TSTP Solution File: SWV888-1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SWV888-1 : 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 : n004.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 : Wed Jul 20 20:14:49 EDT 2022
% Result : Unsatisfiable 0.38s 0.60s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 84
% Syntax : Number of formulae : 455 ( 307 unt; 28 typ; 0 def)
% Number of atoms : 1728 ( 777 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 3388 ( 367 ~; 363 |; 0 &;2658 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 9 con; 0-5 aty)
% Number of variables : 1205 ( 0 ^1205 !; 0 ?;1205 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_ATP__Linkup_Osko__Option__Xnot__None__eq__1__1,type,
c_ATP__Linkup_Osko__Option__Xnot__None__eq__1__1: $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Option__Xnot__Some__eq__1__1,type,
c_ATP__Linkup_Osko__Option__Xnot__Some__eq__1__1: $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Option__Xoption__Xexhaust__1__1,type,
c_ATP__Linkup_Osko__Option__Xoption__Xexhaust__1__1: $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Option__Xoption__Xnchotomy__1__1,type,
c_ATP__Linkup_Osko__Option__Xoption__Xnchotomy__1__1: $i > $i > $i ).
thf(tp_c_Com_OWT,type,
c_Com_OWT: $i > $o ).
thf(tp_c_Com_OWT__bodies,type,
c_Com_OWT__bodies: $o ).
thf(tp_c_Com_Obody,type,
c_Com_Obody: $i > $i ).
thf(tp_c_Com_Ocom_OBODY,type,
c_Com_Ocom_OBODY: $i > $i ).
thf(tp_c_Com_Ocom_OSKIP,type,
c_Com_Ocom_OSKIP: $i ).
thf(tp_c_Com_Ocom_OSemi,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(tp_c_Com_Osko__Com__XWTs__elim__cases__7__1,type,
c_Com_Osko__Com__XWTs__elim__cases__7__1: $i > $i ).
thf(tp_c_Fun_Oid,type,
c_Fun_Oid: $i > $i > $i ).
thf(tp_c_Natural_Oevalc,type,
c_Natural_Oevalc: $i > $i > $i > $o ).
thf(tp_c_Natural_Oevaln,type,
c_Natural_Oevaln: $i > $i > $i > $i > $o ).
thf(tp_c_Natural_Osko__Natural__Xeval__eq__1__1,type,
c_Natural_Osko__Natural__Xeval__eq__1__1: $i > $i > $i > $i ).
thf(tp_c_Natural_Osko__Natural__Xevalc__elim__cases__4__1,type,
c_Natural_Osko__Natural__Xevalc__elim__cases__4__1: $i > $i > $i > $i > $i ).
thf(tp_c_Natural_Osko__Natural__Xevalc__evaln__1__1,type,
c_Natural_Osko__Natural__Xevalc__evaln__1__1: $i > $i > $i > $i ).
thf(tp_c_Natural_Osko__Natural__Xevaln__elim__cases__4__1,type,
c_Natural_Osko__Natural__Xevaln__elim__cases__4__1: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Natural_Osko__Natural__Xevaln__elim__cases__6__1,type,
c_Natural_Osko__Natural__Xevaln__elim__cases__6__1: $i > $i > $i > $i > $i ).
thf(tp_c_Option_Ooption_ONone,type,
c_Option_Ooption_ONone: $i > $i ).
thf(tp_c_Option_Ooption_OSome,type,
c_Option_Ooption_OSome: $i > $i > $i ).
thf(tp_c_Option_Othe,type,
c_Option_Othe: $i > $i > $i ).
thf(tp_c_Suc,type,
c_Suc: $i > $i ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_Com_Ocom,type,
tc_Com_Ocom: $i ).
thf(tp_v_pn,type,
v_pn: $i ).
thf(tp_v_x,type,
v_x: $i ).
thf(tp_v_xa,type,
v_xa: $i ).
thf(1,axiom,
! [V_c: $i,V_s: $i,V_t: $i,V_x: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ~ ( c_Natural_Oevaln @ V_c @ V_s @ V_x @ V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__eq_1) ).
thf(2,axiom,
! [V_c: $i,V_s: $i,V_t: $i,V_n: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ~ ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__evalc_0) ).
thf(3,axiom,
! [V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ V_s @ V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I1_J_0) ).
thf(4,axiom,
! [V_pname_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I18_J_0) ).
thf(5,axiom,
! [V_pname: $i,V_pname_H: $i] :
( ( ( c_Com_Ocom_OBODY @ V_pname )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) )
| ( V_pname = V_pname_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).
