TSTP Solution File: LCL808-1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LCL808-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:26:54 EDT 2022
% Result : Unsatisfiable 1.01s 1.20s
% Output : CNFRefutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 106
% Syntax : Number of formulae : 600 ( 350 unt; 30 typ; 0 def)
% Number of atoms : 2772 (1030 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 4805 ( 562 ~; 732 |; 0 &;3511 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 30 usr; 12 con; 0-4 aty)
% Number of variables : 1379 ( 0 ^1379 !; 0 ?;1379 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(tp_c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(tp_c_InductTermi_OIT,type,
c_InductTermi_OIT: $i > $o ).
thf(tp_c_Lambda_Obeta,type,
c_Lambda_Obeta: $i > $i > $o ).
thf(tp_c_Lambda_OdB_OAbs,type,
c_Lambda_OdB_OAbs: $i > $i ).
thf(tp_c_Lambda_OdB_OApp,type,
c_Lambda_OdB_OApp: $i > $i > $i ).
thf(tp_c_Lambda_OdB_OVar,type,
c_Lambda_OdB_OVar: $i > $i ).
thf(tp_c_Lambda_Olift,type,
c_Lambda_Olift: $i > $i > $i ).
thf(tp_c_Lambda_Osko__Lambda__Xbeta__cases__2__1,type,
c_Lambda_Osko__Lambda__Xbeta__cases__2__1: $i > $i > $i ).
thf(tp_c_Lambda_Osubst,type,
c_Lambda_Osubst: $i > $i > $i > $i ).
thf(tp_c_Nat_Osemiring__1__class_Oof__nat,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).
thf(tp_c_Type_Oshift,type,
c_Type_Oshift: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Otyping,type,
c_Type_Otyping: $i > $i > $i > $o ).
thf(tp_class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(tp_class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
thf(tp_class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
thf(tp_class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(tp_class_Ring__and__Field_Osemiring__1,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(tp_tc_Type_Otype,type,
tc_Type_Otype: $i ).
thf(tp_tc_nat,type,
tc_nat: $i ).
thf(tp_v_T____,type,
v_T____: $i ).
thf(tp_v_Ua____,type,
v_Ua____: $i ).
thf(tp_v_b____,type,
v_b____: $i ).
thf(tp_v_e____,type,
v_e____: $i ).
thf(tp_v_i____,type,
v_i____: $i ).
thf(tp_v_n____,type,
v_n____: $i ).
thf(tp_v_u____,type,
v_u____: $i ).
thf(tp_v_ua______,type,
v_ua______: $i ).
thf(1,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(2,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(3,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(4,axiom,
class_Nat_Osemiring__char__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(5,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(6,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(7,axiom,
c_Type_Otyping @ v_e____ @ v_u____ @ v_T____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_03) ).
thf(8,axiom,
c_InductTermi_OIT @ v_u____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_02) ).
thf(9,axiom,
! [V_ua: $i,V_ia: $i,V_ea: $i,V_T_H: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_b____ @ V_ua @ V_ia ) )
| ~ ( c_Type_Otyping @ V_ea @ V_ua @ v_T____ )
| ~ ( c_InductTermi_OIT @ V_ua )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_ea @ V_ia @ v_T____ @ tc_Type_Otype ) @ v_b____ @ V_T_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
thf(10,axiom,
c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_b____ @ v_Ua____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(11,axiom,
! [V_t: $i,V_k: $i,V_s: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_k ) @ V_s @ V_k )
= V_t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lift_0) ).
thf(12,axiom,
c_InductTermi_OIT @ v_u____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_uIT_0) ).
thf(13,axiom,
! [V_r: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ V_r ) )
| ~ ( c_InductTermi_OIT @ V_r ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lambda_0) ).
thf(14,axiom,
c_InductTermi_OIT @ v_ua______,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var_I3_J_0) ).
thf(15,axiom,
! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) @ ( c_Lambda_Osubst @ V_s @ V_t @ V_i ) )
| ~ ( c_Lambda_Obeta @ V_r @ V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
thf(16,axiom,
! [V_n: $i] : ( c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__IT_0) ).
thf(17,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_True_0) ).
thf(18,axiom,
! [V_t: $i,V_i: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Olift @ V_t @ V_i ) )
| ~ ( c_InductTermi_OIT @ V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__IT_0) ).
thf(19,axiom,
! [V_r: $i,V_i: $i,V_j: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_r @ ( c_Lambda_OdB_OVar @ V_i ) @ V_j ) )
| ~ ( c_InductTermi_OIT @ V_r ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
thf(20,axiom,
! [V_k: $i,V_u: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_k ) @ V_u @ V_k )
= V_u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(21,axiom,
! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ V_t @ V_u ) @ V_s @ V_k )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_t @ V_s @ V_k ) @ ( c_Lambda_Osubst @ V_u @ V_s @ V_k ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(22,axiom,
! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
thf(23,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
thf(24,axiom,
! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OVar @ V_nat_H ) )
| ( V_nat = V_nat_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
thf(25,axiom,
! [V_dB_H: $i,V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(26,axiom,
! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_j ) @ V_u @ V_i )
= ( c_Lambda_OdB_OVar @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lt_0) ).
thf(27,axiom,
! [V_r: $i,V_s: $i] :
( ( c_Lambda_Obeta @ V_r @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ V_r @ V_s ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I2_J_1) ).
thf(28,axiom,
! [V_i: $i,V_t: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) @ V_t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
thf(29,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 )
!= ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H ) )
| ( V_dB1 = V_dB1_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
thf(30,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 )
!= ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H ) )
| ( V_dB2 = V_dB2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
thf(31,axiom,
! [V_s: $i,V_t: $i] : ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_t ) @ ( c_Lambda_Osubst @ V_s @ V_t @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta_0) ).
thf(32,axiom,
! [V_nat: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
thf(33,axiom,
! [V_dB: $i,V_dB_H: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_dB )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) )
| ( V_dB = V_dB_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(34,axiom,
! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
thf(35,axiom,
! [V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OApp @ V_s @ V_t ) @ V_k )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ V_s @ V_k ) @ ( c_Lambda_Olift @ V_t @ V_k ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
thf(36,axiom,
! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_2) ).
thf(37,axiom,
! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_1) ).
thf(38,axiom,
! [V_u: $i,V_s: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ V_u @ V_s ) @ ( c_Lambda_OdB_OApp @ V_u @ V_t ) )
| ~ ( c_Lambda_Obeta @ V_s @ V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appR_0) ).
thf(39,axiom,
! [V_s: $i,V_u: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ V_s @ V_u ) @ ( c_Lambda_OdB_OApp @ V_t @ V_u ) )
| ~ ( c_Lambda_Obeta @ V_s @ V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appL_0) ).
thf(40,axiom,
! [V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
thf(41,axiom,
! [V_r: $i,V_i: $i,V_s: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ V_r @ V_i ) @ ( c_Lambda_Olift @ V_s @ V_i ) )
| ~ ( c_Lambda_Obeta @ V_r @ V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
thf(42,axiom,
! [V_t: $i,V_i: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OApp @ V_t @ ( c_Lambda_OdB_OVar @ V_i ) ) )
| ~ ( c_InductTermi_OIT @ V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
thf(43,axiom,
! [V_s: $i,V_r: $i] :
( ( V_s
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ V_r @ V_s ) ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I2_J_0) ).
thf(44,axiom,
! [V_s: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_s ) @ ( c_Lambda_OdB_OAbs @ V_t ) )
| ~ ( c_Lambda_Obeta @ V_s @ V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs_0) ).
thf(45,axiom,
! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
thf(46,axiom,
! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(47,axiom,
! [V_m: $i] :
~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(48,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(49,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(50,axiom,
! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(51,axiom,
! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(52,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(53,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(54,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(55,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(56,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(57,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(58,axiom,
! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(59,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(60,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(61,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(62,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
thf(63,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
thf(64,axiom,
! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(65,axiom,
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(66,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(67,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(68,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(69,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(70,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
thf(71,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
thf(72,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
thf(73,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
thf(74,axiom,
! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
thf(75,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(76,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[75]) ).
thf(77,negated_conjecture,
~ ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_b____ @ v_u____ @ v_i____ ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(78,plain,
$false = $false,
inference(unfold_def,[status(thm)],[76]) ).
thf(79,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(80,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(81,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(82,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(83,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(84,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(85,plain,
( ( c_Type_Otyping @ v_e____ @ v_u____ @ v_T____ )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(86,plain,
( ( c_InductTermi_OIT @ v_u____ )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(87,plain,
( ( ! [V_ua: $i,V_ia: $i,V_ea: $i,V_T_H: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_b____ @ V_ua @ V_ia ) )
| ~ ( c_Type_Otyping @ V_ea @ V_ua @ v_T____ )
| ~ ( c_InductTermi_OIT @ V_ua )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_ea @ V_ia @ v_T____ @ tc_Type_Otype ) @ v_b____ @ V_T_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(88,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_b____ @ v_Ua____ )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(89,plain,
( ( ! [V_t: $i,V_k: $i,V_s: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_k ) @ V_s @ V_k )
= V_t ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(90,plain,
( ( c_InductTermi_OIT @ v_u____ )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(91,plain,
( ( ! [V_r: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ V_r ) )
| ~ ( c_InductTermi_OIT @ V_r ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(92,plain,
( ( c_InductTermi_OIT @ v_ua______ )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(93,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) @ ( c_Lambda_Osubst @ V_s @ V_t @ V_i ) )
| ~ ( c_Lambda_Obeta @ V_r @ V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(94,plain,
( ( ! [V_n: $i] : ( c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(95,plain,
( ( v_n____ = v_i____ )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(96,plain,
( ( ! [V_t: $i,V_i: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Olift @ V_t @ V_i ) )
| ~ ( c_InductTermi_OIT @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(97,plain,
( ( ! [V_r: $i,V_i: $i,V_j: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_r @ ( c_Lambda_OdB_OVar @ V_i ) @ V_j ) )
| ~ ( c_InductTermi_OIT @ V_r ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(98,plain,
( ( ! [V_k: $i,V_u: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_k ) @ V_u @ V_k )
= V_u ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(99,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ V_t @ V_u ) @ V_s @ V_k )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_t @ V_s @ V_k ) @ ( c_Lambda_Osubst @ V_u @ V_s @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(100,plain,
( ( ! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(101,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(102,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OVar @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(103,plain,
( ( ! [V_dB_H: $i,V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(104,plain,
( ( ! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_j ) @ V_u @ V_i )
= ( c_Lambda_OdB_OVar @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(105,plain,
( ( ! [V_r: $i,V_s: $i] :
( ( c_Lambda_Obeta @ V_r @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ V_r @ V_s ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(106,plain,
( ( ! [V_i: $i,V_t: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) @ V_t ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(107,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 )
!= ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H ) )
| ( V_dB1 = V_dB1_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(108,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 )
!= ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H ) )
| ( V_dB2 = V_dB2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(109,plain,
( ( ! [V_s: $i,V_t: $i] : ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_t ) @ ( c_Lambda_Osubst @ V_s @ V_t @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(110,plain,
( ( ! [V_nat: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(111,plain,
( ( ! [V_dB: $i,V_dB_H: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_dB )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) )
| ( V_dB = V_dB_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(112,plain,
( ( ! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(113,plain,
( ( ! [V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OApp @ V_s @ V_t ) @ V_k )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ V_s @ V_k ) @ ( c_Lambda_Olift @ V_t @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(114,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(115,plain,
( ( ! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(116,plain,
( ( ! [V_u: $i,V_s: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ V_u @ V_s ) @ ( c_Lambda_OdB_OApp @ V_u @ V_t ) )
| ~ ( c_Lambda_Obeta @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(117,plain,
( ( ! [V_s: $i,V_u: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ V_s @ V_u ) @ ( c_Lambda_OdB_OApp @ V_t @ V_u ) )
| ~ ( c_Lambda_Obeta @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(118,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(119,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ V_r @ V_i ) @ ( c_Lambda_Olift @ V_s @ V_i ) )
| ~ ( c_Lambda_Obeta @ V_r @ V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(120,plain,
( ( ! [V_t: $i,V_i: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OApp @ V_t @ ( c_Lambda_OdB_OVar @ V_i ) ) )
| ~ ( c_InductTermi_OIT @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(121,plain,
( ( ! [V_s: $i,V_r: $i] :
( ( V_s
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ V_r @ V_s ) ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(122,plain,
( ( ! [V_s: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_s ) @ ( c_Lambda_OdB_OAbs @ V_t ) )
| ~ ( c_Lambda_Obeta @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(123,plain,
( ( ! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(124,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(125,plain,
( ( ! [V_m: $i] :
~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(126,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(127,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(128,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(129,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(130,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(131,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(132,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(133,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(134,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(135,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(136,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(137,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(138,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(139,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(140,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(141,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(142,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(143,plain,
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(144,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(145,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(146,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(147,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(148,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(149,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(150,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(151,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(152,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(153,plain,
( ( ~ ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_b____ @ v_u____ @ v_i____ ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(154,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[78]) ).
