%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV677-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 02:49:20 PM UTC 2026
% Result : Unsatisfiable 22.70s 3.56s
% Output : CNFRefutation 1.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 333
% Syntax : Number of formulae : 1138 ( 196 unt; 214 def)
% Number of atoms : 2493 ( 911 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 2333 ( 978 ~;1141 |; 0 &)
% ( 214 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 235 ( 233 usr; 215 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 1384 (1384 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [V_m,V_n,V_k] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [V_x,V_y,V_z] : c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [V_n,V_m] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [T_a,V_a] :
( c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [V_k] : c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_k,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [T_a,V_b,V_a,V_c] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [V_n,V_m] : c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [V_x] :
( ~ c_HOL_Oord__class_Oless(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)
| V_x = c_HOL_Ozero__class_Ozero(tc_nat)
| V_x = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [V_m,V_n] : c_GCD_Ogcd__class_Ogcd(V_m,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) = c_GCD_Ogcd__class_Ogcd(V_m,V_n,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [V_m,V_n] :
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [T_a] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [V_m,V_n] :
( c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)) = V_n
| c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [T_a,V_n] :
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Suc(V_n),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Osemiring__0(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [V_m] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [T_a,V_b,V_a,V_c] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(V_b,V_c,T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [T_a,V_b,V_a,V_c] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [V_n,V_m] :
( ~ c_lessequals(c_Suc(V_n),V_m,tc_nat)
| c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f75,axiom,
! [V_m,V_n] :
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != V_m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f92,axiom,
! [V_m,V_n] :
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat) = V_m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,axiom,
! [V_b,V_a] :
( V_a = V_b
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_a,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f111,axiom,
! [V_a,V_b,V_x] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_x,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat),V_x,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f112,axiom,
! [V_a,V_b,V_x] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_x,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat),V_x,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f118,axiom,
! [V_x] : c_Ring__and__Field_Odvd__class_Odvd(V_x,V_x,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f119,axiom,
! [T_a,V_a] :
( c_Ring__and__Field_Odvd__class_Odvd(V_a,V_a,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f122,axiom,
! [V_x] : c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f126,axiom,
! [T_a,V_n] :
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f133,axiom,
! [V_n] : V_n != c_Suc(V_n),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f159,axiom,
! [V_x,V_y,V_z] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_x,c_GCD_Ogcd__class_Ogcd(V_y,V_z,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f204,axiom,
! [T_a,V_x,V_y] :
( c_lessequals(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f230,axiom,
! [T_a] :
( c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f231,axiom,
! [T_a,V_a] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f239,axiom,
! [V_n,V_m] :
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f240,axiom,
! [V_m,V_n] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f252,axiom,
! [V_m,V_n] :
( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f264,axiom,
! [V_a,V_b] :
( V_b = c_HOL_Ozero__class_Ozero(tc_nat)
| c_lessequals(c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat),V_b,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f268,axiom,
! [V_n,V_m] :
( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f292,axiom,
! [V_m,V_n] : c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f301,axiom,
! [V_m] : ~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f321,axiom,
! [T_a,V_b,V_a,V_c] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(V_b,V_c,T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f322,axiom,
! [V_x] : c_GCD_Ogcd__class_Ogcd(V_x,V_x,tc_nat) = V_x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f339,axiom,
! [T_a] :
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Osemiring__0(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f346,axiom,
! [T_a,V_a] :
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f354,axiom,
! [T_a,V_x] :
( c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f360,axiom,
! [T_a,V_a,V_b] :
( V_a = V_b
| c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f367,axiom,
! [T_a,V_a,V_n] :
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f372,axiom,
! [T_a,V_a] :
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f376,axiom,
! [T_a,V_a,V_b,V_c] :
( c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f384,axiom,
! [V_x,V_y] :
( ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
| c_lessequals(V_x,V_y,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f392,axiom,
! [V_m,V_n] :
( ~ c_lessequals(V_m,V_n,tc_nat)
| V_m = V_n
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f398,axiom,
! [V_n] :
( ~ c_lessequals(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f405,axiom,
! [V_n] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f408,axiom,
! [V_m,V_n] : c_lessequals(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_m,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f412,axiom,
! [V_j,V_n,V_k] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f414,axiom,
! [V_l,V_n,V_m] :
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_l,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_l,V_n,tc_nat),c_HOL_Ominus__class_Ominus(V_l,V_m,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f415,axiom,
! [V_k,V_m,V_n] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f416,axiom,
! [V_m,V_k,V_n] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f418,axiom,
! [V_n,V_m] :
( V_m = V_n
| c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f419,axiom,
! [V_k,V_m,V_n] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f420,axiom,
! [V_m] : c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f421,axiom,
! [V_m] : c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f422,axiom,
! [V_i,V_j,V_k] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat) = c_HOL_Ominus__class_Ominus(V_i,c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f423,axiom,
! [V_n] : c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f424,axiom,
! [V_n,V_m] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_n,tc_nat) = V_m,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f425,axiom,
! [V_m,V_n] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_n,tc_nat) = V_m,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f426,axiom,
( v_a != c_HOL_Ozero__class_Ozero(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f441,axiom,
! [V_m,V_n] :
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f455,axiom,
! [T_a,V_a] :
( c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f457,axiom,
! [T_a,V_a] :
( c_Divides_Odiv__class_Omod(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f458,axiom,
! [V_k,V_n] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f459,axiom,
! [V_k,V_n] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f462,axiom,
! [V_n] : ~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f470,axiom,
! [V_n,V_m] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_n,V_m,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f471,axiom,
! [V_i,V_k,V_j,V_l] :
( ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_l,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f480,axiom,
! [T_a] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f492,axiom,
! [V_i,V_j] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_i,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f493,axiom,
! [V_i,V_j,V_k] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat)
| c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f494,axiom,
! [V_i,V_k,V_j] :
( ~ c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f495,axiom,
! [V_x,V_y] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)
| c_GCD_Ogcd__class_Ogcd(V_x,V_y,tc_nat) = V_y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f496,axiom,
! [V_x,V_y] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
| c_GCD_Ogcd__class_Ogcd(V_x,V_y,tc_nat) = V_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f522,axiom,
! [V_n,V_m] :
( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| c_HOL_Oplus__class_Oplus(V_n,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) = V_m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f552,axiom,
! [T_a,V_x] :
( c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f555,axiom,
! [T_a,V_a,V_b] :
( V_a = V_b
| V_b = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f556,axiom,
! [T_a,V_a] :
( c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f558,axiom,
! [T_a,V_x] :
( c_HOL_Oinverse__class_Odivide(V_x,V_x,T_a) = c_HOL_Oone__class_Oone(T_a)
| V_x = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f564,axiom,
! [T_a,V_a,V_b,V_n] :
( V_b = c_HOL_Ozero__class_Ozero(T_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f568,axiom,
! [T_a,V_a,V_n,V_m] :
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_lessequals(V_m,V_n,tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f582,axiom,
! [V_m,V_n] :
( c_lessequals(V_m,V_n,tc_nat)
| c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f583,axiom,
! [V_m,V_n] :
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f593,axiom,
! [V_m,V_n,V_k] :
( ~ c_lessequals(V_k,V_n,tc_nat)
| c_lessequals(V_m,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_k,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f603,axiom,
! [T_a,V_a,V_m,V_n] :
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_lessequals(V_n,V_m,tc_nat)
| c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f604,axiom,
! [V_n,V_m] :
( c_lessequals(V_m,V_n,tc_nat)
| c_lessequals(V_n,V_m,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f608,axiom,
! [V_n] : c_lessequals(V_n,V_n,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f614,axiom,
! [T_a,V_n] :
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a)
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f616,axiom,
! [T_a,V_a] :
( c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f621,axiom,
! [V_m,V_n] :
( ~ c_lessequals(V_m,V_n,tc_nat)
| ~ c_lessequals(V_n,V_m,tc_nat)
| V_m = V_n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f635,axiom,
! [V_m,V_n] : c_lessequals(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f638,negated_conjecture,
class_Ring__and__Field_Ofield(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f639,negated_conjecture,
( c_lessequals(v_n,v_m,tc_nat)
| c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f640,negated_conjecture,
( ~ c_lessequals(v_n,v_m,tc_nat)
| c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f645,axiom,
! [T] :
( class_Ring__and__Field_Ono__zero__divisors(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f646,axiom,
! [T] :
( class_Ring__and__Field_Ocomm__semiring__1(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f650,axiom,
! [T] :
( class_Ring__and__Field_Ozero__neq__one(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f654,axiom,
! [T] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f655,axiom,
! [T] :
( class_Ring__and__Field_Omult__zero(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f656,axiom,
! [T] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f661,axiom,
! [T] :
( class_Power_Opower(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f663,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f665,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f668,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f669,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f670,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f672,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f673,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f675,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f676,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f679,axiom,
class_Divides_Osemiring__div(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f680,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f682,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f684,axiom,
class_Power_Opower(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f691,plain,
! [X0,X1,X2] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f692,plain,
! [X0,X1,X2] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f703,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f704,plain,
! [T_a] :
( ! [V_a] : c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f705,plain,
! [X0,X1] :
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) != c_HOL_Ozero__class_Ozero(X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
inference(cnf_transformation,[status(thm)],[f704]) ).
fof(f706,plain,
! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f711,plain,
! [T_a,V_a] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ! [V_b,V_c] :
( ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f712,plain,
! [X0,X1,X2,X3] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) ),
inference(cnf_transformation,[status(thm)],[f711]) ).
fof(f713,plain,
! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f716,plain,
! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)
| X0 = c_HOL_Ozero__class_Ozero(tc_nat)
| X0 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f723,plain,
! [X0,X1] : c_GCD_Ogcd__class_Ogcd(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) = c_GCD_Ogcd__class_Ogcd(X0,X1,tc_nat),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f738,plain,
! [V_n] :
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| ! [V_m] : c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(miniscoping,[status(thm)],[f37]) ).
fof(f739,plain,
! [X0,X1] :
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(cnf_transformation,[status(thm)],[f738]) ).
fof(f752,plain,
! [X0] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) = c_HOL_Ozero__class_Ozero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X0) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f755,plain,
! [X0,X1] :
( c_Suc(c_Divides_Odiv__class_Omod(X0,X1,tc_nat)) = X1
| c_Divides_Odiv__class_Omod(c_Suc(X0),X1,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X0,X1,tc_nat)) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f760,plain,
! [T_a] :
( ! [V_n] : c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Suc(V_n),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Osemiring__0(T_a) ),
inference(miniscoping,[status(thm)],[f51]) ).
fof(f761,plain,
! [X0,X1] :
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),c_Suc(X1),X0) = c_HOL_Ozero__class_Ozero(X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Osemiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f760]) ).
fof(f762,plain,
! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X0),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f767,plain,
! [T_a,V_a] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ! [V_b,V_c] :
( ~ c_lessequals(V_b,V_c,T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ) ),
inference(miniscoping,[status(thm)],[f57]) ).
fof(f768,plain,
! [X0,X1,X2,X3] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(X1,X3,X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) ),
inference(cnf_transformation,[status(thm)],[f767]) ).
fof(f769,plain,
! [T_a,V_c] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ! [V_b,V_a] :
( ~ c_lessequals(V_b,V_a,T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ) ),
inference(miniscoping,[status(thm)],[f58]) ).
fof(f770,plain,
! [X0,X1,X2,X3] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) ),
inference(cnf_transformation,[status(thm)],[f769]) ).
fof(f771,plain,
! [X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f797,plain,
! [V_n] :
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| ! [V_m] : c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != V_m ),
inference(miniscoping,[status(thm)],[f75]) ).
fof(f798,plain,
! [X0,X1] :
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != X0 ),
inference(cnf_transformation,[status(thm)],[f797]) ).
fof(f823,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0 ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f827,plain,
! [X0,X1] :
( X1 = X0
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X0,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f848,plain,
! [V_a,V_x] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_x,tc_nat)
| ! [V_b] : c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat),V_x,tc_nat) ),
inference(miniscoping,[status(thm)],[f111]) ).
fof(f849,plain,
! [X0,X1,X2] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(X0,X1,tc_nat),X2,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f848]) ).
fof(f850,plain,
! [V_b,V_x] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_x,tc_nat)
| ! [V_a] : c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat),V_x,tc_nat) ),
inference(miniscoping,[status(thm)],[f112]) ).
fof(f851,plain,
! [X0,X1,X2] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(X0,X1,tc_nat),X2,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f850]) ).
fof(f862,plain,
! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_nat),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f863,plain,
! [T_a] :
( ! [V_a] : c_Ring__and__Field_Odvd__class_Odvd(V_a,V_a,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f864,plain,
! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(thm)],[f863]) ).
fof(f869,plain,
! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(X0),tc_nat),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f874,plain,
! [V_n] :
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| ! [T_a] :
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ) ),
inference(miniscoping,[status(thm)],[f126]) ).
fof(f875,plain,
! [X0,X1] :
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X1,X0) = c_HOL_Ozero__class_Ozero(X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
inference(cnf_transformation,[status(thm)],[f874]) ).
fof(f886,plain,
! [X0] : X0 != c_Suc(X0),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f928,plain,
! [V_x,V_y] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)
| ! [V_z] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_x,c_GCD_Ogcd__class_Ogcd(V_y,V_z,tc_nat),tc_nat) ) ),
inference(miniscoping,[status(thm)],[f159]) ).
fof(f929,plain,
! [X0,X1,X2] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_GCD_Ogcd__class_Ogcd(X1,X2,tc_nat),tc_nat) ),
inference(cnf_transformation,[status(thm)],[f928]) ).
fof(f999,plain,
! [X0,X1,X2] :
( c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f1040,plain,
! [X0] :
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f1041,plain,
! [T_a] :
( ! [V_a] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(miniscoping,[status(thm)],[f231]) ).
fof(f1042,plain,
! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(thm)],[f1041]) ).
fof(f1055,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
inference(cnf_transformation,[status(thm)],[f239]) ).
fof(f1056,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f240]) ).
fof(f1074,plain,
! [V_m] :
( V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| ! [V_n] :
( V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
inference(miniscoping,[status(thm)],[f252]) ).
fof(f1075,plain,
! [X0,X1] :
( X0 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(cnf_transformation,[status(thm)],[f1074]) ).
fof(f1094,plain,
! [V_b] :
( V_b = c_HOL_Ozero__class_Ozero(tc_nat)
| ! [V_a] : c_lessequals(c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat),V_b,tc_nat) ),
inference(miniscoping,[status(thm)],[f264]) ).
fof(f1095,plain,
! [X0,X1] :
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_lessequals(c_GCD_Ogcd__class_Ogcd(X0,X1,tc_nat),X1,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f1094]) ).
fof(f1100,plain,
! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ),
inference(cnf_transformation,[status(thm)],[f268]) ).
fof(f1141,plain,
! [X0,X1] : c_HOL_Oplus__class_Oplus(c_Suc(X0),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_Suc(X1),tc_nat),
inference(cnf_transformation,[status(thm)],[f292]) ).
fof(f1156,plain,
! [X0] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(cnf_transformation,[status(thm)],[f301]) ).
fof(f1179,plain,
! [T_a,V_a] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ! [V_b,V_c] :
( ~ c_lessequals(V_b,V_c,T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) ) ),
inference(miniscoping,[status(thm)],[f321]) ).
fof(f1180,plain,
! [X0,X1,X2,X3] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_lessequals(X1,X3,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) ),
inference(cnf_transformation,[status(thm)],[f1179]) ).
fof(f1181,plain,
! [X0] : c_GCD_Ogcd__class_Ogcd(X0,X0,tc_nat) = X0,
inference(cnf_transformation,[status(thm)],[f322]) ).
fof(f1206,plain,
! [X0] :
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(tc_nat),X0) = c_HOL_Oone__class_Oone(X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Osemiring__0(X0) ),
inference(cnf_transformation,[status(thm)],[f339]) ).
fof(f1213,plain,
! [X0,X1] :
( X1 = c_HOL_Ozero__class_Ozero(X0)
| c_HOL_Oinverse__class_Oinverse(X1,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f346]) ).
fof(f1227,plain,
! [T_a] :
( ! [V_x] : c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(miniscoping,[status(thm)],[f354]) ).
fof(f1228,plain,
! [X0,X1] :
( c_HOL_Ominus__class_Ominus(X1,X1,X0) = c_HOL_Ozero__class_Ozero(X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f1227]) ).
fof(f1239,plain,
! [V_a,V_b] :
( V_a = V_b
| ! [T_a] :
( c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ) ),
inference(miniscoping,[status(thm)],[f360]) ).
fof(f1240,plain,
! [X0,X1,X2] :
( X1 = X2
| c_HOL_Ominus__class_Ominus(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f1239]) ).
fof(f1253,plain,
! [T_a,V_a] :
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| ! [V_n] : c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Power_Opower(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(miniscoping,[status(thm)],[f367]) ).
fof(f1254,plain,
! [X0,X1,X2] :
( X1 = c_HOL_Ozero__class_Ozero(X0)
| c_Power_Opower__class_Opower(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0)
| ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
inference(cnf_transformation,[status(thm)],[f1253]) ).
fof(f1262,plain,
! [T_a] :
( ! [V_a] : c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
inference(miniscoping,[status(thm)],[f372]) ).
fof(f1263,plain,
! [X0,X1] :
( c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X1,X0) = c_HOL_Ozero__class_Ozero(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f1262]) ).
fof(f1270,plain,
! [T_a] :
( ! [V_a,V_b,V_c] : c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
inference(miniscoping,[status(thm)],[f376]) ).
fof(f1271,plain,
! [X0,X1,X2,X3] :
( c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),X3,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X3,X0),c_HOL_Oinverse__class_Odivide(X2,X3,X0),X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f1270]) ).
fof(f1280,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X0,X1,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f1289,plain,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| X0 = X1
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f392]) ).
fof(f1298,plain,
! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| X0 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(cnf_transformation,[status(thm)],[f398]) ).
fof(f1311,plain,
! [X0] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),
inference(cnf_transformation,[status(thm)],[f405]) ).
fof(f1314,plain,
! [X0,X1] : c_lessequals(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X0,tc_nat),
inference(cnf_transformation,[status(thm)],[f408]) ).
fof(f1320,plain,
! [V_j,V_k] :
( ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| ! [V_n] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat) ),
inference(miniscoping,[status(thm)],[f412]) ).
fof(f1321,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f1320]) ).
fof(f1323,plain,
! [V_n,V_m] :
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ! [V_l] :
( ~ c_HOL_Oord__class_Oless(V_m,V_l,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_l,V_n,tc_nat),c_HOL_Ominus__class_Ominus(V_l,V_m,tc_nat),tc_nat) ) ),
inference(miniscoping,[status(thm)],[f414]) ).
fof(f1324,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat) ),
inference(cnf_transformation,[status(thm)],[f1323]) ).
fof(f1325,plain,
! [X0,X1,X2] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),
inference(cnf_transformation,[status(thm)],[f415]) ).
fof(f1326,plain,
! [X0,X1,X2] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f1328,plain,
! [X0,X1] :
( X1 = X0
| c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f1329,plain,
! [V_k,V_m] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,tc_nat)
| ! [V_n] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat) ) ),
inference(miniscoping,[status(thm)],[f419]) ).