thf(6,axiom,
! [V_pn: $i,V_s0: $i,V_n: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ V_pn ) @ V_s0 @ ( c_Suc @ V_n ) @ V_s1 )
| ~ ( c_Natural_Oevaln @ ( c_Option_Othe @ ( c_Com_Obody @ V_pn ) @ tc_Com_Ocom ) @ V_s0 @ V_n @ V_s1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OBody_0) ).
thf(7,axiom,
! [V_c0: $i,V_c1: $i,V_s0: $i,V_s2: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_s2 )
| ~ ( c_Natural_Oevalc @ V_c1 @ V_s1 @ V_s2 )
| ~ ( c_Natural_Oevalc @ V_c0 @ V_s0 @ V_s1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OSemi_0) ).
thf(8,axiom,
! [V_com1: $i,V_com2: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I48_J_0) ).
thf(9,axiom,
! [V_pname_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I49_J_0) ).
thf(10,axiom,
! [V_P: $i] :
( ( ( c_Com_Obody @ V_P )
= ( c_Option_Ooption_OSome @ ( c_Com_Osko__Com__XWTs__elim__cases__7__1 @ V_P ) @ tc_Com_Ocom ) )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ V_P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I7_J_0) ).
thf(11,axiom,
! [V_P: $i,V_s: $i,V_n: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( c_Option_Othe @ ( c_Com_Obody @ V_P ) @ tc_Com_Ocom ) @ V_s @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ V_P @ V_n @ V_s @ V_s1 ) @ V_s1 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_n @ V_s1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I6_J_1) ).
thf(12,axiom,
( ( c_Fun_Oid @ v_x @ t_a )
= v_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__def_0) ).
thf(13,axiom,
! [V_s: $i] : ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ V_s @ V_s ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OSkip_0) ).
thf(14,axiom,
! [V_u: $i,V_t: $i,V_c: $i,V_s: $i] :
( ( V_u = V_t )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_u )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com__det_0) ).
thf(15,axiom,
! [V_P: $i,V_s: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ V_P ) @ tc_Com_Ocom ) @ V_s @ V_s1 )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_s1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I6_J_0) ).
thf(16,axiom,
! [V_pn: $i,V_s0: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_pn ) @ V_s0 @ V_s1 )
| ~ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ V_pn ) @ tc_Com_Ocom ) @ V_s0 @ V_s1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OBody_0) ).
thf(17,axiom,
! [V_pname_H: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I19_J_0) ).
thf(18,axiom,
! [V_pn: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ V_pn ) )
| ( ( c_Com_Obody @ V_pn )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OBody_0) ).
thf(19,axiom,
! [V_x: $i,T_a: $i] :
( ( c_Option_Othe @ ( c_Option_Ooption_OSome @ V_x @ T_a ) @ T_a )
= V_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the_Osimps_0) ).
thf(20,axiom,
! [V_com1_H: $i,V_com2_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).
thf(21,axiom,
! [V_y: $i,T_a: $i] :
( ( V_y
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xoption__Xexhaust__1__1 @ V_y @ T_a ) @ T_a ) )
| ( V_y
= ( c_Option_Ooption_ONone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Oexhaust_0) ).
thf(22,axiom,
! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(23,axiom,
! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(24,axiom,
! [V_pn: $i,V_b: $i] :
( ( ( c_Com_Obody @ V_pn )
!= ( c_Option_Ooption_OSome @ V_b @ tc_Com_Ocom ) )
| ~ c_Com_OWT__bodies
| ( c_Com_OWT @ V_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__bodiesD_0) ).
thf(25,axiom,
! [V_c0: $i,V_c1: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) )
| ~ ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ V_c0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OSemi_0) ).
thf(26,axiom,
! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ ( c_Natural_Osko__Natural__Xevalc__evaln__1__1 @ V_c @ V_s @ V_t ) @ V_t )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__evaln_0) ).
thf(27,axiom,
! [V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).
thf(28,axiom,
! [V_c1: $i,V_c2: $i] :
( ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_0) ).
thf(29,axiom,
! [V_c2: $i,V_c1: $i] :
( ( c_Com_OWT @ V_c2 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_1) ).
thf(30,axiom,
! [V_s: $i,V_n: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_s ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OSkip_0) ).
thf(31,axiom,
! [V_x: $i,T_a: $i] :
( ( V_x
= ( c_Option_Ooption_ONone @ T_a ) )
| ( V_x
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xnot__Some__eq__1__1 @ V_x @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Some__eq_0) ).
