%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV282-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 02:47:09 PM UTC 2026
% Result : Unsatisfiable 61.11s 13.23s
% Output : CNFRefutation 11.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 563
% Syntax : Number of formulae : 1949 ( 274 unt; 357 def)
% Number of atoms : 4603 ( 796 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 4873 (2219 ~;2297 |; 0 &)
% ( 357 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 378 ( 376 usr; 358 prp; 0-3 aty)
% Number of functors : 76 ( 76 usr; 15 con; 0-4 aty)
% Number of variables : 2673 (2673 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f28,axiom,
! [T_a] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(T_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [V_A,T_a,V_a] :
( c_in(c_insert(V_a,V_A,T_a),c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [V_S,T_a,V_y,V_x] :
( V_y = V_x
| ~ c_in(V_x,V_S,T_a)
| ~ c_in(V_y,V_S,T_a)
| ~ c_Infinite__Set_Oatmost__one(V_S,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [V_n,V_m] : c_less(c_uminus(c_IntDef_Oint(c_Suc(V_n)),tc_IntDef_Oint),c_IntDef_Oint(V_m),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [V_k,V_m] : c_Divides_Oop_Advd(V_k,c_times(V_m,V_k,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [V_A,V_xs,T_a] :
( c_in(V_xs,c_List_Olists(V_A,T_a),tc_List_Olist(T_a))
| ~ c_in(c_Main_Oin__listsI__1(V_A,V_xs,T_a),V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,axiom,
! [V_n] : c_lessequals(c_0,V_n,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,axiom,
! [V_n] : c_less(V_n,c_Suc(V_n),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [V_n] : ~ c_less(V_n,V_n,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [V_n] : c_less(c_0,c_Suc(V_n),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [T_a,V_x] :
( c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f70,axiom,
! [V_a,V_b,T_a,T_b,V_r] :
( c_in(V_a,c_Relation_ODomain(V_r,T_a,T_b),T_a)
| ~ c_in(c_Pair(V_a,V_b,T_a,T_b),V_r,tc_prod(T_a,T_b)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f76,axiom,
! [V_a,V_b,T_a,T_b,V_r] :
( c_in(V_b,c_Relation_ORange(V_r,T_a,T_b),T_b)
| ~ c_in(c_Pair(V_a,V_b,T_a,T_b),V_r,tc_prod(T_a,T_b)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f98,axiom,
! [V_x,T_a] : c_in(V_x,c_UNIV,T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f104,axiom,
! [V_A,V_B,T_a] :
( V_A = V_B
| c_less(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f110,axiom,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f111,axiom,
! [V_B,V_A,T_a] :
( V_A = V_B
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f112,axiom,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f138,axiom,
class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f154,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f158,axiom,
class_Orderings_Olinorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f171,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f172,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f175,axiom,
class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f181,axiom,
class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f183,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f203,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f210,axiom,
class_Orderings_Oord(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f211,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f214,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f221,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f224,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f236,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f243,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f249,axiom,
! [T_1] : class_Orderings_Oorder(tc_set(T_1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f453,axiom,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_Orderings_Olinorder(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1161,axiom,
! [V_y] : c_Binomial_Obinomial(V_y,c_Suc(c_0)) = V_y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1162,axiom,
! [V_n,V_k] : c_Binomial_Obinomial(c_Suc(V_n),c_Suc(V_k)) = c_plus(c_Binomial_Obinomial(V_n,V_k),c_Binomial_Obinomial(V_n,c_Suc(V_k)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1164,axiom,
! [V_n] : c_Binomial_Obinomial(V_n,c_0) = c_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1165,axiom,
! [V_n] : c_Binomial_Obinomial(V_n,V_n) = c_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1171,axiom,
! [V_xo,T_a] :
( V_xo = c_Datatype_Ooption_ONone
| c_Datatype_Oo2s(V_xo,T_a) != c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1172,axiom,
! [T_a] : c_Datatype_Oo2s(c_Datatype_Ooption_ONone,T_a) = c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1214,axiom,
! [V_y] : c_div(V_y,c_Suc(c_0),tc_nat) = V_y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1215,axiom,
! [V_m,V_n] : c_lessequals(c_div(V_m,V_n,tc_nat),V_m,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1217,axiom,
! [V_m,V_n] :
( c_less(c_div(V_m,V_n,tc_nat),V_m,tc_nat)
| ~ c_less(c_1,V_n,tc_nat)
| ~ c_less(c_0,V_m,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1234,axiom,
! [V_n,V_m] :
( c_lessequals(c_Divides_Oop_Amod(V_m,V_n,tc_nat),V_n,tc_nat)
| ~ c_less(c_0,V_n,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1236,axiom,
! [V_n,V_m] :
( c_less(c_Divides_Oop_Amod(V_m,V_n,tc_nat),V_n,tc_nat)
| ~ c_less(c_0,V_n,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1259,axiom,
! [T_a,V_U,V_A,V_x] :
( V_A = c_emptyset
| c_lessequals(V_U,V_x,T_a)
| ~ c_lessequals(c_Finite__Set_OMax(V_A,T_a),V_x,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_U,V_A,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1262,axiom,
! [T_a,V_U,V_A,V_x] :
( V_A = c_emptyset
| c_less(V_U,V_x,T_a)
| ~ c_less(c_Finite__Set_OMax(V_A,T_a),V_x,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_U,V_A,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1266,axiom,
! [T_a,V_U,V_A,V_x] :
( V_A = c_emptyset
| c_lessequals(V_x,V_U,T_a)
| ~ c_lessequals(V_x,c_Finite__Set_OMin(V_A,T_a),T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_U,V_A,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1268,axiom,
! [T_a,V_A,V_x] :
( V_A = c_emptyset
| c_lessequals(V_x,c_Finite__Set_OMin(V_A,T_a),T_a)
| ~ c_lessequals(V_x,c_Main_OMin__ge__iff__1(V_A,V_x,T_a),T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1269,axiom,
! [T_a,V_U,V_A,V_x] :
( V_A = c_emptyset
| c_less(V_x,V_U,T_a)
| ~ c_less(V_x,c_Finite__Set_OMin(V_A,T_a),T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_U,V_A,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1271,axiom,
! [T_a,V_A,V_x] :
( V_A = c_emptyset
| c_less(V_x,c_Finite__Set_OMin(V_A,T_a),T_a)
| ~ c_less(V_x,c_Main_OMin__gr__iff__1(V_A,V_x,T_a),T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1274,axiom,
! [T_a,V_x,V_A] :
( V_A = c_emptyset
| c_lessequals(c_Finite__Set_OMin(V_A,T_a),V_x,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_x,V_A,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1277,axiom,
! [T_a] :
( c_Finite__Set_Ocard(c_emptyset,T_a) = c_0
| ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1280,axiom,
! [V_A,T_a,V_x] :
( c_Finite__Set_Ocard(c_insert(V_x,V_A,T_a),T_a) = c_Suc(c_Finite__Set_Ocard(V_A,T_a))
| c_in(V_x,V_A,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1282,axiom,
! [V_A,V_a,V_B,T_a] :
( c_in(c_minus(V_A,V_B,tc_set(T_a)),c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(c_minus(V_A,c_insert(V_a,V_B,T_a),tc_set(T_a)),c_Finite__Set_OFinites,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1283,axiom,
! [V_A,V_B,T_a,V_a] :
( c_in(c_minus(V_A,c_insert(V_a,V_B,T_a),tc_set(T_a)),c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(c_minus(V_A,V_B,tc_set(T_a)),c_Finite__Set_OFinites,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1291,axiom,
! [V_a,V_A,T_a] :
( c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(c_insert(V_a,V_A,T_a),c_Finite__Set_OFinites,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1295,axiom,
! [V_y] : c_NatArith_Oof__nat(V_y,tc_nat) = V_y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1344,axiom,
c_IntDef_Onat(c_1) = c_Suc(c_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1352,axiom,
! [V_w,V_z] :
( c_less(V_w,c_plus(V_z,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(V_w,V_z,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1353,axiom,
! [V_w,V_z] :
( c_less(V_w,V_z,tc_IntDef_Oint)
| ~ c_lessequals(V_w,c_minus(V_z,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1354,axiom,
! [V_w,V_z] :
( c_lessequals(V_w,c_minus(V_z,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(V_w,V_z,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1364,axiom,
! [T_a] :
( c_in(c_1,c_IntDef_ONats,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1367,axiom,
! [V_m] : c_HOL_Oabs(c_IntDef_Oint(V_m),tc_IntDef_Oint) = c_IntDef_Oint(V_m),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1370,axiom,
c_0 != c_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1371,axiom,
c_IntDef_Oint(c_1) = c_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1374,axiom,
c_IntDef_Oint(c_0) = c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1376,axiom,
! [V_n] :
( V_n = c_0
| ~ c_lessequals(c_IntDef_Oint(V_n),c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1385,axiom,
! [V_z] :
( c_IntDef_Onat(V_z) = c_0
| ~ c_lessequals(V_z,c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1386,axiom,
c_IntDef_Onat(c_0) = c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1387,axiom,
! [V_n] : c_IntDef_Onat(c_uminus(c_IntDef_Oint(V_n),tc_IntDef_Oint)) = c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1391,axiom,
c_uminus(c_IntDef_Oint(c_0),tc_IntDef_Oint) = c_IntDef_Oint(c_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1394,axiom,
! [V_n] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(V_n)),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1397,axiom,
! [T_a,V_z] :
( c_lessequals(c_0,V_z,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(V_z,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1398,axiom,
! [T_a,V_z] :
( c_lessequals(c_0,c_IntDef_Oof__int(V_z,T_a),T_a)
| ~ c_lessequals(c_0,V_z,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1419,axiom,
! [T_a,V_n] :
( c_in(c_NatArith_Oof__nat(V_n,T_a),c_IntDef_ONats,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1428,axiom,
! [V_m,V_n] :
( c_less(c_IntDef_Oint(V_m),c_IntDef_Oint(V_n),tc_IntDef_Oint)
| ~ c_less(V_m,V_n,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1429,axiom,
! [V_w,V_z] :
( c_less(c_0,V_z,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(V_w),c_IntDef_Onat(V_z),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1431,axiom,
! [V_w,V_z] :
( c_less(c_IntDef_Onat(V_w),c_IntDef_Onat(V_z),tc_nat)
| ~ c_less(c_0,V_z,tc_IntDef_Oint)
| ~ c_less(V_w,V_z,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1454,axiom,
! [V_b,V_a] :
( c_less(V_b,c_Divides_Oop_Amod(V_a,V_b,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(V_b,c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1462,axiom,
! [V_b,V_a] :
( c_less(c_Divides_Oop_Amod(V_a,V_b,tc_IntDef_Oint),V_b,tc_IntDef_Oint)
| ~ c_less(c_0,V_b,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1464,axiom,
! [V_p] : c_Nat_Opower(V_p,c_0,tc_IntDef_Oint) = c_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1478,axiom,
! [V_m] :
( V_m = c_0
| ~ c_Divides_Oop_Advd(c_0,V_m,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1486,axiom,
! [V_x] : c_less(c_0,c_Nat_Opower(c_HOL_Oabs(V_x,tc_IntDef_Oint),c_0,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1597,axiom,
! [V_xs,T_a] :
( V_xs = c_List_Olist_ONil
| c_Nat_Osize(V_xs,tc_List_Olist(T_a)) != c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1598,axiom,
! [T_a] : c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(T_a)) = c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1623,axiom,
! [V_a_H,V_list_H,T_a] : c_List_Olist_ONil != c_List_Olist_OCons(V_a_H,V_list_H,T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1750,axiom,
! [V_xs,T_a] :
( V_xs = c_List_Olist_ONil
| c_emptyset != c_List_Oset(V_xs,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1751,axiom,
! [T_a] : c_emptyset = c_List_Oset(c_List_Olist_ONil,T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1754,axiom,
! [V_xs,T_a] : c_List_Oset(c_List_Oremdups(V_xs,T_a),T_a) = c_List_Oset(V_xs,T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1757,axiom,
! [V_xs,T_a] : c_List_Oset(c_List_Orev(V_xs,T_a),T_a) = c_List_Oset(V_xs,T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1758,axiom,
! [V_xs,T_a] : c_List_Oset(c_List_Orotate1(V_xs,T_a),T_a) = c_List_Oset(V_xs,T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1786,axiom,
! [V_j,V_i] :
( c_List_Oupt(V_i,V_j) = c_List_Olist_ONil
| ~ c_lessequals(V_j,V_i,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1803,axiom,
! [T_a,V_n] :
( c_0 = V_n
| c_0 != c_NatArith_Oof__nat(V_n,T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1805,axiom,
! [T_a,V_n] :
( c_lessequals(c_0,c_NatArith_Oof__nat(V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1806,axiom,
! [T_a,V_n] :
( c_less(c_0,V_n,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1807,axiom,
! [T_a,V_n] :
( c_less(c_0,c_NatArith_Oof__nat(V_n,T_a),T_a)
| ~ c_less(c_0,V_n,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1815,axiom,
! [T_a] :
( c_lessequals(c_NatArith_Oof__nat(c_0,T_a),c_0,T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1816,axiom,
! [T_a,V_m,V_n] :
( c_lessequals(V_m,V_n,tc_nat)
| ~ c_lessequals(c_NatArith_Oof__nat(V_m,T_a),c_NatArith_Oof__nat(V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1818,axiom,
! [T_a,V_m] :
( ~ c_less(c_NatArith_Oof__nat(V_m,T_a),c_0,T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2016,axiom,
c_1 = c_Suc(c_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2017,axiom,
! [V_m,V_n] :
( V_m = V_n
| c_Suc(V_m) != c_Suc(V_n) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2019,axiom,
! [V_n,V_m] :
( c_lessequals(V_n,V_m,tc_nat)
| ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2020,axiom,
! [V_n,V_m] :
( c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat)
| ~ c_lessequals(V_n,V_m,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2021,axiom,
! [V_m,V_n] :
( c_less(V_m,V_n,tc_nat)
| ~ c_less(c_Suc(V_m),c_Suc(V_n),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2022,axiom,
! [V_m,V_n] :
( c_less(c_Suc(V_m),c_Suc(V_n),tc_nat)
| ~ c_less(V_m,V_n,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2023,axiom,
! [V_m] : c_Suc(V_m) != c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2026,axiom,
! [V_y] : c_plus(V_y,c_0,tc_nat) = V_y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2031,axiom,
! [V_m,V_n] :
( V_m = c_0
| c_plus(V_m,V_n,tc_nat) != c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2034,axiom,
! [V_n] : c_minus(c_0,V_n,tc_nat) = c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2040,axiom,
! [V_m,V_n] : c_lessequals(c_minus(V_m,V_n,tc_nat),V_m,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2042,axiom,
! [V_i] :
( V_i = c_0
| ~ c_lessequals(V_i,c_0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2046,axiom,
! [V_n] :
( V_n = c_0
| ~ c_less(V_n,c_Suc(c_0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2047,axiom,
c_less(c_0,c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2050,axiom,
! [V_y] : c_Orderings_Omax(c_0,V_y,tc_nat) = V_y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2051,axiom,
! [V_y] : c_Orderings_Omax(V_y,c_0,tc_nat) = V_y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2053,axiom,
! [V_n] : c_Orderings_Omin(c_0,V_n,tc_nat) = c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2054,axiom,
! [V_n] : c_Orderings_Omin(V_n,c_0,tc_nat) = c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2088,axiom,
! [V_j,V_i] : ~ c_less(c_plus(V_j,V_i,tc_nat),V_i,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2089,axiom,
! [V_n] :
( V_n = c_0
| c_less(c_0,V_n,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2091,axiom,
! [V_n] : ~ c_less(V_n,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2171,axiom,
! [T_a,V_a] :
( c_plus(c_uminus(V_a,T_a),V_a,T_a) = c_0
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2172,axiom,
! [T_a,V_a] :
( V_a = c_0
| c_0 != c_HOL_Oabs(V_a,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2177,axiom,
! [T_a,V_a] :
( c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2180,axiom,
! [T_a] :
( c_lessequals(c_HOL_Oabs(c_0,T_a),c_0,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2182,axiom,
! [T_a,V_a] :
( ~ c_less(c_HOL_Oabs(V_a,T_a),c_0,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2185,axiom,
! [T_a,V_y] :
( c_plus(V_y,c_0,T_a) = V_y
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2198,axiom,
! [T_a,V_y] :
( c_minus(V_y,c_0,T_a) = V_y
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2199,axiom,
! [T_a,V_a,V_b] :
( V_a = V_b
| c_minus(V_a,V_b,T_a) != c_0
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2201,axiom,
! [T_a,V_a,V_b] :
( c_lessequals(c_minus(V_a,V_b,T_a),c_0,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2207,axiom,
! [T_a,V_a] :
( c_lessequals(c_plus(V_a,V_a,T_a),c_0,T_a)
| ~ c_lessequals(V_a,c_0,T_a)
| ~ class_OrderedGroup_Olordered__ab__group(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2216,axiom,
! [T_a,V_y] :
( c_uminus(c_uminus(V_y,T_a),T_a) = V_y
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2230,axiom,
! [T_a,V_a] :
( c_lessequals(c_uminus(V_a,T_a),c_0,T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2231,axiom,
! [T_a,V_b,V_a] :
( c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_uminus(V_b,T_a),c_uminus(V_a,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2232,axiom,
! [T_a,V_a,V_b] :
( c_lessequals(c_uminus(V_b,T_a),c_uminus(V_a,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2234,axiom,
! [T_a,V_a] :
( c_less(c_uminus(V_a,T_a),c_0,T_a)
| ~ c_less(c_0,V_a,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2235,axiom,
! [T_a,V_b,V_a] :
( c_less(V_a,V_b,T_a)
| ~ c_less(c_uminus(V_b,T_a),c_uminus(V_a,T_a),T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2236,axiom,
! [T_a,V_a,V_b] :
( c_less(c_uminus(V_b,T_a),c_uminus(V_a,T_a),T_a)
| ~ c_less(V_a,V_b,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2241,axiom,
! [T_a,V_a] :
( c_lessequals(c_OrderedGroup_Onprt(V_a,T_a),c_0,T_a)
| ~ class_OrderedGroup_Olordered__ab__group(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2253,axiom,
! [T_a,V_x,V_y,V_z] :
( c_less(V_x,V_z,T_a)
| ~ c_less(c_Orderings_Omax(V_x,V_y,T_a),V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2254,axiom,
! [T_a,V_x,V_y,V_z] :
( c_less(V_y,V_z,T_a)
| ~ c_less(c_Orderings_Omax(V_x,V_y,T_a),V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2256,axiom,
! [T_a,V_z,V_x,V_y] :
( c_less(V_z,V_x,T_a)
| ~ c_less(V_z,c_Orderings_Omin(V_x,V_y,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2257,axiom,
! [T_a,V_z,V_x,V_y] :
( c_less(V_z,V_y,T_a)
| ~ c_less(V_z,c_Orderings_Omin(V_x,V_y,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2259,axiom,
! [T_b,V_x,V_y,V_z] :
( c_lessequals(V_x,V_y,T_b)
| ~ c_lessequals(V_x,c_Orderings_Omin(V_y,V_z,T_b),T_b)
| ~ class_Orderings_Olinorder(T_b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2260,axiom,
! [T_b,V_x,V_y,V_z] :
( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(V_x,c_Orderings_Omin(V_y,V_z,T_b),T_b)
| ~ class_Orderings_Olinorder(T_b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2264,axiom,
! [T_b,V_x,V_y,V_z] :
( c_lessequals(V_x,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2265,axiom,
! [T_b,V_x,V_y,V_z] :
( c_lessequals(V_y,V_z,T_b)
| ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2269,axiom,
! [T_a,V_x] :
( ~ c_less(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2278,axiom,
! [V_x] :
( ~ c_Parity_Oeven(c_Suc(V_x),tc_nat)
| ~ c_Parity_Oeven(V_x,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2279,axiom,
! [V_x] :
( c_Parity_Oeven(c_Suc(V_x),tc_nat)
| c_Parity_Oeven(V_x,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2290,axiom,
c_Parity_Oeven(c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2297,axiom,
! [V_x,V_y] :
( c_Parity_Oeven(c_times(V_x,V_y,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(V_x,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2303,axiom,
c_Parity_Oeven(c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2340,axiom,
! [V_i,V_n] :
( c_lessequals(c_Suc(c_0),c_Nat_Opower(V_i,V_n,tc_nat),tc_nat)
| ~ c_lessequals(c_1,V_i,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2344,axiom,
! [V_p] : c_Nat_Opower(V_p,c_0,tc_nat) = c_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2395,axiom,
! [T_a] :
( c_0 != c_1
| ~ class_Ring__and__Field_Oaxclass__0__neq__1(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2511,axiom,
! [T_a] :
( c_lessequals(c_0,c_1,T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2528,axiom,
c_SetInterval_OatLeast(c_0,tc_nat) = c_UNIV,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2530,axiom,
! [T_a,V_i,V_k] :
( c_lessequals(V_k,V_i,T_a)
| ~ c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2531,axiom,
! [T_a,V_k,V_i] :
( c_in(V_i,c_SetInterval_OatLeast(V_k,T_a),T_a)
| ~ c_lessequals(V_k,V_i,T_a)
| ~ class_Orderings_Oord(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2567,axiom,
c_SetInterval_OlessThan(c_0,tc_nat) = c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2569,axiom,
! [T_a,V_i,V_k] :
( c_less(V_i,V_k,T_a)
| ~ c_in(V_i,c_SetInterval_OlessThan(V_k,T_a),T_a)
| ~ class_Orderings_Oord(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2570,axiom,
! [T_a,V_i,V_k] :
( c_in(V_i,c_SetInterval_OlessThan(V_k,T_a),T_a)
| ~ c_less(V_i,V_k,T_a)
| ~ class_Orderings_Oord(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2587,axiom,
! [V_A,T_a] : c_minus(V_A,c_UNIV,tc_set(T_a)) = c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2588,axiom,
! [V_A,T_a] : c_minus(V_A,V_A,tc_set(T_a)) = c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2590,axiom,
! [V_y,T_a] : c_minus(V_y,c_emptyset,tc_set(T_a)) = V_y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2598,axiom,
! [V_A,V_B,T_a] :
( V_A = c_UNIV
| c_inter(V_A,V_B,T_a) != c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2601,axiom,
! [V_y,T_a] : c_inter(c_UNIV,V_y,T_a) = V_y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2612,axiom,
! [T_a] : c_Inter(c_UNIV,T_a) = c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2615,axiom,
! [V_A,T_a] :
( c_Inter(V_A,T_a) = c_UNIV
| c_Main_OInter__UNIV__conv__1__1(V_A,T_a) != c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2618,axiom,
! [V_A,T_a] :
( c_UNIV = c_Inter(V_A,T_a)
| c_Main_OInter__UNIV__conv__2__1(V_A,T_a) != c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2629,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2633,axiom,
! [V_A,T_a] : c_union(V_A,c_UNIV,T_a) = c_UNIV,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2635,axiom,
! [V_A,V_B,T_a] :
( V_A = c_emptyset
| c_union(V_A,V_B,T_a) != c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2649,axiom,
! [T_a] : c_Union(c_UNIV,T_a) = c_UNIV,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2654,axiom,
! [V_A,T_a] :
( c_Union(V_A,T_a) = c_emptyset
| c_Main_OUnion__empty__conv__1(V_A,T_a) != c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2659,axiom,
! [V_A,T_a] :
( V_A = c_emptyset
| c_in(c_Main_Oall__not__in__conv__1(V_A,T_a),V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2668,axiom,
! [V_A,T_a] : c_minus(c_emptyset,V_A,tc_set(T_a)) = c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2671,axiom,
! [V_A,T_a] :
( c_emptyset = c_Union(V_A,T_a)
| c_Main_Oempty__Union__conv__1(V_A,T_a) != c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2672,axiom,
! [V_c,T_a] : ~ c_in(V_c,c_emptyset,T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2673,axiom,
! [V_a,V_A,T_a] : c_emptyset != c_insert(V_a,V_A,T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2684,axiom,
! [V_x,V_A,T_a] : c_in(V_x,c_insert(V_x,V_A,T_a),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2685,axiom,
! [V_a,V_A,T_a,V_b] :
( c_in(V_a,c_insert(V_b,V_A,T_a),T_a)
| ~ c_in(V_a,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2688,axiom,
! [V_x,V_A,T_a,V_B] :
( c_in(V_x,V_B,T_a)
| ~ c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2689,axiom,
! [V_x,V_A,T_a,V_B] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2698,axiom,
! [V_A,T_a] : c_lessequals(V_A,c_UNIV,tc_set(T_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2728,axiom,
! [V_X,V_Y,V_H] :
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2729,axiom,
! [V_X,V_Y,V_H] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2753,axiom,
! [V_nat,V_nat_H] :
( V_nat = V_nat_H
| c_Message_Omsg_ONonce(V_nat) != c_Message_Omsg_ONonce(V_nat_H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2767,axiom,
! [V_X,V_H] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ~ c_in(V_X,V_H,tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2770,axiom,
c_Message_Oparts(c_emptyset) = c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2812,axiom,
! [V_X,V_x] : c_Message_OHPair(V_X,V_x) = c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(V_X,V_x)),V_x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2853,axiom,
c_Message_Oanalz(c_emptyset) = c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2860,axiom,
! [V_N,V_H] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(V_N),V_H,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(V_N),c_Message_Oanalz(V_H),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2862,axiom,
! [V_H] : c_Message_Oanalz(c_Message_Oparts(V_H)) = c_Message_Oparts(V_H),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2878,axiom,
! [V_N,V_H] : c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(V_N),V_H,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(V_N),c_Message_Oparts(V_H),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2899,axiom,
! [V_y] :
( c_Message_OinvKey(V_y) = V_y
| ~ c_in(V_y,c_Message_OsymKeys,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2923,axiom,
! [V_X] : c_in(c_Public_OshrK(V_X),c_Message_OsymKeys,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2933,axiom,
! [V_n,V_m] : c_lessequals(V_n,c_plus(V_n,V_m,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2934,axiom,
! [V_n,V_m] : c_lessequals(V_n,c_plus(V_m,V_n,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2935,axiom,
! [V_m,V_n] :
( c_lessequals(V_m,V_n,tc_nat)
| ~ c_less(V_m,c_Suc(V_n),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2936,axiom,
! [V_m,V_n] :
( c_less(V_m,c_Suc(V_n),tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2937,axiom,
! [V_U,V_evs] :
( ~ c_lessequals(v_sko__urX(V_evs),V_U,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(V_evs),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2938,negated_conjecture,
! [V_U,V_W,V_V] :
( c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(v_evs),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(V_V),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(V_W),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| V_U = V_V
| V_V = V_W
| V_U = V_W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2980,plain,
! [X0] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X0)),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f2981,plain,
! [V_A,T_a] :
( ! [V_a] : c_in(c_insert(V_a,V_A,T_a),c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a)) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f2982,plain,
! [X0,X1,X2] :
( c_in(c_insert(X2,X0,X1),c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(X1)) ),
inference(cnf_transformation,[status(thm)],[f2981]) ).
fof(f2991,plain,
! [V_y,V_x] :
( V_y = V_x
| ! [V_S,T_a] :
( ~ c_in(V_x,V_S,T_a)
| ~ c_in(V_y,V_S,T_a)
| ~ c_Infinite__Set_Oatmost__one(V_S,T_a) ) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f2992,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ c_in(X3,X0,X1)
| ~ c_in(X2,X0,X1)
| ~ c_Infinite__Set_Oatmost__one(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f2991]) ).
fof(f2994,plain,
! [X0,X1] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X0)),tc_IntDef_Oint),c_IntDef_Oint(X1),tc_IntDef_Oint),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f2998,plain,
! [X0,X1] : c_Divides_Oop_Advd(X0,c_times(X1,X0,tc_IntDef_Oint),tc_IntDef_Oint),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f3005,plain,
! [X0,X1,X2] :
( c_in(X1,c_List_Olists(X0,X2),tc_List_Olist(X2))
| ~ c_in(c_Main_Oin__listsI__1(X0,X1,X2),X0,X2) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f3025,plain,
! [X0] : c_lessequals(c_0,X0,tc_nat),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f3026,plain,
! [X0] : c_less(X0,c_Suc(X0),tc_nat),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f3027,plain,
! [X0] : ~ c_less(X0,X0,tc_nat),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f3028,plain,
! [X0] : c_less(c_0,c_Suc(X0),tc_nat),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f3029,plain,
! [T_a] :
( ! [V_x] : c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(miniscoping,[status(thm)],[f68]) ).
fof(f3030,plain,
! [X0,X1] :
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(thm)],[f3029]) ).
fof(f3032,plain,
! [V_a,T_a,T_b,V_r] :
( c_in(V_a,c_Relation_ODomain(V_r,T_a,T_b),T_a)
| ! [V_b] : ~ c_in(c_Pair(V_a,V_b,T_a,T_b),V_r,tc_prod(T_a,T_b)) ),
inference(miniscoping,[status(thm)],[f70]) ).
fof(f3033,plain,
! [X0,X1,X2,X3,X4] :
( c_in(X0,c_Relation_ODomain(X4,X2,X3),X2)
| ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f3032]) ).
fof(f3040,plain,
! [V_b,T_a,T_b,V_r] :
( c_in(V_b,c_Relation_ORange(V_r,T_a,T_b),T_b)
| ! [V_a] : ~ c_in(c_Pair(V_a,V_b,T_a,T_b),V_r,tc_prod(T_a,T_b)) ),
inference(miniscoping,[status(thm)],[f76]) ).
fof(f3041,plain,
! [X0,X1,X2,X3,X4] :
( c_in(X1,c_Relation_ORange(X4,X2,X3),X3)
| ~ c_in(c_Pair(X0,X1,X2,X3),X4,tc_prod(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f3040]) ).
fof(f3064,plain,
! [X0,X1] : c_in(X0,c_UNIV,X1),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f3070,plain,
! [V_A,V_B] :
( V_A = V_B
| ! [T_a] :
( c_less(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a)) ) ),
inference(miniscoping,[status(thm)],[f104]) ).
fof(f3071,plain,
! [X0,X1,X2] :
( X0 = X1
| c_less(X0,X1,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(thm)],[f3070]) ).
fof(f3080,plain,
! [X0,X1,X2] :
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f3081,plain,
! [V_B,V_A] :
( V_A = V_B
| ! [T_a] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ) ),
inference(miniscoping,[status(thm)],[f111]) ).
fof(f3082,plain,
! [X0,X1,X2] :
( X1 = X0
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(thm)],[f3081]) ).
fof(f3083,plain,
! [X0,X1] : c_lessequals(X0,X0,tc_set(X1)),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f3115,plain,
class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f3131,plain,
class_Orderings_Oorder(tc_IntDef_Oint),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f3135,plain,
class_Orderings_Olinorder(tc_IntDef_Oint),
inference(cnf_transformation,[status(thm)],[f158]) ).
fof(f3148,plain,
class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f3149,plain,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f3152,plain,
class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f3158,plain,
class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
inference(cnf_transformation,[status(thm)],[f181]) ).
fof(f3160,plain,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
inference(cnf_transformation,[status(thm)],[f183]) ).
fof(f3181,plain,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f3188,plain,
class_Orderings_Oord(tc_nat),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f3189,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f3192,plain,
class_OrderedGroup_Omonoid__mult(tc_nat),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f3199,plain,
class_Orderings_Oorder(tc_nat),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f3202,plain,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
inference(cnf_transformation,[status(thm)],[f224]) ).
fof(f3214,plain,
class_Ring__and__Field_Oordered__semidom(tc_nat),
inference(cnf_transformation,[status(thm)],[f236]) ).
fof(f3221,plain,
class_Orderings_Olinorder(tc_nat),
inference(cnf_transformation,[status(thm)],[f243]) ).
fof(f3228,plain,
! [X0] : class_Orderings_Oorder(tc_set(X0)),
inference(cnf_transformation,[status(thm)],[f249]) ).
fof(f3433,plain,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f453]) ).
fof(f4141,plain,
! [X0] : c_Binomial_Obinomial(X0,c_Suc(c_0)) = X0,
inference(cnf_transformation,[status(thm)],[f1161]) ).
fof(f4142,plain,
! [X0,X1] : c_Binomial_Obinomial(c_Suc(X0),c_Suc(X1)) = c_plus(c_Binomial_Obinomial(X0,X1),c_Binomial_Obinomial(X0,c_Suc(X1)),tc_nat),
inference(cnf_transformation,[status(thm)],[f1162]) ).
fof(f4144,plain,
! [X0] : c_Binomial_Obinomial(X0,c_0) = c_1,
inference(cnf_transformation,[status(thm)],[f1164]) ).
fof(f4145,plain,
! [X0] : c_Binomial_Obinomial(X0,X0) = c_1,
inference(cnf_transformation,[status(thm)],[f1165]) ).
fof(f4153,plain,
! [V_xo] :
( V_xo = c_Datatype_Ooption_ONone
| ! [T_a] : c_Datatype_Oo2s(V_xo,T_a) != c_emptyset ),
inference(miniscoping,[status(thm)],[f1171]) ).
fof(f4154,plain,
! [X0,X1] :
( X0 = c_Datatype_Ooption_ONone
| c_Datatype_Oo2s(X0,X1) != c_emptyset ),
inference(cnf_transformation,[status(thm)],[f4153]) ).
fof(f4155,plain,
! [X0] : c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X0) = c_emptyset,
inference(cnf_transformation,[status(thm)],[f1172]) ).
fof(f4203,plain,
! [X0] : c_div(X0,c_Suc(c_0),tc_nat) = X0,
inference(cnf_transformation,[status(thm)],[f1214]) ).
fof(f4204,plain,
! [X0,X1] : c_lessequals(c_div(X0,X1,tc_nat),X0,tc_nat),
inference(cnf_transformation,[status(thm)],[f1215]) ).
fof(f4206,plain,
! [X0,X1] :
( c_less(c_div(X0,X1,tc_nat),X0,tc_nat)
| ~ c_less(c_1,X1,tc_nat)
| ~ c_less(c_0,X0,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f1217]) ).
fof(f4229,plain,
! [V_n] :
( ! [V_m] : c_lessequals(c_Divides_Oop_Amod(V_m,V_n,tc_nat),V_n,tc_nat)
| ~ c_less(c_0,V_n,tc_nat) ),
inference(miniscoping,[status(thm)],[f1234]) ).
fof(f4230,plain,
! [X0,X1] :
( c_lessequals(c_Divides_Oop_Amod(X1,X0,tc_nat),X0,tc_nat)
| ~ c_less(c_0,X0,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f4229]) ).
fof(f4232,plain,
! [V_n] :
( ! [V_m] : c_less(c_Divides_Oop_Amod(V_m,V_n,tc_nat),V_n,tc_nat)
| ~ c_less(c_0,V_n,tc_nat) ),
inference(miniscoping,[status(thm)],[f1236]) ).
fof(f4233,plain,
! [X0,X1] :
( c_less(c_Divides_Oop_Amod(X1,X0,tc_nat),X0,tc_nat)
| ~ c_less(c_0,X0,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f4232]) ).
fof(f4261,plain,
! [V_A] :
( V_A = c_emptyset
| ! [T_a,V_U,V_x] :
( c_lessequals(V_U,V_x,T_a)
| ~ c_lessequals(c_Finite__Set_OMax(V_A,T_a),V_x,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_U,V_A,T_a)
| ~ class_Orderings_Olinorder(T_a) ) ),
inference(miniscoping,[status(thm)],[f1259]) ).
fof(f4262,plain,
! [X0,X1,X2,X3] :
( X2 = c_emptyset
| c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_Finite__Set_OMax(X2,X0),X3,X0)
| ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f4261]) ).
fof(f4267,plain,
! [V_A] :
( V_A = c_emptyset
| ! [T_a,V_U,V_x] :
( c_less(V_U,V_x,T_a)
| ~ c_less(c_Finite__Set_OMax(V_A,T_a),V_x,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_U,V_A,T_a)
| ~ class_Orderings_Olinorder(T_a) ) ),
inference(miniscoping,[status(thm)],[f1262]) ).
fof(f4268,plain,
! [X0,X1,X2,X3] :
( X2 = c_emptyset
| c_less(X1,X3,X0)
| ~ c_less(c_Finite__Set_OMax(X2,X0),X3,X0)
| ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f4267]) ).
fof(f4275,plain,
! [V_A] :
( V_A = c_emptyset
| ! [T_a,V_U,V_x] :
( c_lessequals(V_x,V_U,T_a)
| ~ c_lessequals(V_x,c_Finite__Set_OMin(V_A,T_a),T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_U,V_A,T_a)
| ~ class_Orderings_Olinorder(T_a) ) ),
inference(miniscoping,[status(thm)],[f1266]) ).
fof(f4276,plain,
! [X0,X1,X2,X3] :
( X2 = c_emptyset
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(X3,c_Finite__Set_OMin(X2,X0),X0)
| ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f4275]) ).
fof(f4279,plain,
! [V_A] :
( V_A = c_emptyset
| ! [T_a,V_x] :
( c_lessequals(V_x,c_Finite__Set_OMin(V_A,T_a),T_a)
| ~ c_lessequals(V_x,c_Main_OMin__ge__iff__1(V_A,V_x,T_a),T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ class_Orderings_Olinorder(T_a) ) ),
inference(miniscoping,[status(thm)],[f1268]) ).
fof(f4280,plain,
! [X0,X1,X2] :
( X1 = c_emptyset
| c_lessequals(X2,c_Finite__Set_OMin(X1,X0),X0)
| ~ c_lessequals(X2,c_Main_OMin__ge__iff__1(X1,X2,X0),X0)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f4279]) ).
fof(f4281,plain,
! [V_A] :
( V_A = c_emptyset
| ! [T_a,V_U,V_x] :
( c_less(V_x,V_U,T_a)
| ~ c_less(V_x,c_Finite__Set_OMin(V_A,T_a),T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_U,V_A,T_a)
| ~ class_Orderings_Olinorder(T_a) ) ),
inference(miniscoping,[status(thm)],[f1269]) ).
fof(f4282,plain,
! [X0,X1,X2,X3] :
( X2 = c_emptyset
| c_less(X3,X1,X0)
| ~ c_less(X3,c_Finite__Set_OMin(X2,X0),X0)
| ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f4281]) ).
fof(f4285,plain,
! [V_A] :
( V_A = c_emptyset
| ! [T_a,V_x] :
( c_less(V_x,c_Finite__Set_OMin(V_A,T_a),T_a)
| ~ c_less(V_x,c_Main_OMin__gr__iff__1(V_A,V_x,T_a),T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ class_Orderings_Olinorder(T_a) ) ),
inference(miniscoping,[status(thm)],[f1271]) ).
fof(f4286,plain,
! [X0,X1,X2] :
( X1 = c_emptyset
| c_less(X2,c_Finite__Set_OMin(X1,X0),X0)
| ~ c_less(X2,c_Main_OMin__gr__iff__1(X1,X2,X0),X0)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f4285]) ).
fof(f4291,plain,
! [V_A] :
( V_A = c_emptyset
| ! [T_a,V_x] :
( c_lessequals(c_Finite__Set_OMin(V_A,T_a),V_x,T_a)
| ~ c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(V_x,V_A,T_a)
| ~ class_Orderings_Olinorder(T_a) ) ),
inference(miniscoping,[status(thm)],[f1274]) ).
fof(f4292,plain,
! [X0,X1,X2] :
( X2 = c_emptyset
| c_lessequals(c_Finite__Set_OMin(X2,X0),X1,X0)
| ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f4291]) ).
fof(f4297,plain,
! [X0] :
( c_Finite__Set_Ocard(c_emptyset,X0) = c_0
| ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X0)) ),
inference(cnf_transformation,[status(thm)],[f1277]) ).
fof(f4300,plain,
! [X0,X1,X2] :
( c_Finite__Set_Ocard(c_insert(X2,X0,X1),X1) = c_Suc(c_Finite__Set_Ocard(X0,X1))
| c_in(X2,X0,X1)
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(X1)) ),
inference(cnf_transformation,[status(thm)],[f1280]) ).
fof(f4303,plain,
! [V_A,V_B,T_a] :
( c_in(c_minus(V_A,V_B,tc_set(T_a)),c_Finite__Set_OFinites,tc_set(T_a))
| ! [V_a] : ~ c_in(c_minus(V_A,c_insert(V_a,V_B,T_a),tc_set(T_a)),c_Finite__Set_OFinites,tc_set(T_a)) ),
inference(miniscoping,[status(thm)],[f1282]) ).
fof(f4304,plain,
! [X0,X1,X2,X3] :
( c_in(c_minus(X0,X2,tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3))
| ~ c_in(c_minus(X0,c_insert(X1,X2,X3),tc_set(X3)),c_Finite__Set_OFinites,tc_set(X3)) ),
inference(cnf_transformation,[status(thm)],[f4303]) ).
fof(f4305,plain,
! [V_A,V_B,T_a] :
( ! [V_a] : c_in(c_minus(V_A,c_insert(V_a,V_B,T_a),tc_set(T_a)),c_Finite__Set_OFinites,tc_set(T_a))
| ~ c_in(c_minus(V_A,V_B,tc_set(T_a)),c_Finite__Set_OFinites,tc_set(T_a)) ),
inference(miniscoping,[status(thm)],[f1283]) ).
fof(f4306,plain,
! [X0,X1,X2,X3] :
( c_in(c_minus(X0,c_insert(X3,X1,X2),tc_set(X2)),c_Finite__Set_OFinites,tc_set(X2))
| ~ c_in(c_minus(X0,X1,tc_set(X2)),c_Finite__Set_OFinites,tc_set(X2)) ),
inference(cnf_transformation,[status(thm)],[f4305]) ).
fof(f4316,plain,
! [V_A,T_a] :
( c_in(V_A,c_Finite__Set_OFinites,tc_set(T_a))
| ! [V_a] : ~ c_in(c_insert(V_a,V_A,T_a),c_Finite__Set_OFinites,tc_set(T_a)) ),
inference(miniscoping,[status(thm)],[f1291]) ).
fof(f4317,plain,
! [X0,X1,X2] :
( c_in(X1,c_Finite__Set_OFinites,tc_set(X2))
| ~ c_in(c_insert(X0,X1,X2),c_Finite__Set_OFinites,tc_set(X2)) ),
inference(cnf_transformation,[status(thm)],[f4316]) ).
fof(f4322,plain,
! [X0] : c_NatArith_Oof__nat(X0,tc_nat) = X0,
inference(cnf_transformation,[status(thm)],[f1295]) ).
fof(f4379,plain,
c_IntDef_Onat(c_1) = c_Suc(c_0),
inference(cnf_transformation,[status(thm)],[f1344]) ).
fof(f4387,plain,
! [X0,X1] :
( c_less(X0,c_plus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(X0,X1,tc_IntDef_Oint) ),
inference(cnf_transformation,[status(thm)],[f1352]) ).
fof(f4388,plain,
! [X0,X1] :
( c_less(X0,X1,tc_IntDef_Oint)
| ~ c_lessequals(X0,c_minus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(cnf_transformation,[status(thm)],[f1353]) ).
fof(f4389,plain,
! [X0,X1] :
( c_lessequals(X0,c_minus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(X0,X1,tc_IntDef_Oint) ),
inference(cnf_transformation,[status(thm)],[f1354]) ).
fof(f4399,plain,
! [X0] :
( c_in(c_1,c_IntDef_ONats,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0) ),
inference(cnf_transformation,[status(thm)],[f1364]) ).
fof(f4402,plain,
! [X0] : c_HOL_Oabs(c_IntDef_Oint(X0),tc_IntDef_Oint) = c_IntDef_Oint(X0),
inference(cnf_transformation,[status(thm)],[f1367]) ).
fof(f4405,plain,
c_0 != c_1,
inference(cnf_transformation,[status(thm)],[f1370]) ).
fof(f4406,plain,
c_IntDef_Oint(c_1) = c_1,
inference(cnf_transformation,[status(thm)],[f1371]) ).
fof(f4409,plain,
c_IntDef_Oint(c_0) = c_0,
inference(cnf_transformation,[status(thm)],[f1374]) ).
fof(f4411,plain,
! [X0] :
( X0 = c_0
| ~ c_lessequals(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint) ),
inference(cnf_transformation,[status(thm)],[f1376]) ).
fof(f4420,plain,
! [X0] :
( c_IntDef_Onat(X0) = c_0
| ~ c_lessequals(X0,c_0,tc_IntDef_Oint) ),
inference(cnf_transformation,[status(thm)],[f1385]) ).
fof(f4421,plain,
c_IntDef_Onat(c_0) = c_0,
inference(cnf_transformation,[status(thm)],[f1386]) ).
fof(f4422,plain,
! [X0] : c_IntDef_Onat(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint)) = c_0,
inference(cnf_transformation,[status(thm)],[f1387]) ).
fof(f4428,plain,
c_uminus(c_IntDef_Oint(c_0),tc_IntDef_Oint) = c_IntDef_Oint(c_0),
inference(cnf_transformation,[status(thm)],[f1391]) ).
fof(f4431,plain,
! [X0] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(X0)),tc_IntDef_Oint),tc_IntDef_Oint),
inference(cnf_transformation,[status(thm)],[f1394]) ).
fof(f4435,plain,
! [V_z] :
( c_lessequals(c_0,V_z,tc_IntDef_Oint)
| ! [T_a] :
( ~ c_lessequals(c_0,c_IntDef_Oof__int(V_z,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ) ),
inference(miniscoping,[status(thm)],[f1397]) ).