fof(f1330,plain,
! [X0,X1,X2] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X2,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
inference(cnf_transformation,[status(thm)],[f1329]) ).
fof(f1331,plain,
! [X0] : c_HOL_Ominus__class_Ominus(X0,X0,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f1332,plain,
! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0,
inference(cnf_transformation,[status(thm)],[f421]) ).
fof(f1333,plain,
! [X0,X1,X2] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),
inference(cnf_transformation,[status(thm)],[f422]) ).
fof(f1334,plain,
! [X0] : c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(cnf_transformation,[status(thm)],[f423]) ).
fof(f1335,plain,
! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat) = X1,
inference(cnf_transformation,[status(thm)],[f424]) ).
fof(f1336,plain,
! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat) = X0,
inference(cnf_transformation,[status(thm)],[f425]) ).
fof(f1337,plain,
( v_a != c_HOL_Ozero__class_Ozero(t_a)
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(cnf_transformation,[status(thm)],[f426]) ).
fof(f1357,plain,
! [V_n] :
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| ! [V_m] :
( V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) ) ),
inference(miniscoping,[status(thm)],[f441]) ).
fof(f1358,plain,
! [X0,X1] :
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X0 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f1357]) ).
fof(f1377,plain,
! [T_a] :
( ! [V_a] : c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(miniscoping,[status(thm)],[f455]) ).
fof(f1378,plain,
! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(thm)],[f1377]) ).
fof(f1380,plain,
! [T_a] :
( ! [V_a] : c_Divides_Odiv__class_Omod(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Divides_Osemiring__div(T_a) ),
inference(miniscoping,[status(thm)],[f457]) ).
fof(f1381,plain,
! [X0,X1] :
( c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Ozero__class_Ozero(X0)
| ~ class_Divides_Osemiring__div(X0) ),
inference(cnf_transformation,[status(thm)],[f1380]) ).
fof(f1382,plain,
! [X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) ),
inference(cnf_transformation,[status(thm)],[f458]) ).
fof(f1383,plain,
! [X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f459]) ).
fof(f1387,plain,
! [X0] : ~ c_HOL_Oord__class_Oless(X0,X0,tc_nat),
inference(cnf_transformation,[status(thm)],[f462]) ).
fof(f1398,plain,
! [V_m] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)
| ! [V_n] :
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_n,V_m,tc_nat) ) ),
inference(miniscoping,[status(thm)],[f470]) ).
fof(f1399,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f1398]) ).
fof(f1400,plain,
! [V_i,V_j] :
( ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat)
| ! [V_k,V_l] :
( ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_l,tc_nat),tc_nat) ) ),
inference(miniscoping,[status(thm)],[f471]) ).
fof(f1401,plain,
! [X0,X1,X2,X3] :
( ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) ),
inference(cnf_transformation,[status(thm)],[f1400]) ).
fof(f1412,plain,
! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(cnf_transformation,[status(thm)],[f480]) ).
fof(f1426,plain,
! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat),
inference(cnf_transformation,[status(thm)],[f492]) ).
fof(f1427,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
inference(cnf_transformation,[status(thm)],[f493]) ).
fof(f1428,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f494]) ).
fof(f1429,plain,
! [X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X0,tc_nat)
| c_GCD_Ogcd__class_Ogcd(X0,X1,tc_nat) = X1 ),
inference(cnf_transformation,[status(thm)],[f495]) ).
fof(f1430,plain,
! [X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat)
| c_GCD_Ogcd__class_Ogcd(X0,X1,tc_nat) = X0 ),
inference(cnf_transformation,[status(thm)],[f496]) ).
fof(f1473,plain,
! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) = X1 ),
inference(cnf_transformation,[status(thm)],[f522]) ).
fof(f1522,plain,
! [T_a] :
( ! [V_x] : c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(miniscoping,[status(thm)],[f552]) ).
fof(f1523,plain,
! [X0,X1] :
( c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) = c_HOL_Oone__class_Oone(X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(thm)],[f1522]) ).
fof(f1528,plain,
! [V_a,V_b] :
( V_a = V_b
| ! [T_a] :
( V_b = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ) ),
inference(miniscoping,[status(thm)],[f555]) ).
fof(f1529,plain,
! [X0,X1,X2] :
( X1 = X2
| X2 = c_HOL_Ozero__class_Ozero(X0)
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) != c_HOL_Oone__class_Oone(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f1528]) ).
fof(f1530,plain,
! [T_a] :
( ! [V_a] : c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
inference(miniscoping,[status(thm)],[f556]) ).
fof(f1531,plain,
! [X0,X1] :
( c_HOL_Oinverse__class_Oinverse(X1,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f1530]) ).
fof(f1534,plain,
! [X0,X1] :
( c_HOL_Oinverse__class_Odivide(X1,X1,X0) = c_HOL_Oone__class_Oone(X0)
| X1 = c_HOL_Ozero__class_Ozero(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f558]) ).
fof(f1542,plain,
! [T_a,V_b] :
( V_b = c_HOL_Ozero__class_Ozero(T_a)
| ! [V_a,V_n] : c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ),
inference(miniscoping,[status(thm)],[f564]) ).
fof(f1543,plain,
! [X0,X1,X2,X3] :
( X2 = c_HOL_Ozero__class_Ozero(X0)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X3,X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X2,X3,X0),X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f1542]) ).
fof(f1550,plain,
! [T_a,V_a] :
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| ! [V_n,V_m] :
( ~ c_lessequals(V_m,V_n,tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ) ),
inference(miniscoping,[status(thm)],[f568]) ).
fof(f1551,plain,
! [X0,X1,X2,X3] :
( X1 = c_HOL_Ozero__class_Ozero(X0)
| ~ c_lessequals(X3,X2,tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X1,X2,X0),X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f1550]) ).
fof(f1570,plain,
! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(cnf_transformation,[status(thm)],[f582]) ).
fof(f1571,plain,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(cnf_transformation,[status(thm)],[f583]) ).
fof(f1586,plain,
! [V_n,V_k] :
( ~ c_lessequals(V_k,V_n,tc_nat)
| ! [V_m] : c_lessequals(V_m,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_k,tc_nat),tc_nat) ),
inference(miniscoping,[status(thm)],[f593]) ).
fof(f1587,plain,
! [X0,X1,X2] :
( ~ c_lessequals(X2,X1,tc_nat)
| c_lessequals(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X2,tc_nat),tc_nat) ),
inference(cnf_transformation,[status(thm)],[f1586]) ).
fof(f1602,plain,
! [T_a,V_a] :
( V_a = c_HOL_Ozero__class_Ozero(T_a)
| ! [V_m,V_n] :
( ~ c_lessequals(V_n,V_m,tc_nat)
| c_Power_Opower__class_Opower(V_a,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
| ~ class_Ring__and__Field_Ofield(T_a) ) ),
inference(miniscoping,[status(thm)],[f603]) ).
fof(f1603,plain,
! [X0,X1,X2,X3] :
( X1 = c_HOL_Ozero__class_Ozero(X0)
| ~ c_lessequals(X3,X2,tc_nat)
| c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,X3,X0),X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f1602]) ).
fof(f1604,plain,
! [X0,X1] :
( c_lessequals(X1,X0,tc_nat)
| c_lessequals(X0,X1,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f604]) ).
fof(f1610,plain,
! [X0] : c_lessequals(X0,X0,tc_nat),
inference(cnf_transformation,[status(thm)],[f608]) ).
fof(f1620,plain,
! [T_a] :
( ! [V_n] : c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a)
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
inference(miniscoping,[status(thm)],[f614]) ).
fof(f1621,plain,
! [X0,X1] :
( c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X1,X0) = c_HOL_Oone__class_Oone(X0)
| ~ class_OrderedGroup_Omonoid__mult(X0) ),
inference(cnf_transformation,[status(thm)],[f1620]) ).
fof(f1624,plain,
! [T_a] :
( ! [V_a] : c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a
| ~ class_Ring__and__Field_Ofield(T_a) ),
inference(miniscoping,[status(thm)],[f616]) ).
fof(f1625,plain,
! [X0,X1] :
( c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(X0),X0) = X1
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f1624]) ).
fof(f1632,plain,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X1,X0,tc_nat)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f621]) ).
fof(f1657,plain,
! [X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat),
inference(cnf_transformation,[status(thm)],[f635]) ).
fof(f1661,plain,
class_Ring__and__Field_Ofield(t_a),
inference(cnf_transformation,[status(thm)],[f638]) ).
fof(f1662,plain,
( c_lessequals(v_n,v_m,tc_nat)
| c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) ),
inference(cnf_transformation,[status(thm)],[f639]) ).
fof(f1663,plain,
( ~ c_lessequals(v_n,v_m,tc_nat)
| c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a) ),
inference(cnf_transformation,[status(thm)],[f640]) ).
fof(f1668,plain,
! [X0] :
( class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f645]) ).
fof(f1669,plain,
! [X0] :
( class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f646]) ).
fof(f1673,plain,
! [X0] :
( class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f650]) ).
fof(f1677,plain,
! [X0] :
( class_OrderedGroup_Oab__group__add(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f654]) ).
fof(f1678,plain,
! [X0] :
( class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f655]) ).
fof(f1679,plain,
! [X0] :
( class_OrderedGroup_Omonoid__mult(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f656]) ).
fof(f1684,plain,
! [X0] :
( class_Power_Opower(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(thm)],[f661]) ).
fof(f1686,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
inference(cnf_transformation,[status(thm)],[f663]) ).
fof(f1688,plain,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
inference(cnf_transformation,[status(thm)],[f665]) ).
fof(f1691,plain,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
inference(cnf_transformation,[status(thm)],[f668]) ).
fof(f1692,plain,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(cnf_transformation,[status(thm)],[f669]) ).
fof(f1693,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(cnf_transformation,[status(thm)],[f670]) ).
fof(f1695,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(cnf_transformation,[status(thm)],[f672]) ).
fof(f1696,plain,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
inference(cnf_transformation,[status(thm)],[f673]) ).
fof(f1698,plain,
class_Ring__and__Field_Osemiring__0(tc_nat),
inference(cnf_transformation,[status(thm)],[f675]) ).
fof(f1699,plain,
class_Ring__and__Field_Omult__zero(tc_nat),
inference(cnf_transformation,[status(thm)],[f676]) ).
fof(f1702,plain,
class_Divides_Osemiring__div(tc_nat),
inference(cnf_transformation,[status(thm)],[f679]) ).
fof(f1703,plain,
class_Nat_Osemiring__char__0(tc_nat),
inference(cnf_transformation,[status(thm)],[f680]) ).
fof(f1705,plain,
class_Orderings_Olinorder(tc_nat),
inference(cnf_transformation,[status(thm)],[f682]) ).
fof(f1707,plain,
class_Power_Opower(tc_nat),
inference(cnf_transformation,[status(thm)],[f684]) ).
fof(f1708,definition,
( sQ0_spl
<=> class_Ring__and__Field_Ofield(t_a) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f1710,plain,
( sQ0_spl
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(component_clause,[status(thm)],[f1708]) ).
fof(f1711,definition,
( sQ1_spl
<=> v_a = c_HOL_Ozero__class_Ozero(t_a) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f1713,plain,
( sQ1_spl
| v_a != c_HOL_Ozero__class_Ozero(t_a) ),
inference(component_clause,[status(thm)],[f1711]) ).
fof(f1714,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1337,f1708,f1711]) ).
fof(f1715,definition,
( sQ2_spl
<=> c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f1717,plain,
( sQ2_spl
| c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) ),
inference(component_clause,[status(thm)],[f1715]) ).
fof(f1718,definition,
( sQ3_spl
<=> c_lessequals(v_n,v_m,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1720,plain,
( sQ3_spl
| ~ c_lessequals(v_n,v_m,tc_nat) ),
inference(component_clause,[status(thm)],[f1718]) ).
fof(f1721,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1662,f1715,f1718]) ).
fof(f1722,definition,
( sQ4_spl
<=> c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) = c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f1724,plain,
( sQ4_spl
| c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(v_a,c_HOL_Ominus__class_Ominus(v_m,v_n,tc_nat),t_a) ),
inference(component_clause,[status(thm)],[f1722]) ).
fof(f1725,plain,
( ~ sQ3_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1663,f1722,f1718]) ).
fof(f1727,plain,
! [X0] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) = c_HOL_Ozero__class_Ozero(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f752]) ).
fof(f1728,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1710,f1661]) ).
fof(f1729,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f1728]) ).
fof(f1732,plain,
! [X0] : c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(t_a),t_a) = X0,
inference(resolution,[status(thm)],[f1625,f1661]) ).
fof(f1736,plain,
! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = X0,
inference(paramodulation,[status(thm)],[f1332,f1335]) ).
fof(f1738,plain,
! [X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat),
inference(paramodulation,[status(thm)],[f1335,f1657]) ).
fof(f1758,plain,
! [X0,X1,X2] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(paramodulation,[status(thm)],[f691,f713]) ).
fof(f1785,plain,
! [X0,X1,X2] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(paramodulation,[status(thm)],[f692,f713]) ).
fof(f1800,plain,
! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0,
inference(paramodulation,[status(thm)],[f1332,f1336]) ).
fof(f1808,plain,
! [X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat),
inference(paramodulation,[status(thm)],[f1336,f1657]) ).
fof(f1815,plain,
! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),
inference(paramodulation,[status(thm)],[f1800,f692]) ).
fof(f1821,plain,
! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),
inference(forward_demodulation,[status(thm)],[f1800,f1815]) ).
fof(f1859,plain,
! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(paramodulation,[status(thm)],[f1821,f713]) ).
fof(f1875,plain,
! [X0] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oinverse__class_Oinverse(X0,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),X0,t_a) ),
inference(resolution,[status(thm)],[f1213,f1661]) ).
fof(f1880,plain,
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a) = c_HOL_Oone__class_Oone(t_a) ),
inference(paramodulation,[status(thm)],[f1732,f1875]) ).
fof(f1881,plain,
( sQ2_spl
| v_a = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) ),
inference(paramodulation,[status(thm)],[f1875,f1717]) ).
fof(f1883,definition,
( sQ5_spl
<=> c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a) = c_HOL_Oone__class_Oone(t_a) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f1886,definition,
( sQ6_spl
<=> c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f1887,plain,
( ~ sQ6_spl
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a) ),
inference(component_clause,[status(thm)],[f1886]) ).
fof(f1889,plain,
( sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f1880,f1883,f1886]) ).
fof(f1890,definition,
( sQ7_spl
<=> c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f1892,plain,
( sQ7_spl
| c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_m,t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) ),
inference(component_clause,[status(thm)],[f1890]) ).
fof(f1893,plain,
( sQ2_spl
| sQ1_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1881,f1890,f1711,f1715]) ).
fof(f1895,plain,
! [X0] : c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(t_a),X0,t_a) = c_HOL_Ozero__class_Ozero(t_a),
inference(resolution,[status(thm)],[f1263,f1661]) ).
fof(f1906,plain,
! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat)
| ~ c_lessequals(X0,X1,tc_nat)
| X0 = X1 ),
inference(resolution,[status(thm)],[f1289,f1055]) ).
fof(f1907,plain,
class_Ring__and__Field_Ocomm__semiring__1(t_a),
inference(resolution,[status(thm)],[f1669,f1661]) ).
fof(f1916,plain,
! [X0] :
( c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Power_Opower(tc_nat)
| ~ class_Ring__and__Field_Ono__zero__divisors(tc_nat)
| ~ class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
inference(resolution,[status(thm)],[f705,f1699]) ).
fof(f1918,definition,
( sQ8_spl
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f1920,plain,
( sQ8_spl
| ~ class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
inference(component_clause,[status(thm)],[f1918]) ).
fof(f1921,definition,
( sQ9_spl
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f1923,plain,
( sQ9_spl
| ~ class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
inference(component_clause,[status(thm)],[f1921]) ).
fof(f1924,definition,
( sQ10_spl
<=> class_Power_Opower(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f1926,plain,
( sQ10_spl
| ~ class_Power_Opower(tc_nat) ),
inference(component_clause,[status(thm)],[f1924]) ).
fof(f1927,definition,
! [X0] :
( sQ11_spl
<=> c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f1928,plain,
! [X0] :
( ~ sQ11_spl
| c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(component_clause,[status(thm)],[f1927]) ).
fof(f1930,plain,
( sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1916,f1918,f1921,f1924,f1927]) ).
fof(f1931,definition,
( sQ12_spl
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f1933,plain,
( sQ12_spl
| ~ class_Ring__and__Field_Omult__zero(tc_nat) ),
inference(component_clause,[status(thm)],[f1931]) ).
fof(f2012,plain,
! [X0] : c_HOL_Oinverse__class_Oinverse(X0,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),X0,t_a),
inference(resolution,[status(thm)],[f1531,f1661]) ).
fof(f2013,plain,
! [X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| X0 = c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) ),
inference(resolution,[status(thm)],[f1632,f1657]) ).
fof(f2018,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| ~ c_lessequals(X0,X1,tc_nat)
| X0 = X1 ),
inference(resolution,[status(thm)],[f1632,f1280]) ).
fof(f2023,definition,
( sQ13_spl
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f2036,plain,
! [X0,X1,X2] : c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X0,X1,t_a),X2,t_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X0,X2,t_a),c_HOL_Oinverse__class_Odivide(X1,X2,t_a),t_a),
inference(resolution,[status(thm)],[f1271,f1661]) ).
fof(f2039,plain,
class_OrderedGroup_Oab__group__add(t_a),
inference(resolution,[status(thm)],[f1677,f1661]) ).
fof(f2190,plain,
! [X0] :
( c_HOL_Oinverse__class_Odivide(X0,X0,t_a) = c_HOL_Oone__class_Oone(t_a)
| X0 = c_HOL_Ozero__class_Ozero(t_a) ),
inference(resolution,[status(thm)],[f1534,f1661]) ).
fof(f2204,plain,
( c_HOL_Ozero__class_Ozero(t_a) = c_HOL_Oone__class_Oone(t_a)
| c_HOL_Ozero__class_Ozero(t_a) = c_HOL_Ozero__class_Ozero(t_a) ),
inference(paramodulation,[status(thm)],[f1895,f2190]) ).
fof(f2206,plain,
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Oone__class_Oone(t_a)
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a) ),
inference(paramodulation,[status(thm)],[f1732,f2190]) ).
fof(f2210,plain,
! [X0,X1] :
( X1 = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X0,X1,t_a),X1,t_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X0,X1,t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
inference(paramodulation,[status(thm)],[f2190,f2036]) ).
fof(f2211,plain,
! [X0,X1] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X0,X1,t_a),X0,t_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(t_a),c_HOL_Oinverse__class_Odivide(X1,X0,t_a),t_a) ),
inference(paramodulation,[status(thm)],[f2190,f2036]) ).
fof(f2212,definition,
( sQ15_spl
<=> c_HOL_Ozero__class_Ozero(t_a) = c_HOL_Ozero__class_Ozero(t_a) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f2215,plain,
( sQ6_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f2204,f2212,f1886]) ).