thf(32,axiom,
! [V_c: $i,V_s: $i,V_n: $i,V_s_H: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ ( c_Suc @ V_n ) @ V_s_H )
| ~ ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_s_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__Suc_0) ).
thf(33,axiom,
! [V_c1: $i,V_s: $i,V_n: $i,V_c2: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ V_c1 @ V_c2 @ V_n @ V_s @ V_t ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I4_J_0) ).
thf(34,axiom,
! [V_c2: $i,V_c1: $i,V_n: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c2 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ V_c1 @ V_c2 @ V_n @ V_s @ V_t ) @ V_n @ V_t )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I4_J_1) ).
thf(35,axiom,
! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(36,axiom,
! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(37,axiom,
! [V_a: $i,T_a: $i,V_a_H: $i] :
( ( ( c_Option_Ooption_OSome @ V_a @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) )
| ( V_a = V_a_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Oinject_0) ).
thf(38,axiom,
! [V_xa: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_xa @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__None__eq_1) ).
thf(39,axiom,
! [V_a_H: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_a_H @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I3_J_0) ).
thf(40,axiom,
! [V_com1: $i,V_com2: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com1 = V_com1_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
thf(41,axiom,
! [V_com1: $i,V_com2: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com2 = V_com2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).
thf(42,axiom,
! [V_x: $i,T_a: $i] :
( ( V_x
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xnot__None__eq__1__1 @ V_x @ T_a ) @ T_a ) )
| ( V_x
= ( c_Option_Ooption_ONone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__None__eq_0) ).
thf(43,axiom,
! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ ( c_Natural_Osko__Natural__Xeval__eq__1__1 @ V_c @ V_s @ V_t ) @ V_t )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eval__eq_0) ).
thf(44,axiom,
! [T_a: $i,V_y: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Some__eq_1) ).
thf(45,axiom,
! [T_a: $i,V_a_H: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I2_J_0) ).
thf(46,axiom,
! [V_c0: $i,V_c1: $i,V_s0: $i,V_n: $i,V_s2: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ V_c1 @ V_s1 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ V_c0 @ V_s0 @ V_n @ V_s1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln_OSemi_0) ).
thf(47,axiom,
c_Com_OWT @ c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OSkip_0) ).
thf(48,axiom,
! [V_c1: $i,V_s: $i,V_c2: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c1 @ V_s @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ V_c1 @ V_c2 @ V_s @ V_t ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I4_J_0) ).
thf(49,axiom,
! [V_c2: $i,V_c1: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c2 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ V_c1 @ V_c2 @ V_s @ V_t ) @ V_t )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I4_J_1) ).
thf(50,axiom,
! [V_n: $i,V_P: $i,V_s: $i,V_s1: $i] :
( ( V_n
= ( c_Suc @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ V_P @ V_n @ V_s @ V_s1 ) ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_n @ V_s1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I6_J_0) ).
thf(51,axiom,
! [V_v: $i,T_a: $i] :
( ( V_v
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xoption__Xnchotomy__1__1 @ V_v @ T_a ) @ T_a ) )
| ( V_v
= ( c_Option_Ooption_ONone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Onchotomy_0) ).
thf(52,axiom,
! [V_t: $i,V_s: $i,V_n: $i] :
( ( V_t = V_s )
| ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evaln__elim__cases_I1_J_0) ).
thf(53,axiom,
! [V_x: $i,T_a: $i] :
( ( c_Fun_Oid @ V_x @ T_a )
= V_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__apply_0) ).
thf(54,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(55,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[54]) ).
thf(56,negated_conjecture,
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ v_pn ) @ v_x @ v_xa ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(57,negated_conjecture,
c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ v_pn ) @ tc_Com_Ocom ) @ v_x @ v_xa,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(58,plain,
$false = $false,
inference(unfold_def,[status(thm)],[55]) ).
