f_908_2,plain,
! [U_2621,U_2620] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2620,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2621,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(variable_rename,[status(thm)],[f_908_1]) ).
cnf(f_908_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2620,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2621,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(clausify,[status(thm)],[f_908_2]) ).
fof(f_909_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__less__imp__less]) ).
fof(f_909_2,plain,
! [U_2624,U_2623,U_2622] :
( c_Orderings_Oord__class_Oless(U_2622,U_2623,U_2624)
| ~ c_Orderings_Oord__class_Oless__eq(U_2622,c_Groups_Ozero__class_Ozero(U_2622),U_2624)
| ~ c_Orderings_Oord__class_Oless(U_2622,c_Power_Opower__class_Opower(U_2622,U_2623,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2622,U_2624,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__semidom(U_2622) ),
inference(variable_rename,[status(thm)],[f_909_1]) ).
cnf(f_909_3,plain,
( c_Orderings_Oord__class_Oless(U_2622,U_2623,U_2624)
| ~ c_Orderings_Oord__class_Oless__eq(U_2622,c_Groups_Ozero__class_Ozero(U_2622),U_2624)
| ~ c_Orderings_Oord__class_Oless(U_2622,c_Power_Opower__class_Opower(U_2622,U_2623,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2622,U_2624,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__semidom(U_2622) ),
inference(clausify,[status(thm)],[f_909_2]) ).
fof(f_910_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__power2__ge__zero]) ).
fof(f_910_2,plain,
! [U_2627,U_2626,U_2625] :
( c_Orderings_Oord__class_Oless__eq(U_2625,c_Groups_Ozero__class_Ozero(U_2625),c_Groups_Oplus__class_Oplus(U_2625,c_Power_Opower__class_Opower(U_2625,U_2626,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2625,U_2627,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_2625) ),
inference(variable_rename,[status(thm)],[f_910_1]) ).
cnf(f_910_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2625,c_Groups_Ozero__class_Ozero(U_2625),c_Groups_Oplus__class_Oplus(U_2625,c_Power_Opower__class_Opower(U_2625,U_2626,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2625,U_2627,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_2625) ),
inference(clausify,[status(thm)],[f_910_2]) ).
fof(f_911_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))
| V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__power2__le__zero__iff]) ).
fof(f_911_2,plain,
! [U_2630,U_2629,U_2628] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2628,c_Groups_Oplus__class_Oplus(U_2628,c_Power_Opower__class_Opower(U_2628,U_2629,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2628,U_2630,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_2628))
| U_2630 != c_Groups_Ozero__class_Ozero(U_2628)
| U_2629 != c_Groups_Ozero__class_Ozero(U_2628) )
& ( ( U_2630 = c_Groups_Ozero__class_Ozero(U_2628)
& U_2629 = c_Groups_Ozero__class_Ozero(U_2628) )
| ~ c_Orderings_Oord__class_Oless__eq(U_2628,c_Groups_Oplus__class_Oplus(U_2628,c_Power_Opower__class_Opower(U_2628,U_2629,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2628,U_2630,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_2628)) ) )
| ~ class_Rings_Olinordered__idom(U_2628) ),
inference(variable_rename,[status(thm)],[f_911_1]) ).
cnf(f_911_3,plain,
( U_2629 = c_Groups_Ozero__class_Ozero(U_2628)
| ~ c_Orderings_Oord__class_Oless__eq(U_2628,c_Groups_Oplus__class_Oplus(U_2628,c_Power_Opower__class_Opower(U_2628,U_2629,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2628,U_2630,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_2628))
| ~ class_Rings_Olinordered__idom(U_2628) ),
inference(clausify,[status(thm)],[f_911_2]) ).
cnf(f_911_4,plain,
( U_2630 = c_Groups_Ozero__class_Ozero(U_2628)
| ~ c_Orderings_Oord__class_Oless__eq(U_2628,c_Groups_Oplus__class_Oplus(U_2628,c_Power_Opower__class_Opower(U_2628,U_2629,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2628,U_2630,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_2628))
| ~ class_Rings_Olinordered__idom(U_2628) ),
inference(clausify,[status(thm)],[f_911_2]) ).
cnf(f_911_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_2628,c_Groups_Oplus__class_Oplus(U_2628,c_Power_Opower__class_Opower(U_2628,U_2629,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2628,U_2630,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_2628))
| U_2630 != c_Groups_Ozero__class_Ozero(U_2628)
| U_2629 != c_Groups_Ozero__class_Ozero(U_2628)
| ~ class_Rings_Olinordered__idom(U_2628) ),
inference(clausify,[status(thm)],[f_911_2]) ).
fof(f_912_1,plain,
! [V_y,V_x,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__sum__power2__lt__zero]) ).
fof(f_912_2,plain,
! [U_2633,U_2632,U_2631] :
( ~ c_Orderings_Oord__class_Oless(U_2631,c_Groups_Oplus__class_Oplus(U_2631,c_Power_Opower__class_Opower(U_2631,U_2632,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2631,U_2633,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_2631))
| ~ class_Rings_Olinordered__idom(U_2631) ),
inference(variable_rename,[status(thm)],[f_912_1]) ).
cnf(f_912_3,plain,
( ~ c_Orderings_Oord__class_Oless(U_2631,c_Groups_Oplus__class_Oplus(U_2631,c_Power_Opower__class_Opower(U_2631,U_2632,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2631,U_2633,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_2631))
| ~ class_Rings_Olinordered__idom(U_2631) ),
inference(clausify,[status(thm)],[f_912_2]) ).
fof(f_913_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) )
& ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__power2__gt__zero__iff]) ).
fof(f_913_2,plain,
! [U_2636,U_2635,U_2634] :
( ( ( c_Orderings_Oord__class_Oless(U_2634,c_Groups_Ozero__class_Ozero(U_2634),c_Groups_Oplus__class_Oplus(U_2634,c_Power_Opower__class_Opower(U_2634,U_2635,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2634,U_2636,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ( U_2636 = c_Groups_Ozero__class_Ozero(U_2634)
& U_2635 = c_Groups_Ozero__class_Ozero(U_2634) ) )
& ( U_2636 != c_Groups_Ozero__class_Ozero(U_2634)
| U_2635 != c_Groups_Ozero__class_Ozero(U_2634)
| ~ c_Orderings_Oord__class_Oless(U_2634,c_Groups_Ozero__class_Ozero(U_2634),c_Groups_Oplus__class_Oplus(U_2634,c_Power_Opower__class_Opower(U_2634,U_2635,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2634,U_2636,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
| ~ class_Rings_Olinordered__idom(U_2634) ),
inference(variable_rename,[status(thm)],[f_913_1]) ).
cnf(f_913_3,plain,
( U_2636 != c_Groups_Ozero__class_Ozero(U_2634)
| U_2635 != c_Groups_Ozero__class_Ozero(U_2634)
| ~ c_Orderings_Oord__class_Oless(U_2634,c_Groups_Ozero__class_Ozero(U_2634),c_Groups_Oplus__class_Oplus(U_2634,c_Power_Opower__class_Opower(U_2634,U_2635,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2634,U_2636,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_2634) ),
inference(clausify,[status(thm)],[f_913_2]) ).
cnf(f_913_4,plain,
( U_2635 = c_Groups_Ozero__class_Ozero(U_2634)
| c_Orderings_Oord__class_Oless(U_2634,c_Groups_Ozero__class_Ozero(U_2634),c_Groups_Oplus__class_Oplus(U_2634,c_Power_Opower__class_Opower(U_2634,U_2635,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2634,U_2636,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_2634) ),
inference(clausify,[status(thm)],[f_913_2]) ).
cnf(f_913_5,plain,
( U_2636 = c_Groups_Ozero__class_Ozero(U_2634)
| c_Orderings_Oord__class_Oless(U_2634,c_Groups_Ozero__class_Ozero(U_2634),c_Groups_Oplus__class_Oplus(U_2634,c_Power_Opower__class_Opower(U_2634,U_2635,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2634,U_2636,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_2634) ),
inference(clausify,[status(thm)],[f_913_2]) ).
fof(f_914_1,plain,
! [V_y,V_x,T_a] :
( c_Power_Opower__class_Opower(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Power_Opower__class_Opower(T_a,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(T_a,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__sum]) ).
fof(f_914_2,plain,
! [U_2639,U_2638,U_2637] :
( c_Power_Opower__class_Opower(U_2637,c_Groups_Oplus__class_Oplus(U_2637,U_2638,U_2639),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(U_2637,c_Groups_Oplus__class_Oplus(U_2637,c_Power_Opower__class_Opower(U_2637,U_2638,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2637,U_2639,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(c_Groups_Otimes__class_Otimes(U_2637,hAPP(c_Groups_Otimes__class_Otimes(U_2637,c_Int_Onumber__class_Onumber__of(U_2637,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2638)),U_2639))
| ~ class_Int_Onumber__ring(U_2637) ),
inference(variable_rename,[status(thm)],[f_914_1]) ).
cnf(f_914_3,plain,
( c_Power_Opower__class_Opower(U_2637,c_Groups_Oplus__class_Oplus(U_2637,U_2638,U_2639),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(U_2637,c_Groups_Oplus__class_Oplus(U_2637,c_Power_Opower__class_Opower(U_2637,U_2638,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(U_2637,U_2639,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(c_Groups_Otimes__class_Otimes(U_2637,hAPP(c_Groups_Otimes__class_Otimes(U_2637,c_Int_Onumber__class_Onumber__of(U_2637,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2638)),U_2639))
| ~ class_Int_Onumber__ring(U_2637) ),
inference(clausify,[status(thm)],[f_914_2]) ).
fof(f_915_1,plain,
! [V_k,V_a,T_a] :
( V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_k)),c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_even__power__le__0__imp__0]) ).
fof(f_915_2,plain,
! [U_2642,U_2641,U_2640] :
( U_2641 = c_Groups_Ozero__class_Ozero(U_2640)
| ~ c_Orderings_Oord__class_Oless__eq(U_2640,c_Power_Opower__class_Opower(U_2640,U_2641,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2642)),c_Groups_Ozero__class_Ozero(U_2640))
| ~ class_Rings_Olinordered__idom(U_2640) ),
inference(variable_rename,[status(thm)],[f_915_1]) ).
cnf(f_915_3,plain,
( U_2641 = c_Groups_Ozero__class_Ozero(U_2640)
| ~ c_Orderings_Oord__class_Oless__eq(U_2640,c_Power_Opower__class_Opower(U_2640,U_2641,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2642)),c_Groups_Ozero__class_Ozero(U_2640))
| ~ class_Rings_Olinordered__idom(U_2640) ),
inference(clausify,[status(thm)],[f_915_2]) ).
fof(f_916_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__even__power_H]) ).
fof(f_916_2,plain,
! [U_2645,U_2644,U_2643] :
( c_Orderings_Oord__class_Oless__eq(U_2643,c_Groups_Ozero__class_Ozero(U_2643),c_Power_Opower__class_Opower(U_2643,U_2644,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2645)))
| ~ class_Rings_Olinordered__idom(U_2643) ),
inference(variable_rename,[status(thm)],[f_916_1]) ).
cnf(f_916_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2643,c_Groups_Ozero__class_Ozero(U_2643),c_Power_Opower__class_Opower(U_2643,U_2644,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2645)))
| ~ class_Rings_Olinordered__idom(U_2643) ),
inference(clausify,[status(thm)],[f_916_2]) ).
fof(f_917_1,plain,
! [V_n,T_a] :
( c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a)
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__minus1__even]) ).
fof(f_917_2,plain,
! [U_2647,U_2646] :
( c_Power_Opower__class_Opower(U_2646,c_Groups_Ouminus__class_Ouminus(U_2646,c_Groups_Oone__class_Oone(U_2646)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2647)) = c_Groups_Oone__class_Oone(U_2646)
| ~ class_Rings_Oring__1(U_2646) ),
inference(variable_rename,[status(thm)],[f_917_1]) ).
cnf(f_917_3,plain,
( c_Power_Opower__class_Opower(U_2646,c_Groups_Ouminus__class_Ouminus(U_2646,c_Groups_Oone__class_Oone(U_2646)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2647)) = c_Groups_Oone__class_Oone(U_2646)
| ~ class_Rings_Oring__1(U_2646) ),
inference(clausify,[status(thm)],[f_917_2]) ).
fof(f_918_1,plain,
! [V_x,V_y] :
( hAPP(c_NthRoot_Osqrt,V_x) = V_y
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != V_x ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__unique]) ).
fof(f_918_2,plain,
! [U_2649,U_2648] :
( hAPP(c_NthRoot_Osqrt,U_2649) = U_2648
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2648)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2648,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != U_2649 ),
inference(variable_rename,[status(thm)],[f_918_1]) ).
cnf(f_918_3,plain,
( hAPP(c_NthRoot_Osqrt,U_2649) = U_2648
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2648)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2648,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != U_2649 ),
inference(clausify,[status(thm)],[f_918_2]) ).
fof(f_919_1,plain,
! [V_x] :
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_x
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__pow2]) ).
fof(f_919_2,plain,
! [U_2650] :
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2650),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_2650
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2650) ),
inference(variable_rename,[status(thm)],[f_919_1]) ).
cnf(f_919_3,plain,
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2650),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_2650
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2650) ),
inference(clausify,[status(thm)],[f_919_2]) ).
fof(f_920_1,plain,
! [V_x_2] :
( ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_x_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != V_x_2 ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__pow2__iff]) ).
fof(f_920_2,plain,
! [U_2651] :
( ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2651),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_2651
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2651) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2651)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2651),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != U_2651 ) ),
inference(variable_rename,[status(thm)],[f_920_1]) ).
fof(f_920_3,plain,
( ! [U_2653] :
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2653),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_2653
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2653) )
& ! [U_2652] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2652)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2652),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != U_2652 ) ),
inference(miniscope,[status(thm)],[f_920_2]) ).
cnf(f_920_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2652)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2652),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != U_2652 ),
inference(clausify,[status(thm)],[f_920_3]) ).
cnf(f_920_5,plain,
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2653),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_2653
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2653) ),
inference(clausify,[status(thm)],[f_920_3]) ).
fof(f_921_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__pow2__gt__zero]) ).
fof(f_921_2,plain,
! [U_2654] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2654),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2654) ),
inference(variable_rename,[status(thm)],[f_921_1]) ).
cnf(f_921_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2654),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2654) ),
inference(clausify,[status(thm)],[f_921_2]) ).
fof(f_922_1,plain,
! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__sum__squares__ge1]) ).
fof(f_922_2,plain,
! [U_2656,U_2655] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2655,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2655,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2656,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(variable_rename,[status(thm)],[f_922_1]) ).
cnf(f_922_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2655,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2655,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2656,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(clausify,[status(thm)],[f_922_2]) ).
fof(f_923_1,plain,
! [V_x,V_y] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__sum__squares__ge2]) ).
fof(f_923_2,plain,
! [U_2658,U_2657] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2657,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2658,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2657,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(variable_rename,[status(thm)],[f_923_1]) ).
cnf(f_923_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2657,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2658,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2657,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(clausify,[status(thm)],[f_923_2]) ).
fof(f_924_1,plain,
! [V_d,V_b,V_c,V_a] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_c),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_b,V_d),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_a,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_b,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_c,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_d,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__sum__squares__triangle__ineq]) ).
fof(f_924_2,plain,
! [U_2662,U_2661,U_2660,U_2659] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2659,U_2660),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2661,U_2662),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2659,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2661,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2660,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2662,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(variable_rename,[status(thm)],[f_924_1]) ).
cnf(f_924_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2659,U_2660),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2661,U_2662),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2659,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2661,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2660,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2662,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(clausify,[status(thm)],[f_924_2]) ).
fof(f_925_1,plain,
! [V_y,V_x] :
( V_y = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != V_x ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__sum__squares__eq__cancel]) ).
fof(f_925_2,plain,
! [U_2664,U_2663] :
( U_2664 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2663,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2664,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != U_2663 ),
inference(variable_rename,[status(thm)],[f_925_1]) ).
fof(f_925_3,plain,
! [U_2664] :
( ! [U_2663] : hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2663,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2664,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != U_2663
| U_2664 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(miniscope,[status(thm)],[f_925_2]) ).
cnf(f_925_4,plain,
( hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2663,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2664,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != U_2663
| U_2664 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_925_3]) ).