thf(155,plain,
( ( ! [V_ua: $i,V_ia: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_b____ @ V_ua @ V_ia ) )
| ! [V_ea: $i] :
( ~ ( c_Type_Otyping @ V_ea @ V_ua @ v_T____ )
| ~ ( c_InductTermi_OIT @ V_ua )
| ! [V_T_H: $i] :
~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_ea @ V_ia @ v_T____ @ tc_Type_Otype ) @ v_b____ @ V_T_H ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(156,plain,
( ( ! [V_t: $i] :
( ! [V_i: $i] : ( c_InductTermi_OIT @ ( c_Lambda_Olift @ V_t @ V_i ) )
| ~ ( c_InductTermi_OIT @ V_t ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[96]) ).
thf(157,plain,
( ( ! [V_r: $i] :
( ! [V_i: $i,V_j: $i] : ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_r @ ( c_Lambda_OdB_OVar @ V_i ) @ V_j ) )
| ~ ( c_InductTermi_OIT @ V_r ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[97]) ).
thf(158,plain,
( ( ! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[100]) ).
thf(159,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[101]) ).
thf(160,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OVar @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[102]) ).
thf(161,plain,
( ( ! [V_dB_H: $i,V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[103]) ).
thf(162,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i] :
( ! [V_dB2_H: $i] :
( ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 )
!= ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H ) )
| ( V_dB1 = V_dB1_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[107]) ).
thf(163,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 )
!= ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H ) )
| ( V_dB2 = V_dB2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[108]) ).
thf(164,plain,
( ( ! [V_nat: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[110]) ).
thf(165,plain,
( ( ! [V_dB: $i,V_dB_H: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_dB )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) )
| ( V_dB = V_dB_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[111]) ).
thf(166,plain,
( ( ! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[112]) ).
thf(167,plain,
( ( ! [V_x: $i] :
( ! [V_s: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= V_s )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[115]) ).
thf(168,plain,
( ( ! [V_t: $i] :
( ! [V_i: $i] : ( c_InductTermi_OIT @ ( c_Lambda_OdB_OApp @ V_t @ ( c_Lambda_OdB_OVar @ V_i ) ) )
| ~ ( c_InductTermi_OIT @ V_t ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[120]) ).
thf(169,plain,
( ( ! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[123]) ).
thf(170,plain,
( ( ! [T_a: $i,V_z: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ! [V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[126]) ).
thf(171,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[127]) ).
thf(172,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[130]) ).
thf(173,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[131]) ).
thf(174,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[132]) ).
thf(175,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[133]) ).
thf(176,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[134]) ).
thf(177,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[135]) ).
thf(178,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[136]) ).
thf(179,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[137]) ).
thf(180,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[138]) ).
thf(181,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[139]) ).
thf(182,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[140]) ).
thf(183,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[141]) ).
thf(184,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[142]) ).
thf(185,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_a: $i,V_b: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[144]) ).
thf(186,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[145]) ).
thf(187,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[146]) ).
thf(188,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_b: $i,V_a: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[147]) ).
thf(189,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[148]) ).
thf(190,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[149]) ).
thf(191,plain,
( ( ! [T_a: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ T_a )
| ! [V_m: $i,V_n: $i] :
( ( ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) )
| ( V_m = V_n ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[150]) ).
thf(192,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ! [V_m: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[152]) ).
thf(193,plain,
( ( ~ ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_b____ @ v_u____ @ v_i____ ) ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(194,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ! [V_m: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(195,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(196,plain,
( ( ! [T_a: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ T_a )
| ! [V_m: $i,V_n: $i] :
( ( ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) )
| ( V_m = V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(197,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(198,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(199,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_b: $i,V_a: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[188]) ).
thf(200,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(201,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(202,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_a: $i,V_b: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(203,plain,
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(204,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(205,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(206,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(207,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(208,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(209,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(210,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(211,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(212,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(213,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(214,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(215,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(216,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(217,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(218,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(219,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(220,plain,
( ( ! [T_a: $i,V_z: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ! [V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(221,plain,
( ( ! [V_m: $i] :
~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(222,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(223,plain,
( ( ! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(224,plain,
( ( ! [V_s: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_s ) @ ( c_Lambda_OdB_OAbs @ V_t ) )
| ~ ( c_Lambda_Obeta @ V_s @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(225,plain,
( ( ! [V_s: $i,V_r: $i] :
( ( V_s
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ V_r @ V_s ) ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_s ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(226,plain,
( ( ! [V_t: $i] :
( ! [V_i: $i] : ( c_InductTermi_OIT @ ( c_Lambda_OdB_OApp @ V_t @ ( c_Lambda_OdB_OVar @ V_i ) ) )
| ~ ( c_InductTermi_OIT @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(227,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ V_r @ V_i ) @ ( c_Lambda_Olift @ V_s @ V_i ) )
| ~ ( c_Lambda_Obeta @ V_r @ V_s ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(228,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(229,plain,
( ( ! [V_s: $i,V_u: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ V_s @ V_u ) @ ( c_Lambda_OdB_OApp @ V_t @ V_u ) )
| ~ ( c_Lambda_Obeta @ V_s @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(230,plain,
( ( ! [V_u: $i,V_s: $i,V_t: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ V_u @ V_s ) @ ( c_Lambda_OdB_OApp @ V_u @ V_t ) )
| ~ ( c_Lambda_Obeta @ V_s @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(231,plain,
( ( ! [V_x: $i] :
( ! [V_s: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= V_s )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[167]) ).
thf(232,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_i ) @ V_s @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(233,plain,
( ( ! [V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OApp @ V_s @ V_t ) @ V_k )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ V_s @ V_k ) @ ( c_Lambda_Olift @ V_t @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(234,plain,
( ( ! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(235,plain,
( ( ! [V_dB: $i,V_dB_H: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_dB )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) )
| ( V_dB = V_dB_H ) ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(236,plain,
( ( ! [V_nat: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H ) ) )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(237,plain,
( ( ! [V_s: $i,V_t: $i] : ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_t ) @ ( c_Lambda_Osubst @ V_s @ V_t @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(238,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 )
!= ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H ) )
| ( V_dB2 = V_dB2_H ) ) )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(239,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i] :
( ! [V_dB2_H: $i] :
( ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 )
!= ( c_Lambda_OdB_OApp @ V_dB1_H @ V_dB2_H ) )
| ( V_dB1 = V_dB1_H ) ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(240,plain,
( ( ! [V_i: $i,V_t: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) @ V_t ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(241,plain,
( ( ! [V_r: $i,V_s: $i] :
( ( c_Lambda_Obeta @ V_r @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ V_r @ V_s ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_s ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(242,plain,
( ( ! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_j ) @ V_u @ V_i )
= ( c_Lambda_OdB_OVar @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(243,plain,
( ( ! [V_dB_H: $i,V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 ) ) )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(244,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OVar @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(245,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OApp @ V_dB1 @ V_dB2 )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(246,plain,
( ( ! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(247,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ V_t @ V_u ) @ V_s @ V_k )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ V_t @ V_s @ V_k ) @ ( c_Lambda_Osubst @ V_u @ V_s @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(248,plain,
( ( ! [V_k: $i,V_u: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_k ) @ V_u @ V_k )
= V_u ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(249,plain,
( ( ! [V_r: $i] :
( ! [V_i: $i,V_j: $i] : ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ V_r @ ( c_Lambda_OdB_OVar @ V_i ) @ V_j ) )
| ~ ( c_InductTermi_OIT @ V_r ) ) )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(250,plain,
( ( ! [V_t: $i] :
( ! [V_i: $i] : ( c_InductTermi_OIT @ ( c_Lambda_Olift @ V_t @ V_i ) )
| ~ ( c_InductTermi_OIT @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(251,plain,
( ( v_n____ = v_i____ )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(252,plain,
( ( ! [V_n: $i] : ( c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(253,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ V_r @ V_t @ V_i ) @ ( c_Lambda_Osubst @ V_s @ V_t @ V_i ) )
| ~ ( c_Lambda_Obeta @ V_r @ V_s ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(254,plain,
( ( c_InductTermi_OIT @ v_ua______ )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(255,plain,
( ( ! [V_r: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ V_r ) )
| ~ ( c_InductTermi_OIT @ V_r ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(256,plain,
( ( c_InductTermi_OIT @ v_u____ )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(257,plain,
( ( ! [V_t: $i,V_k: $i,V_s: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ V_t @ V_k ) @ V_s @ V_k )
= V_t ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(258,plain,
( ( c_Type_Otyping @ ( c_Type_Oshift @ v_e____ @ v_i____ @ v_T____ @ tc_Type_Otype ) @ v_b____ @ v_Ua____ )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(259,plain,
( ( ! [V_ua: $i,V_ia: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_b____ @ V_ua @ V_ia ) )
| ! [V_ea: $i] :
( ~ ( c_Type_Otyping @ V_ea @ V_ua @ v_T____ )
| ~ ( c_InductTermi_OIT @ V_ua )
| ! [V_T_H: $i] :
~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_ea @ V_ia @ v_T____ @ tc_Type_Otype ) @ v_b____ @ V_T_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(260,plain,