thf(59,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i,V_x: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ~ ( c_Natural_Oevaln @ V_c @ V_s @ V_x @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(60,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i,V_n: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ~ ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(61,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(62,plain,
( ( ! [V_pname_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(63,plain,
( ( ! [V_pname: $i,V_pname_H: $i] :
( ( ( c_Com_Ocom_OBODY @ V_pname )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) )
| ( V_pname = V_pname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(64,plain,
( ( ! [V_pn: $i,V_s0: $i,V_n: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ V_pn ) @ V_s0 @ ( c_Suc @ V_n ) @ V_s1 )
| ~ ( c_Natural_Oevaln @ ( c_Option_Othe @ ( c_Com_Obody @ V_pn ) @ tc_Com_Ocom ) @ V_s0 @ V_n @ V_s1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(65,plain,
( ( ! [V_c0: $i,V_c1: $i,V_s0: $i,V_s2: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_s2 )
| ~ ( c_Natural_Oevalc @ V_c1 @ V_s1 @ V_s2 )
| ~ ( c_Natural_Oevalc @ V_c0 @ V_s0 @ V_s1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(66,plain,
( ( ! [V_com1: $i,V_com2: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(67,plain,
( ( ! [V_pname_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(68,plain,
( ( ! [V_P: $i] :
( ( ( c_Com_Obody @ V_P )
= ( c_Option_Ooption_OSome @ ( c_Com_Osko__Com__XWTs__elim__cases__7__1 @ V_P ) @ tc_Com_Ocom ) )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ V_P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(69,plain,
( ( ! [V_P: $i,V_s: $i,V_n: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( c_Option_Othe @ ( c_Com_Obody @ V_P ) @ tc_Com_Ocom ) @ V_s @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ V_P @ V_n @ V_s @ V_s1 ) @ V_s1 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_n @ V_s1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(70,plain,
( ( ( c_Fun_Oid @ v_x @ t_a )
= v_x )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(71,plain,
( ( ! [V_s: $i] : ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ V_s @ V_s ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(72,plain,
( ( ! [V_u: $i,V_t: $i,V_c: $i,V_s: $i] :
( ( V_u = V_t )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_u )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(73,plain,
( ( ! [V_P: $i,V_s: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ V_P ) @ tc_Com_Ocom ) @ V_s @ V_s1 )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_s1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(74,plain,
( ( ! [V_pn: $i,V_s0: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_pn ) @ V_s0 @ V_s1 )
| ~ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ V_pn ) @ tc_Com_Ocom ) @ V_s0 @ V_s1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(75,plain,
( ( ! [V_pname_H: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(76,plain,
( ( ! [V_pn: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ V_pn ) )
| ( ( c_Com_Obody @ V_pn )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(77,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_Option_Othe @ ( c_Option_Ooption_OSome @ V_x @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(78,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(79,plain,
( ( ! [V_y: $i,T_a: $i] :
( ( V_y
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xoption__Xexhaust__1__1 @ V_y @ T_a ) @ T_a ) )
| ( V_y
= ( c_Option_Ooption_ONone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(80,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(81,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(82,plain,
( ( ! [V_pn: $i,V_b: $i] :
( ( ( c_Com_Obody @ V_pn )
!= ( c_Option_Ooption_OSome @ V_b @ tc_Com_Ocom ) )
| ~ c_Com_OWT__bodies
| ( c_Com_OWT @ V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(83,plain,
( ( ! [V_c0: $i,V_c1: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) )
| ~ ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ V_c0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(84,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ ( c_Natural_Osko__Natural__Xevalc__evaln__1__1 @ V_c @ V_s @ V_t ) @ V_t )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(85,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(86,plain,
( ( ! [V_c1: $i,V_c2: $i] :
( ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(87,plain,
( ( ! [V_c2: $i,V_c1: $i] :
( ( c_Com_OWT @ V_c2 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(88,plain,
( ( ! [V_s: $i,V_n: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_s ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(89,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( V_x
= ( c_Option_Ooption_ONone @ T_a ) )
| ( V_x
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xnot__Some__eq__1__1 @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(90,plain,
( ( ! [V_c: $i,V_s: $i,V_n: $i,V_s_H: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ ( c_Suc @ V_n ) @ V_s_H )
| ~ ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_s_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(91,plain,
( ( ! [V_c1: $i,V_s: $i,V_n: $i,V_c2: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ V_c1 @ V_c2 @ V_n @ V_s @ V_t ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(92,plain,
( ( ! [V_c2: $i,V_c1: $i,V_n: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c2 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ V_c1 @ V_c2 @ V_n @ V_s @ V_t ) @ V_n @ V_t )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(93,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(94,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(95,plain,