fof(f2217,definition,
( sQ16_spl
<=> c_HOL_Oone__class_Oone(t_a) = c_HOL_Oone__class_Oone(t_a) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f2220,plain,
( sQ16_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f2206,f1886,f2217]) ).
fof(f2228,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f1324,f703]) ).
fof(f2231,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) ),
inference(forward_demodulation,[status(thm)],[f1332,f2228]) ).
fof(f2232,plain,
class_Ring__and__Field_Omult__zero(t_a),
inference(resolution,[status(thm)],[f1678,f1661]) ).
fof(f2233,plain,
! [X0] :
( c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),t_a) != c_HOL_Ozero__class_Ozero(t_a)
| ~ class_Power_Opower(t_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(t_a)
| ~ class_Ring__and__Field_Ozero__neq__one(t_a) ),
inference(resolution,[status(thm)],[f2232,f705]) ).
fof(f2234,definition,
( sQ17_spl
<=> class_Ring__and__Field_Ozero__neq__one(t_a) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f2236,plain,
( sQ17_spl
| ~ class_Ring__and__Field_Ozero__neq__one(t_a) ),
inference(component_clause,[status(thm)],[f2234]) ).
fof(f2237,definition,
( sQ18_spl
<=> class_Ring__and__Field_Ono__zero__divisors(t_a) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f2239,plain,
( sQ18_spl
| ~ class_Ring__and__Field_Ono__zero__divisors(t_a) ),
inference(component_clause,[status(thm)],[f2237]) ).
fof(f2240,definition,
( sQ19_spl
<=> class_Power_Opower(t_a) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f2242,plain,
( sQ19_spl
| ~ class_Power_Opower(t_a) ),
inference(component_clause,[status(thm)],[f2240]) ).
fof(f2243,definition,
! [X0] :
( sQ20_spl
<=> c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),t_a) != c_HOL_Ozero__class_Ozero(t_a) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f2244,plain,
! [X0] :
( ~ sQ20_spl
| c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),t_a) != c_HOL_Ozero__class_Ozero(t_a) ),
inference(component_clause,[status(thm)],[f2243]) ).
fof(f2246,plain,
( sQ20_spl
| ~ sQ19_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f2233,f2234,f2237,f2240,f2243]) ).
fof(f2247,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1923,f1691]) ).
fof(f2248,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f2247]) ).
fof(f2249,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1920,f1696]) ).
fof(f2250,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f2249]) ).
fof(f2251,plain,
class_Power_Opower(t_a),
inference(resolution,[status(thm)],[f1684,f1661]) ).
fof(f2253,definition,
( sQ21_spl
<=> class_Ring__and__Field_Omult__zero(t_a) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f2255,plain,
( sQ21_spl
| ~ class_Ring__and__Field_Omult__zero(t_a) ),
inference(component_clause,[status(thm)],[f2253]) ).
fof(f2257,plain,
! [X0,X1,X2] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
inference(resolution,[status(thm)],[f712,f1686]) ).
fof(f2258,definition,
( sQ22_spl
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f2260,plain,
( sQ22_spl
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
inference(component_clause,[status(thm)],[f2258]) ).
fof(f2261,definition,
! [X0,X1,X2] :
( sQ23_spl
<=> ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f2264,plain,
( sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f2257,f2258,f2261]) ).
fof(f2265,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2260,f1695]) ).
fof(f2266,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f2265]) ).
fof(f2271,definition,
( sQ24_spl
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f2272,plain,
( ~ sQ24_spl
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(component_clause,[status(thm)],[f2271]) ).
fof(f2303,plain,
! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(resolution,[status(thm)],[f1571,f1657]) ).
fof(f2308,plain,
! [X0,X1] :
( c_lessequals(X1,X0,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(resolution,[status(thm)],[f1571,f1604]) ).
fof(f2309,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(resolution,[status(thm)],[f1571,f1280]) ).
fof(f2344,plain,
! [X0,X1,X2] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat),
inference(paramodulation,[status(thm)],[f1325,f1657]) ).
fof(f2372,plain,
! [X0,X1,X2] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),
inference(paramodulation,[status(thm)],[f1326,f1657]) ).
fof(f2378,plain,
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(resolution,[status(thm)],[f869,f716]) ).
fof(f2380,plain,
! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(X0),tc_nat),
inference(resolution,[status(thm)],[f869,f1321]) ).
fof(f2381,plain,
! [X0] :
( ~ c_lessequals(c_Suc(X0),X0,tc_nat)
| c_Suc(X0) = X0 ),
inference(resolution,[status(thm)],[f869,f2018]) ).
fof(f2383,definition,
( sQ26_spl
<=> c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f2386,plain,
( sQ24_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f2378,f2383,f2271]) ).
fof(f2387,plain,
! [X0] : ~ c_lessequals(c_Suc(X0),X0,tc_nat),
inference(forward_subsumption_resolution,[status(thm)],[f2381,f886]) ).
fof(f2388,plain,
( ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2272,f762]) ).
fof(f2389,plain,
~ sQ24_spl,
inference(contradiction_clause,[status(thm)],[f2388]) ).
fof(f2412,plain,
! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat),
inference(resolution,[status(thm)],[f2387,f1604]) ).
fof(f2413,plain,
! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat),
inference(resolution,[status(thm)],[f2387,f1280]) ).
fof(f2414,plain,
! [X0] : c_HOL_Ominus__class_Ominus(X0,c_Suc(X0),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(resolution,[status(thm)],[f2412,f1571]) ).
fof(f2432,plain,
! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat),
inference(paramodulation,[status(thm)],[f1336,f2380]) ).
fof(f2448,plain,
! [X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f2303,f1328]) ).
fof(f2449,plain,
! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f1334,f1328]) ).
fof(f2450,plain,
! [X0,X1,X2] :
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f1326,f1328]) ).
fof(f2451,plain,
! [X0,X1,X2] :
( c_HOL_Oplus__class_Oplus(X0,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f1325,f1328]) ).
fof(f2454,plain,
! [X0] :
( X0 = c_Suc(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(X0),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f2414,f1328]) ).
fof(f2456,plain,
! [X0,X1] :
( X1 = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f1859,f1328]) ).
fof(f2457,plain,
! [X0,X1] :
( X0 = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f713,f1328]) ).
fof(f2458,plain,
! [X0] :
( X0 = X0
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f1331,f1328]) ).
fof(f2461,definition,
( sQ27_spl
<=> c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f2463,plain,
( sQ27_spl
| c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(component_clause,[status(thm)],[f2461]) ).
fof(f2469,definition,
! [X0,X1] :
( sQ28_spl
<=> ( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X0
| c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f2472,plain,
( ~ sQ13_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f2448,f2469,f2023]) ).
fof(f2473,definition,
! [X0] :
( sQ29_spl
<=> ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f2476,plain,
( ~ sQ13_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f2449,f2473,f2023]) ).
fof(f2477,plain,
! [X0,X1,X2] :
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(X0,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(forward_demodulation,[status(thm)],[f1326,f2450]) ).
fof(f2478,plain,
! [X0,X1,X2] :
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X2,X0,tc_nat)
| c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(forward_demodulation,[status(thm)],[f1325,f2451]) ).
fof(f2485,definition,
! [X0] :
( sQ30_spl
<=> ( X0 = c_Suc(X0)
| c_HOL_Ominus__class_Ominus(c_Suc(X0),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f2488,plain,
( ~ sQ13_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f2454,f2485,f2023]) ).
fof(f2489,definition,
! [X0,X1] :
( sQ31_spl
<=> ( X1 = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f2492,plain,
( ~ sQ13_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f2456,f2489,f2023]) ).
fof(f2493,definition,
! [X0,X1] :
( sQ32_spl
<=> ( X0 = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f2496,plain,
( ~ sQ13_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f2457,f2493,f2023]) ).
fof(f2497,definition,
! [X0] :
( sQ33_spl
<=> ( X0 = X0
| c_HOL_Ominus__class_Ominus(X0,X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f2500,plain,
( ~ sQ13_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f2458,f2497,f2023]) ).
fof(f2506,plain,
! [X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f1330,f862]) ).
fof(f2507,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f1330,f864]) ).
fof(f2508,definition,
! [X0,X1] :
( sQ34_spl
<=> ( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f2511,definition,
( sQ35_spl
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f2513,plain,
( sQ35_spl
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
inference(component_clause,[status(thm)],[f2511]) ).
fof(f2514,plain,
( ~ sQ35_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f2507,f2508,f2511]) ).
fof(f2520,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat),
inference(resolution,[status(thm)],[f1040,f1696]) ).
fof(f2521,plain,
! [X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ),
inference(resolution,[status(thm)],[f1040,f1673]) ).
fof(f2534,plain,
! [X0] : c_GCD_Ogcd__class_Ogcd(X0,X0,tc_nat) = c_GCD_Ogcd__class_Ogcd(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(paramodulation,[status(thm)],[f1800,f723]) ).
fof(f2540,plain,
! [X0] : X0 = c_GCD_Ogcd__class_Ogcd(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
inference(forward_demodulation,[status(thm)],[f1181,f2534]) ).
fof(f2679,plain,
! [X0,X1,X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat),tc_nat),tc_nat),
inference(paramodulation,[status(thm)],[f713,f1333]) ).
fof(f2680,plain,
! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),tc_nat),
inference(paramodulation,[status(thm)],[f1331,f1333]) ).
fof(f2692,plain,
! [X0,X1,X2] : c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat),tc_nat),
inference(paramodulation,[status(thm)],[f713,f1333]) ).
fof(f2711,plain,
! [X0,X1,X2] :
( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = X0
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f1333,f1328]) ).
fof(f2718,plain,
! [X0,X1,X2] :
( X2 = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X2,X0,tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f1333,f1328]) ).
fof(f2721,plain,
! [X0,X1,X2] : c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat),X0,tc_nat),
inference(paramodulation,[status(thm)],[f1333,f1657]) ).
fof(f2726,plain,
! [X0,X1,X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),tc_nat),
inference(forward_demodulation,[status(thm)],[f1334,f2692]) ).
fof(f2734,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f1427,f1056]) ).
fof(f2748,plain,
c_HOL_Ozero__class_Ozero(t_a) != c_HOL_Oone__class_Oone(t_a),
inference(resolution,[status(thm)],[f2521,f1661]) ).
fof(f2749,plain,
( ~ sQ6_spl
| c_HOL_Ozero__class_Ozero(t_a) != c_HOL_Ozero__class_Ozero(t_a) ),
inference(forward_demodulation,[status(thm)],[f1887,f2748]) ).
fof(f2750,plain,
( ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2749]) ).
fof(f2751,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f2750]) ).
fof(f2863,plain,
! [X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
inference(resolution,[status(thm)],[f1042,f1330]) ).
fof(f2864,definition,
! [X0,X1] :
( sQ36_spl
<=> ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f2867,plain,
( sQ36_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f2863,f2511,f2864]) ).
fof(f2868,plain,
( sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2513,f1693]) ).
fof(f2869,plain,
sQ35_spl,
inference(contradiction_clause,[status(thm)],[f2868]) ).
fof(f2870,plain,
! [X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
inference(resolution,[status(thm)],[f1378,f1330]) ).
fof(f2871,definition,
! [X0,X1] :
( sQ37_spl
<=> ( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f2874,plain,
( sQ37_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f2870,f2511,f2871]) ).
fof(f3054,plain,
! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(c_Suc(X0),X0,tc_nat),tc_nat) = c_Suc(X0),
inference(resolution,[status(thm)],[f1473,f2413]) ).
fof(f3066,plain,
! [X0,X1] :
( X0 = X1
| X1 = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oinverse__class_Odivide(X0,X1,t_a) != c_HOL_Oone__class_Oone(t_a) ),
inference(resolution,[status(thm)],[f1529,f1661]) ).
fof(f3089,plain,
! [X0] :
( X0 = c_HOL_Oone__class_Oone(t_a)
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| X0 != c_HOL_Oone__class_Oone(t_a) ),
inference(paramodulation,[status(thm)],[f1732,f3066]) ).
fof(f3090,plain,
! [X0] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| X0 = X0
| X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oone__class_Oone(t_a) != c_HOL_Oone__class_Oone(t_a) ),
inference(paramodulation,[status(thm)],[f2190,f3066]) ).
fof(f3092,definition,
! [X0] :
( sQ38_spl
<=> ( c_HOL_Ozero__class_Ozero(t_a) = X0
| X0 = c_HOL_Ozero__class_Ozero(t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f3093,plain,
! [X0] :
( ~ sQ38_spl
| c_HOL_Ozero__class_Ozero(t_a) = X0
| X0 = c_HOL_Ozero__class_Ozero(t_a) ),
inference(component_clause,[status(thm)],[f3092]) ).
fof(f3096,definition,
! [X0] :
( sQ39_spl
<=> ( X0 = c_HOL_Oone__class_Oone(t_a)
| X0 != c_HOL_Oone__class_Oone(t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f3099,plain,
( sQ6_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f3089,f3096,f1886]) ).
fof(f3100,definition,
! [X0] :
( sQ40_spl
<=> ( X0 = c_HOL_Ozero__class_Ozero(t_a)
| X0 = X0
| X0 = c_HOL_Ozero__class_Ozero(t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f3103,plain,
( sQ40_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3090,f2217,f3100]) ).
fof(f3169,plain,
! [X0,X1,X2] :
( X1 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,X1,t_a),X2,t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X2,t_a),c_Power_Opower__class_Opower(X1,X2,t_a),t_a) ),
inference(resolution,[status(thm)],[f1543,f1661]) ).
fof(f3176,definition,
! [X0] :
( sQ41_spl
<=> c_Suc(c_Divides_Odiv__class_Omod(X0,c_Suc(X0),tc_nat)) != c_Suc(X0) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f3177,plain,
! [X0] :
( ~ sQ41_spl
| c_Suc(c_Divides_Odiv__class_Omod(X0,c_Suc(X0),tc_nat)) != c_Suc(X0) ),
inference(component_clause,[status(thm)],[f3176]) ).
fof(f3180,plain,
! [X0] : c_HOL_Ominus__class_Ominus(X0,X0,t_a) = c_HOL_Ozero__class_Ozero(t_a),
inference(resolution,[status(thm)],[f1228,f2039]) ).
fof(f3195,definition,
! [X0] :
( sQ42_spl
<=> X0 != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f3196,plain,
! [X0] :
( ~ sQ42_spl
| X0 != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(component_clause,[status(thm)],[f3195]) ).
fof(f3216,plain,
! [X0,X1] :
( c_Power_Opower__class_Opower(X0,X1,t_a) = c_HOL_Ozero__class_Ozero(t_a)
| X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,X0,t_a),X1,t_a) = c_HOL_Oone__class_Oone(t_a) ),
inference(paramodulation,[status(thm)],[f2190,f3169]) ).
fof(f3217,plain,
! [X0,X1,X2] :
( X1 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(X0,X2,t_a) = c_Power_Opower__class_Opower(X1,X2,t_a)
| c_Power_Opower__class_Opower(X1,X2,t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,X1,t_a),X2,t_a) != c_HOL_Oone__class_Oone(t_a) ),
inference(paramodulation,[status(thm)],[f3169,f3066]) ).
fof(f3219,plain,
! [X0,X1,X2,X3] :
( X3 = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X0,c_Power_Opower__class_Opower(X1,X2,t_a),t_a),c_Power_Opower__class_Opower(X3,X2,t_a),t_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X0,c_Power_Opower__class_Opower(X3,X2,t_a),t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X3,t_a),X2,t_a),t_a) ),
inference(paramodulation,[status(thm)],[f3169,f2036]) ).
fof(f3220,plain,
! [X0,X1,X2,X3] :
( X3 = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X0,X1,t_a),X2,t_a),c_Power_Opower__class_Opower(X3,X1,t_a),t_a) = c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,X3,t_a),X1,t_a),c_HOL_Oinverse__class_Odivide(X2,c_Power_Opower__class_Opower(X3,X1,t_a),t_a),t_a) ),
inference(paramodulation,[status(thm)],[f3169,f2036]) ).
fof(f3280,plain,
! [X0,X1,X2] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| ~ c_lessequals(X2,X1,tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X2,t_a),c_Power_Opower__class_Opower(X0,X1,t_a),t_a) ),
inference(resolution,[status(thm)],[f1551,f1661]) ).
fof(f3296,plain,
! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X0,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(resolution,[status(thm)],[f1314,f1571]) ).
fof(f3316,plain,
! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),
inference(resolution,[status(thm)],[f1426,f1428]) ).
fof(f3335,plain,
! [X0,X1,X2] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),t_a),c_Power_Opower__class_Opower(X0,X1,t_a),t_a) ),
inference(resolution,[status(thm)],[f3280,f1314]) ).
fof(f3336,plain,
! [X0,X1,X2,X3] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat),t_a),c_Power_Opower__class_Opower(X0,X1,t_a),t_a) ),
inference(resolution,[status(thm)],[f3280,f2721]) ).
fof(f3337,plain,
! [X0,X1,X2,X3] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(X1,X3,tc_nat),t_a),c_Power_Opower__class_Opower(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),t_a),t_a) ),
inference(resolution,[status(thm)],[f3280,f2372]) ).
fof(f3338,plain,
! [X0,X1,X2,X3] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),t_a),c_Power_Opower__class_Opower(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),t_a),t_a) ),
inference(resolution,[status(thm)],[f3280,f2344]) ).
fof(f3339,plain,
! [X0,X1,X2] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Ominus__class_Ominus(X1,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),t_a),c_Power_Opower__class_Opower(X0,X1,t_a),t_a) ),
inference(resolution,[status(thm)],[f3280,f1657]) ).
fof(f3340,plain,
! [X0,X1] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(X0,X1,t_a),t_a) ),
inference(resolution,[status(thm)],[f3280,f1311]) ).
fof(f3346,plain,
! [X0,X1,X2] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X1,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X1,t_a),c_Power_Opower__class_Opower(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),t_a),t_a) ),
inference(resolution,[status(thm)],[f3280,f1808]) ).
fof(f3347,plain,
! [X0,X1,X2] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X2,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X2,t_a),c_Power_Opower__class_Opower(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),t_a),t_a) ),
inference(resolution,[status(thm)],[f3280,f1738]) ).
fof(f3348,plain,
! [X0,X1,X2] :
( c_HOL_Ominus__class_Ominus(X1,X2,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X2,t_a),c_Power_Opower__class_Opower(X0,X1,t_a),t_a) ),
inference(resolution,[status(thm)],[f3280,f2308]) ).
fof(f3349,plain,
! [X0,X1,X2] :
( c_HOL_Ominus__class_Ominus(X2,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X2,t_a),c_Power_Opower__class_Opower(X0,X1,t_a),t_a) ),
inference(resolution,[status(thm)],[f3280,f1570]) ).
fof(f3352,plain,
! [X0,X1] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Ominus__class_Ominus(X1,X1,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X1,t_a),c_Power_Opower__class_Opower(X0,X1,t_a),t_a) ),
inference(resolution,[status(thm)],[f3280,f1610]) ).