( ( c_InductTermi_OIT @ v_u____ )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(261,plain,
( ( c_Type_Otyping @ v_e____ @ v_u____ @ v_T____ )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(262,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(263,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(264,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(265,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(266,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(267,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(268,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(269,plain,
( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_b____ @ v_u____ @ v_i____ ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(270,plain,
! [SV1: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV1 )
| ! [SY152: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY152 @ SV1 ) @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(271,plain,
! [SV2: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV2 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2 )
= ( c_HOL_Ozero__class_Ozero @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(272,plain,
! [SV3: $i] :
( ( ~ ( class_Nat_Osemiring__char__0 @ SV3 )
| ! [SY153: $i,SY154: $i] :
( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SY153 @ SV3 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY154 @ SV3 ) )
| ( SY153 = SY154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(273,plain,
! [SV4: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV4 )
| ! [SY155: $i,SY156: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY155 @ SV4 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY156 @ SV4 ) @ SV4 )
| ~ ( c_HOL_Oord__class_Oless @ SY155 @ SY156 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(274,plain,
! [SV5: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV5 )
| ! [SY157: $i,SY158: $i] :
( ( c_HOL_Oord__class_Oless @ SY157 @ SY158 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY157 @ SV5 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY158 @ SV5 ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(275,plain,
! [SV6: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV6 )
| ! [SY159: $i,SY160: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY159 @ SY160 @ SV6 )
| ~ ( c_HOL_Oord__class_Oless @ SY160 @ SY159 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(276,plain,
! [SV7: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV7 )
| ! [SY161: $i,SY162: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY161 @ SY162 @ SV7 )
| ~ ( c_HOL_Oord__class_Oless @ SY162 @ SY161 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(277,plain,
! [SV8: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV8 )
| ! [SY163: $i,SY164: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY163 @ SY164 @ SV8 )
| ~ ( c_HOL_Oord__class_Oless @ SY164 @ SY163 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(278,plain,
! [SV9: $i] :
( ( ~ ( class_Orderings_Oorder @ SV9 )
| ! [SY165: $i,SY166: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY165 @ SY166 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SY166 @ SY165 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(279,plain,
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(280,plain,
! [SV10: $i] :
( ( ( SV10
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV10 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(281,plain,
! [SV11: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV11 )
| ! [SY167: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY167 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV11 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY167 @ SV11 ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(282,plain,
! [SV12: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV12 )
| ! [SY168: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY168 @ SV12 ) @ SV12 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY168 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(283,plain,
! [SV13: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV13 )
| ! [SY169: $i,SY170: $i] :
( ( SY169 = SY170 )
| ( c_HOL_Oord__class_Oless @ SY169 @ SY170 @ SV13 )
| ( c_HOL_Oord__class_Oless @ SY170 @ SY169 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(284,plain,
! [SV14: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV14 )
| ! [SY171: $i,SY172: $i] :
( ( c_HOL_Oord__class_Oless @ SY171 @ SY172 @ SV14 )
| ( SY172 = SY171 )
| ( c_HOL_Oord__class_Oless @ SY172 @ SY171 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(285,plain,
! [SV15: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV15 )
| ! [SY173: $i,SY174: $i] :
( ( c_HOL_Oord__class_Oless @ SY173 @ SY174 @ SV15 )
| ( SY174 = SY173 )
| ( c_HOL_Oord__class_Oless @ SY174 @ SY173 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(286,plain,
! [SV16: $i] :
( ( ! [SY175: $i] :
( ( c_HOL_Oord__class_Oless @ SV16 @ SY175 @ tc_nat )
| ( SY175 = SV16 )
| ( c_HOL_Oord__class_Oless @ SY175 @ SV16 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(287,plain,
! [SV17: $i] :
( ( ! [SY176: $i] :
( ( c_HOL_Oord__class_Oless @ SV17 @ SY176 @ tc_nat )
| ( SY176 = SV17 )
| ( c_HOL_Oord__class_Oless @ SY176 @ SV17 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(288,plain,
! [SV18: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV18 )
| ! [SY177: $i,SY178: $i] :
( ( SY177 = SY178 )
| ( c_HOL_Oord__class_Oless @ SY178 @ SY177 @ SV18 )
| ( c_HOL_Oord__class_Oless @ SY177 @ SY178 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(289,plain,
! [SV19: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV19 )
| ! [SY179: $i,SY180: $i] :
( ( c_HOL_Oord__class_Oless @ SY179 @ SY180 @ SV19 )
| ( SY180 = SY179 )
| ( c_HOL_Oord__class_Oless @ SY180 @ SY179 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(290,plain,
! [SV20: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV20 )
| ! [SY181: $i] :
~ ( c_HOL_Oord__class_Oless @ SY181 @ SY181 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(291,plain,
! [SV21: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV21 )
| ! [SY182: $i] :
~ ( c_HOL_Oord__class_Oless @ SY182 @ SY182 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(292,plain,
! [SV22: $i] :
( ( ~ ( class_Orderings_Oorder @ SV22 )
| ! [SY183: $i] :
~ ( c_HOL_Oord__class_Oless @ SY183 @ SY183 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(293,plain,
! [SV23: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV23 @ SV23 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(294,plain,
! [SV24: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV24 @ SV24 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(295,plain,
! [SV25: $i] :
( ( ! [SY184: $i] :
( ~ ( class_Orderings_Opreorder @ SV25 )
| ! [SY185: $i] :
( ( c_HOL_Oord__class_Oless @ SY184 @ SY185 @ SV25 )
| ! [SY186: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY186 @ SY185 @ SV25 )
| ~ ( c_HOL_Oord__class_Oless @ SY184 @ SY186 @ SV25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(296,plain,
! [SV26: $i] :
( ( ! [SY187: $i] :
( ~ ( class_Orderings_Oorder @ SV26 )
| ! [SY188: $i] :
( ( c_HOL_Oord__class_Oless @ SY187 @ SY188 @ SV26 )
| ! [SY189: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY187 @ SY189 @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ SY189 @ SY188 @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(297,plain,
! [SV27: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV27 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(298,plain,
! [SV28: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV28 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(299,plain,
! [SV29: $i] :
( ( ! [SY190: $i,SY191: $i] :
( ( c_Lambda_OdB_OApp @ SV29 @ SY190 )
!= ( c_Lambda_OdB_OVar @ SY191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(300,plain,
! [SV30: $i] :
( ( ! [SY192: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV30 ) @ ( c_Lambda_OdB_OAbs @ SY192 ) )
| ~ ( c_Lambda_Obeta @ SV30 @ SY192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(301,plain,
! [SV31: $i] :
( ( ! [SY193: $i] :
( ( SV31
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SY193 @ SV31 ) ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SY193 ) @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(302,plain,
! [SV32: $i] :
( ( ! [SY194: $i] : ( c_InductTermi_OIT @ ( c_Lambda_OdB_OApp @ SV32 @ ( c_Lambda_OdB_OVar @ SY194 ) ) )
| ~ ( c_InductTermi_OIT @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(303,plain,
! [SV33: $i] :
( ( ! [SY195: $i,SY196: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ SV33 @ SY195 ) @ ( c_Lambda_Olift @ SY196 @ SY195 ) )
| ~ ( c_Lambda_Obeta @ SV33 @ SY196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(304,plain,
! [SV34: $i] :
( ( ! [SY197: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV34 ) @ SY197 )
= ( c_Lambda_OdB_OVar @ SV34 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV34 @ SY197 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(305,plain,
! [SV35: $i] :
( ( ! [SY198: $i,SY199: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ SV35 @ SY198 ) @ ( c_Lambda_OdB_OApp @ SY199 @ SY198 ) )
| ~ ( c_Lambda_Obeta @ SV35 @ SY199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(306,plain,
! [SV36: $i] :
( ( ! [SY200: $i,SY201: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ SV36 @ SY200 ) @ ( c_Lambda_OdB_OApp @ SV36 @ SY201 ) )
| ~ ( c_Lambda_Obeta @ SY200 @ SY201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(307,plain,
! [SV37: $i] :
( ( ! [SY202: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV37 ) @ SY202 @ SV37 )
= SY202 )
| ( c_HOL_Oord__class_Oless @ SV37 @ SV37 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(308,plain,
! [SV38: $i] :
( ( ! [SY203: $i,SY204: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV38 ) @ SY203 @ SY204 )
= ( c_Lambda_OdB_OVar @ SV38 ) )
| ( SV38 = SY204 )
| ( c_HOL_Oord__class_Oless @ SY204 @ SV38 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(309,plain,
! [SV39: $i] :
( ( ! [SY205: $i,SY206: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OApp @ SV39 @ SY205 ) @ SY206 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV39 @ SY206 ) @ ( c_Lambda_Olift @ SY205 @ SY206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(310,plain,
! [SV40: $i] :
( ( ! [SY207: $i] :
( ( c_Lambda_OdB_OVar @ SV40 )
!= ( c_Lambda_OdB_OAbs @ SY207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(311,plain,
! [SV41: $i] :
( ( ! [SY208: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV41 )
!= ( c_Lambda_OdB_OAbs @ SY208 ) )
| ( SV41 = SY208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(312,plain,
! [SV42: $i] :
( ( ! [SY209: $i,SY210: $i] :
( ( c_Lambda_OdB_OVar @ SV42 )
!= ( c_Lambda_OdB_OApp @ SY209 @ SY210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(313,plain,
! [SV43: $i] :
( ( ! [SY211: $i] : ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV43 ) @ SY211 ) @ ( c_Lambda_Osubst @ SV43 @ SY211 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(314,plain,
! [SV44: $i] :
( ( ! [SY212: $i,SY213: $i,SY214: $i] :
( ( ( c_Lambda_OdB_OApp @ SV44 @ SY212 )
!= ( c_Lambda_OdB_OApp @ SY213 @ SY214 ) )
| ( SY212 = SY214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(315,plain,
! [SV45: $i] :
( ( ! [SY215: $i,SY216: $i] :
( ! [SY217: $i] :
( ( c_Lambda_OdB_OApp @ SV45 @ SY215 )
!= ( c_Lambda_OdB_OApp @ SY216 @ SY217 ) )
| ( SV45 = SY216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(316,plain,
! [SV46: $i] :
( ( ! [SY218: $i] :
~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV46 ) @ SY218 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(317,plain,
! [SV47: $i] :
( ( ! [SY219: $i] :
( ( c_Lambda_Obeta @ SV47 @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SV47 @ SY219 ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV47 ) @ SY219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(318,plain,
! [SV48: $i] :
( ( ! [SY220: $i,SY221: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV48 ) @ SY220 @ SY221 )
= ( c_Lambda_OdB_OVar @ SV48 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV48 @ SY221 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(319,plain,
! [SV49: $i] :
( ( ! [SY222: $i,SY223: $i] :
( ( c_Lambda_OdB_OAbs @ SV49 )
!= ( c_Lambda_OdB_OApp @ SY222 @ SY223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(320,plain,
! [SV50: $i] :
( ( ! [SY224: $i] :
( ( ( c_Lambda_OdB_OVar @ SV50 )
!= ( c_Lambda_OdB_OVar @ SY224 ) )
| ( SV50 = SY224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(321,plain,
! [SV51: $i] :
( ( ! [SY225: $i,SY226: $i] :
( ( c_Lambda_OdB_OApp @ SV51 @ SY225 )
!= ( c_Lambda_OdB_OAbs @ SY226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(322,plain,
! [SV52: $i] :
( ( ! [SY227: $i] :
( ( c_Lambda_OdB_OAbs @ SV52 )
!= ( c_Lambda_OdB_OVar @ SY227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(323,plain,
! [SV53: $i] :
( ( ! [SY228: $i,SY229: $i,SY230: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ SV53 @ SY228 ) @ SY229 @ SY230 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV53 @ SY229 @ SY230 ) @ ( c_Lambda_Osubst @ SY228 @ SY229 @ SY230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(324,plain,
! [SV54: $i] :
( ( ! [SY231: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV54 ) @ SY231 @ SV54 )