( ( ! [V_a: $i,T_a: $i,V_a_H: $i] :
( ( ( c_Option_Ooption_OSome @ V_a @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(96,plain,
( ( ! [V_xa: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_xa @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(97,plain,
( ( ! [V_a_H: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_a_H @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(98,plain,
( ( ! [V_com1: $i,V_com2: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com1 = V_com1_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(99,plain,
( ( ! [V_com1: $i,V_com2: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com2 = V_com2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(100,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( V_x
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xnot__None__eq__1__1 @ V_x @ T_a ) @ T_a ) )
| ( V_x
= ( c_Option_Ooption_ONone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(101,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ ( c_Natural_Osko__Natural__Xeval__eq__1__1 @ V_c @ V_s @ V_t ) @ V_t )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(102,plain,
( ( ! [T_a: $i,V_y: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(103,plain,
( ( ! [T_a: $i,V_a_H: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(104,plain,
( ( ! [V_c0: $i,V_c1: $i,V_s0: $i,V_n: $i,V_s2: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ V_c1 @ V_s1 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ V_c0 @ V_s0 @ V_n @ V_s1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(105,plain,
( ( c_Com_OWT @ c_Com_Ocom_OSKIP )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(106,plain,
( ( ! [V_c1: $i,V_s: $i,V_c2: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c1 @ V_s @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ V_c1 @ V_c2 @ V_s @ V_t ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(107,plain,
( ( ! [V_c2: $i,V_c1: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c2 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ V_c1 @ V_c2 @ V_s @ V_t ) @ V_t )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(108,plain,
( ( ! [V_n: $i,V_P: $i,V_s: $i,V_s1: $i] :
( ( V_n
= ( c_Suc @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ V_P @ V_n @ V_s @ V_s1 ) ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_n @ V_s1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(109,plain,
( ( ! [V_v: $i,T_a: $i] :
( ( V_v
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xoption__Xnchotomy__1__1 @ V_v @ T_a ) @ T_a ) )
| ( V_v
= ( c_Option_Ooption_ONone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(110,plain,
( ( ! [V_t: $i,V_s: $i,V_n: $i] :
( ( V_t = V_s )
| ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(111,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_Fun_Oid @ V_x @ T_a )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(112,plain,
( ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ v_pn ) @ v_x @ v_xa ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(113,plain,
( ( c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ v_pn ) @ tc_Com_Ocom ) @ v_x @ v_xa )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(114,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[58]) ).
thf(115,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ! [V_x: $i] :
~ ( c_Natural_Oevaln @ V_c @ V_s @ V_x @ V_t ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(116,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ! [V_n: $i] :
~ ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(117,plain,
( ( ! [V_pname_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[62]) ).
thf(118,plain,
( ( ! [V_pname: $i,V_pname_H: $i] :
( ( ( c_Com_Ocom_OBODY @ V_pname )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) )
| ( V_pname = V_pname_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[63]) ).
thf(119,plain,
( ( ! [V_c0: $i,V_c1: $i,V_s0: $i,V_s2: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_s2 )
| ! [V_s1: $i] :
( ~ ( c_Natural_Oevalc @ V_c1 @ V_s1 @ V_s2 )
| ~ ( c_Natural_Oevalc @ V_c0 @ V_s0 @ V_s1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(120,plain,
( ( ! [V_com1: $i,V_com2: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(121,plain,
( ( ! [V_pname_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(122,plain,
( ( ! [V_u: $i,V_t: $i] :
( ( V_u = V_t )
| ! [V_c: $i,V_s: $i] :
( ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_u )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[72]) ).
thf(123,plain,
( ( ! [V_pname_H: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_combined,[status(esa)],[75]) ).
thf(124,plain,
( ( ! [V_pn: $i] :
( ( ( c_Com_Obody @ V_pn )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) )
| ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ V_pn ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[76]) ).
thf(125,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[78]) ).
thf(126,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[80]) ).
thf(127,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(extcnf_combined,[status(esa)],[81]) ).
thf(128,plain,
( ( ! [V_pn: $i,V_b: $i] :
( ( ( c_Com_Obody @ V_pn )
!= ( c_Option_Ooption_OSome @ V_b @ tc_Com_Ocom ) )
| ~ c_Com_OWT__bodies
| ( c_Com_OWT @ V_b ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[82]) ).
thf(129,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_combined,[status(esa)],[85]) ).
thf(130,plain,
( ( ! [V_c1: $i] :
( ( c_Com_OWT @ V_c1 )
| ! [V_c2: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[86]) ).
thf(131,plain,
( ( ! [V_c2: $i] :
( ( c_Com_OWT @ V_c2 )
| ! [V_c1: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(132,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[93]) ).
thf(133,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[94]) ).