fof(f3353,plain,
! [X0,X1] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),X1,t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_Power_Opower__class_Opower(X0,X1,t_a),t_a) ),
inference(forward_demodulation,[status(thm)],[f1332,f3340]) ).
fof(f3354,plain,
! [X0,X1,X2] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),X1,t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X2,t_a),c_Power_Opower__class_Opower(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),t_a),t_a) ),
inference(forward_demodulation,[status(thm)],[f1335,f3346]) ).
fof(f3355,plain,
! [X0,X1,X2] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),X1,t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X2,t_a),c_Power_Opower__class_Opower(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),t_a),t_a) ),
inference(forward_demodulation,[status(thm)],[f1336,f3347]) ).
fof(f3356,plain,
! [X0,X1] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X1,t_a),c_Power_Opower__class_Opower(X0,X1,t_a),t_a) ),
inference(forward_demodulation,[status(thm)],[f1331,f3352]) ).
fof(f3395,plain,
! [X0,X1] :
( c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X0,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f3296,f1328]) ).
fof(f3401,definition,
! [X0,X1] :
( sQ43_spl
<=> ( c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0
| c_HOL_Ominus__class_Ominus(X0,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f3404,plain,
( ~ sQ13_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f3395,f3401,f2023]) ).
fof(f3452,plain,
! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_Suc(X1),tc_nat) != X0,
inference(resolution,[status(thm)],[f798,f762]) ).
fof(f3457,plain,
! [X0,X1] : c_HOL_Oplus__class_Oplus(c_Suc(X0),X1,tc_nat) != X1,
inference(paramodulation,[status(thm)],[f1821,f3452]) ).
fof(f3570,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(resolution,[status(thm)],[f1412,f1692]) ).
fof(f3571,plain,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f1727,f1688]) ).
fof(f3572,definition,
( sQ44_spl
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f3574,plain,
( sQ44_spl
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(component_clause,[status(thm)],[f3572]) ).
fof(f3575,definition,
( sQ45_spl
<=> c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f3578,plain,
( sQ45_spl
| ~ sQ44_spl ),
inference(split_clause,[status(thm)],[f3571,f3572,f3575]) ).
fof(f3579,plain,
( sQ44_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3574,f1311]) ).
fof(f3580,plain,
sQ44_spl,
inference(contradiction_clause,[status(thm)],[f3579]) ).
fof(f3582,plain,
! [X0] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(t_a),t_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
inference(paramodulation,[status(thm)],[f1732,f2210]) ).
fof(f3583,plain,
! [X0,X1] :
( X1 = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X0,X1,t_a),X1,t_a),c_HOL_Oone__class_Oone(t_a),t_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Odivide(X0,X1,t_a),c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
inference(paramodulation,[status(thm)],[f2210,f2210]) ).
fof(f3625,definition,
! [X0] :
( sQ46_spl
<=> c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(t_a),t_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f3628,plain,
( sQ6_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f3582,f3625,f1886]) ).
fof(f3629,definition,
! [X0,X1] :
( sQ47_spl
<=> ( X1 = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X0,X1,t_a),X1,t_a),c_HOL_Oone__class_Oone(t_a),t_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Odivide(X0,X1,t_a),c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Oone__class_Oone(t_a),t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f3632,plain,
( sQ6_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f3583,f3629,f1886]) ).
fof(f3647,plain,
( c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
inference(resolution,[status(thm)],[f3054,f739]) ).
fof(f3676,plain,
! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat),
inference(paramodulation,[status(thm)],[f3054,f2432]) ).
fof(f3695,definition,
( sQ49_spl
<=> c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f3698,definition,
( sQ50_spl
<=> c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f3699,plain,
( ~ sQ50_spl
| c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(component_clause,[status(thm)],[f3698]) ).
fof(f3701,plain,
( sQ50_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f3647,f3695,f3698]) ).
fof(f3708,plain,
! [X0] : c_HOL_Ominus__class_Ominus(X0,c_Suc(c_Suc(X0)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(resolution,[status(thm)],[f3676,f2309]) ).
fof(f3770,plain,
( ~ c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(resolution,[status(thm)],[f3570,f2018]) ).
fof(f3775,definition,
( sQ51_spl
<=> c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f3776,plain,
( ~ sQ51_spl
| c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(component_clause,[status(thm)],[f3775]) ).
fof(f3778,definition,
( sQ52_spl
<=> c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f3781,plain,
( ~ sQ52_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f3770,f3775,f3778]) ).
fof(f3783,plain,
( ~ sQ51_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3776,f2520]) ).
fof(f3784,plain,
~ sQ51_spl,
inference(contradiction_clause,[status(thm)],[f3783]) ).
fof(f3806,definition,
! [X0] :
( sQ53_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f3807,plain,
! [X0] :
( ~ sQ53_spl
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
inference(component_clause,[status(thm)],[f3806]) ).
fof(f3949,plain,
! [X0] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(t_a),X0,t_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(t_a),c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(t_a),t_a),t_a) ),
inference(paramodulation,[status(thm)],[f1732,f2211]) ).
fof(f3950,plain,
! [X0,X1] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X0,X1,t_a),X0,t_a),c_HOL_Oone__class_Oone(t_a),t_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Odivide(X1,X0,t_a),c_HOL_Oone__class_Oone(t_a),t_a),t_a) ),
inference(paramodulation,[status(thm)],[f2211,f2211]) ).
fof(f3995,definition,
! [X0] :
( sQ54_spl
<=> c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(t_a),X0,t_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(t_a),c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(t_a),t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f3998,plain,
( sQ6_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f3949,f3995,f1886]) ).
fof(f3999,definition,
! [X0,X1] :
( sQ55_spl
<=> ( X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X0,X1,t_a),X0,t_a),c_HOL_Oone__class_Oone(t_a),t_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(t_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Odivide(X1,X0,t_a),c_HOL_Oone__class_Oone(t_a),t_a),t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f4002,plain,
( sQ6_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f3950,f3999,f1886]) ).
fof(f4137,definition,
! [X0] :
( sQ57_spl
<=> ~ class_Nat_Osemiring__char__0(X0) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f4138,plain,
! [X0] :
( ~ sQ57_spl
| ~ class_Nat_Osemiring__char__0(X0) ),
inference(component_clause,[status(thm)],[f4137]) ).
fof(f4140,definition,
! [X1] :
( sQ58_spl
<=> X1 = X1 ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f4144,plain,
( ~ sQ57_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1703,f4138]) ).
fof(f4145,plain,
~ sQ57_spl,
inference(contradiction_clause,[status(thm)],[f4144]) ).
fof(f4156,plain,
! [X0] : c_Divides_Odiv__class_Omod(X0,c_Suc(X0),tc_nat) = X0,
inference(resolution,[status(thm)],[f823,f869]) ).
fof(f4178,plain,
! [X0] :
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X0),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Power_Opower(tc_nat) ),
inference(resolution,[status(thm)],[f761,f1698]) ).
fof(f4180,definition,
! [X0] :
( sQ59_spl
<=> c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X0),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f4183,plain,
( sQ59_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f4178,f1924,f4180]) ).
fof(f4185,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1926,f1707]) ).
fof(f4186,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f4185]) ).
fof(f4187,plain,
! [X0,X1,X2] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_lessequals(X0,X2,tc_nat)
| c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
inference(resolution,[status(thm)],[f768,f1686]) ).
fof(f4188,definition,
! [X0,X1,X2] :
( sQ60_spl
<=> ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_lessequals(X0,X2,tc_nat)
| c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f4191,plain,
( sQ60_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f4187,f2258,f4188]) ).
fof(f4193,plain,
! [X0,X1,X2] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
inference(resolution,[status(thm)],[f770,f1686]) ).
fof(f4194,definition,
! [X0,X1,X2] :
( sQ61_spl
<=> ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X2,tc_nat)
| ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f4197,plain,
( sQ61_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f4193,f2258,f4194]) ).
fof(f4564,plain,
! [X0] :
( X0 = c_Suc(c_Suc(X0))
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(c_Suc(X0)),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f3708,f1328]) ).
fof(f4570,definition,
! [X0] :
( sQ62_spl
<=> ( X0 = c_Suc(c_Suc(X0))
| c_HOL_Ominus__class_Ominus(c_Suc(c_Suc(X0)),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f4573,plain,
( ~ sQ13_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f4564,f4570,f2023]) ).
fof(f4663,plain,
! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_Suc(X0),X1,tc_nat),tc_nat),
inference(resolution,[status(thm)],[f771,f1808]) ).
fof(f4749,plain,
! [X0,X1] :
( c_lessequals(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) ),
inference(resolution,[status(thm)],[f999,f1705]) ).
fof(f4756,plain,
! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ),
inference(resolution,[status(thm)],[f4749,f771]) ).
fof(f5069,plain,
! [X0,X1] :
( X0 = X1
| c_HOL_Ominus__class_Ominus(X0,X1,t_a) != c_HOL_Ozero__class_Ozero(t_a) ),
inference(resolution,[status(thm)],[f1240,f2039]) ).
fof(f5073,plain,
! [X0] :
( X0 = X0
| c_HOL_Ozero__class_Ozero(t_a) != c_HOL_Ozero__class_Ozero(t_a) ),
inference(paramodulation,[status(thm)],[f3180,f5069]) ).
fof(f5074,plain,
( sQ58_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f5073,f2212,f4140]) ).
fof(f5194,plain,
! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(resolution,[status(thm)],[f1381,f1702]) ).
fof(f5197,plain,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| c_GCD_Ogcd__class_Ogcd(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
inference(resolution,[status(thm)],[f1429,f1042]) ).
fof(f5200,plain,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| c_GCD_Ogcd__class_Ogcd(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = X0 ),
inference(resolution,[status(thm)],[f1429,f1378]) ).
fof(f5204,plain,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| c_GCD_Ogcd__class_Ogcd(X0,X0,tc_nat) = X0 ),
inference(resolution,[status(thm)],[f1429,f864]) ).
fof(f5205,definition,
! [X0] :
( sQ63_spl
<=> c_GCD_Ogcd__class_Ogcd(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f5208,plain,
( ~ sQ35_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f5197,f5205,f2511]) ).
fof(f5209,definition,
! [X0] :
( sQ64_spl
<=> c_GCD_Ogcd__class_Ogcd(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = X0 ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f5212,plain,
( ~ sQ35_spl
| sQ64_spl ),
inference(split_clause,[status(thm)],[f5200,f5209,f2511]) ).
fof(f5213,definition,
! [X0] :
( sQ65_spl
<=> c_GCD_Ogcd__class_Ogcd(X0,X0,tc_nat) = X0 ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f5216,plain,
( ~ sQ35_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f5204,f5213,f2511]) ).
fof(f5219,plain,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| c_GCD_Ogcd__class_Ogcd(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
inference(resolution,[status(thm)],[f1430,f1042]) ).
fof(f5222,plain,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| c_GCD_Ogcd__class_Ogcd(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 ),
inference(resolution,[status(thm)],[f1430,f1378]) ).
fof(f5227,definition,
! [X0] :
( sQ66_spl
<=> c_GCD_Ogcd__class_Ogcd(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f5230,plain,
( ~ sQ35_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f5219,f5227,f2511]) ).
fof(f5231,definition,
! [X0] :
( sQ67_spl
<=> c_GCD_Ogcd__class_Ogcd(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f5234,plain,
( ~ sQ35_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f5222,f5231,f2511]) ).
fof(f5307,plain,
! [X0,X1] :
( ~ c_lessequals(X1,X1,tc_nat)
| c_lessequals(X0,X0,tc_nat) ),
inference(paramodulation,[status(thm)],[f1335,f1587]) ).
fof(f5323,definition,
! [X0] :
( sQ68_spl
<=> c_lessequals(X0,X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f5326,definition,
! [X1] :
( sQ69_spl
<=> ~ c_lessequals(X1,X1,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f5327,plain,
! [X0] :
( ~ sQ69_spl
| ~ c_lessequals(X0,X0,tc_nat) ),
inference(component_clause,[status(thm)],[f5326]) ).
fof(f5329,plain,
( sQ69_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f5307,f5323,f5326]) ).
fof(f5334,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X1,X0) = c_HOL_Oone__class_Oone(X0) ),
inference(resolution,[status(thm)],[f1621,f1679]) ).
fof(f5406,plain,
! [X0,X1,X2] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| ~ c_lessequals(X2,X1,tc_nat)
| c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X1,t_a),c_Power_Opower__class_Opower(X0,X2,t_a),t_a) ),
inference(resolution,[status(thm)],[f1603,f1661]) ).
fof(f5538,definition,
! [X0] :
( sQ70_spl
<=> X0 != c_HOL_Ozero__class_Ozero(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f5539,plain,
! [X0] :
( ~ sQ70_spl
| X0 != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(component_clause,[status(thm)],[f5538]) ).
fof(f5542,plain,
( sQ4_spl
| v_a = c_HOL_Ozero__class_Ozero(t_a)
| ~ c_lessequals(v_n,v_m,tc_nat) ),
inference(resolution,[status(thm)],[f5406,f1724]) ).
fof(f5543,plain,
! [X0,X1] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| X0 = c_HOL_Ozero__class_Ozero(t_a)
| ~ c_lessequals(X1,X1,tc_nat)
| c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(X1,X1,tc_nat),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,X0,t_a),X1,t_a) ),
inference(paramodulation,[status(thm)],[f3169,f5406]) ).
fof(f5545,plain,
( sQ4_spl
| sQ1_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f5542,f1718,f1711,f1722]) ).
fof(f5546,plain,
! [X0,X1] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| X0 = c_HOL_Ozero__class_Ozero(t_a)
| ~ c_lessequals(X1,X1,tc_nat)
| c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,X0,t_a),X1,t_a) ),
inference(forward_demodulation,[status(thm)],[f1331,f5543]) ).
fof(f5547,plain,
! [X0,X1] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| ~ c_lessequals(X1,X1,tc_nat)
| c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,X0,t_a),X1,t_a) ),
inference(duplicate_literals_removal,[status(thm)],[f5546]) ).
fof(f5548,plain,
! [X0,X1] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,X0,t_a),X1,t_a) ),
inference(forward_subsumption_resolution,[status(thm)],[f5547,f1610]) ).
fof(f5555,plain,
( sQ3_spl
| c_lessequals(v_m,v_n,tc_nat) ),
inference(resolution,[status(thm)],[f1720,f1604]) ).
fof(f5572,plain,
! [X0] :
( sQ3_spl
| X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,t_a),c_HOL_Ominus__class_Ominus(v_n,v_m,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,v_m,t_a),c_Power_Opower__class_Opower(X0,v_n,t_a),t_a) ),
inference(resolution,[status(thm)],[f5555,f3280]) ).
fof(f5768,definition,
( sQ75_spl
<=> c_Power_Opower__class_Opower(v_a,v_n,t_a) = c_HOL_Ozero__class_Ozero(t_a) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f5769,plain,
( ~ sQ75_spl
| c_Power_Opower__class_Opower(v_a,v_n,t_a) = c_HOL_Ozero__class_Ozero(t_a) ),
inference(component_clause,[status(thm)],[f5768]) ).
fof(f5770,plain,
( sQ75_spl
| c_Power_Opower__class_Opower(v_a,v_n,t_a) != c_HOL_Ozero__class_Ozero(t_a) ),
inference(component_clause,[status(thm)],[f5768]) ).
fof(f5775,plain,
( sQ18_spl
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(resolution,[status(thm)],[f2239,f1668]) ).
fof(f5776,plain,
( sQ18_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f5775,f1708,f2237]) ).
fof(f5777,plain,
( sQ17_spl
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(resolution,[status(thm)],[f2236,f1673]) ).
fof(f5778,plain,
( sQ17_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f5777,f1708,f2234]) ).
fof(f5782,plain,
! [X0] :
( c_Suc(c_Divides_Odiv__class_Omod(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_HOL_Oone__class_Oone(tc_nat)
| c_Suc(c_Divides_Odiv__class_Omod(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f755,f5194]) ).
fof(f5791,plain,
! [X0] :
( c_Suc(c_Divides_Odiv__class_Omod(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = c_HOL_Oone__class_Oone(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(forward_demodulation,[status(thm)],[f5194,f5782]) ).
fof(f5792,plain,
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(forward_demodulation,[status(thm)],[f5194,f5791]) ).
fof(f5793,plain,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat),
inference(forward_subsumption_resolution,[status(thm)],[f5792,f762]) ).
fof(f5797,definition,
! [X0] :
( sQ77_spl
<=> c_Suc(c_Divides_Odiv__class_Omod(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) != c_HOL_Oone__class_Oone(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f5798,plain,
! [X0] :
( ~ sQ77_spl
| c_Suc(c_Divides_Odiv__class_Omod(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) != c_HOL_Oone__class_Oone(tc_nat) ),
inference(component_clause,[status(thm)],[f5797]) ).
fof(f5802,plain,
( ~ sQ77_spl
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oone__class_Oone(tc_nat) ),
inference(forward_demodulation,[status(thm)],[f5194,f5798]) ).
fof(f5807,plain,
! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),
inference(backward_demodulation,[status(thm)],[f5793,f706]) ).
fof(f5879,plain,
( ~ sQ77_spl
| c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
inference(forward_demodulation,[status(thm)],[f5793,f5802]) ).
fof(f5880,plain,
( ~ sQ77_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f5879]) ).
fof(f5881,plain,
~ sQ77_spl,
inference(contradiction_clause,[status(thm)],[f5880]) ).
fof(f5884,definition,
( sQ78_spl
<=> c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f5886,plain,
( sQ78_spl
| c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
inference(component_clause,[status(thm)],[f5884]) ).
fof(f5888,plain,
( sQ78_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f5886]) ).
fof(f5889,plain,
sQ78_spl,
inference(contradiction_clause,[status(thm)],[f5888]) ).
fof(f6337,plain,
! [X0] : c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X0,t_a) = c_HOL_Oone__class_Oone(t_a),
inference(resolution,[status(thm)],[f5334,f1661]) ).
fof(f6403,definition,
( sQ83_spl
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f6405,plain,
( sQ83_spl
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat) ),
inference(component_clause,[status(thm)],[f6403]) ).
fof(f6419,plain,
( sQ83_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6405,f1311]) ).
fof(f6420,plain,
sQ83_spl,
inference(contradiction_clause,[status(thm)],[f6419]) ).
fof(f6649,plain,
! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| ~ c_lessequals(X1,X0,tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X0,t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f5406]) ).
fof(f6650,plain,
! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| ~ c_lessequals(X1,X0,tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X1,t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f5406]) ).
fof(f6651,plain,
! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(t_a),t_a),X1,t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X1,t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3169]) ).
fof(f6653,definition,
! [X0,X1] :
( sQ87_spl
<=> ( ~ c_lessequals(X1,X0,tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X0,t_a),c_HOL_Oone__class_Oone(t_a),t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f6656,plain,
( sQ6_spl
| sQ87_spl ),
inference(split_clause,[status(thm)],[f6649,f6653,f1886]) ).