fof(f4436,plain,
! [X0,X1] :
( c_lessequals(c_0,X1,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(X1,X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f4435]) ).
fof(f4437,plain,
! [X0,X1] :
( c_lessequals(c_0,c_IntDef_Oof__int(X1,X0),X0)
| ~ c_lessequals(c_0,X1,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(thm)],[f1398]) ).
fof(f4471,plain,
! [T_a] :
( ! [V_n] : c_in(c_NatArith_Oof__nat(V_n,T_a),c_IntDef_ONats,T_a)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(T_a) ),
inference(miniscoping,[status(thm)],[f1419]) ).
fof(f4472,plain,
! [X0,X1] :
( c_in(c_NatArith_Oof__nat(X1,X0),c_IntDef_ONats,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0) ),
inference(cnf_transformation,[status(thm)],[f4471]) ).
fof(f4481,plain,
! [X0,X1] :
( c_less(c_IntDef_Oint(X0),c_IntDef_Oint(X1),tc_IntDef_Oint)
| ~ c_less(X0,X1,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f1428]) ).
fof(f4482,plain,
! [V_z] :
( c_less(c_0,V_z,tc_IntDef_Oint)
| ! [V_w] : ~ c_less(c_IntDef_Onat(V_w),c_IntDef_Onat(V_z),tc_nat) ),
inference(miniscoping,[status(thm)],[f1429]) ).
fof(f4483,plain,
! [X0,X1] :
( c_less(c_0,X1,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X0),c_IntDef_Onat(X1),tc_nat) ),
inference(cnf_transformation,[status(thm)],[f4482]) ).
fof(f4485,plain,
! [X0,X1] :
( c_less(c_IntDef_Onat(X0),c_IntDef_Onat(X1),tc_nat)
| ~ c_less(c_0,X1,tc_IntDef_Oint)
| ~ c_less(X0,X1,tc_IntDef_Oint) ),
inference(cnf_transformation,[status(thm)],[f1431]) ).
fof(f4508,plain,
! [V_b] :
( ! [V_a] : c_less(V_b,c_Divides_Oop_Amod(V_a,V_b,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(V_b,c_0,tc_IntDef_Oint) ),
inference(miniscoping,[status(thm)],[f1454]) ).
fof(f4509,plain,
! [X0,X1] :
( c_less(X0,c_Divides_Oop_Amod(X1,X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(X0,c_0,tc_IntDef_Oint) ),
inference(cnf_transformation,[status(thm)],[f4508]) ).
fof(f4518,plain,
! [V_b] :
( ! [V_a] : c_less(c_Divides_Oop_Amod(V_a,V_b,tc_IntDef_Oint),V_b,tc_IntDef_Oint)
| ~ c_less(c_0,V_b,tc_IntDef_Oint) ),
inference(miniscoping,[status(thm)],[f1462]) ).
fof(f4519,plain,
! [X0,X1] :
( c_less(c_Divides_Oop_Amod(X1,X0,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ c_less(c_0,X0,tc_IntDef_Oint) ),
inference(cnf_transformation,[status(thm)],[f4518]) ).
fof(f4522,plain,
! [X0] : c_Nat_Opower(X0,c_0,tc_IntDef_Oint) = c_1,
inference(cnf_transformation,[status(thm)],[f1464]) ).
fof(f4542,plain,
! [X0] :
( X0 = c_0
| ~ c_Divides_Oop_Advd(c_0,X0,tc_IntDef_Oint) ),
inference(cnf_transformation,[status(thm)],[f1478]) ).
fof(f4551,plain,
! [X0] : c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),c_0,tc_IntDef_Oint),tc_IntDef_Oint),
inference(cnf_transformation,[status(thm)],[f1486]) ).
fof(f4710,plain,
! [V_xs] :
( V_xs = c_List_Olist_ONil
| ! [T_a] : c_Nat_Osize(V_xs,tc_List_Olist(T_a)) != c_0 ),
inference(miniscoping,[status(thm)],[f1597]) ).
fof(f4711,plain,
! [X0,X1] :
( X0 = c_List_Olist_ONil
| c_Nat_Osize(X0,tc_List_Olist(X1)) != c_0 ),
inference(cnf_transformation,[status(thm)],[f4710]) ).
fof(f4712,plain,
! [X0] : c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X0)) = c_0,
inference(cnf_transformation,[status(thm)],[f1598]) ).
fof(f4743,plain,
! [X0,X1,X2] : c_List_Olist_ONil != c_List_Olist_OCons(X0,X1,X2),
inference(cnf_transformation,[status(thm)],[f1623]) ).
fof(f4897,plain,
! [V_xs] :
( V_xs = c_List_Olist_ONil
| ! [T_a] : c_emptyset != c_List_Oset(V_xs,T_a) ),
inference(miniscoping,[status(thm)],[f1750]) ).
fof(f4898,plain,
! [X0,X1] :
( X0 = c_List_Olist_ONil
| c_emptyset != c_List_Oset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f4897]) ).
fof(f4899,plain,
! [X0] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X0),
inference(cnf_transformation,[status(thm)],[f1751]) ).
fof(f4903,plain,
! [X0,X1] : c_List_Oset(c_List_Oremdups(X0,X1),X1) = c_List_Oset(X0,X1),
inference(cnf_transformation,[status(thm)],[f1754]) ).
fof(f4908,plain,
! [X0,X1] : c_List_Oset(c_List_Orev(X0,X1),X1) = c_List_Oset(X0,X1),
inference(cnf_transformation,[status(thm)],[f1757]) ).
fof(f4909,plain,
! [X0,X1] : c_List_Oset(c_List_Orotate1(X0,X1),X1) = c_List_Oset(X0,X1),
inference(cnf_transformation,[status(thm)],[f1758]) ).
fof(f4945,plain,
! [X0,X1] :
( c_List_Oupt(X1,X0) = c_List_Olist_ONil
| ~ c_lessequals(X0,X1,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f1786]) ).
fof(f4969,plain,
! [V_n] :
( c_0 = V_n
| ! [T_a] :
( c_0 != c_NatArith_Oof__nat(V_n,T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ) ),
inference(miniscoping,[status(thm)],[f1803]) ).
fof(f4970,plain,
! [X0,X1] :
( c_0 = X1
| c_0 != c_NatArith_Oof__nat(X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(cnf_transformation,[status(thm)],[f4969]) ).
fof(f4972,plain,
! [T_a] :
( ! [V_n] : c_lessequals(c_0,c_NatArith_Oof__nat(V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
inference(miniscoping,[status(thm)],[f1805]) ).
fof(f4973,plain,
! [X0,X1] :
( c_lessequals(c_0,c_NatArith_Oof__nat(X1,X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(cnf_transformation,[status(thm)],[f4972]) ).
fof(f4974,plain,
! [V_n] :
( c_less(c_0,V_n,tc_nat)
| ! [T_a] :
( ~ c_less(c_0,c_NatArith_Oof__nat(V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ) ),
inference(miniscoping,[status(thm)],[f1806]) ).
fof(f4975,plain,
! [X0,X1] :
( c_less(c_0,X1,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(X1,X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(cnf_transformation,[status(thm)],[f4974]) ).
fof(f4976,plain,
! [X0,X1] :
( c_less(c_0,c_NatArith_Oof__nat(X1,X0),X0)
| ~ c_less(c_0,X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(cnf_transformation,[status(thm)],[f1807]) ).
fof(f4988,plain,
! [X0] :
( c_lessequals(c_NatArith_Oof__nat(c_0,X0),c_0,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(cnf_transformation,[status(thm)],[f1815]) ).
fof(f4989,plain,
! [V_m,V_n] :
( c_lessequals(V_m,V_n,tc_nat)
| ! [T_a] :
( ~ c_lessequals(c_NatArith_Oof__nat(V_m,T_a),c_NatArith_Oof__nat(V_n,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ) ),
inference(miniscoping,[status(thm)],[f1816]) ).
fof(f4990,plain,
! [X0,X1,X2] :
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(c_NatArith_Oof__nat(X1,X0),c_NatArith_Oof__nat(X2,X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(cnf_transformation,[status(thm)],[f4989]) ).
fof(f4992,plain,
! [T_a] :
( ! [V_m] : ~ c_less(c_NatArith_Oof__nat(V_m,T_a),c_0,T_a)
| ~ class_Ring__and__Field_Oordered__semidom(T_a) ),
inference(miniscoping,[status(thm)],[f1818]) ).
fof(f4993,plain,
! [X0,X1] :
( ~ c_less(c_NatArith_Oof__nat(X1,X0),c_0,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(cnf_transformation,[status(thm)],[f4992]) ).
fof(f5272,plain,
c_1 = c_Suc(c_0),
inference(cnf_transformation,[status(thm)],[f2016]) ).
fof(f5273,plain,
! [X0,X1] :
( X0 = X1
| c_Suc(X0) != c_Suc(X1) ),
inference(cnf_transformation,[status(thm)],[f2017]) ).
fof(f5275,plain,
! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_Suc(X0),c_Suc(X1),tc_nat) ),
inference(cnf_transformation,[status(thm)],[f2019]) ).
fof(f5276,plain,
! [X0,X1] :
( c_lessequals(c_Suc(X0),c_Suc(X1),tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f2020]) ).
fof(f5277,plain,
! [X0,X1] :
( c_less(X0,X1,tc_nat)
| ~ c_less(c_Suc(X0),c_Suc(X1),tc_nat) ),
inference(cnf_transformation,[status(thm)],[f2021]) ).
fof(f5278,plain,
! [X0,X1] :
( c_less(c_Suc(X0),c_Suc(X1),tc_nat)
| ~ c_less(X0,X1,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f2022]) ).
fof(f5279,plain,
! [X0] : c_Suc(X0) != c_0,
inference(cnf_transformation,[status(thm)],[f2023]) ).
fof(f5282,plain,
! [X0] : c_plus(X0,c_0,tc_nat) = X0,
inference(cnf_transformation,[status(thm)],[f2026]) ).
fof(f5290,plain,
! [V_m] :
( V_m = c_0
| ! [V_n] : c_plus(V_m,V_n,tc_nat) != c_0 ),
inference(miniscoping,[status(thm)],[f2031]) ).
fof(f5291,plain,
! [X0,X1] :
( X0 = c_0
| c_plus(X0,X1,tc_nat) != c_0 ),
inference(cnf_transformation,[status(thm)],[f5290]) ).
fof(f5295,plain,
! [X0] : c_minus(c_0,X0,tc_nat) = c_0,
inference(cnf_transformation,[status(thm)],[f2034]) ).
fof(f5302,plain,
! [X0,X1] : c_lessequals(c_minus(X0,X1,tc_nat),X0,tc_nat),
inference(cnf_transformation,[status(thm)],[f2040]) ).
fof(f5304,plain,
! [X0] :
( X0 = c_0
| ~ c_lessequals(X0,c_0,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f2042]) ).
fof(f5308,plain,
! [X0] :
( X0 = c_0
| ~ c_less(X0,c_Suc(c_0),tc_nat) ),
inference(cnf_transformation,[status(thm)],[f2046]) ).
fof(f5309,plain,
c_less(c_0,c_Suc(c_0),tc_nat),
inference(cnf_transformation,[status(thm)],[f2047]) ).
fof(f5312,plain,
! [X0] : c_Orderings_Omax(c_0,X0,tc_nat) = X0,
inference(cnf_transformation,[status(thm)],[f2050]) ).
fof(f5313,plain,
! [X0] : c_Orderings_Omax(X0,c_0,tc_nat) = X0,
inference(cnf_transformation,[status(thm)],[f2051]) ).
fof(f5315,plain,
! [X0] : c_Orderings_Omin(c_0,X0,tc_nat) = c_0,
inference(cnf_transformation,[status(thm)],[f2053]) ).
fof(f5316,plain,
! [X0] : c_Orderings_Omin(X0,c_0,tc_nat) = c_0,
inference(cnf_transformation,[status(thm)],[f2054]) ).
fof(f5373,plain,
! [X0,X1] : ~ c_less(c_plus(X0,X1,tc_nat),X1,tc_nat),
inference(cnf_transformation,[status(thm)],[f2088]) ).
fof(f5374,plain,
! [X0] :
( X0 = c_0
| c_less(c_0,X0,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f2089]) ).
fof(f5376,plain,
! [X0] : ~ c_less(X0,c_0,tc_nat),
inference(cnf_transformation,[status(thm)],[f2091]) ).
fof(f5473,plain,
! [T_a] :
( ! [V_a] : c_plus(c_uminus(V_a,T_a),V_a,T_a) = c_0
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(miniscoping,[status(thm)],[f2171]) ).
fof(f5474,plain,
! [X0,X1] :
( c_plus(c_uminus(X1,X0),X1,X0) = c_0
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f5473]) ).
fof(f5475,plain,
! [V_a] :
( V_a = c_0
| ! [T_a] :
( c_0 != c_HOL_Oabs(V_a,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ) ),
inference(miniscoping,[status(thm)],[f2172]) ).
fof(f5476,plain,
! [X0,X1] :
( X1 = c_0
| c_0 != c_HOL_Oabs(X1,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f5475]) ).
fof(f5483,plain,
! [T_a] :
( ! [V_a] : c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(miniscoping,[status(thm)],[f2177]) ).
fof(f5484,plain,
! [X0,X1] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f5483]) ).
fof(f5489,plain,
! [X0] :
( c_lessequals(c_HOL_Oabs(c_0,X0),c_0,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f2180]) ).
fof(f5492,plain,
! [T_a] :
( ! [V_a] : ~ c_less(c_HOL_Oabs(V_a,T_a),c_0,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(miniscoping,[status(thm)],[f2182]) ).
fof(f5493,plain,
! [X0,X1] :
( ~ c_less(c_HOL_Oabs(X1,X0),c_0,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(thm)],[f5492]) ).
fof(f5496,plain,
! [T_a] :
( ! [V_y] : c_plus(V_y,c_0,T_a) = V_y
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
inference(miniscoping,[status(thm)],[f2185]) ).
fof(f5497,plain,
! [X0,X1] :
( c_plus(X1,c_0,X0) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[status(thm)],[f5496]) ).
fof(f5522,plain,
! [T_a] :
( ! [V_y] : c_minus(V_y,c_0,T_a) = V_y
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(miniscoping,[status(thm)],[f2198]) ).
fof(f5523,plain,
! [X0,X1] :
( c_minus(X1,c_0,X0) = X1
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f5522]) ).
fof(f5524,plain,
! [V_a,V_b] :
( V_a = V_b
| ! [T_a] :
( c_minus(V_a,V_b,T_a) != c_0
| ~ class_OrderedGroup_Oab__group__add(T_a) ) ),
inference(miniscoping,[status(thm)],[f2199]) ).
fof(f5525,plain,
! [X0,X1,X2] :
( X1 = X2
| c_minus(X1,X2,X0) != c_0
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f5524]) ).
fof(f5527,plain,
! [X0,X1,X2] :
( c_lessequals(c_minus(X1,X2,X0),c_0,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f2201]) ).
fof(f5535,plain,
! [X0,X1] :
( c_lessequals(c_plus(X1,X1,X0),c_0,X0)
| ~ c_lessequals(X1,c_0,X0)
| ~ class_OrderedGroup_Olordered__ab__group(X0) ),
inference(cnf_transformation,[status(thm)],[f2207]) ).
fof(f5548,plain,
! [T_a] :
( ! [V_y] : c_uminus(c_uminus(V_y,T_a),T_a) = V_y
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(miniscoping,[status(thm)],[f2216]) ).
fof(f5549,plain,
! [X0,X1] :
( c_uminus(c_uminus(X1,X0),X0) = X1
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f5548]) ).
fof(f5569,plain,
! [X0,X1] :
( c_lessequals(c_uminus(X1,X0),c_0,X0)
| ~ c_lessequals(c_0,X1,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f2230]) ).
fof(f5570,plain,
! [X0,X1,X2] :
( c_lessequals(X2,X1,X0)
| ~ c_lessequals(c_uminus(X1,X0),c_uminus(X2,X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f2231]) ).
fof(f5571,plain,
! [X0,X1,X2] :
( c_lessequals(c_uminus(X2,X0),c_uminus(X1,X0),X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f2232]) ).
fof(f5573,plain,
! [X0,X1] :
( c_less(c_uminus(X1,X0),c_0,X0)
| ~ c_less(c_0,X1,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f2234]) ).
fof(f5574,plain,
! [X0,X1,X2] :
( c_less(X2,X1,X0)
| ~ c_less(c_uminus(X1,X0),c_uminus(X2,X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f2235]) ).
fof(f5575,plain,
! [X0,X1,X2] :
( c_less(c_uminus(X2,X0),c_uminus(X1,X0),X0)
| ~ c_less(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(thm)],[f2236]) ).
fof(f5581,plain,
! [T_a] :
( ! [V_a] : c_lessequals(c_OrderedGroup_Onprt(V_a,T_a),c_0,T_a)
| ~ class_OrderedGroup_Olordered__ab__group(T_a) ),
inference(miniscoping,[status(thm)],[f2241]) ).
fof(f5582,plain,
! [X0,X1] :
( c_lessequals(c_OrderedGroup_Onprt(X1,X0),c_0,X0)
| ~ class_OrderedGroup_Olordered__ab__group(X0) ),
inference(cnf_transformation,[status(thm)],[f5581]) ).
fof(f5597,plain,
! [T_a,V_x,V_z] :
( c_less(V_x,V_z,T_a)
| ! [V_y] : ~ c_less(c_Orderings_Omax(V_x,V_y,T_a),V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(miniscoping,[status(thm)],[f2253]) ).
fof(f5598,plain,
! [X0,X1,X2,X3] :
( c_less(X1,X3,X0)
| ~ c_less(c_Orderings_Omax(X1,X2,X0),X3,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f5597]) ).
fof(f5599,plain,
! [T_a,V_y,V_z] :
( c_less(V_y,V_z,T_a)
| ! [V_x] : ~ c_less(c_Orderings_Omax(V_x,V_y,T_a),V_z,T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(miniscoping,[status(thm)],[f2254]) ).
fof(f5600,plain,
! [X0,X1,X2,X3] :
( c_less(X2,X3,X0)
| ~ c_less(c_Orderings_Omax(X1,X2,X0),X3,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f5599]) ).
fof(f5602,plain,
! [T_a,V_z,V_x] :
( c_less(V_z,V_x,T_a)
| ! [V_y] : ~ c_less(V_z,c_Orderings_Omin(V_x,V_y,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(miniscoping,[status(thm)],[f2256]) ).
fof(f5603,plain,
! [X0,X1,X2,X3] :
( c_less(X1,X2,X0)
| ~ c_less(X1,c_Orderings_Omin(X2,X3,X0),X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f5602]) ).
fof(f5604,plain,
! [T_a,V_z,V_y] :
( c_less(V_z,V_y,T_a)
| ! [V_x] : ~ c_less(V_z,c_Orderings_Omin(V_x,V_y,T_a),T_a)
| ~ class_Orderings_Olinorder(T_a) ),
inference(miniscoping,[status(thm)],[f2257]) ).
fof(f5605,plain,
! [X0,X1,X2,X3] :
( c_less(X1,X3,X0)
| ~ c_less(X1,c_Orderings_Omin(X2,X3,X0),X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f5604]) ).
fof(f5607,plain,
! [T_b,V_x,V_y] :
( c_lessequals(V_x,V_y,T_b)
| ! [V_z] : ~ c_lessequals(V_x,c_Orderings_Omin(V_y,V_z,T_b),T_b)
| ~ class_Orderings_Olinorder(T_b) ),
inference(miniscoping,[status(thm)],[f2259]) ).
fof(f5608,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X1,X2,X0)
| ~ c_lessequals(X1,c_Orderings_Omin(X2,X3,X0),X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f5607]) ).
fof(f5609,plain,
! [T_b,V_x,V_z] :
( c_lessequals(V_x,V_z,T_b)
| ! [V_y] : ~ c_lessequals(V_x,c_Orderings_Omin(V_y,V_z,T_b),T_b)
| ~ class_Orderings_Olinorder(T_b) ),
inference(miniscoping,[status(thm)],[f2260]) ).
fof(f5610,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X1,X3,X0)
| ~ c_lessequals(X1,c_Orderings_Omin(X2,X3,X0),X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f5609]) ).
fof(f5616,plain,
! [T_b,V_x,V_z] :
( c_lessequals(V_x,V_z,T_b)
| ! [V_y] : ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
inference(miniscoping,[status(thm)],[f2264]) ).
fof(f5617,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_Orderings_Omax(X1,X2,X0),X3,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f5616]) ).
fof(f5618,plain,
! [T_b,V_y,V_z] :
( c_lessequals(V_y,V_z,T_b)
| ! [V_x] : ~ c_lessequals(c_Orderings_Omax(V_x,V_y,T_b),V_z,T_b)
| ~ class_Orderings_Olinorder(T_b) ),
inference(miniscoping,[status(thm)],[f2265]) ).
fof(f5619,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X2,X3,X0)
| ~ c_lessequals(c_Orderings_Omax(X1,X2,X0),X3,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[status(thm)],[f5618]) ).
fof(f5625,plain,
! [T_a] :
( ! [V_x] : ~ c_less(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(miniscoping,[status(thm)],[f2269]) ).
fof(f5626,plain,
! [X0,X1] :
( ~ c_less(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(thm)],[f5625]) ).
fof(f5637,plain,
! [X0] :
( ~ c_Parity_Oeven(c_Suc(X0),tc_nat)
| ~ c_Parity_Oeven(X0,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f2278]) ).
fof(f5638,plain,
! [X0] :
( c_Parity_Oeven(c_Suc(X0),tc_nat)
| c_Parity_Oeven(X0,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f2279]) ).
fof(f5656,plain,
c_Parity_Oeven(c_0,tc_nat),
inference(cnf_transformation,[status(thm)],[f2290]) ).
fof(f5666,plain,
! [V_x] :
( ! [V_y] : c_Parity_Oeven(c_times(V_x,V_y,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(V_x,tc_IntDef_Oint) ),
inference(miniscoping,[status(thm)],[f2297]) ).
fof(f5667,plain,
! [X0,X1] :
( c_Parity_Oeven(c_times(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(X0,tc_IntDef_Oint) ),
inference(cnf_transformation,[status(thm)],[f5666]) ).
fof(f5676,plain,
c_Parity_Oeven(c_0,tc_IntDef_Oint),
inference(cnf_transformation,[status(thm)],[f2303]) ).
fof(f5737,plain,
! [V_i] :
( ! [V_n] : c_lessequals(c_Suc(c_0),c_Nat_Opower(V_i,V_n,tc_nat),tc_nat)
| ~ c_lessequals(c_1,V_i,tc_nat) ),
inference(miniscoping,[status(thm)],[f2340]) ).
fof(f5738,plain,
! [X0,X1] :
( c_lessequals(c_Suc(c_0),c_Nat_Opower(X0,X1,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X0,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f5737]) ).
fof(f5743,plain,
! [X0] : c_Nat_Opower(X0,c_0,tc_nat) = c_1,
inference(cnf_transformation,[status(thm)],[f2344]) ).
fof(f5812,plain,
( c_0 != c_1
| ! [T_a] : ~ class_Ring__and__Field_Oaxclass__0__neq__1(T_a) ),
inference(miniscoping,[status(thm)],[f2395]) ).
fof(f5813,plain,
! [X0] :
( c_0 != c_1
| ~ class_Ring__and__Field_Oaxclass__0__neq__1(X0) ),
inference(cnf_transformation,[status(thm)],[f5812]) ).
fof(f5994,plain,
! [X0] :
( c_lessequals(c_0,c_1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(cnf_transformation,[status(thm)],[f2511]) ).
fof(f6020,plain,
c_SetInterval_OatLeast(c_0,tc_nat) = c_UNIV,
inference(cnf_transformation,[status(thm)],[f2528]) ).
fof(f6023,plain,
! [X0,X1,X2] :
( c_lessequals(X2,X1,X0)
| ~ c_in(X1,c_SetInterval_OatLeast(X2,X0),X0)
| ~ class_Orderings_Oord(X0) ),
inference(cnf_transformation,[status(thm)],[f2530]) ).
fof(f6024,plain,
! [X0,X1,X2] :
( c_in(X2,c_SetInterval_OatLeast(X1,X0),X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oord(X0) ),
inference(cnf_transformation,[status(thm)],[f2531]) ).
fof(f6070,plain,
c_SetInterval_OlessThan(c_0,tc_nat) = c_emptyset,
inference(cnf_transformation,[status(thm)],[f2567]) ).
fof(f6073,plain,
! [X0,X1,X2] :
( c_less(X1,X2,X0)
| ~ c_in(X1,c_SetInterval_OlessThan(X2,X0),X0)
| ~ class_Orderings_Oord(X0) ),
inference(cnf_transformation,[status(thm)],[f2569]) ).
fof(f6074,plain,
! [X0,X1,X2] :
( c_in(X1,c_SetInterval_OlessThan(X2,X0),X0)
| ~ c_less(X1,X2,X0)
| ~ class_Orderings_Oord(X0) ),
inference(cnf_transformation,[status(thm)],[f2570]) ).
fof(f6093,plain,
! [X0,X1] : c_minus(X0,c_UNIV,tc_set(X1)) = c_emptyset,
inference(cnf_transformation,[status(thm)],[f2587]) ).
fof(f6094,plain,
! [X0,X1] : c_minus(X0,X0,tc_set(X1)) = c_emptyset,
inference(cnf_transformation,[status(thm)],[f2588]) ).
fof(f6096,plain,
! [X0,X1] : c_minus(X0,c_emptyset,tc_set(X1)) = X0,
inference(cnf_transformation,[status(thm)],[f2590]) ).
fof(f6107,plain,
! [V_A] :
( V_A = c_UNIV
| ! [V_B,T_a] : c_inter(V_A,V_B,T_a) != c_UNIV ),
inference(miniscoping,[status(thm)],[f2598]) ).
fof(f6108,plain,
! [X0,X1,X2] :
( X0 = c_UNIV
| c_inter(X0,X1,X2) != c_UNIV ),
inference(cnf_transformation,[status(thm)],[f6107]) ).
fof(f6112,plain,
! [X0,X1] : c_inter(c_UNIV,X0,X1) = X0,
inference(cnf_transformation,[status(thm)],[f2601]) ).
fof(f6127,plain,
! [X0] : c_Inter(c_UNIV,X0) = c_emptyset,
inference(cnf_transformation,[status(thm)],[f2612]) ).
fof(f6131,plain,
! [X0,X1] :
( c_Inter(X0,X1) = c_UNIV
| c_Main_OInter__UNIV__conv__1__1(X0,X1) != c_UNIV ),
inference(cnf_transformation,[status(thm)],[f2615]) ).
fof(f6135,plain,
! [X0,X1] :
( c_UNIV = c_Inter(X0,X1)
| c_Main_OInter__UNIV__conv__2__1(X0,X1) != c_UNIV ),
inference(cnf_transformation,[status(thm)],[f2618]) ).
fof(f6147,plain,
c_UNIV != c_emptyset,
inference(cnf_transformation,[status(thm)],[f2629]) ).
fof(f6151,plain,
! [X0,X1] : c_union(X0,c_UNIV,X1) = c_UNIV,
inference(cnf_transformation,[status(thm)],[f2633]) ).
fof(f6153,plain,
! [V_A] :
( V_A = c_emptyset
| ! [V_B,T_a] : c_union(V_A,V_B,T_a) != c_emptyset ),
inference(miniscoping,[status(thm)],[f2635]) ).
fof(f6154,plain,
! [X0,X1,X2] :
( X0 = c_emptyset
| c_union(X0,X1,X2) != c_emptyset ),
inference(cnf_transformation,[status(thm)],[f6153]) ).
fof(f6174,plain,
! [X0] : c_Union(c_UNIV,X0) = c_UNIV,
inference(cnf_transformation,[status(thm)],[f2649]) ).
fof(f6180,plain,
! [X0,X1] :
( c_Union(X0,X1) = c_emptyset
| c_Main_OUnion__empty__conv__1(X0,X1) != c_emptyset ),
inference(cnf_transformation,[status(thm)],[f2654]) ).
fof(f6186,plain,
! [V_A] :
( V_A = c_emptyset
| ! [T_a] : c_in(c_Main_Oall__not__in__conv__1(V_A,T_a),V_A,T_a) ),
inference(miniscoping,[status(thm)],[f2659]) ).
fof(f6187,plain,
! [X0,X1] :
( X0 = c_emptyset
| c_in(c_Main_Oall__not__in__conv__1(X0,X1),X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6186]) ).
fof(f6200,plain,
! [X0,X1] : c_minus(c_emptyset,X0,tc_set(X1)) = c_emptyset,
inference(cnf_transformation,[status(thm)],[f2668]) ).
fof(f6204,plain,
! [X0,X1] :
( c_emptyset = c_Union(X0,X1)
| c_Main_Oempty__Union__conv__1(X0,X1) != c_emptyset ),
inference(cnf_transformation,[status(thm)],[f2671]) ).
fof(f6205,plain,
! [X0,X1] : ~ c_in(X0,c_emptyset,X1),
inference(cnf_transformation,[status(thm)],[f2672]) ).
fof(f6206,plain,
! [X0,X1,X2] : c_emptyset != c_insert(X0,X1,X2),
inference(cnf_transformation,[status(thm)],[f2673]) ).
fof(f6223,plain,
! [X0,X1,X2] : c_in(X0,c_insert(X0,X1,X2),X2),
inference(cnf_transformation,[status(thm)],[f2684]) ).
fof(f6224,plain,
! [V_a,V_A,T_a] :
( ! [V_b] : c_in(V_a,c_insert(V_b,V_A,T_a),T_a)
| ~ c_in(V_a,V_A,T_a) ),
inference(miniscoping,[status(thm)],[f2685]) ).
fof(f6225,plain,
! [X0,X1,X2,X3] :
( c_in(X0,c_insert(X3,X1,X2),X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f6224]) ).
fof(f6228,plain,
! [V_x,T_a,V_B] :
( c_in(V_x,V_B,T_a)
| ! [V_A] : ~ c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) ),
inference(miniscoping,[status(thm)],[f2688]) ).
fof(f6229,plain,
! [X0,X1,X2,X3] :
( c_in(X0,X3,X2)
| ~ c_lessequals(c_insert(X0,X1,X2),X3,tc_set(X2)) ),
inference(cnf_transformation,[status(thm)],[f6228]) ).
fof(f6230,plain,
! [V_A,T_a,V_B] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| ! [V_x] : ~ c_lessequals(c_insert(V_x,V_A,T_a),V_B,tc_set(T_a)) ),
inference(miniscoping,[status(thm)],[f2689]) ).
fof(f6231,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X1,X3,tc_set(X2))
| ~ c_lessequals(c_insert(X0,X1,X2),X3,tc_set(X2)) ),
inference(cnf_transformation,[status(thm)],[f6230]) ).
fof(f6244,plain,
! [X0,X1] : c_lessequals(X0,c_UNIV,tc_set(X1)),
inference(cnf_transformation,[status(thm)],[f2698]) ).
fof(f6280,plain,
! [V_Y,V_H] :
( c_in(V_Y,c_Message_Oparts(V_H),tc_Message_Omsg)
| ! [V_X] : ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(miniscoping,[status(thm)],[f2728]) ).
fof(f6281,plain,
! [X0,X1,X2] :
( c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X0,X1),c_Message_Oparts(X2),tc_Message_Omsg) ),
inference(cnf_transformation,[status(thm)],[f6280]) ).
fof(f6282,plain,
! [V_X,V_H] :
( c_in(V_X,c_Message_Oparts(V_H),tc_Message_Omsg)
| ! [V_Y] : ~ c_in(c_Message_Omsg_OMPair(V_X,V_Y),c_Message_Oparts(V_H),tc_Message_Omsg) ),
inference(miniscoping,[status(thm)],[f2729]) ).
fof(f6283,plain,
! [X0,X1,X2] :
( c_in(X0,c_Message_Oparts(X2),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X0,X1),c_Message_Oparts(X2),tc_Message_Omsg) ),
inference(cnf_transformation,[status(thm)],[f6282]) ).
fof(f6307,plain,
! [X0,X1] :
( X0 = X1
| c_Message_Omsg_ONonce(X0) != c_Message_Omsg_ONonce(X1) ),
inference(cnf_transformation,[status(thm)],[f2753]) ).
fof(f6325,plain,
! [X0,X1] :
( c_in(X0,c_Message_Oparts(X1),tc_Message_Omsg)
| ~ c_in(X0,X1,tc_Message_Omsg) ),
inference(cnf_transformation,[status(thm)],[f2767]) ).
fof(f6328,plain,
c_Message_Oparts(c_emptyset) = c_emptyset,
inference(cnf_transformation,[status(thm)],[f2770]) ).
fof(f6385,plain,
! [X0,X1] : c_Message_OHPair(X0,X1) = c_Message_Omsg_OMPair(c_Message_Omsg_OHash(c_Message_Omsg_OMPair(X0,X1)),X1),
inference(cnf_transformation,[status(thm)],[f2812]) ).
fof(f6436,plain,
c_Message_Oanalz(c_emptyset) = c_emptyset,
inference(cnf_transformation,[status(thm)],[f2853]) ).
fof(f6443,plain,
! [X0,X1] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X0),c_Message_Oanalz(X1),tc_Message_Omsg),
inference(cnf_transformation,[status(thm)],[f2860]) ).
fof(f6445,plain,
! [X0] : c_Message_Oanalz(c_Message_Oparts(X0)) = c_Message_Oparts(X0),
inference(cnf_transformation,[status(thm)],[f2862]) ).
fof(f6462,plain,
! [X0,X1] : c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X0),c_Message_Oparts(X1),tc_Message_Omsg),
inference(cnf_transformation,[status(thm)],[f2878]) ).
fof(f6487,plain,
! [X0] :
( c_Message_OinvKey(X0) = X0
| ~ c_in(X0,c_Message_OsymKeys,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f2899]) ).
fof(f6513,plain,
! [X0] : c_in(c_Public_OshrK(X0),c_Message_OsymKeys,tc_nat),
inference(cnf_transformation,[status(thm)],[f2923]) ).
fof(f6523,plain,
! [X0,X1] : c_lessequals(X0,c_plus(X0,X1,tc_nat),tc_nat),
inference(cnf_transformation,[status(thm)],[f2933]) ).
fof(f6524,plain,
! [X0,X1] : c_lessequals(X0,c_plus(X1,X0,tc_nat),tc_nat),
inference(cnf_transformation,[status(thm)],[f2934]) ).
fof(f6525,plain,
! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_less(X0,c_Suc(X1),tc_nat) ),
inference(cnf_transformation,[status(thm)],[f2935]) ).
fof(f6526,plain,
! [X0,X1] :
( c_less(X0,c_Suc(X1),tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) ),
inference(cnf_transformation,[status(thm)],[f2936]) ).
fof(f6527,plain,
! [X0,X1] :
( ~ c_lessequals(v_sko__urX(X1),X0,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(X1),tc_Message_Omsg) ),
inference(cnf_transformation,[status(thm)],[f2937]) ).
fof(f6528,plain,
! [V_U] :
( c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(v_evs),tc_Message_Omsg)
| ! [V_V] :
( c_in(c_Message_Omsg_ONonce(V_V),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| ! [V_W] :
( c_in(c_Message_Omsg_ONonce(V_W),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| V_U = V_V
| V_V = V_W
| V_U = V_W ) ) ),
inference(miniscoping,[status(thm)],[f2938]) ).
fof(f6529,plain,
! [X0,X1,X2] :
( c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_evs),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(X2),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs_H_H),tc_Message_Omsg)
| X0 = X2
| X2 = X1
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f6528]) ).
fof(f6530,definition,
! [X0] :
( sQ0_spl
<=> ~ class_Ring__and__Field_Oaxclass__0__neq__1(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f6531,plain,
! [X0] :
( ~ sQ0_spl
| ~ class_Ring__and__Field_Oaxclass__0__neq__1(X0) ),
inference(component_clause,[status(thm)],[f6530]) ).
fof(f6533,definition,
( sQ1_spl
<=> c_0 = c_1 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f6536,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f5813,f6530,f6533]) ).
fof(f6539,plain,
! [X0] : c_Finite__Set_Ocard(c_emptyset,X0) = c_0,
inference(forward_subsumption_resolution,[status(thm)],[f4297,f2980]) ).
fof(f6544,plain,
! [X0] : c_div(X0,c_IntDef_Onat(c_1),tc_nat) = X0,
inference(backward_demodulation,[status(thm)],[f4379,f4203]) ).
fof(f6547,plain,
! [X0] : c_Binomial_Obinomial(X0,c_IntDef_Onat(c_1)) = X0,
inference(backward_demodulation,[status(thm)],[f4379,f4141]) ).
fof(f6552,plain,
c_uminus(c_0,tc_IntDef_Oint) = c_IntDef_Oint(c_0),
inference(forward_demodulation,[status(thm)],[f4409,f4428]) ).
fof(f6553,plain,
c_uminus(c_0,tc_IntDef_Oint) = c_0,
inference(forward_demodulation,[status(thm)],[f4409,f6552]) ).
fof(f6560,plain,
c_less(c_0,c_1,tc_IntDef_Oint),
inference(forward_demodulation,[status(thm)],[f4522,f4551]) ).
fof(f6579,plain,
c_IntDef_Onat(c_1) = c_1,
inference(backward_demodulation,[status(thm)],[f5272,f4379]) ).
fof(f6582,plain,
! [X0] :
( X0 = c_0
| ~ c_less(X0,c_1,tc_nat) ),
inference(forward_demodulation,[status(thm)],[f5272,f5308]) ).
fof(f6583,plain,
c_less(c_0,c_1,tc_nat),
inference(forward_demodulation,[status(thm)],[f5272,f5309]) ).
fof(f6669,plain,
! [X0,X1] :
( c_lessequals(c_1,c_Nat_Opower(X0,X1,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X0,tc_nat) ),
inference(forward_demodulation,[status(thm)],[f5272,f5738]) ).
fof(f6681,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f3181,f6531]) ).
fof(f6699,plain,
! [X0] : c_Binomial_Obinomial(X0,c_1) = X0,
inference(backward_demodulation,[status(thm)],[f6579,f6547]) ).
fof(f6702,plain,
! [X0] : c_div(X0,c_1,tc_nat) = X0,
inference(backward_demodulation,[status(thm)],[f6579,f6544]) ).
fof(f6771,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f6681]) ).
fof(f6878,plain,
! [X0,X1] :
( c_in(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X0,tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_Message_Oparts(X0),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6462,f2982]) ).
fof(f6879,plain,
! [X0,X1] :
( c_in(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),X0,tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_Message_Oanalz(X0),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6443,f2982]) ).
fof(f6949,plain,
! [X0,X1,X2] :
( ~ c_in(c_Message_Oanalz(X2),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| X0 = c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f2992,f6879]) ).
fof(f6950,plain,
! [X0,X1,X2] :
( ~ c_in(c_Message_Oparts(X2),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| X0 = c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f2992,f6878]) ).
fof(f6971,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ c_in(X1,c_UNIV,X0)
| ~ c_Infinite__Set_Oatmost__one(c_UNIV,X0) ),
inference(resolution,[status(thm)],[f2992,f3064]) ).
fof(f6972,definition,
( sQ2_spl
<=> c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f6975,definition,
! [X0,X1,X2] :
( sQ3_spl
<=> ( ~ c_in(c_Message_Oanalz(X2),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| X0 = c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f6978,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f6949,f6972,f6975]) ).
fof(f6979,definition,
! [X0,X1,X2] :
( sQ4_spl
<=> ( ~ c_in(c_Message_Oparts(X2),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| X0 = c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f6982,plain,
( sQ4_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f6950,f6972,f6979]) ).
fof(f6990,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ c_Infinite__Set_Oatmost__one(c_UNIV,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f6971,f3064]) ).
fof(f7314,plain,
! [X0,X1,X2] : c_in(X0,c_Relation_ODomain(c_UNIV,X1,X2),X1),
inference(resolution,[status(thm)],[f3033,f3064]) ).
fof(f7409,plain,
! [X0,X1,X2] : c_in(X0,c_Relation_ORange(c_UNIV,X1,X2),X2),
inference(resolution,[status(thm)],[f3041,f3064]) ).
fof(f8371,plain,
! [X0] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X0)),tc_IntDef_Oint),c_0,tc_IntDef_Oint),
inference(paramodulation,[status(thm)],[f4409,f2994]) ).
fof(f8376,plain,
! [X0] : c_Binomial_Obinomial(c_Suc(X0),c_Suc(X0)) = c_plus(c_1,c_Binomial_Obinomial(X0,c_Suc(X0)),tc_nat),
inference(paramodulation,[status(thm)],[f4145,f4142]) ).
fof(f8382,plain,
! [X0] : c_1 = c_plus(c_1,c_Binomial_Obinomial(X0,c_Suc(X0)),tc_nat),
inference(forward_demodulation,[status(thm)],[f4145,f8376]) ).
fof(f8391,plain,
! [X0] : c_Binomial_Obinomial(c_Suc(X0),c_Suc(c_0)) = c_plus(c_Binomial_Obinomial(X0,c_0),c_Binomial_Obinomial(X0,c_1),tc_nat),
inference(paramodulation,[status(thm)],[f5272,f4142]) ).
fof(f8397,plain,
! [X0] : c_Binomial_Obinomial(c_Suc(X0),c_1) = c_plus(c_Binomial_Obinomial(X0,c_0),c_Binomial_Obinomial(X0,c_1),tc_nat),
inference(forward_demodulation,[status(thm)],[f5272,f8391]) ).
fof(f8398,plain,
! [X0] : c_Suc(X0) = c_plus(c_Binomial_Obinomial(X0,c_0),c_Binomial_Obinomial(X0,c_1),tc_nat),
inference(forward_demodulation,[status(thm)],[f6699,f8397]) ).
fof(f8399,plain,
! [X0] : c_Suc(X0) = c_plus(c_1,c_Binomial_Obinomial(X0,c_1),tc_nat),
inference(forward_demodulation,[status(thm)],[f4144,f8398]) ).
fof(f8400,plain,
! [X0] : c_1 = c_Suc(c_Binomial_Obinomial(X0,c_Suc(X0))),
inference(backward_demodulation,[status(thm)],[f8401,f8382]) ).
fof(f8401,plain,
! [X0] : c_Suc(X0) = c_plus(c_1,X0,tc_nat),
inference(forward_demodulation,[status(thm)],[f6699,f8399]) ).
fof(f8448,plain,
! [X0] : c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg),
inference(paramodulation,[status(thm)],[f6328,f6462]) ).
fof(f8449,plain,
! [X0] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg),
inference(paramodulation,[status(thm)],[f6436,f6443]) ).
fof(f8489,plain,
! [X0] :
( c_in(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_Message_Oparts(c_emptyset),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f8448,f6878]) ).
fof(f8492,definition,
( sQ23_spl
<=> c_in(c_Message_Oparts(c_emptyset),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f8494,plain,
( sQ23_spl
| ~ c_in(c_Message_Oparts(c_emptyset),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(component_clause,[status(thm)],[f8492]) ).
fof(f8495,definition,
! [X0] :
( sQ24_spl
<=> c_in(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f8496,plain,
! [X0] :
( ~ sQ24_spl
| c_in(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(component_clause,[status(thm)],[f8495]) ).
fof(f8498,plain,
( sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f8489,f8492,f8495]) ).
fof(f8502,plain,
( sQ23_spl
| ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6328,f8494]) ).
fof(f8503,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8502,f2980]) ).
fof(f8504,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f8503]) ).
fof(f8506,plain,
! [X0,X1] :
( ~ sQ24_spl
| X0 = c_insert(c_Message_Omsg_ONonce(X1),c_emptyset,tc_Message_Omsg)
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f8496,f2992]) ).
fof(f8507,definition,
! [X0,X1] :
( sQ25_spl
<=> ( X0 = c_insert(c_Message_Omsg_ONonce(X1),c_emptyset,tc_Message_Omsg)
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f8510,plain,
( ~ sQ24_spl
| sQ25_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f8506,f6972,f8507,f8495]) ).
fof(f8513,plain,
! [X0,X1] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_emptyset,tc_Message_Omsg),tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),
inference(paramodulation,[status(thm)],[f8449,f6443]) ).
fof(f8514,definition,
( sQ26_spl
<=> c_in(c_Message_Oanalz(c_emptyset),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f8516,plain,
( sQ26_spl
| ~ c_in(c_Message_Oanalz(c_emptyset),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(component_clause,[status(thm)],[f8514]) ).
fof(f8532,plain,
! [X0,X1,X2] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),
inference(paramodulation,[status(thm)],[f8513,f6443]) ).
fof(f8552,plain,
! [X0,X1,X2,X3] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),
inference(paramodulation,[status(thm)],[f8532,f6443]) ).
fof(f8576,plain,
! [X0,X1,X2,X3,X4] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),
inference(paramodulation,[status(thm)],[f8552,f6443]) ).
fof(f8631,plain,
( c_Datatype_Ooption_ONone = c_Datatype_Ooption_ONone
| c_emptyset != c_emptyset ),
inference(paramodulation,[status(thm)],[f4155,f4154]) ).
fof(f8633,definition,
( sQ27_spl
<=> c_emptyset = c_emptyset ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f8635,plain,
( sQ27_spl
| c_emptyset != c_emptyset ),
inference(component_clause,[status(thm)],[f8633]) ).
fof(f8636,definition,
( sQ28_spl
<=> c_Datatype_Ooption_ONone = c_Datatype_Ooption_ONone ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f8639,plain,
( sQ28_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f8631,f8633,f8636]) ).