fof(f_926_1,plain,
! [V_y,V_x] :
( V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != V_y ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__sum__squares__eq__cancel2]) ).
fof(f_926_2,plain,
! [U_2666,U_2665] :
( U_2665 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2665,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2666,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != U_2666 ),
inference(variable_rename,[status(thm)],[f_926_1]) ).
cnf(f_926_3,plain,
( U_2665 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2665,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2666,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != U_2666 ),
inference(clausify,[status(thm)],[f_926_2]) ).
fof(f_927_1,plain,
! [V_ya,V_xa,V_y,V_x] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_xa,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_ya,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_xa,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_ya,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__sum__squares__mult__squared__eq]) ).
fof(f_927_2,plain,
! [U_2670,U_2669,U_2668,U_2667] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2667,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2668,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2669,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2670,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2667,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2668,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2669,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2670,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
inference(variable_rename,[status(thm)],[f_927_1]) ).
cnf(f_927_3,plain,
c_Power_Opower__class_Opower(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2667,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2668,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2669,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2670,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2667,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2668,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2669,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2670,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
inference(clausify,[status(thm)],[f_927_2]) ).
fof(f_928_1,plain,
! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__sum__squares__ge__zero]) ).
fof(f_928_2,plain,
! [U_2672,U_2671] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2671,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2672,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(variable_rename,[status(thm)],[f_928_1]) ).
cnf(f_928_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2671,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2672,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(clausify,[status(thm)],[f_928_2]) ).
fof(f_929_1,plain,
! [V_x] :
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,V_x)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,V_x)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
inference(fof_nnf,[status(thm)],[fact_real__inv__sqrt__pow2]) ).
fof(f_929_2,plain,
! [U_2673] :
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2673)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,U_2673)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2673) ),
inference(variable_rename,[status(thm)],[f_929_1]) ).
cnf(f_929_3,plain,
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,U_2673)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,U_2673)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2673) ),
inference(clausify,[status(thm)],[f_929_2]) ).
fof(f_930_1,plain,
! [V_y,V_x] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)),
inference(fof_nnf,[status(thm)],[fact_real__sum__squared__expand]) ).
fof(f_930_2,plain,
! [U_2675,U_2674] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2674,U_2675),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2674,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2675,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2674)),U_2675)),
inference(variable_rename,[status(thm)],[f_930_1]) ).
cnf(f_930_3,plain,
c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2674,U_2675),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2674,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2675,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2674)),U_2675)),
inference(clausify,[status(thm)],[f_930_2]) ).
fof(f_931_1,plain,
! [V_n,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__strict__mono]) ).
fof(f_931_2,plain,
! [U_2679,U_2678,U_2677,U_2676] :
( c_Orderings_Oord__class_Oless(U_2676,c_Power_Opower__class_Opower(U_2676,U_2677,U_2679),c_Power_Opower__class_Opower(U_2676,U_2678,U_2679))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2679)
| ~ c_Orderings_Oord__class_Oless__eq(U_2676,c_Groups_Ozero__class_Ozero(U_2676),U_2677)
| ~ c_Orderings_Oord__class_Oless(U_2676,U_2677,U_2678)
| ~ class_Rings_Olinordered__semidom(U_2676) ),
inference(variable_rename,[status(thm)],[f_931_1]) ).
cnf(f_931_3,plain,
( c_Orderings_Oord__class_Oless(U_2676,c_Power_Opower__class_Opower(U_2676,U_2677,U_2679),c_Power_Opower__class_Opower(U_2676,U_2678,U_2679))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2679)
| ~ c_Orderings_Oord__class_Oless__eq(U_2676,c_Groups_Ozero__class_Ozero(U_2676),U_2677)
| ~ c_Orderings_Oord__class_Oless(U_2676,U_2677,U_2678)
| ~ class_Rings_Olinordered__semidom(U_2676) ),
inference(clausify,[status(thm)],[f_931_2]) ).
fof(f_932_1,plain,
! [V_n,V_m,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,V_i,V_m),c_Power_Opower__class_Opower(tc_Nat_Onat,V_i,V_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i) ),
inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less]) ).
fof(f_932_2,plain,
! [U_2682,U_2681,U_2680] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2681,U_2682)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,U_2680,U_2681),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2680,U_2682))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2680) ),
inference(variable_rename,[status(thm)],[f_932_1]) ).
cnf(f_932_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2681,U_2682)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,U_2680,U_2681),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2680,U_2682))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2680) ),
inference(clausify,[status(thm)],[f_932_2]) ).
fof(f_933_1,plain,
! [V_n_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,V_n_2))
| ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff]) ).
fof(f_933_2,plain,
! [U_2684,U_2683] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2683,U_2684))
| ( U_2684 != 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_2683) ) )
& ( U_2684 = 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_2683)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2683,U_2684)) ) ),
inference(variable_rename,[status(thm)],[f_933_1]) ).
fof(f_933_3,plain,
( ! [U_2688,U_2686] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2686,U_2688))
| ( U_2688 != 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_2686) ) )
& ! [U_2687,U_2685] :
( U_2687 = 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_2685)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2685,U_2687)) ) ),
inference(miniscope,[status(thm)],[f_933_2]) ).
cnf(f_933_4,plain,
( U_2687 = 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_2685)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2685,U_2687)) ),
inference(clausify,[status(thm)],[f_933_3]) ).
cnf(f_933_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2686)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2686,U_2688)) ),
inference(clausify,[status(thm)],[f_933_3]) ).
cnf(f_933_6,plain,
( U_2688 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2686,U_2688)) ),
inference(clausify,[status(thm)],[f_933_3]) ).
fof(f_934_1,plain,
! [V_n,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) ),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J]) ).
fof(f_934_2,plain,
! [U_2690,U_2689] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,U_2689,U_2690))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2689) ),
inference(variable_rename,[status(thm)],[f_934_1]) ).
cnf(f_934_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,U_2689,U_2690))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2689) ),
inference(clausify,[status(thm)],[f_934_2]) ).
fof(f_935_1,plain,
! [V_z,V_y,V_x] : c_Power_Opower__class_Opower(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_y)),c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_z)),
inference(fof_nnf,[status(thm)],[fact_zpower__zadd__distrib]) ).
fof(f_935_2,plain,
! [U_2693,U_2692,U_2691] : c_Power_Opower__class_Opower(tc_Int_Oint,U_2691,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2692,U_2693)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,U_2691,U_2692)),c_Power_Opower__class_Opower(tc_Int_Oint,U_2691,U_2693)),
inference(variable_rename,[status(thm)],[f_935_1]) ).
cnf(f_935_3,plain,
c_Power_Opower__class_Opower(tc_Int_Oint,U_2691,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2692,U_2693)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,U_2691,U_2692)),c_Power_Opower__class_Opower(tc_Int_Oint,U_2691,U_2693)),
inference(clausify,[status(thm)],[f_935_2]) ).
fof(f_936_1,plain,
! [V_z,V_y,V_x] : c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,V_x,V_y),V_z) = c_Power_Opower__class_Opower(tc_Int_Oint,V_x,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_y),V_z)),
inference(fof_nnf,[status(thm)],[fact_zpower__zpower]) ).
fof(f_936_2,plain,
! [U_2696,U_2695,U_2694] : c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,U_2694,U_2695),U_2696) = c_Power_Opower__class_Opower(tc_Int_Oint,U_2694,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2695),U_2696)),
inference(variable_rename,[status(thm)],[f_936_1]) ).
cnf(f_936_3,plain,
c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,U_2694,U_2695),U_2696) = c_Power_Opower__class_Opower(tc_Int_Oint,U_2694,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2695),U_2696)),
inference(clausify,[status(thm)],[f_936_2]) ).
fof(f_937_1,plain,
! [V_n_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,V_n_2))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
& V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__power__nat__eq]) ).
fof(f_937_2,plain,
! [U_2698,U_2697] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2697,U_2698))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2697)
& U_2698 != 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_2697)
| U_2698 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2697,U_2698)) ) ),
inference(variable_rename,[status(thm)],[f_937_1]) ).
fof(f_937_3,plain,
( ! [U_2702,U_2700] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2700,U_2702))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2700)
& U_2702 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_2701,U_2699] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2699)
| U_2701 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2699,U_2701)) ) ),
inference(miniscope,[status(thm)],[f_937_2]) ).
cnf(f_937_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2699)
| U_2701 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2699,U_2701)) ),
inference(clausify,[status(thm)],[f_937_3]) ).
cnf(f_937_5,plain,
( U_2702 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2700,U_2702)) ),
inference(clausify,[status(thm)],[f_937_3]) ).
cnf(f_937_6,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2700)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2700,U_2702)) ),
inference(clausify,[status(thm)],[f_937_3]) ).
fof(f_938_1,plain,
! [V_wa_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2)))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
& c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_wa_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__power__nat__eq__number__of]) ).
fof(f_938_2,plain,
! [U_2704,U_2703] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2703,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2704)))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2703)
& c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2704) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2703)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2704) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2703,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2704))) ) ),
inference(variable_rename,[status(thm)],[f_938_1]) ).
fof(f_938_3,plain,
( ! [U_2708,U_2706] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2706,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2708)))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2706)
& c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2708) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_2707,U_2705] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2705)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2707) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2705,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2707))) ) ),
inference(miniscope,[status(thm)],[f_938_2]) ).
cnf(f_938_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2705)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2707) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2705,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2707))) ),
inference(clausify,[status(thm)],[f_938_3]) ).
cnf(f_938_5,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2708) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2706,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2708))) ),
inference(clausify,[status(thm)],[f_938_3]) ).
cnf(f_938_6,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2706)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,U_2706,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2708))) ),
inference(clausify,[status(thm)],[f_938_3]) ).
fof(f_939_1,plain,
! [V_n,V_a,T_a] :
( c_Power_Opower__class_Opower(T_a,V_a,V_n) != c_Groups_Ozero__class_Ozero(T_a)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
inference(fof_nnf,[status(thm)],[fact_field__power__not__zero]) ).
fof(f_939_2,plain,
! [U_2711,U_2710,U_2709] :
( c_Power_Opower__class_Opower(U_2709,U_2710,U_2711) != c_Groups_Ozero__class_Ozero(U_2709)
| U_2710 = c_Groups_Ozero__class_Ozero(U_2709)
| ~ class_Rings_Oring__1__no__zero__divisors(U_2709) ),
inference(variable_rename,[status(thm)],[f_939_1]) ).
cnf(f_939_3,plain,
( c_Power_Opower__class_Opower(U_2709,U_2710,U_2711) != c_Groups_Ozero__class_Ozero(U_2709)
| U_2710 = c_Groups_Ozero__class_Ozero(U_2709)
| ~ class_Rings_Oring__1__no__zero__divisors(U_2709) ),
inference(clausify,[status(thm)],[f_939_2]) ).
fof(f_940_1,plain,
! [V_n,V_b,V_a,T_a] :
( c_Power_Opower__class_Opower(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b),V_n) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)),c_Power_Opower__class_Opower(T_a,V_b,V_n))
| ~ class_Groups_Ocomm__monoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__mult__distrib]) ).
fof(f_940_2,plain,
! [U_2715,U_2714,U_2713,U_2712] :
( c_Power_Opower__class_Opower(U_2712,hAPP(c_Groups_Otimes__class_Otimes(U_2712,U_2713),U_2714),U_2715) = hAPP(c_Groups_Otimes__class_Otimes(U_2712,c_Power_Opower__class_Opower(U_2712,U_2713,U_2715)),c_Power_Opower__class_Opower(U_2712,U_2714,U_2715))
| ~ class_Groups_Ocomm__monoid__mult(U_2712) ),
inference(variable_rename,[status(thm)],[f_940_1]) ).
cnf(f_940_3,plain,
( c_Power_Opower__class_Opower(U_2712,hAPP(c_Groups_Otimes__class_Otimes(U_2712,U_2713),U_2714),U_2715) = hAPP(c_Groups_Otimes__class_Otimes(U_2712,c_Power_Opower__class_Opower(U_2712,U_2713,U_2715)),c_Power_Opower__class_Opower(U_2712,U_2714,U_2715))
| ~ class_Groups_Ocomm__monoid__mult(U_2712) ),
inference(clausify,[status(thm)],[f_940_2]) ).
fof(f_941_1,plain,
! [V_n,V_a,T_a] :
( hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)),V_a) = hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),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_941_2,plain,
! [U_2718,U_2717,U_2716] :
( hAPP(c_Groups_Otimes__class_Otimes(U_2716,c_Power_Opower__class_Opower(U_2716,U_2717,U_2718)),U_2717) = hAPP(c_Groups_Otimes__class_Otimes(U_2716,U_2717),c_Power_Opower__class_Opower(U_2716,U_2717,U_2718))
| ~ class_Groups_Omonoid__mult(U_2716) ),
inference(variable_rename,[status(thm)],[f_941_1]) ).
cnf(f_941_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_2716,c_Power_Opower__class_Opower(U_2716,U_2717,U_2718)),U_2717) = hAPP(c_Groups_Otimes__class_Otimes(U_2716,U_2717),c_Power_Opower__class_Opower(U_2716,U_2717,U_2718))
| ~ class_Groups_Omonoid__mult(U_2716) ),
inference(clausify,[status(thm)],[f_941_2]) ).
fof(f_942_1,plain,
! [V_n,T_a] :
( c_Power_Opower__class_Opower(T_a,c_Groups_Oone__class_Oone(T_a),V_n) = c_Groups_Oone__class_Oone(T_a)
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__one]) ).
fof(f_942_2,plain,
! [U_2720,U_2719] :
( c_Power_Opower__class_Opower(U_2719,c_Groups_Oone__class_Oone(U_2719),U_2720) = c_Groups_Oone__class_Oone(U_2719)
| ~ class_Groups_Omonoid__mult(U_2719) ),
inference(variable_rename,[status(thm)],[f_942_1]) ).
cnf(f_942_3,plain,
( c_Power_Opower__class_Opower(U_2719,c_Groups_Oone__class_Oone(U_2719),U_2720) = c_Groups_Oone__class_Oone(U_2719)
| ~ class_Groups_Omonoid__mult(U_2719) ),
inference(clausify,[status(thm)],[f_942_2]) ).
fof(f_943_1,plain,
! [V_n,V_b,V_a,T_a] :
( c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b),V_n) = c_Rings_Oinverse__class_Odivide(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n))
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__divide]) ).
fof(f_943_2,plain,
! [U_2724,U_2723,U_2722,U_2721] :
( c_Power_Opower__class_Opower(U_2721,c_Rings_Oinverse__class_Odivide(U_2721,U_2722,U_2723),U_2724) = c_Rings_Oinverse__class_Odivide(U_2721,c_Power_Opower__class_Opower(U_2721,U_2722,U_2724),c_Power_Opower__class_Opower(U_2721,U_2723,U_2724))
| ~ class_Fields_Ofield__inverse__zero(U_2721) ),
inference(variable_rename,[status(thm)],[f_943_1]) ).
cnf(f_943_3,plain,
( c_Power_Opower__class_Opower(U_2721,c_Rings_Oinverse__class_Odivide(U_2721,U_2722,U_2723),U_2724) = c_Rings_Oinverse__class_Odivide(U_2721,c_Power_Opower__class_Opower(U_2721,U_2722,U_2724),c_Power_Opower__class_Opower(U_2721,U_2723,U_2724))
| ~ class_Fields_Ofield__inverse__zero(U_2721) ),
inference(clausify,[status(thm)],[f_943_2]) ).
fof(f_944_1,plain,
! [V_n,V_m,V_a,T_a] :
( c_Power_Opower__class_Opower(T_a,V_a,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m),V_n)) = c_Power_Opower__class_Opower(T_a,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_944_2,plain,
! [U_2728,U_2727,U_2726,U_2725] :
( c_Power_Opower__class_Opower(U_2725,U_2726,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2727),U_2728)) = c_Power_Opower__class_Opower(U_2725,c_Power_Opower__class_Opower(U_2725,U_2726,U_2727),U_2728)
| ~ class_Groups_Omonoid__mult(U_2725) ),
inference(variable_rename,[status(thm)],[f_944_1]) ).
cnf(f_944_3,plain,
( c_Power_Opower__class_Opower(U_2725,U_2726,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,U_2727),U_2728)) = c_Power_Opower__class_Opower(U_2725,c_Power_Opower__class_Opower(U_2725,U_2726,U_2727),U_2728)
| ~ class_Groups_Omonoid__mult(U_2725) ),
inference(clausify,[status(thm)],[f_944_2]) ).