= SY231 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(325,plain,
! [SV55: $i] :
( ( ! [SY232: $i,SY233: $i] : ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV55 @ ( c_Lambda_OdB_OVar @ SY232 ) @ SY233 ) )
| ~ ( c_InductTermi_OIT @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(326,plain,
! [SV56: $i] :
( ( ! [SY234: $i] : ( c_InductTermi_OIT @ ( c_Lambda_Olift @ SV56 @ SY234 ) )
| ~ ( c_InductTermi_OIT @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(327,plain,
! [SV57: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(328,plain,
! [SV58: $i] :
( ( ! [SY235: $i,SY236: $i,SY237: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV58 @ SY235 @ SY236 ) @ ( c_Lambda_Osubst @ SY237 @ SY235 @ SY236 ) )
| ~ ( c_Lambda_Obeta @ SV58 @ SY237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(329,plain,
! [SV59: $i] :
( ( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV59 ) )
| ~ ( c_InductTermi_OIT @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(330,plain,
! [SV60: $i] :
( ( ! [SY238: $i,SY239: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV60 @ SY238 ) @ SY239 @ SY238 )
= SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(331,plain,
! [SV61: $i] :
( ( ! [SY240: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_b____ @ SV61 @ SY240 ) )
| ! [SY241: $i] :
( ~ ( c_Type_Otyping @ SY241 @ SV61 @ v_T____ )
| ~ ( c_InductTermi_OIT @ SV61 )
| ! [V_T_H: $i] :
~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY241 @ SY240 @ v_T____ @ tc_Type_Otype ) @ v_b____ @ V_T_H ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(332,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(333,plain,
! [SV1: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV1 ) )
= $true )
| ( ( ! [SY152: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY152 @ SV1 ) @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(334,plain,
! [SV2: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV2 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2 )
= ( c_HOL_Ozero__class_Ozero @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(335,plain,
! [SV3: $i] :
( ( ( ~ ( class_Nat_Osemiring__char__0 @ SV3 ) )
= $true )
| ( ( ! [SY153: $i,SY154: $i] :
( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SY153 @ SV3 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY154 @ SV3 ) )
| ( SY153 = SY154 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(336,plain,
! [SV4: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV4 ) )
= $true )
| ( ( ! [SY155: $i,SY156: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY155 @ SV4 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY156 @ SV4 ) @ SV4 )
| ~ ( c_HOL_Oord__class_Oless @ SY155 @ SY156 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(337,plain,
! [SV5: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV5 ) )
= $true )
| ( ( ! [SY157: $i,SY158: $i] :
( ( c_HOL_Oord__class_Oless @ SY157 @ SY158 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY157 @ SV5 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY158 @ SV5 ) @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(338,plain,
! [SV6: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV6 ) )
= $true )
| ( ( ! [SY159: $i,SY160: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY159 @ SY160 @ SV6 )
| ~ ( c_HOL_Oord__class_Oless @ SY160 @ SY159 @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(339,plain,
! [SV7: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV7 ) )
= $true )
| ( ( ! [SY161: $i,SY162: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY161 @ SY162 @ SV7 )
| ~ ( c_HOL_Oord__class_Oless @ SY162 @ SY161 @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(340,plain,
! [SV8: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV8 ) )
= $true )
| ( ( ! [SY163: $i,SY164: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY163 @ SY164 @ SV8 )
| ~ ( c_HOL_Oord__class_Oless @ SY164 @ SY163 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(341,plain,
! [SV9: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV9 ) )
= $true )
| ( ( ! [SY165: $i,SY166: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY165 @ SY166 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SY166 @ SY165 @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(342,plain,
! [SV10: $i] :
( ( ( SV10
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV10 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(343,plain,
! [SV11: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV11 ) )
= $true )
| ( ( ! [SY167: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY167 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV11 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY167 @ SV11 ) @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(344,plain,
! [SV12: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV12 ) )
= $true )
| ( ( ! [SY168: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY168 @ SV12 ) @ SV12 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY168 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(345,plain,
! [SV13: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV13 ) )
= $true )
| ( ( ! [SY169: $i,SY170: $i] :
( ( SY169 = SY170 )
| ( c_HOL_Oord__class_Oless @ SY169 @ SY170 @ SV13 )
| ( c_HOL_Oord__class_Oless @ SY170 @ SY169 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(346,plain,
! [SV14: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV14 ) )
= $true )
| ( ( ! [SY171: $i,SY172: $i] :
( ( c_HOL_Oord__class_Oless @ SY171 @ SY172 @ SV14 )
| ( SY172 = SY171 )
| ( c_HOL_Oord__class_Oless @ SY172 @ SY171 @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(347,plain,
! [SV15: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV15 ) )
= $true )
| ( ( ! [SY173: $i,SY174: $i] :
( ( c_HOL_Oord__class_Oless @ SY173 @ SY174 @ SV15 )
| ( SY174 = SY173 )
| ( c_HOL_Oord__class_Oless @ SY174 @ SY173 @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(348,plain,
! [SV62: $i,SV16: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV16 @ SV62 @ tc_nat )
| ( SV62 = SV16 )
| ( c_HOL_Oord__class_Oless @ SV62 @ SV16 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(349,plain,
! [SV63: $i,SV17: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV17 @ SV63 @ tc_nat )
| ( SV63 = SV17 )
| ( c_HOL_Oord__class_Oless @ SV63 @ SV17 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(350,plain,
! [SV18: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV18 ) )
= $true )
| ( ( ! [SY177: $i,SY178: $i] :
( ( SY177 = SY178 )
| ( c_HOL_Oord__class_Oless @ SY178 @ SY177 @ SV18 )
| ( c_HOL_Oord__class_Oless @ SY177 @ SY178 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(351,plain,
! [SV19: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV19 ) )
= $true )
| ( ( ! [SY179: $i,SY180: $i] :
( ( c_HOL_Oord__class_Oless @ SY179 @ SY180 @ SV19 )
| ( SY180 = SY179 )
| ( c_HOL_Oord__class_Oless @ SY180 @ SY179 @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(352,plain,
! [SV20: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV20 ) )
= $true )
| ( ( ! [SY181: $i] :
~ ( c_HOL_Oord__class_Oless @ SY181 @ SY181 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(353,plain,
! [SV21: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV21 ) )
= $true )
| ( ( ! [SY182: $i] :
~ ( c_HOL_Oord__class_Oless @ SY182 @ SY182 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(354,plain,
! [SV22: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV22 ) )
= $true )
| ( ( ! [SY183: $i] :
~ ( c_HOL_Oord__class_Oless @ SY183 @ SY183 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(355,plain,
! [SV23: $i] :
( ( c_HOL_Oord__class_Oless @ SV23 @ SV23 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(356,plain,
! [SV24: $i] :
( ( c_HOL_Oord__class_Oless @ SV24 @ SV24 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(357,plain,
! [SV64: $i,SV25: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV25 )
| ! [SY243: $i] :
( ( c_HOL_Oord__class_Oless @ SV64 @ SY243 @ SV25 )
| ! [SY244: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY244 @ SY243 @ SV25 )
| ~ ( c_HOL_Oord__class_Oless @ SV64 @ SY244 @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(358,plain,
! [SV65: $i,SV26: $i] :
( ( ~ ( class_Orderings_Oorder @ SV26 )
| ! [SY245: $i] :
( ( c_HOL_Oord__class_Oless @ SV65 @ SY245 @ SV26 )
| ! [SY246: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV65 @ SY246 @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ SY246 @ SY245 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(359,plain,
! [SV27: $i] :
( ( c_HOL_Oord__class_Oless @ SV27 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(360,plain,
! [SV28: $i] :
( ( c_HOL_Oord__class_Oless @ SV28 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(361,plain,
! [SV66: $i,SV29: $i] :
( ( ! [SY247: $i] :
( ( c_Lambda_OdB_OApp @ SV29 @ SV66 )
!= ( c_Lambda_OdB_OVar @ SY247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(362,plain,
! [SV67: $i,SV30: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV30 ) @ ( c_Lambda_OdB_OAbs @ SV67 ) )
| ~ ( c_Lambda_Obeta @ SV30 @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(363,plain,
! [SV68: $i,SV31: $i] :
( ( ( SV31
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SV68 @ SV31 ) ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV68 ) @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(364,plain,
! [SV32: $i] :
( ( ( ! [SY194: $i] : ( c_InductTermi_OIT @ ( c_Lambda_OdB_OApp @ SV32 @ ( c_Lambda_OdB_OVar @ SY194 ) ) ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(365,plain,
! [SV69: $i,SV33: $i] :
( ( ! [SY248: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ SV33 @ SV69 ) @ ( c_Lambda_Olift @ SY248 @ SV69 ) )
| ~ ( c_Lambda_Obeta @ SV33 @ SY248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(366,plain,
! [SV70: $i,SV34: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV34 ) @ SV70 )
= ( c_Lambda_OdB_OVar @ SV34 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV34 @ SV70 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(367,plain,
! [SV71: $i,SV35: $i] :
( ( ! [SY249: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ SV35 @ SV71 ) @ ( c_Lambda_OdB_OApp @ SY249 @ SV71 ) )
| ~ ( c_Lambda_Obeta @ SV35 @ SY249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(368,plain,
! [SV72: $i,SV36: $i] :
( ( ! [SY250: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ SV36 @ SV72 ) @ ( c_Lambda_OdB_OApp @ SV36 @ SY250 ) )
| ~ ( c_Lambda_Obeta @ SV72 @ SY250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(369,plain,
! [SV37: $i] :
( ( ( ! [SY202: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV37 ) @ SY202 @ SV37 )
= SY202 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV37 @ SV37 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(370,plain,
! [SV73: $i,SV38: $i] :
( ( ! [SY251: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV38 ) @ SV73 @ SY251 )
= ( c_Lambda_OdB_OVar @ SV38 ) )
| ( SV38 = SY251 )
| ( c_HOL_Oord__class_Oless @ SY251 @ SV38 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(371,plain,
! [SV74: $i,SV39: $i] :
( ( ! [SY252: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OApp @ SV39 @ SV74 ) @ SY252 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV39 @ SY252 ) @ ( c_Lambda_Olift @ SV74 @ SY252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(372,plain,
! [SV75: $i,SV40: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV40 )
!= ( c_Lambda_OdB_OAbs @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(373,plain,
! [SV76: $i,SV41: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV41 )
!= ( c_Lambda_OdB_OAbs @ SV76 ) )
| ( SV41 = SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(374,plain,
! [SV77: $i,SV42: $i] :
( ( ! [SY253: $i] :
( ( c_Lambda_OdB_OVar @ SV42 )
!= ( c_Lambda_OdB_OApp @ SV77 @ SY253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(375,plain,
! [SV78: $i,SV43: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV43 ) @ SV78 ) @ ( c_Lambda_Osubst @ SV43 @ SV78 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(376,plain,
! [SV79: $i,SV44: $i] :
( ( ! [SY254: $i,SY255: $i] :
( ( ( c_Lambda_OdB_OApp @ SV44 @ SV79 )
!= ( c_Lambda_OdB_OApp @ SY254 @ SY255 ) )
| ( SV79 = SY255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(377,plain,
! [SV80: $i,SV45: $i] :
( ( ! [SY256: $i] :
( ! [SY257: $i] :
( ( c_Lambda_OdB_OApp @ SV45 @ SV80 )
!= ( c_Lambda_OdB_OApp @ SY256 @ SY257 ) )
| ( SV45 = SY256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(378,plain,
! [SV81: $i,SV46: $i] :
( ( ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV46 ) @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(379,plain,
! [SV82: $i,SV47: $i] :
( ( ( c_Lambda_Obeta @ SV47 @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SV47 @ SV82 ) )
| ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV47 ) @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(380,plain,
! [SV83: $i,SV48: $i] :
( ( ! [SY258: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV48 ) @ SV83 @ SY258 )
= ( c_Lambda_OdB_OVar @ SV48 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV48 @ SY258 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(381,plain,
! [SV84: $i,SV49: $i] :
( ( ! [SY259: $i] :
( ( c_Lambda_OdB_OAbs @ SV49 )
!= ( c_Lambda_OdB_OApp @ SV84 @ SY259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(382,plain,