fof(f8640,plain,
( sQ27_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f8635]) ).
fof(f8641,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f8640]) ).
fof(f8694,plain,
! [X0,X1] : c_emptyset != c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),
inference(paramodulation,[status(thm)],[f6462,f6206]) ).
fof(f8695,plain,
! [X0,X1] : c_emptyset != c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),
inference(paramodulation,[status(thm)],[f6443,f6206]) ).
fof(f8729,definition,
( sQ29_spl
<=> c_0 = c_0 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f8759,plain,
! [X0] :
( c_0 = X0
| c_1 != c_Suc(X0) ),
inference(paramodulation,[status(thm)],[f5272,f5273]) ).
fof(f8820,plain,
! [X0,X1] :
( X0 = c_UNIV
| ~ c_lessequals(c_UNIV,X0,tc_set(X1)) ),
inference(resolution,[status(thm)],[f6244,f3082]) ).
fof(f8943,definition,
( sQ32_spl
<=> c_1 = c_1 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f8945,plain,
( sQ32_spl
| c_1 != c_1 ),
inference(component_clause,[status(thm)],[f8943]) ).
fof(f8950,plain,
( sQ32_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f8945]) ).
fof(f8951,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f8950]) ).
fof(f8954,plain,
! [X0] : c_lessequals(X0,X0,tc_nat),
inference(paramodulation,[status(thm)],[f6702,f4204]) ).
fof(f8976,definition,
! [X0] :
( sQ33_spl
<=> ~ c_less(c_0,X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f8977,plain,
! [X0] :
( ~ sQ33_spl
| ~ c_less(c_0,X0,tc_nat) ),
inference(component_clause,[status(thm)],[f8976]) ).
fof(f8980,definition,
! [X0] :
( sQ34_spl
<=> ~ c_less(X0,c_0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f8987,plain,
! [X0] :
( c_less(X0,X0,tc_nat)
| ~ c_less(c_1,c_1,tc_nat)
| ~ c_less(c_0,X0,tc_nat) ),
inference(paramodulation,[status(thm)],[f6702,f4206]) ).
fof(f8988,definition,
( sQ35_spl
<=> c_less(c_0,c_0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f8996,definition,
! [X0] :
( sQ37_spl
<=> ( c_less(c_0,X0,tc_nat)
| ~ c_less(c_0,X0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f9003,definition,
! [X0] :
( sQ39_spl
<=> ( c_less(X0,X0,tc_nat)
| ~ c_less(c_0,X0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f9004,plain,
! [X0] :
( ~ sQ39_spl
| c_less(X0,X0,tc_nat)
| ~ c_less(c_0,X0,tc_nat) ),
inference(component_clause,[status(thm)],[f9003]) ).
fof(f9006,definition,
( sQ40_spl
<=> c_less(c_1,c_1,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f9009,plain,
( ~ sQ40_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f8987,f9003,f9006]) ).
fof(f9010,plain,
( ~ sQ39_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f6583,f9021]) ).
fof(f9021,plain,
! [X0] :
( ~ sQ39_spl
| ~ c_less(c_0,X0,tc_nat) ),
inference(forward_subsumption_resolution,[status(thm)],[f9004,f3027]) ).
fof(f9022,plain,
~ sQ39_spl,
inference(contradiction_clause,[status(thm)],[f9010]) ).
fof(f9028,definition,
( sQ41_spl
<=> c_List_Olist_ONil = c_List_Olist_ONil ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f9036,definition,
! [X0] :
( sQ42_spl
<=> X0 != X0 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f9037,plain,
! [X0] :
( ~ sQ42_spl
| X0 != X0 ),
inference(component_clause,[status(thm)],[f9036]) ).
fof(f9040,plain,
( ~ sQ42_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f9037]) ).
fof(f9041,plain,
~ sQ42_spl,
inference(contradiction_clause,[status(thm)],[f9040]) ).
fof(f9098,definition,
( sQ43_spl
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f9100,plain,
( sQ43_spl
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(component_clause,[status(thm)],[f9098]) ).
fof(f9132,plain,
! [X0,X1] : c_in(c_Message_Omsg_ONonce(X0),c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),tc_Message_Omsg),
inference(paramodulation,[status(thm)],[f6462,f6223]) ).
fof(f9133,plain,
! [X0,X1] : c_in(c_Message_Omsg_ONonce(X0),c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),tc_Message_Omsg),
inference(paramodulation,[status(thm)],[f6443,f6223]) ).
fof(f9134,plain,
! [X0,X1,X2] :
( X2 = c_Message_Omsg_ONonce(X0)
| ~ c_in(X2,c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_Infinite__Set_Oatmost__one(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f9132,f2992]) ).
fof(f9144,plain,
! [X0,X1,X2] :
( X2 = c_Message_Omsg_ONonce(X0)
| ~ c_in(X2,c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_Infinite__Set_Oatmost__one(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f9133,f2992]) ).
fof(f9247,plain,
! [X0,X1] :
( X1 = c_1
| ~ c_in(X1,c_IntDef_ONats,X0)
| ~ c_Infinite__Set_Oatmost__one(c_IntDef_ONats,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0) ),
inference(resolution,[status(thm)],[f4399,f2992]) ).
fof(f10069,plain,
c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_IntDef_Oint(c_0),
inference(paramodulation,[status(thm)],[f4409,f4402]) ).
fof(f10070,plain,
c_HOL_Oabs(c_1,tc_IntDef_Oint) = c_IntDef_Oint(c_1),
inference(paramodulation,[status(thm)],[f4406,f4402]) ).
fof(f10073,plain,
c_HOL_Oabs(c_0,tc_IntDef_Oint) = c_0,
inference(forward_demodulation,[status(thm)],[f4409,f10069]) ).
fof(f10074,plain,
c_HOL_Oabs(c_1,tc_IntDef_Oint) = c_1,
inference(forward_demodulation,[status(thm)],[f4406,f10070]) ).
fof(f10075,plain,
! [X0] : c_times(X0,c_0,tc_IntDef_Oint) = c_0,
inference(resolution,[status(thm)],[f4542,f2998]) ).
fof(f10114,definition,
( sQ47_spl
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f10116,plain,
( sQ47_spl
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat) ),
inference(component_clause,[status(thm)],[f10114]) ).
fof(f10467,definition,
( sQ49_spl
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f10469,plain,
( sQ49_spl
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) ),
inference(component_clause,[status(thm)],[f10467]) ).
fof(f10475,definition,
( sQ50_spl
<=> class_Orderings_Oorder(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f10477,plain,
( sQ50_spl
| ~ class_Orderings_Oorder(tc_nat) ),
inference(component_clause,[status(thm)],[f10475]) ).
fof(f10492,definition,
( sQ52_spl
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f10494,plain,
( sQ52_spl
| ~ class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
inference(component_clause,[status(thm)],[f10492]) ).
fof(f10497,plain,
! [X0] :
( X0 = X0
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
inference(paramodulation,[status(thm)],[f5282,f5497]) ).
fof(f10498,definition,
( sQ53_spl
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f10500,plain,
( sQ53_spl
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
inference(component_clause,[status(thm)],[f10498]) ).
fof(f10502,definition,
! [X0] :
( sQ54_spl
<=> X0 = X0 ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f10505,plain,
( sQ54_spl
| ~ sQ53_spl ),
inference(split_clause,[status(thm)],[f10497,f10498,f10502]) ).
fof(f10506,plain,
( sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10500,f3189]) ).
fof(f10507,plain,
sQ53_spl,
inference(contradiction_clause,[status(thm)],[f10506]) ).
fof(f10514,plain,
! [X0] :
( c_emptyset = c_0
| ~ class_OrderedGroup_Oab__group__add(tc_set(X0)) ),
inference(paramodulation,[status(thm)],[f6094,f5523]) ).
fof(f10516,definition,
( sQ55_spl
<=> class_OrderedGroup_Oab__group__add(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f10521,definition,
! [X0] :
( sQ56_spl
<=> ~ class_OrderedGroup_Oab__group__add(tc_set(X0)) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f10524,definition,
( sQ57_spl
<=> c_emptyset = c_0 ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f10527,plain,
( sQ57_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f10514,f10521,f10524]) ).
fof(f10576,definition,
( sQ62_spl
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f10578,plain,
( sQ62_spl
| ~ class_OrderedGroup_Omonoid__mult(tc_nat) ),
inference(component_clause,[status(thm)],[f10576]) ).
fof(f10592,definition,
( sQ64_spl
<=> class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f10594,plain,
( sQ64_spl
| ~ class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) ),
inference(component_clause,[status(thm)],[f10592]) ).
fof(f10599,definition,
( sQ65_spl
<=> class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f10601,plain,
( sQ65_spl
| ~ class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) ),
inference(component_clause,[status(thm)],[f10599]) ).
fof(f10606,definition,
( sQ66_spl
<=> class_Ring__and__Field_Oordered__idom(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f10621,plain,
! [X0] :
( c_0 = c_1
| ~ c_lessequals(c_1,c_0,tc_set(X0))
| ~ class_Ring__and__Field_Oordered__semidom(tc_set(X0)) ),
inference(resolution,[status(thm)],[f5994,f3082]) ).
fof(f10623,plain,
! [X0] :
( c_0 = c_1
| c_less(c_0,c_1,tc_set(X0))
| ~ class_Ring__and__Field_Oordered__semidom(tc_set(X0)) ),
inference(resolution,[status(thm)],[f5994,f3071]) ).
fof(f10625,definition,
! [X0] :
( sQ67_spl
<=> ( ~ c_lessequals(c_1,c_0,tc_set(X0))
| ~ class_Ring__and__Field_Oordered__semidom(tc_set(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f10628,plain,
( sQ1_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f10621,f10625,f6533]) ).
fof(f10629,definition,
! [X0] :
( sQ68_spl
<=> ( c_less(c_0,c_1,tc_set(X0))
| ~ class_Ring__and__Field_Oordered__semidom(tc_set(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f10632,plain,
( sQ1_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f10623,f10629,f6533]) ).
fof(f10650,plain,
! [X0,X1] :
( X1 = c_emptyset
| c_lessequals(X0,c_Finite__Set_OMax(X1,tc_nat),tc_nat)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ c_in(X0,X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f4262,f8954]) ).
fof(f10654,definition,
! [X0,X1] :
( sQ71_spl
<=> ( X1 = c_emptyset
| c_lessequals(X0,c_Finite__Set_OMax(X1,tc_nat),tc_nat)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ c_in(X0,X1,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f10657,plain,
( sQ71_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f10650,f9098,f10654]) ).
fof(f10658,plain,
( sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9100,f3221]) ).
fof(f10659,plain,
sQ43_spl,
inference(contradiction_clause,[status(thm)],[f10658]) ).
fof(f10696,plain,
! [X0] :
( c_UNIV = c_UNIV
| X0 != c_UNIV ),
inference(paramodulation,[status(thm)],[f6112,f6108]) ).
fof(f10700,definition,
( sQ75_spl
<=> c_emptyset = c_UNIV ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f10704,definition,
! [X0] :
( sQ76_spl
<=> X0 != c_UNIV ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f10705,plain,
! [X0] :
( ~ sQ76_spl
| X0 != c_UNIV ),
inference(component_clause,[status(thm)],[f10704]) ).
fof(f10707,definition,
( sQ77_spl
<=> c_UNIV = c_UNIV ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f10710,plain,
( sQ77_spl
| sQ76_spl ),
inference(split_clause,[status(thm)],[f10696,f10704,f10707]) ).
fof(f10715,plain,
( ~ sQ76_spl
| $false ),
inference(destructive_equality_resolution,[status(thm)],[f10705]) ).
fof(f10716,plain,
~ sQ76_spl,
inference(contradiction_clause,[status(thm)],[f10715]) ).
fof(f10733,plain,
! [X0] :
( X0 = c_emptyset
| c_UNIV != c_emptyset ),
inference(paramodulation,[status(thm)],[f6151,f6154]) ).
fof(f10741,definition,
! [X0] :
( sQ80_spl
<=> X0 = c_emptyset ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f10742,plain,
! [X0] :
( ~ sQ80_spl
| X0 = c_emptyset ),
inference(component_clause,[status(thm)],[f10741]) ).
fof(f10744,plain,
( sQ80_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f10733,f10700,f10741]) ).
fof(f10794,plain,
! [X0,X1] :
( X1 = c_emptyset
| c_less(X0,c_Suc(c_Finite__Set_OMax(X1,tc_nat)),tc_nat)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ c_in(X0,X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f4268,f3026]) ).
fof(f10795,definition,
! [X0,X1] :
( sQ81_spl
<=> ( X1 = c_emptyset
| c_less(X0,c_Suc(c_Finite__Set_OMax(X1,tc_nat)),tc_nat)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ c_in(X0,X1,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f10798,plain,
( sQ81_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f10794,f9098,f10795]) ).
fof(f10846,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ c_in(X2,c_Relation_ODomain(c_UNIV,X0,X1),X0)
| ~ c_Infinite__Set_Oatmost__one(c_Relation_ODomain(c_UNIV,X0,X1),X0) ),
inference(resolution,[status(thm)],[f7314,f2992]) ).
fof(f10847,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ c_Infinite__Set_Oatmost__one(c_Relation_ODomain(c_UNIV,X0,X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f10846,f7314]) ).
fof(f10853,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ c_in(X2,c_Relation_ORange(c_UNIV,X0,X1),X1)
| ~ c_Infinite__Set_Oatmost__one(c_Relation_ORange(c_UNIV,X0,X1),X1) ),
inference(resolution,[status(thm)],[f7409,f2992]) ).
fof(f10854,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ c_Infinite__Set_Oatmost__one(c_Relation_ORange(c_UNIV,X0,X1),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f10853,f7409]) ).
fof(f10859,plain,
( c_Suc(c_0) = c_1
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
inference(paramodulation,[status(thm)],[f8401,f5497]) ).
fof(f10862,definition,
( sQ85_spl
<=> c_Suc(c_0) = c_1 ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f10865,plain,
( sQ85_spl
| ~ sQ53_spl ),
inference(split_clause,[status(thm)],[f10859,f10498,f10862]) ).
fof(f10872,plain,
! [X0] :
( c_0 = c_Binomial_Obinomial(X0,c_Suc(X0))
| c_1 != c_1 ),
inference(paramodulation,[status(thm)],[f8400,f8759]) ).
fof(f10890,definition,
! [X0] :
( sQ86_spl
<=> c_0 = c_Binomial_Obinomial(X0,c_Suc(X0)) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f10893,plain,
( sQ86_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f10872,f8943,f10890]) ).
fof(f10917,plain,
! [X0,X1,X2] :
( X1 = c_emptyset
| c_lessequals(c_div(c_Finite__Set_OMin(X1,tc_nat),X2,tc_nat),X0,tc_nat)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ c_in(X0,X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f4276,f4204]) ).
fof(f10919,plain,
! [X0,X1] :
( X1 = c_emptyset
| c_lessequals(c_0,X0,tc_nat)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ c_in(X0,X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f4276,f3025]) ).
fof(f10920,plain,
! [X0,X1] :
( X1 = c_emptyset
| c_lessequals(c_Finite__Set_OMin(X1,tc_nat),X0,tc_nat)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ c_in(X0,X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f4276,f8954]) ).
fof(f10923,definition,
! [X0,X1,X2] :
( sQ87_spl
<=> ( X1 = c_emptyset
| c_lessequals(c_div(c_Finite__Set_OMin(X1,tc_nat),X2,tc_nat),X0,tc_nat)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ c_in(X0,X1,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f10926,plain,
( sQ87_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f10917,f9098,f10923]) ).
fof(f10927,definition,
! [X0,X1] :
( sQ88_spl
<=> ( X1 = c_emptyset
| c_lessequals(c_0,X0,tc_nat)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ c_in(X0,X1,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f10930,plain,
( sQ88_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f10919,f9098,f10927]) ).
fof(f10931,definition,
! [X0,X1] :
( sQ89_spl
<=> ( X1 = c_emptyset
| c_lessequals(c_Finite__Set_OMin(X1,tc_nat),X0,tc_nat)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ c_in(X0,X1,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f10934,plain,
( sQ89_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f10920,f9098,f10931]) ).
fof(f10940,plain,
( c_0 = c_0
| c_1 = c_0 ),
inference(resolution,[status(thm)],[f5374,f6582]) ).
fof(f10944,plain,
( sQ29_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f10940,f6533,f8729]) ).
fof(f10958,plain,
c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint)) = c_0,
inference(paramodulation,[status(thm)],[f4406,f4422]) ).
fof(f11009,plain,
( c_List_Olist_ONil = c_List_Olist_ONil
| c_0 != c_0 ),
inference(paramodulation,[status(thm)],[f4712,f4711]) ).
fof(f11010,plain,
( sQ41_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f11009,f8729,f9028]) ).
fof(f11017,plain,
! [X0,X1] :
( c_List_Oremdups(X0,X1) = c_List_Olist_ONil
| c_emptyset != c_List_Oset(X0,X1) ),
inference(paramodulation,[status(thm)],[f4903,f4898]) ).
fof(f11022,plain,
! [X0,X1] :
( c_List_Orev(X0,X1) = c_List_Olist_ONil
| c_emptyset != c_List_Oset(X0,X1) ),
inference(paramodulation,[status(thm)],[f4908,f4898]) ).
fof(f11026,plain,
! [X0,X1] :
( c_List_Orotate1(X0,X1) = c_List_Olist_ONil
| c_emptyset != c_List_Oset(X0,X1) ),
inference(paramodulation,[status(thm)],[f4909,f4898]) ).
fof(f11030,plain,
! [X0] :
( X0 = c_emptyset
| c_lessequals(c_0,c_Finite__Set_OMin(X0,tc_nat),tc_nat)
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f4280,f3025]) ).
fof(f11031,definition,
! [X0] :
( sQ93_spl
<=> ( X0 = c_emptyset
| c_lessequals(c_0,c_Finite__Set_OMin(X0,tc_nat),tc_nat)
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_nat)) ) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f11034,plain,
( sQ93_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f11030,f9098,f11031]) ).
fof(f11035,plain,
! [X0,X1] :
( c_Finite__Set_OMin(X1,tc_nat) = c_0
| X1 = c_emptyset
| c_less(c_0,X0,tc_nat)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ c_in(X0,X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f4282,f5374]) ).
fof(f11036,definition,
! [X0,X1] :
( sQ94_spl
<=> ( c_Finite__Set_OMin(X1,tc_nat) = c_0
| X1 = c_emptyset
| c_less(c_0,X0,tc_nat)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ c_in(X0,X1,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f11039,plain,
( sQ94_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f11035,f9098,f11036]) ).
fof(f11044,plain,
! [X0] :
( c_1 = c_0
| c_Suc(X0) != c_0 ),
inference(paramodulation,[status(thm)],[f8401,f5291]) ).
fof(f11050,definition,
! [X0] :
( sQ95_spl
<=> c_Suc(X0) != c_0 ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f11053,plain,
( sQ1_spl
| sQ95_spl ),
inference(split_clause,[status(thm)],[f11044,f11050,f6533]) ).
fof(f11069,plain,
! [X0,X1,X2] :
( X1 = c_emptyset
| c_lessequals(c_minus(c_Finite__Set_OMin(X1,tc_nat),X2,tc_nat),X0,tc_nat)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ c_in(X0,X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f5302,f4276]) ).
fof(f11074,definition,
! [X0,X1,X2] :
( sQ97_spl
<=> ( X1 = c_emptyset
| c_lessequals(c_minus(c_Finite__Set_OMin(X1,tc_nat),X2,tc_nat),X0,tc_nat)
| ~ c_in(X1,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ c_in(X0,X1,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f11077,plain,
( sQ97_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f11069,f9098,f11074]) ).
fof(f11093,definition,
! [X0] :
( sQ98_spl
<=> X0 = c_1 ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f11094,plain,
! [X0] :
( ~ sQ98_spl
| X0 = c_1 ),
inference(component_clause,[status(thm)],[f11093]) ).
fof(f11118,plain,
! [X0] : ~ c_less(c_Suc(X0),X0,tc_nat),
inference(paramodulation,[status(thm)],[f8401,f5373]) ).
fof(f11130,plain,
( c_uminus(c_0,tc_IntDef_Oint) = c_0
| ~ class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) ),
inference(paramodulation,[status(thm)],[f6553,f5549]) ).
fof(f11131,definition,
( sQ100_spl
<=> c_uminus(c_0,tc_IntDef_Oint) = c_0 ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f11134,plain,
( sQ100_spl
| ~ sQ64_spl ),
inference(split_clause,[status(thm)],[f11130,f10592,f11131]) ).
fof(f11135,plain,
( sQ64_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10594,f3115]) ).
fof(f11136,plain,
sQ64_spl,
inference(contradiction_clause,[status(thm)],[f11135]) ).
fof(f11191,plain,
! [X0] :
( c_Main_OMin__gr__iff__1(X0,c_0,tc_nat) = c_0
| X0 = c_emptyset
| c_less(c_0,c_Finite__Set_OMin(X0,tc_nat),tc_nat)
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f4286,f5374]) ).
fof(f11192,definition,
! [X0] :
( sQ106_spl
<=> ( c_Main_OMin__gr__iff__1(X0,c_0,tc_nat) = c_0
| X0 = c_emptyset
| c_less(c_0,c_Finite__Set_OMin(X0,tc_nat),tc_nat)
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_nat)) ) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f11195,plain,
( sQ106_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f11191,f9098,f11192]) ).
fof(f11580,definition,
! [X0] :
( sQ111_spl
<=> ~ class_Orderings_Oorder(tc_set(X0)) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f11581,plain,
! [X0] :
( ~ sQ111_spl
| ~ class_Orderings_Oorder(tc_set(X0)) ),
inference(component_clause,[status(thm)],[f11580]) ).
fof(f11597,plain,
! [X0] :
( c_Finite__Set_OMin(X0,tc_nat) = c_0
| X0 = c_emptyset
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ c_in(c_0,X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f4292,f5304]) ).
fof(f11604,definition,
! [X0] :
( sQ114_spl
<=> ( c_Finite__Set_OMin(X0,tc_nat) = c_0
| X0 = c_emptyset
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_nat))
| ~ c_in(c_0,X0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f11607,plain,
( sQ114_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f11597,f9098,f11604]) ).
fof(f11620,plain,
( c_Message_OsymKeys = c_emptyset
| c_Message_OinvKey(c_Main_Oall__not__in__conv__1(c_Message_OsymKeys,tc_nat)) = c_Main_Oall__not__in__conv__1(c_Message_OsymKeys,tc_nat) ),
inference(resolution,[status(thm)],[f6487,f6187]) ).
fof(f11630,definition,
( sQ115_spl
<=> c_Message_OinvKey(c_Main_Oall__not__in__conv__1(c_Message_OsymKeys,tc_nat)) = c_Main_Oall__not__in__conv__1(c_Message_OsymKeys,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f11633,definition,
( sQ116_spl
<=> c_Message_OsymKeys = c_emptyset ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f11634,plain,
( ~ sQ116_spl
| c_Message_OsymKeys = c_emptyset ),
inference(component_clause,[status(thm)],[f11633]) ).
fof(f11636,plain,
( sQ116_spl
| sQ115_spl ),
inference(split_clause,[status(thm)],[f11620,f11630,f11633]) ).
fof(f11758,plain,
! [X0,X1] :
( ~ sQ116_spl
| ~ c_in(X0,c_Message_OsymKeys,X1) ),
inference(backward_demodulation,[status(thm)],[f11634,f6205]) ).
fof(f11967,plain,
( ~ sQ116_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f6513,f11758]) ).
fof(f12011,plain,
~ sQ116_spl,
inference(contradiction_clause,[status(thm)],[f11967]) ).
fof(f12069,plain,
! [X0,X1] :
( c_Finite__Set_Ocard(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X0,tc_Message_Omsg)),tc_Message_Omsg) = c_Suc(c_Finite__Set_Ocard(c_Message_Oparts(X0),tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X1),c_Message_Oparts(X0),tc_Message_Omsg)
| ~ c_in(c_Message_Oparts(X0),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6462,f4300]) ).
fof(f12070,plain,
! [X0,X1] :
( c_Finite__Set_Ocard(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),X0,tc_Message_Omsg)),tc_Message_Omsg) = c_Suc(c_Finite__Set_Ocard(c_Message_Oanalz(X0),tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X1),c_Message_Oanalz(X0),tc_Message_Omsg)
| ~ c_in(c_Message_Oanalz(X0),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6443,f4300]) ).
fof(f12323,plain,
! [X0] :
( c_Finite__Set_Ocard(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg),tc_Message_Omsg) = c_Suc(c_Finite__Set_Ocard(c_Message_Oparts(c_emptyset),tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_Message_Oparts(c_emptyset),tc_Message_Omsg)
| ~ c_in(c_Message_Oparts(c_emptyset),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f8448,f12069]) ).
fof(f12326,definition,
! [X0] :
( sQ124_spl
<=> ( c_Finite__Set_Ocard(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg),tc_Message_Omsg) = c_Suc(c_Finite__Set_Ocard(c_Message_Oparts(c_emptyset),tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_Message_Oparts(c_emptyset),tc_Message_Omsg) ) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f12327,plain,
! [X0] :
( ~ sQ124_spl
| c_Finite__Set_Ocard(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg),tc_Message_Omsg) = c_Suc(c_Finite__Set_Ocard(c_Message_Oparts(c_emptyset),tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_Message_Oparts(c_emptyset),tc_Message_Omsg) ),
inference(component_clause,[status(thm)],[f12326]) ).
fof(f12329,plain,
( sQ124_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f12323,f8492,f12326]) ).
fof(f12338,plain,
! [X0] :
( ~ sQ124_spl
| c_Finite__Set_Ocard(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg),tc_Message_Omsg) = c_Suc(c_Finite__Set_Ocard(c_Message_Oparts(c_emptyset),tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg) ),
inference(forward_demodulation,[status(thm)],[f6328,f12327]) ).
fof(f12339,plain,
! [X0] :
( ~ sQ124_spl
| c_Finite__Set_Ocard(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg),tc_Message_Omsg) = c_Suc(c_Finite__Set_Ocard(c_emptyset,tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg) ),
inference(forward_demodulation,[status(thm)],[f6328,f12338]) ).
fof(f12340,plain,
! [X0] :
( ~ sQ124_spl
| c_Finite__Set_Ocard(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg),tc_Message_Omsg) = c_Suc(c_0)
| c_in(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg) ),
inference(forward_demodulation,[status(thm)],[f6539,f12339]) ).
fof(f12341,plain,
! [X0] :
( ~ sQ124_spl
| c_Finite__Set_Ocard(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg),tc_Message_Omsg) = c_1
| c_in(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg) ),
inference(forward_demodulation,[status(thm)],[f5272,f12340]) ).
fof(f12342,plain,
! [X0] :
( ~ sQ124_spl
| c_Finite__Set_Ocard(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg),tc_Message_Omsg) = c_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f12341,f6205]) ).
fof(f12343,plain,
! [X0] :
( ~ sQ124_spl
| c_1 = c_Suc(c_Finite__Set_Ocard(c_emptyset,tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg)
| ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f12342,f4300]) ).
fof(f12344,definition,
( sQ125_spl
<=> c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f12347,definition,
! [X0] :
( sQ126_spl
<=> c_in(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f12348,plain,
! [X0] :
( ~ sQ126_spl
| c_in(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg) ),
inference(component_clause,[status(thm)],[f12347]) ).
fof(f12350,definition,
( sQ127_spl
<=> c_1 = c_Suc(c_Finite__Set_Ocard(c_emptyset,tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f12353,plain,
( ~ sQ124_spl
| sQ127_spl
| sQ126_spl
| ~ sQ125_spl ),
inference(split_clause,[status(thm)],[f12343,f12344,f12347,f12350,f12326]) ).
fof(f12354,plain,
( sQ65_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10601,f3160]) ).
fof(f12355,plain,
sQ65_spl,
inference(contradiction_clause,[status(thm)],[f12354]) ).
fof(f12356,plain,
( sQ62_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10578,f3192]) ).
fof(f12357,plain,
sQ62_spl,
inference(contradiction_clause,[status(thm)],[f12356]) ).
fof(f12448,plain,
! [X0] :
( c_Finite__Set_Ocard(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg),tc_Message_Omsg) = c_Suc(c_Finite__Set_Ocard(c_Message_Oanalz(c_emptyset),tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_Message_Oanalz(c_emptyset),tc_Message_Omsg)
| ~ c_in(c_Message_Oanalz(c_emptyset),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f8449,f12070]) ).
fof(f12455,definition,
! [X0] :
( sQ128_spl
<=> ( c_Finite__Set_Ocard(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg),tc_Message_Omsg) = c_Suc(c_Finite__Set_Ocard(c_Message_Oanalz(c_emptyset),tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_Message_Oanalz(c_emptyset),tc_Message_Omsg) ) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f12458,plain,
( sQ128_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f12448,f8514,f12455]) ).
fof(f12467,plain,
( sQ26_spl
| ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6436,f8516]) ).
fof(f12468,plain,
( sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12467,f2980]) ).
fof(f12469,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f12468]) ).
fof(f13000,plain,
! [X0,X1,X2] :
( c_in(c_minus(X0,c_Message_Oparts(X2),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_minus(X0,c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6462,f4304]) ).
fof(f13001,plain,
! [X0,X1,X2] :
( c_in(c_minus(X0,c_Message_Oanalz(X2),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_minus(X0,c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6443,f4304]) ).
fof(f13004,plain,
! [X0,X1,X2] :
( c_in(c_minus(X0,c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X2),X1,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_minus(X0,c_Message_Oparts(X1),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6462,f4306]) ).
fof(f13005,plain,
! [X0,X1,X2] :
( c_in(c_minus(X0,c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X2),X1,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_minus(X0,c_Message_Oanalz(X1),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6443,f4306]) ).
fof(f13013,plain,
! [X0,X1] :
( c_in(c_minus(X0,c_Message_Oparts(c_emptyset),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_minus(X0,c_insert(c_Message_Omsg_ONonce(X1),c_emptyset,tc_Message_Omsg),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f8448,f13000]) ).
fof(f13019,plain,
! [X0,X1] :
( c_in(c_minus(X0,c_emptyset,tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_minus(X0,c_insert(c_Message_Omsg_ONonce(X1),c_emptyset,tc_Message_Omsg),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6328,f13013]) ).
fof(f13020,plain,
! [X0,X1] :
( c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_minus(X0,c_insert(c_Message_Omsg_ONonce(X1),c_emptyset,tc_Message_Omsg),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6096,f13019]) ).
fof(f13076,plain,
! [X0,X1,X2,X3] :
( X2 = c_minus(X0,c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X3),X1,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_in(X2,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_minus(X0,c_Message_Oparts(X1),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13004,f2992]) ).
fof(f13083,definition,
! [X0,X1,X2,X3] :
( sQ129_spl
<=> ( X2 = c_minus(X0,c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X3),X1,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_in(X2,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_minus(X0,c_Message_Oparts(X1),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f13086,plain,
( ~ sQ2_spl
| sQ129_spl ),
inference(split_clause,[status(thm)],[f13076,f13083,f6972]) ).
fof(f13097,plain,
! [X0,X1,X2,X3] :
( X2 = c_minus(X0,c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X3),X1,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_in(X2,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_minus(X0,c_Message_Oanalz(X1),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13005,f2992]) ).
fof(f13104,definition,
! [X0,X1,X2,X3] :
( sQ130_spl
<=> ( X2 = c_minus(X0,c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X3),X1,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_in(X2,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_minus(X0,c_Message_Oanalz(X1),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f13107,plain,
( ~ sQ2_spl
| sQ130_spl ),
inference(split_clause,[status(thm)],[f13097,f13104,f6972]) ).
fof(f13141,definition,
! [X0,X1] :
( sQ131_spl
<=> ( ~ c_in(c_minus(X0,c_insert(c_Message_Omsg_ONonce(X1),c_emptyset,tc_Message_Omsg),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f13142,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ c_in(c_minus(X0,c_insert(c_Message_Omsg_ONonce(X1),c_emptyset,tc_Message_Omsg),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(component_clause,[status(thm)],[f13141]) ).
fof(f13145,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ c_in(c_minus(X0,c_insert(c_Message_Omsg_ONonce(X1),c_emptyset,tc_Message_Omsg),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_subsumption_resolution,[status(thm)],[f13142,f13020]) ).
fof(f13146,plain,
! [X0] :
( ~ sQ131_spl
| ~ c_in(c_minus(X0,c_emptyset,tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13145,f4306]) ).
fof(f13152,plain,
( ~ sQ24_spl
| ~ sQ131_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f8496,f13153]) ).
fof(f13153,plain,
! [X0] :
( ~ sQ131_spl
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6096,f13146]) ).
fof(f13154,plain,
( ~ sQ24_spl
| ~ sQ131_spl ),
inference(contradiction_clause,[status(thm)],[f13152]) ).
fof(f13282,plain,
! [X0] :
( c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_minus(c_emptyset,c_Message_Oparts(X0),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6200,f13004]) ).
fof(f13292,definition,
! [X0] :
( sQ135_spl
<=> ~ c_in(c_minus(c_emptyset,c_Message_Oparts(X0),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f13293,plain,
! [X0] :
( ~ sQ135_spl
| ~ c_in(c_minus(c_emptyset,c_Message_Oparts(X0),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(component_clause,[status(thm)],[f13292]) ).
fof(f13295,plain,
( sQ125_spl
| sQ135_spl ),
inference(split_clause,[status(thm)],[f13282,f13292,f12344]) ).
fof(f13304,plain,
( ~ sQ126_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f12348,f6205]) ).
fof(f13305,plain,
~ sQ126_spl,
inference(contradiction_clause,[status(thm)],[f13304]) ).
fof(f13306,plain,
( ~ sQ135_spl
| ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6200,f13293]) ).
fof(f13307,plain,
( ~ sQ135_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13306,f2980]) ).
fof(f13308,plain,
~ sQ135_spl,
inference(contradiction_clause,[status(thm)],[f13307]) ).
fof(f13354,definition,
! [X0] :
( sQ137_spl
<=> c_in(c_minus(c_emptyset,c_Message_Oanalz(X0),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f13358,definition,
! [X0,X1] :
( sQ138_spl
<=> c_in(c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),c_Message_Oanalz(X1),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f13359,plain,
! [X0,X1] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),c_Message_Oanalz(X1),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(component_clause,[status(thm)],[f13358]) ).
fof(f13379,definition,
! [X0] :
( sQ139_spl
<=> c_in(c_minus(c_emptyset,c_Message_Oparts(X0),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f13383,definition,
! [X0,X1] :
( sQ140_spl
<=> c_in(c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),c_Message_Oparts(X1),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f13399,plain,
! [X0] :
( c_in(c_minus(c_emptyset,c_Message_Oanalz(X0),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6200,f13001]) ).
fof(f13400,plain,
! [X0,X1] :
( c_in(c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),c_Message_Oanalz(X1),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6094,f13001]) ).
fof(f13407,plain,
( sQ137_spl
| ~ sQ125_spl ),
inference(split_clause,[status(thm)],[f13399,f12344,f13354]) ).
fof(f13408,plain,
( sQ138_spl
| ~ sQ125_spl ),
inference(split_clause,[status(thm)],[f13400,f12344,f13358]) ).
fof(f13419,plain,
! [X0,X1,X2] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oanalz(X2),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13359,f13001]) ).
fof(f13420,plain,
! [X0,X1,X2] :
( ~ sQ138_spl
| X0 = c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)),c_Message_Oanalz(X2),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13359,f2992]) ).
fof(f13425,plain,
! [X0,X1] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oanalz(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg))),c_Message_Oanalz(c_Message_Oparts(X1)),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6462,f13359]) ).
fof(f13434,definition,
! [X0,X1,X2] :
( sQ141_spl
<=> ( X0 = c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)),c_Message_Oanalz(X2),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f13437,plain,
( ~ sQ138_spl
| sQ141_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f13420,f6972,f13434,f13358]) ).
fof(f13443,plain,
! [X0,X1] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),c_Message_Oanalz(c_Message_Oparts(X1)),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6445,f13425]) ).
fof(f13444,plain,
! [X0,X1] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),c_Message_Oparts(X1),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6445,f13443]) ).
fof(f13457,plain,
! [X0,X1,X2] :
( ~ sQ138_spl
| X0 = c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)),c_Message_Oparts(X2),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13444,f2992]) ).
fof(f13471,definition,
! [X0,X1,X2] :
( sQ142_spl
<=> ( X0 = c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)),c_Message_Oparts(X2),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f13474,plain,
( ~ sQ138_spl
| sQ142_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f13457,f6972,f13471,f13358]) ).
fof(f13494,plain,
! [X0,X1,X2,X3] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),X3,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oanalz(X3),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13419,f13001]) ).
fof(f13495,plain,
! [X0,X1,X2,X3] :
( ~ sQ138_spl
| X0 = c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),X3,tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oanalz(X3),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13419,f2992]) ).
fof(f13496,plain,
! [X0,X1,X2,X3] :
( ~ sQ138_spl
| c_in(c_minus(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_emptyset,tc_Message_Omsg),tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f8552,f13419]) ).
fof(f13497,plain,
! [X0,X1,X2] :
( ~ sQ138_spl
| c_in(c_minus(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X2),c_emptyset,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f8532,f13419]) ).
fof(f13498,plain,
! [X0,X1] :
( ~ sQ138_spl
| c_in(c_minus(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),c_Message_Oanalz(c_emptyset),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f8513,f13419]) ).
fof(f13499,plain,
! [X0,X1,X2] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)),tc_Message_Omsg)),c_Message_Oanalz(c_Message_Oparts(X2)),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6462,f13419]) ).
fof(f13508,definition,
! [X0,X1,X2,X3] :
( sQ143_spl
<=> ( X0 = c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),X3,tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oanalz(X3),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f13511,plain,
( ~ sQ138_spl
| sQ143_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f13495,f6972,f13508,f13358]) ).
fof(f13512,plain,
! [X0,X1,X2,X3] :
( ~ sQ138_spl
| c_in(c_minus(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f8513,f13496]) ).
fof(f13513,plain,
! [X0,X1,X2] :
( ~ sQ138_spl
| c_in(c_minus(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_insert(c_Message_Omsg_ONonce(X2),c_emptyset,tc_Message_Omsg),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f8449,f13497]) ).
fof(f13514,plain,
! [X0,X1] :
( ~ sQ138_spl
| c_in(c_minus(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),c_emptyset,tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6436,f13498]) ).
fof(f13515,plain,
! [X0,X1] :
( ~ sQ138_spl
| c_in(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6096,f13514]) ).
fof(f13516,plain,
! [X0,X1,X2] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oanalz(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg),tc_Message_Omsg))),c_Message_Oanalz(c_Message_Oparts(X2)),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6462,f13499]) ).
fof(f13517,plain,
! [X0,X1,X2] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oanalz(c_Message_Oparts(X2)),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6445,f13516]) ).
fof(f13518,plain,
! [X0,X1,X2] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(X2),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6445,f13517]) ).
fof(f13558,plain,
! [X0,X1,X2] :
( ~ sQ138_spl
| X0 = c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_emptyset,tc_Message_Omsg),tc_Message_Omsg)
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13515,f2992]) ).
fof(f13559,definition,
! [X0,X1,X2] :
( sQ144_spl
<=> ( X0 = c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_emptyset,tc_Message_Omsg),tc_Message_Omsg)
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f13562,plain,
( ~ sQ138_spl
| sQ144_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f13558,f6972,f13559,f13358]) ).
fof(f13563,plain,
! [X0,X1,X2,X3] :
( ~ sQ138_spl
| X0 = c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),X3,tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(X3),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13518,f2992]) ).
fof(f13576,definition,
! [X0,X1,X2,X3] :
( sQ145_spl
<=> ( X0 = c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),X3,tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(X3),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f13579,plain,
( ~ sQ138_spl
| sQ145_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f13563,f6972,f13576,f13358]) ).
fof(f13601,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),X4,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oanalz(X4),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13494,f13001]) ).
fof(f13602,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ138_spl
| X0 = c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),X4,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oanalz(X4),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13494,f2992]) ).
fof(f13603,plain,
! [X0,X1,X2,X3] :
( ~ sQ138_spl
| c_in(c_minus(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X3),c_emptyset,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f8552,f13494]) ).
fof(f13604,plain,
! [X0,X1,X2] :
( ~ sQ138_spl
| c_in(c_minus(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_Message_Oanalz(c_emptyset),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f8532,f13494]) ).
fof(f13605,plain,
! [X0,X1,X2,X3] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X2),X3,tc_Message_Omsg)),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oanalz(c_Message_Oparts(X3)),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6462,f13494]) ).
fof(f13609,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f8513,f13494]) ).
fof(f13614,definition,
! [X0,X1,X2,X3,X4] :
( sQ146_spl
<=> ( X0 = c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),X4,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oanalz(X4),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f13617,plain,
( ~ sQ138_spl
| sQ146_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f13602,f6972,f13614,f13358]) ).
fof(f13618,plain,
! [X0,X1,X2,X3] :
( ~ sQ138_spl
| c_in(c_minus(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_insert(c_Message_Omsg_ONonce(X3),c_emptyset,tc_Message_Omsg),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f8449,f13603]) ).
fof(f13619,plain,
! [X0,X1,X2] :
( ~ sQ138_spl
| c_in(c_minus(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_emptyset,tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6436,f13604]) ).
fof(f13620,plain,
! [X0,X1,X2] :
( ~ sQ138_spl
| c_in(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6096,f13619]) ).
fof(f13621,plain,
! [X0,X1,X2,X3] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),X3,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg)),c_Message_Oanalz(c_Message_Oparts(X3)),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6462,f13605]) ).
fof(f13622,plain,
! [X0,X1,X2,X3] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oanalz(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),X3,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg))),c_Message_Oanalz(c_Message_Oparts(X3)),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6462,f13621]) ).
fof(f13623,plain,
! [X0,X1,X2,X3] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),X3,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oanalz(c_Message_Oparts(X3)),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6445,f13622]) ).
fof(f13624,plain,
! [X0,X1,X2,X3] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),X3,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(X3),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6445,f13623]) ).
fof(f13629,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ138_spl
| c_in(c_minus(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f8576,f13609]) ).
fof(f13641,plain,
! [X0,X1,X2,X3] :
( ~ sQ138_spl
| X0 = c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13620,f2992]) ).
fof(f13642,definition,
! [X0,X1,X2,X3] :
( sQ147_spl
<=> ( X0 = c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f13645,plain,
( ~ sQ138_spl
| sQ147_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f13641,f6972,f13642,f13358]) ).
fof(f13646,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ138_spl
| X0 = c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),X4,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(X4),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13624,f2992]) ).
fof(f13658,definition,
! [X0,X1,X2,X3,X4] :
( sQ148_spl
<=> ( X0 = c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),X4,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(X4),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f13661,plain,
( ~ sQ138_spl
| sQ148_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f13646,f6972,f13658,f13358]) ).
fof(f13685,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),X4,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(X4),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13000,f13624]) ).
fof(f13691,plain,
! [X0] :
( c_in(c_minus(c_emptyset,c_Message_Oparts(X0),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6200,f13000]) ).
fof(f13692,plain,
! [X0,X1] :
( c_in(c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),c_Message_Oparts(X1),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6094,f13000]) ).
fof(f13699,plain,
( sQ139_spl
| ~ sQ125_spl ),
inference(split_clause,[status(thm)],[f13691,f12344,f13379]) ).
fof(f13700,plain,
( sQ140_spl
| ~ sQ125_spl ),
inference(split_clause,[status(thm)],[f13692,f12344,f13383]) ).
fof(f13738,plain,
! [X0,X1,X2,X3] :
( ~ sQ138_spl
| X0 = c_minus(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_insert(c_Message_Omsg_ONonce(X3),c_emptyset,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13513,f2992]) ).
fof(f13740,definition,
! [X0,X1,X2,X3] :
( sQ149_spl
<=> ( X0 = c_minus(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_insert(c_Message_Omsg_ONonce(X3),c_emptyset,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f13743,plain,
( ~ sQ138_spl
| sQ149_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f13738,f6972,f13740,f13358]) ).
fof(f13744,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),X5,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oanalz(X5),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13601,f13001]) ).
fof(f13745,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ138_spl
| X0 = c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),X5,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oanalz(X5),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13601,f2992]) ).
fof(f13746,plain,
! [X0,X1,X2,X3] :
( ~ sQ138_spl
| c_in(c_minus(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_Message_Oanalz(c_emptyset),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f8552,f13601]) ).
fof(f13752,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_insert(c_Message_Omsg_ONonce(X4),c_emptyset,tc_Message_Omsg),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f8449,f13601]) ).
fof(f13756,definition,
! [X0,X1,X2,X3,X4,X5] :
( sQ150_spl
<=> ( X0 = c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),X5,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oanalz(X5),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f13759,plain,
( ~ sQ138_spl
| sQ150_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f13745,f6972,f13756,f13358]) ).
fof(f13760,plain,
! [X0,X1,X2,X3] :
( ~ sQ138_spl
| c_in(c_minus(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_emptyset,tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6436,f13746]) ).
fof(f13761,plain,
! [X0,X1,X2,X3] :
( ~ sQ138_spl
| c_in(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6096,f13760]) ).
fof(f13772,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ138_spl
| c_in(c_minus(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_insert(c_Message_Omsg_ONonce(X4),c_emptyset,tc_Message_Omsg),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f8576,f13752]) ).
fof(f13785,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ138_spl
| X0 = c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13761,f2992]) ).