fof(f6657,definition,
! [X0,X1] :
( sQ88_spl
<=> ( ~ c_lessequals(X1,X0,tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X1,t_a),t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f6660,plain,
( sQ6_spl
| sQ88_spl ),
inference(split_clause,[status(thm)],[f6650,f6657,f1886]) ).
fof(f6661,definition,
! [X0,X1] :
( sQ89_spl
<=> c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(t_a),t_a),X1,t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X0,X1,t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f6664,plain,
( sQ6_spl
| sQ89_spl ),
inference(split_clause,[status(thm)],[f6651,f6661,f1886]) ).
fof(f6789,plain,
! [X0] :
( c_HOL_Oone__class_Oone(tc_nat) = X0
| ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f827,f5807]) ).
fof(f6790,plain,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = X0
| ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f827,f1042]) ).
fof(f6792,plain,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| X0 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
inference(resolution,[status(thm)],[f827,f1378]) ).
fof(f6797,plain,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| X0 = X0
| ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_nat) ),
inference(resolution,[status(thm)],[f827,f864]) ).
fof(f6798,definition,
! [X0] :
( sQ92_spl
<=> ( c_HOL_Oone__class_Oone(tc_nat) = X0
| ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f6801,plain,
( ~ sQ35_spl
| sQ92_spl ),
inference(split_clause,[status(thm)],[f6790,f6798,f2511]) ).
fof(f6802,definition,
! [X0] :
( sQ93_spl
<=> ( X0 = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f6805,plain,
( ~ sQ35_spl
| sQ93_spl ),
inference(split_clause,[status(thm)],[f6792,f6802,f2511]) ).
fof(f6806,definition,
! [X0] :
( sQ94_spl
<=> ( X0 = X0
| ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f6809,plain,
( ~ sQ35_spl
| sQ94_spl ),
inference(split_clause,[status(thm)],[f6797,f6806,f2511]) ).
fof(f7285,plain,
! [X0,X1,X2] :
( X0 = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f1758,f1328]) ).
fof(f7296,definition,
! [X0,X1,X2] :
( sQ95_spl
<=> ( X0 = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f7299,plain,
( ~ sQ13_spl
| sQ95_spl ),
inference(split_clause,[status(thm)],[f7285,f7296,f2023]) ).
fof(f7546,plain,
! [X0,X1,X2] :
( X1 = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f1785,f1328]) ).
fof(f7555,definition,
! [X0,X1,X2] :
( sQ96_spl
<=> ( X1 = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f7558,plain,
( ~ sQ13_spl
| sQ96_spl ),
inference(split_clause,[status(thm)],[f7546,f7555,f2023]) ).
fof(f7882,plain,
! [X0] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_HOL_Oone__class_Oone(t_a),t_a),X0,t_a) = c_HOL_Oone__class_Oone(t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3216]) ).
fof(f7884,plain,
! [X0] :
( ~ sQ20_spl
| X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,X0,t_a),c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oone__class_Oone(t_a)
| c_HOL_Ozero__class_Ozero(t_a) != c_HOL_Ozero__class_Ozero(t_a) ),
inference(paramodulation,[status(thm)],[f3216,f2244]) ).
fof(f7889,definition,
! [X0] :
( sQ98_spl
<=> c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_HOL_Oone__class_Oone(t_a),t_a),X0,t_a) = c_HOL_Oone__class_Oone(t_a) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f7892,plain,
( sQ6_spl
| sQ98_spl ),
inference(split_clause,[status(thm)],[f7882,f7889,f1886]) ).
fof(f7894,definition,
! [X0] :
( sQ99_spl
<=> ( X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,X0,t_a),c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oone__class_Oone(t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f7897,plain,
( ~ sQ20_spl
| sQ99_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f7884,f2212,f7894,f2243]) ).
fof(f7905,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2242,f2251]) ).
fof(f7906,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f7905]) ).
fof(f7907,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2255,f2232]) ).
fof(f7908,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f7907]) ).
fof(f8128,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),X1,tc_nat) ),
inference(resolution,[status(thm)],[f849,f1042]) ).
fof(f8130,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(X0,X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f849,f1378]) ).
fof(f8137,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(X0,X1,tc_nat),X0,tc_nat) ),
inference(resolution,[status(thm)],[f849,f864]) ).
fof(f8139,definition,
! [X0,X1] :
( sQ100_spl
<=> c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),X1,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f8142,plain,
( ~ sQ35_spl
| sQ100_spl ),
inference(split_clause,[status(thm)],[f8128,f8139,f2511]) ).
fof(f8143,definition,
! [X0,X1] :
( sQ101_spl
<=> c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(X0,X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f8146,plain,
( ~ sQ35_spl
| sQ101_spl ),
inference(split_clause,[status(thm)],[f8130,f8143,f2511]) ).
fof(f8147,definition,
! [X0,X1] :
( sQ102_spl
<=> c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(X0,X1,tc_nat),X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f8150,plain,
( ~ sQ35_spl
| sQ102_spl ),
inference(split_clause,[status(thm)],[f8137,f8147,f2511]) ).
fof(f8155,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
inference(resolution,[status(thm)],[f851,f1042]) ).
fof(f8164,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(X0,X1,tc_nat),X1,tc_nat) ),
inference(resolution,[status(thm)],[f851,f864]) ).
fof(f8166,definition,
! [X0,X1] :
( sQ103_spl
<=> c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f8169,plain,
( ~ sQ35_spl
| sQ103_spl ),
inference(split_clause,[status(thm)],[f8155,f8166,f2511]) ).
fof(f8171,definition,
! [X0,X1] :
( sQ104_spl
<=> c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(X0,X1,tc_nat),X1,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f8174,plain,
( ~ sQ35_spl
| sQ104_spl ),
inference(split_clause,[status(thm)],[f8164,f8171,f2511]) ).
fof(f8559,plain,
! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(X0,X1,t_a) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X1,t_a)
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(t_a),t_a),X1,t_a) != c_HOL_Oone__class_Oone(t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3217]) ).
fof(f8563,definition,
! [X0,X1] :
( sQ108_spl
<=> ( c_Power_Opower__class_Opower(X0,X1,t_a) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X1,t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(t_a),t_a),X1,t_a) != c_HOL_Oone__class_Oone(t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f8566,plain,
( sQ6_spl
| sQ108_spl ),
inference(split_clause,[status(thm)],[f8559,f8563,f1886]) ).
fof(f9213,plain,
! [X0] :
( X0 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(t_a),X0,t_a) = c_HOL_Ozero__class_Ozero(t_a)
| ~ class_Ring__and__Field_Omult__zero(t_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(t_a)
| ~ class_Ring__and__Field_Ozero__neq__one(t_a) ),
inference(resolution,[status(thm)],[f875,f2251]) ).
fof(f9214,plain,
! [X0] :
( X0 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Omult__zero(tc_nat)
| ~ class_Ring__and__Field_Ono__zero__divisors(tc_nat)
| ~ class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
inference(resolution,[status(thm)],[f875,f1707]) ).
fof(f9215,definition,
! [X0] :
( sQ111_spl
<=> ( X0 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(t_a),X0,t_a) = c_HOL_Ozero__class_Ozero(t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f9218,plain,
( sQ111_spl
| ~ sQ21_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f9213,f2234,f2237,f2253,f9215]) ).
fof(f9219,definition,
! [X0] :
( sQ112_spl
<=> ( X0 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f9222,plain,
( sQ112_spl
| ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f9214,f1918,f1921,f1931,f9219]) ).
fof(f9223,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1933,f1699]) ).
fof(f9224,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f9223]) ).
fof(f9271,plain,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X0,X0,tc_nat) ),
inference(paramodulation,[status(thm)],[f1331,f1056]) ).
fof(f9277,definition,
( sQ113_spl
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f9281,definition,
! [X0] :
( sQ114_spl
<=> c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f9282,plain,
! [X0] :
( ~ sQ114_spl
| c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(component_clause,[status(thm)],[f9281]) ).
fof(f9285,definition,
! [X0] :
( sQ115_spl
<=> c_HOL_Oord__class_Oless(X0,X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f9286,plain,
! [X0] :
( ~ sQ115_spl
| c_HOL_Oord__class_Oless(X0,X0,tc_nat) ),
inference(component_clause,[status(thm)],[f9285]) ).
fof(f9288,plain,
( ~ sQ113_spl
| sQ115_spl ),
inference(split_clause,[status(thm)],[f9271,f9285,f9277]) ).
fof(f9289,plain,
( ~ sQ115_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9286,f1387]) ).
fof(f9290,plain,
~ sQ115_spl,
inference(contradiction_clause,[status(thm)],[f9289]) ).
fof(f9291,plain,
( ~ sQ114_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9282,f1156]) ).
fof(f9292,plain,
~ sQ114_spl,
inference(contradiction_clause,[status(thm)],[f9291]) ).
fof(f9305,plain,
! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(paramodulation,[status(thm)],[f1334,f1055]) ).
fof(f9323,definition,
! [X0] :
( sQ116_spl
<=> ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f9326,plain,
( sQ116_spl
| sQ113_spl ),
inference(split_clause,[status(thm)],[f9305,f9277,f9323]) ).
fof(f9327,definition,
! [X0] :
( sQ117_spl
<=> ~ c_HOL_Oord__class_Oless(X0,X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f9365,plain,
! [X0,X1,X2] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X0,c_Power_Opower__class_Opower(X1,X2,t_a),t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X2,t_a),t_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(t_a),t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(t_a),t_a),X2,t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3219]) ).
fof(f9373,plain,
! [X0,X1,X2] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X0,c_Power_Opower__class_Opower(X1,X2,t_a),t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X2,t_a),t_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X0,c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X2,t_a),t_a),c_Power_Opower__class_Opower(X1,X2,t_a),t_a) ),
inference(paramodulation,[status(thm)],[f1732,f3219]) ).
fof(f9400,definition,
! [X0,X1,X2] :
( sQ118_spl
<=> c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X0,c_Power_Opower__class_Opower(X1,X2,t_a),t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X2,t_a),t_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(t_a),t_a),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(t_a),t_a),X2,t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f9403,plain,
( sQ6_spl
| sQ118_spl ),
inference(split_clause,[status(thm)],[f9365,f9400,f1886]) ).
fof(f9409,definition,
! [X0,X1,X2] :
( sQ119_spl
<=> c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X0,c_Power_Opower__class_Opower(X1,X2,t_a),t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X2,t_a),t_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X0,c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X2,t_a),t_a),c_Power_Opower__class_Opower(X1,X2,t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f9412,plain,
( sQ6_spl
| sQ119_spl ),
inference(split_clause,[status(thm)],[f9373,f9409,f1886]) ).
fof(f9457,plain,
! [X0] : c_HOL_Ominus__class_Ominus(X0,c_Suc(X0),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(paramodulation,[status(thm)],[f3054,f713]) ).
fof(f9476,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(paramodulation,[status(thm)],[f713,f1055]) ).
fof(f9497,definition,
! [X0,X1] :
( sQ120_spl
<=> ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f9500,plain,
( sQ120_spl
| sQ113_spl ),
inference(split_clause,[status(thm)],[f9476,f9277,f9497]) ).
fof(f9501,definition,
! [X0,X1] :
( sQ121_spl
<=> c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f9502,plain,
! [X0,X1] :
( ~ sQ121_spl
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat) ),
inference(component_clause,[status(thm)],[f9501]) ).
fof(f9510,plain,
( ~ sQ121_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9502,f1426]) ).
fof(f9511,plain,
~ sQ121_spl,
inference(contradiction_clause,[status(thm)],[f9510]) ).
fof(f9596,plain,
! [X0,X1,X2] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X0,X1,t_a),X2,t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X1,t_a),t_a) = c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X0,X1,t_a),c_HOL_Oinverse__class_Odivide(X2,c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X1,t_a),t_a),t_a) ),
inference(paramodulation,[status(thm)],[f1732,f3220]) ).
fof(f9604,plain,
! [X0,X1,X2] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X0,X1,t_a),X2,t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X1,t_a),t_a) = c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(t_a),t_a),X1,t_a),c_HOL_Oinverse__class_Odivide(X2,c_HOL_Oone__class_Oone(t_a),t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3220]) ).
fof(f9625,definition,
! [X0,X1,X2] :
( sQ122_spl
<=> c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X0,X1,t_a),X2,t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X1,t_a),t_a) = c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X0,X1,t_a),c_HOL_Oinverse__class_Odivide(X2,c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X1,t_a),t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f9628,plain,
( sQ6_spl
| sQ122_spl ),
inference(split_clause,[status(thm)],[f9596,f9625,f1886]) ).
fof(f9634,definition,
! [X0,X1,X2] :
( sQ123_spl
<=> c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X0,X1,t_a),X2,t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X1,t_a),t_a) = c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(t_a),t_a),X1,t_a),c_HOL_Oinverse__class_Odivide(X2,c_HOL_Oone__class_Oone(t_a),t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f9637,plain,
( sQ6_spl
| sQ123_spl ),
inference(split_clause,[status(thm)],[f9604,f9634,f1886]) ).
fof(f9663,plain,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(paramodulation,[status(thm)],[f2414,f1055]) ).
fof(f9680,definition,
! [X0] :
( sQ124_spl
<=> ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f9683,plain,
( sQ124_spl
| sQ113_spl ),
inference(split_clause,[status(thm)],[f9663,f9277,f9680]) ).
fof(f9684,definition,
! [X0] :
( sQ125_spl
<=> c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f9685,plain,
! [X0] :
( ~ sQ125_spl
| c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat) ),
inference(component_clause,[status(thm)],[f9684]) ).
fof(f9693,plain,
( ~ sQ125_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9685,f2413]) ).
fof(f9694,plain,
~ sQ125_spl,
inference(contradiction_clause,[status(thm)],[f9693]) ).
fof(f9720,plain,
! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| X0 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f1334,f1906]) ).
fof(f9731,plain,
! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_lessequals(c_Suc(X0),X0,tc_nat)
| c_Suc(X0) = X0 ),
inference(paramodulation,[status(thm)],[f2414,f1906]) ).
fof(f9733,plain,
! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat)
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X0 ),
inference(paramodulation,[status(thm)],[f713,f1906]) ).
fof(f9735,plain,
! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_lessequals(X0,X0,tc_nat)
| X0 = X0 ),
inference(paramodulation,[status(thm)],[f1331,f1906]) ).
fof(f9740,definition,
! [X0] :
( sQ126_spl
<=> ( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| X0 = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f9743,plain,
( sQ113_spl
| sQ126_spl ),
inference(split_clause,[status(thm)],[f9720,f9740,f9277]) ).
fof(f9749,definition,
! [X0] :
( sQ127_spl
<=> ( ~ c_lessequals(c_Suc(X0),X0,tc_nat)
| c_Suc(X0) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f9752,plain,
( sQ113_spl
| sQ127_spl ),
inference(split_clause,[status(thm)],[f9731,f9749,f9277]) ).
fof(f9753,definition,
! [X0,X1] :
( sQ128_spl
<=> ( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat)
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f9756,plain,
( sQ113_spl
| sQ128_spl ),
inference(split_clause,[status(thm)],[f9733,f9753,f9277]) ).
fof(f9757,definition,
! [X0] :
( sQ129_spl
<=> ( ~ c_lessequals(X0,X0,tc_nat)
| X0 = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f9760,plain,
( sQ113_spl
| sQ129_spl ),
inference(split_clause,[status(thm)],[f9735,f9757,f9277]) ).
fof(f9772,plain,
! [X0] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
inference(paramodulation,[status(thm)],[f1334,f2013]) ).
fof(f9795,definition,
! [X0] :
( sQ132_spl
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f9798,plain,
( ~ sQ44_spl
| sQ132_spl ),
inference(split_clause,[status(thm)],[f9772,f9795,f3572]) ).
fof(f10068,definition,
! [X0] :
( sQ134_spl
<=> X0 != v_m ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f10069,plain,
! [X0] :
( ~ sQ134_spl
| X0 != v_m ),
inference(component_clause,[status(thm)],[f10068]) ).
fof(f10083,plain,
( ~ sQ134_spl
| $false ),
inference(destructive_equality_resolution,[status(thm)],[f10069]) ).
fof(f10084,plain,
~ sQ134_spl,
inference(contradiction_clause,[status(thm)],[f10083]) ).
fof(f10273,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_GCD_Ogcd__class_Ogcd(X0,X1,tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f929,f1042]) ).
fof(f10275,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_GCD_Ogcd__class_Ogcd(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f929,f1378]) ).
fof(f10283,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_GCD_Ogcd__class_Ogcd(X1,X0,tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f929,f864]) ).
fof(f10284,definition,
! [X0,X1] :
( sQ138_spl
<=> ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_GCD_Ogcd__class_Ogcd(X0,X1,tc_nat),tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f10287,plain,
( ~ sQ35_spl
| sQ138_spl ),
inference(split_clause,[status(thm)],[f10273,f10284,f2511]) ).
fof(f10288,definition,
! [X0,X1] :
( sQ139_spl
<=> ( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_GCD_Ogcd__class_Ogcd(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f10291,plain,
( ~ sQ35_spl
| sQ139_spl ),
inference(split_clause,[status(thm)],[f10275,f10288,f2511]) ).
fof(f10292,definition,
! [X0,X1] :
( sQ140_spl
<=> ( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_GCD_Ogcd__class_Ogcd(X1,X0,tc_nat),tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f10295,plain,
( ~ sQ35_spl
| sQ140_spl ),
inference(split_clause,[status(thm)],[f10283,f10292,f2511]) ).
fof(f10351,plain,
! [X0] :
( ~ sQ41_spl
| c_Suc(X0) != c_Suc(X0) ),
inference(forward_demodulation,[status(thm)],[f4156,f3177]) ).
fof(f10352,plain,
( ~ sQ41_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f10351]) ).
fof(f10353,plain,
~ sQ41_spl,
inference(contradiction_clause,[status(thm)],[f10352]) ).
fof(f11012,definition,
! [X0] :
( sQ160_spl
<=> c_HOL_Oord__class_Oless(v_m,X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f11013,plain,
! [X0] :
( ~ sQ160_spl
| c_HOL_Oord__class_Oless(v_m,X0,tc_nat) ),
inference(component_clause,[status(thm)],[f11012]) ).
fof(f11053,plain,
( ~ sQ160_spl
| $false ),
inference(resolution,[status(thm)],[f11013,f3316]) ).
fof(f11063,plain,
~ sQ160_spl,
inference(contradiction_clause,[status(thm)],[f11053]) ).
fof(f11774,plain,
( ~ sQ70_spl
| $false ),
inference(destructive_equality_resolution,[status(thm)],[f5539]) ).
fof(f11775,plain,
~ sQ70_spl,
inference(contradiction_clause,[status(thm)],[f11774]) ).
fof(f11776,plain,
( ~ sQ69_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5327,f1610]) ).
fof(f11777,plain,
~ sQ69_spl,
inference(contradiction_clause,[status(thm)],[f11776]) ).
fof(f11778,plain,
! [X0] :
( ~ sQ53_spl
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
inference(forward_subsumption_resolution,[status(thm)],[f3807,f4663]) ).