! [SV85: $i,SV50: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV50 )
!= ( c_Lambda_OdB_OVar @ SV85 ) )
| ( SV50 = SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(383,plain,
! [SV86: $i,SV51: $i] :
( ( ! [SY260: $i] :
( ( c_Lambda_OdB_OApp @ SV51 @ SV86 )
!= ( c_Lambda_OdB_OAbs @ SY260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(384,plain,
! [SV87: $i,SV52: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV52 )
!= ( c_Lambda_OdB_OVar @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(385,plain,
! [SV88: $i,SV53: $i] :
( ( ! [SY261: $i,SY262: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ SV53 @ SV88 ) @ SY261 @ SY262 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV53 @ SY261 @ SY262 ) @ ( c_Lambda_Osubst @ SV88 @ SY261 @ SY262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(386,plain,
! [SV89: $i,SV54: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV54 ) @ SV89 @ SV54 )
= SV89 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(387,plain,
! [SV55: $i] :
( ( ( ! [SY232: $i,SY233: $i] : ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV55 @ ( c_Lambda_OdB_OVar @ SY232 ) @ SY233 ) ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(388,plain,
! [SV56: $i] :
( ( ( ! [SY234: $i] : ( c_InductTermi_OIT @ ( c_Lambda_Olift @ SV56 @ SY234 ) ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(389,plain,
! [SV90: $i,SV58: $i] :
( ( ! [SY263: $i,SY264: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV58 @ SV90 @ SY263 ) @ ( c_Lambda_Osubst @ SY264 @ SV90 @ SY263 ) )
| ~ ( c_Lambda_Obeta @ SV58 @ SY264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(390,plain,
! [SV59: $i] :
( ( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV59 ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(391,plain,
! [SV91: $i,SV60: $i] :
( ( ! [SY265: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV60 @ SV91 ) @ SY265 @ SV91 )
= SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(392,plain,
! [SV92: $i,SV61: $i] :
( ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_b____ @ SV61 @ SV92 ) )
| ! [SY266: $i] :
( ~ ( c_Type_Otyping @ SY266 @ SV61 @ v_T____ )
| ~ ( c_InductTermi_OIT @ SV61 )
| ! [SY267: $i] :
~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY266 @ SV92 @ v_T____ @ tc_Type_Otype ) @ v_b____ @ SY267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(393,plain,
! [SV1: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV1 )
= $false )
| ( ( ! [SY152: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY152 @ SV1 ) @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(394,plain,
! [SV2: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV2 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV2 )
= ( c_HOL_Ozero__class_Ozero @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(395,plain,
! [SV3: $i] :
( ( ( class_Nat_Osemiring__char__0 @ SV3 )
= $false )
| ( ( ! [SY153: $i,SY154: $i] :
( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SY153 @ SV3 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY154 @ SV3 ) )
| ( SY153 = SY154 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(396,plain,
! [SV4: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV4 )
= $false )
| ( ( ! [SY155: $i,SY156: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY155 @ SV4 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY156 @ SV4 ) @ SV4 )
| ~ ( c_HOL_Oord__class_Oless @ SY155 @ SY156 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(397,plain,
! [SV5: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV5 )
= $false )
| ( ( ! [SY157: $i,SY158: $i] :
( ( c_HOL_Oord__class_Oless @ SY157 @ SY158 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY157 @ SV5 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY158 @ SV5 ) @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(398,plain,
! [SV6: $i] :
( ( ( class_Orderings_Opreorder @ SV6 )
= $false )
| ( ( ! [SY159: $i,SY160: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY159 @ SY160 @ SV6 )
| ~ ( c_HOL_Oord__class_Oless @ SY160 @ SY159 @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(399,plain,
! [SV7: $i] :
( ( ( class_Orderings_Opreorder @ SV7 )
= $false )
| ( ( ! [SY161: $i,SY162: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY161 @ SY162 @ SV7 )
| ~ ( c_HOL_Oord__class_Oless @ SY162 @ SY161 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(400,plain,
! [SV8: $i] :
( ( ( class_Orderings_Olinorder @ SV8 )
= $false )
| ( ( ! [SY163: $i,SY164: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY163 @ SY164 @ SV8 )
| ~ ( c_HOL_Oord__class_Oless @ SY164 @ SY163 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(401,plain,
! [SV9: $i] :
( ( ( class_Orderings_Oorder @ SV9 )
= $false )
| ( ( ! [SY165: $i,SY166: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY165 @ SY166 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SY166 @ SY165 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(402,plain,
! [SV11: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV11 )
= $false )
| ( ( ! [SY167: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY167 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV11 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY167 @ SV11 ) @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(403,plain,
! [SV12: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV12 )
= $false )
| ( ( ! [SY168: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY168 @ SV12 ) @ SV12 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY168 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(404,plain,
! [SV13: $i] :
( ( ( class_Orderings_Olinorder @ SV13 )
= $false )
| ( ( ! [SY169: $i,SY170: $i] :
( ( SY169 = SY170 )
| ( c_HOL_Oord__class_Oless @ SY169 @ SY170 @ SV13 )
| ( c_HOL_Oord__class_Oless @ SY170 @ SY169 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(405,plain,
! [SV14: $i] :
( ( ( class_Orderings_Olinorder @ SV14 )
= $false )
| ( ( ! [SY171: $i,SY172: $i] :
( ( c_HOL_Oord__class_Oless @ SY171 @ SY172 @ SV14 )
| ( SY172 = SY171 )
| ( c_HOL_Oord__class_Oless @ SY172 @ SY171 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(406,plain,
! [SV15: $i] :
( ( ( class_Orderings_Olinorder @ SV15 )
= $false )
| ( ( ! [SY173: $i,SY174: $i] :
( ( c_HOL_Oord__class_Oless @ SY173 @ SY174 @ SV15 )
| ( SY174 = SY173 )
| ( c_HOL_Oord__class_Oless @ SY174 @ SY173 @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(407,plain,
! [SV62: $i,SV16: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV16 @ SV62 @ tc_nat )
= $true )
| ( ( ( SV62 = SV16 )
| ( c_HOL_Oord__class_Oless @ SV62 @ SV16 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(408,plain,
! [SV63: $i,SV17: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV17 @ SV63 @ tc_nat )
= $true )
| ( ( ( SV63 = SV17 )
| ( c_HOL_Oord__class_Oless @ SV63 @ SV17 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(409,plain,
! [SV18: $i] :
( ( ( class_Orderings_Olinorder @ SV18 )
= $false )
| ( ( ! [SY177: $i,SY178: $i] :
( ( SY177 = SY178 )
| ( c_HOL_Oord__class_Oless @ SY178 @ SY177 @ SV18 )
| ( c_HOL_Oord__class_Oless @ SY177 @ SY178 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(410,plain,
! [SV19: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV19 )
= $false )
| ( ( ! [SY179: $i,SY180: $i] :
( ( c_HOL_Oord__class_Oless @ SY179 @ SY180 @ SV19 )
| ( SY180 = SY179 )
| ( c_HOL_Oord__class_Oless @ SY180 @ SY179 @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(411,plain,
! [SV20: $i] :
( ( ( class_Orderings_Opreorder @ SV20 )
= $false )
| ( ( ! [SY181: $i] :
~ ( c_HOL_Oord__class_Oless @ SY181 @ SY181 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(412,plain,
! [SV21: $i] :
( ( ( class_Orderings_Olinorder @ SV21 )
= $false )
| ( ( ! [SY182: $i] :
~ ( c_HOL_Oord__class_Oless @ SY182 @ SY182 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(413,plain,
! [SV22: $i] :
( ( ( class_Orderings_Oorder @ SV22 )
= $false )
| ( ( ! [SY183: $i] :
~ ( c_HOL_Oord__class_Oless @ SY183 @ SY183 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(414,plain,
! [SV64: $i,SV25: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV25 ) )
= $true )
| ( ( ! [SY243: $i] :
( ( c_HOL_Oord__class_Oless @ SV64 @ SY243 @ SV25 )
| ! [SY244: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY244 @ SY243 @ SV25 )
| ~ ( c_HOL_Oord__class_Oless @ SV64 @ SY244 @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(415,plain,
! [SV65: $i,SV26: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV26 ) )
= $true )
| ( ( ! [SY245: $i] :
( ( c_HOL_Oord__class_Oless @ SV65 @ SY245 @ SV26 )
| ! [SY246: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV65 @ SY246 @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ SY246 @ SY245 @ SV26 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(416,plain,
! [SV93: $i,SV66: $i,SV29: $i] :
( ( ( ( c_Lambda_OdB_OApp @ SV29 @ SV66 )
!= ( c_Lambda_OdB_OVar @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(417,plain,
! [SV67: $i,SV30: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV30 ) @ ( c_Lambda_OdB_OAbs @ SV67 ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV30 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(418,plain,
! [SV68: $i,SV31: $i] :
( ( ( SV31
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SV68 @ SV31 ) ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV68 ) @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[363]) ).
thf(419,plain,
! [SV94: $i,SV32: $i] :
( ( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OApp @ SV32 @ ( c_Lambda_OdB_OVar @ SV94 ) ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV32 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(420,plain,
! [SV95: $i,SV69: $i,SV33: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ SV33 @ SV69 ) @ ( c_Lambda_Olift @ SV95 @ SV69 ) )
| ~ ( c_Lambda_Obeta @ SV33 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(421,plain,
! [SV70: $i,SV34: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV34 ) @ SV70 )
= ( c_Lambda_OdB_OVar @ SV34 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV34 @ SV70 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(422,plain,
! [SV96: $i,SV71: $i,SV35: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ SV35 @ SV71 ) @ ( c_Lambda_OdB_OApp @ SV96 @ SV71 ) )
| ~ ( c_Lambda_Obeta @ SV35 @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(423,plain,
! [SV97: $i,SV72: $i,SV36: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ SV36 @ SV72 ) @ ( c_Lambda_OdB_OApp @ SV36 @ SV97 ) )
| ~ ( c_Lambda_Obeta @ SV72 @ SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(424,plain,
! [SV98: $i,SV37: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV37 ) @ SV98 @ SV37 )
= SV98 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV37 @ SV37 @ tc_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(425,plain,
! [SV99: $i,SV73: $i,SV38: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV38 ) @ SV73 @ SV99 )
= ( c_Lambda_OdB_OVar @ SV38 ) )
| ( SV38 = SV99 )
| ( c_HOL_Oord__class_Oless @ SV99 @ SV38 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(426,plain,
! [SV100: $i,SV74: $i,SV39: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OApp @ SV39 @ SV74 ) @ SV100 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV39 @ SV100 ) @ ( c_Lambda_Olift @ SV74 @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(427,plain,
! [SV75: $i,SV40: $i] :
( ( ( c_Lambda_OdB_OVar @ SV40 )
= ( c_Lambda_OdB_OAbs @ SV75 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(428,plain,
! [SV76: $i,SV41: $i] :
( ( ( ( ( c_Lambda_OdB_OAbs @ SV41 )
!= ( c_Lambda_OdB_OAbs @ SV76 ) ) )
= $true )
| ( ( SV41 = SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(429,plain,
! [SV101: $i,SV77: $i,SV42: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV42 )
!= ( c_Lambda_OdB_OApp @ SV77 @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(430,plain,
! [SV102: $i,SV79: $i,SV44: $i] :
( ( ! [SY268: $i] :
( ( ( c_Lambda_OdB_OApp @ SV44 @ SV79 )
!= ( c_Lambda_OdB_OApp @ SV102 @ SY268 ) )
| ( SV79 = SY268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(431,plain,
! [SV103: $i,SV80: $i,SV45: $i] :
( ( ! [SY269: $i] :
( ( c_Lambda_OdB_OApp @ SV45 @ SV80 )
!= ( c_Lambda_OdB_OApp @ SV103 @ SY269 ) )
| ( SV45 = SV103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(432,plain,
! [SV81: $i,SV46: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV46 ) @ SV81 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(433,plain,
! [SV82: $i,SV47: $i] :
( ( ( c_Lambda_Obeta @ SV47 @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SV47 @ SV82 ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV47 ) @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(434,plain,
! [SV104: $i,SV83: $i,SV48: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV48 ) @ SV83 @ SV104 )
= ( c_Lambda_OdB_OVar @ SV48 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV48 @ SV104 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(435,plain,
! [SV105: $i,SV84: $i,SV49: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV49 )
!= ( c_Lambda_OdB_OApp @ SV84 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(436,plain,
! [SV85: $i,SV50: $i] :
( ( ( ( ( c_Lambda_OdB_OVar @ SV50 )
!= ( c_Lambda_OdB_OVar @ SV85 ) ) )
= $true )
| ( ( SV50 = SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[382]) ).
