TSTP Solution File: LCL853-1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LCL853-1 : 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 : n019.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 12:27:15 EDT 2022
% Result : Unsatisfiable 0.19s 0.51s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 62
% Syntax : Number of formulae : 396 ( 235 unt; 14 typ; 0 def)
% Number of atoms : 1887 ( 749 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 2947 ( 369 ~; 509 |; 0 &;2069 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 972 ( 0 ^ 972 !; 0 ?; 972 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(tp_c_InductTermi_OIT,type,
c_InductTermi_OIT: $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_Osubst,type,
c_Lambda_Osubst: $i > $i > $i > $i ).
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_tc_nat,type,
tc_nat: $i ).
thf(tp_v_s____,type,
v_s____: $i ).
thf(tp_v_ta____,type,
v_ta____: $i ).
thf(1,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(2,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(3,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(4,axiom,
! [V_r: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ V_r ) )
| ~ ( c_InductTermi_OIT @ V_r ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).
thf(5,axiom,
c_InductTermi_OIT @ v_ta____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_I4_J_0) ).
thf(6,axiom,
! [V_n: $i] : ( c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).
thf(7,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/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).
thf(8,axiom,
c_InductTermi_OIT @ v_s____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_I2_J_0) ).
thf(9,axiom,
! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
thf(10,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
thf(11,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/sandbox/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
thf(12,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(13,axiom,
! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
thf(15,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/sandbox/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
thf(16,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
thf(17,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/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).
thf(18,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/sandbox/benchmark/theBenchmark.p',cls_subst__Var_1) ).
thf(19,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/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(20,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/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(21,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/sandbox/benchmark/theBenchmark.p',cls_subst__Var_2) ).
thf(22,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/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
thf(23,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
thf(24,axiom,
! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(25,axiom,
! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(26,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/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(27,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/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(28,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/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(29,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/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(30,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/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(31,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/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(33,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/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(34,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/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(35,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/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(36,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
thf(37,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
thf(38,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/sandbox/benchmark/theBenchmark.p',cls_subst__lt_0) ).
thf(39,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/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(40,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(41,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
thf(42,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/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(43,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/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(44,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/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(45,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/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(46,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/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(47,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(48,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[47]) ).
thf(49,negated_conjecture,
~ ( c_InductTermi_OIT @ v_s____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(50,plain,
$false = $false,
inference(unfold_def,[status(thm)],[48]) ).
thf(51,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(52,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(53,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(54,plain,
( ( ! [V_r: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ V_r ) )
| ~ ( c_InductTermi_OIT @ V_r ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(55,plain,
( ( c_InductTermi_OIT @ v_ta____ )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(56,plain,
( ( ! [V_n: $i] : ( c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(57,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)],[7]) ).
thf(58,plain,
( ( c_InductTermi_OIT @ v_s____ )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(59,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)],[9]) ).
thf(60,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)],[10]) ).
thf(61,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)],[11]) ).
thf(62,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)],[12]) ).
thf(63,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)],[13]) ).
thf(64,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)],[14]) ).
thf(65,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)],[15]) ).
thf(66,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)],[16]) ).
thf(67,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)],[17]) ).
thf(68,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)],[18]) ).
thf(69,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)],[19]) ).
thf(70,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)],[20]) ).
thf(71,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)],[21]) ).
thf(72,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)],[22]) ).
thf(73,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)],[23]) ).
thf(74,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(75,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(76,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)],[26]) ).
thf(77,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)],[27]) ).
thf(78,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)],[28]) ).
thf(79,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)],[29]) ).
thf(80,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)],[30]) ).
thf(81,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)],[31]) ).
thf(82,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)],[32]) ).
thf(83,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)],[33]) ).
thf(84,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)],[34]) ).
thf(85,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)],[35]) ).
thf(86,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)],[36]) ).
thf(87,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)],[37]) ).
thf(88,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)],[38]) ).
thf(89,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)],[39]) ).
thf(90,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)],[40]) ).
thf(91,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)],[41]) ).
thf(92,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)],[42]) ).
thf(93,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)],[43]) ).
thf(94,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)],[44]) ).
thf(95,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)],[45]) ).
thf(96,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)],[46]) ).
thf(97,plain,
( ( ~ ( c_InductTermi_OIT @ v_s____ ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(98,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[50]) ).
thf(99,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)],[57]) ).
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(extcnf_combined,[status(esa)],[59]) ).
thf(101,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)],[60]) ).
thf(102,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)],[61]) ).
thf(103,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)],[62]) ).
thf(104,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)],[63]) ).
thf(105,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)],[65]) ).
thf(106,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)],[66]) ).
thf(107,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)],[68]) ).
thf(108,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)],[69]) ).
thf(109,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)],[70]) ).
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(extcnf_combined,[status(esa)],[73]) ).
thf(111,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)],[76]) ).
thf(112,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)],[77]) ).
thf(113,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)],[78]) ).
thf(114,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)],[79]) ).
thf(115,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)],[80]) ).
thf(116,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)],[81]) ).
thf(117,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)],[82]) ).
thf(118,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)],[83]) ).
thf(119,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)],[84]) ).
thf(120,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)],[85]) ).
thf(121,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)],[86]) ).
thf(122,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)],[87]) ).
thf(123,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)],[90]) ).
thf(124,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)],[91]) ).
thf(125,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)],[93]) ).
thf(126,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)],[94]) ).
thf(127,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)],[95]) ).
thf(128,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)],[96]) ).
thf(129,plain,
( ( ~ ( c_InductTermi_OIT @ v_s____ ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(130,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)],[128]) ).
thf(131,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)],[127]) ).
thf(132,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)],[126]) ).
thf(133,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)],[125]) ).
thf(134,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)],[92]) ).
thf(135,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)],[124]) ).
thf(136,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)],[123]) ).
thf(137,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)],[89]) ).
thf(138,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)],[88]) ).
thf(139,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)],[122]) ).
thf(140,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)],[121]) ).
thf(141,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)],[120]) ).
thf(142,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)],[119]) ).
thf(143,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)],[118]) ).
thf(144,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)],[117]) ).
thf(145,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)],[116]) ).
thf(146,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)],[115]) ).
thf(147,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)],[114]) ).
thf(148,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)],[113]) ).
thf(149,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)],[112]) ).
thf(150,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)],[111]) ).
thf(151,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(152,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(153,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)],[110]) ).
thf(154,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)],[72]) ).
thf(155,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)],[71]) ).
thf(156,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)],[109]) ).
thf(157,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)],[108]) ).
thf(158,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)],[107]) ).
thf(159,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)],[67]) ).
thf(160,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)],[106]) ).
thf(161,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)],[105]) ).
thf(162,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)],[64]) ).
thf(163,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)],[104]) ).
thf(164,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)],[103]) ).
thf(165,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)],[102]) ).
thf(166,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)],[101]) ).
thf(167,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)],[100]) ).
thf(168,plain,
( ( c_InductTermi_OIT @ v_s____ )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(169,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)],[99]) ).