fof(f13786,definition,
! [X0,X1,X2,X3,X4] :
( sQ151_spl
<=> ( X0 = c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f13789,plain,
( ~ sQ138_spl
| sQ151_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f13785,f6972,f13786,f13358]) ).
fof(f13790,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),X5,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(X5),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13685,f13000]) ).
fof(f13791,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ138_spl
| X0 = c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),X5,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(X5),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13685,f2992]) ).
fof(f13802,definition,
! [X0,X1,X2,X3,X4,X5] :
( sQ152_spl
<=> ( X0 = c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),X5,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(X5),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f13805,plain,
( ~ sQ138_spl
| sQ152_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f13791,f6972,f13802,f13358]) ).
fof(f13833,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ138_spl
| X0 = c_minus(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_insert(c_Message_Omsg_ONonce(X4),c_emptyset,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13618,f2992]) ).
fof(f13835,definition,
! [X0,X1,X2,X3,X4] :
( sQ153_spl
<=> ( X0 = c_minus(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_insert(c_Message_Omsg_ONonce(X4),c_emptyset,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f13838,plain,
( ~ sQ138_spl
| sQ153_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f13833,f6972,f13835,f13358]) ).
fof(f13868,plain,
! [X0] : c_lessequals(c_1,c_Suc(X0),tc_nat),
inference(paramodulation,[status(thm)],[f8401,f6523]) ).
fof(f13873,plain,
! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat),
inference(paramodulation,[status(thm)],[f8401,f6524]) ).
fof(f13999,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),X6,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oanalz(X6),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13744,f13001]) ).
fof(f14000,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ138_spl
| X0 = c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),X6,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oanalz(X6),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13744,f2992]) ).
fof(f14006,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_insert(c_Message_Omsg_ONonce(X5),c_emptyset,tc_Message_Omsg),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f8449,f13744]) ).
fof(f14007,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_emptyset,tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6436,f13744]) ).
fof(f14010,definition,
! [X0,X1,X2,X3,X4,X5,X6] :
( sQ155_spl
<=> ( X0 = c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),X6,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oanalz(X6),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f14013,plain,
( ~ sQ138_spl
| sQ155_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f14000,f6972,f14010,f13358]) ).
fof(f14026,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ138_spl
| c_in(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6096,f14007]) ).
fof(f14027,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ138_spl
| c_in(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f8576,f14026]) ).
fof(f14040,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ138_spl
| X0 = c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f14027,f2992]) ).
fof(f14041,definition,
! [X0,X1,X2,X3,X4,X5] :
( sQ156_spl
<=> ( X0 = c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f14044,plain,
( ~ sQ138_spl
| sQ156_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f14040,f6972,f14041,f13358]) ).
fof(f14045,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),X6,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(X6),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13790,f13000]) ).
fof(f14046,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ138_spl
| X0 = c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),X6,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(X6),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13790,f2992]) ).
fof(f14052,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_insert(c_Message_Omsg_ONonce(X5),c_emptyset,tc_Message_Omsg),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f8448,f13790]) ).
fof(f14056,definition,
! [X0,X1,X2,X3,X4,X5,X6] :
( sQ157_spl
<=> ( X0 = c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),X6,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(X6),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f14059,plain,
( ~ sQ138_spl
| sQ157_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f14046,f6972,f14056,f13358]) ).
fof(f14087,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ138_spl
| X0 = c_minus(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13512,f2992]) ).
fof(f14088,definition,
! [X0,X1,X2,X3,X4] :
( sQ158_spl
<=> ( X0 = c_minus(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f14091,plain,
( ~ sQ138_spl
| sQ158_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f14087,f6972,f14088,f13358]) ).
fof(f14094,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ138_spl
| X0 = c_minus(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_insert(c_Message_Omsg_ONonce(X5),c_emptyset,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13772,f2992]) ).
fof(f14096,definition,
! [X0,X1,X2,X3,X4,X5] :
( sQ159_spl
<=> ( X0 = c_minus(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_insert(c_Message_Omsg_ONonce(X5),c_emptyset,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f14099,plain,
( ~ sQ138_spl
| sQ159_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f14094,f6972,f14096,f13358]) ).
fof(f14100,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_insert(c_Message_Omsg_ONonce(X6),X7,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oanalz(X7),tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13999,f13001]) ).
fof(f14101,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ138_spl
| X0 = c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_insert(c_Message_Omsg_ONonce(X6),X7,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oanalz(X7),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13999,f2992]) ).
fof(f14108,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_emptyset,tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6436,f13999]) ).
fof(f14111,definition,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( sQ160_spl
<=> ( X0 = c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_insert(c_Message_Omsg_ONonce(X6),X7,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oanalz(X7),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f14114,plain,
( ~ sQ138_spl
| sQ160_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f14101,f6972,f14111,f13358]) ).
fof(f14129,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ138_spl
| c_in(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6096,f14108]) ).
fof(f14144,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ138_spl
| X0 = c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_insert(c_Message_Omsg_ONonce(X6),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f14129,f2992]) ).
fof(f14145,definition,
! [X0,X1,X2,X3,X4,X5,X6] :
( sQ161_spl
<=> ( X0 = c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_insert(c_Message_Omsg_ONonce(X6),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f14148,plain,
( ~ sQ138_spl
| sQ161_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f14144,f6972,f14145,f13358]) ).
fof(f14150,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ138_spl
| X0 = c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_insert(c_Message_Omsg_ONonce(X6),X7,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(X7),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f14045,f2992]) ).
fof(f14157,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ138_spl
| c_in(c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_emptyset,tc_set(tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6328,f14045]) ).
fof(f14160,definition,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( sQ162_spl
<=> ( X0 = c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_insert(c_Message_Omsg_ONonce(X6),X7,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oparts(X7),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f14163,plain,
( ~ sQ138_spl
| sQ162_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f14150,f6972,f14160,f13358]) ).
fof(f14178,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ138_spl
| c_in(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f6096,f14157]) ).
fof(f14193,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ138_spl
| X0 = c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_insert(c_Message_Omsg_ONonce(X6),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f14178,f2992]) ).
fof(f14194,definition,
! [X0,X1,X2,X3,X4,X5,X6] :
( sQ163_spl
<=> ( X0 = c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_insert(c_Message_Omsg_ONonce(X6),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f14197,plain,
( ~ sQ138_spl
| sQ163_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f14193,f6972,f14194,f13358]) ).
fof(f14202,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ138_spl
| X0 = c_minus(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f13629,f2992]) ).
fof(f14203,definition,
! [X0,X1,X2,X3,X4,X5] :
( sQ164_spl
<=> ( X0 = c_minus(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f14206,plain,
( ~ sQ138_spl
| sQ164_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f14202,f6972,f14203,f13358]) ).
fof(f14209,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ138_spl
| X0 = c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_insert(c_Message_Omsg_ONonce(X6),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_insert(c_Message_Omsg_ONonce(X6),c_emptyset,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f14006,f2992]) ).
fof(f14211,definition,
! [X0,X1,X2,X3,X4,X5,X6] :
( sQ165_spl
<=> ( X0 = c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_insert(c_Message_Omsg_ONonce(X6),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_insert(c_Message_Omsg_ONonce(X6),c_emptyset,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f14214,plain,
( ~ sQ138_spl
| sQ165_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f14209,f6972,f14211,f13358]) ).
fof(f14217,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ138_spl
| X0 = c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_insert(c_Message_Omsg_ONonce(X6),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_insert(c_Message_Omsg_ONonce(X6),c_emptyset,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f14052,f2992]) ).
fof(f14219,definition,
! [X0,X1,X2,X3,X4,X5,X6] :
( sQ166_spl
<=> ( X0 = c_minus(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_insert(c_Message_Omsg_ONonce(X6),c_emptyset,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_insert(c_Message_Omsg_ONonce(X6),c_emptyset,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f14222,plain,
( ~ sQ138_spl
| sQ166_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f14217,f6972,f14219,f13358]) ).
fof(f14224,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ138_spl
| X0 = c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_insert(c_Message_Omsg_ONonce(X6),c_insert(c_Message_Omsg_ONonce(X7),X8,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oanalz(X8),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_Infinite__Set_Oatmost__one(c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f14100,f2992]) ).
fof(f14234,definition,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( sQ167_spl
<=> ( X0 = c_minus(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X2),c_insert(c_Message_Omsg_ONonce(X3),c_insert(c_Message_Omsg_ONonce(X4),c_insert(c_Message_Omsg_ONonce(X5),c_insert(c_Message_Omsg_ONonce(X6),c_insert(c_Message_Omsg_ONonce(X7),X8,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)),c_Message_Oanalz(X8),tc_set(tc_Message_Omsg))
| ~ c_in(X0,c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ) ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f14237,plain,
( ~ sQ138_spl
| sQ167_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f14224,f6972,f14234,f13358]) ).
fof(f14341,plain,
( c_1 = c_0
| ~ c_lessequals(c_1,c_0,tc_IntDef_Oint) ),
inference(paramodulation,[status(thm)],[f4406,f4411]) ).
fof(f14342,definition,
( sQ168_spl
<=> c_lessequals(c_0,c_0,tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f14346,definition,
( sQ169_spl
<=> c_lessequals(c_1,c_0,tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f14349,plain,
( sQ1_spl
| ~ sQ169_spl ),
inference(split_clause,[status(thm)],[f14341,f14346,f6533]) ).
fof(f14351,plain,
( ~ class_Orderings_Oorder(tc_IntDef_Oint)
| c_IntDef_Onat(c_0) = c_0 ),
inference(resolution,[status(thm)],[f4420,f3030]) ).
fof(f14352,definition,
( sQ170_spl
<=> c_IntDef_Onat(c_0) = c_0 ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f14355,definition,
( sQ171_spl
<=> class_Orderings_Oorder(tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f14357,plain,
( sQ171_spl
| ~ class_Orderings_Oorder(tc_IntDef_Oint) ),
inference(component_clause,[status(thm)],[f14355]) ).
fof(f14358,plain,
( ~ sQ171_spl
| sQ170_spl ),
inference(split_clause,[status(thm)],[f14351,f14352,f14355]) ).
fof(f14360,definition,
! [X0] :
( sQ172_spl
<=> ( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f14361,plain,
! [X0] :
( ~ sQ172_spl
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(component_clause,[status(thm)],[f14360]) ).
fof(f14365,plain,
! [X0] :
( c_in(X0,c_IntDef_ONats,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) ),
inference(paramodulation,[status(thm)],[f4322,f4472]) ).
fof(f14366,definition,
! [X0] :
( sQ173_spl
<=> c_in(X0,c_IntDef_ONats,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f14367,plain,
! [X0] :
( ~ sQ173_spl
| c_in(X0,c_IntDef_ONats,tc_nat) ),
inference(component_clause,[status(thm)],[f14366]) ).
fof(f14369,plain,
( sQ173_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f14365,f10467,f14366]) ).
fof(f14370,plain,
( sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10469,f3202]) ).
fof(f14371,plain,
sQ49_spl,
inference(contradiction_clause,[status(thm)],[f14370]) ).
fof(f14372,plain,
! [X0] :
( ~ sQ173_spl
| c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat)) ),
inference(resolution,[status(thm)],[f14367,f3080]) ).
fof(f14374,plain,
! [X0,X1] :
( ~ sQ173_spl
| X0 = X1
| ~ c_in(X0,c_IntDef_ONats,tc_nat)
| ~ c_Infinite__Set_Oatmost__one(c_IntDef_ONats,tc_nat) ),
inference(resolution,[status(thm)],[f14367,f2992]) ).
fof(f14375,definition,
( sQ174_spl
<=> c_Infinite__Set_Oatmost__one(c_IntDef_ONats,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f14378,definition,
! [X0,X1] :
( sQ175_spl
<=> ( X0 = X1
| ~ c_in(X0,c_IntDef_ONats,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f14381,plain,
( ~ sQ173_spl
| sQ175_spl
| ~ sQ174_spl ),
inference(split_clause,[status(thm)],[f14374,f14375,f14378,f14366]) ).
fof(f14382,plain,
( ~ sQ173_spl
| c_IntDef_ONats = c_UNIV ),
inference(resolution,[status(thm)],[f14372,f8820]) ).
fof(f14387,plain,
! [X0,X1,X2,X3] :
( ~ sQ173_spl
| X2 = X3
| ~ c_Infinite__Set_Oatmost__one(c_Relation_ORange(c_IntDef_ONats,X0,X1),X1) ),
inference(backward_demodulation,[status(thm)],[f14382,f10854]) ).
fof(f14388,plain,
! [X0,X1,X2,X3] :
( ~ sQ173_spl
| X2 = X3
| ~ c_Infinite__Set_Oatmost__one(c_Relation_ODomain(c_IntDef_ONats,X0,X1),X0) ),
inference(backward_demodulation,[status(thm)],[f14382,f10847]) ).
fof(f14390,plain,
! [X0,X1] :
( ~ sQ173_spl
| X0 = c_IntDef_ONats
| ~ c_lessequals(c_UNIV,X0,tc_set(X1)) ),
inference(backward_demodulation,[status(thm)],[f14382,f8820]) ).
fof(f14391,plain,
! [X0,X1] :
( ~ sQ173_spl
| c_minus(X0,c_IntDef_ONats,tc_set(X1)) = c_emptyset ),
inference(backward_demodulation,[status(thm)],[f14382,f6093]) ).
fof(f14395,plain,
! [X0] :
( ~ sQ173_spl
| c_Inter(c_IntDef_ONats,X0) = c_emptyset ),
inference(backward_demodulation,[status(thm)],[f14382,f6127]) ).
fof(f14397,plain,
( ~ sQ173_spl
| c_IntDef_ONats != c_emptyset ),
inference(backward_demodulation,[status(thm)],[f14382,f6147]) ).
fof(f14404,plain,
! [X0,X1,X2] :
( ~ sQ173_spl
| X0 = c_IntDef_ONats
| c_inter(X0,X1,X2) != c_UNIV ),
inference(backward_demodulation,[status(thm)],[f14382,f6108]) ).
fof(f14408,plain,
! [X0,X1] :
( ~ sQ173_spl
| c_union(X0,c_UNIV,X1) = c_IntDef_ONats ),
inference(backward_demodulation,[status(thm)],[f14382,f6151]) ).
fof(f14410,plain,
( ~ sQ173_spl
| c_SetInterval_OatLeast(c_0,tc_nat) = c_IntDef_ONats ),
inference(backward_demodulation,[status(thm)],[f14382,f6020]) ).
fof(f14413,plain,
! [X0,X1,X2] :
( ~ sQ173_spl
| X1 = X2
| ~ c_Infinite__Set_Oatmost__one(c_IntDef_ONats,X0) ),
inference(backward_demodulation,[status(thm)],[f14382,f6990]) ).
fof(f14414,plain,
! [X0] :
( ~ sQ173_spl
| c_Union(c_UNIV,X0) = c_IntDef_ONats ),
inference(backward_demodulation,[status(thm)],[f14382,f6174]) ).
fof(f14417,plain,
! [X0,X1] :
( ~ sQ173_spl
| c_inter(c_IntDef_ONats,X0,X1) = X0 ),
inference(backward_demodulation,[status(thm)],[f14382,f6112]) ).
fof(f14419,plain,
! [X0,X1] :
( ~ sQ173_spl
| c_in(X0,c_IntDef_ONats,X1) ),
inference(backward_demodulation,[status(thm)],[f14382,f3064]) ).
fof(f14439,plain,
! [X0,X1] :
( ~ sQ173_spl
| c_IntDef_ONats = c_Inter(X0,X1)
| c_Main_OInter__UNIV__conv__2__1(X0,X1) != c_UNIV ),
inference(backward_demodulation,[status(thm)],[f14382,f6135]) ).
fof(f14441,plain,
! [X0,X1] :
( ~ sQ173_spl
| c_Inter(X0,X1) = c_IntDef_ONats
| c_Main_OInter__UNIV__conv__1__1(X0,X1) != c_UNIV ),
inference(backward_demodulation,[status(thm)],[f14382,f6131]) ).
fof(f14444,definition,
! [X0,X1] :
( sQ176_spl
<=> ~ c_Infinite__Set_Oatmost__one(c_Relation_ORange(c_IntDef_ONats,X0,X1),X1) ),
introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition]) ).
fof(f14447,definition,
! [X2,X3] :
( sQ177_spl
<=> X2 = X3 ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f14448,plain,
! [X0,X1] :
( ~ sQ177_spl
| X0 = X1 ),
inference(component_clause,[status(thm)],[f14447]) ).
fof(f14450,plain,
( ~ sQ173_spl
| sQ177_spl
| sQ176_spl ),
inference(split_clause,[status(thm)],[f14387,f14444,f14447,f14366]) ).
fof(f14451,definition,
! [X0,X1] :
( sQ178_spl
<=> ~ c_Infinite__Set_Oatmost__one(c_Relation_ODomain(c_IntDef_ONats,X0,X1),X0) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f14454,plain,
( ~ sQ173_spl
| sQ177_spl
| sQ178_spl ),
inference(split_clause,[status(thm)],[f14388,f14451,f14447,f14366]) ).
fof(f14456,plain,
! [X0,X1] :
( ~ sQ173_spl
| X0 = c_IntDef_ONats
| ~ c_lessequals(c_IntDef_ONats,X0,tc_set(X1)) ),
inference(forward_demodulation,[status(thm)],[f14382,f14390]) ).
fof(f14460,plain,
! [X0,X1,X2] :
( ~ sQ173_spl
| X0 = c_IntDef_ONats
| c_inter(X0,X1,X2) != c_IntDef_ONats ),
inference(forward_demodulation,[status(thm)],[f14382,f14404]) ).
fof(f14461,plain,
! [X0,X1] :
( ~ sQ173_spl
| c_union(X0,c_IntDef_ONats,X1) = c_IntDef_ONats ),
inference(forward_demodulation,[status(thm)],[f14382,f14408]) ).
fof(f14463,definition,
! [X0] :
( sQ179_spl
<=> ~ c_Infinite__Set_Oatmost__one(c_IntDef_ONats,X0) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f14466,plain,
( ~ sQ173_spl
| sQ177_spl
| sQ179_spl ),
inference(split_clause,[status(thm)],[f14413,f14463,f14447,f14366]) ).
fof(f14467,plain,
! [X0] :
( ~ sQ173_spl
| c_Union(c_IntDef_ONats,X0) = c_IntDef_ONats ),
inference(forward_demodulation,[status(thm)],[f14382,f14414]) ).
fof(f14472,plain,
! [X0,X1] :
( ~ sQ173_spl
| X1 = c_1
| ~ c_Infinite__Set_Oatmost__one(c_IntDef_ONats,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f9247,f14419]) ).
fof(f14477,plain,
! [X0,X1] :
( ~ sQ173_spl
| c_IntDef_ONats = c_Inter(X0,X1)
| c_Main_OInter__UNIV__conv__2__1(X0,X1) != c_IntDef_ONats ),
inference(forward_demodulation,[status(thm)],[f14382,f14439]) ).
fof(f14478,plain,
! [X0,X1] :
( ~ sQ173_spl
| c_Inter(X0,X1) = c_IntDef_ONats
| c_Main_OInter__UNIV__conv__1__1(X0,X1) != c_IntDef_ONats ),
inference(forward_demodulation,[status(thm)],[f14382,f14441]) ).
fof(f14480,definition,
! [X0] :
( sQ180_spl
<=> ( ~ c_Infinite__Set_Oatmost__one(c_IntDef_ONats,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f14483,plain,
( ~ sQ173_spl
| sQ98_spl
| sQ180_spl ),
inference(split_clause,[status(thm)],[f14472,f14480,f11093,f14366]) ).
fof(f14484,definition,
! [X1] :
( sQ181_spl
<=> X1 = c_0 ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f14485,plain,
! [X0] :
( ~ sQ181_spl
| X0 = c_0 ),
inference(component_clause,[status(thm)],[f14484]) ).
fof(f14488,plain,
( ~ sQ177_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f8694,f14448]) ).
fof(f14535,plain,
~ sQ177_spl,
inference(contradiction_clause,[status(thm)],[f14488]) ).
fof(f14574,plain,
! [X0,X1] :
( c_in(c_Message_Oparts(X1),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6462,f4317]) ).
fof(f14840,definition,
! [X0] :
( sQ182_spl
<=> ~ c_in(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f14841,plain,
! [X0] :
( ~ sQ182_spl
| ~ c_in(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(component_clause,[status(thm)],[f14840]) ).
fof(f14920,plain,
! [X0] :
( ~ class_Orderings_Oorder(tc_IntDef_Oint)
| ~ c_lessequals(c_plus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f4387,f5626]) ).
fof(f14921,definition,
! [X0] :
( sQ183_spl
<=> ~ c_lessequals(c_plus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f14924,plain,
( ~ sQ171_spl
| sQ183_spl ),
inference(split_clause,[status(thm)],[f14920,f14921,f14355]) ).
fof(f14925,plain,
( sQ171_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14357,f3131]) ).
fof(f14926,plain,
sQ171_spl,
inference(contradiction_clause,[status(thm)],[f14925]) ).
fof(f15518,plain,
! [X0] :
( ~ class_Orderings_Oorder(tc_IntDef_Oint)
| c_less(c_minus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f4388,f3030]) ).
fof(f15519,definition,
! [X0] :
( sQ184_spl
<=> c_less(c_minus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f15520,plain,
! [X0] :
( ~ sQ184_spl
| c_less(c_minus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
inference(component_clause,[status(thm)],[f15519]) ).
fof(f15522,plain,
( ~ sQ171_spl
| sQ184_spl ),
inference(split_clause,[status(thm)],[f15518,f15519,f14355]) ).
fof(f16993,plain,
! [X0] :
( c_lessequals(c_0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(tc_nat) ),
inference(resolution,[status(thm)],[f4436,f3025]) ).
fof(f16994,definition,
! [X0] :
( sQ185_spl
<=> c_lessequals(c_0,X0,tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition]) ).
fof(f16995,plain,
! [X0] :
( ~ sQ185_spl
| c_lessequals(c_0,X0,tc_IntDef_Oint) ),
inference(component_clause,[status(thm)],[f16994]) ).
fof(f16997,plain,
( sQ185_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f16993,f10606,f16994]) ).
fof(f16998,plain,
! [X0,X1] :
( c_lessequals(c_0,X1,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_0,X1,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(resolution,[status(thm)],[f4437,f4436]) ).
fof(f17001,definition,
! [X1] :
( sQ186_spl
<=> ( c_lessequals(c_0,X1,tc_IntDef_Oint)
| ~ c_lessequals(c_0,X1,tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition]) ).
fof(f17004,plain,
( sQ186_spl
| sQ172_spl ),
inference(split_clause,[status(thm)],[f16998,f14360,f17001]) ).
fof(f17006,plain,
( ~ sQ172_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f3160,f17007]) ).
fof(f17007,plain,
! [X0] :
( ~ sQ172_spl
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f14361]) ).
fof(f17008,plain,
~ sQ172_spl,
inference(contradiction_clause,[status(thm)],[f17006]) ).
fof(f17030,definition,
! [X0] :
( sQ187_spl
<=> c_lessequals(X0,X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f17050,plain,
! [X0] :
( ~ class_Orderings_Oorder(tc_IntDef_Oint)
| ~ c_less(X0,X0,tc_nat) ),
inference(resolution,[status(thm)],[f4481,f5626]) ).
fof(f17051,plain,
! [X0] :
( c_less(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ c_less(c_1,X0,tc_nat) ),
inference(paramodulation,[status(thm)],[f4406,f4481]) ).
fof(f17055,definition,
! [X0] :
( sQ188_spl
<=> ~ c_less(X0,X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ188_spl])],[split_symbol_definition]) ).
fof(f17058,plain,
( ~ sQ171_spl
| sQ188_spl ),
inference(split_clause,[status(thm)],[f17050,f17055,f14355]) ).
fof(f17075,plain,
! [X0] :
( c_less(c_0,c_0,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X0),c_0,tc_nat) ),
inference(paramodulation,[status(thm)],[f4421,f4483]) ).
fof(f17077,definition,
! [X0] :
( sQ189_spl
<=> ~ c_less(c_IntDef_Onat(X0),c_0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f17080,definition,
( sQ190_spl
<=> c_less(c_0,c_0,tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f17083,plain,
( sQ190_spl
| sQ189_spl ),
inference(split_clause,[status(thm)],[f17075,f17077,f17080]) ).
fof(f17084,definition,
! [X0] :
( sQ191_spl
<=> ~ c_less(c_IntDef_Onat(X0),c_1,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition]) ).
fof(f17085,plain,
! [X0] :
( ~ sQ191_spl
| ~ c_less(c_IntDef_Onat(X0),c_1,tc_nat) ),
inference(component_clause,[status(thm)],[f17084]) ).
fof(f17087,definition,
( sQ192_spl
<=> c_less(c_0,c_1,tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ192_spl])],[split_symbol_definition]) ).
fof(f17089,plain,
( sQ192_spl
| ~ c_less(c_0,c_1,tc_IntDef_Oint) ),
inference(component_clause,[status(thm)],[f17087]) ).
fof(f17117,plain,
! [X0] :
( ~ class_Orderings_Oorder(tc_nat)
| ~ c_less(c_0,X0,tc_IntDef_Oint)
| ~ c_less(X0,X0,tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f4485,f5626]) ).
fof(f17122,plain,
! [X0] :
( c_less(c_IntDef_Onat(X0),c_0,tc_nat)
| ~ c_less(c_0,c_0,tc_IntDef_Oint)
| ~ c_less(X0,c_0,tc_IntDef_Oint) ),
inference(paramodulation,[status(thm)],[f4421,f4485]) ).
fof(f17123,plain,
! [X0] :
( c_less(c_IntDef_Onat(X0),c_1,tc_nat)
| ~ c_less(c_0,c_1,tc_IntDef_Oint)
| ~ c_less(X0,c_1,tc_IntDef_Oint) ),
inference(paramodulation,[status(thm)],[f6579,f4485]) ).
fof(f17124,definition,
! [X0] :
( sQ193_spl
<=> ( ~ c_less(c_0,X0,tc_IntDef_Oint)
| ~ c_less(X0,X0,tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f17127,plain,
( ~ sQ50_spl
| sQ193_spl ),
inference(split_clause,[status(thm)],[f17117,f17124,f10475]) ).
fof(f17129,definition,
! [X0] :
( sQ194_spl
<=> ( c_less(c_IntDef_Onat(X0),c_0,tc_nat)
| ~ c_less(X0,c_0,tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ194_spl])],[split_symbol_definition]) ).
fof(f17130,plain,
! [X0] :
( ~ sQ194_spl
| c_less(c_IntDef_Onat(X0),c_0,tc_nat)
| ~ c_less(X0,c_0,tc_IntDef_Oint) ),
inference(component_clause,[status(thm)],[f17129]) ).
fof(f17132,plain,
( ~ sQ190_spl
| sQ194_spl ),
inference(split_clause,[status(thm)],[f17122,f17129,f17080]) ).
fof(f17133,definition,
! [X0] :
( sQ195_spl
<=> ( c_less(c_IntDef_Onat(X0),c_1,tc_nat)
| ~ c_less(X0,c_1,tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition]) ).
fof(f17134,plain,
! [X0] :
( ~ sQ195_spl
| c_less(c_IntDef_Onat(X0),c_1,tc_nat)
| ~ c_less(X0,c_1,tc_IntDef_Oint) ),
inference(component_clause,[status(thm)],[f17133]) ).
fof(f17136,plain,
( ~ sQ192_spl
| sQ195_spl ),
inference(split_clause,[status(thm)],[f17123,f17133,f17087]) ).
fof(f17137,plain,
( sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10477,f3199]) ).
fof(f17138,plain,
sQ50_spl,
inference(contradiction_clause,[status(thm)],[f17137]) ).
fof(f17139,plain,
( ~ sQ195_spl
| ~ sQ191_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f6560,f17142]) ).
fof(f17142,plain,
! [X0] :
( ~ sQ195_spl
| ~ sQ191_spl
| ~ c_less(X0,c_1,tc_IntDef_Oint) ),
inference(forward_subsumption_resolution,[status(thm)],[f17134,f17085]) ).
fof(f17143,plain,
( ~ sQ194_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f8371,f17145]) ).
fof(f17145,plain,
! [X0] :
( ~ sQ194_spl
| ~ c_less(X0,c_0,tc_IntDef_Oint) ),
inference(forward_subsumption_resolution,[status(thm)],[f17130,f5376]) ).
fof(f17146,plain,
( ~ sQ195_spl
| ~ sQ191_spl ),
inference(contradiction_clause,[status(thm)],[f17139]) ).
fof(f17147,plain,
~ sQ194_spl,
inference(contradiction_clause,[status(thm)],[f17143]) ).
fof(f17148,plain,
( sQ192_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17089,f6560]) ).
fof(f17149,plain,
sQ192_spl,
inference(contradiction_clause,[status(thm)],[f17148]) ).
fof(f17259,plain,
( ~ sQ182_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14841,f8496]) ).
fof(f17260,plain,
( ~ sQ182_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f17259]) ).
fof(f17261,plain,
( ~ sQ98_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f4405,f11094]) ).
fof(f17267,plain,
~ sQ98_spl,
inference(contradiction_clause,[status(thm)],[f17261]) ).
fof(f17414,plain,
( ~ sQ185_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f4431,f16995]) ).
fof(f17426,plain,
~ sQ185_spl,
inference(contradiction_clause,[status(thm)],[f17414]) ).
fof(f17430,definition,
! [X0] :
( sQ203_spl
<=> c_lessequals(c_0,X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f17434,plain,
( sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10116,f3214]) ).
fof(f17435,plain,
sQ47_spl,
inference(contradiction_clause,[status(thm)],[f17434]) ).
fof(f17439,definition,
( sQ204_spl
<=> c_lessequals(c_0,c_0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f17783,plain,
! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X0,c_NatArith_Oof__nat(X1,tc_nat),tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat) ),
inference(paramodulation,[status(thm)],[f4322,f4990]) ).
fof(f17784,plain,
! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_NatArith_Oof__nat(X0,tc_nat),X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat) ),
inference(paramodulation,[status(thm)],[f4322,f4990]) ).
fof(f17794,definition,
! [X0,X1] :
( sQ207_spl
<=> ( c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X0,c_NatArith_Oof__nat(X1,tc_nat),tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f17797,plain,
( sQ207_spl
| ~ sQ47_spl ),
inference(split_clause,[status(thm)],[f17783,f10114,f17794]) ).
fof(f17798,definition,
! [X0,X1] :
( sQ208_spl
<=> ( c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_NatArith_Oof__nat(X0,tc_nat),X1,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ208_spl])],[split_symbol_definition]) ).
fof(f17801,plain,
( sQ208_spl
| ~ sQ47_spl ),
inference(split_clause,[status(thm)],[f17784,f10114,f17798]) ).
fof(f17802,plain,
! [X0] :
( ~ c_less(X0,c_0,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat) ),
inference(paramodulation,[status(thm)],[f4322,f4993]) ).
fof(f17803,plain,
( sQ34_spl
| ~ sQ47_spl ),
inference(split_clause,[status(thm)],[f17802,f10114,f8980]) ).
fof(f17820,plain,
! [X0] :
( c_less(c_1,c_Suc(X0),tc_nat)
| ~ c_less(c_0,X0,tc_nat) ),
inference(paramodulation,[status(thm)],[f5272,f5278]) ).
fof(f17841,plain,
( c_lessequals(c_0,c_0,tc_IntDef_Oint)
| ~ class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
inference(paramodulation,[status(thm)],[f10073,f5484]) ).
fof(f17842,plain,
( sQ168_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f17841,f10492,f14342]) ).
fof(f17843,plain,
( sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10494,f3152]) ).
fof(f17844,plain,
sQ52_spl,
inference(contradiction_clause,[status(thm)],[f17843]) ).
fof(f17845,plain,
( c_lessequals(c_0,c_1,tc_IntDef_Oint)
| ~ class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
inference(paramodulation,[status(thm)],[f10074,f5484]) ).
fof(f17846,definition,
( sQ209_spl
<=> c_lessequals(c_0,c_1,tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f17849,plain,
( sQ209_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f17845,f10492,f17846]) ).
fof(f17890,plain,
( ~ c_less(c_1,c_0,tc_IntDef_Oint)
| ~ class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
inference(paramodulation,[status(thm)],[f10074,f5493]) ).
fof(f17892,definition,
( sQ210_spl
<=> c_less(c_1,c_0,tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f17895,plain,
( ~ sQ210_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f17890,f10492,f17892]) ).
fof(f17900,definition,
( sQ211_spl
<=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f17904,definition,
! [X0] :
( sQ212_spl
<=> ( c_lessequals(X0,c_0,tc_nat)
| ~ c_lessequals(X0,c_0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ212_spl])],[split_symbol_definition]) ).
fof(f17973,definition,
! [X0] :
( sQ218_spl
<=> ( c_less(X0,c_0,tc_nat)
| ~ c_less(X0,c_0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f18061,plain,
( ~ sQ33_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f3028,f8977]) ).
fof(f18075,plain,
~ sQ33_spl,
inference(contradiction_clause,[status(thm)],[f18061]) ).
fof(f18164,definition,
( sQ225_spl
<=> class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f18166,plain,
( sQ225_spl
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
inference(component_clause,[status(thm)],[f18164]) ).
fof(f18219,plain,
! [X0] :
( ~ sQ173_spl
| X0 = c_emptyset
| c_IntDef_ONats != c_emptyset ),
inference(paramodulation,[status(thm)],[f14461,f6154]) ).
fof(f18222,definition,
( sQ226_spl
<=> c_IntDef_ONats = c_emptyset ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f18227,plain,
( ~ sQ173_spl
| sQ80_spl
| ~ sQ226_spl ),
inference(split_clause,[status(thm)],[f18219,f18222,f10741,f14366]) ).
fof(f18229,plain,
( ~ sQ173_spl
| ~ sQ80_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f14397,f10742]) ).
fof(f18242,plain,
( ~ sQ173_spl
| ~ sQ80_spl ),
inference(contradiction_clause,[status(thm)],[f18229]) ).
fof(f18587,plain,
! [X0] :
( c_lessequals(X0,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
inference(paramodulation,[status(thm)],[f6553,f5570]) ).
fof(f18590,plain,
! [X0] :
( c_lessequals(c_0,X0,tc_IntDef_Oint)
| ~ c_lessequals(c_uminus(X0,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
inference(paramodulation,[status(thm)],[f6553,f5570]) ).
fof(f18592,definition,
! [X0] :
( sQ227_spl
<=> ( c_lessequals(X0,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f18595,plain,
( sQ227_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f18587,f18164,f18592]) ).
fof(f18596,definition,
! [X0] :
( sQ228_spl
<=> ( c_lessequals(c_0,X0,tc_IntDef_Oint)
| ~ c_lessequals(c_uminus(X0,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f18599,plain,
( sQ228_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f18590,f18164,f18596]) ).
fof(f18600,plain,
( sQ225_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f18166,f3148]) ).
fof(f18601,plain,
sQ225_spl,
inference(contradiction_clause,[status(thm)],[f18600]) ).
fof(f18607,plain,
! [X0] :
( c_lessequals(c_0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(X0,c_0,tc_IntDef_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
inference(paramodulation,[status(thm)],[f6553,f5571]) ).
fof(f18610,plain,
! [X0] :
( c_lessequals(c_uminus(X0,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_0,X0,tc_IntDef_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
inference(paramodulation,[status(thm)],[f6553,f5571]) ).
fof(f18611,definition,
! [X0] :
( sQ229_spl
<=> ( c_lessequals(c_0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(X0,c_0,tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f18614,plain,
( sQ229_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f18607,f18164,f18611]) ).
fof(f18615,definition,
! [X0] :
( sQ230_spl
<=> ( c_lessequals(c_uminus(X0,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_0,X0,tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f18618,plain,
( sQ230_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f18610,f18164,f18615]) ).
fof(f18636,plain,
( ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_NatArith_Oof__nat(c_0,tc_nat) = c_0 ),
inference(resolution,[status(thm)],[f5304,f4988]) ).
fof(f18655,definition,
( sQ234_spl
<=> c_NatArith_Oof__nat(c_0,tc_nat) = c_0 ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f18658,plain,
( ~ sQ47_spl
| sQ234_spl ),
inference(split_clause,[status(thm)],[f18636,f18655,f10114]) ).
fof(f18675,plain,
! [X0] :
( ~ c_less(c_0,X0,tc_nat)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
inference(resolution,[status(thm)],[f5573,f5376]) ).
fof(f18680,plain,
( sQ33_spl
| ~ sQ211_spl ),
inference(split_clause,[status(thm)],[f18675,f17900,f8976]) ).
fof(f18713,plain,
! [X0] :
( c_less(X0,c_0,tc_IntDef_Oint)
| ~ c_less(c_0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
inference(paramodulation,[status(thm)],[f6553,f5574]) ).
fof(f18716,plain,
! [X0] :
( c_less(c_0,X0,tc_IntDef_Oint)
| ~ c_less(c_uminus(X0,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
inference(paramodulation,[status(thm)],[f6553,f5574]) ).
fof(f18717,definition,
! [X0] :
( sQ237_spl
<=> ( c_less(X0,c_0,tc_IntDef_Oint)
| ~ c_less(c_0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f18720,plain,
( sQ237_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f18713,f18164,f18717]) ).
fof(f18721,definition,
! [X0] :
( sQ238_spl
<=> ( c_less(c_0,X0,tc_IntDef_Oint)
| ~ c_less(c_uminus(X0,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f18724,plain,
( sQ238_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f18716,f18164,f18721]) ).
fof(f18732,plain,
! [X0] :
( c_less(c_0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(X0,c_0,tc_IntDef_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
inference(paramodulation,[status(thm)],[f6553,f5575]) ).
fof(f18735,plain,
! [X0] :
( c_less(c_uminus(X0,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_0,X0,tc_IntDef_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
inference(paramodulation,[status(thm)],[f6553,f5575]) ).
fof(f18737,definition,
! [X0] :
( sQ239_spl
<=> ( c_less(c_0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(X0,c_0,tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f18740,plain,
( sQ239_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f18732,f18164,f18737]) ).
fof(f18741,definition,
! [X0] :
( sQ240_spl
<=> ( c_less(c_uminus(X0,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_0,X0,tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f18744,plain,
( sQ240_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f18735,f18164,f18741]) ).
fof(f18806,plain,
! [X0] :
( ~ c_less(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint)
| ~ class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
inference(paramodulation,[status(thm)],[f4402,f5493]) ).
fof(f18807,plain,
! [X0] :
( c_lessequals(c_0,c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
inference(paramodulation,[status(thm)],[f4402,f5484]) ).
fof(f18810,definition,
! [X0] :
( sQ245_spl
<=> ~ c_less(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f18813,plain,
( sQ245_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f18806,f10492,f18810]) ).
fof(f18814,definition,
! [X0] :
( sQ246_spl
<=> c_lessequals(c_0,c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ246_spl])],[split_symbol_definition]) ).
fof(f18817,plain,
( sQ246_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f18807,f10492,f18814]) ).
fof(f18892,plain,
! [X0] :
( c_less(c_IntDef_Onat(X0),c_0,tc_nat)
| ~ c_less(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(X0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(paramodulation,[status(thm)],[f10958,f4485]) ).
fof(f18896,definition,
! [X0] :
( sQ249_spl
<=> ( c_less(c_IntDef_Onat(X0),c_0,tc_nat)
| ~ c_less(X0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f18897,plain,
! [X0] :
( ~ sQ249_spl
| c_less(c_IntDef_Onat(X0),c_0,tc_nat)
| ~ c_less(X0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(component_clause,[status(thm)],[f18896]) ).
fof(f18899,definition,
( sQ250_spl
<=> c_less(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f18902,plain,
( ~ sQ250_spl
| sQ249_spl ),
inference(split_clause,[status(thm)],[f18892,f18896,f18899]) ).
fof(f18903,plain,
! [X0] :
( ~ sQ249_spl
| ~ c_less(X0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_subsumption_resolution,[status(thm)],[f18897,f5376]) ).
fof(f18915,plain,
! [X0] :
( ~ sQ173_spl
| c_IntDef_ONats = c_IntDef_ONats
| X0 != c_IntDef_ONats ),
inference(paramodulation,[status(thm)],[f14417,f14460]) ).
fof(f18920,definition,
! [X0] :
( sQ251_spl
<=> X0 != c_IntDef_ONats ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f18921,plain,
! [X0] :
( ~ sQ251_spl
| X0 != c_IntDef_ONats ),
inference(component_clause,[status(thm)],[f18920]) ).
fof(f18923,definition,
( sQ252_spl
<=> c_IntDef_ONats = c_IntDef_ONats ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f18926,plain,
( ~ sQ173_spl
| sQ252_spl
| sQ251_spl ),
inference(split_clause,[status(thm)],[f18915,f18920,f18923,f14366]) ).
fof(f18927,definition,
! [X0] :
( sQ253_spl
<=> X0 = c_IntDef_ONats ),
introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition]) ).
fof(f18928,plain,
! [X0] :
( ~ sQ253_spl
| X0 = c_IntDef_ONats ),
inference(component_clause,[status(thm)],[f18927]) ).
fof(f18931,plain,
( ~ sQ251_spl
| $false ),
inference(destructive_equality_resolution,[status(thm)],[f18921]) ).
fof(f18932,plain,
~ sQ251_spl,
inference(contradiction_clause,[status(thm)],[f18931]) ).
fof(f18957,plain,
! [X0,X1,X2] :
( ~ c_lessequals(c_Orderings_Omax(X0,X2,tc_IntDef_Oint),X1,tc_IntDef_Oint)
| c_less(X0,c_plus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ class_Orderings_Olinorder(tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f5598,f4387]) ).
fof(f18958,plain,
! [X0,X1] :
( c_less(X0,c_Suc(c_Orderings_Omax(X0,X1,tc_nat)),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f5598,f3026]) ).
fof(f18959,plain,
! [X0,X1] :
( c_less(c_0,X1,tc_nat)
| ~ c_less(X0,X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(paramodulation,[status(thm)],[f5312,f5598]) ).
fof(f18960,plain,
! [X0,X1] :
( c_less(X0,X1,tc_nat)
| ~ c_less(X0,X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(paramodulation,[status(thm)],[f5313,f5598]) ).
fof(f18961,definition,
( sQ254_spl
<=> class_Orderings_Olinorder(tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f18963,plain,
( sQ254_spl
| ~ class_Orderings_Olinorder(tc_IntDef_Oint) ),
inference(component_clause,[status(thm)],[f18961]) ).
fof(f18964,definition,
! [X0,X1,X2] :
( sQ255_spl
<=> ( ~ c_lessequals(c_Orderings_Omax(X0,X2,tc_IntDef_Oint),X1,tc_IntDef_Oint)
| c_less(X0,c_plus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f18967,plain,
( sQ255_spl
| ~ sQ254_spl ),
inference(split_clause,[status(thm)],[f18957,f18961,f18964]) ).
fof(f18968,definition,
! [X0,X1] :
( sQ256_spl
<=> c_less(X0,c_Suc(c_Orderings_Omax(X0,X1,tc_nat)),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f18971,plain,
( sQ256_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f18958,f9098,f18968]) ).
fof(f18972,definition,
! [X0,X1] :
( sQ257_spl
<=> ( c_less(c_0,X1,tc_nat)
| ~ c_less(X0,X1,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f18975,plain,
( sQ257_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f18959,f9098,f18972]) ).
fof(f18976,definition,
! [X0,X1] :
( sQ258_spl
<=> ( c_less(X0,X1,tc_nat)
| ~ c_less(X0,X1,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ258_spl])],[split_symbol_definition]) ).
fof(f18979,plain,
( sQ258_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f18960,f9098,f18976]) ).
fof(f18980,plain,
( sQ254_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f18963,f3135]) ).
fof(f18981,plain,
sQ254_spl,
inference(contradiction_clause,[status(thm)],[f18980]) ).
fof(f18982,plain,
! [X0,X1,X2] :
( ~ c_lessequals(c_Orderings_Omax(X2,X0,tc_IntDef_Oint),X1,tc_IntDef_Oint)
| c_less(X0,c_plus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ class_Orderings_Olinorder(tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f5600,f4387]) ).
fof(f18983,plain,
! [X0,X1] :
( c_less(X0,c_Suc(c_Orderings_Omax(X1,X0,tc_nat)),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f5600,f3026]) ).
fof(f18986,definition,
! [X0,X1,X2] :
( sQ259_spl
<=> ( ~ c_lessequals(c_Orderings_Omax(X2,X0,tc_IntDef_Oint),X1,tc_IntDef_Oint)
| c_less(X0,c_plus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f18989,plain,
( sQ259_spl
| ~ sQ254_spl ),
inference(split_clause,[status(thm)],[f18982,f18961,f18986]) ).
fof(f18990,definition,
! [X0,X1] :
( sQ260_spl
<=> c_less(X0,c_Suc(c_Orderings_Omax(X1,X0,tc_nat)),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f18993,plain,
( sQ260_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f18983,f9098,f18990]) ).
fof(f19015,definition,
( sQ261_spl
<=> c_lessequals(c_1,c_1,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f19023,plain,
! [X0,X1,X2] :
( ~ c_less(c_0,c_Orderings_Omin(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X0,c_Orderings_Omin(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint),X1,tc_IntDef_Oint)
| ~ class_Orderings_Olinorder(tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f5603,f4519]) ).
fof(f19024,plain,
! [X0] :
( c_less(X0,c_0,tc_nat)
| ~ c_less(X0,c_0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(paramodulation,[status(thm)],[f5315,f5603]) ).