fof(f_945_1,plain,
! [V_n,V_a,T_a] :
( c_Rings_Oinverse__class_Oinverse(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)) = c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_n)
| ~ class_Rings_Odivision__ring__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__inverse]) ).
fof(f_945_2,plain,
! [U_2731,U_2730,U_2729] :
( c_Rings_Oinverse__class_Oinverse(U_2729,c_Power_Opower__class_Opower(U_2729,U_2730,U_2731)) = c_Power_Opower__class_Opower(U_2729,c_Rings_Oinverse__class_Oinverse(U_2729,U_2730),U_2731)
| ~ class_Rings_Odivision__ring__inverse__zero(U_2729) ),
inference(variable_rename,[status(thm)],[f_945_1]) ).
cnf(f_945_3,plain,
( c_Rings_Oinverse__class_Oinverse(U_2729,c_Power_Opower__class_Opower(U_2729,U_2730,U_2731)) = c_Power_Opower__class_Opower(U_2729,c_Rings_Oinverse__class_Oinverse(U_2729,U_2730),U_2731)
| ~ class_Rings_Odivision__ring__inverse__zero(U_2729) ),
inference(clausify,[status(thm)],[f_945_2]) ).
fof(f_946_1,plain,
! [V_a,T_a] :
( c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__one__right]) ).
fof(f_946_2,plain,
! [U_2733,U_2732] :
( c_Power_Opower__class_Opower(U_2732,U_2733,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2733
| ~ class_Groups_Omonoid__mult(U_2732) ),
inference(variable_rename,[status(thm)],[f_946_1]) ).
cnf(f_946_3,plain,
( c_Power_Opower__class_Opower(U_2732,U_2733,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2733
| ~ class_Groups_Omonoid__mult(U_2732) ),
inference(clausify,[status(thm)],[f_946_2]) ).
fof(f_947_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__power]) ).
fof(f_947_2,plain,
! [U_2736,U_2735,U_2734] :
( c_Orderings_Oord__class_Oless__eq(U_2734,c_Groups_Ozero__class_Ozero(U_2734),c_Power_Opower__class_Opower(U_2734,U_2735,U_2736))
| ~ c_Orderings_Oord__class_Oless__eq(U_2734,c_Groups_Ozero__class_Ozero(U_2734),U_2735)
| ~ class_Rings_Olinordered__semidom(U_2734) ),
inference(variable_rename,[status(thm)],[f_947_1]) ).
cnf(f_947_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2734,c_Groups_Ozero__class_Ozero(U_2734),c_Power_Opower__class_Opower(U_2734,U_2735,U_2736))
| ~ c_Orderings_Oord__class_Oless__eq(U_2734,c_Groups_Ozero__class_Ozero(U_2734),U_2735)
| ~ class_Rings_Olinordered__semidom(U_2734) ),
inference(clausify,[status(thm)],[f_947_2]) ).
fof(f_948_1,plain,
! [V_n,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__mono]) ).
fof(f_948_2,plain,
! [U_2740,U_2739,U_2738,U_2737] :
( c_Orderings_Oord__class_Oless__eq(U_2737,c_Power_Opower__class_Opower(U_2737,U_2738,U_2740),c_Power_Opower__class_Opower(U_2737,U_2739,U_2740))
| ~ c_Orderings_Oord__class_Oless__eq(U_2737,c_Groups_Ozero__class_Ozero(U_2737),U_2738)
| ~ c_Orderings_Oord__class_Oless__eq(U_2737,U_2738,U_2739)
| ~ class_Rings_Olinordered__semidom(U_2737) ),
inference(variable_rename,[status(thm)],[f_948_1]) ).
cnf(f_948_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2737,c_Power_Opower__class_Opower(U_2737,U_2738,U_2740),c_Power_Opower__class_Opower(U_2737,U_2739,U_2740))
| ~ c_Orderings_Oord__class_Oless__eq(U_2737,c_Groups_Ozero__class_Ozero(U_2737),U_2738)
| ~ c_Orderings_Oord__class_Oless__eq(U_2737,U_2738,U_2739)
| ~ class_Rings_Olinordered__semidom(U_2737) ),
inference(clausify,[status(thm)],[f_948_2]) ).
fof(f_949_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__power]) ).
fof(f_949_2,plain,
! [U_2743,U_2742,U_2741] :
( c_Orderings_Oord__class_Oless(U_2741,c_Groups_Ozero__class_Ozero(U_2741),c_Power_Opower__class_Opower(U_2741,U_2742,U_2743))
| ~ c_Orderings_Oord__class_Oless(U_2741,c_Groups_Ozero__class_Ozero(U_2741),U_2742)
| ~ class_Rings_Olinordered__semidom(U_2741) ),
inference(variable_rename,[status(thm)],[f_949_1]) ).
cnf(f_949_3,plain,
( c_Orderings_Oord__class_Oless(U_2741,c_Groups_Ozero__class_Ozero(U_2741),c_Power_Opower__class_Opower(U_2741,U_2742,U_2743))
| ~ c_Orderings_Oord__class_Oless(U_2741,c_Groups_Ozero__class_Ozero(U_2741),U_2742)
| ~ class_Rings_Olinordered__semidom(U_2741) ),
inference(clausify,[status(thm)],[f_949_2]) ).
fof(f_950_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__le__power]) ).
fof(f_950_2,plain,
! [U_2746,U_2745,U_2744] :
( c_Orderings_Oord__class_Oless__eq(U_2744,c_Groups_Oone__class_Oone(U_2744),c_Power_Opower__class_Opower(U_2744,U_2745,U_2746))
| ~ c_Orderings_Oord__class_Oless__eq(U_2744,c_Groups_Oone__class_Oone(U_2744),U_2745)
| ~ class_Rings_Olinordered__semidom(U_2744) ),
inference(variable_rename,[status(thm)],[f_950_1]) ).
cnf(f_950_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2744,c_Groups_Oone__class_Oone(U_2744),c_Power_Opower__class_Opower(U_2744,U_2745,U_2746))
| ~ c_Orderings_Oord__class_Oless__eq(U_2744,c_Groups_Oone__class_Oone(U_2744),U_2745)
| ~ class_Rings_Olinordered__semidom(U_2744) ),
inference(clausify,[status(thm)],[f_950_2]) ).
fof(f_951_1,plain,
! [V_n_2,V_a_2,T_a] :
( ( ( c_Power_Opower__class_Opower(T_a,V_a_2,V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
| c_Power_Opower__class_Opower(T_a,V_a_2,V_n_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Ozero__neq__one(T_a)
| ~ class_Rings_Ono__zero__divisors(T_a)
| ~ class_Rings_Omult__zero(T_a)
| ~ class_Power_Opower(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff]) ).
fof(f_951_2,plain,
! [U_2749,U_2748,U_2747] :
( ( ( c_Power_Opower__class_Opower(U_2747,U_2748,U_2749) = c_Groups_Ozero__class_Ozero(U_2747)
| U_2749 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2748 != c_Groups_Ozero__class_Ozero(U_2747) )
& ( ( U_2749 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2748 = c_Groups_Ozero__class_Ozero(U_2747) )
| c_Power_Opower__class_Opower(U_2747,U_2748,U_2749) != c_Groups_Ozero__class_Ozero(U_2747) ) )
| ~ class_Rings_Ozero__neq__one(U_2747)
| ~ class_Rings_Ono__zero__divisors(U_2747)
| ~ class_Rings_Omult__zero(U_2747)
| ~ class_Power_Opower(U_2747) ),
inference(variable_rename,[status(thm)],[f_951_1]) ).
cnf(f_951_3,plain,
( U_2748 = c_Groups_Ozero__class_Ozero(U_2747)
| c_Power_Opower__class_Opower(U_2747,U_2748,U_2749) != c_Groups_Ozero__class_Ozero(U_2747)
| ~ class_Rings_Ozero__neq__one(U_2747)
| ~ class_Rings_Ono__zero__divisors(U_2747)
| ~ class_Rings_Omult__zero(U_2747)
| ~ class_Power_Opower(U_2747) ),
inference(clausify,[status(thm)],[f_951_2]) ).
cnf(f_951_4,plain,
( U_2749 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(U_2747,U_2748,U_2749) != c_Groups_Ozero__class_Ozero(U_2747)
| ~ class_Rings_Ozero__neq__one(U_2747)
| ~ class_Rings_Ono__zero__divisors(U_2747)
| ~ class_Rings_Omult__zero(U_2747)
| ~ class_Power_Opower(U_2747) ),
inference(clausify,[status(thm)],[f_951_2]) ).
cnf(f_951_5,plain,
( c_Power_Opower__class_Opower(U_2747,U_2748,U_2749) = c_Groups_Ozero__class_Ozero(U_2747)
| U_2749 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2748 != c_Groups_Ozero__class_Ozero(U_2747)
| ~ class_Rings_Ozero__neq__one(U_2747)
| ~ class_Rings_Ono__zero__divisors(U_2747)
| ~ class_Rings_Omult__zero(U_2747)
| ~ class_Power_Opower(U_2747) ),
inference(clausify,[status(thm)],[f_951_2]) ).
fof(f_952_1,plain,
! [V_n_2,V_ma_2,V_a_2,T_a] :
( ( ( c_Power_Opower__class_Opower(T_a,V_a_2,V_ma_2) = 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
| c_Power_Opower__class_Opower(T_a,V_a_2,V_ma_2) != c_Power_Opower__class_Opower(T_a,V_a_2,V_n_2) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__inject__exp]) ).
fof(f_952_2,plain,
! [U_2753,U_2752,U_2751,U_2750] :
( ( ( c_Power_Opower__class_Opower(U_2750,U_2751,U_2752) = c_Power_Opower__class_Opower(U_2750,U_2751,U_2753)
| U_2752 != U_2753 )
& ( U_2752 = U_2753
| c_Power_Opower__class_Opower(U_2750,U_2751,U_2752) != c_Power_Opower__class_Opower(U_2750,U_2751,U_2753) ) )
| ~ c_Orderings_Oord__class_Oless(U_2750,c_Groups_Oone__class_Oone(U_2750),U_2751)
| ~ class_Rings_Olinordered__semidom(U_2750) ),
inference(variable_rename,[status(thm)],[f_952_1]) ).
cnf(f_952_3,plain,
( U_2752 = U_2753
| c_Power_Opower__class_Opower(U_2750,U_2751,U_2752) != c_Power_Opower__class_Opower(U_2750,U_2751,U_2753)
| ~ c_Orderings_Oord__class_Oless(U_2750,c_Groups_Oone__class_Oone(U_2750),U_2751)
| ~ class_Rings_Olinordered__semidom(U_2750) ),
inference(clausify,[status(thm)],[f_952_2]) ).
cnf(f_952_4,plain,
( c_Power_Opower__class_Opower(U_2750,U_2751,U_2752) = c_Power_Opower__class_Opower(U_2750,U_2751,U_2753)
| U_2752 != U_2753
| ~ c_Orderings_Oord__class_Oless(U_2750,c_Groups_Oone__class_Oone(U_2750),U_2751)
| ~ class_Rings_Olinordered__semidom(U_2750) ),
inference(clausify,[status(thm)],[f_952_2]) ).
fof(f_953_1,plain,
! [V_n,V_a,V_b,T_a] :
( c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b),V_n) = c_Rings_Oinverse__class_Odivide(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n))
| V_b = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__power__divide]) ).
fof(f_953_2,plain,
! [U_2757,U_2756,U_2755,U_2754] :
( c_Power_Opower__class_Opower(U_2754,c_Rings_Oinverse__class_Odivide(U_2754,U_2756,U_2755),U_2757) = c_Rings_Oinverse__class_Odivide(U_2754,c_Power_Opower__class_Opower(U_2754,U_2756,U_2757),c_Power_Opower__class_Opower(U_2754,U_2755,U_2757))
| U_2755 = c_Groups_Ozero__class_Ozero(U_2754)
| ~ class_Fields_Ofield(U_2754) ),
inference(variable_rename,[status(thm)],[f_953_1]) ).
cnf(f_953_3,plain,
( c_Power_Opower__class_Opower(U_2754,c_Rings_Oinverse__class_Odivide(U_2754,U_2756,U_2755),U_2757) = c_Rings_Oinverse__class_Odivide(U_2754,c_Power_Opower__class_Opower(U_2754,U_2756,U_2757),c_Power_Opower__class_Opower(U_2754,U_2755,U_2757))
| U_2755 = c_Groups_Ozero__class_Ozero(U_2754)
| ~ class_Fields_Ofield(U_2754) ),
inference(clausify,[status(thm)],[f_953_2]) ).
fof(f_954_1,plain,
! [V_a,T_a] :
( c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)
| ~ class_Power_Opower(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__0]) ).
fof(f_954_2,plain,
! [U_2759,U_2758] :
( c_Power_Opower__class_Opower(U_2758,U_2759,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2758)
| ~ class_Power_Opower(U_2758) ),
inference(variable_rename,[status(thm)],[f_954_1]) ).
cnf(f_954_3,plain,
( c_Power_Opower__class_Opower(U_2758,U_2759,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2758)
| ~ class_Power_Opower(U_2758) ),
inference(clausify,[status(thm)],[f_954_2]) ).
fof(f_955_1,plain,
! [V_n,V_m,V_a,T_a] :
( c_Power_Opower__class_Opower(T_a,V_a,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m)),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_955_2,plain,
! [U_2763,U_2762,U_2761,U_2760] :
( c_Power_Opower__class_Opower(U_2760,U_2761,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2762,U_2763)) = hAPP(c_Groups_Otimes__class_Otimes(U_2760,c_Power_Opower__class_Opower(U_2760,U_2761,U_2762)),c_Power_Opower__class_Opower(U_2760,U_2761,U_2763))
| ~ class_Groups_Omonoid__mult(U_2760) ),
inference(variable_rename,[status(thm)],[f_955_1]) ).
cnf(f_955_3,plain,
( c_Power_Opower__class_Opower(U_2760,U_2761,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2762,U_2763)) = hAPP(c_Groups_Otimes__class_Otimes(U_2760,c_Power_Opower__class_Opower(U_2760,U_2761,U_2762)),c_Power_Opower__class_Opower(U_2760,U_2761,U_2763))
| ~ class_Groups_Omonoid__mult(U_2760) ),
inference(clausify,[status(thm)],[f_955_2]) ).
fof(f_956_1,plain,
! [V_n,V_a,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)) = c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a),V_n)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__one__over]) ).
fof(f_956_2,plain,
! [U_2766,U_2765,U_2764] :
( c_Rings_Oinverse__class_Odivide(U_2764,c_Groups_Oone__class_Oone(U_2764),c_Power_Opower__class_Opower(U_2764,U_2765,U_2766)) = c_Power_Opower__class_Opower(U_2764,c_Rings_Oinverse__class_Odivide(U_2764,c_Groups_Oone__class_Oone(U_2764),U_2765),U_2766)
| ~ class_Fields_Ofield__inverse__zero(U_2764) ),
inference(variable_rename,[status(thm)],[f_956_1]) ).
cnf(f_956_3,plain,
( c_Rings_Oinverse__class_Odivide(U_2764,c_Groups_Oone__class_Oone(U_2764),c_Power_Opower__class_Opower(U_2764,U_2765,U_2766)) = c_Power_Opower__class_Opower(U_2764,c_Rings_Oinverse__class_Odivide(U_2764,c_Groups_Oone__class_Oone(U_2764),U_2765),U_2766)
| ~ class_Fields_Ofield__inverse__zero(U_2764) ),
inference(clausify,[status(thm)],[f_956_2]) ).
fof(f_957_1,plain,
! [V_n,V_a,T_a] :
( c_Rings_Oinverse__class_Oinverse(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)) = c_Power_Opower__class_Opower(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_n)
| V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Odivision__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__power__inverse]) ).
fof(f_957_2,plain,
! [U_2769,U_2768,U_2767] :
( c_Rings_Oinverse__class_Oinverse(U_2767,c_Power_Opower__class_Opower(U_2767,U_2768,U_2769)) = c_Power_Opower__class_Opower(U_2767,c_Rings_Oinverse__class_Oinverse(U_2767,U_2768),U_2769)
| U_2768 = c_Groups_Ozero__class_Ozero(U_2767)
| ~ class_Rings_Odivision__ring(U_2767) ),
inference(variable_rename,[status(thm)],[f_957_1]) ).