fof(f11779,plain,
( ~ sQ50_spl
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(forward_demodulation,[status(thm)],[f1332,f3699]) ).
fof(f11780,plain,
( ~ sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f11779,f762]) ).
fof(f11781,plain,
~ sQ50_spl,
inference(contradiction_clause,[status(thm)],[f11780]) ).
fof(f11782,plain,
( ~ sQ42_spl
| $false ),
inference(destructive_equality_resolution,[status(thm)],[f3196]) ).
fof(f11783,plain,
~ sQ42_spl,
inference(contradiction_clause,[status(thm)],[f11782]) ).
fof(f11784,plain,
( sQ27_spl
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(forward_demodulation,[status(thm)],[f1334,f2463]) ).
fof(f11785,plain,
( sQ27_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f11784]) ).
fof(f11786,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f11785]) ).
fof(f11789,plain,
( ~ sQ53_spl
| $false ),
inference(resolution,[status(thm)],[f11778,f1156]) ).
fof(f11802,plain,
~ sQ53_spl,
inference(contradiction_clause,[status(thm)],[f11789]) ).
fof(f11972,definition,
( sQ170_spl
<=> c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_a,v_a,t_a),v_n,t_a) = c_HOL_Oone__class_Oone(t_a) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f12343,definition,
! [X0,X1] :
( sQ171_spl
<=> c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f12344,plain,
! [X0,X1] :
( ~ sQ171_spl
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(component_clause,[status(thm)],[f12343]) ).
fof(f12351,definition,
! [X0,X1] :
( sQ173_spl
<=> c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f12352,plain,
! [X0,X1] :
( ~ sQ173_spl
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) ),
inference(component_clause,[status(thm)],[f12351]) ).
fof(f12355,plain,
( ~ sQ171_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12344,f1156]) ).
fof(f12356,plain,
~ sQ171_spl,
inference(contradiction_clause,[status(thm)],[f12355]) ).
fof(f12540,plain,
! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X0,tc_nat) ),
inference(resolution,[status(thm)],[f2231,f4663]) ).
fof(f12550,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) ),
inference(paramodulation,[status(thm)],[f1800,f2231]) ).
fof(f12556,definition,
! [X0] :
( sQ178_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),X0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f12559,definition,
! [X1] :
( sQ179_spl
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f12560,plain,
! [X0] :
( ~ sQ179_spl
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
inference(component_clause,[status(thm)],[f12559]) ).
fof(f12562,plain,
( sQ179_spl
| sQ178_spl ),
inference(split_clause,[status(thm)],[f12540,f12556,f12559]) ).
fof(f12582,definition,
! [X0,X1] :
( sQ184_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f12585,plain,
( sQ113_spl
| sQ184_spl ),
inference(split_clause,[status(thm)],[f12550,f12582,f9277]) ).
fof(f12665,plain,
( ~ sQ179_spl
| $false ),
inference(resolution,[status(thm)],[f12560,f1156]) ).
fof(f12679,plain,
~ sQ179_spl,
inference(contradiction_clause,[status(thm)],[f12665]) ).
fof(f12767,plain,
! [X0] : c_GCD_Ogcd__class_Ogcd(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
inference(resolution,[status(thm)],[f5807,f1430]) ).
fof(f12864,plain,
! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(X0,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X0,t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3335]) ).
fof(f12877,plain,
! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(X0,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_Divides_Odiv__class_Omod(X0,X1,tc_nat),t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3335]) ).
fof(f12891,definition,
! [X0,X1] :
( sQ185_spl
<=> c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(X0,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X0,t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition]) ).
fof(f12894,plain,
( sQ6_spl
| sQ185_spl ),
inference(split_clause,[status(thm)],[f12864,f12891,f1886]) ).
fof(f12917,definition,
! [X0,X1] :
( sQ186_spl
<=> c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(X0,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_Divides_Odiv__class_Omod(X0,X1,tc_nat),t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition]) ).
fof(f12920,plain,
( sQ6_spl
| sQ186_spl ),
inference(split_clause,[status(thm)],[f12877,f12917,f1886]) ).
fof(f13032,definition,
! [X0,X1] :
( sQ189_spl
<=> ( ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f13033,plain,
! [X0,X1] :
( ~ sQ189_spl
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
inference(component_clause,[status(thm)],[f13032]) ).
fof(f13036,plain,
! [X0,X1] :
( ~ sQ189_spl
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ),
inference(forward_subsumption_resolution,[status(thm)],[f13033,f1387]) ).
fof(f13039,plain,
! [X0,X1] :
( ~ sQ189_spl
| c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ),
inference(backward_subsumption_resolution,[status(thm)],[f1100,f13036]) ).
fof(f13063,plain,
( ~ sQ189_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13039,f13036]) ).
fof(f13064,plain,
~ sQ189_spl,
inference(contradiction_clause,[status(thm)],[f13063]) ).
fof(f13068,plain,
! [X0,X1,X2] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X0,t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3336]) ).
fof(f13092,plain,
! [X0,X1,X2] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat),t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3336]) ).
fof(f13106,definition,
! [X0,X1,X2] :
( sQ190_spl
<=> c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X0,t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f13109,plain,
( sQ6_spl
| sQ190_spl ),
inference(split_clause,[status(thm)],[f13068,f13106,f1886]) ).
fof(f13135,definition,
! [X0,X1,X2] :
( sQ191_spl
<=> c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat),t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition]) ).
fof(f13138,plain,
( sQ6_spl
| sQ191_spl ),
inference(split_clause,[status(thm)],[f13092,f13135,f1886]) ).
fof(f13214,plain,
! [X0,X1,X2] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3337]) ).
fof(f13232,plain,
! [X0,X1,X2] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3337]) ).
fof(f13255,definition,
! [X0,X1,X2] :
( sQ192_spl
<=> c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ192_spl])],[split_symbol_definition]) ).
fof(f13258,plain,
( sQ6_spl
| sQ192_spl ),
inference(split_clause,[status(thm)],[f13214,f13255,f1886]) ).
fof(f13281,definition,
! [X0,X1,X2] :
( sQ193_spl
<=> c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f13284,plain,
( sQ6_spl
| sQ193_spl ),
inference(split_clause,[status(thm)],[f13232,f13281,f1886]) ).
fof(f13330,plain,
( ~ sQ173_spl
| $false ),
inference(resolution,[status(thm)],[f12352,f1156]) ).
fof(f13348,plain,
~ sQ173_spl,
inference(contradiction_clause,[status(thm)],[f13330]) ).
fof(f13380,plain,
! [X0,X1,X2] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3338]) ).
fof(f13398,plain,
! [X0,X1,X2] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3338]) ).
fof(f13422,definition,
! [X0,X1,X2] :
( sQ194_spl
<=> c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ194_spl])],[split_symbol_definition]) ).
fof(f13425,plain,
( sQ6_spl
| sQ194_spl ),
inference(split_clause,[status(thm)],[f13380,f13422,f1886]) ).
fof(f13449,definition,
! [X0,X1,X2] :
( sQ195_spl
<=> c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition]) ).
fof(f13452,plain,
( sQ6_spl
| sQ195_spl ),
inference(split_clause,[status(thm)],[f13398,f13449,f1886]) ).
fof(f13588,definition,
! [X0] :
( sQ200_spl
<=> ( c_Power_Opower__class_Opower(X0,v_n,t_a) = c_Power_Opower__class_Opower(v_a,v_n,t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,v_a,t_a),v_n,t_a) != c_HOL_Oone__class_Oone(t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition]) ).
fof(f13607,plain,
! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X0,t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3339]) ).
fof(f13625,plain,
! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3339]) ).
fof(f13639,definition,
! [X0,X1] :
( sQ204_spl
<=> c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X0,t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f13642,plain,
( sQ6_spl
| sQ204_spl ),
inference(split_clause,[status(thm)],[f13607,f13639,f1886]) ).
fof(f13669,definition,
! [X0,X1] :
( sQ205_spl
<=> c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ205_spl])],[split_symbol_definition]) ).
fof(f13672,plain,
( sQ6_spl
| sQ205_spl ),
inference(split_clause,[status(thm)],[f13625,f13669,f1886]) ).
fof(f13794,plain,
! [X0] :
( sQ75_spl
| v_a = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(X0,v_n,t_a) = c_Power_Opower__class_Opower(v_a,v_n,t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,v_a,t_a),v_n,t_a) != c_HOL_Oone__class_Oone(t_a) ),
inference(resolution,[status(thm)],[f5770,f3217]) ).
fof(f13795,plain,
( sQ75_spl
| v_a = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v_a,v_a,t_a),v_n,t_a) = c_HOL_Oone__class_Oone(t_a) ),
inference(resolution,[status(thm)],[f5770,f3216]) ).
fof(f13797,plain,
( sQ75_spl
| sQ1_spl
| sQ200_spl ),
inference(split_clause,[status(thm)],[f13794,f13588,f1711,f5768]) ).
fof(f13798,plain,
( sQ75_spl
| sQ1_spl
| sQ170_spl ),
inference(split_clause,[status(thm)],[f13795,f11972,f1711,f5768]) ).
fof(f13834,plain,
! [X0] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),X0,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X0,t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3353]) ).
fof(f13837,plain,
! [X0] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),X0,t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3353]) ).
fof(f13855,definition,
! [X0] :
( sQ207_spl
<=> c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),X0,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X0,t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f13858,plain,
( sQ6_spl
| sQ207_spl ),
inference(split_clause,[status(thm)],[f13834,f13855,f1886]) ).
fof(f13865,definition,
! [X0] :
( sQ209_spl
<=> c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),X0,t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_HOL_Ozero__class_Ozero(tc_nat),t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f13868,plain,
( sQ6_spl
| sQ209_spl ),
inference(split_clause,[status(thm)],[f13837,f13865,f1886]) ).
fof(f13982,plain,
! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),X0,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3354]) ).
fof(f13984,plain,
! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),X0,t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X1,t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3354]) ).
fof(f14013,definition,
! [X0,X1] :
( sQ211_spl
<=> c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),X0,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f14016,plain,
( sQ6_spl
| sQ211_spl ),
inference(split_clause,[status(thm)],[f13982,f14013,f1886]) ).
fof(f14019,definition,
! [X0,X1] :
( sQ212_spl
<=> c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),X0,t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X1,t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ212_spl])],[split_symbol_definition]) ).
fof(f14022,plain,
( sQ6_spl
| sQ212_spl ),
inference(split_clause,[status(thm)],[f13984,f14019,f1886]) ).
fof(f14198,definition,
! [X0] :
( sQ213_spl
<=> ( X0 = c_HOL_Ozero__class_Ozero(tc_nat)
| X0 != c_HOL_Oone__class_Oone(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition]) ).
fof(f14199,plain,
! [X0] :
( ~ sQ213_spl
| X0 = c_HOL_Ozero__class_Ozero(tc_nat)
| X0 != c_HOL_Oone__class_Oone(tc_nat) ),
inference(component_clause,[status(thm)],[f14198]) ).
fof(f14203,plain,
( ~ sQ213_spl
| c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(destructive_equality_resolution,[status(thm)],[f14199]) ).
fof(f14204,plain,
( ~ sQ213_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14203,f2520]) ).
fof(f14205,plain,
~ sQ213_spl,
inference(contradiction_clause,[status(thm)],[f14204]) ).
fof(f14206,plain,
! [X0,X1] :
( X0 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
inference(forward_demodulation,[status(thm)],[f5793,f1075]) ).
fof(f14207,plain,
! [X0,X1] :
( X0 = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| X1 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
inference(forward_demodulation,[status(thm)],[f5793,f14206]) ).
fof(f14208,plain,
! [X0,X1] :
( X0 = c_HOL_Oone__class_Oone(tc_nat)
| X1 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
inference(forward_demodulation,[status(thm)],[f5793,f14207]) ).
fof(f14212,plain,
! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
| X0 = c_HOL_Oone__class_Oone(tc_nat)
| X0 != c_HOL_Oone__class_Oone(tc_nat) ),
inference(paramodulation,[status(thm)],[f1736,f14208]) ).
fof(f14222,definition,
! [X0] :
( sQ214_spl
<=> ( X0 = c_HOL_Oone__class_Oone(tc_nat)
| X0 != c_HOL_Oone__class_Oone(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ214_spl])],[split_symbol_definition]) ).
fof(f14225,plain,
( sQ51_spl
| sQ214_spl ),
inference(split_clause,[status(thm)],[f14212,f14222,f3775]) ).
fof(f14563,definition,
( sQ217_spl
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Suc(v_m) ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f14564,plain,
( ~ sQ217_spl
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Suc(v_m) ),
inference(component_clause,[status(thm)],[f14563]) ).
fof(f14567,definition,
( sQ218_spl
<=> v_m = c_Suc(v_m) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f14568,plain,
( ~ sQ218_spl
| v_m = c_Suc(v_m) ),
inference(component_clause,[status(thm)],[f14567]) ).
fof(f14573,plain,
( ~ sQ217_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14564,f762]) ).
fof(f14574,plain,
~ sQ217_spl,
inference(contradiction_clause,[status(thm)],[f14573]) ).
fof(f14575,plain,
( ~ sQ218_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14568,f886]) ).
fof(f14576,plain,
~ sQ218_spl,
inference(contradiction_clause,[status(thm)],[f14575]) ).
fof(f14593,definition,
( sQ219_spl
<=> c_Suc(c_Suc(v_m)) = v_m ),
introduced(definition,[new_symbols(definition,[sQ219_spl])],[split_symbol_definition]) ).
fof(f14594,plain,
( ~ sQ219_spl
| c_Suc(c_Suc(v_m)) = v_m ),
inference(component_clause,[status(thm)],[f14593]) ).
fof(f14596,definition,
( sQ220_spl
<=> c_Suc(c_Suc(v_m)) = c_HOL_Ozero__class_Ozero(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f14597,plain,
( ~ sQ220_spl
| c_Suc(c_Suc(v_m)) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(component_clause,[status(thm)],[f14596]) ).
fof(f14609,plain,
( ~ sQ220_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14597,f762]) ).
fof(f14610,plain,
~ sQ220_spl,
inference(contradiction_clause,[status(thm)],[f14609]) ).
fof(f14614,plain,
( ~ sQ219_spl
| c_HOL_Oord__class_Oless(v_m,v_m,tc_nat) ),
inference(paramodulation,[status(thm)],[f14594,f3676]) ).
fof(f14665,plain,
( ~ sQ219_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14614,f1387]) ).
fof(f14666,plain,
~ sQ219_spl,
inference(contradiction_clause,[status(thm)],[f14665]) ).
fof(f15078,plain,
! [X0] :
( c_GCD_Ogcd__class_Ogcd(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(resolution,[status(thm)],[f1095,f1298]) ).
fof(f15109,definition,
! [X0] :
( sQ225_spl
<=> c_GCD_Ogcd__class_Ogcd(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f15110,plain,
! [X0] :
( ~ sQ225_spl
| c_GCD_Ogcd__class_Ogcd(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(component_clause,[status(thm)],[f15109]) ).
fof(f15112,plain,
( sQ225_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f15078,f2023,f15109]) ).
fof(f15132,plain,
! [X0] :
( ~ sQ225_spl
| X0 = c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(forward_demodulation,[status(thm)],[f2540,f15110]) ).
fof(f15194,plain,
( ~ sQ11_spl
| ~ sQ225_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1928,f15132]) ).
fof(f15235,plain,
( ~ sQ11_spl
| ~ sQ225_spl ),
inference(contradiction_clause,[status(thm)],[f15194]) ).
fof(f16591,definition,
! [X0] :
( sQ237_spl
<=> ( c_Suc(X0) = X0
| c_HOL_Ominus__class_Ominus(X0,c_Suc(X0),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f16592,plain,
! [X0] :
( ~ sQ237_spl
| c_Suc(X0) = X0
| c_HOL_Ominus__class_Ominus(X0,c_Suc(X0),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(component_clause,[status(thm)],[f16591]) ).
fof(f16600,plain,
! [X0] :
( ~ sQ237_spl
| c_Suc(X0) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(forward_demodulation,[status(thm)],[f9457,f16592]) ).
fof(f16601,plain,
! [X0] :
( ~ sQ237_spl
| c_Suc(X0) = X0 ),
inference(trivial_equality_resolution,[status(thm)],[f16600]) ).
fof(f16602,plain,
( ~ sQ237_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f16601,f886]) ).
fof(f16603,plain,
~ sQ237_spl,
inference(contradiction_clause,[status(thm)],[f16602]) ).
fof(f16789,definition,
! [X0] :
( sQ240_spl
<=> c_Suc(X0) != c_Suc(X0) ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f16790,plain,
! [X0] :
( ~ sQ240_spl
| c_Suc(X0) != c_Suc(X0) ),
inference(component_clause,[status(thm)],[f16789]) ).
fof(f16797,plain,
( ~ sQ240_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f16790]) ).
fof(f16798,plain,
~ sQ240_spl,
inference(contradiction_clause,[status(thm)],[f16797]) ).
fof(f17189,plain,
! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_Suc(X1),tc_nat) != X1,
inference(paramodulation,[status(thm)],[f1141,f3457]) ).
fof(f17427,plain,
! [X0,X1] : c_HOL_Oplus__class_Oplus(c_Suc(X0),X1,tc_nat) != X0,
inference(paramodulation,[status(thm)],[f1821,f17189]) ).
fof(f18032,definition,
! [X0] :
( sQ248_spl
<=> v_m = c_HOL_Oplus__class_Oplus(c_Suc(v_m),X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f18033,plain,
! [X0] :
( ~ sQ248_spl
| v_m = c_HOL_Oplus__class_Oplus(c_Suc(v_m),X0,tc_nat) ),
inference(component_clause,[status(thm)],[f18032]) ).
fof(f18036,definition,
! [X0] :
( sQ249_spl
<=> v_m = c_HOL_Oplus__class_Oplus(X0,c_Suc(v_m),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f18037,plain,
! [X0] :
( ~ sQ249_spl
| v_m = c_HOL_Oplus__class_Oplus(X0,c_Suc(v_m),tc_nat) ),
inference(component_clause,[status(thm)],[f18036]) ).
fof(f18085,plain,
( ~ sQ249_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f18037,f17189]) ).
fof(f18086,plain,
~ sQ249_spl,
inference(contradiction_clause,[status(thm)],[f18085]) ).
fof(f18087,plain,
( ~ sQ248_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f18033,f17427]) ).
fof(f18088,plain,
~ sQ248_spl,
inference(contradiction_clause,[status(thm)],[f18087]) ).
fof(f18597,plain,
! [X0] : c_HOL_Oplus__class_Oplus(c_Suc(X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(paramodulation,[status(thm)],[f5793,f1141]) ).
fof(f18598,plain,
! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X0),tc_nat),
inference(paramodulation,[status(thm)],[f5793,f1141]) ).
fof(f18640,plain,
! [X0] : c_Suc(X0) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(forward_demodulation,[status(thm)],[f1800,f18597]) ).
fof(f18641,plain,
! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = c_Suc(X0),
inference(forward_demodulation,[status(thm)],[f1736,f18598]) ).