fof(f19025,plain,
! [X0,X1] :
( c_less(X0,X1,tc_nat)
| ~ c_less(X0,c_0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(paramodulation,[status(thm)],[f5316,f5603]) ).
fof(f19026,definition,
! [X0,X1,X2] :
( sQ262_spl
<=> ( ~ c_less(c_0,c_Orderings_Omin(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X0,c_Orderings_Omin(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint),X1,tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f19029,plain,
( sQ262_spl
| ~ sQ254_spl ),
inference(split_clause,[status(thm)],[f19023,f18961,f19026]) ).
fof(f19030,plain,
( sQ218_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19024,f9098,f17973]) ).
fof(f19031,definition,
! [X0,X1] :
( sQ263_spl
<=> ( c_less(X0,X1,tc_nat)
| ~ c_less(X0,c_0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ263_spl])],[split_symbol_definition]) ).
fof(f19034,plain,
( sQ263_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19025,f9098,f19031]) ).
fof(f19041,plain,
! [X0,X1] :
( c_less(c_0,X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| c_Orderings_Omin(X0,X1,tc_nat) = c_0 ),
inference(resolution,[status(thm)],[f5374,f5603]) ).
fof(f19051,definition,
! [X0,X1] :
( sQ265_spl
<=> ( c_less(c_0,X0,tc_nat)
| c_Orderings_Omin(X0,X1,tc_nat) = c_0 ) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f19054,plain,
( ~ sQ43_spl
| sQ265_spl ),
inference(split_clause,[status(thm)],[f19041,f19051,f9098]) ).
fof(f19156,plain,
! [X0,X1,X2] :
( ~ c_less(c_0,c_Orderings_Omin(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X0,c_Orderings_Omin(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint),X2,tc_IntDef_Oint)
| ~ class_Orderings_Olinorder(tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f5605,f4519]) ).
fof(f19157,plain,
! [X0,X1] :
( c_Orderings_Omin(X1,X0,tc_nat) = c_0
| c_less(c_0,X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f5605,f5374]) ).
fof(f19160,definition,
! [X0,X1,X2] :
( sQ266_spl
<=> ( ~ c_less(c_0,c_Orderings_Omin(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X0,c_Orderings_Omin(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint),X2,tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f19163,plain,
( sQ266_spl
| ~ sQ254_spl ),
inference(split_clause,[status(thm)],[f19156,f18961,f19160]) ).
fof(f19164,definition,
! [X0,X1] :
( sQ267_spl
<=> ( c_Orderings_Omin(X1,X0,tc_nat) = c_0
| c_less(c_0,X0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ267_spl])],[split_symbol_definition]) ).
fof(f19167,plain,
( sQ267_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19157,f9098,f19164]) ).
fof(f19171,plain,
! [X0,X1,X2] :
( c_lessequals(c_minus(c_Orderings_Omin(X0,X1,tc_nat),X2,tc_nat),X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f5608,f5302]) ).
fof(f19172,plain,
! [X0,X1,X2] :
( c_lessequals(c_div(c_Orderings_Omin(X0,X1,tc_nat),X2,tc_nat),X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f5608,f4204]) ).
fof(f19173,plain,
! [X0] :
( c_lessequals(c_0,X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f5608,f3025]) ).
fof(f19174,plain,
! [X0,X1] :
( c_lessequals(c_Orderings_Omin(X0,X1,tc_nat),X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f5608,f8954]) ).
fof(f19176,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(c_Orderings_Omin(X1,X2,X0),X1,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(resolution,[status(thm)],[f5608,f3030]) ).
fof(f19177,plain,
! [X0] :
( c_lessequals(X0,c_0,tc_nat)
| ~ c_lessequals(X0,c_0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(paramodulation,[status(thm)],[f5315,f5608]) ).
fof(f19178,plain,
! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X0,c_0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(paramodulation,[status(thm)],[f5316,f5608]) ).
fof(f19179,definition,
! [X0,X1,X2] :
( sQ268_spl
<=> c_lessequals(c_minus(c_Orderings_Omin(X0,X1,tc_nat),X2,tc_nat),X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ268_spl])],[split_symbol_definition]) ).
fof(f19182,plain,
( sQ268_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19171,f9098,f19179]) ).
fof(f19183,definition,
! [X0,X1,X2] :
( sQ269_spl
<=> c_lessequals(c_div(c_Orderings_Omin(X0,X1,tc_nat),X2,tc_nat),X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f19186,plain,
( sQ269_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19172,f9098,f19183]) ).
fof(f19187,plain,
( sQ203_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19173,f9098,f17430]) ).
fof(f19188,definition,
! [X0,X1] :
( sQ270_spl
<=> c_lessequals(c_Orderings_Omin(X0,X1,tc_nat),X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f19189,plain,
! [X0,X1] :
( ~ sQ270_spl
| c_lessequals(c_Orderings_Omin(X0,X1,tc_nat),X0,tc_nat) ),
inference(component_clause,[status(thm)],[f19188]) ).
fof(f19191,plain,
( sQ270_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19174,f9098,f19188]) ).
fof(f19192,plain,
! [X0,X1,X2] :
( c_lessequals(c_Orderings_Omin(X1,X2,X0),X1,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f19176,f3433]) ).
fof(f19193,plain,
( sQ212_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19177,f9098,f17904]) ).
fof(f19194,definition,
! [X0,X1] :
( sQ271_spl
<=> ( c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X0,c_0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f19197,plain,
( sQ271_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19178,f9098,f19194]) ).
fof(f19275,plain,
! [X0,X1,X2] :
( c_lessequals(c_minus(c_Orderings_Omin(X0,X1,tc_nat),X2,tc_nat),X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f5610,f5302]) ).
fof(f19276,plain,
! [X0,X1,X2] :
( c_lessequals(c_div(c_Orderings_Omin(X0,X1,tc_nat),X2,tc_nat),X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f5610,f4204]) ).
fof(f19278,plain,
! [X0,X1] :
( c_lessequals(c_Orderings_Omin(X0,X1,tc_nat),X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f5610,f8954]) ).
fof(f19280,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(c_Orderings_Omin(X1,X2,X0),X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(resolution,[status(thm)],[f5610,f3030]) ).
fof(f19283,definition,
! [X0,X1,X2] :
( sQ272_spl
<=> c_lessequals(c_minus(c_Orderings_Omin(X0,X1,tc_nat),X2,tc_nat),X1,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ272_spl])],[split_symbol_definition]) ).
fof(f19286,plain,
( sQ272_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19275,f9098,f19283]) ).
fof(f19287,definition,
! [X0,X1,X2] :
( sQ273_spl
<=> c_lessequals(c_div(c_Orderings_Omin(X0,X1,tc_nat),X2,tc_nat),X1,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ273_spl])],[split_symbol_definition]) ).
fof(f19290,plain,
( sQ273_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19276,f9098,f19287]) ).
fof(f19292,definition,
! [X0,X1] :
( sQ274_spl
<=> c_lessequals(c_Orderings_Omin(X0,X1,tc_nat),X1,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ274_spl])],[split_symbol_definition]) ).
fof(f19293,plain,
! [X0,X1] :
( ~ sQ274_spl
| c_lessequals(c_Orderings_Omin(X0,X1,tc_nat),X1,tc_nat) ),
inference(component_clause,[status(thm)],[f19292]) ).
fof(f19295,plain,
( sQ274_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19278,f9098,f19292]) ).
fof(f19296,plain,
! [X0,X1,X2] :
( c_lessequals(c_Orderings_Omin(X1,X2,X0),X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f19280,f3433]) ).
fof(f19300,plain,
! [X0,X1,X2] :
( ~ c_less(c_Orderings_Omax(X0,X2,tc_IntDef_Oint),X1,tc_IntDef_Oint)
| c_lessequals(X0,c_minus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ class_Orderings_Olinorder(tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f5617,f4389]) ).
fof(f19301,plain,
! [X0,X1] :
( c_lessequals(X0,c_Suc(c_Orderings_Omax(X0,X1,tc_nat)),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f5617,f13873]) ).
fof(f19302,plain,
! [X0,X1,X2] :
( c_lessequals(X0,c_plus(X1,c_Orderings_Omax(X0,X2,tc_nat),tc_nat),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f5617,f6524]) ).
fof(f19303,plain,
! [X0,X1,X2] :
( c_lessequals(X0,c_plus(c_Orderings_Omax(X0,X1,tc_nat),X2,tc_nat),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f5617,f6523]) ).
fof(f19304,plain,
! [X0,X1] :
( c_lessequals(X0,c_Orderings_Omax(X0,X1,tc_nat),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f5617,f8954]) ).
fof(f19306,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,c_Orderings_Omax(X1,X2,X0),X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(resolution,[status(thm)],[f5617,f3030]) ).
fof(f19307,plain,
! [X0,X1] :
( c_lessequals(c_0,X1,tc_nat)
| ~ c_lessequals(X0,X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(paramodulation,[status(thm)],[f5312,f5617]) ).
fof(f19308,plain,
! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X0,X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(paramodulation,[status(thm)],[f5313,f5617]) ).
fof(f19309,definition,
! [X0,X1,X2] :
( sQ275_spl
<=> ( ~ c_less(c_Orderings_Omax(X0,X2,tc_IntDef_Oint),X1,tc_IntDef_Oint)
| c_lessequals(X0,c_minus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ275_spl])],[split_symbol_definition]) ).
fof(f19312,plain,
( sQ275_spl
| ~ sQ254_spl ),
inference(split_clause,[status(thm)],[f19300,f18961,f19309]) ).
fof(f19313,definition,
! [X0,X1] :
( sQ276_spl
<=> c_lessequals(X0,c_Suc(c_Orderings_Omax(X0,X1,tc_nat)),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ276_spl])],[split_symbol_definition]) ).
fof(f19316,plain,
( sQ276_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19301,f9098,f19313]) ).
fof(f19317,definition,
! [X0,X1,X2] :
( sQ277_spl
<=> c_lessequals(X0,c_plus(X1,c_Orderings_Omax(X0,X2,tc_nat),tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ277_spl])],[split_symbol_definition]) ).
fof(f19320,plain,
( sQ277_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19302,f9098,f19317]) ).
fof(f19321,definition,
! [X0,X1,X2] :
( sQ278_spl
<=> c_lessequals(X0,c_plus(c_Orderings_Omax(X0,X1,tc_nat),X2,tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ278_spl])],[split_symbol_definition]) ).
fof(f19324,plain,
( sQ278_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19303,f9098,f19321]) ).
fof(f19325,definition,
! [X0,X1] :
( sQ279_spl
<=> c_lessequals(X0,c_Orderings_Omax(X0,X1,tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ279_spl])],[split_symbol_definition]) ).
fof(f19326,plain,
! [X0,X1] :
( ~ sQ279_spl
| c_lessequals(X0,c_Orderings_Omax(X0,X1,tc_nat),tc_nat) ),
inference(component_clause,[status(thm)],[f19325]) ).
fof(f19328,plain,
( sQ279_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19304,f9098,f19325]) ).
fof(f19329,plain,
! [X0,X1,X2] :
( c_lessequals(X1,c_Orderings_Omax(X1,X2,X0),X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f19306,f3433]) ).
fof(f19330,definition,
! [X0,X1] :
( sQ280_spl
<=> ( c_lessequals(c_0,X1,tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ280_spl])],[split_symbol_definition]) ).
fof(f19333,plain,
( sQ280_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19307,f9098,f19330]) ).
fof(f19334,definition,
! [X0,X1] :
( sQ281_spl
<=> ( c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ281_spl])],[split_symbol_definition]) ).
fof(f19337,plain,
( sQ281_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19308,f9098,f19334]) ).
fof(f19339,plain,
! [X0,X1,X2] :
( ~ c_less(c_Orderings_Omax(X2,X0,tc_IntDef_Oint),X1,tc_IntDef_Oint)
| c_lessequals(X0,c_minus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ class_Orderings_Olinorder(tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f5619,f4389]) ).
fof(f19340,plain,
! [X0,X1] :
( c_lessequals(X0,c_Suc(c_Orderings_Omax(X1,X0,tc_nat)),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f5619,f13873]) ).
fof(f19341,plain,
! [X0,X1,X2] :
( c_lessequals(X0,c_plus(X1,c_Orderings_Omax(X2,X0,tc_nat),tc_nat),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f5619,f6524]) ).
fof(f19342,plain,
! [X0,X1,X2] :
( c_lessequals(X0,c_plus(c_Orderings_Omax(X1,X0,tc_nat),X2,tc_nat),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f5619,f6523]) ).
fof(f19343,plain,
! [X0,X1] :
( c_lessequals(X0,c_Orderings_Omax(X1,X0,tc_nat),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f5619,f8954]) ).
fof(f19345,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,c_Orderings_Omax(X2,X1,X0),X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(resolution,[status(thm)],[f5619,f3030]) ).
fof(f19348,definition,
! [X0,X1,X2] :
( sQ282_spl
<=> ( ~ c_less(c_Orderings_Omax(X2,X0,tc_IntDef_Oint),X1,tc_IntDef_Oint)
| c_lessequals(X0,c_minus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ282_spl])],[split_symbol_definition]) ).
fof(f19351,plain,
( sQ282_spl
| ~ sQ254_spl ),
inference(split_clause,[status(thm)],[f19339,f18961,f19348]) ).
fof(f19352,definition,
! [X0,X1] :
( sQ283_spl
<=> c_lessequals(X0,c_Suc(c_Orderings_Omax(X1,X0,tc_nat)),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ283_spl])],[split_symbol_definition]) ).
fof(f19355,plain,
( sQ283_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19340,f9098,f19352]) ).
fof(f19356,definition,
! [X0,X1,X2] :
( sQ284_spl
<=> c_lessequals(X0,c_plus(X1,c_Orderings_Omax(X2,X0,tc_nat),tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ284_spl])],[split_symbol_definition]) ).
fof(f19359,plain,
( sQ284_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19341,f9098,f19356]) ).
fof(f19360,definition,
! [X0,X1,X2] :
( sQ285_spl
<=> c_lessequals(X0,c_plus(c_Orderings_Omax(X1,X0,tc_nat),X2,tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ285_spl])],[split_symbol_definition]) ).
fof(f19363,plain,
( sQ285_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19342,f9098,f19360]) ).
fof(f19364,definition,
! [X0,X1] :
( sQ286_spl
<=> c_lessequals(X0,c_Orderings_Omax(X1,X0,tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f19365,plain,
! [X0,X1] :
( ~ sQ286_spl
| c_lessequals(X0,c_Orderings_Omax(X1,X0,tc_nat),tc_nat) ),
inference(component_clause,[status(thm)],[f19364]) ).
fof(f19367,plain,
( sQ286_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19343,f9098,f19364]) ).
fof(f19368,plain,
! [X0,X1,X2] :
( c_lessequals(X1,c_Orderings_Omax(X2,X1,X0),X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f19345,f3433]) ).
fof(f19395,plain,
( ~ c_Parity_Oeven(c_1,tc_nat)
| ~ c_Parity_Oeven(c_0,tc_nat) ),
inference(paramodulation,[status(thm)],[f5272,f5637]) ).
fof(f19396,definition,
( sQ287_spl
<=> c_Parity_Oeven(c_0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ287_spl])],[split_symbol_definition]) ).
fof(f19398,plain,
( sQ287_spl
| ~ c_Parity_Oeven(c_0,tc_nat) ),
inference(component_clause,[status(thm)],[f19396]) ).
fof(f19399,definition,
( sQ288_spl
<=> c_Parity_Oeven(c_1,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ288_spl])],[split_symbol_definition]) ).
fof(f19402,plain,
( ~ sQ288_spl
| ~ sQ287_spl ),
inference(split_clause,[status(thm)],[f19395,f19396,f19399]) ).
fof(f19403,plain,
( sQ287_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f19398,f5656]) ).
fof(f19404,plain,
sQ287_spl,
inference(contradiction_clause,[status(thm)],[f19403]) ).
fof(f19543,plain,
! [X0] :
( ~ sQ249_spl
| ~ c_less(c_1,X0,tc_IntDef_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f18903,f5575]) ).
fof(f19545,definition,
! [X0] :
( sQ290_spl
<=> ~ c_less(c_1,X0,tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ290_spl])],[split_symbol_definition]) ).
fof(f19546,plain,
! [X0] :
( ~ sQ290_spl
| ~ c_less(c_1,X0,tc_IntDef_Oint) ),
inference(component_clause,[status(thm)],[f19545]) ).
fof(f19548,plain,
( ~ sQ249_spl
| sQ290_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f19543,f18164,f19545,f18896]) ).
fof(f19549,plain,
! [X0] :
( ~ sQ290_spl
| ~ c_less(c_1,X0,tc_nat) ),
inference(backward_subsumption_resolution,[status(thm)],[f17051,f19546]) ).
fof(f19551,plain,
! [X0] :
( ~ sQ290_spl
| ~ c_less(c_0,X0,tc_nat) ),
inference(backward_subsumption_resolution,[status(thm)],[f17820,f19549]) ).
fof(f19552,plain,
( ~ sQ290_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f19551,f8976,f19545]) ).
fof(f19553,plain,
! [X0,X1,X2] :
( ~ sQ270_spl
| c_lessequals(c_Orderings_Omin(c_Orderings_Omin(X0,X1,tc_nat),X2,tc_nat),X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f19189,f5610]) ).
fof(f19554,plain,
! [X0,X1,X2] :
( ~ sQ270_spl
| c_lessequals(c_Orderings_Omin(c_Orderings_Omin(X0,X1,tc_nat),X2,tc_nat),X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f19189,f5608]) ).
fof(f19558,definition,
! [X0,X1,X2] :
( sQ291_spl
<=> c_lessequals(c_Orderings_Omin(c_Orderings_Omin(X0,X1,tc_nat),X2,tc_nat),X1,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f19561,plain,
( ~ sQ270_spl
| sQ291_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19553,f9098,f19558,f19188]) ).
fof(f19562,definition,
! [X0,X1,X2] :
( sQ292_spl
<=> c_lessequals(c_Orderings_Omin(c_Orderings_Omin(X0,X1,tc_nat),X2,tc_nat),X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ292_spl])],[split_symbol_definition]) ).
fof(f19565,plain,
( ~ sQ270_spl
| sQ292_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19554,f9098,f19562,f19188]) ).
fof(f19566,plain,
! [X0,X1,X2] :
( ~ sQ274_spl
| c_lessequals(c_Orderings_Omin(X0,c_Orderings_Omin(X1,X2,tc_nat),tc_nat),X2,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f19293,f5610]) ).
fof(f19567,plain,
! [X0,X1,X2] :
( ~ sQ274_spl
| c_lessequals(c_Orderings_Omin(X0,c_Orderings_Omin(X1,X2,tc_nat),tc_nat),X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f19293,f5608]) ).
fof(f19571,definition,
! [X0,X1,X2] :
( sQ293_spl
<=> c_lessequals(c_Orderings_Omin(X0,c_Orderings_Omin(X1,X2,tc_nat),tc_nat),X2,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f19574,plain,
( ~ sQ274_spl
| sQ293_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19566,f9098,f19571,f19292]) ).
fof(f19575,definition,
! [X0,X1,X2] :
( sQ294_spl
<=> c_lessequals(c_Orderings_Omin(X0,c_Orderings_Omin(X1,X2,tc_nat),tc_nat),X1,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ294_spl])],[split_symbol_definition]) ).
fof(f19578,plain,
( ~ sQ274_spl
| sQ294_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19567,f9098,f19575,f19292]) ).
fof(f19579,plain,
! [X0,X1,X2] :
( ~ sQ279_spl
| c_lessequals(X0,c_Orderings_Omax(c_Orderings_Omax(X1,X0,tc_nat),X2,tc_nat),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f19326,f5619]) ).
fof(f19580,plain,
! [X0,X1,X2] :
( ~ sQ279_spl
| c_lessequals(X0,c_Orderings_Omax(c_Orderings_Omax(X0,X1,tc_nat),X2,tc_nat),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f19326,f5617]) ).
fof(f19583,definition,
! [X0,X1,X2] :
( sQ295_spl
<=> c_lessequals(X0,c_Orderings_Omax(c_Orderings_Omax(X1,X0,tc_nat),X2,tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ295_spl])],[split_symbol_definition]) ).
fof(f19586,plain,
( ~ sQ279_spl
| sQ295_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19579,f9098,f19583,f19325]) ).
fof(f19587,definition,
! [X0,X1,X2] :
( sQ296_spl
<=> c_lessequals(X0,c_Orderings_Omax(c_Orderings_Omax(X0,X1,tc_nat),X2,tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ296_spl])],[split_symbol_definition]) ).
fof(f19590,plain,
( ~ sQ279_spl
| sQ296_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19580,f9098,f19587,f19325]) ).
fof(f19591,plain,
! [X0,X1,X2] :
( ~ sQ286_spl
| c_lessequals(X0,c_Orderings_Omax(X1,c_Orderings_Omax(X2,X0,tc_nat),tc_nat),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f19365,f5619]) ).
fof(f19592,plain,
! [X0,X1,X2] :
( ~ sQ286_spl
| c_lessequals(X0,c_Orderings_Omax(X1,c_Orderings_Omax(X0,X2,tc_nat),tc_nat),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f19365,f5617]) ).
fof(f19595,definition,
! [X0,X1,X2] :
( sQ297_spl
<=> c_lessequals(X0,c_Orderings_Omax(X1,c_Orderings_Omax(X2,X0,tc_nat),tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ297_spl])],[split_symbol_definition]) ).
fof(f19598,plain,
( ~ sQ286_spl
| sQ297_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19591,f9098,f19595,f19364]) ).
fof(f19599,definition,
! [X0,X1,X2] :
( sQ298_spl
<=> c_lessequals(X0,c_Orderings_Omax(X1,c_Orderings_Omax(X0,X2,tc_nat),tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ298_spl])],[split_symbol_definition]) ).
fof(f19602,plain,
( ~ sQ286_spl
| sQ298_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f19592,f9098,f19599,f19364]) ).
fof(f19657,definition,
( sQ300_spl
<=> c_Parity_Oeven(c_0,tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ300_spl])],[split_symbol_definition]) ).
fof(f19661,plain,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_IntDef_Onat(c_OrderedGroup_Onprt(X0,tc_IntDef_Oint)) = c_0 ),
inference(resolution,[status(thm)],[f4420,f5582]) ).
fof(f19662,plain,
! [X0] :
( ~ c_lessequals(X0,c_0,tc_IntDef_Oint)
| ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_IntDef_Onat(c_plus(X0,X0,tc_IntDef_Oint)) = c_0 ),
inference(resolution,[status(thm)],[f4420,f5535]) ).
fof(f19663,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint)
| c_IntDef_Onat(c_HOL_Oabs(c_0,tc_IntDef_Oint)) = c_0 ),
inference(resolution,[status(thm)],[f4420,f5489]) ).
fof(f19664,plain,
( ~ class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint)
| c_IntDef_Onat(c_NatArith_Oof__nat(c_0,tc_IntDef_Oint)) = c_0 ),
inference(resolution,[status(thm)],[f4420,f4988]) ).
fof(f19665,plain,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_IntDef_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint)
| c_IntDef_Onat(c_minus(X0,X1,tc_IntDef_Oint)) = c_0 ),
inference(resolution,[status(thm)],[f4420,f5527]) ).
fof(f19667,plain,
! [X0] :
( ~ c_lessequals(c_0,X0,tc_IntDef_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint)
| c_IntDef_Onat(c_uminus(X0,tc_IntDef_Oint)) = c_0 ),
inference(resolution,[status(thm)],[f4420,f5569]) ).
fof(f19669,definition,
! [X0] :
( sQ301_spl
<=> c_IntDef_Onat(c_OrderedGroup_Onprt(X0,tc_IntDef_Oint)) = c_0 ),
introduced(definition,[new_symbols(definition,[sQ301_spl])],[split_symbol_definition]) ).
fof(f19672,definition,
( sQ302_spl
<=> class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ302_spl])],[split_symbol_definition]) ).
fof(f19674,plain,
( sQ302_spl
| ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) ),
inference(component_clause,[status(thm)],[f19672]) ).
fof(f19675,plain,
( ~ sQ302_spl
| sQ301_spl ),
inference(split_clause,[status(thm)],[f19661,f19669,f19672]) ).
fof(f19676,definition,
! [X0] :
( sQ303_spl
<=> ( ~ c_lessequals(X0,c_0,tc_IntDef_Oint)
| c_IntDef_Onat(c_plus(X0,X0,tc_IntDef_Oint)) = c_0 ) ),
introduced(definition,[new_symbols(definition,[sQ303_spl])],[split_symbol_definition]) ).
fof(f19679,plain,
( ~ sQ302_spl
| sQ303_spl ),
inference(split_clause,[status(thm)],[f19662,f19676,f19672]) ).
fof(f19680,definition,
( sQ304_spl
<=> c_IntDef_Onat(c_HOL_Oabs(c_0,tc_IntDef_Oint)) = c_0 ),
introduced(definition,[new_symbols(definition,[sQ304_spl])],[split_symbol_definition]) ).
fof(f19683,plain,
( ~ sQ52_spl
| sQ304_spl ),
inference(split_clause,[status(thm)],[f19663,f19680,f10492]) ).
fof(f19684,definition,
( sQ305_spl
<=> c_IntDef_Onat(c_NatArith_Oof__nat(c_0,tc_IntDef_Oint)) = c_0 ),
introduced(definition,[new_symbols(definition,[sQ305_spl])],[split_symbol_definition]) ).
fof(f19685,plain,
( ~ sQ305_spl
| c_IntDef_Onat(c_NatArith_Oof__nat(c_0,tc_IntDef_Oint)) = c_0 ),
inference(component_clause,[status(thm)],[f19684]) ).
fof(f19687,definition,
( sQ306_spl
<=> class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ306_spl])],[split_symbol_definition]) ).
fof(f19689,plain,
( sQ306_spl
| ~ class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
inference(component_clause,[status(thm)],[f19687]) ).
fof(f19690,plain,
( ~ sQ306_spl
| sQ305_spl ),
inference(split_clause,[status(thm)],[f19664,f19684,f19687]) ).
fof(f19691,definition,
! [X0,X1] :
( sQ307_spl
<=> ( ~ c_lessequals(X0,X1,tc_IntDef_Oint)
| c_IntDef_Onat(c_minus(X0,X1,tc_IntDef_Oint)) = c_0 ) ),
introduced(definition,[new_symbols(definition,[sQ307_spl])],[split_symbol_definition]) ).
fof(f19694,plain,
( ~ sQ225_spl
| sQ307_spl ),
inference(split_clause,[status(thm)],[f19665,f19691,f18164]) ).
fof(f19695,definition,
! [X0] :
( sQ308_spl
<=> ( ~ c_lessequals(c_0,X0,tc_IntDef_Oint)
| c_IntDef_Onat(c_uminus(X0,tc_IntDef_Oint)) = c_0 ) ),
introduced(definition,[new_symbols(definition,[sQ308_spl])],[split_symbol_definition]) ).
fof(f19698,plain,
( ~ sQ225_spl
| sQ308_spl ),
inference(split_clause,[status(thm)],[f19667,f19695,f18164]) ).
fof(f19700,plain,
( sQ302_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f19674,f3149]) ).
fof(f19701,plain,
sQ302_spl,
inference(contradiction_clause,[status(thm)],[f19700]) ).
fof(f19708,plain,
! [X0] :
( ~ sQ305_spl
| c_less(c_IntDef_Onat(X0),c_0,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(c_0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(X0,c_NatArith_Oof__nat(c_0,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(paramodulation,[status(thm)],[f19685,f4485]) ).
fof(f19712,definition,
! [X0] :
( sQ309_spl
<=> ( c_less(c_IntDef_Onat(X0),c_0,tc_nat)
| ~ c_less(X0,c_NatArith_Oof__nat(c_0,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ309_spl])],[split_symbol_definition]) ).
fof(f19713,plain,
! [X0] :
( ~ sQ309_spl
| c_less(c_IntDef_Onat(X0),c_0,tc_nat)
| ~ c_less(X0,c_NatArith_Oof__nat(c_0,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(component_clause,[status(thm)],[f19712]) ).
fof(f19715,definition,
( sQ310_spl
<=> c_less(c_0,c_NatArith_Oof__nat(c_0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ310_spl])],[split_symbol_definition]) ).
fof(f19717,plain,
( sQ310_spl
| ~ c_less(c_0,c_NatArith_Oof__nat(c_0,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(component_clause,[status(thm)],[f19715]) ).
fof(f19718,plain,
( ~ sQ305_spl
| ~ sQ310_spl
| sQ309_spl ),
inference(split_clause,[status(thm)],[f19708,f19712,f19715,f19684]) ).
fof(f19719,plain,
( ~ sQ111_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f11581,f3228]) ).
fof(f19720,plain,
~ sQ111_spl,
inference(contradiction_clause,[status(thm)],[f19719]) ).
fof(f19721,plain,
( sQ306_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f19689,f3158]) ).
fof(f19722,plain,
sQ306_spl,
inference(contradiction_clause,[status(thm)],[f19721]) ).
fof(f19723,plain,
! [X0] :
( ~ sQ309_spl
| ~ c_less(X0,c_NatArith_Oof__nat(c_0,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_subsumption_resolution,[status(thm)],[f19713,f5376]) ).
fof(f19758,plain,
! [X0] :
( ~ sQ173_spl
| c_IntDef_ONats = c_emptyset
| c_Main_OInter__UNIV__conv__2__1(c_IntDef_ONats,X0) != c_IntDef_ONats ),
inference(paramodulation,[status(thm)],[f14395,f14477]) ).
fof(f19760,definition,
! [X0] :
( sQ311_spl
<=> c_Main_OInter__UNIV__conv__2__1(c_IntDef_ONats,X0) != c_IntDef_ONats ),
introduced(definition,[new_symbols(definition,[sQ311_spl])],[split_symbol_definition]) ).
fof(f19763,plain,
( ~ sQ173_spl
| sQ226_spl
| sQ311_spl ),
inference(split_clause,[status(thm)],[f19758,f19760,f18222,f14366]) ).
fof(f19768,plain,
! [X0] :
( ~ sQ173_spl
| c_emptyset = c_IntDef_ONats
| c_Main_OInter__UNIV__conv__1__1(c_IntDef_ONats,X0) != c_IntDef_ONats ),
inference(paramodulation,[status(thm)],[f14395,f14478]) ).
fof(f19770,definition,
! [X0] :
( sQ313_spl
<=> c_Main_OInter__UNIV__conv__1__1(c_IntDef_ONats,X0) != c_IntDef_ONats ),
introduced(definition,[new_symbols(definition,[sQ313_spl])],[split_symbol_definition]) ).
fof(f19771,plain,
! [X0] :
( ~ sQ313_spl
| c_Main_OInter__UNIV__conv__1__1(c_IntDef_ONats,X0) != c_IntDef_ONats ),
inference(component_clause,[status(thm)],[f19770]) ).
fof(f19773,plain,
( ~ sQ173_spl
| sQ226_spl
| sQ313_spl ),
inference(split_clause,[status(thm)],[f19768,f19770,f18222,f14366]) ).
fof(f19794,plain,
! [X0] :
( c_Parity_Oeven(c_0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X0,tc_IntDef_Oint) ),
inference(paramodulation,[status(thm)],[f10075,f5667]) ).
fof(f19796,definition,
! [X0] :
( sQ317_spl
<=> ~ c_Parity_Oeven(X0,tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ317_spl])],[split_symbol_definition]) ).
fof(f19797,plain,
! [X0] :
( ~ sQ317_spl
| ~ c_Parity_Oeven(X0,tc_IntDef_Oint) ),
inference(component_clause,[status(thm)],[f19796]) ).
fof(f19799,plain,
( sQ300_spl
| sQ317_spl ),
inference(split_clause,[status(thm)],[f19794,f19796,f19657]) ).
fof(f19800,plain,
( ~ sQ317_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f5676,f19797]) ).
fof(f19801,plain,
~ sQ317_spl,
inference(contradiction_clause,[status(thm)],[f19800]) ).
fof(f19821,plain,
( ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_List_Oupt(c_0,c_NatArith_Oof__nat(c_0,tc_nat)) = c_List_Olist_ONil ),
inference(resolution,[status(thm)],[f4945,f4988]) ).
fof(f19830,plain,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_List_Oupt(c_NatArith_Oof__nat(X0,tc_nat),c_0) = c_List_Olist_ONil ),
inference(resolution,[status(thm)],[f4945,f4973]) ).
fof(f19831,plain,
( ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_List_Oupt(c_1,c_0) = c_List_Olist_ONil ),
inference(resolution,[status(thm)],[f4945,f5994]) ).
fof(f19842,plain,
! [X0] :
( ~ class_Orderings_Oorder(tc_nat)
| c_List_Oupt(X0,X0) = c_List_Olist_ONil ),
inference(resolution,[status(thm)],[f4945,f3030]) ).
fof(f19863,definition,
( sQ323_spl
<=> c_List_Oupt(c_0,c_NatArith_Oof__nat(c_0,tc_nat)) = c_List_Olist_ONil ),
introduced(definition,[new_symbols(definition,[sQ323_spl])],[split_symbol_definition]) ).
fof(f19866,plain,
( ~ sQ47_spl
| sQ323_spl ),
inference(split_clause,[status(thm)],[f19821,f19863,f10114]) ).
fof(f19887,definition,
! [X0] :
( sQ329_spl
<=> c_List_Oupt(c_NatArith_Oof__nat(X0,tc_nat),c_0) = c_List_Olist_ONil ),
introduced(definition,[new_symbols(definition,[sQ329_spl])],[split_symbol_definition]) ).
fof(f19890,plain,
( ~ sQ47_spl
| sQ329_spl ),
inference(split_clause,[status(thm)],[f19830,f19887,f10114]) ).
fof(f19891,definition,
( sQ330_spl
<=> c_List_Oupt(c_1,c_0) = c_List_Olist_ONil ),
introduced(definition,[new_symbols(definition,[sQ330_spl])],[split_symbol_definition]) ).
fof(f19894,plain,
( ~ sQ47_spl
| sQ330_spl ),
inference(split_clause,[status(thm)],[f19831,f19891,f10114]) ).
fof(f19903,definition,
! [X0] :
( sQ333_spl
<=> c_List_Oupt(X0,X0) = c_List_Olist_ONil ),
introduced(definition,[new_symbols(definition,[sQ333_spl])],[split_symbol_definition]) ).
fof(f19906,plain,
( ~ sQ50_spl
| sQ333_spl ),
inference(split_clause,[status(thm)],[f19842,f19903,f10475]) ).
fof(f19954,plain,
! [X0] :
( c_lessequals(c_1,c_1,tc_nat)
| ~ c_lessequals(c_1,X0,tc_nat) ),
inference(paramodulation,[status(thm)],[f5743,f6669]) ).
fof(f19955,definition,
! [X0] :
( sQ334_spl
<=> ~ c_lessequals(c_1,X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ334_spl])],[split_symbol_definition]) ).
fof(f19956,plain,
! [X0] :
( ~ sQ334_spl
| ~ c_lessequals(c_1,X0,tc_nat) ),
inference(component_clause,[status(thm)],[f19955]) ).
fof(f19958,plain,
( sQ261_spl
| sQ334_spl ),
inference(split_clause,[status(thm)],[f19954,f19955,f19015]) ).
fof(f19959,plain,
( ~ sQ334_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f13868,f19956]) ).
fof(f19961,plain,
~ sQ334_spl,
inference(contradiction_clause,[status(thm)],[f19959]) ).
fof(f20092,definition,
! [X0] :
( sQ340_spl
<=> ( ~ class_OrderedGroup_Oab__group__add(X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ340_spl])],[split_symbol_definition]) ).
fof(f20093,plain,
! [X0] :
( ~ sQ340_spl
| ~ class_OrderedGroup_Oab__group__add(X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(component_clause,[status(thm)],[f20092]) ).
fof(f20107,plain,
! [X0] :
( c_0 = X0
| c_0 != X0
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat) ),
inference(paramodulation,[status(thm)],[f4322,f4970]) ).
fof(f20108,definition,
! [X0] :
( sQ342_spl
<=> ( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ342_spl])],[split_symbol_definition]) ).
fof(f20109,plain,
! [X0] :
( ~ sQ342_spl
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(component_clause,[status(thm)],[f20108]) ).
fof(f20113,definition,
! [X0] :
( sQ343_spl
<=> ( c_0 = X0
| c_0 != X0 ) ),
introduced(definition,[new_symbols(definition,[sQ343_spl])],[split_symbol_definition]) ).
fof(f20116,plain,
( sQ343_spl
| ~ sQ47_spl ),
inference(split_clause,[status(thm)],[f20107,f10114,f20113]) ).
fof(f20127,plain,
! [X0] :
( c_IntDef_Oint(X0) = c_0
| c_0 != c_IntDef_Oint(X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
inference(paramodulation,[status(thm)],[f4402,f5476]) ).
fof(f20135,definition,
! [X0] :
( sQ345_spl
<=> ( c_IntDef_Oint(X0) = c_0
| c_0 != c_IntDef_Oint(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ345_spl])],[split_symbol_definition]) ).
fof(f20138,plain,
( sQ345_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f20127,f10492,f20135]) ).
fof(f20217,plain,
! [X0] :
( c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) ),
inference(resolution,[status(thm)],[f5525,f5295]) ).
fof(f20225,plain,
! [X0,X1] :
( ~ sQ173_spl
| X1 = c_IntDef_ONats
| c_emptyset != c_0
| ~ class_OrderedGroup_Oab__group__add(tc_set(X0)) ),
inference(paramodulation,[status(thm)],[f14391,f5525]) ).
fof(f20230,plain,
( sQ181_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f20217,f10516,f14484]) ).
fof(f20238,plain,
( ~ sQ173_spl
| sQ253_spl
| ~ sQ57_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f20225,f10521,f10524,f18927,f14366]) ).
fof(f20264,plain,
( ~ sQ309_spl
| ~ sQ184_spl
| $false ),
inference(resolution,[status(thm)],[f15520,f19723]) ).
fof(f20265,plain,
! [X0,X1] :
( ~ sQ184_spl
| c_less(c_minus(c_Orderings_Omin(X0,X1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),X1,tc_IntDef_Oint)
| ~ class_Orderings_Olinorder(tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f15520,f5605]) ).
fof(f20266,plain,
! [X0,X1] :
( ~ sQ184_spl
| c_less(c_minus(c_Orderings_Omin(X0,X1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ class_Orderings_Olinorder(tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f15520,f5603]) ).
fof(f20269,plain,
( ~ sQ309_spl
| ~ sQ184_spl ),
inference(contradiction_clause,[status(thm)],[f20264]) ).
fof(f20270,definition,
! [X0,X1] :
( sQ347_spl
<=> c_less(c_minus(c_Orderings_Omin(X0,X1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),X1,tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ347_spl])],[split_symbol_definition]) ).
fof(f20273,plain,
( ~ sQ184_spl
| sQ347_spl
| ~ sQ254_spl ),
inference(split_clause,[status(thm)],[f20265,f18961,f20270,f15519]) ).
fof(f20274,definition,
! [X0,X1] :
( sQ348_spl
<=> c_less(c_minus(c_Orderings_Omin(X0,X1,tc_IntDef_Oint),c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ348_spl])],[split_symbol_definition]) ).
fof(f20277,plain,
( ~ sQ184_spl
| sQ348_spl
| ~ sQ254_spl ),
inference(split_clause,[status(thm)],[f20266,f18961,f20274,f15519]) ).
fof(f20325,plain,
! [X0] :
( ~ sQ173_spl
| c_lessequals(c_0,X0,tc_nat)
| ~ c_in(X0,c_IntDef_ONats,tc_nat)
| ~ class_Orderings_Oord(tc_nat) ),
inference(paramodulation,[status(thm)],[f14410,f6023]) ).
fof(f20331,definition,
( sQ350_spl
<=> class_Orderings_Oord(tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ350_spl])],[split_symbol_definition]) ).
fof(f20333,plain,
( sQ350_spl
| ~ class_Orderings_Oord(tc_nat) ),
inference(component_clause,[status(thm)],[f20331]) ).
fof(f20334,definition,
! [X0] :
( sQ351_spl
<=> ( c_lessequals(c_0,X0,tc_nat)
| ~ c_in(X0,c_IntDef_ONats,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ351_spl])],[split_symbol_definition]) ).
fof(f20337,plain,
( ~ sQ173_spl
| sQ351_spl
| ~ sQ350_spl ),
inference(split_clause,[status(thm)],[f20325,f20331,f20334,f14366]) ).
fof(f20338,plain,
( sQ350_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f20333,f3188]) ).
fof(f20339,plain,
sQ350_spl,
inference(contradiction_clause,[status(thm)],[f20338]) ).
fof(f20346,plain,
! [X0] :
( ~ sQ173_spl
| c_in(X0,c_IntDef_ONats,tc_nat)
| ~ c_lessequals(c_0,X0,tc_nat)
| ~ class_Orderings_Oord(tc_nat) ),
inference(paramodulation,[status(thm)],[f14410,f6024]) ).
fof(f20347,definition,
! [X0] :
( sQ352_spl
<=> ( c_in(X0,c_IntDef_ONats,tc_nat)
| ~ c_lessequals(c_0,X0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ352_spl])],[split_symbol_definition]) ).
fof(f20350,plain,
( ~ sQ173_spl
| sQ352_spl
| ~ sQ350_spl ),
inference(split_clause,[status(thm)],[f20346,f20331,f20347,f14366]) ).
fof(f20388,plain,
! [X0] :
( ~ sQ173_spl
| c_IntDef_ONats = c_emptyset
| c_Main_OUnion__empty__conv__1(c_IntDef_ONats,X0) != c_emptyset ),
inference(paramodulation,[status(thm)],[f14467,f6180]) ).
fof(f20393,definition,
! [X0] :
( sQ354_spl
<=> c_Main_OUnion__empty__conv__1(c_IntDef_ONats,X0) != c_emptyset ),
introduced(definition,[new_symbols(definition,[sQ354_spl])],[split_symbol_definition]) ).
fof(f20396,plain,
( ~ sQ173_spl
| sQ226_spl
| sQ354_spl ),
inference(split_clause,[status(thm)],[f20388,f20393,f18222,f14366]) ).
fof(f20399,plain,
! [X0] :
( ~ sQ173_spl
| c_emptyset = c_IntDef_ONats
| c_Main_Oempty__Union__conv__1(c_IntDef_ONats,X0) != c_emptyset ),
inference(paramodulation,[status(thm)],[f14467,f6204]) ).
fof(f20404,definition,
! [X0] :
( sQ356_spl
<=> c_Main_Oempty__Union__conv__1(c_IntDef_ONats,X0) != c_emptyset ),
introduced(definition,[new_symbols(definition,[sQ356_spl])],[split_symbol_definition]) ).
fof(f20407,plain,
( ~ sQ173_spl
| sQ226_spl
| sQ356_spl ),
inference(split_clause,[status(thm)],[f20399,f20404,f18222,f14366]) ).
fof(f20413,plain,
! [X0] :
( c_List_Oremdups(c_List_Olist_ONil,X0) = c_List_Olist_ONil
| c_emptyset != c_emptyset ),
inference(paramodulation,[status(thm)],[f4899,f11017]) ).
fof(f20414,definition,
! [X0] :
( sQ357_spl
<=> c_List_Oremdups(c_List_Olist_ONil,X0) = c_List_Olist_ONil ),
introduced(definition,[new_symbols(definition,[sQ357_spl])],[split_symbol_definition]) ).
fof(f20417,plain,
( sQ357_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f20413,f8633,f20414]) ).
fof(f20429,plain,
! [X0] :
( c_List_Orev(c_List_Olist_ONil,X0) = c_List_Olist_ONil
| c_emptyset != c_emptyset ),
inference(paramodulation,[status(thm)],[f4899,f11022]) ).
fof(f20431,definition,
! [X0] :
( sQ358_spl
<=> c_List_Orev(c_List_Olist_ONil,X0) = c_List_Olist_ONil ),
introduced(definition,[new_symbols(definition,[sQ358_spl])],[split_symbol_definition]) ).
fof(f20434,plain,
( sQ358_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f20429,f8633,f20431]) ).
fof(f20440,plain,
! [X0] :
( c_List_Orotate1(c_List_Olist_ONil,X0) = c_List_Olist_ONil
| c_emptyset != c_emptyset ),
inference(paramodulation,[status(thm)],[f4899,f11026]) ).
fof(f20442,definition,
! [X0] :
( sQ359_spl
<=> c_List_Orotate1(c_List_Olist_ONil,X0) = c_List_Olist_ONil ),
introduced(definition,[new_symbols(definition,[sQ359_spl])],[split_symbol_definition]) ).
fof(f20445,plain,
( sQ359_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f20440,f8633,f20442]) ).
fof(f20449,plain,
! [X0] :
( c_IntDef_Onat(c_Orderings_Omin(c_0,X0,tc_IntDef_Oint)) = c_0
| ~ class_Orderings_Olinorder(tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f19192,f4420]) ).
fof(f20450,plain,
! [X0] :
( c_Orderings_Omin(c_0,X0,tc_nat) = c_0
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f19192,f5304]) ).
fof(f20451,plain,
! [X0,X1] :
( c_less(c_Orderings_Omin(c_minus(X0,c_1,tc_IntDef_Oint),X1,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ class_Orderings_Olinorder(tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f19192,f4388]) ).
fof(f20452,plain,
! [X0,X1] :
( c_List_Oupt(X0,c_Orderings_Omin(X0,X1,tc_nat)) = c_List_Olist_ONil
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f19192,f4945]) ).
fof(f20455,plain,
( c_lessequals(c_0,c_0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(paramodulation,[status(thm)],[f5315,f19192]) ).