thf(170,plain,
( ( ! [V_n: $i] : ( c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(171,plain,
( ( c_InductTermi_OIT @ v_ta____ )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(172,plain,
( ( ! [V_r: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ V_r ) )
| ~ ( c_InductTermi_OIT @ V_r ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(173,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(174,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(175,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(176,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(177,plain,
( ( c_InductTermi_OIT @ v_s____ )
= $false ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(178,plain,
! [SV1: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV1 )
| ! [SY106: $i,SY107: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY106 @ SY107 @ SV1 )
| ~ ( c_HOL_Oord__class_Oless @ SY107 @ SY106 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(179,plain,
! [SV2: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV2 )
| ! [SY108: $i,SY109: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY108 @ SY109 @ SV2 )
| ~ ( c_HOL_Oord__class_Oless @ SY109 @ SY108 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(180,plain,
! [SV3: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV3 )
| ! [SY110: $i,SY111: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY110 @ SY111 @ SV3 )
| ~ ( c_HOL_Oord__class_Oless @ SY111 @ SY110 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(181,plain,
! [SV4: $i] :
( ( ~ ( class_Orderings_Oorder @ SV4 )
| ! [SY112: $i,SY113: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY112 @ SY113 @ SV4 )
| ~ ( c_HOL_Oord__class_Oless @ SY113 @ SY112 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(182,plain,
! [SV5: $i] :
( ( ! [SY114: $i,SY115: $i,SY116: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ SV5 @ SY114 ) @ SY115 @ SY116 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV5 @ SY115 @ SY116 ) @ ( c_Lambda_Osubst @ SY114 @ SY115 @ SY116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(183,plain,
! [SV6: $i] :
( ( ! [SY117: $i,SY118: $i] :
( ( c_Lambda_OdB_OApp @ SV6 @ SY117 )
!= ( c_Lambda_OdB_OAbs @ SY118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(184,plain,
! [SV7: $i] :
( ( ! [SY119: $i,SY120: $i] :
( ( c_Lambda_OdB_OAbs @ SV7 )
!= ( c_Lambda_OdB_OApp @ SY119 @ SY120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(185,plain,
! [SV8: $i] :
( ( ! [SY121: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV8 ) @ SY121 @ SV8 )
= SY121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(186,plain,
! [SV9: $i] :
( ( ! [SY122: $i,SY123: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV9 ) @ SY122 @ SY123 )
= ( c_Lambda_OdB_OVar @ SV9 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV9 @ SY123 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(187,plain,
! [SV10: $i] :
( ( ! [SY124: $i,SY125: $i] :
( ! [SY126: $i] :
( ( c_Lambda_OdB_OApp @ SV10 @ SY124 )
!= ( c_Lambda_OdB_OApp @ SY125 @ SY126 ) )
| ( SV10 = SY125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(188,plain,
! [SV11: $i] :
( ( ! [SY127: $i,SY128: $i,SY129: $i] :
( ( ( c_Lambda_OdB_OApp @ SV11 @ SY127 )
!= ( c_Lambda_OdB_OApp @ SY128 @ SY129 ) )
| ( SY127 = SY129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(189,plain,
! [SV12: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV12 )
| ! [SY130: $i,SY131: $i] :
( ( SY130 = SY131 )
| ( c_HOL_Oord__class_Oless @ SY130 @ SY131 @ SV12 )
| ( c_HOL_Oord__class_Oless @ SY131 @ SY130 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(190,plain,
! [SV13: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV13 )
| ! [SY132: $i,SY133: $i] :
( ( c_HOL_Oord__class_Oless @ SY132 @ SY133 @ SV13 )
| ( SY133 = SY132 )
| ( c_HOL_Oord__class_Oless @ SY133 @ SY132 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(191,plain,
! [SV14: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV14 )
| ! [SY134: $i,SY135: $i] :
( ( c_HOL_Oord__class_Oless @ SY134 @ SY135 @ SV14 )
| ( SY135 = SY134 )
| ( c_HOL_Oord__class_Oless @ SY135 @ SY134 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(192,plain,
! [SV15: $i] :
( ( ! [SY136: $i] :
( ( c_HOL_Oord__class_Oless @ SV15 @ SY136 @ tc_nat )
| ( SY136 = SV15 )
| ( c_HOL_Oord__class_Oless @ SY136 @ SV15 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(193,plain,
! [SV16: $i] :
( ( ! [SY137: $i] :
( ( c_HOL_Oord__class_Oless @ SV16 @ SY137 @ tc_nat )
| ( SY137 = SV16 )
| ( c_HOL_Oord__class_Oless @ SY137 @ SV16 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(194,plain,
! [SV17: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV17 )
| ! [SY138: $i,SY139: $i] :
( ( SY138 = SY139 )
| ( c_HOL_Oord__class_Oless @ SY139 @ SY138 @ SV17 )
| ( c_HOL_Oord__class_Oless @ SY138 @ SY139 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(195,plain,
! [SV18: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV18 )
| ! [SY140: $i,SY141: $i] :
( ( c_HOL_Oord__class_Oless @ SY140 @ SY141 @ SV18 )
| ( SY141 = SY140 )
| ( c_HOL_Oord__class_Oless @ SY141 @ SY140 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(196,plain,
! [SV19: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV19 )
| ! [SY142: $i] :
~ ( c_HOL_Oord__class_Oless @ SY142 @ SY142 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(197,plain,
! [SV20: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV20 )
| ! [SY143: $i] :
~ ( c_HOL_Oord__class_Oless @ SY143 @ SY143 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(198,plain,
! [SV21: $i] :
( ( ~ ( class_Orderings_Oorder @ SV21 )
| ! [SY144: $i] :
~ ( c_HOL_Oord__class_Oless @ SY144 @ SY144 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(199,plain,
! [SV22: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV22 @ SV22 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(200,plain,
! [SV23: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV23 @ SV23 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(201,plain,
! [SV24: $i] :
( ( ! [SY145: $i,SY146: $i] :
( ( c_Lambda_OdB_OVar @ SV24 )
!= ( c_Lambda_OdB_OApp @ SY145 @ SY146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(202,plain,
! [SV25: $i] :
( ( ! [SY147: $i,SY148: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OApp @ SV25 @ SY147 ) @ SY148 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV25 @ SY148 ) @ ( c_Lambda_Olift @ SY147 @ SY148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(203,plain,
! [SV26: $i] :
( ( ! [SY149: $i,SY150: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV26 ) @ SY149 @ SY150 )
= ( c_Lambda_OdB_OVar @ SV26 ) )
| ( SV26 = SY150 )
| ( c_HOL_Oord__class_Oless @ SY150 @ SV26 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(204,plain,
! [SV27: $i] :
( ( ! [SY151: $i] :
( ~ ( class_Orderings_Opreorder @ SV27 )
| ! [SY152: $i] :
( ( c_HOL_Oord__class_Oless @ SY151 @ SY152 @ SV27 )
| ! [SY153: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY153 @ SY152 @ SV27 )
| ~ ( c_HOL_Oord__class_Oless @ SY151 @ SY153 @ SV27 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(205,plain,
! [SV28: $i] :
( ( ! [SY154: $i] :
( ~ ( class_Orderings_Oorder @ SV28 )
| ! [SY155: $i] :