thf(134,plain,
( ( ! [V_a: $i,T_a: $i,V_a_H: $i] :
( ( ( c_Option_Ooption_OSome @ V_a @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[95]) ).
thf(135,plain,
( ( ! [V_xa: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_xa @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[96]) ).
thf(136,plain,
( ( ! [V_a_H: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_a_H @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[97]) ).
thf(137,plain,
( ( ! [V_com1: $i,V_com2: $i,V_com1_H: $i] :
( ! [V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com1 = V_com1_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[98]) ).
thf(138,plain,
( ( ! [V_com1: $i,V_com2: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com2 = V_com2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[99]) ).
thf(139,plain,
( ( ! [T_a: $i,V_y: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[102]) ).
thf(140,plain,
( ( ! [T_a: $i,V_a_H: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[103]) ).
thf(141,plain,
( ( ! [V_c0: $i,V_c1: $i,V_s0: $i,V_n: $i,V_s2: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_n @ V_s2 )
| ! [V_s1: $i] :
( ~ ( c_Natural_Oevaln @ V_c1 @ V_s1 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ V_c0 @ V_s0 @ V_n @ V_s1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[104]) ).
thf(142,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ! [V_n: $i] :
~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[110]) ).
thf(143,plain,
( ( c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ v_pn ) @ tc_Com_Ocom ) @ v_x @ v_xa )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(144,plain,
( ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ v_pn ) @ v_x @ v_xa ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(145,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_Fun_Oid @ V_x @ T_a )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(146,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ! [V_n: $i] :
~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(147,plain,
( ( ! [V_v: $i,T_a: $i] :
( ( V_v
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xoption__Xnchotomy__1__1 @ V_v @ T_a ) @ T_a ) )
| ( V_v
= ( c_Option_Ooption_ONone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(148,plain,
( ( ! [V_n: $i,V_P: $i,V_s: $i,V_s1: $i] :
( ( V_n
= ( c_Suc @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ V_P @ V_n @ V_s @ V_s1 ) ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_n @ V_s1 ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(149,plain,
( ( ! [V_c2: $i,V_c1: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c2 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ V_c1 @ V_c2 @ V_s @ V_t ) @ V_t )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(150,plain,
( ( ! [V_c1: $i,V_s: $i,V_c2: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c1 @ V_s @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ V_c1 @ V_c2 @ V_s @ V_t ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(151,plain,
( ( c_Com_OWT @ c_Com_Ocom_OSKIP )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(152,plain,
( ( ! [V_c0: $i,V_c1: $i,V_s0: $i,V_n: $i,V_s2: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_n @ V_s2 )
| ! [V_s1: $i] :
( ~ ( c_Natural_Oevaln @ V_c1 @ V_s1 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ V_c0 @ V_s0 @ V_n @ V_s1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(153,plain,
( ( ! [T_a: $i,V_a_H: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(154,plain,
( ( ! [T_a: $i,V_y: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(155,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ ( c_Natural_Osko__Natural__Xeval__eq__1__1 @ V_c @ V_s @ V_t ) @ V_t )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(156,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( V_x
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xnot__None__eq__1__1 @ V_x @ T_a ) @ T_a ) )
| ( V_x
= ( c_Option_Ooption_ONone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(157,plain,
( ( ! [V_com1: $i,V_com2: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com2 = V_com2_H ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(158,plain,
( ( ! [V_com1: $i,V_com2: $i,V_com1_H: $i] :
( ! [V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com1 = V_com1_H ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(159,plain,
( ( ! [V_a_H: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_a_H @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(160,plain,
( ( ! [V_xa: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_xa @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(161,plain,
( ( ! [V_a: $i,T_a: $i,V_a_H: $i] :
( ( ( c_Option_Ooption_OSome @ V_a @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(162,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(163,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(164,plain,