fof(f20459,definition,
! [X0] :
( sQ360_spl
<=> c_IntDef_Onat(c_Orderings_Omin(c_0,X0,tc_IntDef_Oint)) = c_0 ),
introduced(definition,[new_symbols(definition,[sQ360_spl])],[split_symbol_definition]) ).
fof(f20462,plain,
( sQ360_spl
| ~ sQ254_spl ),
inference(split_clause,[status(thm)],[f20449,f18961,f20459]) ).
fof(f20463,definition,
! [X0] :
( sQ361_spl
<=> c_Orderings_Omin(c_0,X0,tc_nat) = c_0 ),
introduced(definition,[new_symbols(definition,[sQ361_spl])],[split_symbol_definition]) ).
fof(f20466,plain,
( sQ361_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f20450,f9098,f20463]) ).
fof(f20467,definition,
! [X0,X1] :
( sQ362_spl
<=> c_less(c_Orderings_Omin(c_minus(X0,c_1,tc_IntDef_Oint),X1,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ362_spl])],[split_symbol_definition]) ).
fof(f20470,plain,
( sQ362_spl
| ~ sQ254_spl ),
inference(split_clause,[status(thm)],[f20451,f18961,f20467]) ).
fof(f20471,definition,
! [X0,X1] :
( sQ363_spl
<=> c_List_Oupt(X0,c_Orderings_Omin(X0,X1,tc_nat)) = c_List_Olist_ONil ),
introduced(definition,[new_symbols(definition,[sQ363_spl])],[split_symbol_definition]) ).
fof(f20474,plain,
( sQ363_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f20452,f9098,f20471]) ).
fof(f20475,plain,
( sQ204_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f20455,f9098,f17439]) ).
fof(f20485,plain,
! [X0] :
( c_IntDef_Onat(c_Orderings_Omin(X0,c_0,tc_IntDef_Oint)) = c_0
| ~ class_Orderings_Olinorder(tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f19296,f4420]) ).
fof(f20486,plain,
! [X0] :
( c_Orderings_Omin(X0,c_0,tc_nat) = c_0
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f19296,f5304]) ).
fof(f20487,plain,
! [X0,X1] :
( c_less(c_Orderings_Omin(X0,c_minus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),X1,tc_IntDef_Oint)
| ~ class_Orderings_Olinorder(tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f19296,f4388]) ).
fof(f20488,plain,
! [X0,X1] :
( c_List_Oupt(X0,c_Orderings_Omin(X1,X0,tc_nat)) = c_List_Olist_ONil
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f19296,f4945]) ).
fof(f20495,definition,
! [X0] :
( sQ364_spl
<=> c_IntDef_Onat(c_Orderings_Omin(X0,c_0,tc_IntDef_Oint)) = c_0 ),
introduced(definition,[new_symbols(definition,[sQ364_spl])],[split_symbol_definition]) ).
fof(f20498,plain,
( sQ364_spl
| ~ sQ254_spl ),
inference(split_clause,[status(thm)],[f20485,f18961,f20495]) ).
fof(f20499,definition,
! [X0] :
( sQ365_spl
<=> c_Orderings_Omin(X0,c_0,tc_nat) = c_0 ),
introduced(definition,[new_symbols(definition,[sQ365_spl])],[split_symbol_definition]) ).
fof(f20502,plain,
( sQ365_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f20486,f9098,f20499]) ).
fof(f20503,definition,
! [X0,X1] :
( sQ366_spl
<=> c_less(c_Orderings_Omin(X0,c_minus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint),X1,tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ366_spl])],[split_symbol_definition]) ).
fof(f20506,plain,
( sQ366_spl
| ~ sQ254_spl ),
inference(split_clause,[status(thm)],[f20487,f18961,f20503]) ).
fof(f20507,definition,
! [X0,X1] :
( sQ367_spl
<=> c_List_Oupt(X0,c_Orderings_Omin(X1,X0,tc_nat)) = c_List_Olist_ONil ),
introduced(definition,[new_symbols(definition,[sQ367_spl])],[split_symbol_definition]) ).
fof(f20510,plain,
( sQ367_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f20488,f9098,f20507]) ).
fof(f20523,plain,
! [X0,X1] :
( c_List_Oupt(c_Orderings_Omax(X0,X1,tc_nat),X0) = c_List_Olist_ONil
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f19329,f4945]) ).
fof(f20527,plain,
! [X0] :
( c_lessequals(X0,X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(paramodulation,[status(thm)],[f5313,f19329]) ).
fof(f20530,definition,
! [X0,X1] :
( sQ368_spl
<=> c_List_Oupt(c_Orderings_Omax(X0,X1,tc_nat),X0) = c_List_Olist_ONil ),
introduced(definition,[new_symbols(definition,[sQ368_spl])],[split_symbol_definition]) ).
fof(f20533,plain,
( sQ368_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f20523,f9098,f20530]) ).
fof(f20535,plain,
( sQ187_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f20527,f9098,f17030]) ).
fof(f20539,plain,
! [X0,X1] :
( c_List_Oupt(c_Orderings_Omax(X0,X1,tc_nat),X1) = c_List_Olist_ONil
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f19368,f4945]) ).
fof(f20546,definition,
! [X0,X1] :
( sQ369_spl
<=> c_List_Oupt(c_Orderings_Omax(X0,X1,tc_nat),X1) = c_List_Olist_ONil ),
introduced(definition,[new_symbols(definition,[sQ369_spl])],[split_symbol_definition]) ).
fof(f20549,plain,
( sQ369_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f20539,f9098,f20546]) ).
fof(f20901,plain,
! [X0] :
( c_less(X0,c_0,tc_nat)
| ~ c_in(X0,c_emptyset,tc_nat)
| ~ class_Orderings_Oord(tc_nat) ),
inference(paramodulation,[status(thm)],[f6070,f6073]) ).
fof(f20907,definition,
! [X0] :
( sQ373_spl
<=> ( c_less(X0,c_0,tc_nat)
| ~ c_in(X0,c_emptyset,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ373_spl])],[split_symbol_definition]) ).
fof(f20910,plain,
( sQ373_spl
| ~ sQ350_spl ),
inference(split_clause,[status(thm)],[f20901,f20331,f20907]) ).
fof(f20917,plain,
! [X0] :
( c_in(X0,c_emptyset,tc_nat)
| ~ c_less(X0,c_0,tc_nat)
| ~ class_Orderings_Oord(tc_nat) ),
inference(paramodulation,[status(thm)],[f6070,f6074]) ).
fof(f20918,definition,
! [X0] :
( sQ374_spl
<=> ( c_in(X0,c_emptyset,tc_nat)
| ~ c_less(X0,c_0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ374_spl])],[split_symbol_definition]) ).
fof(f20921,plain,
( sQ374_spl
| ~ sQ350_spl ),
inference(split_clause,[status(thm)],[f20917,f20331,f20918]) ).
fof(f20968,plain,
( c_plus(c_0,c_0,tc_IntDef_Oint) = c_0
| ~ class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) ),
inference(paramodulation,[status(thm)],[f6553,f5474]) ).
fof(f20972,definition,
( sQ377_spl
<=> c_plus(c_0,c_0,tc_IntDef_Oint) = c_0 ),
introduced(definition,[new_symbols(definition,[sQ377_spl])],[split_symbol_definition]) ).
fof(f20975,plain,
( sQ377_spl
| ~ sQ64_spl ),
inference(split_clause,[status(thm)],[f20968,f10592,f20972]) ).
fof(f21069,definition,
! [X0] :
( sQ381_spl
<=> X0 = c_List_Olist_ONil ),
introduced(definition,[new_symbols(definition,[sQ381_spl])],[split_symbol_definition]) ).
fof(f21070,plain,
! [X0] :
( ~ sQ381_spl
| X0 = c_List_Olist_ONil ),
inference(component_clause,[status(thm)],[f21069]) ).
fof(f21079,plain,
( ~ sQ181_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f5279,f14485]) ).
fof(f21096,plain,
~ sQ181_spl,
inference(contradiction_clause,[status(thm)],[f21079]) ).
fof(f22180,plain,
! [X0,X1,X2] :
( c_in(X0,c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X2),X1,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(X0,c_Message_Oanalz(X1),tc_Message_Omsg) ),
inference(paramodulation,[status(thm)],[f6443,f6225]) ).
fof(f22181,plain,
! [X0,X1,X2] :
( c_in(X0,c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X2),X1,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(X0,c_Message_Oparts(X1),tc_Message_Omsg) ),
inference(paramodulation,[status(thm)],[f6462,f6225]) ).
fof(f22184,plain,
! [X0,X1,X2] :
( X0 = c_Message_Omsg_ONonce(X2)
| ~ c_Infinite__Set_Oatmost__one(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X2),X1,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(X0,c_Message_Oanalz(X1),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f22180,f9144]) ).
fof(f22293,plain,
! [X0,X1,X2] :
( c_in(c_Message_Omsg_ONonce(X0),X2,tc_Message_Omsg)
| ~ c_lessequals(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),X2,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6443,f6229]) ).
fof(f22294,plain,
! [X0,X1,X2] :
( c_in(c_Message_Omsg_ONonce(X0),X2,tc_Message_Omsg)
| ~ c_lessequals(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),X2,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6462,f6229]) ).
fof(f22298,plain,
! [X0,X1,X2] : c_lessequals(X0,c_insert(X1,X0,X2),tc_set(X2)),
inference(resolution,[status(thm)],[f6231,f3083]) ).
fof(f22300,plain,
! [X0,X1,X2] :
( c_lessequals(c_Message_Oanalz(X1),X2,tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),X2,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6443,f6231]) ).
fof(f22301,plain,
! [X0,X1,X2] :
( c_lessequals(c_Message_Oparts(X1),X2,tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),X2,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6462,f6231]) ).
fof(f22326,plain,
! [X0,X1,X2] :
( c_lessequals(X0,c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_in(c_Main_OsubsetI__1(X0,c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)),tc_Message_Omsg),c_Message_Oparts(X2),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f22181,f3080]) ).
fof(f22327,plain,
! [X0,X1,X2] :
( c_in(X2,c_List_Olists(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),tc_Message_Omsg),tc_List_Olist(tc_Message_Omsg))
| ~ c_in(c_Main_Oin__listsI__1(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),X2,tc_Message_Omsg),c_Message_Oparts(X1),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f22181,f3005]) ).
fof(f22328,plain,
! [X0,X1,X2] :
( X0 = c_Message_Omsg_ONonce(X2)
| ~ c_Infinite__Set_Oatmost__one(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X2),X1,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(X0,c_Message_Oparts(X1),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f22181,f9134]) ).
fof(f22345,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(tc_set(tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_Orderings_Omax(X1,c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),X2,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f22293,f19368]) ).
fof(f22346,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(tc_set(tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_Orderings_Omax(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),X2,tc_set(tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f22293,f19329]) ).
fof(f22349,plain,
! [X0,X1] :
( ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f22293,f3030]) ).
fof(f22357,definition,
! [X0,X1,X2] :
( sQ383_spl
<=> c_in(c_Message_Omsg_ONonce(X0),c_Orderings_Omax(X1,c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),X2,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_Message_Omsg) ),
introduced(definition,[new_symbols(definition,[sQ383_spl])],[split_symbol_definition]) ).
fof(f22360,definition,
( sQ384_spl
<=> class_Orderings_Olinorder(tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ384_spl])],[split_symbol_definition]) ).
fof(f22363,plain,
( ~ sQ384_spl
| sQ383_spl ),
inference(split_clause,[status(thm)],[f22345,f22357,f22360]) ).
fof(f22364,definition,
! [X0,X1,X2] :
( sQ385_spl
<=> c_in(c_Message_Omsg_ONonce(X0),c_Orderings_Omax(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),X2,tc_set(tc_Message_Omsg)),tc_Message_Omsg) ),
introduced(definition,[new_symbols(definition,[sQ385_spl])],[split_symbol_definition]) ).
fof(f22367,plain,
( ~ sQ384_spl
| sQ385_spl ),
inference(split_clause,[status(thm)],[f22346,f22364,f22360]) ).
fof(f22368,definition,
! [X0,X1] :
( sQ386_spl
<=> c_in(c_Message_Omsg_ONonce(X0),c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),tc_Message_Omsg) ),
introduced(definition,[new_symbols(definition,[sQ386_spl])],[split_symbol_definition]) ).
fof(f22371,definition,
( sQ387_spl
<=> class_Orderings_Oorder(tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ387_spl])],[split_symbol_definition]) ).
fof(f22373,plain,
( sQ387_spl
| ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg)) ),
inference(component_clause,[status(thm)],[f22371]) ).
fof(f22374,plain,
( ~ sQ387_spl
| sQ386_spl ),
inference(split_clause,[status(thm)],[f22349,f22368,f22371]) ).
fof(f22377,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(tc_set(tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_Orderings_Omax(X1,c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X2,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f22294,f19368]) ).
fof(f22378,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(tc_set(tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_Orderings_Omax(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),X2,tc_set(tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f22294,f19329]) ).
fof(f22381,plain,
! [X0,X1] :
( ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f22294,f3030]) ).
fof(f22389,definition,
! [X0,X1,X2] :
( sQ388_spl
<=> c_in(c_Message_Omsg_ONonce(X0),c_Orderings_Omax(X1,c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X2,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_Message_Omsg) ),
introduced(definition,[new_symbols(definition,[sQ388_spl])],[split_symbol_definition]) ).
fof(f22392,plain,
( ~ sQ384_spl
| sQ388_spl ),
inference(split_clause,[status(thm)],[f22377,f22389,f22360]) ).
fof(f22393,definition,
! [X0,X1,X2] :
( sQ389_spl
<=> c_in(c_Message_Omsg_ONonce(X0),c_Orderings_Omax(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),X2,tc_set(tc_Message_Omsg)),tc_Message_Omsg) ),
introduced(definition,[new_symbols(definition,[sQ389_spl])],[split_symbol_definition]) ).
fof(f22396,plain,
( ~ sQ384_spl
| sQ389_spl ),
inference(split_clause,[status(thm)],[f22378,f22393,f22360]) ).
fof(f22397,definition,
! [X0,X1] :
( sQ390_spl
<=> c_in(c_Message_Omsg_ONonce(X0),c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg)),tc_Message_Omsg) ),
introduced(definition,[new_symbols(definition,[sQ390_spl])],[split_symbol_definition]) ).
fof(f22400,plain,
( ~ sQ387_spl
| sQ390_spl ),
inference(split_clause,[status(thm)],[f22381,f22397,f22371]) ).
fof(f22403,plain,
( sQ387_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f22373,f3228]) ).
fof(f22404,plain,
sQ387_spl,
inference(contradiction_clause,[status(thm)],[f22403]) ).
fof(f22437,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(X0),c_Orderings_Omax(X1,c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X2),X0,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f22300,f19368]) ).
fof(f22438,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(X0),c_Orderings_Omax(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),X0,tc_Message_Omsg)),X2,tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f22300,f19329]) ).
fof(f22440,plain,
! [X0,X1] : c_lessequals(c_Message_Oanalz(X0),c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),X0,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(resolution,[status(thm)],[f22300,f3083]) ).
fof(f22441,plain,
! [X0,X1] :
( ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(X0),c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),X0,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f22300,f3030]) ).
fof(f22449,definition,
! [X0,X1,X2] :
( sQ391_spl
<=> c_lessequals(c_Message_Oanalz(X0),c_Orderings_Omax(X1,c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X2),X0,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ391_spl])],[split_symbol_definition]) ).
fof(f22452,plain,
( ~ sQ384_spl
| sQ391_spl ),
inference(split_clause,[status(thm)],[f22437,f22449,f22360]) ).
fof(f22453,definition,
! [X0,X1,X2] :
( sQ392_spl
<=> c_lessequals(c_Message_Oanalz(X0),c_Orderings_Omax(c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),X0,tc_Message_Omsg)),X2,tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ392_spl])],[split_symbol_definition]) ).
fof(f22456,plain,
( ~ sQ384_spl
| sQ392_spl ),
inference(split_clause,[status(thm)],[f22438,f22453,f22360]) ).
fof(f22457,definition,
! [X0,X1] :
( sQ393_spl
<=> c_lessequals(c_Message_Oanalz(X0),c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),X0,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ393_spl])],[split_symbol_definition]) ).
fof(f22460,plain,
( ~ sQ387_spl
| sQ393_spl ),
inference(split_clause,[status(thm)],[f22441,f22457,f22371]) ).
fof(f22471,plain,
! [X0,X1,X2] : c_in(c_Message_Omsg_ONonce(X0),c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),c_insert(c_Message_Omsg_ONonce(X0),X2,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg),
inference(resolution,[status(thm)],[f22440,f22293]) ).
fof(f22776,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(X0),c_Orderings_Omax(X1,c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X2),X0,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f22301,f19368]) ).
fof(f22777,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(X0),c_Orderings_Omax(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X0,tc_Message_Omsg)),X2,tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f22301,f19329]) ).
fof(f22780,plain,
! [X0,X1] :
( ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(X0),c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X0,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f22301,f3030]) ).
fof(f22788,definition,
! [X0,X1,X2] :
( sQ394_spl
<=> c_lessequals(c_Message_Oparts(X0),c_Orderings_Omax(X1,c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X2),X0,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ394_spl])],[split_symbol_definition]) ).
fof(f22791,plain,
( ~ sQ384_spl
| sQ394_spl ),
inference(split_clause,[status(thm)],[f22776,f22788,f22360]) ).
fof(f22792,definition,
! [X0,X1,X2] :
( sQ395_spl
<=> c_lessequals(c_Message_Oparts(X0),c_Orderings_Omax(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X0,tc_Message_Omsg)),X2,tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ395_spl])],[split_symbol_definition]) ).
fof(f22795,plain,
( ~ sQ384_spl
| sQ395_spl ),
inference(split_clause,[status(thm)],[f22777,f22792,f22360]) ).
fof(f22796,definition,
! [X0,X1] :
( sQ396_spl
<=> c_lessequals(c_Message_Oparts(X0),c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X0,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ396_spl])],[split_symbol_definition]) ).
fof(f22799,plain,
( ~ sQ387_spl
| sQ396_spl ),
inference(split_clause,[status(thm)],[f22780,f22796,f22371]) ).
fof(f23003,plain,
! [X0,X1,X2,X3] :
( ~ c_in(c_Message_Omsg_OMPair(X3,X0),c_Message_Oparts(X2),tc_Message_Omsg)
| c_in(X0,c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f6281,f22181]) ).
fof(f23021,plain,
! [X0,X1,X2,X3] :
( ~ c_in(c_Message_Omsg_OMPair(X0,X3),c_Message_Oparts(X2),tc_Message_Omsg)
| c_in(X0,c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f6283,f22181]) ).
fof(f23053,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X1,c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X2),X3,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_in(c_Message_Omsg_OMPair(X0,c_Main_OsubsetI__1(X1,c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X2),X3,tc_Message_Omsg)),tc_Message_Omsg)),c_Message_Oparts(X3),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f23003,f3080]) ).
fof(f23055,plain,
! [X0,X1,X2,X3,X4] :
( c_in(X1,c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X4),X3,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X0,c_Message_Omsg_OMPair(X1,X2)),c_Message_Oparts(X3),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f23003,f6283]) ).
fof(f23057,plain,
! [X0,X1,X2,X3] :
( X1 = c_Message_Omsg_ONonce(X3)
| ~ c_Infinite__Set_Oatmost__one(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X3),X2,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X0,X1),c_Message_Oparts(X2),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f23003,f9134]) ).
fof(f23078,plain,
! [X0,X1,X2,X3] :
( X0 = c_Message_Omsg_ONonce(X3)
| ~ c_Infinite__Set_Oatmost__one(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X3),X2,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X0,X1),c_Message_Oparts(X2),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f23021,f9134]) ).
fof(f23119,plain,
! [X0,X1,X2,X3,X4] :
( c_in(X1,c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X4),X3,tc_Message_Omsg)),tc_Message_Omsg)
| ~ c_in(c_Message_OHPair(X0,c_Message_Omsg_OMPair(X1,X2)),c_Message_Oparts(X3),tc_Message_Omsg) ),
inference(paramodulation,[status(thm)],[f6385,f23055]) ).
fof(f23377,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_in(c_Message_OHPair(X3,c_Message_Omsg_OMPair(X0,X4)),X2,tc_Message_Omsg)
| c_in(X0,c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X2,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f23119,f6325]) ).
fof(f23597,plain,
! [X0,X1] :
( ~ sQ173_spl
| c_insert(X0,c_IntDef_ONats,X1) = c_IntDef_ONats ),
inference(resolution,[status(thm)],[f22298,f14456]) ).
fof(f23609,plain,
! [X0,X1,X2] :
( ~ sQ173_spl
| ~ c_in(c_Message_OHPair(X1,c_Message_Omsg_OMPair(X0,X2)),c_IntDef_ONats,tc_Message_Omsg)
| c_in(X0,c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg) ),
inference(paramodulation,[status(thm)],[f23597,f23377]) ).
fof(f23610,plain,
! [X0,X1,X2] :
( ~ sQ173_spl
| X0 = c_Message_Omsg_ONonce(X2)
| ~ c_Infinite__Set_Oatmost__one(c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X0,X1),c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg) ),
inference(paramodulation,[status(thm)],[f23597,f23078]) ).
fof(f23613,plain,
! [X0,X1,X2] :
( ~ sQ173_spl
| X1 = c_Message_Omsg_ONonce(X2)
| ~ c_Infinite__Set_Oatmost__one(c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X0,X1),c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg) ),
inference(paramodulation,[status(thm)],[f23597,f23057]) ).
fof(f23629,plain,
! [X0,X1] :
( ~ sQ173_spl
| c_in(c_Message_Omsg_ONonce(X0),c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X1),c_IntDef_ONats,tc_Message_Omsg)),tc_Message_Omsg) ),
inference(paramodulation,[status(thm)],[f23597,f22471]) ).
fof(f23635,plain,
! [X0,X1] :
( ~ sQ173_spl
| X0 = c_Message_Omsg_ONonce(X1)
| ~ c_Infinite__Set_Oatmost__one(c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg)
| ~ c_in(X0,c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg) ),
inference(paramodulation,[status(thm)],[f23597,f22328]) ).
fof(f23636,plain,
! [X0,X1] :
( ~ sQ173_spl
| X0 = c_Message_Omsg_ONonce(X1)
| ~ c_Infinite__Set_Oatmost__one(c_Message_Oanalz(c_IntDef_ONats),tc_Message_Omsg)
| ~ c_in(X0,c_Message_Oanalz(c_IntDef_ONats),tc_Message_Omsg) ),
inference(paramodulation,[status(thm)],[f23597,f22184]) ).
fof(f23637,plain,
! [X0,X1] :
( ~ sQ173_spl
| c_in(c_Message_Omsg_ONonce(X1),X0,tc_Message_Omsg)
| ~ c_lessequals(c_Message_Oparts(c_IntDef_ONats),X0,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f23597,f22294]) ).
fof(f23638,plain,
! [X0,X1] :
( ~ sQ173_spl
| c_in(c_Message_Omsg_ONonce(X1),X0,tc_Message_Omsg)
| ~ c_lessequals(c_Message_Oanalz(c_IntDef_ONats),X0,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f23597,f22293]) ).
fof(f23656,plain,
( ~ sQ173_spl
| c_emptyset != c_Message_Oanalz(c_IntDef_ONats) ),
inference(paramodulation,[status(thm)],[f23597,f8695]) ).
fof(f23739,plain,
! [X0] :
( ~ sQ173_spl
| c_in(X0,c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg) ),
inference(forward_subsumption_resolution,[status(thm)],[f23609,f14419]) ).
fof(f23740,definition,
! [X0,X1,X2] :
( sQ397_spl
<=> ( X0 = c_Message_Omsg_ONonce(X2)
| ~ c_in(c_Message_Omsg_OMPair(X0,X1),c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg) ) ),
introduced(definition,[new_symbols(definition,[sQ397_spl])],[split_symbol_definition]) ).
fof(f23743,definition,
( sQ398_spl
<=> c_Infinite__Set_Oatmost__one(c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg) ),
introduced(definition,[new_symbols(definition,[sQ398_spl])],[split_symbol_definition]) ).
fof(f23746,plain,
( ~ sQ173_spl
| ~ sQ398_spl
| sQ397_spl ),
inference(split_clause,[status(thm)],[f23610,f23740,f23743,f14366]) ).
fof(f23747,definition,
! [X0,X1,X2] :
( sQ399_spl
<=> ( X1 = c_Message_Omsg_ONonce(X2)
| ~ c_in(c_Message_Omsg_OMPair(X0,X1),c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg) ) ),
introduced(definition,[new_symbols(definition,[sQ399_spl])],[split_symbol_definition]) ).
fof(f23750,plain,
( ~ sQ173_spl
| ~ sQ398_spl
| sQ399_spl ),
inference(split_clause,[status(thm)],[f23613,f23747,f23743,f14366]) ).
fof(f23761,plain,
! [X0] :
( ~ sQ173_spl
| c_in(c_Message_Omsg_ONonce(X0),c_Message_Oanalz(c_IntDef_ONats),tc_Message_Omsg) ),
inference(forward_demodulation,[status(thm)],[f23597,f23629]) ).
fof(f23762,definition,
! [X0,X1] :
( sQ400_spl
<=> ( X0 = c_Message_Omsg_ONonce(X1)
| ~ c_in(X0,c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg) ) ),
introduced(definition,[new_symbols(definition,[sQ400_spl])],[split_symbol_definition]) ).
fof(f23765,plain,
( ~ sQ173_spl
| ~ sQ398_spl
| sQ400_spl ),
inference(split_clause,[status(thm)],[f23635,f23762,f23743,f14366]) ).
fof(f23766,definition,
! [X0,X1] :
( sQ401_spl
<=> ( X0 = c_Message_Omsg_ONonce(X1)
| ~ c_in(X0,c_Message_Oanalz(c_IntDef_ONats),tc_Message_Omsg) ) ),
introduced(definition,[new_symbols(definition,[sQ401_spl])],[split_symbol_definition]) ).
fof(f23767,plain,
! [X0,X1] :
( ~ sQ401_spl
| X0 = c_Message_Omsg_ONonce(X1)
| ~ c_in(X0,c_Message_Oanalz(c_IntDef_ONats),tc_Message_Omsg) ),
inference(component_clause,[status(thm)],[f23766]) ).
fof(f23769,definition,
( sQ402_spl
<=> c_Infinite__Set_Oatmost__one(c_Message_Oanalz(c_IntDef_ONats),tc_Message_Omsg) ),
introduced(definition,[new_symbols(definition,[sQ402_spl])],[split_symbol_definition]) ).
fof(f23772,plain,
( ~ sQ173_spl
| ~ sQ402_spl
| sQ401_spl ),
inference(split_clause,[status(thm)],[f23636,f23766,f23769,f14366]) ).
fof(f23949,definition,
! [X0] :
( sQ404_spl
<=> c_in(c_Message_Omsg_ONonce(X0),c_Message_Oanalz(c_IntDef_ONats),tc_Message_Omsg) ),
introduced(definition,[new_symbols(definition,[sQ404_spl])],[split_symbol_definition]) ).
fof(f23959,definition,
! [X0] :
( sQ407_spl
<=> c_in(c_Message_Omsg_ONonce(X0),c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg) ),
introduced(definition,[new_symbols(definition,[sQ407_spl])],[split_symbol_definition]) ).
fof(f23962,definition,
( sQ408_spl
<=> c_Finite__Set_Ocard(c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg) = c_Suc(c_Finite__Set_Ocard(c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ408_spl])],[split_symbol_definition]) ).
fof(f23963,plain,
( ~ sQ408_spl
| c_Finite__Set_Ocard(c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg) = c_Suc(c_Finite__Set_Ocard(c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg)) ),
inference(component_clause,[status(thm)],[f23962]) ).
fof(f24023,plain,
( ~ sQ381_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f4743,f21070]) ).
fof(f24024,plain,
( ~ sQ313_spl
| ~ sQ253_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f19771,f18928]) ).
fof(f24045,plain,
( ~ sQ340_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f3115,f24046]) ).
fof(f24046,plain,
! [X0] :
( ~ sQ340_spl
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f20093]) ).
fof(f24052,plain,
~ sQ381_spl,
inference(contradiction_clause,[status(thm)],[f24023]) ).
fof(f24053,plain,
( ~ sQ313_spl
| ~ sQ253_spl ),
inference(contradiction_clause,[status(thm)],[f24024]) ).
fof(f24091,plain,
~ sQ340_spl,
inference(contradiction_clause,[status(thm)],[f24045]) ).
fof(f24113,plain,
! [X0,X1] :
( ~ sQ173_spl
| c_lessequals(X0,c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),c_IntDef_ONats,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f23739,f22326]) ).
fof(f24115,plain,
! [X0,X1] :
( ~ sQ173_spl
| c_in(X0,c_List_Olists(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),c_IntDef_ONats,tc_Message_Omsg)),tc_Message_Omsg),tc_List_Olist(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f23739,f22327]) ).
fof(f24124,plain,
! [X0] :
( ~ sQ173_spl
| c_lessequals(X0,c_Message_Oparts(c_IntDef_ONats),tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f23597,f24113]) ).
fof(f24125,plain,
! [X0] :
( ~ sQ173_spl
| c_in(X0,c_List_Olists(c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg),tc_List_Olist(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f23597,f24115]) ).
fof(f24138,plain,
! [X0] :
( ~ sQ173_spl
| c_lessequals(X0,c_Message_Oparts(c_IntDef_ONats),tc_set(tc_Message_Omsg))
| ~ class_Orderings_Olinorder(tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f24124,f5619]) ).
fof(f24142,definition,
! [X0] :
( sQ409_spl
<=> c_lessequals(X0,c_Message_Oparts(c_IntDef_ONats),tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ409_spl])],[split_symbol_definition]) ).
fof(f24145,plain,
( ~ sQ173_spl
| sQ409_spl
| ~ sQ384_spl ),
inference(split_clause,[status(thm)],[f24138,f22360,f24142,f14366]) ).
fof(f24152,plain,
! [X0,X1] :
( ~ sQ173_spl
| ~ sQ401_spl
| c_Message_Omsg_ONonce(X0) = c_Message_Omsg_ONonce(X1) ),
inference(resolution,[status(thm)],[f23767,f23761]) ).
fof(f24153,definition,
! [X0] :
( sQ410_spl
<=> c_Main_Oall__not__in__conv__1(c_Message_Oanalz(c_IntDef_ONats),tc_Message_Omsg) = c_Message_Omsg_ONonce(X0) ),
introduced(definition,[new_symbols(definition,[sQ410_spl])],[split_symbol_definition]) ).
fof(f24154,plain,
! [X0] :
( ~ sQ410_spl
| c_Main_Oall__not__in__conv__1(c_Message_Oanalz(c_IntDef_ONats),tc_Message_Omsg) = c_Message_Omsg_ONonce(X0) ),
inference(component_clause,[status(thm)],[f24153]) ).
fof(f24156,definition,
( sQ411_spl
<=> c_Message_Oanalz(c_IntDef_ONats) = c_emptyset ),
introduced(definition,[new_symbols(definition,[sQ411_spl])],[split_symbol_definition]) ).
fof(f24157,plain,
( ~ sQ411_spl
| c_Message_Oanalz(c_IntDef_ONats) = c_emptyset ),
inference(component_clause,[status(thm)],[f24156]) ).
fof(f24160,plain,
! [X0,X1] :
( ~ sQ173_spl
| ~ sQ401_spl
| X0 = X1 ),
inference(backward_subsumption_resolution,[status(thm)],[f6307,f24152]) ).
fof(f24161,plain,
( ~ sQ173_spl
| ~ sQ401_spl
| sQ177_spl ),
inference(split_clause,[status(thm)],[f24160,f14447,f23766,f14366]) ).
fof(f24162,plain,
( ~ sQ411_spl
| ~ sQ173_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f24157,f23656]) ).
fof(f24163,plain,
( ~ sQ411_spl
| ~ sQ173_spl ),
inference(contradiction_clause,[status(thm)],[f24162]) ).
fof(f24172,definition,
! [X0,X1] :
( sQ414_spl
<=> c_Message_Omsg_ONonce(X0) = c_Message_Omsg_ONonce(X1) ),
introduced(definition,[new_symbols(definition,[sQ414_spl])],[split_symbol_definition]) ).
fof(f24173,plain,
! [X0,X1] :
( ~ sQ414_spl
| c_Message_Omsg_ONonce(X0) = c_Message_Omsg_ONonce(X1) ),
inference(component_clause,[status(thm)],[f24172]) ).
fof(f24177,plain,
! [X0,X1] :
( ~ sQ414_spl
| X0 = X1 ),
inference(backward_subsumption_resolution,[status(thm)],[f6307,f24173]) ).
fof(f24178,plain,
( ~ sQ414_spl
| sQ177_spl ),
inference(split_clause,[status(thm)],[f24177,f14447,f24172]) ).
fof(f24182,plain,
! [X0,X1] :
( ~ sQ410_spl
| X0 = X1
| c_Message_Omsg_ONonce(X0) != c_Main_Oall__not__in__conv__1(c_Message_Oanalz(c_IntDef_ONats),tc_Message_Omsg) ),
inference(paramodulation,[status(thm)],[f24154,f6307]) ).
fof(f24250,plain,
! [X0] :
( ~ sQ410_spl
| c_emptyset != c_Message_Oparts(c_insert(c_Main_Oall__not__in__conv__1(c_Message_Oanalz(c_IntDef_ONats),tc_Message_Omsg),X0,tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f24154,f8694]) ).
fof(f24742,plain,
! [X0,X1] :
( ~ sQ410_spl
| X0 = X1 ),
inference(forward_subsumption_resolution,[status(thm)],[f24182,f24154]) ).
fof(f24743,plain,
( ~ sQ410_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f24250,f24742]) ).
fof(f24744,plain,
~ sQ410_spl,
inference(contradiction_clause,[status(thm)],[f24743]) ).
fof(f25015,plain,
! [X0] :
( ~ sQ173_spl
| c_lessequals(X0,c_List_Olists(c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg),tc_set(tc_List_Olist(tc_Message_Omsg))) ),
inference(resolution,[status(thm)],[f24125,f3080]) ).
fof(f25018,plain,
! [X0] :
( ~ sQ173_spl
| c_in(X0,c_List_Olists(c_List_Olists(c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg),tc_List_Olist(tc_Message_Omsg)),tc_List_Olist(tc_List_Olist(tc_Message_Omsg))) ),
inference(resolution,[status(thm)],[f24125,f3005]) ).
fof(f25042,plain,
! [X0,X1,X2] :
( c_lessequals(c_Message_Oparts(c_Message_Oparts(X1)),X2,tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg))),X2,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6462,f22301]) ).
fof(f25054,plain,
! [X0,X1,X2] :
( c_in(c_Message_Omsg_ONonce(X0),X2,tc_Message_Omsg)
| ~ c_lessequals(c_Message_Oparts(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg))),X2,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6462,f22294]) ).
fof(f25064,plain,
! [X0,X1] :
( c_in(c_Message_Oparts(c_Message_Oparts(X1)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_Message_Oparts(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg))),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6462,f14574]) ).
fof(f25082,plain,
! [X0,X1] :
( c_in(c_Message_Oparts(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X0,tc_Message_Omsg))),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_Message_Oparts(c_Message_Oparts(X0)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6462,f6878]) ).
fof(f25237,plain,
! [X0] :
( ~ sQ173_spl
| c_lessequals(X0,c_List_Olists(c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg),tc_set(tc_List_Olist(tc_Message_Omsg)))
| ~ class_Orderings_Olinorder(tc_set(tc_List_Olist(tc_Message_Omsg))) ),
inference(resolution,[status(thm)],[f25015,f5619]) ).
fof(f25241,definition,
( sQ415_spl
<=> class_Orderings_Olinorder(tc_set(tc_List_Olist(tc_Message_Omsg))) ),
introduced(definition,[new_symbols(definition,[sQ415_spl])],[split_symbol_definition]) ).
fof(f25244,definition,
! [X0] :
( sQ416_spl
<=> c_lessequals(X0,c_List_Olists(c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg),tc_set(tc_List_Olist(tc_Message_Omsg))) ),
introduced(definition,[new_symbols(definition,[sQ416_spl])],[split_symbol_definition]) ).
fof(f25247,plain,
( ~ sQ173_spl
| sQ416_spl
| ~ sQ415_spl ),
inference(split_clause,[status(thm)],[f25237,f25241,f25244,f14366]) ).
fof(f25265,plain,
( ~ sQ408_spl
| c_less(c_Finite__Set_Ocard(c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg),c_Finite__Set_Ocard(c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg),tc_nat) ),
inference(paramodulation,[status(thm)],[f23963,f3026]) ).
fof(f25272,plain,
( ~ sQ408_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f25265,f3027]) ).
fof(f25273,plain,
~ sQ408_spl,
inference(contradiction_clause,[status(thm)],[f25272]) ).
fof(f25283,plain,
! [X0,X1] :
( ~ sQ173_spl
| ~ class_Orderings_Olinorder(tc_set(tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_Orderings_Omax(X1,c_Message_Oparts(c_IntDef_ONats),tc_set(tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f23637,f19368]) ).
fof(f25284,plain,
! [X0,X1] :
( ~ sQ173_spl
| ~ class_Orderings_Olinorder(tc_set(tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_Orderings_Omax(c_Message_Oparts(c_IntDef_ONats),X1,tc_set(tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f23637,f19329]) ).
fof(f25287,plain,
! [X0] :
( ~ sQ173_spl
| ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f23637,f3030]) ).
fof(f25288,definition,
! [X0,X1] :
( sQ418_spl
<=> c_in(c_Message_Omsg_ONonce(X0),c_Orderings_Omax(X1,c_Message_Oparts(c_IntDef_ONats),tc_set(tc_Message_Omsg)),tc_Message_Omsg) ),
introduced(definition,[new_symbols(definition,[sQ418_spl])],[split_symbol_definition]) ).
fof(f25291,plain,
( ~ sQ173_spl
| ~ sQ384_spl
| sQ418_spl ),
inference(split_clause,[status(thm)],[f25283,f25288,f22360,f14366]) ).
fof(f25292,definition,
! [X0,X1] :
( sQ419_spl
<=> c_in(c_Message_Omsg_ONonce(X0),c_Orderings_Omax(c_Message_Oparts(c_IntDef_ONats),X1,tc_set(tc_Message_Omsg)),tc_Message_Omsg) ),
introduced(definition,[new_symbols(definition,[sQ419_spl])],[split_symbol_definition]) ).
fof(f25295,plain,
( ~ sQ173_spl
| ~ sQ384_spl
| sQ419_spl ),
inference(split_clause,[status(thm)],[f25284,f25292,f22360,f14366]) ).
fof(f25296,plain,
( ~ sQ173_spl
| ~ sQ387_spl
| sQ407_spl ),
inference(split_clause,[status(thm)],[f25287,f23959,f22371,f14366]) ).
fof(f25395,plain,
! [X0,X1] :
( ~ sQ173_spl
| ~ class_Orderings_Olinorder(tc_set(tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_Orderings_Omax(X1,c_Message_Oanalz(c_IntDef_ONats),tc_set(tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f23638,f19368]) ).
fof(f25396,plain,
! [X0,X1] :
( ~ sQ173_spl
| ~ class_Orderings_Olinorder(tc_set(tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_Orderings_Omax(c_Message_Oanalz(c_IntDef_ONats),X1,tc_set(tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f23638,f19329]) ).
fof(f25399,plain,
! [X0] :
( ~ sQ173_spl
| ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_Message_Oanalz(c_IntDef_ONats),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f23638,f3030]) ).
fof(f25400,definition,
! [X0,X1] :
( sQ420_spl
<=> c_in(c_Message_Omsg_ONonce(X0),c_Orderings_Omax(X1,c_Message_Oanalz(c_IntDef_ONats),tc_set(tc_Message_Omsg)),tc_Message_Omsg) ),
introduced(definition,[new_symbols(definition,[sQ420_spl])],[split_symbol_definition]) ).
fof(f25403,plain,
( ~ sQ173_spl
| ~ sQ384_spl
| sQ420_spl ),
inference(split_clause,[status(thm)],[f25395,f25400,f22360,f14366]) ).
fof(f25404,definition,
! [X0,X1] :
( sQ421_spl
<=> c_in(c_Message_Omsg_ONonce(X0),c_Orderings_Omax(c_Message_Oanalz(c_IntDef_ONats),X1,tc_set(tc_Message_Omsg)),tc_Message_Omsg) ),
introduced(definition,[new_symbols(definition,[sQ421_spl])],[split_symbol_definition]) ).
fof(f25407,plain,
( ~ sQ173_spl
| ~ sQ384_spl
| sQ421_spl ),
inference(split_clause,[status(thm)],[f25396,f25404,f22360,f14366]) ).
fof(f25408,plain,
( ~ sQ173_spl
| ~ sQ387_spl
| sQ404_spl ),
inference(split_clause,[status(thm)],[f25399,f23949,f22371,f14366]) ).
fof(f25412,plain,
! [X0,X1] :
( c_Finite__Set_Ocard(c_Message_Oparts(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X0,tc_Message_Omsg))),tc_Message_Omsg) = c_Suc(c_Finite__Set_Ocard(c_Message_Oparts(c_Message_Oparts(X0)),tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X1),c_Message_Oparts(c_Message_Oparts(X0)),tc_Message_Omsg)
| ~ c_in(c_Message_Oparts(c_Message_Oparts(X0)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f6462,f12069]) ).
fof(f25633,plain,
! [X0] :
( ~ sQ173_spl
| c_lessequals(X0,c_List_Olists(c_List_Olists(c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg),tc_List_Olist(tc_Message_Omsg)),tc_set(tc_List_Olist(tc_List_Olist(tc_Message_Omsg)))) ),
inference(resolution,[status(thm)],[f25018,f3080]) ).
fof(f25777,plain,
! [X0,X1,X2] :
( c_less(X1,c_Suc(X2),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| ~ c_lessequals(c_Orderings_Omax(X0,X1,tc_nat),X2,tc_nat) ),
inference(resolution,[status(thm)],[f6526,f5600]) ).
fof(f25778,plain,
! [X0,X1,X2] :
( c_less(X0,c_Suc(X2),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| ~ c_lessequals(c_Orderings_Omax(X0,X1,tc_nat),X2,tc_nat) ),
inference(resolution,[status(thm)],[f6526,f5598]) ).
fof(f25785,plain,
! [X0] :
( ~ class_Orderings_Oorder(tc_nat)
| ~ c_lessequals(c_Suc(X0),X0,tc_nat) ),
inference(resolution,[status(thm)],[f6526,f5626]) ).
fof(f25786,definition,
! [X0,X1,X2] :
( sQ422_spl
<=> ( c_less(X1,c_Suc(X2),tc_nat)
| ~ c_lessequals(c_Orderings_Omax(X0,X1,tc_nat),X2,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ422_spl])],[split_symbol_definition]) ).
fof(f25789,plain,
( ~ sQ43_spl
| sQ422_spl ),
inference(split_clause,[status(thm)],[f25777,f25786,f9098]) ).
fof(f25790,definition,
! [X0,X1,X2] :
( sQ423_spl
<=> ( c_less(X0,c_Suc(X2),tc_nat)
| ~ c_lessequals(c_Orderings_Omax(X0,X1,tc_nat),X2,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ423_spl])],[split_symbol_definition]) ).
fof(f25793,plain,
( ~ sQ43_spl
| sQ423_spl ),
inference(split_clause,[status(thm)],[f25778,f25790,f9098]) ).
fof(f25794,definition,
! [X0] :
( sQ424_spl
<=> ~ c_lessequals(c_Suc(X0),X0,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ424_spl])],[split_symbol_definition]) ).
fof(f25797,plain,
( ~ sQ50_spl
| sQ424_spl ),
inference(split_clause,[status(thm)],[f25785,f25794,f10475]) ).
fof(f25798,plain,
! [X0,X1,X2] :
( c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(X2),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| X1 = X2
| X2 = X0
| X1 = X0
| ~ c_lessequals(v_sko__urX(v_evs_H_H),X0,tc_nat) ),
inference(resolution,[status(thm)],[f6527,f6529]) ).
fof(f25799,plain,
! [X0,X1,X2] :
( ~ c_lessequals(v_sko__urX(v_evs_H),X2,tc_nat)
| c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs),tc_Message_Omsg)
| X1 = X2
| X2 = X0
| X1 = X0
| ~ c_lessequals(v_sko__urX(v_evs_H_H),X0,tc_nat) ),
inference(resolution,[status(thm)],[f25798,f6527]) ).
fof(f25800,plain,
! [X0,X1,X2] :
( ~ c_lessequals(v_sko__urX(v_evs),X1,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs_H),X2,tc_nat)
| X1 = X2
| X2 = X0
| X1 = X0
| ~ c_lessequals(v_sko__urX(v_evs_H_H),X0,tc_nat) ),
inference(resolution,[status(thm)],[f25799,f6527]) ).
fof(f25803,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs_H),X2,tc_nat)
| X0 = X2
| X2 = c_Orderings_Omax(X1,v_sko__urX(v_evs_H_H),tc_nat)
| X0 = c_Orderings_Omax(X1,v_sko__urX(v_evs_H_H),tc_nat) ),
inference(resolution,[status(thm)],[f25800,f19368]) ).
fof(f25804,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs_H),X2,tc_nat)
| X0 = X2
| X2 = c_Orderings_Omax(v_sko__urX(v_evs_H_H),X1,tc_nat)
| X0 = c_Orderings_Omax(v_sko__urX(v_evs_H_H),X1,tc_nat) ),
inference(resolution,[status(thm)],[f25800,f19329]) ).