thf(437,plain,
! [SV106: $i,SV86: $i,SV51: $i] :
( ( ( ( c_Lambda_OdB_OApp @ SV51 @ SV86 )
!= ( c_Lambda_OdB_OAbs @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(438,plain,
! [SV87: $i,SV52: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV52 )
= ( c_Lambda_OdB_OVar @ SV87 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(439,plain,
! [SV107: $i,SV88: $i,SV53: $i] :
( ( ! [SY270: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ SV53 @ SV88 ) @ SV107 @ SY270 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV53 @ SV107 @ SY270 ) @ ( c_Lambda_Osubst @ SV88 @ SV107 @ SY270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(440,plain,
! [SV108: $i,SV55: $i] :
( ( ( ! [SY271: $i] : ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV55 @ ( c_Lambda_OdB_OVar @ SV108 ) @ SY271 ) ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV55 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(441,plain,
! [SV109: $i,SV56: $i] :
( ( ( c_InductTermi_OIT @ ( c_Lambda_Olift @ SV56 @ SV109 ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV56 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(442,plain,
! [SV110: $i,SV90: $i,SV58: $i] :
( ( ! [SY272: $i] :
( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV58 @ SV90 @ SV110 ) @ ( c_Lambda_Osubst @ SY272 @ SV90 @ SV110 ) )
| ~ ( c_Lambda_Obeta @ SV58 @ SY272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(443,plain,
! [SV59: $i] :
( ( ( c_InductTermi_OIT @ SV59 )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(444,plain,
! [SV111: $i,SV91: $i,SV60: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV60 @ SV91 ) @ SV111 @ SV91 )
= SV60 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(445,plain,
! [SV92: $i,SV61: $i] :
( ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_b____ @ SV61 @ SV92 ) )
= $true )
| ( ( ! [SY266: $i] :
( ~ ( c_Type_Otyping @ SY266 @ SV61 @ v_T____ )
| ~ ( c_InductTermi_OIT @ SV61 )
| ! [SY267: $i] :
~ ( c_Type_Otyping @ ( c_Type_Oshift @ SY266 @ SV92 @ v_T____ @ tc_Type_Otype ) @ v_b____ @ SY267 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(446,plain,
! [SV1: $i,SV112: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV112 @ SV1 ) @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV1 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(447,plain,
! [SV3: $i,SV113: $i] :
( ( ( ! [SY273: $i] :
( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV113 @ SV3 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY273 @ SV3 ) )
| ( SV113 = SY273 ) ) )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(448,plain,
! [SV4: $i,SV114: $i] :
( ( ( ! [SY274: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV114 @ SV4 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY274 @ SV4 ) @ SV4 )
| ~ ( c_HOL_Oord__class_Oless @ SV114 @ SY274 @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(449,plain,
! [SV5: $i,SV115: $i] :
( ( ( ! [SY275: $i] :
( ( c_HOL_Oord__class_Oless @ SV115 @ SY275 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV115 @ SV5 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY275 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(450,plain,
! [SV6: $i,SV116: $i] :
( ( ( ! [SY276: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV116 @ SY276 @ SV6 )
| ~ ( c_HOL_Oord__class_Oless @ SY276 @ SV116 @ SV6 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(451,plain,
! [SV7: $i,SV117: $i] :
( ( ( ! [SY277: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV117 @ SY277 @ SV7 )
| ~ ( c_HOL_Oord__class_Oless @ SY277 @ SV117 @ SV7 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(452,plain,
! [SV8: $i,SV118: $i] :
( ( ( ! [SY278: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV118 @ SY278 @ SV8 )
| ~ ( c_HOL_Oord__class_Oless @ SY278 @ SV118 @ SV8 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(453,plain,
! [SV9: $i,SV119: $i] :
( ( ( ! [SY279: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV119 @ SY279 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SY279 @ SV119 @ SV9 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(454,plain,
! [SV11: $i,SV120: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV120 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV11 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV120 @ SV11 ) @ SV11 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(455,plain,
! [SV121: $i,SV12: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV121 @ SV12 ) @ SV12 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV121 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(456,plain,
! [SV13: $i,SV122: $i] :
( ( ( ! [SY280: $i] :
( ( SV122 = SY280 )
| ( c_HOL_Oord__class_Oless @ SV122 @ SY280 @ SV13 )
| ( c_HOL_Oord__class_Oless @ SY280 @ SV122 @ SV13 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(457,plain,
! [SV14: $i,SV123: $i] :
( ( ( ! [SY281: $i] :
( ( c_HOL_Oord__class_Oless @ SV123 @ SY281 @ SV14 )
| ( SY281 = SV123 )
| ( c_HOL_Oord__class_Oless @ SY281 @ SV123 @ SV14 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(458,plain,
! [SV15: $i,SV124: $i] :
( ( ( ! [SY282: $i] :
( ( c_HOL_Oord__class_Oless @ SV124 @ SY282 @ SV15 )
| ( SY282 = SV124 )
| ( c_HOL_Oord__class_Oless @ SY282 @ SV124 @ SV15 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(459,plain,
! [SV16: $i,SV62: $i] :
( ( ( SV62 = SV16 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV62 @ SV16 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV16 @ SV62 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(460,plain,
! [SV17: $i,SV63: $i] :
( ( ( SV63 = SV17 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV63 @ SV17 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV17 @ SV63 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(461,plain,
! [SV18: $i,SV125: $i] :
( ( ( ! [SY283: $i] :
( ( SV125 = SY283 )
| ( c_HOL_Oord__class_Oless @ SY283 @ SV125 @ SV18 )
| ( c_HOL_Oord__class_Oless @ SV125 @ SY283 @ SV18 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(462,plain,
! [SV19: $i,SV126: $i] :
( ( ( ! [SY284: $i] :
( ( c_HOL_Oord__class_Oless @ SV126 @ SY284 @ SV19 )
| ( SY284 = SV126 )
| ( c_HOL_Oord__class_Oless @ SY284 @ SV126 @ SV19 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(463,plain,
! [SV20: $i,SV127: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV127 @ SV127 @ SV20 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(464,plain,
! [SV21: $i,SV128: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV128 @ SV128 @ SV21 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(465,plain,
! [SV22: $i,SV129: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV129 @ SV129 @ SV22 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(466,plain,
! [SV64: $i,SV25: $i] :
( ( ( class_Orderings_Opreorder @ SV25 )
= $false )
| ( ( ! [SY243: $i] :
( ( c_HOL_Oord__class_Oless @ SV64 @ SY243 @ SV25 )
| ! [SY244: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY244 @ SY243 @ SV25 )
| ~ ( c_HOL_Oord__class_Oless @ SV64 @ SY244 @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(467,plain,
! [SV65: $i,SV26: $i] :
( ( ( class_Orderings_Oorder @ SV26 )
= $false )
| ( ( ! [SY245: $i] :
( ( c_HOL_Oord__class_Oless @ SV65 @ SY245 @ SV26 )
| ! [SY246: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV65 @ SY246 @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ SY246 @ SY245 @ SV26 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(468,plain,
! [SV93: $i,SV66: $i,SV29: $i] :
( ( ( c_Lambda_OdB_OApp @ SV29 @ SV66 )
= ( c_Lambda_OdB_OVar @ SV93 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(469,plain,
! [SV67: $i,SV30: $i] :
( ( ( c_Lambda_Obeta @ SV30 @ SV67 )
= $false )
| ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV30 ) @ ( c_Lambda_OdB_OAbs @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(470,plain,
! [SV31: $i,SV68: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV68 ) @ SV31 )
= $false )
| ( ( SV31
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SV68 @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(471,plain,
! [SV94: $i,SV32: $i] :
( ( ( c_InductTermi_OIT @ SV32 )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OApp @ SV32 @ ( c_Lambda_OdB_OVar @ SV94 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(472,plain,
! [SV95: $i,SV69: $i,SV33: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ SV33 @ SV69 ) @ ( c_Lambda_Olift @ SV95 @ SV69 ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV33 @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(473,plain,
! [SV70: $i,SV34: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV34 @ SV70 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV34 ) @ SV70 )
= ( c_Lambda_OdB_OVar @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(474,plain,
! [SV96: $i,SV71: $i,SV35: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ SV35 @ SV71 ) @ ( c_Lambda_OdB_OApp @ SV96 @ SV71 ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV35 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(475,plain,
! [SV97: $i,SV72: $i,SV36: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ SV36 @ SV72 ) @ ( c_Lambda_OdB_OApp @ SV36 @ SV97 ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV72 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(476,plain,
! [SV99: $i,SV73: $i,SV38: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV38 ) @ SV73 @ SV99 )
= ( c_Lambda_OdB_OVar @ SV38 ) )
= $true )
| ( ( ( SV38 = SV99 )
| ( c_HOL_Oord__class_Oless @ SV99 @ SV38 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[425]) ).