cnf(f_957_3,plain,
( c_Rings_Oinverse__class_Oinverse(U_2767,c_Power_Opower__class_Opower(U_2767,U_2768,U_2769)) = c_Power_Opower__class_Opower(U_2767,c_Rings_Oinverse__class_Oinverse(U_2767,U_2768),U_2769)
| U_2768 = c_Groups_Ozero__class_Ozero(U_2767)
| ~ class_Rings_Odivision__ring(U_2767) ),
inference(clausify,[status(thm)],[f_957_2]) ).
fof(f_958_1,plain,
! [V_b,V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_b,V_n))
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__base]) ).
fof(f_958_2,plain,
! [U_2773,U_2772,U_2771,U_2770] :
( c_Orderings_Oord__class_Oless(U_2770,U_2771,U_2773)
| ~ c_Orderings_Oord__class_Oless__eq(U_2770,c_Groups_Ozero__class_Ozero(U_2770),U_2773)
| ~ c_Orderings_Oord__class_Oless(U_2770,c_Power_Opower__class_Opower(U_2770,U_2771,U_2772),c_Power_Opower__class_Opower(U_2770,U_2773,U_2772))
| ~ class_Rings_Olinordered__semidom(U_2770) ),
inference(variable_rename,[status(thm)],[f_958_1]) ).
cnf(f_958_3,plain,
( c_Orderings_Oord__class_Oless(U_2770,U_2771,U_2773)
| ~ c_Orderings_Oord__class_Oless__eq(U_2770,c_Groups_Ozero__class_Ozero(U_2770),U_2773)
| ~ c_Orderings_Oord__class_Oless(U_2770,c_Power_Opower__class_Opower(U_2770,U_2771,U_2772),c_Power_Opower__class_Opower(U_2770,U_2773,U_2772))
| ~ class_Rings_Olinordered__semidom(U_2770) ),
inference(clausify,[status(thm)],[f_958_2]) ).
fof(f_959_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),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_959_2,plain,
! [U_2776,U_2775,U_2774] :
( c_Orderings_Oord__class_Oless(U_2774,c_Groups_Oone__class_Oone(U_2774),hAPP(c_Groups_Otimes__class_Otimes(U_2774,U_2775),c_Power_Opower__class_Opower(U_2774,U_2775,U_2776)))
| ~ c_Orderings_Oord__class_Oless(U_2774,c_Groups_Oone__class_Oone(U_2774),U_2775)
| ~ class_Rings_Olinordered__semidom(U_2774) ),
inference(variable_rename,[status(thm)],[f_959_1]) ).
cnf(f_959_3,plain,
( c_Orderings_Oord__class_Oless(U_2774,c_Groups_Oone__class_Oone(U_2774),hAPP(c_Groups_Otimes__class_Otimes(U_2774,U_2775),c_Power_Opower__class_Opower(U_2774,U_2775,U_2776)))
| ~ c_Orderings_Oord__class_Oless(U_2774,c_Groups_Oone__class_Oone(U_2774),U_2775)
| ~ class_Rings_Olinordered__semidom(U_2774) ),
inference(clausify,[status(thm)],[f_959_2]) ).
fof(f_960_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),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_960_2,plain,
! [U_2779,U_2778,U_2777] :
( c_Orderings_Oord__class_Oless(U_2777,c_Power_Opower__class_Opower(U_2777,U_2778,U_2779),hAPP(c_Groups_Otimes__class_Otimes(U_2777,U_2778),c_Power_Opower__class_Opower(U_2777,U_2778,U_2779)))
| ~ c_Orderings_Oord__class_Oless(U_2777,c_Groups_Oone__class_Oone(U_2777),U_2778)
| ~ class_Rings_Olinordered__semidom(U_2777) ),
inference(variable_rename,[status(thm)],[f_960_1]) ).
cnf(f_960_3,plain,
( c_Orderings_Oord__class_Oless(U_2777,c_Power_Opower__class_Opower(U_2777,U_2778,U_2779),hAPP(c_Groups_Otimes__class_Otimes(U_2777,U_2778),c_Power_Opower__class_Opower(U_2777,U_2778,U_2779)))
| ~ c_Orderings_Oord__class_Oless(U_2777,c_Groups_Oone__class_Oone(U_2777),U_2778)
| ~ class_Rings_Olinordered__semidom(U_2777) ),
inference(clausify,[status(thm)],[f_960_2]) ).
fof(f_961_1,plain,
! [V_n,T_a] :
( ( ( c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Ozero__class_Ozero(T_a)
| V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Power_Opower__class_Opower(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Oone__class_Oone(T_a)
| V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Osemiring__0(T_a)
| ~ class_Power_Opower(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__0__left]) ).
fof(f_961_2,plain,
! [U_2781,U_2780] :
( ( ( c_Power_Opower__class_Opower(U_2780,c_Groups_Ozero__class_Ozero(U_2780),U_2781) = c_Groups_Ozero__class_Ozero(U_2780)
| U_2781 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Power_Opower__class_Opower(U_2780,c_Groups_Ozero__class_Ozero(U_2780),U_2781) = c_Groups_Oone__class_Oone(U_2780)
| U_2781 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Osemiring__0(U_2780)
| ~ class_Power_Opower(U_2780) ),
inference(variable_rename,[status(thm)],[f_961_1]) ).
cnf(f_961_3,plain,
( c_Power_Opower__class_Opower(U_2780,c_Groups_Ozero__class_Ozero(U_2780),U_2781) = c_Groups_Oone__class_Oone(U_2780)
| U_2781 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Osemiring__0(U_2780)
| ~ class_Power_Opower(U_2780) ),
inference(clausify,[status(thm)],[f_961_2]) ).
cnf(f_961_4,plain,
( c_Power_Opower__class_Opower(U_2780,c_Groups_Ozero__class_Ozero(U_2780),U_2781) = c_Groups_Ozero__class_Ozero(U_2780)
| U_2781 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Osemiring__0(U_2780)
| ~ class_Power_Opower(U_2780) ),
inference(clausify,[status(thm)],[f_961_2]) ).
fof(f_962_1,plain,
! [V_n,V_a,T_a] :
( c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n) = hAPP(c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),V_n)),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_962_2,plain,
! [U_2784,U_2783,U_2782] :
( c_Power_Opower__class_Opower(U_2782,c_Groups_Ouminus__class_Ouminus(U_2782,U_2783),U_2784) = hAPP(c_Groups_Otimes__class_Otimes(U_2782,c_Power_Opower__class_Opower(U_2782,c_Groups_Ouminus__class_Ouminus(U_2782,c_Groups_Oone__class_Oone(U_2782)),U_2784)),c_Power_Opower__class_Opower(U_2782,U_2783,U_2784))
| ~ class_Rings_Oring__1(U_2782) ),
inference(variable_rename,[status(thm)],[f_962_1]) ).
cnf(f_962_3,plain,
( c_Power_Opower__class_Opower(U_2782,c_Groups_Ouminus__class_Ouminus(U_2782,U_2783),U_2784) = hAPP(c_Groups_Otimes__class_Otimes(U_2782,c_Power_Opower__class_Opower(U_2782,c_Groups_Ouminus__class_Ouminus(U_2782,c_Groups_Oone__class_Oone(U_2782)),U_2784)),c_Power_Opower__class_Opower(U_2782,U_2783,U_2784))
| ~ class_Rings_Oring__1(U_2782) ),
inference(clausify,[status(thm)],[f_962_2]) ).
fof(f_963_1,plain,
! [V_y_2,V_x_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_b_2,V_x_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_y_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_b_2,V_x_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_y_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff]) ).
fof(f_963_2,plain,
! [U_2788,U_2787,U_2786,U_2785] :
( ( ( c_Orderings_Oord__class_Oless(U_2785,c_Power_Opower__class_Opower(U_2785,U_2786,U_2787),c_Power_Opower__class_Opower(U_2785,U_2786,U_2788))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2787,U_2788) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2787,U_2788)
| ~ c_Orderings_Oord__class_Oless(U_2785,c_Power_Opower__class_Opower(U_2785,U_2786,U_2787),c_Power_Opower__class_Opower(U_2785,U_2786,U_2788)) ) )
| ~ c_Orderings_Oord__class_Oless(U_2785,c_Groups_Oone__class_Oone(U_2785),U_2786)
| ~ class_Rings_Olinordered__semidom(U_2785) ),
inference(variable_rename,[status(thm)],[f_963_1]) ).
cnf(f_963_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2787,U_2788)
| ~ c_Orderings_Oord__class_Oless(U_2785,c_Power_Opower__class_Opower(U_2785,U_2786,U_2787),c_Power_Opower__class_Opower(U_2785,U_2786,U_2788))
| ~ c_Orderings_Oord__class_Oless(U_2785,c_Groups_Oone__class_Oone(U_2785),U_2786)
| ~ class_Rings_Olinordered__semidom(U_2785) ),
inference(clausify,[status(thm)],[f_963_2]) ).
cnf(f_963_4,plain,
( c_Orderings_Oord__class_Oless(U_2785,c_Power_Opower__class_Opower(U_2785,U_2786,U_2787),c_Power_Opower__class_Opower(U_2785,U_2786,U_2788))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2787,U_2788)
| ~ c_Orderings_Oord__class_Oless(U_2785,c_Groups_Oone__class_Oone(U_2785),U_2786)
| ~ class_Rings_Olinordered__semidom(U_2785) ),
inference(clausify,[status(thm)],[f_963_2]) ).
fof(f_964_1,plain,
! [V_n,V_m,V_a,T_a] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__exp]) ).
fof(f_964_2,plain,
! [U_2792,U_2791,U_2790,U_2789] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2791,U_2792)
| ~ c_Orderings_Oord__class_Oless(U_2789,c_Power_Opower__class_Opower(U_2789,U_2790,U_2791),c_Power_Opower__class_Opower(U_2789,U_2790,U_2792))
| ~ c_Orderings_Oord__class_Oless(U_2789,c_Groups_Oone__class_Oone(U_2789),U_2790)
| ~ class_Rings_Olinordered__semidom(U_2789) ),
inference(variable_rename,[status(thm)],[f_964_1]) ).
cnf(f_964_3,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2791,U_2792)
| ~ c_Orderings_Oord__class_Oless(U_2789,c_Power_Opower__class_Opower(U_2789,U_2790,U_2791),c_Power_Opower__class_Opower(U_2789,U_2790,U_2792))
| ~ c_Orderings_Oord__class_Oless(U_2789,c_Groups_Oone__class_Oone(U_2789),U_2790)
| ~ class_Rings_Olinordered__semidom(U_2789) ),
inference(clausify,[status(thm)],[f_964_2]) ).
fof(f_965_1,plain,
! [V_a,V_N,V_n,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_a,V_N))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__strict__increasing]) ).
fof(f_965_2,plain,
! [U_2796,U_2795,U_2794,U_2793] :
( c_Orderings_Oord__class_Oless(U_2793,c_Power_Opower__class_Opower(U_2793,U_2796,U_2794),c_Power_Opower__class_Opower(U_2793,U_2796,U_2795))
| ~ c_Orderings_Oord__class_Oless(U_2793,c_Groups_Oone__class_Oone(U_2793),U_2796)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2794,U_2795)
| ~ class_Rings_Olinordered__semidom(U_2793) ),
inference(variable_rename,[status(thm)],[f_965_1]) ).
cnf(f_965_3,plain,
( c_Orderings_Oord__class_Oless(U_2793,c_Power_Opower__class_Opower(U_2793,U_2796,U_2794),c_Power_Opower__class_Opower(U_2793,U_2796,U_2795))
| ~ c_Orderings_Oord__class_Oless(U_2793,c_Groups_Oone__class_Oone(U_2793),U_2796)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2794,U_2795)
| ~ class_Rings_Olinordered__semidom(U_2793) ),
inference(clausify,[status(thm)],[f_965_2]) ).
fof(f_966_1,plain,
! [V_a,V_N,V_n,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n),c_Power_Opower__class_Opower(T_a,V_a,V_N))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__increasing]) ).
fof(f_966_2,plain,
! [U_2800,U_2799,U_2798,U_2797] :
( c_Orderings_Oord__class_Oless__eq(U_2797,c_Power_Opower__class_Opower(U_2797,U_2800,U_2798),c_Power_Opower__class_Opower(U_2797,U_2800,U_2799))
| ~ c_Orderings_Oord__class_Oless__eq(U_2797,c_Groups_Oone__class_Oone(U_2797),U_2800)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2798,U_2799)
| ~ class_Rings_Olinordered__semidom(U_2797) ),
inference(variable_rename,[status(thm)],[f_966_1]) ).
cnf(f_966_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2797,c_Power_Opower__class_Opower(U_2797,U_2800,U_2798),c_Power_Opower__class_Opower(U_2797,U_2800,U_2799))
| ~ c_Orderings_Oord__class_Oless__eq(U_2797,c_Groups_Oone__class_Oone(U_2797),U_2800)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2798,U_2799)
| ~ class_Rings_Olinordered__semidom(U_2797) ),
inference(clausify,[status(thm)],[f_966_2]) ).
fof(f_967_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),c_Power_Opower__class_Opower(T_a,V_a,V_n)),c_Power_Opower__class_Opower(T_a,V_a,V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__Suc__less]) ).
fof(f_967_2,plain,
! [U_2803,U_2802,U_2801] :
( c_Orderings_Oord__class_Oless(U_2801,hAPP(c_Groups_Otimes__class_Otimes(U_2801,U_2802),c_Power_Opower__class_Opower(U_2801,U_2802,U_2803)),c_Power_Opower__class_Opower(U_2801,U_2802,U_2803))
| ~ c_Orderings_Oord__class_Oless(U_2801,U_2802,c_Groups_Oone__class_Oone(U_2801))
| ~ c_Orderings_Oord__class_Oless(U_2801,c_Groups_Ozero__class_Ozero(U_2801),U_2802)
| ~ class_Rings_Olinordered__semidom(U_2801) ),
inference(variable_rename,[status(thm)],[f_967_1]) ).
cnf(f_967_3,plain,
( c_Orderings_Oord__class_Oless(U_2801,hAPP(c_Groups_Otimes__class_Otimes(U_2801,U_2802),c_Power_Opower__class_Opower(U_2801,U_2802,U_2803)),c_Power_Opower__class_Opower(U_2801,U_2802,U_2803))
| ~ c_Orderings_Oord__class_Oless(U_2801,U_2802,c_Groups_Oone__class_Oone(U_2801))
| ~ c_Orderings_Oord__class_Oless(U_2801,c_Groups_Ozero__class_Ozero(U_2801),U_2802)
| ~ class_Rings_Olinordered__semidom(U_2801) ),
inference(clausify,[status(thm)],[f_967_2]) ).
fof(f_968_1,plain,
! [V_a,V_N,V_n,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_N),c_Power_Opower__class_Opower(T_a,V_a,V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing]) ).
fof(f_968_2,plain,
! [U_2807,U_2806,U_2805,U_2804] :
( c_Orderings_Oord__class_Oless(U_2804,c_Power_Opower__class_Opower(U_2804,U_2807,U_2806),c_Power_Opower__class_Opower(U_2804,U_2807,U_2805))
| ~ c_Orderings_Oord__class_Oless(U_2804,U_2807,c_Groups_Oone__class_Oone(U_2804))
| ~ c_Orderings_Oord__class_Oless(U_2804,c_Groups_Ozero__class_Ozero(U_2804),U_2807)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2805,U_2806)
| ~ class_Rings_Olinordered__semidom(U_2804) ),
inference(variable_rename,[status(thm)],[f_968_1]) ).
cnf(f_968_3,plain,
( c_Orderings_Oord__class_Oless(U_2804,c_Power_Opower__class_Opower(U_2804,U_2807,U_2806),c_Power_Opower__class_Opower(U_2804,U_2807,U_2805))
| ~ c_Orderings_Oord__class_Oless(U_2804,U_2807,c_Groups_Oone__class_Oone(U_2804))
| ~ c_Orderings_Oord__class_Oless(U_2804,c_Groups_Ozero__class_Ozero(U_2804),U_2807)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2805,U_2806)
| ~ class_Rings_Olinordered__semidom(U_2804) ),
inference(clausify,[status(thm)],[f_968_2]) ).