fof(f25808,plain,
! [X0,X1] :
( ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs_H),X1,tc_nat)
| X0 = X1
| X1 = v_sko__urX(v_evs_H_H)
| X0 = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f25800,f8954]) ).
fof(f25809,plain,
! [X0,X1] :
( ~ class_Orderings_Oorder(tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs_H),X1,tc_nat)
| X0 = X1
| X1 = v_sko__urX(v_evs_H_H)
| X0 = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f25800,f3030]) ).
fof(f25810,definition,
! [X0,X1,X2] :
( sQ425_spl
<=> ( ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs_H),X2,tc_nat)
| X0 = X2
| X2 = c_Orderings_Omax(X1,v_sko__urX(v_evs_H_H),tc_nat)
| X0 = c_Orderings_Omax(X1,v_sko__urX(v_evs_H_H),tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ425_spl])],[split_symbol_definition]) ).
fof(f25813,plain,
( ~ sQ43_spl
| sQ425_spl ),
inference(split_clause,[status(thm)],[f25803,f25810,f9098]) ).
fof(f25814,definition,
! [X0,X1,X2] :
( sQ426_spl
<=> ( ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs_H),X2,tc_nat)
| X0 = X2
| X2 = c_Orderings_Omax(v_sko__urX(v_evs_H_H),X1,tc_nat)
| X0 = c_Orderings_Omax(v_sko__urX(v_evs_H_H),X1,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ426_spl])],[split_symbol_definition]) ).
fof(f25817,plain,
( ~ sQ43_spl
| sQ426_spl ),
inference(split_clause,[status(thm)],[f25804,f25814,f9098]) ).
fof(f25818,definition,
! [X0,X1] :
( sQ427_spl
<=> ( ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs_H),X1,tc_nat)
| X0 = X1
| X1 = v_sko__urX(v_evs_H_H)
| X0 = v_sko__urX(v_evs_H_H) ) ),
introduced(definition,[new_symbols(definition,[sQ427_spl])],[split_symbol_definition]) ).
fof(f25821,plain,
( ~ sQ50_spl
| sQ427_spl ),
inference(split_clause,[status(thm)],[f25809,f25818,f10475]) ).
fof(f25824,plain,
! [X0,X1] :
( ~ class_Orderings_Olinorder(tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| X0 = c_Orderings_Omax(X1,v_sko__urX(v_evs_H),tc_nat)
| c_Orderings_Omax(X1,v_sko__urX(v_evs_H),tc_nat) = v_sko__urX(v_evs_H_H)
| X0 = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f25808,f19368]) ).
fof(f25825,plain,
! [X0,X1] :
( ~ class_Orderings_Olinorder(tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| X0 = c_Orderings_Omax(v_sko__urX(v_evs_H),X1,tc_nat)
| c_Orderings_Omax(v_sko__urX(v_evs_H),X1,tc_nat) = v_sko__urX(v_evs_H_H)
| X0 = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f25808,f19329]) ).
fof(f25826,plain,
! [X0] :
( ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| X0 = c_Suc(v_sko__urX(v_evs_H))
| c_Suc(v_sko__urX(v_evs_H)) = v_sko__urX(v_evs_H_H)
| X0 = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f25808,f13873]) ).
fof(f25829,plain,
! [X0] :
( ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| X0 = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H)
| X0 = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f25808,f8954]) ).
fof(f25831,definition,
! [X0,X1] :
( sQ428_spl
<=> ( ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| X0 = c_Orderings_Omax(X1,v_sko__urX(v_evs_H),tc_nat)
| c_Orderings_Omax(X1,v_sko__urX(v_evs_H),tc_nat) = v_sko__urX(v_evs_H_H)
| X0 = v_sko__urX(v_evs_H_H) ) ),
introduced(definition,[new_symbols(definition,[sQ428_spl])],[split_symbol_definition]) ).
fof(f25834,plain,
( ~ sQ43_spl
| sQ428_spl ),
inference(split_clause,[status(thm)],[f25824,f25831,f9098]) ).
fof(f25835,definition,
! [X0,X1] :
( sQ429_spl
<=> ( ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| X0 = c_Orderings_Omax(v_sko__urX(v_evs_H),X1,tc_nat)
| c_Orderings_Omax(v_sko__urX(v_evs_H),X1,tc_nat) = v_sko__urX(v_evs_H_H)
| X0 = v_sko__urX(v_evs_H_H) ) ),
introduced(definition,[new_symbols(definition,[sQ429_spl])],[split_symbol_definition]) ).
fof(f25838,plain,
( ~ sQ43_spl
| sQ429_spl ),
inference(split_clause,[status(thm)],[f25825,f25835,f9098]) ).
fof(f25839,definition,
! [X0] :
( sQ430_spl
<=> ( ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| X0 = c_Suc(v_sko__urX(v_evs_H))
| X0 = v_sko__urX(v_evs_H_H) ) ),
introduced(definition,[new_symbols(definition,[sQ430_spl])],[split_symbol_definition]) ).
fof(f25840,plain,
! [X0] :
( ~ sQ430_spl
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| X0 = c_Suc(v_sko__urX(v_evs_H))
| X0 = v_sko__urX(v_evs_H_H) ),
inference(component_clause,[status(thm)],[f25839]) ).
fof(f25842,definition,
( sQ431_spl
<=> c_Suc(v_sko__urX(v_evs_H)) = v_sko__urX(v_evs_H_H) ),
introduced(definition,[new_symbols(definition,[sQ431_spl])],[split_symbol_definition]) ).
fof(f25843,plain,
( ~ sQ431_spl
| c_Suc(v_sko__urX(v_evs_H)) = v_sko__urX(v_evs_H_H) ),
inference(component_clause,[status(thm)],[f25842]) ).
fof(f25845,plain,
( sQ431_spl
| sQ430_spl ),
inference(split_clause,[status(thm)],[f25826,f25839,f25842]) ).
fof(f25846,definition,
! [X0] :
( sQ432_spl
<=> ( ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| X0 = v_sko__urX(v_evs_H)
| X0 = v_sko__urX(v_evs_H_H) ) ),
introduced(definition,[new_symbols(definition,[sQ432_spl])],[split_symbol_definition]) ).
fof(f25847,plain,
! [X0] :
( ~ sQ432_spl
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| X0 = v_sko__urX(v_evs_H)
| X0 = v_sko__urX(v_evs_H_H) ),
inference(component_clause,[status(thm)],[f25846]) ).
fof(f25849,definition,
( sQ433_spl
<=> v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H) ),
introduced(definition,[new_symbols(definition,[sQ433_spl])],[split_symbol_definition]) ).
fof(f25850,plain,
( ~ sQ433_spl
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs_H_H) ),
inference(component_clause,[status(thm)],[f25849]) ).
fof(f25852,plain,
( sQ433_spl
| sQ432_spl ),
inference(split_clause,[status(thm)],[f25829,f25846,f25849]) ).
fof(f25856,plain,
! [X0] :
( ~ sQ432_spl
| ~ class_Orderings_Olinorder(tc_nat)
| c_Orderings_Omax(X0,v_sko__urX(v_evs),tc_nat) = v_sko__urX(v_evs_H)
| c_Orderings_Omax(X0,v_sko__urX(v_evs),tc_nat) = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f25847,f19368]) ).
fof(f25858,plain,
( ~ sQ432_spl
| c_Suc(v_sko__urX(v_evs)) = v_sko__urX(v_evs_H)
| c_Suc(v_sko__urX(v_evs)) = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f25847,f13873]) ).
fof(f25861,plain,
( ~ sQ432_spl
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H)
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f25847,f8954]) ).
fof(f25863,definition,
! [X0] :
( sQ434_spl
<=> ( c_Orderings_Omax(X0,v_sko__urX(v_evs),tc_nat) = v_sko__urX(v_evs_H)
| c_Orderings_Omax(X0,v_sko__urX(v_evs),tc_nat) = v_sko__urX(v_evs_H_H) ) ),
introduced(definition,[new_symbols(definition,[sQ434_spl])],[split_symbol_definition]) ).
fof(f25864,plain,
! [X0] :
( ~ sQ434_spl
| c_Orderings_Omax(X0,v_sko__urX(v_evs),tc_nat) = v_sko__urX(v_evs_H)
| c_Orderings_Omax(X0,v_sko__urX(v_evs),tc_nat) = v_sko__urX(v_evs_H_H) ),
inference(component_clause,[status(thm)],[f25863]) ).
fof(f25866,plain,
( ~ sQ432_spl
| ~ sQ43_spl
| sQ434_spl ),
inference(split_clause,[status(thm)],[f25856,f25863,f9098,f25846]) ).
fof(f25871,definition,
( sQ436_spl
<=> c_Suc(v_sko__urX(v_evs)) = v_sko__urX(v_evs_H_H) ),
introduced(definition,[new_symbols(definition,[sQ436_spl])],[split_symbol_definition]) ).
fof(f25872,plain,
( ~ sQ436_spl
| c_Suc(v_sko__urX(v_evs)) = v_sko__urX(v_evs_H_H) ),
inference(component_clause,[status(thm)],[f25871]) ).
fof(f25874,definition,
( sQ437_spl
<=> c_Suc(v_sko__urX(v_evs)) = v_sko__urX(v_evs_H) ),
introduced(definition,[new_symbols(definition,[sQ437_spl])],[split_symbol_definition]) ).
fof(f25875,plain,
( ~ sQ437_spl
| c_Suc(v_sko__urX(v_evs)) = v_sko__urX(v_evs_H) ),
inference(component_clause,[status(thm)],[f25874]) ).
fof(f25877,plain,
( ~ sQ432_spl
| sQ437_spl
| sQ436_spl ),
inference(split_clause,[status(thm)],[f25858,f25871,f25874,f25846]) ).
fof(f25878,definition,
( sQ438_spl
<=> v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
introduced(definition,[new_symbols(definition,[sQ438_spl])],[split_symbol_definition]) ).
fof(f25879,plain,
( ~ sQ438_spl
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(component_clause,[status(thm)],[f25878]) ).
fof(f25881,definition,
( sQ439_spl
<=> v_sko__urX(v_evs) = v_sko__urX(v_evs_H) ),
introduced(definition,[new_symbols(definition,[sQ439_spl])],[split_symbol_definition]) ).
fof(f25882,plain,
( ~ sQ439_spl
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H) ),
inference(component_clause,[status(thm)],[f25881]) ).
fof(f25884,plain,
( ~ sQ432_spl
| sQ439_spl
| sQ438_spl ),
inference(split_clause,[status(thm)],[f25861,f25878,f25881,f25846]) ).
fof(f25890,plain,
! [X0] :
( ~ sQ430_spl
| ~ sQ433_spl
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| X0 = c_Suc(v_sko__urX(v_evs_H))
| X0 = v_sko__urX(v_evs_H) ),
inference(backward_demodulation,[status(thm)],[f25850,f25840]) ).
fof(f25914,plain,
! [X0] :
( ~ sQ430_spl
| ~ sQ433_spl
| ~ class_Orderings_Olinorder(tc_nat)
| c_Orderings_Omax(v_sko__urX(v_evs),X0,tc_nat) = c_Suc(v_sko__urX(v_evs_H))
| c_Orderings_Omax(v_sko__urX(v_evs),X0,tc_nat) = v_sko__urX(v_evs_H) ),
inference(resolution,[status(thm)],[f25890,f19329]) ).
fof(f25915,plain,
( ~ sQ430_spl
| ~ sQ433_spl
| c_Suc(v_sko__urX(v_evs)) = c_Suc(v_sko__urX(v_evs_H))
| c_Suc(v_sko__urX(v_evs)) = v_sko__urX(v_evs_H) ),
inference(resolution,[status(thm)],[f25890,f13873]) ).
fof(f25918,plain,
( ~ sQ430_spl
| ~ sQ433_spl
| v_sko__urX(v_evs) = c_Suc(v_sko__urX(v_evs_H))
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H) ),
inference(resolution,[status(thm)],[f25890,f8954]) ).
fof(f25924,definition,
! [X0] :
( sQ441_spl
<=> ( c_Orderings_Omax(v_sko__urX(v_evs),X0,tc_nat) = c_Suc(v_sko__urX(v_evs_H))
| c_Orderings_Omax(v_sko__urX(v_evs),X0,tc_nat) = v_sko__urX(v_evs_H) ) ),
introduced(definition,[new_symbols(definition,[sQ441_spl])],[split_symbol_definition]) ).
fof(f25925,plain,
! [X0] :
( ~ sQ441_spl
| c_Orderings_Omax(v_sko__urX(v_evs),X0,tc_nat) = c_Suc(v_sko__urX(v_evs_H))
| c_Orderings_Omax(v_sko__urX(v_evs),X0,tc_nat) = v_sko__urX(v_evs_H) ),
inference(component_clause,[status(thm)],[f25924]) ).
fof(f25927,plain,
( ~ sQ430_spl
| ~ sQ433_spl
| ~ sQ43_spl
| sQ441_spl ),
inference(split_clause,[status(thm)],[f25914,f25924,f9098,f25849,f25839]) ).
fof(f25928,definition,
( sQ442_spl
<=> c_Suc(v_sko__urX(v_evs)) = c_Suc(v_sko__urX(v_evs_H)) ),
introduced(definition,[new_symbols(definition,[sQ442_spl])],[split_symbol_definition]) ).
fof(f25929,plain,
( ~ sQ442_spl
| c_Suc(v_sko__urX(v_evs)) = c_Suc(v_sko__urX(v_evs_H)) ),
inference(component_clause,[status(thm)],[f25928]) ).
fof(f25930,plain,
( sQ442_spl
| c_Suc(v_sko__urX(v_evs)) != c_Suc(v_sko__urX(v_evs_H)) ),
inference(component_clause,[status(thm)],[f25928]) ).
fof(f25931,plain,
( ~ sQ430_spl
| ~ sQ433_spl
| sQ442_spl
| sQ437_spl ),
inference(split_clause,[status(thm)],[f25915,f25874,f25928,f25849,f25839]) ).
fof(f25932,definition,
( sQ443_spl
<=> v_sko__urX(v_evs) = c_Suc(v_sko__urX(v_evs_H)) ),
introduced(definition,[new_symbols(definition,[sQ443_spl])],[split_symbol_definition]) ).
fof(f25933,plain,
( ~ sQ443_spl
| v_sko__urX(v_evs) = c_Suc(v_sko__urX(v_evs_H)) ),
inference(component_clause,[status(thm)],[f25932]) ).
fof(f25934,plain,
( sQ443_spl
| v_sko__urX(v_evs) != c_Suc(v_sko__urX(v_evs_H)) ),
inference(component_clause,[status(thm)],[f25932]) ).
fof(f25935,plain,
( ~ sQ430_spl
| ~ sQ433_spl
| sQ443_spl
| sQ439_spl ),
inference(split_clause,[status(thm)],[f25918,f25881,f25932,f25849,f25839]) ).
fof(f25938,plain,
( ~ sQ431_spl
| ~ sQ433_spl
| c_Suc(v_sko__urX(v_evs_H)) = v_sko__urX(v_evs_H) ),
inference(forward_demodulation,[status(thm)],[f25850,f25843]) ).
fof(f25959,plain,
( ~ sQ431_spl
| ~ sQ433_spl
| c_less(v_sko__urX(v_evs_H),v_sko__urX(v_evs_H),tc_nat) ),
inference(paramodulation,[status(thm)],[f25938,f3026]) ).
fof(f25961,definition,
( sQ444_spl
<=> c_Parity_Oeven(v_sko__urX(v_evs_H),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ444_spl])],[split_symbol_definition]) ).
fof(f25966,plain,
( ~ sQ431_spl
| ~ sQ433_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f25959,f3027]) ).
fof(f25967,plain,
( ~ sQ431_spl
| ~ sQ433_spl ),
inference(contradiction_clause,[status(thm)],[f25966]) ).
fof(f25970,plain,
( ~ sQ437_spl
| ~ sQ439_spl
| c_Suc(v_sko__urX(v_evs)) = v_sko__urX(v_evs) ),
inference(backward_demodulation,[status(thm)],[f25882,f25875]) ).
fof(f25987,plain,
! [X0] :
( ~ sQ441_spl
| ~ sQ439_spl
| c_Orderings_Omax(v_sko__urX(v_evs),X0,tc_nat) = c_Suc(v_sko__urX(v_evs_H))
| c_Orderings_Omax(v_sko__urX(v_evs),X0,tc_nat) = v_sko__urX(v_evs) ),
inference(forward_demodulation,[status(thm)],[f25882,f25925]) ).
fof(f25988,plain,
! [X0] :
( ~ sQ441_spl
| ~ sQ439_spl
| c_Orderings_Omax(v_sko__urX(v_evs),X0,tc_nat) = c_Suc(v_sko__urX(v_evs))
| c_Orderings_Omax(v_sko__urX(v_evs),X0,tc_nat) = v_sko__urX(v_evs) ),
inference(forward_demodulation,[status(thm)],[f25882,f25987]) ).
fof(f25992,plain,
! [X0] :
( ~ sQ430_spl
| ~ sQ433_spl
| ~ sQ439_spl
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| X0 = c_Suc(v_sko__urX(v_evs_H))
| X0 = v_sko__urX(v_evs) ),
inference(forward_demodulation,[status(thm)],[f25882,f25890]) ).
fof(f25993,plain,
! [X0] :
( ~ sQ430_spl
| ~ sQ433_spl
| ~ sQ439_spl
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| X0 = c_Suc(v_sko__urX(v_evs))
| X0 = v_sko__urX(v_evs) ),
inference(forward_demodulation,[status(thm)],[f25882,f25992]) ).
fof(f26039,plain,
( ~ sQ443_spl
| ~ c_Parity_Oeven(v_sko__urX(v_evs),tc_nat)
| ~ c_Parity_Oeven(v_sko__urX(v_evs_H),tc_nat) ),
inference(paramodulation,[status(thm)],[f25933,f5637]) ).
fof(f26040,plain,
( ~ sQ443_spl
| c_less(c_0,v_sko__urX(v_evs),tc_nat) ),
inference(paramodulation,[status(thm)],[f25933,f3028]) ).
fof(f26053,plain,
( ~ sQ443_spl
| c_less(v_sko__urX(v_evs_H),v_sko__urX(v_evs),tc_nat) ),
inference(paramodulation,[status(thm)],[f25933,f3026]) ).
fof(f26055,definition,
( sQ445_spl
<=> c_Parity_Oeven(v_sko__urX(v_evs),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ445_spl])],[split_symbol_definition]) ).
fof(f26057,plain,
( sQ445_spl
| ~ c_Parity_Oeven(v_sko__urX(v_evs),tc_nat) ),
inference(component_clause,[status(thm)],[f26055]) ).
fof(f26059,plain,
( ~ sQ443_spl
| ~ sQ445_spl
| ~ sQ444_spl ),
inference(split_clause,[status(thm)],[f26039,f25961,f26055,f25932]) ).
fof(f26060,plain,
! [X0] :
( ~ sQ437_spl
| c_less(X0,v_sko__urX(v_evs_H),tc_nat)
| ~ c_lessequals(X0,v_sko__urX(v_evs),tc_nat) ),
inference(paramodulation,[status(thm)],[f25875,f6526]) ).
fof(f26061,plain,
! [X0] :
( ~ sQ437_spl
| c_lessequals(X0,v_sko__urX(v_evs),tc_nat)
| ~ c_less(X0,v_sko__urX(v_evs_H),tc_nat) ),
inference(paramodulation,[status(thm)],[f25875,f6525]) ).
fof(f26066,plain,
( ~ sQ437_spl
| c_less(c_0,v_sko__urX(v_evs_H),tc_nat) ),
inference(paramodulation,[status(thm)],[f25875,f3028]) ).
fof(f26069,plain,
! [X0] :
( ~ sQ437_spl
| c_less(X0,v_sko__urX(v_evs),tc_nat)
| ~ c_less(c_Suc(X0),v_sko__urX(v_evs_H),tc_nat) ),
inference(paramodulation,[status(thm)],[f25875,f5277]) ).
fof(f26070,plain,
! [X0] :
( ~ sQ437_spl
| c_less(v_sko__urX(v_evs),X0,tc_nat)
| ~ c_less(v_sko__urX(v_evs_H),c_Suc(X0),tc_nat) ),
inference(paramodulation,[status(thm)],[f25875,f5277]) ).
fof(f26072,plain,
! [X0] :
( ~ sQ437_spl
| c_lessequals(v_sko__urX(v_evs_H),c_Suc(X0),tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat) ),
inference(paramodulation,[status(thm)],[f25875,f5276]) ).
fof(f26076,plain,
( ~ sQ437_spl
| c_lessequals(v_sko__urX(v_evs),v_sko__urX(v_evs_H),tc_nat) ),
inference(paramodulation,[status(thm)],[f25875,f13873]) ).
fof(f26077,plain,
( ~ sQ437_spl
| ~ c_less(v_sko__urX(v_evs_H),v_sko__urX(v_evs),tc_nat) ),
inference(paramodulation,[status(thm)],[f25875,f11118]) ).
fof(f26083,plain,
( ~ sQ437_spl
| ~ sQ443_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f26077,f26053]) ).
fof(f26084,plain,
( ~ sQ437_spl
| ~ sQ443_spl ),
inference(contradiction_clause,[status(thm)],[f26083]) ).
fof(f26085,plain,
( ~ sQ442_spl
| ~ sQ443_spl
| c_Suc(v_sko__urX(v_evs)) = v_sko__urX(v_evs) ),
inference(forward_demodulation,[status(thm)],[f25933,f25929]) ).
fof(f26127,plain,
( ~ sQ442_spl
| ~ sQ443_spl
| c_less(v_sko__urX(v_evs),v_sko__urX(v_evs),tc_nat) ),
inference(paramodulation,[status(thm)],[f26085,f3026]) ).
fof(f26131,plain,
( ~ sQ442_spl
| ~ sQ443_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f26127,f3027]) ).
fof(f26132,plain,
( ~ sQ442_spl
| ~ sQ443_spl ),
inference(contradiction_clause,[status(thm)],[f26131]) ).
fof(f26144,plain,
( sQ443_spl
| ~ sQ442_spl
| v_sko__urX(v_evs) != c_Suc(v_sko__urX(v_evs)) ),
inference(forward_demodulation,[status(thm)],[f25929,f25934]) ).
fof(f26235,definition,
( sQ448_spl
<=> c_Suc(v_sko__urX(v_evs)) = v_sko__urX(v_evs) ),
introduced(definition,[new_symbols(definition,[sQ448_spl])],[split_symbol_definition]) ).
fof(f26236,plain,
( ~ sQ448_spl
| c_Suc(v_sko__urX(v_evs)) = v_sko__urX(v_evs) ),
inference(component_clause,[status(thm)],[f26235]) ).
fof(f26247,plain,
( ~ sQ448_spl
| sQ443_spl
| ~ sQ442_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f26236,f26144]) ).
fof(f26248,plain,
( ~ sQ448_spl
| sQ443_spl
| ~ sQ442_spl ),
inference(contradiction_clause,[status(thm)],[f26247]) ).
fof(f26470,plain,
! [X0,X1,X2] :
( c_less(X1,c_Divides_Oop_Amod(X2,c_Orderings_Omax(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ class_Orderings_Olinorder(tc_IntDef_Oint)
| ~ c_less(c_Orderings_Omax(X0,X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f4509,f5600]) ).
fof(f26471,plain,
! [X0,X1,X2] :
( c_less(X0,c_Divides_Oop_Amod(X2,c_Orderings_Omax(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ class_Orderings_Olinorder(tc_IntDef_Oint)
| ~ c_less(c_Orderings_Omax(X0,X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f4509,f5598]) ).
fof(f26472,definition,
! [X0,X1,X2] :
( sQ451_spl
<=> ( c_less(X1,c_Divides_Oop_Amod(X2,c_Orderings_Omax(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Orderings_Omax(X0,X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ451_spl])],[split_symbol_definition]) ).
fof(f26475,plain,
( ~ sQ254_spl
| sQ451_spl ),
inference(split_clause,[status(thm)],[f26470,f26472,f18961]) ).
fof(f26476,definition,
! [X0,X1,X2] :
( sQ452_spl
<=> ( c_less(X0,c_Divides_Oop_Amod(X2,c_Orderings_Omax(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Orderings_Omax(X0,X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ452_spl])],[split_symbol_definition]) ).
fof(f26479,plain,
( ~ sQ254_spl
| sQ452_spl ),
inference(split_clause,[status(thm)],[f26471,f26476,f18961]) ).
fof(f26507,definition,
! [X0] :
( sQ457_spl
<=> c_lessequals(X0,c_Suc(v_sko__urX(v_evs)),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ457_spl])],[split_symbol_definition]) ).
fof(f26508,plain,
! [X0] :
( ~ sQ457_spl
| c_lessequals(X0,c_Suc(v_sko__urX(v_evs)),tc_nat) ),
inference(component_clause,[status(thm)],[f26507]) ).
fof(f26525,definition,
( sQ460_spl
<=> c_lessequals(v_sko__urX(v_evs),v_sko__urX(v_evs),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ460_spl])],[split_symbol_definition]) ).
fof(f26527,plain,
( sQ460_spl
| ~ c_lessequals(v_sko__urX(v_evs),v_sko__urX(v_evs),tc_nat) ),
inference(component_clause,[status(thm)],[f26525]) ).
fof(f26536,plain,
! [X0] :
( ~ sQ457_spl
| c_lessequals(X0,v_sko__urX(v_evs),tc_nat) ),
inference(resolution,[status(thm)],[f26508,f5275]) ).
fof(f26541,plain,
! [X0] :
( ~ sQ457_spl
| c_lessequals(X0,v_sko__urX(v_evs),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f26536,f5619]) ).
fof(f26544,definition,
! [X0] :
( sQ462_spl
<=> c_lessequals(X0,v_sko__urX(v_evs),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ462_spl])],[split_symbol_definition]) ).
fof(f26545,plain,
! [X0] :
( ~ sQ462_spl
| c_lessequals(X0,v_sko__urX(v_evs),tc_nat) ),
inference(component_clause,[status(thm)],[f26544]) ).
fof(f26547,plain,
( ~ sQ457_spl
| sQ462_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f26541,f9098,f26544,f26507]) ).
fof(f26619,plain,
! [X0] :
( ~ sQ173_spl
| c_lessequals(X0,c_List_Olists(c_List_Olists(c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg),tc_List_Olist(tc_Message_Omsg)),tc_set(tc_List_Olist(tc_List_Olist(tc_Message_Omsg))))
| ~ class_Orderings_Olinorder(tc_set(tc_List_Olist(tc_List_Olist(tc_Message_Omsg)))) ),
inference(resolution,[status(thm)],[f25633,f5619]) ).
fof(f26623,definition,
( sQ465_spl
<=> class_Orderings_Olinorder(tc_set(tc_List_Olist(tc_List_Olist(tc_Message_Omsg)))) ),
introduced(definition,[new_symbols(definition,[sQ465_spl])],[split_symbol_definition]) ).
fof(f26626,definition,
! [X0] :
( sQ466_spl
<=> c_lessequals(X0,c_List_Olists(c_List_Olists(c_Message_Oparts(c_IntDef_ONats),tc_Message_Omsg),tc_List_Olist(tc_Message_Omsg)),tc_set(tc_List_Olist(tc_List_Olist(tc_Message_Omsg)))) ),
introduced(definition,[new_symbols(definition,[sQ466_spl])],[split_symbol_definition]) ).
fof(f26629,plain,
( ~ sQ173_spl
| sQ466_spl
| ~ sQ465_spl ),
inference(split_clause,[status(thm)],[f26619,f26623,f26626,f14366]) ).
fof(f26903,plain,
! [X0,X1] :
( ~ sQ441_spl
| ~ sQ439_spl
| c_Orderings_Omax(v_sko__urX(v_evs),X1,tc_nat) = v_sko__urX(v_evs)
| c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| ~ c_lessequals(c_Suc(v_sko__urX(v_evs)),X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(paramodulation,[status(thm)],[f25988,f5617]) ).
fof(f26907,definition,
! [X0] :
( sQ467_spl
<=> c_Orderings_Omax(v_sko__urX(v_evs),X0,tc_nat) = v_sko__urX(v_evs) ),
introduced(definition,[new_symbols(definition,[sQ467_spl])],[split_symbol_definition]) ).
fof(f26908,plain,
! [X0] :
( ~ sQ467_spl
| c_Orderings_Omax(v_sko__urX(v_evs),X0,tc_nat) = v_sko__urX(v_evs) ),
inference(component_clause,[status(thm)],[f26907]) ).
fof(f26920,definition,
! [X0] :
( sQ470_spl
<=> ( c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| ~ c_lessequals(c_Suc(v_sko__urX(v_evs)),X0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ470_spl])],[split_symbol_definition]) ).
fof(f26921,plain,
! [X0] :
( ~ sQ470_spl
| c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| ~ c_lessequals(c_Suc(v_sko__urX(v_evs)),X0,tc_nat) ),
inference(component_clause,[status(thm)],[f26920]) ).
fof(f26923,plain,
( ~ sQ441_spl
| ~ sQ439_spl
| sQ467_spl
| sQ470_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f26903,f9098,f26920,f26907,f25881,f25924]) ).
fof(f26945,plain,
! [X0,X1] :
( ~ sQ467_spl
| c_less(X1,X0,tc_nat)
| ~ c_less(v_sko__urX(v_evs),X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(paramodulation,[status(thm)],[f26908,f5600]) ).
fof(f26949,definition,
! [X0,X1] :
( sQ473_spl
<=> ( c_lessequals(X1,X0,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ473_spl])],[split_symbol_definition]) ).
fof(f26950,plain,
! [X0,X1] :
( ~ sQ473_spl
| c_lessequals(X1,X0,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat) ),
inference(component_clause,[status(thm)],[f26949]) ).
fof(f26957,definition,
! [X0,X1] :
( sQ475_spl
<=> ( c_less(X1,X0,tc_nat)
| ~ c_less(v_sko__urX(v_evs),X0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ475_spl])],[split_symbol_definition]) ).
fof(f26958,plain,
! [X0,X1] :
( ~ sQ475_spl
| c_less(X1,X0,tc_nat)
| ~ c_less(v_sko__urX(v_evs),X0,tc_nat) ),
inference(component_clause,[status(thm)],[f26957]) ).
fof(f26960,plain,
( ~ sQ467_spl
| sQ475_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f26945,f9098,f26957,f26907]) ).
fof(f26971,plain,
! [X0] :
( ~ sQ473_spl
| c_lessequals(X0,c_Suc(v_sko__urX(v_evs)),tc_nat) ),
inference(resolution,[status(thm)],[f26950,f13873]) ).
fof(f27098,plain,
! [X0] :
( ~ sQ473_spl
| c_lessequals(X0,c_Suc(v_sko__urX(v_evs)),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(resolution,[status(thm)],[f26971,f5619]) ).
fof(f27104,plain,
( ~ sQ473_spl
| sQ457_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f27098,f9098,f26507,f26949]) ).
fof(f27120,plain,
! [X0] :
( ~ sQ475_spl
| c_less(X0,c_Suc(v_sko__urX(v_evs)),tc_nat) ),
inference(resolution,[status(thm)],[f26958,f3026]) ).
fof(f27125,plain,
( ~ sQ475_spl
| $false ),
inference(resolution,[status(thm)],[f27120,f11118]) ).
fof(f27136,plain,
~ sQ475_spl,
inference(contradiction_clause,[status(thm)],[f27125]) ).
fof(f27155,plain,
( ~ sQ470_spl
| c_lessequals(v_sko__urX(v_evs),c_Suc(c_Suc(v_sko__urX(v_evs))),tc_nat) ),
inference(resolution,[status(thm)],[f26921,f13873]) ).
fof(f27173,plain,
( ~ sQ430_spl
| ~ sQ433_spl
| ~ sQ439_spl
| ~ sQ470_spl
| c_Suc(c_Suc(v_sko__urX(v_evs))) = c_Suc(v_sko__urX(v_evs))
| c_Suc(c_Suc(v_sko__urX(v_evs))) = v_sko__urX(v_evs) ),
inference(resolution,[status(thm)],[f27155,f25993]) ).
fof(f27182,definition,
( sQ492_spl
<=> c_Suc(c_Suc(v_sko__urX(v_evs))) = v_sko__urX(v_evs) ),
introduced(definition,[new_symbols(definition,[sQ492_spl])],[split_symbol_definition]) ).
fof(f27183,plain,
( ~ sQ492_spl
| c_Suc(c_Suc(v_sko__urX(v_evs))) = v_sko__urX(v_evs) ),
inference(component_clause,[status(thm)],[f27182]) ).
fof(f27184,plain,
( sQ492_spl
| c_Suc(c_Suc(v_sko__urX(v_evs))) != v_sko__urX(v_evs) ),
inference(component_clause,[status(thm)],[f27182]) ).
fof(f27185,definition,
( sQ493_spl
<=> c_Suc(c_Suc(v_sko__urX(v_evs))) = c_Suc(v_sko__urX(v_evs)) ),
introduced(definition,[new_symbols(definition,[sQ493_spl])],[split_symbol_definition]) ).
fof(f27186,plain,
( ~ sQ493_spl
| c_Suc(c_Suc(v_sko__urX(v_evs))) = c_Suc(v_sko__urX(v_evs)) ),
inference(component_clause,[status(thm)],[f27185]) ).
fof(f27187,plain,
( sQ493_spl
| c_Suc(c_Suc(v_sko__urX(v_evs))) != c_Suc(v_sko__urX(v_evs)) ),
inference(component_clause,[status(thm)],[f27185]) ).
fof(f27188,plain,
( ~ sQ430_spl
| ~ sQ433_spl
| ~ sQ439_spl
| ~ sQ470_spl
| sQ493_spl
| sQ492_spl ),
inference(split_clause,[status(thm)],[f27173,f27182,f27185,f26920,f25881,f25849,f25839]) ).
fof(f27210,plain,
( ~ sQ492_spl
| ~ c_less(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs)),tc_nat) ),
inference(paramodulation,[status(thm)],[f27183,f11118]) ).
fof(f27221,plain,
( ~ sQ492_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f27210,f3026]) ).
fof(f27222,plain,
~ sQ492_spl,
inference(contradiction_clause,[status(thm)],[f27221]) ).
fof(f27246,plain,
( ~ sQ493_spl
| c_less(c_Suc(v_sko__urX(v_evs)),c_Suc(v_sko__urX(v_evs)),tc_nat) ),
inference(paramodulation,[status(thm)],[f27186,f3026]) ).
fof(f27250,plain,
( ~ sQ493_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f27246,f3027]) ).
fof(f27251,plain,
~ sQ493_spl,
inference(contradiction_clause,[status(thm)],[f27250]) ).
fof(f27252,plain,
! [X0] :
( ~ sQ434_spl
| ~ sQ439_spl
| c_Orderings_Omax(X0,v_sko__urX(v_evs),tc_nat) = v_sko__urX(v_evs)
| c_Orderings_Omax(X0,v_sko__urX(v_evs),tc_nat) = v_sko__urX(v_evs_H_H) ),
inference(forward_demodulation,[status(thm)],[f25882,f25864]) ).
fof(f27255,plain,
! [X0,X1,X2] :
( ~ sQ439_spl
| ~ c_lessequals(v_sko__urX(v_evs),X1,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),X2,tc_nat)
| X1 = X2
| X2 = X0
| X1 = X0
| ~ c_lessequals(v_sko__urX(v_evs_H_H),X0,tc_nat) ),
inference(forward_demodulation,[status(thm)],[f25882,f25800]) ).
fof(f27257,plain,
! [X0] :
( ~ sQ430_spl
| ~ sQ439_spl
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| X0 = c_Suc(v_sko__urX(v_evs))
| X0 = v_sko__urX(v_evs_H_H) ),
inference(forward_demodulation,[status(thm)],[f25882,f25840]) ).
fof(f27272,plain,
! [X0] :
( ~ sQ432_spl
| ~ sQ439_spl
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| X0 = v_sko__urX(v_evs)
| X0 = v_sko__urX(v_evs_H_H) ),
inference(forward_demodulation,[status(thm)],[f25882,f25847]) ).
fof(f27277,plain,
( sQ443_spl
| ~ sQ439_spl
| v_sko__urX(v_evs) != c_Suc(v_sko__urX(v_evs)) ),
inference(forward_demodulation,[status(thm)],[f25882,f25934]) ).
fof(f27278,plain,
( sQ442_spl
| ~ sQ439_spl
| c_Suc(v_sko__urX(v_evs)) != c_Suc(v_sko__urX(v_evs)) ),
inference(forward_demodulation,[status(thm)],[f25882,f25930]) ).
fof(f27279,plain,
( sQ442_spl
| ~ sQ439_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f27278]) ).
fof(f27280,plain,
( sQ442_spl
| ~ sQ439_spl ),
inference(contradiction_clause,[status(thm)],[f27279]) ).
fof(f27281,plain,
( sQ493_spl
| ~ sQ437_spl
| c_Suc(c_Suc(v_sko__urX(v_evs))) != v_sko__urX(v_evs_H) ),
inference(backward_demodulation,[status(thm)],[f25875,f27187]) ).
fof(f27283,plain,
! [X0] :
( ~ sQ437_spl
| ~ sQ462_spl
| c_less(X0,v_sko__urX(v_evs_H),tc_nat) ),
inference(forward_subsumption_resolution,[status(thm)],[f26060,f26545]) ).
fof(f27284,plain,
! [X0] :
( ~ sQ437_spl
| ~ sQ462_spl
| c_less(X0,v_sko__urX(v_evs),tc_nat) ),
inference(forward_subsumption_resolution,[status(thm)],[f26069,f27283]) ).
fof(f27286,plain,
( ~ sQ437_spl
| ~ sQ462_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f26077,f27284]) ).
fof(f27287,plain,
( ~ sQ437_spl
| ~ sQ462_spl ),
inference(contradiction_clause,[status(thm)],[f27286]) ).
fof(f27294,plain,
! [X0] :
( ~ sQ432_spl
| ~ sQ438_spl
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| X0 = v_sko__urX(v_evs_H)
| X0 = v_sko__urX(v_evs) ),
inference(forward_demodulation,[status(thm)],[f25879,f25847]) ).
fof(f27316,plain,
! [X0] :
( ~ sQ430_spl
| ~ sQ438_spl
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| X0 = c_Suc(v_sko__urX(v_evs_H))
| X0 = v_sko__urX(v_evs) ),
inference(forward_demodulation,[status(thm)],[f25879,f25840]) ).
fof(f27323,plain,
( sQ493_spl
| ~ sQ437_spl
| c_Suc(v_sko__urX(v_evs_H)) != v_sko__urX(v_evs_H) ),
inference(forward_demodulation,[status(thm)],[f25875,f27281]) ).
fof(f27362,plain,
! [X0,X1,X2] :
( c_lessequals(c_Divides_Oop_Amod(X2,c_Orderings_Omin(X0,X1,tc_nat),tc_nat),X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| ~ c_less(c_0,c_Orderings_Omin(X0,X1,tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f4230,f5610]) ).
fof(f27363,plain,
! [X0,X1,X2] :
( c_lessequals(c_Divides_Oop_Amod(X2,c_Orderings_Omin(X0,X1,tc_nat),tc_nat),X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| ~ c_less(c_0,c_Orderings_Omin(X0,X1,tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f4230,f5608]) ).
fof(f27364,definition,
! [X0,X1,X2] :
( sQ495_spl
<=> ( c_lessequals(c_Divides_Oop_Amod(X2,c_Orderings_Omin(X0,X1,tc_nat),tc_nat),X1,tc_nat)
| ~ c_less(c_0,c_Orderings_Omin(X0,X1,tc_nat),tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ495_spl])],[split_symbol_definition]) ).
fof(f27367,plain,
( ~ sQ43_spl
| sQ495_spl ),
inference(split_clause,[status(thm)],[f27362,f27364,f9098]) ).
fof(f27368,definition,
! [X0,X1,X2] :
( sQ496_spl
<=> ( c_lessequals(c_Divides_Oop_Amod(X2,c_Orderings_Omin(X0,X1,tc_nat),tc_nat),X0,tc_nat)
| ~ c_less(c_0,c_Orderings_Omin(X0,X1,tc_nat),tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ496_spl])],[split_symbol_definition]) ).
fof(f27371,plain,
( ~ sQ43_spl
| sQ496_spl ),
inference(split_clause,[status(thm)],[f27363,f27368,f9098]) ).
fof(f27402,plain,
! [X0] :
( ~ sQ437_spl
| ~ class_Orderings_Olinorder(tc_nat)
| c_less(c_Orderings_Omin(X0,v_sko__urX(v_evs),tc_nat),v_sko__urX(v_evs_H),tc_nat) ),
inference(resolution,[status(thm)],[f26060,f19296]) ).
fof(f27403,plain,
! [X0] :
( ~ sQ437_spl
| ~ class_Orderings_Olinorder(tc_nat)
| c_less(c_Orderings_Omin(v_sko__urX(v_evs),X0,tc_nat),v_sko__urX(v_evs_H),tc_nat) ),
inference(resolution,[status(thm)],[f26060,f19192]) ).
fof(f27408,plain,
( ~ sQ437_spl
| ~ class_Orderings_Oorder(tc_nat)
| c_less(v_sko__urX(v_evs),v_sko__urX(v_evs_H),tc_nat) ),
inference(resolution,[status(thm)],[f26060,f3030]) ).
fof(f27412,definition,
( sQ498_spl
<=> c_less(c_0,v_sko__urX(v_evs),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ498_spl])],[split_symbol_definition]) ).
fof(f27414,plain,
( sQ498_spl
| ~ c_less(c_0,v_sko__urX(v_evs),tc_nat) ),
inference(component_clause,[status(thm)],[f27412]) ).
fof(f27416,definition,
! [X0] :
( sQ499_spl
<=> c_less(c_Orderings_Omin(X0,v_sko__urX(v_evs),tc_nat),v_sko__urX(v_evs_H),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ499_spl])],[split_symbol_definition]) ).
fof(f27419,plain,
( ~ sQ437_spl
| ~ sQ43_spl
| sQ499_spl ),
inference(split_clause,[status(thm)],[f27402,f27416,f9098,f25874]) ).
fof(f27420,definition,
! [X0] :
( sQ500_spl
<=> c_less(c_Orderings_Omin(v_sko__urX(v_evs),X0,tc_nat),v_sko__urX(v_evs_H),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ500_spl])],[split_symbol_definition]) ).
fof(f27423,plain,
( ~ sQ437_spl
| ~ sQ43_spl
| sQ500_spl ),
inference(split_clause,[status(thm)],[f27403,f27420,f9098,f25874]) ).
fof(f27424,definition,
( sQ501_spl
<=> c_less(v_sko__urX(v_evs),v_sko__urX(v_evs_H),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ501_spl])],[split_symbol_definition]) ).
fof(f27427,plain,
( ~ sQ437_spl
| ~ sQ50_spl
| sQ501_spl ),
inference(split_clause,[status(thm)],[f27408,f27424,f10475,f25874]) ).
fof(f27439,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(c_Message_Oparts(X0)),c_Orderings_Omax(X1,c_Message_Oparts(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X2),X0,tc_Message_Omsg))),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f25042,f19368]) ).
fof(f27440,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(c_Message_Oparts(X0)),c_Orderings_Omax(c_Message_Oparts(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X0,tc_Message_Omsg))),X2,tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f25042,f19329]) ).
fof(f27443,plain,
! [X0,X1] :
( ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(c_Message_Oparts(X0)),c_Message_Oparts(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X0,tc_Message_Omsg))),tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f25042,f3030]) ).
fof(f27454,definition,
! [X0,X1,X2] :
( sQ502_spl
<=> c_lessequals(c_Message_Oparts(c_Message_Oparts(X0)),c_Orderings_Omax(X1,c_Message_Oparts(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X2),X0,tc_Message_Omsg))),tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ502_spl])],[split_symbol_definition]) ).
fof(f27457,plain,
( ~ sQ384_spl
| sQ502_spl ),
inference(split_clause,[status(thm)],[f27439,f27454,f22360]) ).
fof(f27458,definition,
! [X0,X1,X2] :
( sQ503_spl
<=> c_lessequals(c_Message_Oparts(c_Message_Oparts(X0)),c_Orderings_Omax(c_Message_Oparts(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X0,tc_Message_Omsg))),X2,tc_set(tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ503_spl])],[split_symbol_definition]) ).
fof(f27461,plain,
( ~ sQ384_spl
| sQ503_spl ),
inference(split_clause,[status(thm)],[f27440,f27458,f22360]) ).
fof(f27462,definition,
! [X0,X1] :
( sQ504_spl
<=> c_lessequals(c_Message_Oparts(c_Message_Oparts(X0)),c_Message_Oparts(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),X0,tc_Message_Omsg))),tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ504_spl])],[split_symbol_definition]) ).
fof(f27465,plain,
( ~ sQ387_spl
| sQ504_spl ),
inference(split_clause,[status(thm)],[f27443,f27462,f22371]) ).
fof(f27484,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(tc_set(tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_Orderings_Omax(X1,c_Message_Oparts(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X2,tc_Message_Omsg))),tc_set(tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f25054,f19368]) ).
fof(f27485,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Olinorder(tc_set(tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_Orderings_Omax(c_Message_Oparts(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg))),X2,tc_set(tc_Message_Omsg)),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f25054,f19329]) ).