( ( ! [V_c2: $i,V_c1: $i,V_n: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c2 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ V_c1 @ V_c2 @ V_n @ V_s @ V_t ) @ V_n @ V_t )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(165,plain,
( ( ! [V_c1: $i,V_s: $i,V_n: $i,V_c2: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ V_c1 @ V_c2 @ V_n @ V_s @ V_t ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(166,plain,
( ( ! [V_c: $i,V_s: $i,V_n: $i,V_s_H: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ ( c_Suc @ V_n ) @ V_s_H )
| ~ ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_s_H ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(167,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( V_x
= ( c_Option_Ooption_ONone @ T_a ) )
| ( V_x
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xnot__Some__eq__1__1 @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(168,plain,
( ( ! [V_s: $i,V_n: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_s ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(169,plain,
( ( ! [V_c2: $i] :
( ( c_Com_OWT @ V_c2 )
| ! [V_c1: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(170,plain,
( ( ! [V_c1: $i] :
( ( c_Com_OWT @ V_c1 )
| ! [V_c2: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(171,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(172,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ ( c_Natural_Osko__Natural__Xevalc__evaln__1__1 @ V_c @ V_s @ V_t ) @ V_t )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(173,plain,
( ( ! [V_c0: $i,V_c1: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) )
| ~ ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ V_c0 ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(174,plain,
( ( ! [V_pn: $i,V_b: $i] :
( ( ( c_Com_Obody @ V_pn )
!= ( c_Option_Ooption_OSome @ V_b @ tc_Com_Ocom ) )
| ~ c_Com_OWT__bodies
| ( c_Com_OWT @ V_b ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(175,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(176,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(177,plain,
( ( ! [V_y: $i,T_a: $i] :
( ( V_y
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xoption__Xexhaust__1__1 @ V_y @ T_a ) @ T_a ) )
| ( V_y
= ( c_Option_Ooption_ONone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(178,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(179,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_Option_Othe @ ( c_Option_Ooption_OSome @ V_x @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(180,plain,
( ( ! [V_pn: $i] :
( ( ( c_Com_Obody @ V_pn )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) )
| ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ V_pn ) ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(181,plain,
( ( ! [V_pname_H: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(182,plain,
( ( ! [V_pn: $i,V_s0: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_pn ) @ V_s0 @ V_s1 )
| ~ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ V_pn ) @ tc_Com_Ocom ) @ V_s0 @ V_s1 ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(183,plain,
( ( ! [V_P: $i,V_s: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ V_P ) @ tc_Com_Ocom ) @ V_s @ V_s1 )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_s1 ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(184,plain,
( ( ! [V_u: $i,V_t: $i] :
( ( V_u = V_t )
| ! [V_c: $i,V_s: $i] :
( ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_u )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(185,plain,
( ( ! [V_s: $i] : ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ V_s @ V_s ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(186,plain,
( ( ( c_Fun_Oid @ v_x @ t_a )
= v_x )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(187,plain,
( ( ! [V_P: $i,V_s: $i,V_n: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( c_Option_Othe @ ( c_Com_Obody @ V_P ) @ tc_Com_Ocom ) @ V_s @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ V_P @ V_n @ V_s @ V_s1 ) @ V_s1 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_n @ V_s1 ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(188,plain,
( ( ! [V_P: $i] :
( ( ( c_Com_Obody @ V_P )
= ( c_Option_Ooption_OSome @ ( c_Com_Osko__Com__XWTs__elim__cases__7__1 @ V_P ) @ tc_Com_Ocom ) )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ V_P ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(189,plain,
( ( ! [V_pname_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(190,plain,
( ( ! [V_com1: $i,V_com2: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(191,plain,
( ( ! [V_c0: $i,V_c1: $i,V_s0: $i,V_s2: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_s2 )
| ! [V_s1: $i] :
( ~ ( c_Natural_Oevalc @ V_c1 @ V_s1 @ V_s2 )
| ~ ( c_Natural_Oevalc @ V_c0 @ V_s0 @ V_s1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(192,plain,
( ( ! [V_pn: $i,V_s0: $i,V_n: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ V_pn ) @ V_s0 @ ( c_Suc @ V_n ) @ V_s1 )