thf(477,plain,
! [SV76: $i,SV41: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV41 )
= ( c_Lambda_OdB_OAbs @ SV76 ) )
= $false )
| ( ( SV41 = SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(478,plain,
! [SV101: $i,SV77: $i,SV42: $i] :
( ( ( c_Lambda_OdB_OVar @ SV42 )
= ( c_Lambda_OdB_OApp @ SV77 @ SV101 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(479,plain,
! [SV130: $i,SV102: $i,SV79: $i,SV44: $i] :
( ( ( ( c_Lambda_OdB_OApp @ SV44 @ SV79 )
!= ( c_Lambda_OdB_OApp @ SV102 @ SV130 ) )
| ( SV79 = SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(480,plain,
! [SV103: $i,SV80: $i,SV45: $i] :
( ( ( ! [SY269: $i] :
( ( c_Lambda_OdB_OApp @ SV45 @ SV80 )
!= ( c_Lambda_OdB_OApp @ SV103 @ SY269 ) ) )
= $true )
| ( ( SV45 = SV103 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(481,plain,
! [SV82: $i,SV47: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV47 ) @ SV82 )
= $false )
| ( ( c_Lambda_Obeta @ SV47 @ ( c_Lambda_Osko__Lambda__Xbeta__cases__2__1 @ SV47 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(482,plain,
! [SV104: $i,SV83: $i,SV48: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV48 ) @ SV83 @ SV104 )
= ( c_Lambda_OdB_OVar @ SV48 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV48 @ SV104 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(483,plain,
! [SV105: $i,SV84: $i,SV49: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV49 )
= ( c_Lambda_OdB_OApp @ SV84 @ SV105 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[435]) ).
thf(484,plain,
! [SV85: $i,SV50: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV50 )
= ( c_Lambda_OdB_OVar @ SV85 ) )
= $false )
| ( ( SV50 = SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(485,plain,
! [SV106: $i,SV86: $i,SV51: $i] :
( ( ( c_Lambda_OdB_OApp @ SV51 @ SV86 )
= ( c_Lambda_OdB_OAbs @ SV106 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(486,plain,
! [SV131: $i,SV107: $i,SV88: $i,SV53: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ SV53 @ SV88 ) @ SV107 @ SV131 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV53 @ SV107 @ SV131 ) @ ( c_Lambda_Osubst @ SV88 @ SV107 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(487,plain,
! [SV132: $i,SV108: $i,SV55: $i] :
( ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV55 @ ( c_Lambda_OdB_OVar @ SV108 ) @ SV132 ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV55 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(488,plain,
! [SV109: $i,SV56: $i] :
( ( ( c_InductTermi_OIT @ SV56 )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Olift @ SV56 @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(489,plain,
! [SV133: $i,SV110: $i,SV90: $i,SV58: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV58 @ SV90 @ SV110 ) @ ( c_Lambda_Osubst @ SV133 @ SV90 @ SV110 ) )
| ~ ( c_Lambda_Obeta @ SV58 @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(490,plain,
! [SV92: $i,SV61: $i,SV134: $i] :
( ( ( ~ ( c_Type_Otyping @ SV134 @ SV61 @ v_T____ )
| ~ ( c_InductTermi_OIT @ SV61 )
| ! [SY285: $i] :
~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV134 @ SV92 @ v_T____ @ tc_Type_Otype ) @ v_b____ @ SY285 ) )
= $true )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_b____ @ SV61 @ SV92 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(491,plain,
! [SV1: $i,SV112: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV112 @ SV1 ) @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ SV1 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(492,plain,
! [SV135: $i,SV3: $i,SV113: $i] :
( ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV113 @ SV3 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV135 @ SV3 ) )
| ( SV113 = SV135 ) )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(493,plain,
! [SV136: $i,SV4: $i,SV114: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV114 @ SV4 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV136 @ SV4 ) @ SV4 )
| ~ ( c_HOL_Oord__class_Oless @ SV114 @ SV136 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(494,plain,
! [SV5: $i,SV137: $i,SV115: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV115 @ SV137 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV115 @ SV5 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV137 @ SV5 ) @ SV5 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(495,plain,
! [SV6: $i,SV138: $i,SV116: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV116 @ SV138 @ SV6 )
| ~ ( c_HOL_Oord__class_Oless @ SV138 @ SV116 @ SV6 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(496,plain,
! [SV7: $i,SV139: $i,SV117: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV117 @ SV139 @ SV7 )
| ~ ( c_HOL_Oord__class_Oless @ SV139 @ SV117 @ SV7 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(497,plain,
! [SV8: $i,SV140: $i,SV118: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV118 @ SV140 @ SV8 )
| ~ ( c_HOL_Oord__class_Oless @ SV140 @ SV118 @ SV8 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(498,plain,
! [SV9: $i,SV141: $i,SV119: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV119 @ SV141 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV141 @ SV119 @ SV9 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(499,plain,
! [SV11: $i,SV120: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV120 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV11 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV120 @ SV11 ) @ SV11 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(500,plain,
! [SV121: $i,SV12: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV121 @ SV12 ) @ SV12 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV121 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(501,plain,
! [SV13: $i,SV142: $i,SV122: $i] :
( ( ( ( SV122 = SV142 )
| ( c_HOL_Oord__class_Oless @ SV122 @ SV142 @ SV13 )
| ( c_HOL_Oord__class_Oless @ SV142 @ SV122 @ SV13 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(502,plain,
! [SV14: $i,SV143: $i,SV123: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV123 @ SV143 @ SV14 )
| ( SV143 = SV123 )
| ( c_HOL_Oord__class_Oless @ SV143 @ SV123 @ SV14 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(503,plain,
! [SV15: $i,SV144: $i,SV124: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV124 @ SV144 @ SV15 )
| ( SV144 = SV124 )
| ( c_HOL_Oord__class_Oless @ SV144 @ SV124 @ SV15 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(504,plain,
! [SV18: $i,SV145: $i,SV125: $i] :
( ( ( ( SV125 = SV145 )
| ( c_HOL_Oord__class_Oless @ SV145 @ SV125 @ SV18 )
| ( c_HOL_Oord__class_Oless @ SV125 @ SV145 @ SV18 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(505,plain,
! [SV19: $i,SV146: $i,SV126: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV126 @ SV146 @ SV19 )
| ( SV146 = SV126 )
| ( c_HOL_Oord__class_Oless @ SV146 @ SV126 @ SV19 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(506,plain,
! [SV20: $i,SV127: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV127 @ SV127 @ SV20 )
= $false )
| ( ( class_Orderings_Opreorder @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(507,plain,
! [SV21: $i,SV128: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV128 @ SV128 @ SV21 )
= $false )
| ( ( class_Orderings_Olinorder @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(508,plain,
! [SV22: $i,SV129: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV129 @ SV129 @ SV22 )
= $false )
| ( ( class_Orderings_Oorder @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(509,plain,
! [SV25: $i,SV147: $i,SV64: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV64 @ SV147 @ SV25 )
| ! [SY286: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY286 @ SV147 @ SV25 )
| ~ ( c_HOL_Oord__class_Oless @ SV64 @ SY286 @ SV25 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(510,plain,
! [SV26: $i,SV148: $i,SV65: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV65 @ SV148 @ SV26 )
| ! [SY287: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV65 @ SY287 @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ SY287 @ SV148 @ SV26 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(511,plain,
! [SV69: $i,SV95: $i,SV33: $i] :
( ( ( c_Lambda_Obeta @ SV33 @ SV95 )
= $false )
| ( ( c_Lambda_Obeta @ ( c_Lambda_Olift @ SV33 @ SV69 ) @ ( c_Lambda_Olift @ SV95 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(512,plain,
! [SV71: $i,SV96: $i,SV35: $i] :
( ( ( c_Lambda_Obeta @ SV35 @ SV96 )
= $false )
| ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ SV35 @ SV71 ) @ ( c_Lambda_OdB_OApp @ SV96 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(513,plain,
! [SV36: $i,SV97: $i,SV72: $i] :
( ( ( c_Lambda_Obeta @ SV72 @ SV97 )
= $false )
| ( ( c_Lambda_Obeta @ ( c_Lambda_OdB_OApp @ SV36 @ SV72 ) @ ( c_Lambda_OdB_OApp @ SV36 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(514,plain,
! [SV73: $i,SV99: $i,SV38: $i] :
( ( ( SV38 = SV99 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV99 @ SV38 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV38 ) @ SV73 @ SV99 )
= ( c_Lambda_OdB_OVar @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(515,plain,
! [SV130: $i,SV102: $i,SV79: $i,SV44: $i] :
( ( ( ( ( c_Lambda_OdB_OApp @ SV44 @ SV79 )
!= ( c_Lambda_OdB_OApp @ SV102 @ SV130 ) ) )
= $true )
| ( ( SV79 = SV130 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[479]) ).
thf(516,plain,
! [SV149: $i,SV103: $i,SV80: $i,SV45: $i] :
( ( ( ( ( c_Lambda_OdB_OApp @ SV45 @ SV80 )
!= ( c_Lambda_OdB_OApp @ SV103 @ SV149 ) ) )
= $true )
| ( ( SV45 = SV103 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(517,plain,
! [SV83: $i,SV104: $i,SV48: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV48 @ SV104 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV48 ) @ SV83 @ SV104 )
= ( c_Lambda_OdB_OVar @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(518,plain,
! [SV132: $i,SV108: $i,SV55: $i] :
( ( ( c_InductTermi_OIT @ SV55 )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV55 @ ( c_Lambda_OdB_OVar @ SV108 ) @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(519,plain,
! [SV133: $i,SV110: $i,SV90: $i,SV58: $i] :
( ( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV58 @ SV90 @ SV110 ) @ ( c_Lambda_Osubst @ SV133 @ SV90 @ SV110 ) )
= $true )
| ( ( ~ ( c_Lambda_Obeta @ SV58 @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(520,plain,
! [SV92: $i,SV61: $i,SV134: $i] :
( ( ( ~ ( c_Type_Otyping @ SV134 @ SV61 @ v_T____ ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV61 )
| ! [SY285: $i] :
~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV134 @ SV92 @ v_T____ @ tc_Type_Otype ) @ v_b____ @ SY285 ) )
= $true )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_b____ @ SV61 @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(521,plain,
! [SV135: $i,SV3: $i,SV113: $i] :
( ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV113 @ SV3 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV135 @ SV3 ) ) )
= $true )
| ( ( SV113 = SV135 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(522,plain,
! [SV136: $i,SV4: $i,SV114: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV114 @ SV4 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV136 @ SV4 ) @ SV4 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV114 @ SV136 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(523,plain,
! [SV5: $i,SV137: $i,SV115: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV115 @ SV137 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV115 @ SV5 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV137 @ SV5 ) @ SV5 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(524,plain,
! [SV6: $i,SV138: $i,SV116: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV116 @ SV138 @ SV6 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV138 @ SV116 @ SV6 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(525,plain,
! [SV7: $i,SV139: $i,SV117: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV117 @ SV139 @ SV7 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV139 @ SV117 @ SV7 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[496]) ).
thf(526,plain,
! [SV8: $i,SV140: $i,SV118: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV118 @ SV140 @ SV8 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV140 @ SV118 @ SV8 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[497]) ).
thf(527,plain,
! [SV9: $i,SV141: $i,SV119: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV119 @ SV141 @ SV9 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV141 @ SV119 @ SV9 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[498]) ).
thf(528,plain,
! [SV120: $i,SV11: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV11 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV120 @ SV11 ) @ SV11 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV120 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(529,plain,
! [SV12: $i,SV121: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV121 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV12 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV121 @ SV12 ) @ SV12 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(530,plain,
! [SV13: $i,SV142: $i,SV122: $i] :
( ( ( SV122 = SV142 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV122 @ SV142 @ SV13 )
| ( c_HOL_Oord__class_Oless @ SV142 @ SV122 @ SV13 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[501]) ).
thf(531,plain,
! [SV14: $i,SV143: $i,SV123: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV123 @ SV143 @ SV14 )
= $true )
| ( ( ( SV143 = SV123 )
| ( c_HOL_Oord__class_Oless @ SV143 @ SV123 @ SV14 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[502]) ).