fof(f_969_1,plain,
! [V_b,V_n,V_a,T_a] :
( V_a = V_b
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| c_Power_Opower__class_Opower(T_a,V_a,V_n) != c_Power_Opower__class_Opower(T_a,V_b,V_n)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__eq__imp__eq__base]) ).
fof(f_969_2,plain,
! [U_2811,U_2810,U_2809,U_2808] :
( U_2809 = U_2811
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2810)
| ~ c_Orderings_Oord__class_Oless__eq(U_2808,c_Groups_Ozero__class_Ozero(U_2808),U_2811)
| ~ c_Orderings_Oord__class_Oless__eq(U_2808,c_Groups_Ozero__class_Ozero(U_2808),U_2809)
| c_Power_Opower__class_Opower(U_2808,U_2809,U_2810) != c_Power_Opower__class_Opower(U_2808,U_2811,U_2810)
| ~ class_Rings_Olinordered__semidom(U_2808) ),
inference(variable_rename,[status(thm)],[f_969_1]) ).
cnf(f_969_3,plain,
( U_2809 = U_2811
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2810)
| ~ c_Orderings_Oord__class_Oless__eq(U_2808,c_Groups_Ozero__class_Ozero(U_2808),U_2811)
| ~ c_Orderings_Oord__class_Oless__eq(U_2808,c_Groups_Ozero__class_Ozero(U_2808),U_2809)
| c_Power_Opower__class_Opower(U_2808,U_2809,U_2810) != c_Power_Opower__class_Opower(U_2808,U_2811,U_2810)
| ~ class_Rings_Olinordered__semidom(U_2808) ),
inference(clausify,[status(thm)],[f_969_2]) ).
fof(f_970_1,plain,
! [V_a,V_N,V_n,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_N),c_Power_Opower__class_Opower(T_a,V_a,V_n))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__decreasing]) ).
fof(f_970_2,plain,
! [U_2815,U_2814,U_2813,U_2812] :
( c_Orderings_Oord__class_Oless__eq(U_2812,c_Power_Opower__class_Opower(U_2812,U_2815,U_2814),c_Power_Opower__class_Opower(U_2812,U_2815,U_2813))
| ~ c_Orderings_Oord__class_Oless__eq(U_2812,U_2815,c_Groups_Oone__class_Oone(U_2812))
| ~ c_Orderings_Oord__class_Oless__eq(U_2812,c_Groups_Ozero__class_Ozero(U_2812),U_2815)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2813,U_2814)
| ~ class_Rings_Olinordered__semidom(U_2812) ),
inference(variable_rename,[status(thm)],[f_970_1]) ).
cnf(f_970_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2812,c_Power_Opower__class_Opower(U_2812,U_2815,U_2814),c_Power_Opower__class_Opower(U_2812,U_2815,U_2813))
| ~ c_Orderings_Oord__class_Oless__eq(U_2812,U_2815,c_Groups_Oone__class_Oone(U_2812))
| ~ c_Orderings_Oord__class_Oless__eq(U_2812,c_Groups_Ozero__class_Ozero(U_2812),U_2815)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2813,U_2814)
| ~ class_Rings_Olinordered__semidom(U_2812) ),
inference(clausify,[status(thm)],[f_970_2]) ).
fof(f_971_1,plain,
! [V_y_2,V_x_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_b_2,V_x_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_b_2,V_x_2),c_Power_Opower__class_Opower(T_a,V_b_2,V_y_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__increasing__iff]) ).
fof(f_971_2,plain,
! [U_2819,U_2818,U_2817,U_2816] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2816,c_Power_Opower__class_Opower(U_2816,U_2817,U_2818),c_Power_Opower__class_Opower(U_2816,U_2817,U_2819))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2818,U_2819) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2818,U_2819)
| ~ c_Orderings_Oord__class_Oless__eq(U_2816,c_Power_Opower__class_Opower(U_2816,U_2817,U_2818),c_Power_Opower__class_Opower(U_2816,U_2817,U_2819)) ) )
| ~ c_Orderings_Oord__class_Oless(U_2816,c_Groups_Oone__class_Oone(U_2816),U_2817)
| ~ class_Rings_Olinordered__semidom(U_2816) ),
inference(variable_rename,[status(thm)],[f_971_1]) ).
cnf(f_971_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2818,U_2819)
| ~ c_Orderings_Oord__class_Oless__eq(U_2816,c_Power_Opower__class_Opower(U_2816,U_2817,U_2818),c_Power_Opower__class_Opower(U_2816,U_2817,U_2819))
| ~ c_Orderings_Oord__class_Oless(U_2816,c_Groups_Oone__class_Oone(U_2816),U_2817)
| ~ class_Rings_Olinordered__semidom(U_2816) ),
inference(clausify,[status(thm)],[f_971_2]) ).
cnf(f_971_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2816,c_Power_Opower__class_Opower(U_2816,U_2817,U_2818),c_Power_Opower__class_Opower(U_2816,U_2817,U_2819))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2818,U_2819)
| ~ c_Orderings_Oord__class_Oless(U_2816,c_Groups_Oone__class_Oone(U_2816),U_2817)
| ~ class_Rings_Olinordered__semidom(U_2816) ),
inference(clausify,[status(thm)],[f_971_2]) ).
fof(f_972_1,plain,
! [V_n,V_m,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_m),c_Power_Opower__class_Opower(T_a,V_a,V_n))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__exp]) ).
fof(f_972_2,plain,
! [U_2823,U_2822,U_2821,U_2820] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2822,U_2823)
| ~ c_Orderings_Oord__class_Oless__eq(U_2820,c_Power_Opower__class_Opower(U_2820,U_2821,U_2822),c_Power_Opower__class_Opower(U_2820,U_2821,U_2823))
| ~ c_Orderings_Oord__class_Oless(U_2820,c_Groups_Oone__class_Oone(U_2820),U_2821)
| ~ class_Rings_Olinordered__semidom(U_2820) ),
inference(variable_rename,[status(thm)],[f_972_1]) ).
cnf(f_972_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2822,U_2823)
| ~ c_Orderings_Oord__class_Oless__eq(U_2820,c_Power_Opower__class_Opower(U_2820,U_2821,U_2822),c_Power_Opower__class_Opower(U_2820,U_2821,U_2823))
| ~ c_Orderings_Oord__class_Oless(U_2820,c_Groups_Oone__class_Oone(U_2820),U_2821)
| ~ class_Rings_Olinordered__semidom(U_2820) ),
inference(clausify,[status(thm)],[f_972_2]) ).
fof(f_973_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(T_a,V_a,V_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__less__power]) ).
fof(f_973_2,plain,
! [U_2826,U_2825,U_2824] :
( c_Orderings_Oord__class_Oless(U_2824,c_Groups_Oone__class_Oone(U_2824),c_Power_Opower__class_Opower(U_2824,U_2825,U_2826))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2826)
| ~ c_Orderings_Oord__class_Oless(U_2824,c_Groups_Oone__class_Oone(U_2824),U_2825)
| ~ class_Rings_Olinordered__semidom(U_2824) ),
inference(variable_rename,[status(thm)],[f_973_1]) ).
cnf(f_973_3,plain,
( c_Orderings_Oord__class_Oless(U_2824,c_Groups_Oone__class_Oone(U_2824),c_Power_Opower__class_Opower(U_2824,U_2825,U_2826))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2826)
| ~ c_Orderings_Oord__class_Oless(U_2824,c_Groups_Oone__class_Oone(U_2824),U_2825)
| ~ class_Rings_Olinordered__semidom(U_2824) ),
inference(clausify,[status(thm)],[f_973_2]) ).
fof(f_974_1,plain,
! [V_z] : c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_z,
inference(fof_nnf,[status(thm)],[fact_csqrt]) ).
fof(f_974_2,plain,
! [U_2827] : c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(U_2827),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_2827,
inference(variable_rename,[status(thm)],[f_974_1]) ).
cnf(f_974_3,plain,
c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(U_2827),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_2827,
inference(clausify,[status(thm)],[f_974_2]) ).
fof(f_975_1,plain,
! [V_x] : hAPP(c_Transcendental_Oarctan,V_x) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Transcendental_Oarctan,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))))),
inference(fof_nnf,[status(thm)],[fact_arctan__half]) ).
fof(f_975_2,plain,
! [U_2828] : hAPP(c_Transcendental_Oarctan,U_2828) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Transcendental_Oarctan,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2828,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2828,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))))),
inference(variable_rename,[status(thm)],[f_975_1]) ).
cnf(f_975_3,plain,
hAPP(c_Transcendental_Oarctan,U_2828) = hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Transcendental_Oarctan,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2828,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2828,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))))),
inference(clausify,[status(thm)],[f_975_2]) ).
fof(f_976_1,plain,
hAPP(c_Transcendental_Oarctan,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_arctan__zero__zero]) ).
cnf(f_976_2,plain,
hAPP(c_Transcendental_Oarctan,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_976_1]) ).
fof(f_977_1,plain,
! [V_x] : hAPP(c_Transcendental_Oarctan,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,V_x)),
inference(fof_nnf,[status(thm)],[fact_arctan__minus]) ).
fof(f_977_2,plain,
! [U_2829] : hAPP(c_Transcendental_Oarctan,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2829)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,U_2829)),
inference(variable_rename,[status(thm)],[f_977_1]) ).
cnf(f_977_3,plain,
hAPP(c_Transcendental_Oarctan,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2829)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,U_2829)),
inference(clausify,[status(thm)],[f_977_2]) ).
fof(f_978_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,V_x),hAPP(c_Transcendental_Oarctan,V_y))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_arctan__monotone_H]) ).
fof(f_978_2,plain,
! [U_2831,U_2830] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,U_2830),hAPP(c_Transcendental_Oarctan,U_2831))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2830,U_2831) ),
inference(variable_rename,[status(thm)],[f_978_1]) ).
cnf(f_978_3,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,U_2830),hAPP(c_Transcendental_Oarctan,U_2831))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2830,U_2831) ),
inference(clausify,[status(thm)],[f_978_2]) ).
fof(f_979_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,V_x),hAPP(c_Transcendental_Oarctan,V_y))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_arctan__monotone]) ).
fof(f_979_2,plain,
! [U_2833,U_2832] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,U_2832),hAPP(c_Transcendental_Oarctan,U_2833))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2832,U_2833) ),
inference(variable_rename,[status(thm)],[f_979_1]) ).
cnf(f_979_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Transcendental_Oarctan,U_2832),hAPP(c_Transcendental_Oarctan,U_2833))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2832,U_2833) ),
inference(clausify,[status(thm)],[f_979_2]) ).
fof(f_980_1,plain,
! [V_x_2] : c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oarctan,V_x_2,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x_2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(fof_nnf,[status(thm)],[fact_DERIV__arctan]) ).
fof(f_980_2,plain,
! [U_2834] : c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oarctan,U_2834,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2834,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(variable_rename,[status(thm)],[f_980_1]) ).
cnf(f_980_3,plain,
c_Deriv_Oderiv(tc_RealDef_Oreal,c_Transcendental_Oarctan,U_2834,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2834,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(clausify,[status(thm)],[f_980_2]) ).
fof(f_981_1,plain,
! [V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact_cos__x__y__le__one]) ).
fof(f_981_2,plain,
! [U_2836,U_2835] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2835,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2835,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2836,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[f_981_1]) ).
cnf(f_981_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2835,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2835,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2836,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_981_2]) ).
fof(f_982_1,plain,
! [V_y,V_u,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_x,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,V_y,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),V_u)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_u,hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__sum__squares__less]) ).
fof(f_982_2,plain,
! [U_2839,U_2838,U_2837] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2837,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2839,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),U_2838)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2839),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2838,hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2837),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2838,hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
inference(variable_rename,[status(thm)],[f_982_1]) ).
cnf(f_982_3,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_NthRoot_Osqrt,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2837,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,U_2839,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),U_2838)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2839),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2838,hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2837),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2838,hAPP(c_NthRoot_Osqrt,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
inference(clausify,[status(thm)],[f_982_2]) ).
fof(f_983_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_n))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__power__abs]) ).
fof(f_983_2,plain,
! [U_2842,U_2841,U_2840] :
( c_Orderings_Oord__class_Oless__eq(U_2840,c_Groups_Ozero__class_Ozero(U_2840),c_Power_Opower__class_Opower(U_2840,c_Groups_Oabs__class_Oabs(U_2840,U_2841),U_2842))
| ~ class_Rings_Olinordered__idom(U_2840) ),
inference(variable_rename,[status(thm)],[f_983_1]) ).
cnf(f_983_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2840,c_Groups_Ozero__class_Ozero(U_2840),c_Power_Opower__class_Opower(U_2840,c_Groups_Oabs__class_Oabs(U_2840,U_2841),U_2842))
| ~ class_Rings_Olinordered__idom(U_2840) ),
inference(clausify,[status(thm)],[f_983_2]) ).
fof(f_984_1,plain,
! [V_n,V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n)) = c_Power_Opower__class_Opower(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_n)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__abs]) ).
fof(f_984_2,plain,
! [U_2845,U_2844,U_2843] :
( c_Groups_Oabs__class_Oabs(U_2843,c_Power_Opower__class_Opower(U_2843,U_2844,U_2845)) = c_Power_Opower__class_Opower(U_2843,c_Groups_Oabs__class_Oabs(U_2843,U_2844),U_2845)
| ~ class_Rings_Olinordered__idom(U_2843) ),
inference(variable_rename,[status(thm)],[f_984_1]) ).
cnf(f_984_3,plain,
( c_Groups_Oabs__class_Oabs(U_2843,c_Power_Opower__class_Opower(U_2843,U_2844,U_2845)) = c_Power_Opower__class_Opower(U_2843,c_Groups_Oabs__class_Oabs(U_2843,U_2844),U_2845)
| ~ class_Rings_Olinordered__idom(U_2843) ),
inference(clausify,[status(thm)],[f_984_2]) ).
fof(f_985_1,plain,
! [V_n,V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n)) = c_Groups_Oabs__class_Oabs(T_a,c_Power_Opower__class_Opower(T_a,V_a,V_n))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__power__minus]) ).
fof(f_985_2,plain,
! [U_2848,U_2847,U_2846] :
( c_Groups_Oabs__class_Oabs(U_2846,c_Power_Opower__class_Opower(U_2846,c_Groups_Ouminus__class_Ouminus(U_2846,U_2847),U_2848)) = c_Groups_Oabs__class_Oabs(U_2846,c_Power_Opower__class_Opower(U_2846,U_2847,U_2848))
| ~ class_Rings_Olinordered__idom(U_2846) ),
inference(variable_rename,[status(thm)],[f_985_1]) ).
cnf(f_985_3,plain,
( c_Groups_Oabs__class_Oabs(U_2846,c_Power_Opower__class_Opower(U_2846,c_Groups_Ouminus__class_Ouminus(U_2846,U_2847),U_2848)) = c_Groups_Oabs__class_Oabs(U_2846,c_Power_Opower__class_Opower(U_2846,U_2847,U_2848))
| ~ class_Rings_Olinordered__idom(U_2846) ),
inference(clausify,[status(thm)],[f_985_2]) ).
fof(f_986_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(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_986_2,plain,
! [U_2851,U_2850,U_2849] :
( U_2850 = 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_2850),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2849),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2851)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2849,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[f_986_1]) ).
cnf(f_986_3,plain,
( U_2850 = 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_2850),hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,U_2849),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2851)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2849,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_986_2]) ).
fof(f_987_1,plain,
! [V_y,V_x,T_a] :
( 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(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_987_2,plain,
! [U_2854,U_2853,U_2852] :
( hAPP(c_Groups_Otimes__class_Otimes(U_2852,c_Groups_Oabs__class_Oabs(U_2852,U_2854)),U_2853) = c_Groups_Oabs__class_Oabs(U_2852,hAPP(c_Groups_Otimes__class_Otimes(U_2852,U_2854),U_2853))
| ~ c_Orderings_Oord__class_Oless__eq(U_2852,c_Groups_Ozero__class_Ozero(U_2852),U_2853)
| ~ class_Rings_Olinordered__idom(U_2852) ),
inference(variable_rename,[status(thm)],[f_987_1]) ).
cnf(f_987_3,plain,
( hAPP(c_Groups_Otimes__class_Otimes(U_2852,c_Groups_Oabs__class_Oabs(U_2852,U_2854)),U_2853) = c_Groups_Oabs__class_Oabs(U_2852,hAPP(c_Groups_Otimes__class_Otimes(U_2852,U_2854),U_2853))
| ~ c_Orderings_Oord__class_Oless__eq(U_2852,c_Groups_Ozero__class_Ozero(U_2852),U_2853)
| ~ class_Rings_Olinordered__idom(U_2852) ),
inference(clausify,[status(thm)],[f_987_2]) ).