( ( c_HOL_Oord__class_Oless @ SY154 @ SY155 @ SV28 )
| ! [SY156: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY154 @ SY156 @ SV28 )
| ~ ( c_HOL_Oord__class_Oless @ SY156 @ SY155 @ SV28 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(206,plain,
! [SV29: $i] :
( ( ! [SY157: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV29 ) @ SY157 @ SV29 )
= SY157 )
| ( c_HOL_Oord__class_Oless @ SV29 @ SV29 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(207,plain,
! [SV30: $i] :
( ( ! [SY158: $i,SY159: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV30 @ SY158 ) @ SY159 @ SY158 )
= SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(208,plain,
! [SV31: $i] :
( ( ! [SY160: $i,SY161: $i] :
( ( c_Lambda_OdB_OApp @ SV31 @ SY160 )
!= ( c_Lambda_OdB_OVar @ SY161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(209,plain,
! [SV32: $i] :
( ( ! [SY162: $i] : ( c_InductTermi_OIT @ ( c_Lambda_OdB_OApp @ SV32 @ ( c_Lambda_OdB_OVar @ SY162 ) ) )
| ~ ( c_InductTermi_OIT @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(210,plain,
! [SV33: $i] :
( ( ! [SY163: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV33 ) @ SY163 )
= ( c_Lambda_OdB_OVar @ SV33 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV33 @ SY163 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(211,plain,
! [SV34: $i] :
( ( ! [SY164: $i] :
( ( c_Lambda_OdB_OVar @ SV34 )
!= ( c_Lambda_OdB_OAbs @ SY164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(212,plain,
! [SV35: $i] :
( ( ! [SY165: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV35 )
!= ( c_Lambda_OdB_OAbs @ SY165 ) )
| ( SV35 = SY165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(213,plain,
! [SV36: $i] :
( ( ! [SY166: $i,SY167: $i] : ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV36 @ ( c_Lambda_OdB_OVar @ SY166 ) @ SY167 ) )
| ~ ( c_InductTermi_OIT @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(214,plain,
! [SV37: $i] :
( ( ! [SY168: $i] :
( ( ( c_Lambda_OdB_OVar @ SV37 )
!= ( c_Lambda_OdB_OVar @ SY168 ) )
| ( SV37 = SY168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(215,plain,
! [SV38: $i] :
( ( ! [SY169: $i] :
( ( c_Lambda_OdB_OAbs @ SV38 )
!= ( c_Lambda_OdB_OVar @ SY169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(216,plain,
! [SV39: $i] :
( ( ! [SY170: $i] : ( c_InductTermi_OIT @ ( c_Lambda_Olift @ SV39 @ SY170 ) )
| ~ ( c_InductTermi_OIT @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(217,plain,
! [SV40: $i] :
( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(218,plain,
! [SV41: $i] :
( ( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV41 ) )
| ~ ( c_InductTermi_OIT @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(219,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(220,plain,
! [SV1: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV1 ) )
= $true )
| ( ( ! [SY106: $i,SY107: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY106 @ SY107 @ SV1 )
| ~ ( c_HOL_Oord__class_Oless @ SY107 @ SY106 @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(221,plain,
! [SV2: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV2 ) )
= $true )
| ( ( ! [SY108: $i,SY109: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY108 @ SY109 @ SV2 )
| ~ ( c_HOL_Oord__class_Oless @ SY109 @ SY108 @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(222,plain,
! [SV3: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV3 ) )
= $true )
| ( ( ! [SY110: $i,SY111: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY110 @ SY111 @ SV3 )
| ~ ( c_HOL_Oord__class_Oless @ SY111 @ SY110 @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(223,plain,
! [SV4: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV4 ) )
= $true )
| ( ( ! [SY112: $i,SY113: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY112 @ SY113 @ SV4 )
| ~ ( c_HOL_Oord__class_Oless @ SY113 @ SY112 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(224,plain,
! [SV42: $i,SV5: $i] :
( ( ! [SY171: $i,SY172: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ SV5 @ SV42 ) @ SY171 @ SY172 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV5 @ SY171 @ SY172 ) @ ( c_Lambda_Osubst @ SV42 @ SY171 @ SY172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(225,plain,
! [SV43: $i,SV6: $i] :
( ( ! [SY173: $i] :
( ( c_Lambda_OdB_OApp @ SV6 @ SV43 )
!= ( c_Lambda_OdB_OAbs @ SY173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(226,plain,
! [SV44: $i,SV7: $i] :
( ( ! [SY174: $i] :
( ( c_Lambda_OdB_OAbs @ SV7 )
!= ( c_Lambda_OdB_OApp @ SV44 @ SY174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(227,plain,
! [SV45: $i,SV8: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV8 ) @ SV45 @ SV8 )
= SV45 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(228,plain,
! [SV46: $i,SV9: $i] :
( ( ! [SY175: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV9 ) @ SV46 @ SY175 )
= ( c_Lambda_OdB_OVar @ SV9 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV9 @ SY175 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(229,plain,
! [SV47: $i,SV10: $i] :
( ( ! [SY176: $i] :
( ! [SY177: $i] :
( ( c_Lambda_OdB_OApp @ SV10 @ SV47 )
!= ( c_Lambda_OdB_OApp @ SY176 @ SY177 ) )
| ( SV10 = SY176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(230,plain,
! [SV48: $i,SV11: $i] :
( ( ! [SY178: $i,SY179: $i] :
( ( ( c_Lambda_OdB_OApp @ SV11 @ SV48 )
!= ( c_Lambda_OdB_OApp @ SY178 @ SY179 ) )
| ( SV48 = SY179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(231,plain,
! [SV12: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV12 ) )
= $true )
| ( ( ! [SY130: $i,SY131: $i] :
( ( SY130 = SY131 )
| ( c_HOL_Oord__class_Oless @ SY130 @ SY131 @ SV12 )
| ( c_HOL_Oord__class_Oless @ SY131 @ SY130 @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(232,plain,
! [SV13: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV13 ) )
= $true )
| ( ( ! [SY132: $i,SY133: $i] :
( ( c_HOL_Oord__class_Oless @ SY132 @ SY133 @ SV13 )
| ( SY133 = SY132 )
| ( c_HOL_Oord__class_Oless @ SY133 @ SY132 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(233,plain,
! [SV14: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV14 ) )
= $true )
| ( ( ! [SY134: $i,SY135: $i] :
( ( c_HOL_Oord__class_Oless @ SY134 @ SY135 @ SV14 )
| ( SY135 = SY134 )
| ( c_HOL_Oord__class_Oless @ SY135 @ SY134 @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(234,plain,
! [SV49: $i,SV15: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV15 @ SV49 @ tc_nat )
| ( SV49 = SV15 )
| ( c_HOL_Oord__class_Oless @ SV49 @ SV15 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(235,plain,
! [SV50: $i,SV16: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV16 @ SV50 @ tc_nat )
| ( SV50 = SV16 )
| ( c_HOL_Oord__class_Oless @ SV50 @ SV16 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(236,plain,
! [SV17: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV17 ) )
= $true )
| ( ( ! [SY138: $i,SY139: $i] :
( ( SY138 = SY139 )
| ( c_HOL_Oord__class_Oless @ SY139 @ SY138 @ SV17 )
| ( c_HOL_Oord__class_Oless @ SY138 @ SY139 @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(237,plain,
! [SV18: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV18 ) )
= $true )
| ( ( ! [SY140: $i,SY141: $i] :