thf(532,plain,
! [SV15: $i,SV144: $i,SV124: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV124 @ SV144 @ SV15 )
= $true )
| ( ( ( SV144 = SV124 )
| ( c_HOL_Oord__class_Oless @ SV144 @ SV124 @ SV15 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(533,plain,
! [SV18: $i,SV145: $i,SV125: $i] :
( ( ( SV125 = SV145 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV145 @ SV125 @ SV18 )
| ( c_HOL_Oord__class_Oless @ SV125 @ SV145 @ SV18 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(534,plain,
! [SV19: $i,SV146: $i,SV126: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV126 @ SV146 @ SV19 )
= $true )
| ( ( ( SV146 = SV126 )
| ( c_HOL_Oord__class_Oless @ SV146 @ SV126 @ SV19 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(535,plain,
! [SV25: $i,SV147: $i,SV64: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV64 @ SV147 @ SV25 )
= $true )
| ( ( ! [SY286: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY286 @ SV147 @ SV25 )
| ~ ( c_HOL_Oord__class_Oless @ SV64 @ SY286 @ SV25 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(536,plain,
! [SV26: $i,SV148: $i,SV65: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV65 @ SV148 @ SV26 )
= $true )
| ( ( ! [SY287: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV65 @ SY287 @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ SY287 @ SV148 @ SV26 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[510]) ).
thf(537,plain,
! [SV130: $i,SV102: $i,SV79: $i,SV44: $i] :
( ( ( ( c_Lambda_OdB_OApp @ SV44 @ SV79 )
= ( c_Lambda_OdB_OApp @ SV102 @ SV130 ) )
= $false )
| ( ( SV79 = SV130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(538,plain,
! [SV149: $i,SV103: $i,SV80: $i,SV45: $i] :
( ( ( ( c_Lambda_OdB_OApp @ SV45 @ SV80 )
= ( c_Lambda_OdB_OApp @ SV103 @ SV149 ) )
= $false )
| ( ( SV45 = SV103 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(539,plain,
! [SV110: $i,SV90: $i,SV133: $i,SV58: $i] :
( ( ( c_Lambda_Obeta @ SV58 @ SV133 )
= $false )
| ( ( c_Lambda_Obeta @ ( c_Lambda_Osubst @ SV58 @ SV90 @ SV110 ) @ ( c_Lambda_Osubst @ SV133 @ SV90 @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(540,plain,
! [SV92: $i,SV61: $i,SV134: $i] :
( ( ( c_Type_Otyping @ SV134 @ SV61 @ v_T____ )
= $false )
| ( ( ~ ( c_InductTermi_OIT @ SV61 )
| ! [SY285: $i] :
~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV134 @ SV92 @ v_T____ @ tc_Type_Otype ) @ v_b____ @ SY285 ) )
= $true )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_b____ @ SV61 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(541,plain,
! [SV135: $i,SV3: $i,SV113: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV113 @ SV3 )
= ( c_Nat_Osemiring__1__class_Oof__nat @ SV135 @ SV3 ) )
= $false )
| ( ( SV113 = SV135 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(542,plain,
! [SV4: $i,SV136: $i,SV114: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV114 @ SV136 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV114 @ SV4 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV136 @ SV4 ) @ SV4 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(543,plain,
! [SV137: $i,SV5: $i,SV115: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV115 @ SV5 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV137 @ SV5 ) @ SV5 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV115 @ SV137 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(544,plain,
! [SV6: $i,SV138: $i,SV116: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV116 @ SV138 @ SV6 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV138 @ SV116 @ SV6 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(545,plain,
! [SV7: $i,SV139: $i,SV117: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV117 @ SV139 @ SV7 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV139 @ SV117 @ SV7 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(546,plain,
! [SV8: $i,SV140: $i,SV118: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV118 @ SV140 @ SV8 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV140 @ SV118 @ SV8 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(547,plain,
! [SV9: $i,SV141: $i,SV119: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV119 @ SV141 @ SV9 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV141 @ SV119 @ SV9 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(548,plain,
! [SV13: $i,SV142: $i,SV122: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV122 @ SV142 @ SV13 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV142 @ SV122 @ SV13 )
= $true )
| ( ( SV122 = SV142 )
= $true )
| ( ( class_Orderings_Olinorder @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[530]) ).
thf(549,plain,
! [SV14: $i,SV123: $i,SV143: $i] :
( ( ( SV143 = SV123 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV143 @ SV123 @ SV14 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV123 @ SV143 @ SV14 )
= $true )
| ( ( class_Orderings_Olinorder @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[531]) ).
thf(550,plain,
! [SV15: $i,SV124: $i,SV144: $i] :
( ( ( SV144 = SV124 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV144 @ SV124 @ SV15 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV124 @ SV144 @ SV15 )
= $true )
| ( ( class_Orderings_Olinorder @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[532]) ).
thf(551,plain,
! [SV18: $i,SV125: $i,SV145: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV145 @ SV125 @ SV18 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV125 @ SV145 @ SV18 )
= $true )
| ( ( SV125 = SV145 )
= $true )
| ( ( class_Orderings_Olinorder @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[533]) ).
thf(552,plain,
! [SV19: $i,SV126: $i,SV146: $i] :
( ( ( SV146 = SV126 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV146 @ SV126 @ SV19 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV126 @ SV146 @ SV19 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[534]) ).
thf(553,plain,
! [SV64: $i,SV25: $i,SV147: $i,SV150: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV150 @ SV147 @ SV25 )
| ~ ( c_HOL_Oord__class_Oless @ SV64 @ SV150 @ SV25 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV64 @ SV147 @ SV25 )
= $true )
| ( ( class_Orderings_Opreorder @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(554,plain,
! [SV148: $i,SV26: $i,SV151: $i,SV65: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV65 @ SV151 @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ SV151 @ SV148 @ SV26 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV65 @ SV148 @ SV26 )
= $true )
| ( ( class_Orderings_Oorder @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(555,plain,
! [SV92: $i,SV134: $i,SV61: $i] :
( ( ( ~ ( c_InductTermi_OIT @ SV61 ) )
= $true )
| ( ( ! [SY285: $i] :
~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV134 @ SV92 @ v_T____ @ tc_Type_Otype ) @ v_b____ @ SY285 ) )
= $true )
| ( ( c_Type_Otyping @ SV134 @ SV61 @ v_T____ )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_b____ @ SV61 @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[540]) ).
thf(556,plain,
! [SV6: $i,SV116: $i,SV138: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV138 @ SV116 @ SV6 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV116 @ SV138 @ SV6 )
= $false )
| ( ( class_Orderings_Opreorder @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(557,plain,
! [SV7: $i,SV117: $i,SV139: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV139 @ SV117 @ SV7 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV117 @ SV139 @ SV7 )
= $false )
| ( ( class_Orderings_Opreorder @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(558,plain,
! [SV8: $i,SV118: $i,SV140: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV140 @ SV118 @ SV8 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV118 @ SV140 @ SV8 )
= $false )
| ( ( class_Orderings_Olinorder @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(559,plain,
! [SV9: $i,SV119: $i,SV141: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV141 @ SV119 @ SV9 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV119 @ SV141 @ SV9 )
= $false )
| ( ( class_Orderings_Oorder @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(560,plain,
! [SV64: $i,SV25: $i,SV147: $i,SV150: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV150 @ SV147 @ SV25 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV64 @ SV150 @ SV25 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV64 @ SV147 @ SV25 )
= $true )
| ( ( class_Orderings_Opreorder @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(561,plain,
! [SV148: $i,SV26: $i,SV151: $i,SV65: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV65 @ SV151 @ SV26 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV151 @ SV148 @ SV26 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV65 @ SV148 @ SV26 )
= $true )
| ( ( class_Orderings_Oorder @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(562,plain,
! [SV92: $i,SV134: $i,SV61: $i] :
( ( ( c_InductTermi_OIT @ SV61 )
= $false )
| ( ( ! [SY285: $i] :
~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV134 @ SV92 @ v_T____ @ tc_Type_Otype ) @ v_b____ @ SY285 ) )
= $true )
| ( ( c_Type_Otyping @ SV134 @ SV61 @ v_T____ )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_b____ @ SV61 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(563,plain,
! [SV64: $i,SV25: $i,SV147: $i,SV150: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV150 @ SV147 @ SV25 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV64 @ SV150 @ SV25 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV64 @ SV147 @ SV25 )
= $true )
| ( ( class_Orderings_Opreorder @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(564,plain,
! [SV148: $i,SV26: $i,SV151: $i,SV65: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV65 @ SV151 @ SV26 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV151 @ SV148 @ SV26 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV65 @ SV148 @ SV26 )
= $true )
| ( ( class_Orderings_Oorder @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(565,plain,
! [SV61: $i,SV152: $i,SV92: $i,SV134: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV134 @ SV92 @ v_T____ @ tc_Type_Otype ) @ v_b____ @ SV152 ) )
= $true )
| ( ( c_InductTermi_OIT @ SV61 )
= $false )
| ( ( c_Type_Otyping @ SV134 @ SV61 @ v_T____ )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_b____ @ SV61 @ SV92 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(566,plain,
! [SV147: $i,SV25: $i,SV150: $i,SV64: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV64 @ SV150 @ SV25 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV150 @ SV147 @ SV25 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV64 @ SV147 @ SV25 )
= $true )
| ( ( class_Orderings_Opreorder @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(567,plain,
! [SV65: $i,SV26: $i,SV148: $i,SV151: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV151 @ SV148 @ SV26 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV65 @ SV151 @ SV26 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV65 @ SV148 @ SV26 )
= $true )
| ( ( class_Orderings_Oorder @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(568,plain,
! [SV61: $i,SV152: $i,SV92: $i,SV134: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV134 @ SV92 @ v_T____ @ tc_Type_Otype ) @ v_b____ @ SV152 )
= $false )
| ( ( c_InductTermi_OIT @ SV61 )
= $false )
| ( ( c_Type_Otyping @ SV134 @ SV61 @ v_T____ )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ v_b____ @ SV61 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(569,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[251,568,567,566,559,558,557,556,552,551,550,549,548,543,542,541,539,538,537,529,528,518,517,514,513,512,511,508,507,506,491,488,486,485,484,483,481,478,477,473,471,470,469,468,460,459,444,443,438,432,427,426,424,394,386,375,360,359,356,355,342,332,327,279,269,267,266,265,264,263,262,261,260,258,256,254]) ).
thf(570,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[569]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : LCL808-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jul 2 15:01:08 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.38 .
% 0.20/0.40
% 0.20/0.40 No.of.Axioms: 75
% 0.20/0.40
% 0.20/0.40 Length.of.Defs: 0
% 0.20/0.40
% 0.20/0.40 Contains.Choice.Funs: false
% 0.20/0.43 ..
% 0.20/0.45 (rf:0,axioms:75,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:77,loop_count:0,foatp_calls:0,translation:fof_full)............................
% 1.01/1.20
% 1.01/1.20 ********************************
% 1.01/1.20 * All subproblems solved! *
% 1.01/1.20 ********************************
% 1.01/1.20 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:75,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:569,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.14/1.35
% 1.14/1.35 %**** Beginning of derivation protocol ****
% 1.14/1.35 % SZS output start CNFRefutation
% See solution above
% 1.14/1.35
% 1.14/1.35 %**** End of derivation protocol ****
% 1.14/1.35 %**** no. of clauses in derivation: 570 ****
% 1.14/1.35 %**** clause counter: 569 ****
% 1.14/1.35
% 1.14/1.35 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:75,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:569,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------