fof(f_988_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,hAPP(c_Groups_Otimes__class_Otimes(T_a,V_a),V_b)) = 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_988_2,plain,
! [U_2857,U_2856,U_2855] :
( c_Groups_Oabs__class_Oabs(U_2855,hAPP(c_Groups_Otimes__class_Otimes(U_2855,U_2856),U_2857)) = hAPP(c_Groups_Otimes__class_Otimes(U_2855,c_Groups_Oabs__class_Oabs(U_2855,U_2856)),c_Groups_Oabs__class_Oabs(U_2855,U_2857))
| ( ~ c_Orderings_Oord__class_Oless__eq(U_2855,U_2857,c_Groups_Ozero__class_Ozero(U_2855))
& ~ c_Orderings_Oord__class_Oless__eq(U_2855,c_Groups_Ozero__class_Ozero(U_2855),U_2857) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_2855,U_2856,c_Groups_Ozero__class_Ozero(U_2855))
& ~ c_Orderings_Oord__class_Oless__eq(U_2855,c_Groups_Ozero__class_Ozero(U_2855),U_2856) )
| ~ class_Rings_Oordered__ring__abs(U_2855) ),
inference(variable_rename,[status(thm)],[f_988_1]) ).
cnf(f_988_3,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2855,c_Groups_Ozero__class_Ozero(U_2855),U_2857)
| ~ c_Orderings_Oord__class_Oless__eq(U_2855,c_Groups_Ozero__class_Ozero(U_2855),U_2856)
| c_Groups_Oabs__class_Oabs(U_2855,hAPP(c_Groups_Otimes__class_Otimes(U_2855,U_2856),U_2857)) = hAPP(c_Groups_Otimes__class_Otimes(U_2855,c_Groups_Oabs__class_Oabs(U_2855,U_2856)),c_Groups_Oabs__class_Oabs(U_2855,U_2857))
| ~ class_Rings_Oordered__ring__abs(U_2855) ),
inference(clausify,[status(thm)],[f_988_2]) ).
cnf(f_988_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2855,U_2857,c_Groups_Ozero__class_Ozero(U_2855))
| ~ c_Orderings_Oord__class_Oless__eq(U_2855,c_Groups_Ozero__class_Ozero(U_2855),U_2856)
| c_Groups_Oabs__class_Oabs(U_2855,hAPP(c_Groups_Otimes__class_Otimes(U_2855,U_2856),U_2857)) = hAPP(c_Groups_Otimes__class_Otimes(U_2855,c_Groups_Oabs__class_Oabs(U_2855,U_2856)),c_Groups_Oabs__class_Oabs(U_2855,U_2857))
| ~ class_Rings_Oordered__ring__abs(U_2855) ),
inference(clausify,[status(thm)],[f_988_2]) ).
cnf(f_988_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2855,c_Groups_Ozero__class_Ozero(U_2855),U_2857)
| ~ c_Orderings_Oord__class_Oless__eq(U_2855,U_2856,c_Groups_Ozero__class_Ozero(U_2855))
| c_Groups_Oabs__class_Oabs(U_2855,hAPP(c_Groups_Otimes__class_Otimes(U_2855,U_2856),U_2857)) = hAPP(c_Groups_Otimes__class_Otimes(U_2855,c_Groups_Oabs__class_Oabs(U_2855,U_2856)),c_Groups_Oabs__class_Oabs(U_2855,U_2857))
| ~ class_Rings_Oordered__ring__abs(U_2855) ),
inference(clausify,[status(thm)],[f_988_2]) ).
cnf(f_988_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2855,U_2857,c_Groups_Ozero__class_Ozero(U_2855))
| ~ c_Orderings_Oord__class_Oless__eq(U_2855,U_2856,c_Groups_Ozero__class_Ozero(U_2855))
| c_Groups_Oabs__class_Oabs(U_2855,hAPP(c_Groups_Otimes__class_Otimes(U_2855,U_2856),U_2857)) = hAPP(c_Groups_Otimes__class_Otimes(U_2855,c_Groups_Oabs__class_Oabs(U_2855,U_2856)),c_Groups_Oabs__class_Oabs(U_2855,U_2857))
| ~ class_Rings_Oordered__ring__abs(U_2855) ),
inference(clausify,[status(thm)],[f_988_2]) ).
fof(f_989_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_989_2,plain,
! [U_2859,U_2858] :
( c_Groups_Oabs__class_Oabs(U_2858,U_2859) = c_Groups_Ouminus__class_Ouminus(U_2858,U_2859)
| ~ c_Orderings_Oord__class_Oless__eq(U_2858,U_2859,c_Groups_Ozero__class_Ozero(U_2858))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2858) ),
inference(variable_rename,[status(thm)],[f_989_1]) ).
cnf(f_989_3,plain,
( c_Groups_Oabs__class_Oabs(U_2858,U_2859) = c_Groups_Ouminus__class_Ouminus(U_2858,U_2859)
| ~ c_Orderings_Oord__class_Oless__eq(U_2858,U_2859,c_Groups_Ozero__class_Ozero(U_2858))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2858) ),
inference(clausify,[status(thm)],[f_989_2]) ).
fof(f_990_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_990_2,plain,
! [U_2861,U_2860] :
( c_Orderings_Oord__class_Oless__eq(U_2860,c_Groups_Ouminus__class_Ouminus(U_2860,c_Groups_Oabs__class_Oabs(U_2860,U_2861)),c_Groups_Ozero__class_Ozero(U_2860))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2860) ),
inference(variable_rename,[status(thm)],[f_990_1]) ).
cnf(f_990_3,plain,
( c_Orderings_Oord__class_Oless__eq(U_2860,c_Groups_Ouminus__class_Ouminus(U_2860,c_Groups_Oabs__class_Oabs(U_2860,U_2861)),c_Groups_Ozero__class_Ozero(U_2860))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2860) ),
inference(clausify,[status(thm)],[f_990_2]) ).
fof(f_991_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_991_2,plain,
! [U_2863,U_2862] :
( c_Groups_Oabs__class_Oabs(U_2862,U_2863) = c_Groups_Ouminus__class_Ouminus(U_2862,U_2863)
| ~ c_Orderings_Oord__class_Oless(U_2862,U_2863,c_Groups_Ozero__class_Ozero(U_2862))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2862) ),
inference(variable_rename,[status(thm)],[f_991_1]) ).
cnf(f_991_3,plain,
( c_Groups_Oabs__class_Oabs(U_2862,U_2863) = c_Groups_Ouminus__class_Ouminus(U_2862,U_2863)
| ~ c_Orderings_Oord__class_Oless(U_2862,U_2863,c_Groups_Ozero__class_Ozero(U_2862))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2862) ),
inference(clausify,[status(thm)],[f_991_2]) ).
fof(f_992_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_992_2,plain,
! [U_2865,U_2864] :
( ( ( c_Groups_Oabs__class_Oabs(U_2864,U_2865) = U_2865
| c_Orderings_Oord__class_Oless(U_2864,U_2865,c_Groups_Ozero__class_Ozero(U_2864)) )
& ( c_Groups_Oabs__class_Oabs(U_2864,U_2865) = c_Groups_Ouminus__class_Ouminus(U_2864,U_2865)
| ~ c_Orderings_Oord__class_Oless(U_2864,U_2865,c_Groups_Ozero__class_Ozero(U_2864)) ) )
| ~ class_Groups_Oabs__if(U_2864) ),
inference(variable_rename,[status(thm)],[f_992_1]) ).
cnf(f_992_3,plain,
( c_Groups_Oabs__class_Oabs(U_2864,U_2865) = c_Groups_Ouminus__class_Ouminus(U_2864,U_2865)
| ~ c_Orderings_Oord__class_Oless(U_2864,U_2865,c_Groups_Ozero__class_Ozero(U_2864))
| ~ class_Groups_Oabs__if(U_2864) ),
inference(clausify,[status(thm)],[f_992_2]) ).
cnf(f_992_4,plain,
( c_Groups_Oabs__class_Oabs(U_2864,U_2865) = U_2865
| c_Orderings_Oord__class_Oless(U_2864,U_2865,c_Groups_Ozero__class_Ozero(U_2864))
| ~ class_Groups_Oabs__if(U_2864) ),
inference(clausify,[status(thm)],[f_992_2]) ).
fof(f_993_1,plain,
! [V_x,V_y,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oabs__class_Oabs(T_a,V_x),V_y) = c_Groups_Oabs__class_Oabs(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__div__pos]) ).
fof(f_993_2,plain,
! [U_2868,U_2867,U_2866] :
( c_Rings_Oinverse__class_Odivide(U_2866,c_Groups_Oabs__class_Oabs(U_2866,U_2868),U_2867) = c_Groups_Oabs__class_Oabs(U_2866,c_Rings_Oinverse__class_Odivide(U_2866,U_2868,U_2867))
| ~ c_Orderings_Oord__class_Oless(U_2866,c_Groups_Ozero__class_Ozero(U_2866),U_2867)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2866) ),
inference(variable_rename,[status(thm)],[f_993_1]) ).
cnf(f_993_3,plain,
( c_Rings_Oinverse__class_Odivide(U_2866,c_Groups_Oabs__class_Oabs(U_2866,U_2868),U_2867) = c_Groups_Oabs__class_Oabs(U_2866,c_Rings_Oinverse__class_Odivide(U_2866,U_2868,U_2867))
| ~ c_Orderings_Oord__class_Oless(U_2866,c_Groups_Ozero__class_Ozero(U_2866),U_2867)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2866) ),
inference(clausify,[status(thm)],[f_993_2]) ).
fof(f_994_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_994_2,plain,
! [U_2869] :
( c_Groups_Oabs__class_Oabs(U_2869,c_Groups_Oone__class_Oone(U_2869)) = c_Groups_Oone__class_Oone(U_2869)
| ~ class_Rings_Olinordered__idom(U_2869) ),
inference(variable_rename,[status(thm)],[f_994_1]) ).
cnf(f_994_3,plain,
( c_Groups_Oabs__class_Oabs(U_2869,c_Groups_Oone__class_Oone(U_2869)) = c_Groups_Oone__class_Oone(U_2869)
| ~ class_Rings_Olinordered__idom(U_2869) ),
inference(clausify,[status(thm)],[f_994_2]) ).
fof(f_995_1,plain,
! [V_x] : c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x)),
inference(fof_nnf,[status(thm)],[fact_real__sgn__eq]) ).
fof(f_995_2,plain,
! [U_2870] : c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_2870) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2870,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2870)),
inference(variable_rename,[status(thm)],[f_995_1]) ).
cnf(f_995_3,plain,
c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_2870) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2870,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2870)),
inference(clausify,[status(thm)],[f_995_2]) ).
fof(f_996_1,plain,
! [V_d,V_b,V_c,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,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(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_996_2,plain,
! [U_2875,U_2874,U_2873,U_2872,U_2871] :
( c_Orderings_Oord__class_Oless(U_2871,hAPP(c_Groups_Otimes__class_Otimes(U_2871,c_Groups_Oabs__class_Oabs(U_2871,U_2872)),c_Groups_Oabs__class_Oabs(U_2871,U_2874)),hAPP(c_Groups_Otimes__class_Otimes(U_2871,U_2873),U_2875))
| ~ c_Orderings_Oord__class_Oless(U_2871,c_Groups_Oabs__class_Oabs(U_2871,U_2874),U_2875)
| ~ c_Orderings_Oord__class_Oless(U_2871,c_Groups_Oabs__class_Oabs(U_2871,U_2872),U_2873)
| ~ class_Rings_Olinordered__idom(U_2871) ),
inference(variable_rename,[status(thm)],[f_996_1]) ).
cnf(f_996_3,plain,
( c_Orderings_Oord__class_Oless(U_2871,hAPP(c_Groups_Otimes__class_Otimes(U_2871,c_Groups_Oabs__class_Oabs(U_2871,U_2872)),c_Groups_Oabs__class_Oabs(U_2871,U_2874)),hAPP(c_Groups_Otimes__class_Otimes(U_2871,U_2873),U_2875))
| ~ c_Orderings_Oord__class_Oless(U_2871,c_Groups_Oabs__class_Oabs(U_2871,U_2874),U_2875)
| ~ c_Orderings_Oord__class_Oless(U_2871,c_Groups_Oabs__class_Oabs(U_2871,U_2872),U_2873)
| ~ class_Rings_Olinordered__idom(U_2871) ),
inference(clausify,[status(thm)],[f_996_2]) ).
fof(f_997_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_997_2,plain,
! [U_2877,U_2876] :
( class_Lattices_Oboolean__algebra(tc_fun(U_2877,U_2876))
| ~ class_Lattices_Oboolean__algebra(U_2876) ),
inference(variable_rename,[status(thm)],[f_997_1]) ).
cnf(f_997_3,plain,
( class_Lattices_Oboolean__algebra(tc_fun(U_2877,U_2876))
| ~ class_Lattices_Oboolean__algebra(U_2876) ),
inference(clausify,[status(thm)],[f_997_2]) ).
fof(f_998_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_998_2,plain,
! [U_2879,U_2878] :
( class_Orderings_Opreorder(tc_fun(U_2879,U_2878))
| ~ class_Orderings_Opreorder(U_2878) ),
inference(variable_rename,[status(thm)],[f_998_1]) ).
cnf(f_998_3,plain,
( class_Orderings_Opreorder(tc_fun(U_2879,U_2878))
| ~ class_Orderings_Opreorder(U_2878) ),
inference(clausify,[status(thm)],[f_998_2]) ).
fof(f_999_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_999_2,plain,
! [U_2881,U_2880] :
( class_Orderings_Oorder(tc_fun(U_2881,U_2880))
| ~ class_Orderings_Oorder(U_2880) ),
inference(variable_rename,[status(thm)],[f_999_1]) ).
cnf(f_999_3,plain,
( class_Orderings_Oorder(tc_fun(U_2881,U_2880))
| ~ class_Orderings_Oorder(U_2880) ),
inference(clausify,[status(thm)],[f_999_2]) ).
fof(f_1000_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_1000_2,plain,
! [U_2883,U_2882] :
( class_Orderings_Oord(tc_fun(U_2883,U_2882))
| ~ class_Orderings_Oord(U_2882) ),
inference(variable_rename,[status(thm)],[f_1000_1]) ).
cnf(f_1000_3,plain,
( class_Orderings_Oord(tc_fun(U_2883,U_2882))
| ~ class_Orderings_Oord(U_2882) ),
inference(clausify,[status(thm)],[f_1000_2]) ).
fof(f_1001_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_1001_2,plain,
! [U_2885,U_2884] :
( class_Groups_Ouminus(tc_fun(U_2885,U_2884))
| ~ class_Groups_Ouminus(U_2884) ),
inference(variable_rename,[status(thm)],[f_1001_1]) ).
cnf(f_1001_3,plain,
( class_Groups_Ouminus(tc_fun(U_2885,U_2884))
| ~ class_Groups_Ouminus(U_2884) ),
inference(clausify,[status(thm)],[f_1001_2]) ).
fof(f_1002_1,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
cnf(f_1002_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1002_1]) ).
fof(f_1003_1,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add]) ).
cnf(f_1003_2,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1003_1]) ).
fof(f_1004_1,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le]) ).
cnf(f_1004_2,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1004_1]) ).
fof(f_1005_1,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__comm__semiring__strict]) ).
cnf(f_1005_2,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1005_1]) ).
fof(f_1006_1,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1__strict]) ).
cnf(f_1006_2,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1006_1]) ).
fof(f_1007_1,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__strict]) ).
cnf(f_1007_2,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1007_1]) ).
fof(f_1008_1,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add]) ).
cnf(f_1008_2,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1008_1]) ).
fof(f_1009_1,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add__abs]) ).
cnf(f_1009_2,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1009_1]) ).
fof(f_1010_1,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__comm__monoid__add]) ).
cnf(f_1010_2,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1010_1]) ).
fof(f_1011_1,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__group__add]) ).
cnf(f_1011_2,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1011_1]) ).
fof(f_1012_1,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__ab__semigroup__add]) ).
cnf(f_1012_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1012_1]) ).
fof(f_1013_1,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__1__no__zero__divisors]) ).