( ( c_HOL_Oord__class_Oless @ SY140 @ SY141 @ SV18 )
| ( SY141 = SY140 )
| ( c_HOL_Oord__class_Oless @ SY141 @ SY140 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(238,plain,
! [SV19: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV19 ) )
= $true )
| ( ( ! [SY142: $i] :
~ ( c_HOL_Oord__class_Oless @ SY142 @ SY142 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(239,plain,
! [SV20: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV20 ) )
= $true )
| ( ( ! [SY143: $i] :
~ ( c_HOL_Oord__class_Oless @ SY143 @ SY143 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(240,plain,
! [SV21: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV21 ) )
= $true )
| ( ( ! [SY144: $i] :
~ ( c_HOL_Oord__class_Oless @ SY144 @ SY144 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(241,plain,
! [SV22: $i] :
( ( c_HOL_Oord__class_Oless @ SV22 @ SV22 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(242,plain,
! [SV23: $i] :
( ( c_HOL_Oord__class_Oless @ SV23 @ SV23 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(243,plain,
! [SV51: $i,SV24: $i] :
( ( ! [SY180: $i] :
( ( c_Lambda_OdB_OVar @ SV24 )
!= ( c_Lambda_OdB_OApp @ SV51 @ SY180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(244,plain,
! [SV52: $i,SV25: $i] :
( ( ! [SY181: $i] :
( ( c_Lambda_Olift @ ( c_Lambda_OdB_OApp @ SV25 @ SV52 ) @ SY181 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV25 @ SY181 ) @ ( c_Lambda_Olift @ SV52 @ SY181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(245,plain,
! [SV53: $i,SV26: $i] :
( ( ! [SY182: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV26 ) @ SV53 @ SY182 )
= ( c_Lambda_OdB_OVar @ SV26 ) )
| ( SV26 = SY182 )
| ( c_HOL_Oord__class_Oless @ SY182 @ SV26 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(246,plain,
! [SV54: $i,SV27: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV27 )
| ! [SY183: $i] :
( ( c_HOL_Oord__class_Oless @ SV54 @ SY183 @ SV27 )
| ! [SY184: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY184 @ SY183 @ SV27 )
| ~ ( c_HOL_Oord__class_Oless @ SV54 @ SY184 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(247,plain,
! [SV55: $i,SV28: $i] :
( ( ~ ( class_Orderings_Oorder @ SV28 )
| ! [SY185: $i] :
( ( c_HOL_Oord__class_Oless @ SV55 @ SY185 @ SV28 )
| ! [SY186: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV55 @ SY186 @ SV28 )
| ~ ( c_HOL_Oord__class_Oless @ SY186 @ SY185 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(248,plain,
! [SV29: $i] :
( ( ( ! [SY157: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV29 ) @ SY157 @ SV29 )
= SY157 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV29 @ SV29 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(249,plain,
! [SV56: $i,SV30: $i] :
( ( ! [SY187: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV30 @ SV56 ) @ SY187 @ SV56 )
= SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(250,plain,
! [SV57: $i,SV31: $i] :
( ( ! [SY188: $i] :
( ( c_Lambda_OdB_OApp @ SV31 @ SV57 )
!= ( c_Lambda_OdB_OVar @ SY188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(251,plain,
! [SV32: $i] :
( ( ( ! [SY162: $i] : ( c_InductTermi_OIT @ ( c_Lambda_OdB_OApp @ SV32 @ ( c_Lambda_OdB_OVar @ SY162 ) ) ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(252,plain,
! [SV58: $i,SV33: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV33 ) @ SV58 )
= ( c_Lambda_OdB_OVar @ SV33 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV33 @ SV58 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(253,plain,
! [SV59: $i,SV34: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV34 )
!= ( c_Lambda_OdB_OAbs @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(254,plain,
! [SV60: $i,SV35: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV35 )
!= ( c_Lambda_OdB_OAbs @ SV60 ) )
| ( SV35 = SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(255,plain,
! [SV36: $i] :
( ( ( ! [SY166: $i,SY167: $i] : ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV36 @ ( c_Lambda_OdB_OVar @ SY166 ) @ SY167 ) ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(256,plain,
! [SV61: $i,SV37: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV37 )
!= ( c_Lambda_OdB_OVar @ SV61 ) )
| ( SV37 = SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(257,plain,
! [SV62: $i,SV38: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV38 )
!= ( c_Lambda_OdB_OVar @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(258,plain,
! [SV39: $i] :
( ( ( ! [SY170: $i] : ( c_InductTermi_OIT @ ( c_Lambda_Olift @ SV39 @ SY170 ) ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(259,plain,
! [SV41: $i] :
( ( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV41 ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(260,plain,
! [SV1: $i] :
( ( ( class_Orderings_Opreorder @ SV1 )
= $false )
| ( ( ! [SY106: $i,SY107: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY106 @ SY107 @ SV1 )
| ~ ( c_HOL_Oord__class_Oless @ SY107 @ SY106 @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(261,plain,
! [SV2: $i] :
( ( ( class_Orderings_Opreorder @ SV2 )
= $false )
| ( ( ! [SY108: $i,SY109: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY108 @ SY109 @ SV2 )
| ~ ( c_HOL_Oord__class_Oless @ SY109 @ SY108 @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(262,plain,
! [SV3: $i] :
( ( ( class_Orderings_Olinorder @ SV3 )
= $false )
| ( ( ! [SY110: $i,SY111: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY110 @ SY111 @ SV3 )
| ~ ( c_HOL_Oord__class_Oless @ SY111 @ SY110 @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(263,plain,
! [SV4: $i] :
( ( ( class_Orderings_Oorder @ SV4 )
= $false )
| ( ( ! [SY112: $i,SY113: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY112 @ SY113 @ SV4 )
| ~ ( c_HOL_Oord__class_Oless @ SY113 @ SY112 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(264,plain,
! [SV63: $i,SV42: $i,SV5: $i] :
( ( ! [SY189: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ SV5 @ SV42 ) @ SV63 @ SY189 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV5 @ SV63 @ SY189 ) @ ( c_Lambda_Osubst @ SV42 @ SV63 @ SY189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(265,plain,
! [SV64: $i,SV43: $i,SV6: $i] :
( ( ( ( c_Lambda_OdB_OApp @ SV6 @ SV43 )
!= ( c_Lambda_OdB_OAbs @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(266,plain,
! [SV65: $i,SV44: $i,SV7: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV7 )
!= ( c_Lambda_OdB_OApp @ SV44 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(267,plain,
! [SV66: $i,SV46: $i,SV9: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV9 ) @ SV46 @ SV66 )
= ( c_Lambda_OdB_OVar @ SV9 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV9 @ SV66 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(268,plain,
! [SV67: $i,SV47: $i,SV10: $i] :
( ( ! [SY190: $i] :
( ( c_Lambda_OdB_OApp @ SV10 @ SV47 )
!= ( c_Lambda_OdB_OApp @ SV67 @ SY190 ) )
| ( SV10 = SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(269,plain,
! [SV68: $i,SV48: $i,SV11: $i] :
( ( ! [SY191: $i] :
( ( ( c_Lambda_OdB_OApp @ SV11 @ SV48 )
!= ( c_Lambda_OdB_OApp @ SV68 @ SY191 ) )
| ( SV48 = SY191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(270,plain,
! [SV12: $i] :
( ( ( class_Orderings_Olinorder @ SV12 )
= $false )