fof(f27488,plain,
! [X0,X1] :
( ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_Message_Oparts(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg))),tc_Message_Omsg) ),
inference(resolution,[status(thm)],[f25054,f3030]) ).
fof(f27499,definition,
! [X0,X1,X2] :
( sQ505_spl
<=> c_in(c_Message_Omsg_ONonce(X0),c_Orderings_Omax(X1,c_Message_Oparts(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X2,tc_Message_Omsg))),tc_set(tc_Message_Omsg)),tc_Message_Omsg) ),
introduced(definition,[new_symbols(definition,[sQ505_spl])],[split_symbol_definition]) ).
fof(f27502,plain,
( ~ sQ384_spl
| sQ505_spl ),
inference(split_clause,[status(thm)],[f27484,f27499,f22360]) ).
fof(f27503,definition,
! [X0,X1,X2] :
( sQ506_spl
<=> c_in(c_Message_Omsg_ONonce(X0),c_Orderings_Omax(c_Message_Oparts(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg))),X2,tc_set(tc_Message_Omsg)),tc_Message_Omsg) ),
introduced(definition,[new_symbols(definition,[sQ506_spl])],[split_symbol_definition]) ).
fof(f27506,plain,
( ~ sQ384_spl
| sQ506_spl ),
inference(split_clause,[status(thm)],[f27485,f27503,f22360]) ).
fof(f27507,definition,
! [X0,X1] :
( sQ507_spl
<=> c_in(c_Message_Omsg_ONonce(X0),c_Message_Oparts(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),X1,tc_Message_Omsg))),tc_Message_Omsg) ),
introduced(definition,[new_symbols(definition,[sQ507_spl])],[split_symbol_definition]) ).
fof(f27510,plain,
( ~ sQ387_spl
| sQ507_spl ),
inference(split_clause,[status(thm)],[f27488,f27507,f22371]) ).
fof(f27532,plain,
! [X0] :
( ~ sQ437_spl
| c_lessequals(c_Divides_Oop_Amod(X0,v_sko__urX(v_evs_H),tc_nat),v_sko__urX(v_evs),tc_nat)
| ~ c_less(c_0,v_sko__urX(v_evs_H),tc_nat) ),
inference(resolution,[status(thm)],[f4233,f26061]) ).
fof(f27534,plain,
! [X0,X1,X2] :
( c_less(c_Divides_Oop_Amod(X2,c_Orderings_Omin(X0,X1,tc_nat),tc_nat),X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| ~ c_less(c_0,c_Orderings_Omin(X0,X1,tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f4233,f5605]) ).
fof(f27535,plain,
! [X0,X1,X2] :
( c_less(c_Divides_Oop_Amod(X2,c_Orderings_Omin(X0,X1,tc_nat),tc_nat),X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| ~ c_less(c_0,c_Orderings_Omin(X0,X1,tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f4233,f5603]) ).
fof(f27537,definition,
( sQ508_spl
<=> c_less(c_0,v_sko__urX(v_evs_H),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ508_spl])],[split_symbol_definition]) ).
fof(f27539,plain,
( sQ508_spl
| ~ c_less(c_0,v_sko__urX(v_evs_H),tc_nat) ),
inference(component_clause,[status(thm)],[f27537]) ).
fof(f27540,definition,
! [X0] :
( sQ509_spl
<=> c_lessequals(c_Divides_Oop_Amod(X0,v_sko__urX(v_evs_H),tc_nat),v_sko__urX(v_evs),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ509_spl])],[split_symbol_definition]) ).
fof(f27543,plain,
( ~ sQ437_spl
| sQ509_spl
| ~ sQ508_spl ),
inference(split_clause,[status(thm)],[f27532,f27537,f27540,f25874]) ).
fof(f27545,definition,
! [X0,X1,X2] :
( sQ510_spl
<=> ( c_less(c_Divides_Oop_Amod(X2,c_Orderings_Omin(X0,X1,tc_nat),tc_nat),X1,tc_nat)
| ~ c_less(c_0,c_Orderings_Omin(X0,X1,tc_nat),tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ510_spl])],[split_symbol_definition]) ).
fof(f27548,plain,
( ~ sQ43_spl
| sQ510_spl ),
inference(split_clause,[status(thm)],[f27534,f27545,f9098]) ).
fof(f27549,definition,
! [X0,X1,X2] :
( sQ511_spl
<=> ( c_less(c_Divides_Oop_Amod(X2,c_Orderings_Omin(X0,X1,tc_nat),tc_nat),X0,tc_nat)
| ~ c_less(c_0,c_Orderings_Omin(X0,X1,tc_nat),tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ511_spl])],[split_symbol_definition]) ).
fof(f27552,plain,
( ~ sQ43_spl
| sQ511_spl ),
inference(split_clause,[status(thm)],[f27535,f27549,f9098]) ).
fof(f27553,plain,
( sQ508_spl
| ~ sQ437_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f27539,f26066]) ).
fof(f27554,plain,
( sQ508_spl
| ~ sQ437_spl ),
inference(contradiction_clause,[status(thm)],[f27553]) ).
fof(f27555,plain,
( sQ310_spl
| ~ c_less(c_0,c_0,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f4976,f19717]) ).
fof(f27557,plain,
( sQ310_spl
| ~ sQ35_spl
| ~ sQ306_spl ),
inference(split_clause,[status(thm)],[f27555,f19687,f8988,f19715]) ).
fof(f27615,plain,
( ~ sQ432_spl
| ~ sQ438_spl
| c_Suc(v_sko__urX(v_evs)) = v_sko__urX(v_evs_H)
| c_Suc(v_sko__urX(v_evs)) = v_sko__urX(v_evs) ),
inference(resolution,[status(thm)],[f27294,f13873]) ).
fof(f27632,plain,
( ~ sQ432_spl
| ~ sQ438_spl
| sQ437_spl
| sQ448_spl ),
inference(split_clause,[status(thm)],[f27615,f26235,f25874,f25878,f25846]) ).
fof(f27646,plain,
! [X0] :
( ~ sQ437_spl
| ~ c_lessequals(v_sko__urX(v_evs_H),X0,tc_nat)
| c_less(v_sko__urX(v_evs),X0,tc_nat) ),
inference(resolution,[status(thm)],[f26070,f6526]) ).
fof(f27652,plain,
! [X0] :
( ~ sQ437_spl
| ~ class_Orderings_Olinorder(tc_nat)
| c_less(v_sko__urX(v_evs),c_Orderings_Omax(X0,v_sko__urX(v_evs_H),tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f27646,f19368]) ).
fof(f27653,plain,
! [X0] :
( ~ sQ437_spl
| ~ class_Orderings_Olinorder(tc_nat)
| c_less(v_sko__urX(v_evs),c_Orderings_Omax(v_sko__urX(v_evs_H),X0,tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f27646,f19329]) ).
fof(f27659,definition,
! [X0] :
( sQ522_spl
<=> c_less(v_sko__urX(v_evs),c_Orderings_Omax(X0,v_sko__urX(v_evs_H),tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ522_spl])],[split_symbol_definition]) ).
fof(f27662,plain,
( ~ sQ437_spl
| ~ sQ43_spl
| sQ522_spl ),
inference(split_clause,[status(thm)],[f27652,f27659,f9098,f25874]) ).
fof(f27663,definition,
! [X0] :
( sQ523_spl
<=> c_less(v_sko__urX(v_evs),c_Orderings_Omax(v_sko__urX(v_evs_H),X0,tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ523_spl])],[split_symbol_definition]) ).
fof(f27666,plain,
( ~ sQ437_spl
| ~ sQ43_spl
| sQ523_spl ),
inference(split_clause,[status(thm)],[f27653,f27663,f9098,f25874]) ).
fof(f27676,plain,
( ~ sQ437_spl
| c_lessequals(v_sko__urX(v_evs_H),v_sko__urX(v_evs_H),tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),v_sko__urX(v_evs),tc_nat) ),
inference(paramodulation,[status(thm)],[f25875,f26072]) ).
fof(f27677,definition,
( sQ524_spl
<=> c_lessequals(v_sko__urX(v_evs_H),v_sko__urX(v_evs_H),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ524_spl])],[split_symbol_definition]) ).
fof(f27680,plain,
( ~ sQ437_spl
| sQ524_spl
| ~ sQ460_spl ),
inference(split_clause,[status(thm)],[f27676,f26525,f27677,f25874]) ).
fof(f27681,plain,
( sQ460_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f26527,f8954]) ).
fof(f27682,plain,
sQ460_spl,
inference(contradiction_clause,[status(thm)],[f27681]) ).
fof(f27716,plain,
! [X0] :
( c_in(c_Message_Oparts(c_Message_Oparts(c_emptyset)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f8448,f25064]) ).
fof(f27722,definition,
! [X0] :
( sQ525_spl
<=> ~ c_in(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ525_spl])],[split_symbol_definition]) ).
fof(f27723,plain,
! [X0] :
( ~ sQ525_spl
| ~ c_in(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(component_clause,[status(thm)],[f27722]) ).
fof(f27725,definition,
( sQ526_spl
<=> c_in(c_Message_Oparts(c_Message_Oparts(c_emptyset)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ526_spl])],[split_symbol_definition]) ).
fof(f27728,plain,
( sQ526_spl
| sQ525_spl ),
inference(split_clause,[status(thm)],[f27716,f27722,f27725]) ).
fof(f27731,plain,
! [X0] :
( ~ sQ525_spl
| ~ c_in(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(forward_demodulation,[status(thm)],[f8448,f27723]) ).
fof(f27732,plain,
( ~ sQ525_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f27731,f8496]) ).
fof(f27733,plain,
( ~ sQ525_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f27732]) ).
fof(f27769,plain,
( ~ sQ437_spl
| ~ sQ430_spl
| ~ sQ438_spl
| v_sko__urX(v_evs_H) = c_Suc(v_sko__urX(v_evs_H))
| v_sko__urX(v_evs_H) = v_sko__urX(v_evs) ),
inference(resolution,[status(thm)],[f27316,f26076]) ).
fof(f27774,plain,
( ~ sQ430_spl
| ~ sQ438_spl
| c_Suc(v_sko__urX(v_evs)) = c_Suc(v_sko__urX(v_evs_H))
| c_Suc(v_sko__urX(v_evs)) = v_sko__urX(v_evs) ),
inference(resolution,[status(thm)],[f27316,f13873]) ).
fof(f27779,definition,
( sQ527_spl
<=> v_sko__urX(v_evs_H) = c_Suc(v_sko__urX(v_evs_H)) ),
introduced(definition,[new_symbols(definition,[sQ527_spl])],[split_symbol_definition]) ).
fof(f27780,plain,
( ~ sQ527_spl
| v_sko__urX(v_evs_H) = c_Suc(v_sko__urX(v_evs_H)) ),
inference(component_clause,[status(thm)],[f27779]) ).
fof(f27782,plain,
( ~ sQ437_spl
| ~ sQ430_spl
| ~ sQ438_spl
| sQ527_spl
| sQ439_spl ),
inference(split_clause,[status(thm)],[f27769,f25881,f27779,f25878,f25839,f25874]) ).
fof(f27791,plain,
( ~ sQ430_spl
| ~ sQ438_spl
| sQ442_spl
| sQ448_spl ),
inference(split_clause,[status(thm)],[f27774,f26235,f25928,f25878,f25839]) ).
fof(f27794,plain,
( ~ sQ431_spl
| ~ sQ438_spl
| c_Suc(v_sko__urX(v_evs_H)) = v_sko__urX(v_evs) ),
inference(forward_demodulation,[status(thm)],[f25879,f25843]) ).
fof(f27795,plain,
( ~ sQ431_spl
| ~ sQ438_spl
| sQ443_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f27794,f25934]) ).
fof(f27796,plain,
( ~ sQ431_spl
| ~ sQ438_spl
| sQ443_spl ),
inference(contradiction_clause,[status(thm)],[f27795]) ).
fof(f27836,plain,
( ~ sQ437_spl
| ~ sQ439_spl
| sQ448_spl ),
inference(split_clause,[status(thm)],[f25970,f26235,f25881,f25874]) ).
fof(f27839,plain,
( sQ443_spl
| ~ sQ439_spl
| ~ sQ437_spl
| v_sko__urX(v_evs) != v_sko__urX(v_evs_H) ),
inference(forward_demodulation,[status(thm)],[f25875,f27277]) ).
fof(f27840,plain,
( sQ443_spl
| ~ sQ439_spl
| ~ sQ437_spl
| v_sko__urX(v_evs) != v_sko__urX(v_evs) ),
inference(forward_demodulation,[status(thm)],[f25882,f27839]) ).
fof(f27841,plain,
( sQ443_spl
| ~ sQ439_spl
| ~ sQ437_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f27840]) ).
fof(f27842,plain,
( sQ443_spl
| ~ sQ439_spl
| ~ sQ437_spl ),
inference(contradiction_clause,[status(thm)],[f27841]) ).
fof(f27891,plain,
( ~ sQ527_spl
| sQ493_spl
| ~ sQ437_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f27780,f27323]) ).
fof(f27892,plain,
( ~ sQ527_spl
| sQ493_spl
| ~ sQ437_spl ),
inference(contradiction_clause,[status(thm)],[f27891]) ).
fof(f27900,plain,
! [X0] :
( ~ sQ430_spl
| ~ sQ439_spl
| ~ sQ436_spl
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| X0 = v_sko__urX(v_evs_H_H)
| X0 = v_sko__urX(v_evs_H_H) ),
inference(forward_demodulation,[status(thm)],[f25872,f27257]) ).
fof(f27901,plain,
! [X0] :
( ~ sQ430_spl
| ~ sQ439_spl
| ~ sQ436_spl
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| X0 = v_sko__urX(v_evs_H_H) ),
inference(duplicate_literals_removal,[status(thm)],[f27900]) ).
fof(f27902,plain,
( sQ493_spl
| ~ sQ436_spl
| c_Suc(v_sko__urX(v_evs_H_H)) != c_Suc(v_sko__urX(v_evs)) ),
inference(forward_demodulation,[status(thm)],[f25872,f27187]) ).
fof(f27903,plain,
( sQ493_spl
| ~ sQ436_spl
| c_Suc(v_sko__urX(v_evs_H_H)) != v_sko__urX(v_evs_H_H) ),
inference(forward_demodulation,[status(thm)],[f25872,f27902]) ).
fof(f27904,plain,
( sQ492_spl
| ~ sQ436_spl
| c_Suc(v_sko__urX(v_evs_H_H)) != v_sko__urX(v_evs) ),
inference(forward_demodulation,[status(thm)],[f25872,f27184]) ).
fof(f27937,plain,
! [X0] :
( ~ sQ436_spl
| c_less(X0,v_sko__urX(v_evs_H_H),tc_nat)
| ~ c_lessequals(X0,v_sko__urX(v_evs),tc_nat) ),
inference(paramodulation,[status(thm)],[f25872,f6526]) ).
fof(f27938,plain,
! [X0] :
( ~ sQ436_spl
| c_lessequals(X0,v_sko__urX(v_evs),tc_nat)
| ~ c_less(X0,v_sko__urX(v_evs_H_H),tc_nat) ),
inference(paramodulation,[status(thm)],[f25872,f6525]) ).
fof(f27941,plain,
( ~ sQ436_spl
| c_Parity_Oeven(v_sko__urX(v_evs_H_H),tc_nat)
| c_Parity_Oeven(v_sko__urX(v_evs),tc_nat) ),
inference(paramodulation,[status(thm)],[f25872,f5638]) ).
fof(f27942,plain,
( ~ sQ436_spl
| ~ c_Parity_Oeven(v_sko__urX(v_evs_H_H),tc_nat)
| ~ c_Parity_Oeven(v_sko__urX(v_evs),tc_nat) ),
inference(paramodulation,[status(thm)],[f25872,f5637]) ).
fof(f27943,plain,
( ~ sQ436_spl
| c_less(c_0,v_sko__urX(v_evs_H_H),tc_nat) ),
inference(paramodulation,[status(thm)],[f25872,f3028]) ).
fof(f27946,plain,
! [X0] :
( ~ sQ436_spl
| c_less(X0,v_sko__urX(v_evs),tc_nat)
| ~ c_less(c_Suc(X0),v_sko__urX(v_evs_H_H),tc_nat) ),
inference(paramodulation,[status(thm)],[f25872,f5277]) ).
fof(f27947,plain,
! [X0] :
( ~ sQ436_spl
| c_less(v_sko__urX(v_evs),X0,tc_nat)
| ~ c_less(v_sko__urX(v_evs_H_H),c_Suc(X0),tc_nat) ),
inference(paramodulation,[status(thm)],[f25872,f5277]) ).
fof(f27949,plain,
! [X0] :
( ~ sQ436_spl
| c_lessequals(v_sko__urX(v_evs_H_H),c_Suc(X0),tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat) ),
inference(paramodulation,[status(thm)],[f25872,f5276]) ).
fof(f27954,plain,
( ~ sQ436_spl
| ~ c_less(v_sko__urX(v_evs_H_H),v_sko__urX(v_evs),tc_nat) ),
inference(paramodulation,[status(thm)],[f25872,f11118]) ).
fof(f27958,plain,
! [X0] :
( ~ sQ436_spl
| ~ sQ462_spl
| c_less(X0,v_sko__urX(v_evs_H_H),tc_nat) ),
inference(forward_subsumption_resolution,[status(thm)],[f27937,f26545]) ).
fof(f27959,definition,
( sQ530_spl
<=> c_Parity_Oeven(v_sko__urX(v_evs_H_H),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ530_spl])],[split_symbol_definition]) ).
fof(f27960,plain,
( ~ sQ530_spl
| c_Parity_Oeven(v_sko__urX(v_evs_H_H),tc_nat) ),
inference(component_clause,[status(thm)],[f27959]) ).
fof(f27962,plain,
( ~ sQ436_spl
| sQ530_spl
| sQ445_spl ),
inference(split_clause,[status(thm)],[f27941,f26055,f27959,f25871]) ).
fof(f27963,plain,
( ~ sQ436_spl
| ~ sQ530_spl
| ~ sQ445_spl ),
inference(split_clause,[status(thm)],[f27942,f26055,f27959,f25871]) ).
fof(f27964,plain,
! [X0] :
( ~ sQ436_spl
| ~ sQ462_spl
| c_less(X0,v_sko__urX(v_evs),tc_nat) ),
inference(forward_subsumption_resolution,[status(thm)],[f27946,f27958]) ).
fof(f27966,plain,
( ~ sQ436_spl
| ~ sQ462_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f27954,f27964]) ).
fof(f27967,plain,
( ~ sQ436_spl
| ~ sQ462_spl ),
inference(contradiction_clause,[status(thm)],[f27966]) ).
fof(f28066,plain,
! [X0,X1] :
( ~ c_less(c_0,X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_less(c_0,X1,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(resolution,[status(thm)],[f4975,f4976]) ).
fof(f28067,plain,
( sQ37_spl
| sQ342_spl ),
inference(split_clause,[status(thm)],[f28066,f20108,f8996]) ).
fof(f28070,plain,
( ~ sQ342_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f3214,f28072]) ).
fof(f28072,plain,
! [X0] :
( ~ sQ342_spl
| ~ class_Ring__and__Field_Oordered__semidom(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f20109]) ).
fof(f28075,plain,
~ sQ342_spl,
inference(contradiction_clause,[status(thm)],[f28070]) ).
fof(f28084,plain,
( ~ sQ430_spl
| ~ sQ439_spl
| ~ sQ436_spl
| v_sko__urX(v_evs) = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f27901,f8954]) ).
fof(f28098,plain,
( ~ sQ430_spl
| ~ sQ439_spl
| ~ sQ436_spl
| sQ438_spl ),
inference(split_clause,[status(thm)],[f28084,f25878,f25871,f25881,f25839]) ).
fof(f28113,plain,
! [X0] :
( ~ sQ436_spl
| ~ c_less(c_0,v_sko__urX(v_evs_H_H),tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X0,v_sko__urX(v_evs_H_H),tc_nat),v_sko__urX(v_evs),tc_nat) ),
inference(resolution,[status(thm)],[f27938,f4233]) ).
fof(f28115,definition,
! [X0] :
( sQ535_spl
<=> c_lessequals(c_Divides_Oop_Amod(X0,v_sko__urX(v_evs_H_H),tc_nat),v_sko__urX(v_evs),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ535_spl])],[split_symbol_definition]) ).
fof(f28118,definition,
( sQ536_spl
<=> c_less(c_0,v_sko__urX(v_evs_H_H),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ536_spl])],[split_symbol_definition]) ).
fof(f28120,plain,
( sQ536_spl
| ~ c_less(c_0,v_sko__urX(v_evs_H_H),tc_nat) ),
inference(component_clause,[status(thm)],[f28118]) ).
fof(f28121,plain,
( ~ sQ436_spl
| ~ sQ536_spl
| sQ535_spl ),
inference(split_clause,[status(thm)],[f28113,f28115,f28118,f25871]) ).
fof(f28123,plain,
! [X0] :
( ~ sQ436_spl
| ~ c_less(c_0,v_sko__urX(v_evs),tc_nat)
| c_less(c_Divides_Oop_Amod(X0,v_sko__urX(v_evs),tc_nat),v_sko__urX(v_evs_H_H),tc_nat) ),
inference(resolution,[status(thm)],[f27937,f4230]) ).
fof(f28126,plain,
! [X0] :
( ~ sQ436_spl
| ~ class_Orderings_Olinorder(tc_nat)
| c_less(c_Orderings_Omin(X0,v_sko__urX(v_evs),tc_nat),v_sko__urX(v_evs_H_H),tc_nat) ),
inference(resolution,[status(thm)],[f27937,f19296]) ).
fof(f28127,plain,
! [X0] :
( ~ sQ436_spl
| ~ class_Orderings_Olinorder(tc_nat)
| c_less(c_Orderings_Omin(v_sko__urX(v_evs),X0,tc_nat),v_sko__urX(v_evs_H_H),tc_nat) ),
inference(resolution,[status(thm)],[f27937,f19192]) ).
fof(f28132,plain,
( ~ sQ436_spl
| ~ class_Orderings_Oorder(tc_nat)
| c_less(v_sko__urX(v_evs),v_sko__urX(v_evs_H_H),tc_nat) ),
inference(resolution,[status(thm)],[f27937,f3030]) ).
fof(f28133,definition,
! [X0] :
( sQ537_spl
<=> c_less(c_Divides_Oop_Amod(X0,v_sko__urX(v_evs),tc_nat),v_sko__urX(v_evs_H_H),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ537_spl])],[split_symbol_definition]) ).
fof(f28136,plain,
( ~ sQ436_spl
| ~ sQ498_spl
| sQ537_spl ),
inference(split_clause,[status(thm)],[f28123,f28133,f27412,f25871]) ).
fof(f28137,definition,
! [X0] :
( sQ538_spl
<=> c_less(c_Orderings_Omin(X0,v_sko__urX(v_evs),tc_nat),v_sko__urX(v_evs_H_H),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ538_spl])],[split_symbol_definition]) ).
fof(f28140,plain,
( ~ sQ436_spl
| ~ sQ43_spl
| sQ538_spl ),
inference(split_clause,[status(thm)],[f28126,f28137,f9098,f25871]) ).
fof(f28141,definition,
! [X0] :
( sQ539_spl
<=> c_less(c_Orderings_Omin(v_sko__urX(v_evs),X0,tc_nat),v_sko__urX(v_evs_H_H),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ539_spl])],[split_symbol_definition]) ).
fof(f28144,plain,
( ~ sQ436_spl
| ~ sQ43_spl
| sQ539_spl ),
inference(split_clause,[status(thm)],[f28127,f28141,f9098,f25871]) ).
fof(f28145,definition,
( sQ540_spl
<=> c_less(v_sko__urX(v_evs),v_sko__urX(v_evs_H_H),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ540_spl])],[split_symbol_definition]) ).
fof(f28148,plain,
( ~ sQ436_spl
| ~ sQ50_spl
| sQ540_spl ),
inference(split_clause,[status(thm)],[f28132,f28145,f10475,f25871]) ).
fof(f28187,plain,
! [X0] :
( c_in(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ c_in(c_Message_Oparts(c_Message_Oparts(c_emptyset)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f8448,f25082]) ).
fof(f28193,definition,
! [X0] :
( sQ545_spl
<=> c_in(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ545_spl])],[split_symbol_definition]) ).
fof(f28196,plain,
( sQ545_spl
| ~ sQ526_spl ),
inference(split_clause,[status(thm)],[f28187,f27725,f28193]) ).
fof(f28201,plain,
! [X0] :
( c_Finite__Set_Ocard(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) = c_Suc(c_Finite__Set_Ocard(c_Message_Oparts(c_Message_Oparts(c_emptyset)),tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_Message_Oparts(c_Message_Oparts(c_emptyset)),tc_Message_Omsg)
| ~ c_in(c_Message_Oparts(c_Message_Oparts(c_emptyset)),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
inference(paramodulation,[status(thm)],[f8448,f25412]) ).
fof(f28212,definition,
! [X0] :
( sQ546_spl
<=> ( c_Finite__Set_Ocard(c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X0),c_emptyset,tc_Message_Omsg)),tc_Message_Omsg) = c_Suc(c_Finite__Set_Ocard(c_Message_Oparts(c_Message_Oparts(c_emptyset)),tc_Message_Omsg))
| c_in(c_Message_Omsg_ONonce(X0),c_Message_Oparts(c_Message_Oparts(c_emptyset)),tc_Message_Omsg) ) ),
introduced(definition,[new_symbols(definition,[sQ546_spl])],[split_symbol_definition]) ).
fof(f28215,plain,
( sQ546_spl
| ~ sQ526_spl ),
inference(split_clause,[status(thm)],[f28201,f27725,f28212]) ).
fof(f28241,plain,
! [X0] :
( ~ sQ436_spl
| c_lessequals(c_div(v_sko__urX(v_evs_H_H),X0,tc_nat),v_sko__urX(v_evs),tc_nat)
| ~ c_less(c_1,X0,tc_nat)
| ~ c_less(c_0,v_sko__urX(v_evs_H_H),tc_nat) ),
inference(resolution,[status(thm)],[f4206,f27938]) ).
fof(f28243,plain,
! [X0,X1,X2] :
( c_less(c_div(c_Orderings_Omin(X0,X1,tc_nat),X2,tc_nat),X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| ~ c_less(c_1,X2,tc_nat)
| ~ c_less(c_0,c_Orderings_Omin(X0,X1,tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f4206,f5605]) ).
fof(f28244,plain,
! [X0,X1,X2] :
( c_less(c_div(c_Orderings_Omin(X0,X1,tc_nat),X2,tc_nat),X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| ~ c_less(c_1,X2,tc_nat)
| ~ c_less(c_0,c_Orderings_Omin(X0,X1,tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f4206,f5603]) ).
fof(f28246,definition,
! [X0] :
( sQ547_spl
<=> ( c_lessequals(c_div(v_sko__urX(v_evs_H_H),X0,tc_nat),v_sko__urX(v_evs),tc_nat)
| ~ c_less(c_1,X0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ547_spl])],[split_symbol_definition]) ).
fof(f28249,plain,
( ~ sQ436_spl
| sQ547_spl
| ~ sQ536_spl ),
inference(split_clause,[status(thm)],[f28241,f28118,f28246,f25871]) ).
fof(f28251,definition,
! [X0,X1,X2] :
( sQ548_spl
<=> ( c_less(c_div(c_Orderings_Omin(X0,X1,tc_nat),X2,tc_nat),X1,tc_nat)
| ~ c_less(c_1,X2,tc_nat)
| ~ c_less(c_0,c_Orderings_Omin(X0,X1,tc_nat),tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ548_spl])],[split_symbol_definition]) ).
fof(f28254,plain,
( ~ sQ43_spl
| sQ548_spl ),
inference(split_clause,[status(thm)],[f28243,f28251,f9098]) ).
fof(f28255,definition,
! [X0,X1,X2] :
( sQ549_spl
<=> ( c_less(c_div(c_Orderings_Omin(X0,X1,tc_nat),X2,tc_nat),X0,tc_nat)
| ~ c_less(c_1,X2,tc_nat)
| ~ c_less(c_0,c_Orderings_Omin(X0,X1,tc_nat),tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ549_spl])],[split_symbol_definition]) ).
fof(f28258,plain,
( ~ sQ43_spl
| sQ549_spl ),
inference(split_clause,[status(thm)],[f28244,f28255,f9098]) ).
fof(f28260,plain,
( sQ536_spl
| ~ sQ436_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f28120,f27943]) ).
fof(f28261,plain,
( sQ536_spl
| ~ sQ436_spl ),
inference(contradiction_clause,[status(thm)],[f28260]) ).
fof(f28269,plain,
! [X0] :
( ~ sQ436_spl
| ~ c_lessequals(v_sko__urX(v_evs_H_H),X0,tc_nat)
| c_less(v_sko__urX(v_evs),X0,tc_nat) ),
inference(resolution,[status(thm)],[f27947,f6526]) ).
fof(f28274,plain,
! [X0] :
( ~ sQ279_spl
| ~ sQ436_spl
| c_less(v_sko__urX(v_evs),c_Orderings_Omax(v_sko__urX(v_evs_H_H),X0,tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f28269,f19326]) ).
fof(f28275,plain,
! [X0] :
( ~ sQ436_spl
| ~ class_Orderings_Olinorder(tc_nat)
| c_less(v_sko__urX(v_evs),c_Orderings_Omax(X0,v_sko__urX(v_evs_H_H),tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f28269,f19368]) ).
fof(f28276,plain,
! [X0] :
( ~ sQ436_spl
| ~ class_Orderings_Olinorder(tc_nat)
| c_less(v_sko__urX(v_evs),c_Orderings_Omax(v_sko__urX(v_evs_H_H),X0,tc_nat),tc_nat) ),
inference(resolution,[status(thm)],[f28269,f19329]) ).
fof(f28277,plain,
( ~ sQ436_spl
| c_less(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat) ),
inference(resolution,[status(thm)],[f28269,f13873]) ).
fof(f28282,definition,
! [X0] :
( sQ550_spl
<=> c_less(v_sko__urX(v_evs),c_Orderings_Omax(X0,v_sko__urX(v_evs_H_H),tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ550_spl])],[split_symbol_definition]) ).
fof(f28285,plain,
( ~ sQ436_spl
| ~ sQ43_spl
| sQ550_spl ),
inference(split_clause,[status(thm)],[f28275,f28282,f9098,f25871]) ).
fof(f28286,definition,
! [X0] :
( sQ551_spl
<=> c_less(v_sko__urX(v_evs),c_Orderings_Omax(v_sko__urX(v_evs_H_H),X0,tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ551_spl])],[split_symbol_definition]) ).
fof(f28289,plain,
( ~ sQ436_spl
| ~ sQ43_spl
| sQ551_spl ),
inference(split_clause,[status(thm)],[f28276,f28286,f9098,f25871]) ).
fof(f28295,plain,
! [X0,X1,X2] :
( ~ sQ439_spl
| ~ class_Orderings_Olinorder(tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),X2,tc_nat)
| X0 = X2
| X2 = c_Orderings_Omax(X1,v_sko__urX(v_evs_H_H),tc_nat)
| X0 = c_Orderings_Omax(X1,v_sko__urX(v_evs_H_H),tc_nat) ),
inference(resolution,[status(thm)],[f27255,f19368]) ).
fof(f28296,plain,
! [X0,X1,X2] :
( ~ sQ439_spl
| ~ class_Orderings_Olinorder(tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),X2,tc_nat)
| X0 = X2
| X2 = c_Orderings_Omax(v_sko__urX(v_evs_H_H),X1,tc_nat)
| X0 = c_Orderings_Omax(v_sko__urX(v_evs_H_H),X1,tc_nat) ),
inference(resolution,[status(thm)],[f27255,f19329]) ).
fof(f28301,plain,
! [X0,X1] :
( ~ sQ439_spl
| ~ class_Orderings_Oorder(tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),X1,tc_nat)
| X0 = X1
| X1 = v_sko__urX(v_evs_H_H)
| X0 = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f27255,f3030]) ).
fof(f28302,definition,
! [X0,X1,X2] :
( sQ552_spl
<=> ( ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),X2,tc_nat)
| X0 = X2
| X2 = c_Orderings_Omax(X1,v_sko__urX(v_evs_H_H),tc_nat)
| X0 = c_Orderings_Omax(X1,v_sko__urX(v_evs_H_H),tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ552_spl])],[split_symbol_definition]) ).
fof(f28305,plain,
( ~ sQ439_spl
| ~ sQ43_spl
| sQ552_spl ),
inference(split_clause,[status(thm)],[f28295,f28302,f9098,f25881]) ).
fof(f28306,definition,
! [X0,X1,X2] :
( sQ553_spl
<=> ( ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),X2,tc_nat)
| X0 = X2
| X2 = c_Orderings_Omax(v_sko__urX(v_evs_H_H),X1,tc_nat)
| X0 = c_Orderings_Omax(v_sko__urX(v_evs_H_H),X1,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ553_spl])],[split_symbol_definition]) ).
fof(f28309,plain,
( ~ sQ439_spl
| ~ sQ43_spl
| sQ553_spl ),
inference(split_clause,[status(thm)],[f28296,f28306,f9098,f25881]) ).
fof(f28310,definition,
! [X0,X1] :
( sQ554_spl
<=> ( ~ c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),X1,tc_nat)
| X0 = X1
| X1 = v_sko__urX(v_evs_H_H)
| X0 = v_sko__urX(v_evs_H_H) ) ),
introduced(definition,[new_symbols(definition,[sQ554_spl])],[split_symbol_definition]) ).
fof(f28313,plain,
( ~ sQ439_spl
| ~ sQ50_spl
| sQ554_spl ),
inference(split_clause,[status(thm)],[f28301,f28310,f10475,f25881]) ).
fof(f28320,plain,
( ~ sQ436_spl
| c_lessequals(v_sko__urX(v_evs_H_H),v_sko__urX(v_evs_H_H),tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs),v_sko__urX(v_evs),tc_nat) ),
inference(paramodulation,[status(thm)],[f25872,f27949]) ).
fof(f28321,definition,
( sQ555_spl
<=> c_lessequals(v_sko__urX(v_evs_H_H),v_sko__urX(v_evs_H_H),tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ555_spl])],[split_symbol_definition]) ).
fof(f28324,plain,
( ~ sQ436_spl
| sQ555_spl
| ~ sQ460_spl ),
inference(split_clause,[status(thm)],[f28320,f26525,f28321,f25871]) ).
fof(f28410,plain,
! [X0,X1] :
( ~ sQ434_spl
| ~ sQ439_spl
| c_Orderings_Omax(X1,v_sko__urX(v_evs),tc_nat) = v_sko__urX(v_evs)
| c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs_H_H),X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) ),
inference(paramodulation,[status(thm)],[f27252,f5619]) ).
fof(f28422,definition,
! [X0] :
( sQ558_spl
<=> c_Orderings_Omax(X0,v_sko__urX(v_evs),tc_nat) = v_sko__urX(v_evs) ),
introduced(definition,[new_symbols(definition,[sQ558_spl])],[split_symbol_definition]) ).
fof(f28423,plain,
! [X0] :
( ~ sQ558_spl
| c_Orderings_Omax(X0,v_sko__urX(v_evs),tc_nat) = v_sko__urX(v_evs) ),
inference(component_clause,[status(thm)],[f28422]) ).
fof(f28431,definition,
! [X0] :
( sQ560_spl
<=> ( c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs_H_H),X0,tc_nat) ) ),
introduced(definition,[new_symbols(definition,[sQ560_spl])],[split_symbol_definition]) ).
fof(f28432,plain,
! [X0] :
( ~ sQ560_spl
| c_lessequals(v_sko__urX(v_evs),X0,tc_nat)
| ~ c_lessequals(v_sko__urX(v_evs_H_H),X0,tc_nat) ),
inference(component_clause,[status(thm)],[f28431]) ).
fof(f28434,plain,
( ~ sQ434_spl
| ~ sQ439_spl
| sQ558_spl
| sQ560_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f28410,f9098,f28431,f28422,f25881,f25863]) ).
fof(f28467,plain,
( ~ sQ436_spl
| ~ sQ438_spl
| c_less(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs)),tc_nat) ),
inference(backward_demodulation,[status(thm)],[f25879,f28277]) ).
fof(f28533,plain,
( ~ sQ443_spl
| sQ498_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f26040,f27414]) ).
fof(f28534,plain,
( ~ sQ443_spl
| sQ498_spl ),
inference(contradiction_clause,[status(thm)],[f28533]) ).
fof(f28541,plain,
( ~ sQ530_spl
| ~ sQ438_spl
| c_Parity_Oeven(v_sko__urX(v_evs),tc_nat) ),
inference(forward_demodulation,[status(thm)],[f25879,f27960]) ).
fof(f28542,plain,
( ~ sQ530_spl
| ~ sQ438_spl
| sQ445_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f28541,f26057]) ).
fof(f28543,plain,
( ~ sQ530_spl
| ~ sQ438_spl
| sQ445_spl ),
inference(contradiction_clause,[status(thm)],[f28542]) ).
fof(f28548,plain,
( ~ sQ436_spl
| ~ sQ438_spl
| ~ sQ448_spl
| c_less(v_sko__urX(v_evs),v_sko__urX(v_evs),tc_nat) ),
inference(forward_demodulation,[status(thm)],[f26236,f28467]) ).
fof(f28549,plain,
( ~ sQ436_spl
| ~ sQ438_spl
| ~ sQ448_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f28548,f3027]) ).
fof(f28550,plain,
( ~ sQ436_spl
| ~ sQ438_spl
| ~ sQ448_spl ),
inference(contradiction_clause,[status(thm)],[f28549]) ).
fof(f28708,plain,
( ~ sQ560_spl
| c_lessequals(v_sko__urX(v_evs),c_Suc(v_sko__urX(v_evs_H_H)),tc_nat) ),
inference(resolution,[status(thm)],[f28432,f13873]) ).
fof(f28725,plain,
! [X0,X1] :
( ~ sQ173_spl
| c_lessequals(X0,c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),c_IntDef_ONats,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f23053,f23739]) ).
fof(f28797,plain,
! [X0,X1] :
( ~ sQ173_spl
| c_lessequals(X0,c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),c_IntDef_ONats,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ class_Orderings_Olinorder(tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[f28725,f5619]) ).
fof(f28801,definition,
! [X0,X1] :
( sQ570_spl
<=> c_lessequals(X0,c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X1),c_IntDef_ONats,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
introduced(definition,[new_symbols(definition,[sQ570_spl])],[split_symbol_definition]) ).
fof(f28804,plain,
( ~ sQ173_spl
| sQ570_spl
| ~ sQ384_spl ),
inference(split_clause,[status(thm)],[f28797,f22360,f28801,f14366]) ).
fof(f28823,plain,
( ~ sQ560_spl
| ~ sQ432_spl
| ~ sQ439_spl
| c_Suc(v_sko__urX(v_evs_H_H)) = v_sko__urX(v_evs)
| c_Suc(v_sko__urX(v_evs_H_H)) = v_sko__urX(v_evs_H_H) ),
inference(resolution,[status(thm)],[f27272,f28708]) ).
fof(f28834,definition,
( sQ571_spl
<=> c_Suc(v_sko__urX(v_evs_H_H)) = v_sko__urX(v_evs_H_H) ),
introduced(definition,[new_symbols(definition,[sQ571_spl])],[split_symbol_definition]) ).
fof(f28835,plain,
( ~ sQ571_spl
| c_Suc(v_sko__urX(v_evs_H_H)) = v_sko__urX(v_evs_H_H) ),
inference(component_clause,[status(thm)],[f28834]) ).
fof(f28837,definition,
( sQ572_spl
<=> c_Suc(v_sko__urX(v_evs_H_H)) = v_sko__urX(v_evs) ),
introduced(definition,[new_symbols(definition,[sQ572_spl])],[split_symbol_definition]) ).
fof(f28838,plain,
( ~ sQ572_spl
| c_Suc(v_sko__urX(v_evs_H_H)) = v_sko__urX(v_evs) ),
inference(component_clause,[status(thm)],[f28837]) ).
fof(f28840,plain,
( ~ sQ560_spl
| ~ sQ432_spl
| ~ sQ439_spl
| sQ572_spl
| sQ571_spl ),
inference(split_clause,[status(thm)],[f28823,f28834,f28837,f25881,f25846,f28431]) ).
fof(f28847,plain,
( ~ sQ571_spl
| sQ493_spl
| ~ sQ436_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f28835,f27903]) ).
fof(f28848,plain,
( ~ sQ571_spl
| sQ493_spl
| ~ sQ436_spl ),
inference(contradiction_clause,[status(thm)],[f28847]) ).
fof(f28859,plain,
( ~ sQ558_spl
| ~ sQ279_spl
| ~ sQ436_spl
| c_less(v_sko__urX(v_evs),v_sko__urX(v_evs),tc_nat) ),
inference(paramodulation,[status(thm)],[f28423,f28274]) ).
fof(f28868,plain,
( ~ sQ558_spl
| ~ sQ279_spl
| ~ sQ436_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f28859,f3027]) ).
fof(f28869,plain,
( ~ sQ558_spl
| ~ sQ279_spl
| ~ sQ436_spl ),
inference(contradiction_clause,[status(thm)],[f28868]) ).
fof(f28870,plain,
( ~ sQ572_spl
| sQ492_spl
| ~ sQ436_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f28838,f27904]) ).
fof(f28871,plain,
( ~ sQ572_spl
| sQ492_spl
| ~ sQ436_spl ),
inference(contradiction_clause,[status(thm)],[f28870]) ).
fof(f28872,plain,
$false,
inference(sat_refutation,[status(thm)],[f6536,f6771,f6978,f6982,f8498,f8504,f8510,f8639,f8641,f8951,f9009,f9022,f9041,f10505,f10507,f10527,f10628,f10632,f10657,f10659,f10710,f10716,f10744,f10798,f10865,f10893,f10926,f10930,f10934,f10944,f11010,f11034,f11039,f11053,f11077,f11134,f11136,f11195,f11607,f11636,f12011,f12329,f12353,f12355,f12357,f12458,f12469,f13086,f13107,f13154,f13295,f13305,f13308,f13407,f13408,f13437,f13474,f13511,f13562,f13579,f13617,f13645,f13661,f13699,f13700,f13743,f13759,f13789,f13805,f13838,f14013,f14044,f14059,f14091,f14099,f14114,f14148,f14163,f14197,f14206,f14214,f14222,f14237,f14349,f14358,f14369,f14371,f14381,f14450,f14454,f14466,f14483,f14535,f14924,f14926,f15522,f16997,f17004,f17008,f17058,f17083,f17127,f17132,f17136,f17138,f17146,f17147,f17149,f17260,f17267,f17426,f17435,f17797,f17801,f17803,f17842,f17844,f17849,f17895,f18075,f18227,f18242,f18595,f18599,f18601,f18614,f18618,f18658,f18680,f18720,f18724,f18740,f18744,f18813,f18817,f18902,f18926,f18932,f18967,f18971,f18975,f18979,f18981,f18989,f18993,f19029,f19030,f19034,f19054,f19163,f19167,f19182,f19186,f19187,f19191,f19193,f19197,f19286,f19290,f19295,f19312,f19316,f19320,f19324,f19328,f19333,f19337,f19351,f19355,f19359,f19363,f19367,f19402,f19404,f19548,f19552,f19561,f19565,f19574,f19578,f19586,f19590,f19598,f19602,f19675,f19679,f19683,f19690,f19694,f19698,f19701,f19718,f19720,f19722,f19763,f19773,f19799,f19801,f19866,f19890,f19894,f19906,f19958,f19961,f20116,f20138,f20230,f20238,f20269,f20273,f20277,f20337,f20339,f20350,f20396,f20407,f20417,f20434,f20445,f20462,f20466,f20470,f20474,f20475,f20498,f20502,f20506,f20510,f20533,f20535,f20549,f20910,f20921,f20975,f21096,f22363,f22367,f22374,f22392,f22396,f22400,f22404,f22452,f22456,f22460,f22791,f22795,f22799,f23746,f23750,f23765,f23772,f24052,f24053,f24091,f24145,f24161,f24163,f24178,f24744,f25247,f25273,f25291,f25295,f25296,f25403,f25407,f25408,f25789,f25793,f25797,f25813,f25817,f25821,f25834,f25838,f25845,f25852,f25866,f25877,f25884,f25927,f25931,f25935,f25967,f26059,f26084,f26132,f26248,f26475,f26479,f26547,f26629,f26923,f26960,f27104,f27136,f27188,f27222,f27251,f27280,f27287,f27367,f27371,f27419,f27423,f27427,f27457,f27461,f27465,f27502,f27506,f27510,f27543,f27548,f27552,f27554,f27557,f27632,f27662,f27666,f27680,f27682,f27728,f27733,f27782,f27791,f27796,f27836,f27842,f27892,f27962,f27963,f27967,f28067,f28075,f28098,f28121,f28136,f28140,f28144,f28148,f28196,f28215,f28249,f28254,f28258,f28261,f28285,f28289,f28305,f28309,f28313,f28324,f28434,f28534,f28543,f28550,f28804,f28840,f28848,f28869,f28871]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV282-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n009.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Mon Sep 21 08:38:03 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.14/5.50 % Drodi V4.1.1
% 61.11/13.23 % Refutation found
% 61.11/13.23 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 61.11/13.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 37.30/13.40 % Elapsed time: 7.996346 seconds
% 37.30/13.40 % CPU time: 61.867393 seconds
% 37.30/13.40 % Total memory used: 1.075 GB
% 37.30/13.40 % Net memory used: 1.042 GB
%------------------------------------------------------------------------------