cnf(f_1013_2,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1013_1]) ).
fof(f_1014_1,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__cancel__semiring]) ).
cnf(f_1014_2,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1014_1]) ).
fof(f_1015_1,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring__strict]) ).
cnf(f_1015_2,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1015_1]) ).
fof(f_1016_1,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__no__zero__divisors]) ).
cnf(f_1016_2,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1016_1]) ).
fof(f_1017_1,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__comm__semiring]) ).
cnf(f_1017_2,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1017_1]) ).
fof(f_1018_1,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1]) ).
cnf(f_1018_2,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1018_1]) ).
fof(f_1019_1,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add]) ).
cnf(f_1019_2,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1019_1]) ).
fof(f_1020_1,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__semigroup__add]) ).
cnf(f_1020_2,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1020_1]) ).
fof(f_1021_1,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]) ).
cnf(f_1021_2,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1021_1]) ).
fof(f_1022_1,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]) ).
cnf(f_1022_2,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1022_1]) ).
fof(f_1023_1,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__mult]) ).
cnf(f_1023_2,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1023_1]) ).
fof(f_1024_1,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__mult]) ).
cnf(f_1024_2,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1024_1]) ).
fof(f_1025_1,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__add]) ).
cnf(f_1025_2,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1025_1]) ).
fof(f_1026_1,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]) ).
cnf(f_1026_2,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1026_1]) ).
fof(f_1027_1,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring__abs]) ).
cnf(f_1027_2,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1027_1]) ).
fof(f_1028_1,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ono__zero__divisors]) ).
cnf(f_1028_2,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1028_1]) ).
fof(f_1029_1,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__add]) ).
cnf(f_1029_2,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1029_1]) ).
fof(f_1030_1,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]) ).
cnf(f_1030_2,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1030_1]) ).
fof(f_1031_1,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]) ).
cnf(f_1031_2,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1031_1]) ).
fof(f_1032_1,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__1]) ).
cnf(f_1032_2,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1032_1]) ).
fof(f_1033_1,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]) ).
cnf(f_1033_2,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1033_1]) ).
fof(f_1034_1,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__group__add]) ).
cnf(f_1034_2,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1034_1]) ).
fof(f_1035_1,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ozero__neq__one]) ).
cnf(f_1035_2,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1035_1]) ).
fof(f_1036_1,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]) ).
cnf(f_1036_2,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1036_1]) ).
fof(f_1037_1,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]) ).
cnf(f_1037_2,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1037_1]) ).
fof(f_1038_1,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]) ).
cnf(f_1038_2,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1038_1]) ).
fof(f_1039_1,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]) ).
cnf(f_1039_2,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1039_1]) ).
fof(f_1040_1,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring__1]) ).
cnf(f_1040_2,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1040_1]) ).
fof(f_1041_1,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]) ).
cnf(f_1041_2,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1041_1]) ).
fof(f_1042_1,plain,
class_Rings_Osemiring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring__1]) ).
cnf(f_1042_2,plain,
class_Rings_Osemiring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1042_1]) ).
fof(f_1043_1,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]) ).
cnf(f_1043_2,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1043_1]) ).
fof(f_1044_1,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]) ).
cnf(f_1044_2,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1044_1]) ).
fof(f_1045_1,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]) ).
cnf(f_1045_2,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1045_1]) ).
fof(f_1046_1,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oorder]) ).
cnf(f_1046_2,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1046_1]) ).
fof(f_1047_1,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Oring__char__0]) ).
cnf(f_1047_2,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1047_1]) ).
fof(f_1048_1,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]) ).
cnf(f_1048_2,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1048_1]) ).
fof(f_1049_1,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring]) ).
cnf(f_1049_2,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1049_1]) ).
fof(f_1050_1,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oord]) ).
cnf(f_1050_2,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1050_1]) ).
fof(f_1051_1,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ouminus]) ).
cnf(f_1051_2,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1051_1]) ).
fof(f_1052_1,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]) ).
cnf(f_1052_2,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1052_1]) ).
fof(f_1053_1,plain,
class_Groups_Oabs__if(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oabs__if]) ).
cnf(f_1053_2,plain,
class_Groups_Oabs__if(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1053_1]) ).
fof(f_1054_1,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__1]) ).
cnf(f_1054_2,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1054_1]) ).
fof(f_1055_1,plain,
class_Power_Opower(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Power_Opower]) ).
cnf(f_1055_2,plain,
class_Power_Opower(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1055_1]) ).
fof(f_1056_1,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ozero]) ).
cnf(f_1056_2,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1056_1]) ).
fof(f_1057_1,plain,
class_Rings_Oring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring]) ).
cnf(f_1057_2,plain,
class_Rings_Oring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1057_1]) ).
fof(f_1058_1,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oidom]) ).
cnf(f_1058_2,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1058_1]) ).
fof(f_1059_1,plain,
class_Int_Onumber(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Onumber]) ).
cnf(f_1059_2,plain,
class_Int_Onumber(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1059_1]) ).
fof(f_1060_1,plain,
class_Groups_Oone(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oone]) ).
cnf(f_1060_2,plain,
class_Groups_Oone(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1060_1]) ).
fof(f_1061_1,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
cnf(f_1061_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1061_1]) ).
fof(f_1062_1,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add]) ).
cnf(f_1062_2,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1062_1]) ).
fof(f_1063_1,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le]) ).
cnf(f_1063_2,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1063_1]) ).
fof(f_1064_1,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict]) ).
cnf(f_1064_2,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1064_1]) ).
fof(f_1065_1,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring__strict]) ).
cnf(f_1065_2,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1065_1]) ).
fof(f_1066_1,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add]) ).
cnf(f_1066_2,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1066_1]) ).
fof(f_1067_1,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__comm__monoid__add]) ).
cnf(f_1067_2,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1067_1]) ).
fof(f_1068_1,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add]) ).
cnf(f_1068_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1068_1]) ).
fof(f_1069_1,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__cancel__semiring]) ).
cnf(f_1069_2,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1069_1]) ).
fof(f_1070_1,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__comm__semiring]) ).
cnf(f_1070_2,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1070_1]) ).
fof(f_1071_1,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]) ).
cnf(f_1071_2,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1071_1]) ).
fof(f_1072_1,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]) ).
cnf(f_1072_2,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1072_1]) ).
fof(f_1073_1,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]) ).
cnf(f_1073_2,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1073_1]) ).
fof(f_1074_1,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__mult]) ).
cnf(f_1074_2,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1074_1]) ).
fof(f_1075_1,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__mult]) ).
cnf(f_1075_2,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1075_1]) ).
fof(f_1076_1,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__add]) ).
cnf(f_1076_2,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1076_1]) ).
fof(f_1077_1,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]) ).
cnf(f_1077_2,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1077_1]) ).
fof(f_1078_1,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ono__zero__divisors]) ).
cnf(f_1078_2,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1078_1]) ).
fof(f_1079_1,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__add]) ).
cnf(f_1079_2,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1079_1]) ).
fof(f_1080_1,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]) ).
cnf(f_1080_2,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1080_1]) ).
fof(f_1081_1,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]) ).
cnf(f_1081_2,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1081_1]) ).
fof(f_1082_1,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ozero__neq__one]) ).
cnf(f_1082_2,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1082_1]) ).
fof(f_1083_1,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]) ).
cnf(f_1083_2,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1083_1]) ).
fof(f_1084_1,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]) ).
cnf(f_1084_2,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1084_1]) ).
fof(f_1085_1,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]) ).
cnf(f_1085_2,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1085_1]) ).
fof(f_1086_1,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]) ).
cnf(f_1086_2,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1086_1]) ).
fof(f_1087_1,plain,
class_Rings_Osemiring__1(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__1]) ).
cnf(f_1087_2,plain,
class_Rings_Osemiring__1(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1087_1]) ).
fof(f_1088_1,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]) ).
cnf(f_1088_2,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1088_1]) ).
fof(f_1089_1,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]) ).
cnf(f_1089_2,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1089_1]) ).
fof(f_1090_1,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]) ).
cnf(f_1090_2,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1090_1]) ).
fof(f_1091_1,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]) ).
cnf(f_1091_2,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1091_1]) ).
fof(f_1092_1,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oord]) ).
cnf(f_1092_2,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1092_1]) ).
fof(f_1093_1,plain,
class_Power_Opower(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Power_Opower]) ).
cnf(f_1093_2,plain,
class_Power_Opower(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1093_1]) ).
fof(f_1094_1,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ozero]) ).
cnf(f_1094_2,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1094_1]) ).
fof(f_1095_1,plain,
class_Int_Onumber(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Int_Onumber]) ).
cnf(f_1095_2,plain,
class_Int_Onumber(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1095_1]) ).
fof(f_1096_1,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oone]) ).
cnf(f_1096_2,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1096_1]) ).
fof(f_1097_1,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]) ).
cnf(f_1097_2,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1097_1]) ).
fof(f_1098_1,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]) ).
cnf(f_1098_2,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1098_1]) ).
fof(f_1099_1,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]) ).
cnf(f_1099_2,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1099_1]) ).
fof(f_1100_1,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oord]) ).
cnf(f_1100_2,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1100_1]) ).
fof(f_1101_1,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]) ).
cnf(f_1101_2,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1101_1]) ).
fof(f_1102_1,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
cnf(f_1102_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1102_1]) ).
fof(f_1103_1,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add]) ).
cnf(f_1103_2,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1103_1]) ).
fof(f_1104_1,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le]) ).
cnf(f_1104_2,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1104_1]) ).
fof(f_1105_1,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict]) ).
cnf(f_1105_2,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1105_1]) ).
fof(f_1106_1,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero]) ).
cnf(f_1106_2,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1106_1]) ).
fof(f_1107_1,plain,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict]) ).
cnf(f_1107_2,plain,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1107_1]) ).
fof(f_1108_1,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra]) ).
cnf(f_1108_2,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1108_1]) ).
fof(f_1109_1,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__strict]) ).
cnf(f_1109_2,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1109_1]) ).
fof(f_1110_1,plain,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero]) ).
cnf(f_1110_2,plain,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1110_1]) ).
fof(f_1111_1,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1]) ).
cnf(f_1111_2,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1111_1]) ).
fof(f_1112_1,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add]) ).
cnf(f_1112_2,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1112_1]) ).
fof(f_1113_1,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs]) ).
cnf(f_1113_2,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1113_1]) ).
fof(f_1114_1,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra]) ).
cnf(f_1114_2,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1114_1]) ).
fof(f_1115_1,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add]) ).
cnf(f_1115_2,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1115_1]) ).
fof(f_1116_1,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Olinordered__ab__group__add]) ).
cnf(f_1116_2,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1116_1]) ).
fof(f_1117_1,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add]) ).
cnf(f_1117_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1117_1]) ).
fof(f_1118_1,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors]) ).
cnf(f_1118_2,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1118_1]) ).
fof(f_1119_1,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__cancel__semiring]) ).
cnf(f_1119_2,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1119_1]) ).
fof(f_1120_1,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__vector]) ).
cnf(f_1120_2,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1120_1]) ).
fof(f_1121_1,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring__strict]) ).
cnf(f_1121_2,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1121_1]) ).
fof(f_1122_1,plain,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__field]) ).
cnf(f_1122_2,plain,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1122_1]) ).
fof(f_1123_1,plain,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__no__zero__divisors]) ).
cnf(f_1123_2,plain,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1123_1]) ).
fof(f_1124_1,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__comm__semiring]) ).
cnf(f_1124_2,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1124_1]) ).
fof(f_1125_1,plain,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__1]) ).
cnf(f_1125_2,plain,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1125_1]) ).
fof(f_1126_1,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add]) ).
cnf(f_1126_2,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1126_1]) ).
fof(f_1127_1,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__semigroup__add]) ).
cnf(f_1127_2,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1127_1]) ).
fof(f_1128_1,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring]) ).
cnf(f_1128_2,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1128_1]) ).
fof(f_1129_1,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield__inverse__zero]) ).
cnf(f_1129_2,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1129_1]) ).
fof(f_1130_1,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).
cnf(f_1130_2,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1130_1]) ).
fof(f_1131_1,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__mult]) ).
cnf(f_1131_2,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1131_1]) ).
fof(f_1132_1,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__mult]) ).
cnf(f_1132_2,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1132_1]) ).
fof(f_1133_1,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__add]) ).
cnf(f_1133_2,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1133_1]) ).
fof(f_1134_1,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field]) ).
cnf(f_1134_2,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1134_1]) ).
fof(f_1135_1,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__semiring]) ).
cnf(f_1135_2,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1135_1]) ).
fof(f_1136_1,plain,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring__abs]) ).
cnf(f_1136_2,plain,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1136_1]) ).
fof(f_1137_1,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ono__zero__divisors]) ).
cnf(f_1137_2,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1137_1]) ).
fof(f_1138_1,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__add]) ).
cnf(f_1138_2,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1138_1]) ).
fof(f_1139_1,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring]) ).
cnf(f_1139_2,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1139_1]) ).
fof(f_1140_1,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]) ).
cnf(f_1140_2,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1140_1]) ).
fof(f_1141_1,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
cnf(f_1141_2,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1141_1]) ).
fof(f_1142_1,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring]) ).
cnf(f_1142_2,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1142_1]) ).
fof(f_1143_1,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring]) ).
cnf(f_1143_2,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1143_1]) ).
fof(f_1144_1,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__group__add]) ).
cnf(f_1144_2,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1144_1]) ).
fof(f_1145_1,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ozero__neq__one]) ).
cnf(f_1145_2,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1145_1]) ).
fof(f_1146_1,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring]) ).
cnf(f_1146_2,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1146_1]) ).
fof(f_1147_1,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
cnf(f_1147_2,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1147_1]) ).
fof(f_1148_1,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
cnf(f_1148_2,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1148_1]) ).
fof(f_1149_1,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]) ).
cnf(f_1149_2,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1149_1]) ).
fof(f_1150_1,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring__1]) ).
cnf(f_1150_2,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1150_1]) ).
fof(f_1151_1,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]) ).
cnf(f_1151_2,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1151_1]) ).
fof(f_1152_1,plain,
class_Rings_Osemiring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__1]) ).
cnf(f_1152_2,plain,
class_Rings_Osemiring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1152_1]) ).
fof(f_1153_1,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__0]) ).
cnf(f_1153_2,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1153_1]) ).
fof(f_1154_1,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]) ).
cnf(f_1154_2,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1154_1]) ).
fof(f_1155_1,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Omult__zero]) ).
cnf(f_1155_2,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1155_1]) ).
fof(f_1156_1,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).
cnf(f_1156_2,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1156_1]) ).
fof(f_1157_1,plain,
class_Int_Oring__char__0(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Int_Oring__char__0]) ).
cnf(f_1157_2,plain,
class_Int_Oring__char__0(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1157_1]) ).
fof(f_1158_1,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Int_Onumber__ring]) ).
cnf(f_1158_2,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1158_1]) ).
fof(f_1159_1,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring]) ).
cnf(f_1159_2,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1159_1]) ).
fof(f_1160_1,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Oord]) ).
cnf(f_1160_2,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1160_1]) ).
fof(f_1161_1,plain,
class_Groups_Ouminus(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ouminus]) ).
cnf(f_1161_2,plain,
class_Groups_Ouminus(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1161_1]) ).
fof(f_1162_1,plain,
class_Groups_Osgn__if(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Osgn__if]) ).
cnf(f_1162_2,plain,
class_Groups_Osgn__if(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1162_1]) ).
fof(f_1163_1,plain,
class_Groups_Oabs__if(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oabs__if]) ).
cnf(f_1163_2,plain,
class_Groups_Oabs__if(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1163_1]) ).
fof(f_1164_1,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1]) ).
cnf(f_1164_2,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1164_1]) ).
fof(f_1165_1,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield]) ).
cnf(f_1165_2,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1165_1]) ).
fof(f_1166_1,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Power_Opower]) ).
cnf(f_1166_2,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1166_1]) ).
fof(f_1167_1,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ozero]) ).
cnf(f_1167_2,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1167_1]) ).
fof(f_1168_1,plain,
class_SEQ_Obanach(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__SEQ_Obanach]) ).
cnf(f_1168_2,plain,
class_SEQ_Obanach(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1168_1]) ).
fof(f_1169_1,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring]) ).
cnf(f_1169_2,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1169_1]) ).
fof(f_1170_1,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oidom]) ).
cnf(f_1170_2,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1170_1]) ).
fof(f_1171_1,plain,
class_Int_Onumber(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Int_Onumber]) ).
cnf(f_1171_2,plain,
class_Int_Onumber(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1171_1]) ).
fof(f_1172_1,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oone]) ).
cnf(f_1172_2,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1172_1]) ).
fof(f_1173_1,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
cnf(f_1173_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1173_1]) ).
fof(f_1174_1,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra]) ).
cnf(f_1174_2,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1174_1]) ).
fof(f_1175_1,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero]) ).
cnf(f_1175_2,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1175_1]) ).