| ( ( ! [SY130: $i,SY131: $i] :
( ( SY130 = SY131 )
| ( c_HOL_Oord__class_Oless @ SY130 @ SY131 @ SV12 )
| ( c_HOL_Oord__class_Oless @ SY131 @ SY130 @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(271,plain,
! [SV13: $i] :
( ( ( class_Orderings_Olinorder @ SV13 )
= $false )
| ( ( ! [SY132: $i,SY133: $i] :
( ( c_HOL_Oord__class_Oless @ SY132 @ SY133 @ SV13 )
| ( SY133 = SY132 )
| ( c_HOL_Oord__class_Oless @ SY133 @ SY132 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(272,plain,
! [SV14: $i] :
( ( ( class_Orderings_Olinorder @ SV14 )
= $false )
| ( ( ! [SY134: $i,SY135: $i] :
( ( c_HOL_Oord__class_Oless @ SY134 @ SY135 @ SV14 )
| ( SY135 = SY134 )
| ( c_HOL_Oord__class_Oless @ SY135 @ SY134 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(273,plain,
! [SV49: $i,SV15: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV15 @ SV49 @ tc_nat )
= $true )
| ( ( ( SV49 = SV15 )
| ( c_HOL_Oord__class_Oless @ SV49 @ SV15 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(274,plain,
! [SV50: $i,SV16: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV16 @ SV50 @ tc_nat )
= $true )
| ( ( ( SV50 = SV16 )
| ( c_HOL_Oord__class_Oless @ SV50 @ SV16 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(275,plain,
! [SV17: $i] :
( ( ( class_Orderings_Olinorder @ SV17 )
= $false )
| ( ( ! [SY138: $i,SY139: $i] :
( ( SY138 = SY139 )
| ( c_HOL_Oord__class_Oless @ SY139 @ SY138 @ SV17 )
| ( c_HOL_Oord__class_Oless @ SY138 @ SY139 @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(276,plain,
! [SV18: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV18 )
= $false )
| ( ( ! [SY140: $i,SY141: $i] :
( ( c_HOL_Oord__class_Oless @ SY140 @ SY141 @ SV18 )
| ( SY141 = SY140 )
| ( c_HOL_Oord__class_Oless @ SY141 @ SY140 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(277,plain,
! [SV19: $i] :
( ( ( class_Orderings_Opreorder @ SV19 )
= $false )
| ( ( ! [SY142: $i] :
~ ( c_HOL_Oord__class_Oless @ SY142 @ SY142 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(278,plain,
! [SV20: $i] :
( ( ( class_Orderings_Olinorder @ SV20 )
= $false )
| ( ( ! [SY143: $i] :
~ ( c_HOL_Oord__class_Oless @ SY143 @ SY143 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(279,plain,
! [SV21: $i] :
( ( ( class_Orderings_Oorder @ SV21 )
= $false )
| ( ( ! [SY144: $i] :
~ ( c_HOL_Oord__class_Oless @ SY144 @ SY144 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(280,plain,
! [SV69: $i,SV51: $i,SV24: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV24 )
!= ( c_Lambda_OdB_OApp @ SV51 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(281,plain,
! [SV70: $i,SV52: $i,SV25: $i] :
( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OApp @ SV25 @ SV52 ) @ SV70 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ SV25 @ SV70 ) @ ( c_Lambda_Olift @ SV52 @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(282,plain,
! [SV71: $i,SV53: $i,SV26: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV26 ) @ SV53 @ SV71 )
= ( c_Lambda_OdB_OVar @ SV26 ) )
| ( SV26 = SV71 )
| ( c_HOL_Oord__class_Oless @ SV71 @ SV26 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(283,plain,
! [SV54: $i,SV27: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV27 ) )
= $true )
| ( ( ! [SY183: $i] :
( ( c_HOL_Oord__class_Oless @ SV54 @ SY183 @ SV27 )
| ! [SY184: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY184 @ SY183 @ SV27 )
| ~ ( c_HOL_Oord__class_Oless @ SV54 @ SY184 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(284,plain,
! [SV55: $i,SV28: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV28 ) )
= $true )
| ( ( ! [SY185: $i] :
( ( c_HOL_Oord__class_Oless @ SV55 @ SY185 @ SV28 )
| ! [SY186: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV55 @ SY186 @ SV28 )
| ~ ( c_HOL_Oord__class_Oless @ SY186 @ SY185 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(285,plain,
! [SV72: $i,SV29: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV29 ) @ SV72 @ SV29 )
= SV72 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV29 @ SV29 @ tc_nat )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(286,plain,
! [SV73: $i,SV56: $i,SV30: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ SV30 @ SV56 ) @ SV73 @ SV56 )
= SV30 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(287,plain,
! [SV74: $i,SV57: $i,SV31: $i] :
( ( ( ( c_Lambda_OdB_OApp @ SV31 @ SV57 )
!= ( c_Lambda_OdB_OVar @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(288,plain,
! [SV75: $i,SV32: $i] :
( ( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OApp @ SV32 @ ( c_Lambda_OdB_OVar @ SV75 ) ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV32 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(289,plain,
! [SV58: $i,SV33: $i] :
( ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV33 ) @ SV58 )
= ( c_Lambda_OdB_OVar @ SV33 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV33 @ SV58 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(290,plain,
! [SV59: $i,SV34: $i] :
( ( ( c_Lambda_OdB_OVar @ SV34 )
= ( c_Lambda_OdB_OAbs @ SV59 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(291,plain,
! [SV60: $i,SV35: $i] :
( ( ( ( ( c_Lambda_OdB_OAbs @ SV35 )
!= ( c_Lambda_OdB_OAbs @ SV60 ) ) )
= $true )
| ( ( SV35 = SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(292,plain,
! [SV76: $i,SV36: $i] :
( ( ( ! [SY192: $i] : ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV36 @ ( c_Lambda_OdB_OVar @ SV76 ) @ SY192 ) ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV36 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(293,plain,
! [SV61: $i,SV37: $i] :
( ( ( ( ( c_Lambda_OdB_OVar @ SV37 )
!= ( c_Lambda_OdB_OVar @ SV61 ) ) )
= $true )
| ( ( SV37 = SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(294,plain,
! [SV62: $i,SV38: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV38 )
= ( c_Lambda_OdB_OVar @ SV62 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(295,plain,
! [SV77: $i,SV39: $i] :
( ( ( c_InductTermi_OIT @ ( c_Lambda_Olift @ SV39 @ SV77 ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV39 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(296,plain,
! [SV41: $i] :
( ( ( c_InductTermi_OIT @ SV41 )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(297,plain,
! [SV1: $i,SV78: $i] :
( ( ( ! [SY193: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV78 @ SY193 @ SV1 )
| ~ ( c_HOL_Oord__class_Oless @ SY193 @ SV78 @ SV1 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(298,plain,
! [SV2: $i,SV79: $i] :
( ( ( ! [SY194: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV79 @ SY194 @ SV2 )
| ~ ( c_HOL_Oord__class_Oless @ SY194 @ SV79 @ SV2 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(299,plain,
! [SV3: $i,SV80: $i] :
( ( ( ! [SY195: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV80 @ SY195 @ SV3 )
| ~ ( c_HOL_Oord__class_Oless @ SY195 @ SV80 @ SV3 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(300,plain,
! [SV4: $i,SV81: $i] :
( ( ( ! [SY196: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV81 @ SY196 @ SV4 )
| ~ ( c_HOL_Oord__class_Oless @ SY196 @ SV81 @ SV4 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(301,plain,
! [SV82: $i,SV63: $i,SV42: $i,SV5: $i] :
( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OApp @ SV5 @ SV42 ) @ SV63 @ SV82 )
= ( c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ SV5 @ SV63 @ SV82 ) @ ( c_Lambda_Osubst @ SV42 @ SV63 @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(302,plain,
! [SV64: $i,SV43: $i,SV6: $i] :
( ( ( c_Lambda_OdB_OApp @ SV6 @ SV43 )
= ( c_Lambda_OdB_OAbs @ SV64 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(303,plain,
! [SV65: $i,SV44: $i,SV7: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV7 )
= ( c_Lambda_OdB_OApp @ SV44 @ SV65 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(304,plain,
! [SV66: $i,SV46: $i,SV9: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV9 ) @ SV46 @ SV66 )
= ( c_Lambda_OdB_OVar @ SV9 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV9 @ SV66 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(305,plain,
! [SV67: $i,SV47: $i,SV10: $i] :
( ( ( ! [SY190: $i] :
( ( c_Lambda_OdB_OApp @ SV10 @ SV47 )
!= ( c_Lambda_OdB_OApp @ SV67 @ SY190 ) ) )
= $true )
| ( ( SV10 = SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(306,plain,
! [SV83: $i,SV68: $i,SV48: $i,SV11: $i] :
( ( ( ( c_Lambda_OdB_OApp @ SV11 @ SV48 )
!= ( c_Lambda_OdB_OApp @ SV68 @ SV83 ) )
| ( SV48 = SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(307,plain,
! [SV12: $i,SV84: $i] :
( ( ( ! [SY197: $i] :
( ( SV84 = SY197 )
| ( c_HOL_Oord__class_Oless @ SV84 @ SY197 @ SV12 )
| ( c_HOL_Oord__class_Oless @ SY197 @ SV84 @ SV12 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(308,plain,
! [SV13: $i,SV85: $i] :
( ( ( ! [SY198: $i] :
( ( c_HOL_Oord__class_Oless @ SV85 @ SY198 @ SV13 )
| ( SY198 = SV85 )
| ( c_HOL_Oord__class_Oless @ SY198 @ SV85 @ SV13 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(309,plain,
! [SV14: $i,SV86: $i] :
( ( ( ! [SY199: $i] :
( ( c_HOL_Oord__class_Oless @ SV86 @ SY199 @ SV14 )
| ( SY199 = SV86 )
| ( c_HOL_Oord__class_Oless @ SY199 @ SV86 @ SV14 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(310,plain,
! [SV15: $i,SV49: $i] :
( ( ( SV49 = SV15 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV49 @ SV15 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV15 @ SV49 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(311,plain,
! [SV16: $i,SV50: $i] :
( ( ( SV50 = SV16 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV50 @ SV16 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV16 @ SV50 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(312,plain,
! [SV17: $i,SV87: $i] :
( ( ( ! [SY200: $i] :
( ( SV87 = SY200 )
| ( c_HOL_Oord__class_Oless @ SY200 @ SV87 @ SV17 )
| ( c_HOL_Oord__class_Oless @ SV87 @ SY200 @ SV17 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(313,plain,
! [SV18: $i,SV88: $i] :
( ( ( ! [SY201: $i] :
( ( c_HOL_Oord__class_Oless @ SV88 @ SY201 @ SV18 )
| ( SY201 = SV88 )
| ( c_HOL_Oord__class_Oless @ SY201 @ SV88 @ SV18 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(314,plain,
! [SV19: $i,SV89: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV89 @ SV89 @ SV19 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(315,plain,
! [SV20: $i,SV90: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV90 @ SV90 @ SV20 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(316,plain,
! [SV21: $i,SV91: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV91 @ SV91 @ SV21 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(317,plain,
! [SV69: $i,SV51: $i,SV24: $i] :
( ( ( c_Lambda_OdB_OVar @ SV24 )
= ( c_Lambda_OdB_OApp @ SV51 @ SV69 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(318,plain,
! [SV71: $i,SV53: $i,SV26: $i] :
( ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV26 ) @ SV53 @ SV71 )
= ( c_Lambda_OdB_OVar @ SV26 ) )
= $true )
| ( ( ( SV26 = SV71 )
| ( c_HOL_Oord__class_Oless @ SV71 @ SV26 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(319,plain,
! [SV54: $i,SV27: $i] :
( ( ( class_Orderings_Opreorder @ SV27 )
= $false )
| ( ( ! [SY183: $i] :
( ( c_HOL_Oord__class_Oless @ SV54 @ SY183 @ SV27 )
| ! [SY184: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY184 @ SY183 @ SV27 )
| ~ ( c_HOL_Oord__class_Oless @ SV54 @ SY184 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(320,plain,
! [SV55: $i,SV28: $i] :
( ( ( class_Orderings_Oorder @ SV28 )
= $false )
| ( ( ! [SY185: $i] :
( ( c_HOL_Oord__class_Oless @ SV55 @ SY185 @ SV28 )
| ! [SY186: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV55 @ SY186 @ SV28 )
| ~ ( c_HOL_Oord__class_Oless @ SY186 @ SY185 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(321,plain,
! [SV74: $i,SV57: $i,SV31: $i] :
( ( ( c_Lambda_OdB_OApp @ SV31 @ SV57 )
= ( c_Lambda_OdB_OVar @ SV74 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(322,plain,
! [SV75: $i,SV32: $i] :
( ( ( c_InductTermi_OIT @ SV32 )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_OdB_OApp @ SV32 @ ( c_Lambda_OdB_OVar @ SV75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(323,plain,
! [SV58: $i,SV33: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV33 @ SV58 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV33 ) @ SV58 )
= ( c_Lambda_OdB_OVar @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(324,plain,
! [SV60: $i,SV35: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV35 )
= ( c_Lambda_OdB_OAbs @ SV60 ) )
= $false )
| ( ( SV35 = SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(325,plain,
! [SV92: $i,SV76: $i,SV36: $i] :
( ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV36 @ ( c_Lambda_OdB_OVar @ SV76 ) @ SV92 ) )
= $true )
| ( ( ~ ( c_InductTermi_OIT @ SV36 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(326,plain,
! [SV61: $i,SV37: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV37 )
= ( c_Lambda_OdB_OVar @ SV61 ) )
= $false )
| ( ( SV37 = SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(327,plain,
! [SV77: $i,SV39: $i] :
( ( ( c_InductTermi_OIT @ SV39 )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Olift @ SV39 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(328,plain,
! [SV1: $i,SV93: $i,SV78: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV78 @ SV93 @ SV1 )
| ~ ( c_HOL_Oord__class_Oless @ SV93 @ SV78 @ SV1 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(329,plain,
! [SV2: $i,SV94: $i,SV79: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV79 @ SV94 @ SV2 )
| ~ ( c_HOL_Oord__class_Oless @ SV94 @ SV79 @ SV2 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(330,plain,
! [SV3: $i,SV95: $i,SV80: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV80 @ SV95 @ SV3 )
| ~ ( c_HOL_Oord__class_Oless @ SV95 @ SV80 @ SV3 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(331,plain,
! [SV4: $i,SV96: $i,SV81: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV81 @ SV96 @ SV4 )
| ~ ( c_HOL_Oord__class_Oless @ SV96 @ SV81 @ SV4 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(332,plain,
! [SV46: $i,SV66: $i,SV9: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV9 @ SV66 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV9 ) @ SV46 @ SV66 )
= ( c_Lambda_OdB_OVar @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(333,plain,
! [SV97: $i,SV67: $i,SV47: $i,SV10: $i] :
( ( ( ( ( c_Lambda_OdB_OApp @ SV10 @ SV47 )
!= ( c_Lambda_OdB_OApp @ SV67 @ SV97 ) ) )
= $true )