fof(f18688,plain,
! [X0,X1] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),X0,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3355]) ).
fof(f18721,definition,
! [X0,X1] :
( sQ257_spl
<=> c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),X0,t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f18724,plain,
( sQ6_spl
| sQ257_spl ),
inference(split_clause,[status(thm)],[f18688,f18721,f1886]) ).
fof(f18839,plain,
! [X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X0,t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3348]) ).
fof(f18842,plain,
! [X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X1,t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3348]) ).
fof(f18872,definition,
! [X0,X1] :
( sQ271_spl
<=> ( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X0,t_a),t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f18875,plain,
( sQ6_spl
| sQ271_spl ),
inference(split_clause,[status(thm)],[f18839,f18872,f1886]) ).
fof(f18882,definition,
! [X0,X1] :
( sQ273_spl
<=> ( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X1,t_a),c_HOL_Oone__class_Oone(t_a),t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ273_spl])],[split_symbol_definition]) ).
fof(f18885,plain,
( sQ6_spl
| sQ273_spl ),
inference(split_clause,[status(thm)],[f18842,f18882,f1886]) ).
fof(f19003,plain,
! [X0] : c_HOL_Ominus__class_Ominus(c_Suc(X0),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0,
inference(paramodulation,[status(thm)],[f18640,f1336]) ).
fof(f19009,plain,
! [X0] : c_HOL_Ominus__class_Ominus(c_Suc(X0),X0,tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
inference(paramodulation,[status(thm)],[f18640,f1335]) ).
fof(f19278,plain,
! [X0,X1] :
( c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X0,t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3349]) ).
fof(f19281,plain,
! [X0,X1] :
( c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X1,t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3349]) ).
fof(f19294,definition,
! [X0,X1] :
( sQ275_spl
<=> ( c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X0,t_a),t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ275_spl])],[split_symbol_definition]) ).
fof(f19297,plain,
( sQ6_spl
| sQ275_spl ),
inference(split_clause,[status(thm)],[f19278,f19294,f1886]) ).
fof(f19304,definition,
! [X0,X1] :
( sQ277_spl
<=> ( c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X1,t_a),c_HOL_Oone__class_Oone(t_a),t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ277_spl])],[split_symbol_definition]) ).
fof(f19307,plain,
( sQ6_spl
| sQ277_spl ),
inference(split_clause,[status(thm)],[f19281,f19304,f1886]) ).
fof(f19362,plain,
! [X0] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(resolution,[status(thm)],[f2477,f1332]) ).
fof(f19366,plain,
! [X0,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f1334,f2477]) ).
fof(f19384,plain,
! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(c_Suc(X0),X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(X0),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f9457,f2477]) ).
fof(f19386,plain,
! [X0,X1,X2] :
( c_HOL_Oplus__class_Oplus(X0,X2,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f713,f2477]) ).
fof(f19388,plain,
! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f1331,f2477]) ).
fof(f19401,definition,
! [X0] :
( sQ279_spl
<=> c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ279_spl])],[split_symbol_definition]) ).
fof(f19404,plain,
( sQ279_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f19362,f2461,f19401]) ).
fof(f19405,definition,
! [X0,X1] :
( sQ280_spl
<=> ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ280_spl])],[split_symbol_definition]) ).
fof(f19408,plain,
( ~ sQ13_spl
| sQ280_spl ),
inference(split_clause,[status(thm)],[f19366,f19405,f2023]) ).
fof(f19422,definition,
! [X0,X1] :
( sQ281_spl
<=> ( c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(c_Suc(X0),X1,tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(X0),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ281_spl])],[split_symbol_definition]) ).
fof(f19425,plain,
( ~ sQ13_spl
| sQ281_spl ),
inference(split_clause,[status(thm)],[f19384,f19422,f2023]) ).
fof(f19430,definition,
! [X0,X1,X2] :
( sQ282_spl
<=> ( c_HOL_Oplus__class_Oplus(X0,X2,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ282_spl])],[split_symbol_definition]) ).
fof(f19433,plain,
( ~ sQ13_spl
| sQ282_spl ),
inference(split_clause,[status(thm)],[f19386,f19430,f2023]) ).
fof(f19434,definition,
! [X0,X1] :
( sQ283_spl
<=> ( c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ283_spl])],[split_symbol_definition]) ).
fof(f19437,plain,
( ~ sQ13_spl
| sQ283_spl ),
inference(split_clause,[status(thm)],[f19388,f19434,f2023]) ).
fof(f19443,plain,
! [X0] :
( c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(resolution,[status(thm)],[f19003,f2477]) ).
fof(f19444,plain,
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(resolution,[status(thm)],[f19003,f1328]) ).
fof(f19467,definition,
( sQ284_spl
<=> c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ284_spl])],[split_symbol_definition]) ).
fof(f19469,plain,
( sQ284_spl
| c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(component_clause,[status(thm)],[f19467]) ).
fof(f19470,definition,
! [X0] :
( sQ285_spl
<=> c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ285_spl])],[split_symbol_definition]) ).
fof(f19473,plain,
( sQ285_spl
| ~ sQ284_spl ),
inference(split_clause,[status(thm)],[f19443,f19467,f19470]) ).
fof(f19474,definition,
( sQ286_spl
<=> c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f19477,plain,
( sQ286_spl
| ~ sQ284_spl ),
inference(split_clause,[status(thm)],[f19444,f19467,f19474]) ).
fof(f19488,plain,
( sQ284_spl
| c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(forward_demodulation,[status(thm)],[f5793,f19469]) ).
fof(f19489,plain,
( sQ284_spl
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(forward_demodulation,[status(thm)],[f1331,f19488]) ).
fof(f19490,plain,
( sQ284_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f19489]) ).
fof(f19491,plain,
sQ284_spl,
inference(contradiction_clause,[status(thm)],[f19490]) ).
fof(f19533,plain,
! [X0,X1,X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_lessequals(X0,X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
inference(resolution,[status(thm)],[f1180,f1686]) ).
fof(f19534,definition,
! [X0,X1,X2] :
( sQ288_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_lessequals(X0,X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ288_spl])],[split_symbol_definition]) ).
fof(f19537,plain,
( sQ288_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f19533,f2258,f19534]) ).
fof(f19742,plain,
! [X0] :
( c_HOL_Oplus__class_Oplus(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(resolution,[status(thm)],[f2478,f19003]) ).
fof(f19749,plain,
! [X0] :
( c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(resolution,[status(thm)],[f2478,f1332]) ).
fof(f19755,plain,
! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f1334,f2478]) ).
fof(f19773,plain,
! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X0),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(X0),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f9457,f2478]) ).
fof(f19775,plain,
! [X0,X1,X2] :
( c_HOL_Oplus__class_Oplus(X2,X0,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f713,f2478]) ).
fof(f19777,plain,
! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) = c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f1331,f2478]) ).
fof(f19778,definition,
! [X0] :
( sQ289_spl
<=> c_HOL_Oplus__class_Oplus(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ289_spl])],[split_symbol_definition]) ).
fof(f19781,plain,
( sQ289_spl
| ~ sQ284_spl ),
inference(split_clause,[status(thm)],[f19742,f19467,f19778]) ).
fof(f19795,definition,
! [X0] :
( sQ291_spl
<=> c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f19798,plain,
( sQ291_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f19749,f2461,f19795]) ).
fof(f19805,definition,
! [X0,X1] :
( sQ293_spl
<=> ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f19808,plain,
( ~ sQ13_spl
| sQ293_spl ),
inference(split_clause,[status(thm)],[f19755,f19805,f2023]) ).
fof(f19822,definition,
! [X0,X1] :
( sQ294_spl
<=> ( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X0),tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(X0),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ294_spl])],[split_symbol_definition]) ).
fof(f19825,plain,
( ~ sQ13_spl
| sQ294_spl ),
inference(split_clause,[status(thm)],[f19773,f19822,f2023]) ).
fof(f19830,definition,
! [X0,X1,X2] :
( sQ295_spl
<=> ( c_HOL_Oplus__class_Oplus(X2,X0,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ295_spl])],[split_symbol_definition]) ).
fof(f19833,plain,
( ~ sQ13_spl
| sQ295_spl ),
inference(split_clause,[status(thm)],[f19775,f19830,f2023]) ).
fof(f19834,definition,
! [X0,X1] :
( sQ296_spl
<=> ( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) = c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ296_spl])],[split_symbol_definition]) ).
fof(f19837,plain,
( ~ sQ13_spl
| sQ296_spl ),
inference(split_clause,[status(thm)],[f19777,f19834,f2023]) ).
fof(f19850,plain,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f2506,f1042]) ).
fof(f19852,plain,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f2506,f1378]) ).
fof(f19860,plain,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ominus__class_Ominus(X0,X0,tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f2506,f864]) ).
fof(f19861,definition,
! [X0] :
( sQ297_spl
<=> c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ominus__class_Ominus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ297_spl])],[split_symbol_definition]) ).
fof(f19864,plain,
( ~ sQ35_spl
| sQ297_spl ),
inference(split_clause,[status(thm)],[f19850,f19861,f2511]) ).
fof(f19866,definition,
! [X0] :
( sQ298_spl
<=> c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ298_spl])],[split_symbol_definition]) ).
fof(f19869,plain,
( ~ sQ35_spl
| sQ298_spl ),
inference(split_clause,[status(thm)],[f19852,f19866,f2511]) ).
fof(f19871,definition,
! [X0] :
( sQ299_spl
<=> c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ominus__class_Ominus(X0,X0,tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ299_spl])],[split_symbol_definition]) ).
fof(f19874,plain,
( ~ sQ35_spl
| sQ299_spl ),
inference(split_clause,[status(thm)],[f19860,f19871,f2511]) ).
fof(f20422,plain,
! [X0,X1,X2,X3] :
( c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X2,tc_nat),tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X2,tc_nat),tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f2679,f2478]) ).
fof(f20423,plain,
! [X0,X1,X2,X3] :
( c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X2,tc_nat),tc_nat),X3,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X2,tc_nat),tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f2679,f2477]) ).
fof(f20426,plain,
! [X0,X1,X2] :
( X1 = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X2,tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X2,tc_nat),tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f2679,f1328]) ).
fof(f20480,definition,
! [X0,X1,X2,X3] :
( sQ300_spl
<=> ( c_HOL_Oplus__class_Oplus(X3,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X2,tc_nat),tc_nat),tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X2,tc_nat),tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ300_spl])],[split_symbol_definition]) ).
fof(f20483,plain,
( ~ sQ13_spl
| sQ300_spl ),
inference(split_clause,[status(thm)],[f20422,f20480,f2023]) ).
fof(f20484,definition,
! [X0,X1,X2,X3] :
( sQ301_spl
<=> ( c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X2,tc_nat),tc_nat),X3,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X2,tc_nat),tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ301_spl])],[split_symbol_definition]) ).
fof(f20487,plain,
( ~ sQ13_spl
| sQ301_spl ),
inference(split_clause,[status(thm)],[f20423,f20484,f2023]) ).
fof(f20488,definition,
! [X0,X1,X2] :
( sQ302_spl
<=> ( X1 = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X2,tc_nat),tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X2,tc_nat),tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ302_spl])],[split_symbol_definition]) ).
fof(f20491,plain,
( ~ sQ13_spl
| sQ302_spl ),
inference(split_clause,[status(thm)],[f20426,f20488,f2023]) ).
fof(f20575,plain,
( ~ sQ75_spl
| v_a = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) ),
inference(paramodulation,[status(thm)],[f5769,f3356]) ).
fof(f20576,plain,
! [X0] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X0,t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3356]) ).
fof(f20579,plain,
! [X0] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X0,t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
inference(paramodulation,[status(thm)],[f6337,f3356]) ).
fof(f20599,definition,
( sQ303_spl
<=> c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ303_spl])],[split_symbol_definition]) ).
fof(f20600,plain,
( ~ sQ303_spl
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(t_a),c_Power_Opower__class_Opower(v_a,v_n,t_a),t_a) ),
inference(component_clause,[status(thm)],[f20599]) ).
fof(f20602,plain,
( ~ sQ75_spl
| sQ1_spl
| sQ303_spl ),
inference(split_clause,[status(thm)],[f20575,f20599,f1711,f5768]) ).
fof(f20603,definition,
! [X0] :
( sQ304_spl
<=> c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(t_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X0,t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ304_spl])],[split_symbol_definition]) ).
fof(f20606,plain,
( sQ6_spl
| sQ304_spl ),
inference(split_clause,[status(thm)],[f20576,f20603,f1886]) ).
fof(f20614,definition,
! [X0] :
( sQ306_spl
<=> c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X0,t_a),c_HOL_Oone__class_Oone(t_a),t_a) ),
introduced(definition,[new_symbols(definition,[sQ306_spl])],[split_symbol_definition]) ).
fof(f20617,plain,
( sQ6_spl
| sQ306_spl ),
inference(split_clause,[status(thm)],[f20579,f20614,f1886]) ).
fof(f20632,plain,
( ~ sQ303_spl
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v_a,t_a),c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Ozero__class_Ozero(t_a) ),
inference(forward_demodulation,[status(thm)],[f1895,f20600]) ).
fof(f20633,plain,
( ~ sQ303_spl
| ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f20632,f2244]) ).
fof(f20634,plain,
( ~ sQ303_spl
| ~ sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f20633]) ).
fof(f20808,plain,
! [X0,X1,X2] :
( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f2680,f2478]) ).
fof(f20809,plain,
! [X0,X1,X2] :
( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat),X2,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f2680,f2477]) ).
fof(f20812,plain,
! [X0,X1] :
( X1 = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f2680,f1328]) ).
fof(f20863,definition,
! [X0,X1,X2] :
( sQ307_spl
<=> ( c_HOL_Oplus__class_Oplus(X2,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat),tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ307_spl])],[split_symbol_definition]) ).
fof(f20866,plain,
( ~ sQ13_spl
| sQ307_spl ),
inference(split_clause,[status(thm)],[f20808,f20863,f2023]) ).
fof(f20867,definition,
! [X0,X1,X2] :
( sQ308_spl
<=> ( c_HOL_Oplus__class_Oplus(X1,X2,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat),X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ308_spl])],[split_symbol_definition]) ).
fof(f20870,plain,
( ~ sQ13_spl
| sQ308_spl ),
inference(split_clause,[status(thm)],[f20809,f20867,f2023]) ).
fof(f20871,definition,
! [X0,X1] :
( sQ309_spl
<=> ( X1 = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ309_spl])],[split_symbol_definition]) ).
fof(f20874,plain,
( ~ sQ13_spl
| sQ309_spl ),
inference(split_clause,[status(thm)],[f20812,f20871,f2023]) ).
fof(f21237,plain,
( c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat)
| ~ class_Power_Opower(tc_nat) ),
inference(resolution,[status(thm)],[f1206,f1698]) ).
fof(f21239,definition,
( sQ310_spl
<=> c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ310_spl])],[split_symbol_definition]) ).
fof(f21242,plain,
( sQ310_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f21237,f1924,f21239]) ).
fof(f22176,plain,
! [X0,X1,X2,X3] :
( c_HOL_Oplus__class_Oplus(X3,X0,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f2726,f2478]) ).
fof(f22177,plain,
! [X0,X1,X2,X3] :
( c_HOL_Oplus__class_Oplus(X0,X3,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),X3,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f2726,f2477]) ).
fof(f22232,definition,
! [X0,X1,X2,X3] :
( sQ311_spl
<=> ( c_HOL_Oplus__class_Oplus(X3,X0,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ311_spl])],[split_symbol_definition]) ).
fof(f22235,plain,
( ~ sQ13_spl
| sQ311_spl ),
inference(split_clause,[status(thm)],[f22176,f22232,f2023]) ).
fof(f22236,definition,
! [X0,X1,X2,X3] :
( sQ312_spl
<=> ( c_HOL_Oplus__class_Oplus(X0,X3,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),X3,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ312_spl])],[split_symbol_definition]) ).
fof(f22239,plain,
( ~ sQ13_spl
| sQ312_spl ),
inference(split_clause,[status(thm)],[f22177,f22236,f2023]) ).
fof(f23241,plain,
! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_HOL_Oone__class_Oone(t_a),
inference(resolution,[status(thm)],[f1523,f1907]) ).
fof(f23242,plain,
! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
inference(resolution,[status(thm)],[f1523,f1693]) ).
fof(f23262,plain,
! [X0,X1] :
( X1 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),t_a)
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,X1,t_a),c_HOL_Ozero__class_Ozero(tc_nat),t_a) != c_HOL_Oone__class_Oone(t_a) ),
inference(paramodulation,[status(thm)],[f23241,f3217]) ).
fof(f23318,definition,
! [X0,X1] :
( sQ313_spl
<=> ( X1 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),t_a) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,X1,t_a),c_HOL_Ozero__class_Ozero(tc_nat),t_a) != c_HOL_Oone__class_Oone(t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ313_spl])],[split_symbol_definition]) ).
fof(f23321,plain,
( sQ6_spl
| sQ313_spl ),
inference(split_clause,[status(thm)],[f23262,f23318,f1886]) ).
fof(f23496,plain,
! [X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f1334,f2711]) ).
fof(f23509,plain,
! [X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f1331,f2711]) ).
fof(f23560,definition,
! [X0,X1] :
( sQ318_spl
<=> ( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ318_spl])],[split_symbol_definition]) ).
fof(f23563,plain,
( sQ318_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f23496,f2023,f23560]) ).
fof(f23568,definition,
! [X0,X1] :
( sQ319_spl
<=> ( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ319_spl])],[split_symbol_definition]) ).
fof(f23571,plain,
( sQ319_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f23509,f2023,f23568]) ).
fof(f23671,definition,
! [X0] :
( sQ320_spl
<=> c_GCD_Ogcd__class_Ogcd(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ320_spl])],[split_symbol_definition]) ).
fof(f23672,plain,
! [X0] :
( ~ sQ320_spl
| c_GCD_Ogcd__class_Ogcd(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
inference(component_clause,[status(thm)],[f23671]) ).
fof(f23675,plain,
( ~ sQ320_spl
| c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Oone__class_Oone(tc_nat) ),
inference(forward_demodulation,[status(thm)],[f12767,f23672]) ).
fof(f23676,plain,
( ~ sQ320_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f23675]) ).
fof(f23677,plain,
~ sQ320_spl,
inference(contradiction_clause,[status(thm)],[f23676]) ).
fof(f23697,plain,
! [X0,X1] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(X0,X1,t_a) != c_HOL_Ozero__class_Ozero(t_a)
| ~ class_Ring__and__Field_Omult__zero(t_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(t_a)
| ~ class_Ring__and__Field_Ozero__neq__one(t_a) ),
inference(resolution,[status(thm)],[f1254,f2251]) ).
fof(f23698,plain,
! [X0,X1] :
( X0 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(X0,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Omult__zero(tc_nat)
| ~ class_Ring__and__Field_Ono__zero__divisors(tc_nat)
| ~ class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
inference(resolution,[status(thm)],[f1254,f1707]) ).
fof(f23699,definition,
! [X0,X1] :
( sQ321_spl
<=> ( X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(X0,X1,t_a) != c_HOL_Ozero__class_Ozero(t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ321_spl])],[split_symbol_definition]) ).