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]) ).
cnf(f_1176_2,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1176_1]) ).
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]) ).
cnf(f_1177_2,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1177_1]) ).
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]) ).
cnf(f_1178_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1178_1]) ).
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]) ).
cnf(f_1179_2,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1179_1]) ).
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]) ).
cnf(f_1180_2,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1180_1]) ).
fof(f_1181_1,plain,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__field]) ).
cnf(f_1181_2,plain,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1181_1]) ).
fof(f_1182_1,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors]) ).
cnf(f_1182_2,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1182_1]) ).
fof(f_1183_1,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add]) ).
cnf(f_1183_2,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1183_1]) ).
fof(f_1184_1,plain,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield__inverse__zero]) ).
cnf(f_1184_2,plain,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1184_1]) ).
fof(f_1185_1,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__mult]) ).
cnf(f_1185_2,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1185_1]) ).
fof(f_1186_1,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult]) ).
cnf(f_1186_2,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1186_1]) ).
fof(f_1187_1,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__add]) ).
cnf(f_1187_2,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1187_1]) ).
fof(f_1188_1,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ono__zero__divisors]) ).
cnf(f_1188_2,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1188_1]) ).
fof(f_1189_1,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__add]) ).
cnf(f_1189_2,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1189_1]) ).
fof(f_1190_1,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
cnf(f_1190_2,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1190_1]) ).
fof(f_1191_1,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Odivision__ring]) ).
cnf(f_1191_2,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1191_1]) ).
fof(f_1192_1,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring]) ).
cnf(f_1192_2,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1192_1]) ).
fof(f_1193_1,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__group__add]) ).
cnf(f_1193_2,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1193_1]) ).
fof(f_1194_1,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ozero__neq__one]) ).
cnf(f_1194_2,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1194_1]) ).
fof(f_1195_1,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__mult]) ).
cnf(f_1195_2,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1195_1]) ).
fof(f_1196_1,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring__1]) ).
cnf(f_1196_2,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1196_1]) ).
fof(f_1197_1,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__add]) ).
cnf(f_1197_2,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1197_1]) ).
fof(f_1198_1,plain,
class_Rings_Osemiring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__1]) ).
cnf(f_1198_2,plain,
class_Rings_Osemiring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1198_1]) ).
fof(f_1199_1,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__0]) ).
cnf(f_1199_2,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1199_1]) ).
fof(f_1200_1,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]) ).
cnf(f_1200_2,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1200_1]) ).
fof(f_1201_1,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Omult__zero]) ).
cnf(f_1201_2,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1201_1]) ).
fof(f_1202_1,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Int_Oring__char__0]) ).
cnf(f_1202_2,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1202_1]) ).
fof(f_1203_1,plain,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Int_Onumber__ring]) ).
cnf(f_1203_2,plain,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1203_1]) ).
fof(f_1204_1,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring]) ).
cnf(f_1204_2,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1204_1]) ).
fof(f_1205_1,plain,
class_Groups_Ouminus(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ouminus]) ).
cnf(f_1205_2,plain,
class_Groups_Ouminus(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1205_1]) ).
fof(f_1206_1,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1]) ).
cnf(f_1206_2,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1206_1]) ).
fof(f_1207_1,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield]) ).
cnf(f_1207_2,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1207_1]) ).
fof(f_1208_1,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Power_Opower]) ).
cnf(f_1208_2,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1208_1]) ).
fof(f_1209_1,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]) ).
cnf(f_1209_2,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1209_1]) ).
fof(f_1210_1,plain,
class_SEQ_Obanach(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__SEQ_Obanach]) ).
cnf(f_1210_2,plain,
class_SEQ_Obanach(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1210_1]) ).
fof(f_1211_1,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring]) ).
cnf(f_1211_2,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1211_1]) ).
fof(f_1212_1,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oidom]) ).
cnf(f_1212_2,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1212_1]) ).
fof(f_1213_1,plain,
class_Int_Onumber(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Int_Onumber]) ).
cnf(f_1213_2,plain,
class_Int_Onumber(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1213_1]) ).
fof(f_1214_1,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oone]) ).
cnf(f_1214_2,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1214_1]) ).
fof(f_1215_1,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add]) ).
cnf(f_1215_2,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1215_1]) ).
fof(f_1216_1,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le]) ).
cnf(f_1216_2,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1216_1]) ).
fof(f_1217_1,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict]) ).
cnf(f_1217_2,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1217_1]) ).
fof(f_1218_1,plain,
class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict]) ).
cnf(f_1218_2,plain,
class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1218_1]) ).
fof(f_1219_1,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add]) ).
cnf(f_1219_2,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1219_1]) ).
fof(f_1220_1,plain,
class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add]) ).
cnf(f_1220_2,plain,
class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1220_1]) ).
fof(f_1221_1,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add]) ).
cnf(f_1221_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1221_1]) ).
fof(f_1222_1,plain,
class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring]) ).
cnf(f_1222_2,plain,
class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1222_1]) ).
fof(f_1223_1,plain,
class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring]) ).
cnf(f_1223_2,plain,
class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1223_1]) ).
fof(f_1224_1,plain,
class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add]) ).
cnf(f_1224_2,plain,
class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1224_1]) ).
fof(f_1225_1,plain,
class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring]) ).
cnf(f_1225_2,plain,
class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1225_1]) ).
fof(f_1226_1,plain,
class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom]) ).
cnf(f_1226_2,plain,
class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1226_1]) ).
fof(f_1227_1,plain,
class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult]) ).
cnf(f_1227_2,plain,
class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1227_1]) ).
fof(f_1228_1,plain,
class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult]) ).
cnf(f_1228_2,plain,
class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1228_1]) ).
fof(f_1229_1,plain,
class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add]) ).
cnf(f_1229_2,plain,
class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1229_1]) ).
fof(f_1230_1,plain,
class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring]) ).
cnf(f_1230_2,plain,
class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1230_1]) ).
fof(f_1231_1,plain,
class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors]) ).
cnf(f_1231_2,plain,
class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1231_1]) ).
fof(f_1232_1,plain,
class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add]) ).
cnf(f_1232_2,plain,
class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1232_1]) ).
fof(f_1233_1,plain,
class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1]) ).
cnf(f_1233_2,plain,
class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1233_1]) ).
fof(f_1234_1,plain,
class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring]) ).
cnf(f_1234_2,plain,
class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1234_1]) ).
fof(f_1235_1,plain,
class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one]) ).
cnf(f_1235_2,plain,
class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1235_1]) ).
fof(f_1236_1,plain,
class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder]) ).
cnf(f_1236_2,plain,
class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1236_1]) ).
fof(f_1237_1,plain,
class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder]) ).
cnf(f_1237_2,plain,
class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1237_1]) ).
fof(f_1238_1,plain,
class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult]) ).
cnf(f_1238_2,plain,
class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1238_1]) ).
fof(f_1239_1,plain,
class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add]) ).
cnf(f_1239_2,plain,
class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1239_1]) ).
fof(f_1240_1,plain,
class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1]) ).
cnf(f_1240_2,plain,
class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1240_1]) ).
fof(f_1241_1,plain,
class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0]) ).
cnf(f_1241_2,plain,
class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1241_1]) ).
fof(f_1242_1,plain,
class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero]) ).
cnf(f_1242_2,plain,
class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1242_1]) ).
fof(f_1243_1,plain,
class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Oorder]) ).
cnf(f_1243_2,plain,
class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1243_1]) ).
fof(f_1244_1,plain,
class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring]) ).
cnf(f_1244_2,plain,
class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1244_1]) ).
fof(f_1245_1,plain,
class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Oord]) ).
cnf(f_1245_2,plain,
class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1245_1]) ).
fof(f_1246_1,plain,
class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Power_Opower]) ).
cnf(f_1246_2,plain,
class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1246_1]) ).
fof(f_1247_1,plain,
class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ozero]) ).
cnf(f_1247_2,plain,
class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1247_1]) ).
fof(f_1248_1,plain,
class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Int_Onumber]) ).
cnf(f_1248_2,plain,
class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1248_1]) ).
fof(f_1249_1,plain,
class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oone]) ).
cnf(f_1249_2,plain,
class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1249_1]) ).
fof(f_1250_1,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e),
inference(negate,[status(cth)],[conj_0]) ).
cnf(f_1250_2,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v_da____),v_m____),v_e),
inference(clausify,[status(thm)],[f_1250_1]) ).
cnf(f_48_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_48_6]) ).
cnf(f_48_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_48_7]) ).
cnf(f_48_12_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_48_12]) ).
cnf(f_49_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_49_6]) ).
cnf(f_49_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_49_7]) ).
cnf(f_49_12_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_49_12]) ).
cnf(f_62_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_62_5]) ).
cnf(f_63_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_63_5]) ).
cnf(f_171_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_171_6]) ).
cnf(f_171_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_171_7]) ).
cnf(f_171_12_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_171_12]) ).
cnf(f_172_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_172_6]) ).
cnf(f_172_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_172_7]) ).
cnf(f_172_12_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_172_12]) ).
cnf(f_418_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_418_6]) ).
cnf(f_418_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_418_7]) ).
cnf(f_418_12_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_418_12]) ).
cnf(f_419_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_419_6]) ).
cnf(f_419_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_419_7]) ).
cnf(f_419_12_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_419_12]) ).
cnf(f_420_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_420_6]) ).
cnf(f_420_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_420_7]) ).
cnf(f_420_12_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_420_12]) ).
cnf(f_421_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_421_6]) ).
cnf(f_421_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_421_7]) ).
cnf(f_421_12_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_421_12]) ).
cnf(f_436_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_436_5]) ).
cnf(f_437_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_437_5]) ).
cnf(f_438_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_438_5]) ).
cnf(f_439_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_439_5]) ).
cnf(f_441_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_441_6]) ).
cnf(f_441_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_441_7]) ).
cnf(f_441_12_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_441_12]) ).
cnf(f_442_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_442_6]) ).
cnf(f_442_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_442_7]) ).
cnf(f_442_12_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_442_12]) ).
cnf(f_443_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_443_6]) ).
cnf(f_443_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_443_7]) ).
cnf(f_443_12_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_443_12]) ).
cnf(f_444_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_444_6]) ).
cnf(f_444_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_444_7]) ).
cnf(f_444_12_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_444_12]) ).
cnf(f_619_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_619_6]) ).
cnf(f_699_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_699_4]) ).
cnf(f_699_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_699_5]) ).
cnf(f_699_6_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_699_6]) ).
cnf(f_699_7_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_699_7]) ).
cnf(f_699_8_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_699_8]) ).
cnf(f_699_9_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_699_9]) ).
cnf(f_699_10_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_699_10]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( hAPP(Eq_x_0,Eq_x_1) = hAPP(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( c_Groups_Ozero__class_Ozero(Eq_x_0) = c_Groups_Ozero__class_Ozero(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( c_Rings_Oinverse__class_Odivide(Eq_x_0,Eq_x_1,Eq_x_2) = c_Rings_Oinverse__class_Odivide(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,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_8,axiom,
( c_Groups_Otimes__class_Otimes(Eq_x_0,Eq_x_1) = c_Groups_Otimes__class_Otimes(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( 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_10,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_11,axiom,
( c_Rings_Oinverse__class_Oinverse(Eq_x_0,Eq_x_1) = c_Rings_Oinverse__class_Oinverse(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,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_13,axiom,
( c_Int_Onumber__class_Onumber__of(Eq_x_0,Eq_x_1) = c_Int_Onumber__class_Onumber__of(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( c_Int_Osucc(Eq_x_0) = c_Int_Osucc(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,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_16,axiom,
( c_Transcendental_Oexp(Eq_x_0) = c_Transcendental_Oexp(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,axiom,
( c_Int_Opred(Eq_x_0) = c_Int_Opred(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( c_Int_OBit1(Eq_x_0) = c_Int_OBit1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,axiom,
( c_Int_OBit0(Eq_x_0) = c_Int_OBit0(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_20,axiom,
( c_Power_Opower__class_Opower(Eq_x_0,Eq_x_1,Eq_x_2) = c_Power_Opower__class_Opower(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_21,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(Eq_x_0) = c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,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_23,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_24,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_25,axiom,
( sK5(Eq_x_0,Eq_x_1,Eq_x_2) = sK5(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_26,axiom,
( 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_27,axiom,
( sK7(Eq_x_0,Eq_x_1,Eq_x_2) = sK7(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( sK8(Eq_x_0,Eq_x_1,Eq_x_2) = sK8(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_29,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_30,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_31,axiom,
( sK11(Eq_x_0,Eq_x_1,Eq_x_2) = sK11(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_32,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_33,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_34,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_35,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_36,axiom,
( class_Fields_Olinordered__field(Eq_y_0)
| ~ class_Fields_Olinordered__field(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,axiom,
( class_Fields_Olinordered__field__inverse__zero(Eq_y_0)
| ~ class_Fields_Olinordered__field__inverse__zero(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_38,axiom,
( class_Fields_Ofield__inverse__zero(Eq_y_0)
| ~ class_Fields_Ofield__inverse__zero(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,axiom,
( class_Fields_Ofield(Eq_y_0)
| ~ class_Fields_Ofield(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( class_Rings_Odivision__ring(Eq_y_0)
| ~ class_Rings_Odivision__ring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_41,axiom,
( class_Rings_Odivision__ring__inverse__zero(Eq_y_0)
| ~ class_Rings_Odivision__ring__inverse__zero(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_42,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_43,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_44,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_45,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_46,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_47,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_48,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_49,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_50,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_51,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_52,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_53,axiom,
( class_RealVector_Oreal__normed__field(Eq_y_0)
| ~ class_RealVector_Oreal__normed__field(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_54,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_55,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_56,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_57,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_58,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_59,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_60,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_61,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_62,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_63,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_64,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_65,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_66,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_67,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_68,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_69,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_70,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_71,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_72,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_73,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_74,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_75,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_76,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_77,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_78,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_79,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_80,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_81,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_82,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_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_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_85,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_86,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_87,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_88,axiom,
( class_Int_Onumber(Eq_y_0)
| ~ class_Int_Onumber(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_89,axiom,
( c_Deriv_Oderiv(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ c_Deriv_Oderiv(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_90,axiom,
( class_Int_Onumber__ring(Eq_y_0)
| ~ class_Int_Onumber__ring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_91,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_92,axiom,
( class_SEQ_Obanach(Eq_y_0)
| ~ class_SEQ_Obanach(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_93,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_94,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_95,axiom,
( class_Lattices_Oboolean__algebra(Eq_y_0)
| ~ class_Lattices_Oboolean__algebra(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_96,axiom,
( class_Rings_Oidom(Eq_y_0)
| ~ class_Rings_Oidom(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_97,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_98,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_99,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_100,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_101,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_102,axiom,
( c_Int_Oiszero(Eq_y_0,Eq_y_1)
| ~ c_Int_Oiszero(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_103,axiom,
( class_Rings_Osemiring__1(Eq_y_0)
| ~ class_Rings_Osemiring__1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_104,axiom,
( hBOOL(Eq_y_0)
| ~ hBOOL(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_105,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_106,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_107,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_108,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_109,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_110,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW216+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
% 0.08/0.41 % Computer : n010.cluster.edu
% 0.08/0.41 % Model : x86_64 x86_64
% 0.08/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.41 % Memory : 8046.5625MB
% 0.08/0.41 % OS : Linux 6.8.0-71-generic
% 0.08/0.41 % CPULimit : 300
% 0.08/0.41 % WCLimit : 300
% 0.08/0.41 % DateTime : Sun Sep 20 05:10:38 UTC 2026
% 0.08/0.41 % CPUTime :
% 165.19/165.56 % SZS status Theorem for theBenchmark
% 165.19/165.56 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------