| ( ( SV10 = SV67 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(334,plain,
! [SV83: $i,SV68: $i,SV48: $i,SV11: $i] :
( ( ( ( ( c_Lambda_OdB_OApp @ SV11 @ SV48 )
!= ( c_Lambda_OdB_OApp @ SV68 @ SV83 ) ) )
= $true )
| ( ( SV48 = SV83 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(335,plain,
! [SV12: $i,SV98: $i,SV84: $i] :
( ( ( ( SV84 = SV98 )
| ( c_HOL_Oord__class_Oless @ SV84 @ SV98 @ SV12 )
| ( c_HOL_Oord__class_Oless @ SV98 @ SV84 @ SV12 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(336,plain,
! [SV13: $i,SV99: $i,SV85: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV85 @ SV99 @ SV13 )
| ( SV99 = SV85 )
| ( c_HOL_Oord__class_Oless @ SV99 @ SV85 @ SV13 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(337,plain,
! [SV14: $i,SV100: $i,SV86: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV86 @ SV100 @ SV14 )
| ( SV100 = SV86 )
| ( c_HOL_Oord__class_Oless @ SV100 @ SV86 @ SV14 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(338,plain,
! [SV17: $i,SV101: $i,SV87: $i] :
( ( ( ( SV87 = SV101 )
| ( c_HOL_Oord__class_Oless @ SV101 @ SV87 @ SV17 )
| ( c_HOL_Oord__class_Oless @ SV87 @ SV101 @ SV17 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(339,plain,
! [SV18: $i,SV102: $i,SV88: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV88 @ SV102 @ SV18 )
| ( SV102 = SV88 )
| ( c_HOL_Oord__class_Oless @ SV102 @ SV88 @ SV18 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(340,plain,
! [SV19: $i,SV89: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV89 @ SV89 @ SV19 )
= $false )
| ( ( class_Orderings_Opreorder @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(341,plain,
! [SV20: $i,SV90: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV90 @ SV90 @ SV20 )
= $false )
| ( ( class_Orderings_Olinorder @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(342,plain,
! [SV21: $i,SV91: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV91 @ SV91 @ SV21 )
= $false )
| ( ( class_Orderings_Oorder @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(343,plain,
! [SV53: $i,SV71: $i,SV26: $i] :
( ( ( SV26 = SV71 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV71 @ SV26 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV26 ) @ SV53 @ SV71 )
= ( c_Lambda_OdB_OVar @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(344,plain,
! [SV27: $i,SV103: $i,SV54: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV54 @ SV103 @ SV27 )
| ! [SY202: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY202 @ SV103 @ SV27 )
| ~ ( c_HOL_Oord__class_Oless @ SV54 @ SY202 @ SV27 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(345,plain,
! [SV28: $i,SV104: $i,SV55: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV55 @ SV104 @ SV28 )
| ! [SY203: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV55 @ SY203 @ SV28 )
| ~ ( c_HOL_Oord__class_Oless @ SY203 @ SV104 @ SV28 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(346,plain,
! [SV92: $i,SV76: $i,SV36: $i] :
( ( ( c_InductTermi_OIT @ SV36 )
= $false )
| ( ( c_InductTermi_OIT @ ( c_Lambda_Osubst @ SV36 @ ( c_Lambda_OdB_OVar @ SV76 ) @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(347,plain,
! [SV1: $i,SV93: $i,SV78: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV78 @ SV93 @ SV1 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV93 @ SV78 @ SV1 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(348,plain,
! [SV2: $i,SV94: $i,SV79: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV79 @ SV94 @ SV2 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV94 @ SV79 @ SV2 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(349,plain,
! [SV3: $i,SV95: $i,SV80: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV80 @ SV95 @ SV3 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV95 @ SV80 @ SV3 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(350,plain,
! [SV4: $i,SV96: $i,SV81: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV81 @ SV96 @ SV4 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV96 @ SV81 @ SV4 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(351,plain,
! [SV97: $i,SV67: $i,SV47: $i,SV10: $i] :
( ( ( ( c_Lambda_OdB_OApp @ SV10 @ SV47 )
= ( c_Lambda_OdB_OApp @ SV67 @ SV97 ) )
= $false )
| ( ( SV10 = SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(352,plain,
! [SV83: $i,SV68: $i,SV48: $i,SV11: $i] :
( ( ( ( c_Lambda_OdB_OApp @ SV11 @ SV48 )
= ( c_Lambda_OdB_OApp @ SV68 @ SV83 ) )
= $false )
| ( ( SV48 = SV83 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(353,plain,
! [SV12: $i,SV98: $i,SV84: $i] :
( ( ( SV84 = SV98 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV84 @ SV98 @ SV12 )
| ( c_HOL_Oord__class_Oless @ SV98 @ SV84 @ SV12 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(354,plain,
! [SV13: $i,SV99: $i,SV85: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV85 @ SV99 @ SV13 )
= $true )
| ( ( ( SV99 = SV85 )
| ( c_HOL_Oord__class_Oless @ SV99 @ SV85 @ SV13 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(355,plain,
! [SV14: $i,SV100: $i,SV86: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV86 @ SV100 @ SV14 )
= $true )
| ( ( ( SV100 = SV86 )
| ( c_HOL_Oord__class_Oless @ SV100 @ SV86 @ SV14 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(356,plain,
! [SV17: $i,SV101: $i,SV87: $i] :
( ( ( SV87 = SV101 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV101 @ SV87 @ SV17 )
| ( c_HOL_Oord__class_Oless @ SV87 @ SV101 @ SV17 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(357,plain,
! [SV18: $i,SV102: $i,SV88: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV88 @ SV102 @ SV18 )
= $true )
| ( ( ( SV102 = SV88 )
| ( c_HOL_Oord__class_Oless @ SV102 @ SV88 @ SV18 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(358,plain,
! [SV27: $i,SV103: $i,SV54: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV54 @ SV103 @ SV27 )
= $true )
| ( ( ! [SY202: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY202 @ SV103 @ SV27 )
| ~ ( c_HOL_Oord__class_Oless @ SV54 @ SY202 @ SV27 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(359,plain,
! [SV28: $i,SV104: $i,SV55: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV55 @ SV104 @ SV28 )
= $true )
| ( ( ! [SY203: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV55 @ SY203 @ SV28 )
| ~ ( c_HOL_Oord__class_Oless @ SY203 @ SV104 @ SV28 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(360,plain,
! [SV1: $i,SV93: $i,SV78: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV78 @ SV93 @ SV1 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV93 @ SV78 @ SV1 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(361,plain,
! [SV2: $i,SV94: $i,SV79: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV79 @ SV94 @ SV2 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV94 @ SV79 @ SV2 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(362,plain,
! [SV3: $i,SV95: $i,SV80: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV80 @ SV95 @ SV3 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV95 @ SV80 @ SV3 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(363,plain,
! [SV4: $i,SV96: $i,SV81: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV81 @ SV96 @ SV4 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV96 @ SV81 @ SV4 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(364,plain,