fof(f23702,plain,
( sQ321_spl
| ~ sQ21_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f23697,f2234,f2237,f2253,f23699]) ).
fof(f23703,definition,
! [X0,X1] :
( sQ322_spl
<=> ( X0 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_Power_Opower__class_Opower(X0,X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ322_spl])],[split_symbol_definition]) ).
fof(f23706,plain,
( sQ322_spl
| ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f23698,f1918,f1921,f1931,f23703]) ).
fof(f24268,plain,
! [X0,X1] :
( X0 = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oone__class_Oone(t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,X0,t_a),X1,t_a) ),
inference(forward_demodulation,[status(thm)],[f23241,f5548]) ).
fof(f24272,plain,
! [X0] :
( c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oone__class_Oone(t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),X0,t_a) ),
inference(paramodulation,[status(thm)],[f2012,f24268]) ).
fof(f24275,plain,
! [X0,X1] :
( X1 = c_HOL_Ozero__class_Ozero(t_a)
| X1 = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oone__class_Oone(t_a) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X0,t_a) ),
inference(paramodulation,[status(thm)],[f2190,f24268]) ).
fof(f24299,plain,
! [X0,X1,X2] :
( X1 = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oinverse__class_Odivide(X1,X1,t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(X0,X2,t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X1,t_a),X2,t_a)
| c_HOL_Oone__class_Oone(t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oinverse__class_Odivide(X1,X1,t_a),t_a),X2,t_a) != c_HOL_Oone__class_Oone(t_a) ),
inference(paramodulation,[status(thm)],[f24268,f3217]) ).
fof(f24310,definition,
! [X0] :
( sQ327_spl
<=> c_HOL_Oone__class_Oone(t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(t_a),t_a),X0,t_a) ),
introduced(definition,[new_symbols(definition,[sQ327_spl])],[split_symbol_definition]) ).
fof(f24313,plain,
( sQ6_spl
| sQ327_spl ),
inference(split_clause,[status(thm)],[f24272,f24310,f1886]) ).
fof(f24318,definition,
! [X0] :
( sQ329_spl
<=> c_HOL_Oone__class_Oone(t_a) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(t_a),X0,t_a) ),
introduced(definition,[new_symbols(definition,[sQ329_spl])],[split_symbol_definition]) ).
fof(f24322,plain,
( sQ38_spl
| sQ329_spl ),
inference(split_clause,[status(thm)],[f24275,f24318,f3092]) ).
fof(f24346,definition,
! [X0,X1,X2] :
( sQ330_spl
<=> ( X1 = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oinverse__class_Odivide(X1,X1,t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_Power_Opower__class_Opower(X0,X2,t_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X1,t_a),X2,t_a)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oinverse__class_Odivide(X1,X1,t_a),t_a),X2,t_a) != c_HOL_Oone__class_Oone(t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ330_spl])],[split_symbol_definition]) ).
fof(f24349,plain,
( sQ6_spl
| sQ330_spl ),
inference(split_clause,[status(thm)],[f24299,f24346,f1886]) ).
fof(f24355,plain,
! [X0] :
( ~ sQ38_spl
| X0 = c_HOL_Ozero__class_Ozero(t_a) ),
inference(duplicate_literals_removal,[status(thm)],[f3093]) ).
fof(f24356,plain,
( sQ75_spl
| ~ sQ38_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f5770,f24355]) ).
fof(f24382,plain,
( sQ75_spl
| ~ sQ38_spl ),
inference(contradiction_clause,[status(thm)],[f24356]) ).
fof(f24440,plain,
! [X0,X1] :
( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0,tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f9457,f2718]) ).
fof(f24442,plain,
! [X0,X1,X2,X3] :
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),X3,tc_nat),X0,tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f2726,f2718]) ).
fof(f24443,plain,
! [X0,X1,X2] :
( c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat),tc_nat),X1,tc_nat),X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f2680,f2718]) ).
fof(f24444,plain,
! [X0,X1,X2,X3] :
( c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat),X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat),X3,tc_nat),tc_nat),X1,tc_nat),X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f2679,f2718]) ).
fof(f24445,plain,
! [X0,X1,X2] :
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),X0,tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f713,f2718]) ).
fof(f24446,plain,
! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f1331,f2718]) ).
fof(f24480,definition,
! [X0,X1] :
( sQ331_spl
<=> ( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0,tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ331_spl])],[split_symbol_definition]) ).
fof(f24483,plain,
( sQ331_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f24440,f2023,f24480]) ).
fof(f24484,definition,
! [X0,X1,X2,X3] :
( sQ332_spl
<=> ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),X3,tc_nat) = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),X3,tc_nat),X0,tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ332_spl])],[split_symbol_definition]) ).
fof(f24487,plain,
( sQ332_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f24442,f2023,f24484]) ).
fof(f24488,definition,
! [X0,X1,X2] :
( sQ333_spl
<=> ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat),tc_nat),X1,tc_nat),X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ333_spl])],[split_symbol_definition]) ).
fof(f24491,plain,
( sQ333_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f24443,f2023,f24488]) ).
fof(f24492,definition,
! [X0,X1,X2,X3] :
( sQ334_spl
<=> ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat),X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat),X3,tc_nat),tc_nat),X1,tc_nat),X2,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ334_spl])],[split_symbol_definition]) ).
fof(f24495,plain,
( sQ334_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f24444,f2023,f24492]) ).
fof(f24496,definition,
! [X0,X1,X2] :
( sQ335_spl
<=> ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),X0,tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ335_spl])],[split_symbol_definition]) ).
fof(f24499,plain,
( sQ335_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f24445,f2023,f24496]) ).
fof(f24500,definition,
! [X0,X1] :
( sQ336_spl
<=> ( c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ336_spl])],[split_symbol_definition]) ).
fof(f24503,plain,
( sQ336_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f24446,f2023,f24500]) ).
fof(f24866,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1,tc_nat),tc_nat) ),
inference(paramodulation,[status(thm)],[f19009,f2734]) ).
fof(f24922,definition,
! [X0,X1] :
( sQ338_spl
<=> c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1,tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ338_spl])],[split_symbol_definition]) ).
fof(f24925,definition,
( sQ339_spl
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ339_spl])],[split_symbol_definition]) ).
fof(f24927,plain,
( sQ339_spl
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(component_clause,[status(thm)],[f24925]) ).
fof(f24928,plain,
( ~ sQ339_spl
| sQ338_spl ),
inference(split_clause,[status(thm)],[f24866,f24922,f24925]) ).
fof(f24929,definition,
! [X0,X1] :
( sQ340_spl
<=> c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ340_spl])],[split_symbol_definition]) ).
fof(f24930,plain,
! [X0,X1] :
( ~ sQ340_spl
| c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat),tc_nat) ),
inference(component_clause,[status(thm)],[f24929]) ).
fof(f24950,definition,
! [X0,X1] :
( sQ344_spl
<=> c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ344_spl])],[split_symbol_definition]) ).
fof(f24951,plain,
! [X0,X1] :
( ~ sQ344_spl
| c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
inference(component_clause,[status(thm)],[f24950]) ).
fof(f24954,definition,
! [X0,X1] :
( sQ345_spl
<=> c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ345_spl])],[split_symbol_definition]) ).
fof(f24955,plain,
! [X0,X1] :
( ~ sQ345_spl
| c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat),tc_nat) ),
inference(component_clause,[status(thm)],[f24954]) ).
fof(f24961,plain,
! [X0] :
( ~ sQ345_spl
| c_HOL_Oord__class_Oless(X0,X0,tc_nat) ),
inference(forward_demodulation,[status(thm)],[f1336,f24955]) ).
fof(f24962,plain,
( ~ sQ345_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f24961,f1387]) ).
fof(f24963,plain,
~ sQ345_spl,
inference(contradiction_clause,[status(thm)],[f24962]) ).
fof(f24964,plain,
( ~ sQ344_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f24951,f3316]) ).
fof(f24965,plain,
~ sQ344_spl,
inference(contradiction_clause,[status(thm)],[f24964]) ).
fof(f24966,plain,
! [X0] :
( ~ sQ340_spl
| c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
inference(forward_demodulation,[status(thm)],[f1334,f24930]) ).
fof(f24967,plain,
( ~ sQ340_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f24966,f1156]) ).
fof(f24968,plain,
~ sQ340_spl,
inference(contradiction_clause,[status(thm)],[f24967]) ).
fof(f24969,plain,
( sQ339_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f24927,f3570]) ).
fof(f24970,plain,
sQ339_spl,
inference(contradiction_clause,[status(thm)],[f24969]) ).
fof(f25219,definition,
( sQ346_spl
<=> class_Ring__and__Field_Ocomm__semiring__1(t_a) ),
introduced(definition,[new_symbols(definition,[sQ346_spl])],[split_symbol_definition]) ).
fof(f25221,plain,
( sQ346_spl
| ~ class_Ring__and__Field_Ocomm__semiring__1(t_a) ),
inference(component_clause,[status(thm)],[f25219]) ).
fof(f25224,plain,
( sQ346_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f25221,f1907]) ).
fof(f25225,plain,
sQ346_spl,
inference(contradiction_clause,[status(thm)],[f25224]) ).
fof(f25783,plain,
! [X0,X1] :
( c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))) = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),X0,tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f3708,f2718]) ).
fof(f25794,plain,
! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(c_Suc(X0)),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(c_Suc(X0)),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f3708,f2478]) ).
fof(f25795,plain,
! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(c_Suc(c_Suc(X0)),X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(c_Suc(X0)),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
inference(paramodulation,[status(thm)],[f3708,f2477]) ).
fof(f25819,definition,
! [X0,X1] :
( sQ348_spl
<=> ( c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))) = c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),X0,tc_nat),X1,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ348_spl])],[split_symbol_definition]) ).
fof(f25822,plain,
( sQ348_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f25783,f2023,f25819]) ).
fof(f25835,definition,
! [X0,X1] :
( sQ349_spl
<=> ( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_Suc(c_Suc(X0)),tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(c_Suc(X0)),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ349_spl])],[split_symbol_definition]) ).
fof(f25838,plain,
( ~ sQ13_spl
| sQ349_spl ),
inference(split_clause,[status(thm)],[f25794,f25835,f2023]) ).
fof(f25839,definition,
! [X0,X1] :
( sQ350_spl
<=> ( c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(c_Suc(c_Suc(X0)),X1,tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(c_Suc(X0)),X0,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ350_spl])],[split_symbol_definition]) ).
fof(f25842,plain,
( ~ sQ13_spl
| sQ350_spl ),
inference(split_clause,[status(thm)],[f25795,f25839,f2023]) ).
fof(f26235,definition,
! [X0] :
( sQ352_spl
<=> ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ352_spl])],[split_symbol_definition]) ).
fof(f26236,plain,
! [X0] :
( ~ sQ352_spl
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
inference(component_clause,[status(thm)],[f26235]) ).
fof(f26243,definition,
! [X0,X1] :
( sQ354_spl
<=> ( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ354_spl])],[split_symbol_definition]) ).
fof(f26244,plain,
! [X0,X1] :
( ~ sQ354_spl
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(component_clause,[status(thm)],[f26243]) ).
fof(f26247,plain,
! [X0,X1] :
( ~ sQ354_spl
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(forward_demodulation,[status(thm)],[f23242,f26244]) ).
fof(f26248,plain,
! [X0,X1] :
( ~ sQ354_spl
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ),
inference(forward_subsumption_resolution,[status(thm)],[f26247,f1387]) ).
fof(f26253,plain,
! [X0,X1] :
( ~ sQ354_spl
| c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ),
inference(backward_subsumption_resolution,[status(thm)],[f4756,f26248]) ).
fof(f26292,plain,
( ~ sQ354_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f26253,f26248]) ).
fof(f26293,plain,
~ sQ354_spl,
inference(contradiction_clause,[status(thm)],[f26292]) ).
fof(f26442,plain,
( ~ sQ352_spl
| $false ),
inference(resolution,[status(thm)],[f26236,f869]) ).
fof(f26443,plain,
~ sQ352_spl,
inference(contradiction_clause,[status(thm)],[f26442]) ).
fof(f27493,plain,
! [X0,X1] :
( X1 = c_HOL_Ozero__class_Ozero(tc_nat)
| X0 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) ),
inference(forward_demodulation,[status(thm)],[f5793,f1358]) ).
fof(f27498,plain,
! [X0] :
( X0 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) != c_Suc(X0) ),
inference(paramodulation,[status(thm)],[f18641,f27493]) ).
fof(f27513,definition,
! [X0] :
( sQ355_spl
<=> ( X0 = c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) != c_Suc(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ355_spl])],[split_symbol_definition]) ).
fof(f27516,plain,
( sQ51_spl
| sQ355_spl ),
inference(split_clause,[status(thm)],[f27498,f27513,f3775]) ).
fof(f27545,definition,
! [X0] :
( sQ357_spl
<=> ( X0 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) != c_Suc(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ357_spl])],[split_symbol_definition]) ).
fof(f27546,plain,
! [X0] :
( ~ sQ357_spl
| X0 = c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) != c_Suc(X0) ),
inference(component_clause,[status(thm)],[f27545]) ).
fof(f27633,plain,
( ~ sQ357_spl
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
inference(resolution,[status(thm)],[f27546,f5793]) ).
fof(f27636,plain,
( ~ sQ357_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f27633,f3775,f27545]) ).
fof(f28840,plain,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f1382,f1042]) ).
fof(f28842,plain,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f1382,f1378]) ).
fof(f28850,plain,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oplus__class_Oplus(X0,X0,tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f1382,f864]) ).
fof(f28852,definition,
! [X0] :
( sQ365_spl
<=> c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ365_spl])],[split_symbol_definition]) ).
fof(f28855,plain,
( ~ sQ35_spl
| sQ365_spl ),
inference(split_clause,[status(thm)],[f28840,f28852,f2511]) ).
fof(f28857,definition,
! [X0] :
( sQ366_spl
<=> c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ366_spl])],[split_symbol_definition]) ).
fof(f28860,plain,
( ~ sQ35_spl
| sQ366_spl ),
inference(split_clause,[status(thm)],[f28842,f28857,f2511]) ).
fof(f28861,definition,
! [X0] :
( sQ367_spl
<=> c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oplus__class_Oplus(X0,X0,tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ367_spl])],[split_symbol_definition]) ).
fof(f28864,plain,
( ~ sQ35_spl
| sQ367_spl ),
inference(split_clause,[status(thm)],[f28850,f28861,f2511]) ).
fof(f28868,plain,
! [X0] :
( c_HOL_Oone__class_Oone(tc_nat) = X0
| ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f1383,f6789]) ).
fof(f28879,plain,
! [X0] :
( c_HOL_Oone__class_Oone(tc_nat) = X0
| ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_Suc(X0),tc_nat) ),
inference(forward_demodulation,[status(thm)],[f18641,f28868]) ).
fof(f29145,plain,
( c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(paramodulation,[status(thm)],[f5793,f28879]) ).
fof(f29154,definition,
( sQ375_spl
<=> c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ375_spl])],[split_symbol_definition]) ).
fof(f29157,plain,
( sQ51_spl
| ~ sQ375_spl ),
inference(split_clause,[status(thm)],[f29145,f29154,f3775]) ).
fof(f29358,plain,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f1399,f1042]) ).
fof(f29370,plain,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X0,tc_nat) ),
inference(resolution,[status(thm)],[f1399,f864]) ).
fof(f29371,definition,
! [X0] :
( sQ376_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ376_spl])],[split_symbol_definition]) ).
fof(f29374,plain,
( ~ sQ35_spl
| sQ376_spl ),
inference(split_clause,[status(thm)],[f29358,f29371,f2511]) ).
fof(f29377,definition,
! [X0] :
( sQ377_spl
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ377_spl])],[split_symbol_definition]) ).
fof(f29380,plain,
( ~ sQ35_spl
| sQ377_spl ),
inference(split_clause,[status(thm)],[f29370,f29377,f2511]) ).
fof(f29657,plain,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X0,tc_nat) ),
inference(resolution,[status(thm)],[f1401,f1387]) ).
fof(f29688,plain,
sQ117_spl,
inference(split_clause,[status(thm)],[f29657,f9327]) ).
fof(f30222,plain,
( sQ3_spl
| sQ7_spl
| v_a = c_HOL_Ozero__class_Ozero(t_a) ),
inference(resolution,[status(thm)],[f1892,f5572]) ).
fof(f30224,plain,
( sQ3_spl
| sQ7_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f30222,f1713]) ).
fof(f30225,plain,
( sQ3_spl
| sQ7_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f30224]) ).
fof(f30226,plain,
$false,
inference(sat_refutation,[status(thm)],[f1714,f1721,f1725,f1729,f1889,f1893,f1930,f2215,f2220,f2246,f2248,f2250,f2264,f2266,f2386,f2389,f2472,f2476,f2488,f2492,f2496,f2500,f2514,f2751,f2867,f2869,f2874,f3099,f3103,f3404,f3578,f3580,f3628,f3632,f3701,f3781,f3784,f3998,f4002,f4145,f4183,f4186,f4191,f4197,f4573,f5074,f5208,f5212,f5216,f5230,f5234,f5329,f5545,f5776,f5778,f5881,f5889,f6420,f6656,f6660,f6664,f6801,f6805,f6809,f7299,f7558,f7892,f7897,f7906,f7908,f8142,f8146,f8150,f8169,f8174,f8566,f9218,f9222,f9224,f9288,f9290,f9292,f9326,f9403,f9412,f9500,f9511,f9628,f9637,f9683,f9694,f9743,f9752,f9756,f9760,f9798,f10084,f10287,f10291,f10295,f10353,f11063,f11775,f11777,f11781,f11783,f11786,f11802,f12356,f12562,f12585,f12679,f12894,f12920,f13064,f13109,f13138,f13258,f13284,f13348,f13425,f13452,f13642,f13672,f13797,f13798,f13858,f13868,f14016,f14022,f14205,f14225,f14574,f14576,f14610,f14666,f15112,f15235,f16603,f16798,f18086,f18088,f18724,f18875,f18885,f19297,f19307,f19404,f19408,f19425,f19433,f19437,f19473,f19477,f19491,f19537,f19781,f19798,f19808,f19825,f19833,f19837,f19864,f19869,f19874,f20483,f20487,f20491,f20602,f20606,f20617,f20634,f20866,f20870,f20874,f21242,f22235,f22239,f23321,f23563,f23571,f23677,f23702,f23706,f24313,f24322,f24349,f24382,f24483,f24487,f24491,f24495,f24499,f24503,f24928,f24963,f24965,f24968,f24970,f25225,f25822,f25838,f25842,f26293,f26443,f27516,f27636,f28855,f28860,f28864,f29157,f29374,f29380,f29688,f30225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV677-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 09:18:50 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.41 % Drodi V4.1.1
% 22.70/3.56 % Refutation found
% 22.70/3.56 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 22.70/3.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.86/3.75 % Elapsed time: 3.368407 seconds
% 1.86/3.75 % CPU time: 25.281808 seconds
% 1.86/3.75 % Total memory used: 377.248 MB
% 1.86/3.75 % Net memory used: 347.871 MB
%------------------------------------------------------------------------------