! [SV12: $i,SV98: $i,SV84: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV84 @ SV98 @ SV12 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV98 @ SV84 @ SV12 )
= $true )
| ( ( SV84 = SV98 )
= $true )
| ( ( class_Orderings_Olinorder @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(365,plain,
! [SV13: $i,SV85: $i,SV99: $i] :
( ( ( SV99 = SV85 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV99 @ SV85 @ SV13 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV85 @ SV99 @ SV13 )
= $true )
| ( ( class_Orderings_Olinorder @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(366,plain,
! [SV14: $i,SV86: $i,SV100: $i] :
( ( ( SV100 = SV86 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV100 @ SV86 @ SV14 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV86 @ SV100 @ SV14 )
= $true )
| ( ( class_Orderings_Olinorder @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(367,plain,
! [SV17: $i,SV87: $i,SV101: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV101 @ SV87 @ SV17 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV87 @ SV101 @ SV17 )
= $true )
| ( ( SV87 = SV101 )
= $true )
| ( ( class_Orderings_Olinorder @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(368,plain,
! [SV18: $i,SV88: $i,SV102: $i] :
( ( ( SV102 = SV88 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV102 @ SV88 @ SV18 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV88 @ SV102 @ SV18 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(369,plain,
! [SV54: $i,SV27: $i,SV103: $i,SV105: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV105 @ SV103 @ SV27 )
| ~ ( c_HOL_Oord__class_Oless @ SV54 @ SV105 @ SV27 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV54 @ SV103 @ SV27 )
= $true )
| ( ( class_Orderings_Opreorder @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(370,plain,
! [SV104: $i,SV28: $i,SV106: $i,SV55: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV55 @ SV106 @ SV28 )
| ~ ( c_HOL_Oord__class_Oless @ SV106 @ SV104 @ SV28 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV55 @ SV104 @ SV28 )
= $true )
| ( ( class_Orderings_Oorder @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(371,plain,
! [SV1: $i,SV78: $i,SV93: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV93 @ SV78 @ SV1 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV78 @ SV93 @ SV1 )
= $false )
| ( ( class_Orderings_Opreorder @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(372,plain,
! [SV2: $i,SV79: $i,SV94: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV94 @ SV79 @ SV2 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV79 @ SV94 @ SV2 )
= $false )
| ( ( class_Orderings_Opreorder @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(373,plain,
! [SV3: $i,SV80: $i,SV95: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV95 @ SV80 @ SV3 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV80 @ SV95 @ SV3 )
= $false )
| ( ( class_Orderings_Olinorder @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(374,plain,
! [SV4: $i,SV81: $i,SV96: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV96 @ SV81 @ SV4 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV81 @ SV96 @ SV4 )
= $false )
| ( ( class_Orderings_Oorder @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(375,plain,
! [SV54: $i,SV27: $i,SV103: $i,SV105: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV105 @ SV103 @ SV27 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV54 @ SV105 @ SV27 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV54 @ SV103 @ SV27 )
= $true )
| ( ( class_Orderings_Opreorder @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(376,plain,
! [SV104: $i,SV28: $i,SV106: $i,SV55: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV55 @ SV106 @ SV28 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV106 @ SV104 @ SV28 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV55 @ SV104 @ SV28 )
= $true )
| ( ( class_Orderings_Oorder @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(377,plain,
! [SV54: $i,SV27: $i,SV103: $i,SV105: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV105 @ SV103 @ SV27 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV54 @ SV105 @ SV27 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV54 @ SV103 @ SV27 )
= $true )
| ( ( class_Orderings_Opreorder @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(378,plain,
! [SV104: $i,SV28: $i,SV106: $i,SV55: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV55 @ SV106 @ SV28 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV106 @ SV104 @ SV28 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV55 @ SV104 @ SV28 )
= $true )
| ( ( class_Orderings_Oorder @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(379,plain,
! [SV103: $i,SV27: $i,SV105: $i,SV54: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV54 @ SV105 @ SV27 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV105 @ SV103 @ SV27 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV54 @ SV103 @ SV27 )
= $true )
| ( ( class_Orderings_Opreorder @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(380,plain,
! [SV55: $i,SV28: $i,SV104: $i,SV106: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV106 @ SV104 @ SV28 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV55 @ SV106 @ SV28 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV55 @ SV104 @ SV28 )
= $true )
| ( ( class_Orderings_Oorder @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(381,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[168,380,379,374,373,372,371,368,367,366,365,364,352,351,346,343,342,341,340,332,327,326,324,323,322,321,317,311,310,303,302,301,296,294,290,286,285,281,242,241,227,219,217,177,175,174,173,171]) ).
thf(382,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[381]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL853-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 4 07:07:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.37 .
% 0.13/0.37
% 0.13/0.37 No.of.Axioms: 47
% 0.13/0.37
% 0.13/0.37 Length.of.Defs: 0
% 0.13/0.37
% 0.13/0.37 Contains.Choice.Funs: false
% 0.19/0.40 .
% 0.19/0.40 (rf:0,axioms:47,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:49,loop_count:0,foatp_calls:0,translation:fof_full)...................
% 0.19/0.51
% 0.19/0.51 ********************************
% 0.19/0.51 * All subproblems solved! *
% 0.19/0.51 ********************************
% 0.19/0.51 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:47,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:381,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.38/0.55
% 0.38/0.55 %**** Beginning of derivation protocol ****
% 0.38/0.55 % SZS output start CNFRefutation
% See solution above
% 0.38/0.55
% 0.38/0.55 %**** End of derivation protocol ****
% 0.38/0.55 %**** no. of clauses in derivation: 382 ****
% 0.38/0.55 %**** clause counter: 381 ****
% 0.38/0.55
% 0.38/0.55 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:47,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:381,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------