| ~ ( c_Natural_Oevaln @ ( c_Option_Othe @ ( c_Com_Obody @ V_pn ) @ tc_Com_Ocom ) @ V_s0 @ V_n @ V_s1 ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(193,plain,
( ( ! [V_pname: $i,V_pname_H: $i] :
( ( ( c_Com_Ocom_OBODY @ V_pname )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) )
| ( V_pname = V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(194,plain,
( ( ! [V_pname_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(195,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ V_s @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(196,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ! [V_n: $i] :
~ ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(197,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ! [V_x: $i] :
~ ( c_Natural_Oevaln @ V_c @ V_s @ V_x @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(198,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(199,plain,
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ v_pn ) @ v_x @ v_xa )
= $false ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(200,plain,
! [SV1: $i] :
( ( ! [SY138: $i] :
( ( c_Fun_Oid @ SV1 @ SY138 )
= SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(201,plain,
! [SV2: $i] :
( ( ! [SY139: $i] :
( ( SV2 = SY139 )
| ! [SY140: $i] :
~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SY139 @ SY140 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(202,plain,
! [SV3: $i] :
( ( ! [SY141: $i] :
( ( SV3
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xoption__Xnchotomy__1__1 @ SV3 @ SY141 ) @ SY141 ) )
| ( SV3
= ( c_Option_Ooption_ONone @ SY141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(203,plain,
! [SV4: $i] :
( ( ! [SY142: $i,SY143: $i,SY144: $i] :
( ( SV4
= ( c_Suc @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SY142 @ SV4 @ SY143 @ SY144 ) ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SY142 ) @ SY143 @ SV4 @ SY144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(204,plain,
! [SV5: $i] :
( ( ! [SY145: $i,SY146: $i,SY147: $i] :
( ( c_Natural_Oevalc @ SV5 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SY145 @ SV5 @ SY146 @ SY147 ) @ SY147 )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SY145 @ SV5 ) @ SY146 @ SY147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(205,plain,
! [SV6: $i] :
( ( ! [SY148: $i,SY149: $i,SY150: $i] :
( ( c_Natural_Oevalc @ SV6 @ SY148 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV6 @ SY149 @ SY148 @ SY150 ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV6 @ SY149 ) @ SY148 @ SY150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(206,plain,
! [SV7: $i] :
( ( ! [SY151: $i,SY152: $i,SY153: $i,SY154: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV7 @ SY151 ) @ SY152 @ SY153 @ SY154 )
| ! [SY155: $i] :
( ~ ( c_Natural_Oevaln @ SY151 @ SY155 @ SY153 @ SY154 )
| ~ ( c_Natural_Oevaln @ SV7 @ SY152 @ SY153 @ SY155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(207,plain,
! [SV8: $i] :
( ( ! [SY156: $i] :
( ( c_Option_Ooption_ONone @ SV8 )
!= ( c_Option_Ooption_OSome @ SY156 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(208,plain,
! [SV9: $i] :
( ( ! [SY157: $i] :
( ( c_Option_Ooption_ONone @ SV9 )
!= ( c_Option_Ooption_OSome @ SY157 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(209,plain,
! [SV10: $i] :
( ( ! [SY158: $i,SY159: $i] :
( ( c_Natural_Oevaln @ SV10 @ SY158 @ ( c_Natural_Osko__Natural__Xeval__eq__1__1 @ SV10 @ SY158 @ SY159 ) @ SY159 )
| ~ ( c_Natural_Oevalc @ SV10 @ SY158 @ SY159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(210,plain,
! [SV11: $i] :
( ( ! [SY160: $i] :
( ( SV11
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xnot__None__eq__1__1 @ SV11 @ SY160 ) @ SY160 ) )
| ( SV11
= ( c_Option_Ooption_ONone @ SY160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(211,plain,
! [SV12: $i] :
( ( ! [SY161: $i,SY162: $i,SY163: $i] :
( ( ( c_Com_Ocom_OSemi @ SV12 @ SY161 )
!= ( c_Com_Ocom_OSemi @ SY162 @ SY163 ) )
| ( SY161 = SY163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(212,plain,
! [SV13: $i] :
( ( ! [SY164: $i,SY165: $i] :
( ! [SY166: $i] :
( ( c_Com_Ocom_OSemi @ SV13 @ SY164 )
!= ( c_Com_Ocom_OSemi @ SY165 @ SY166 ) )
| ( SV13 = SY165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(213,plain,
! [SV14: $i] :
( ( ! [SY167: $i] :
( ( c_Option_Ooption_OSome @ SV14 @ SY167 )
!= ( c_Option_Ooption_ONone @ SY167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(214,plain,
! [SV15: $i] :
( ( ! [SY168: $i] :
( ( c_Option_Ooption_OSome @ SV15 @ SY168 )
!= ( c_Option_Ooption_ONone @ SY168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(215,plain,
! [SV16: $i] :
( ( ! [SY169: $i,SY170: $i] :
( ( ( c_Option_Ooption_OSome @ SV16 @ SY169 )
!= ( c_Option_Ooption_OSome @ SY170 @ SY169 ) )
| ( SV16 = SY170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(216,plain,
! [SV17: $i] :
( ( ! [SY171: $i] :
( ( ( c_Suc @ SV17 )
!= ( c_Suc @ SY171 ) )
| ( SV17 = SY171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(217,plain,
! [SV18: $i] :
( ( ! [SY172: $i] :
( ( ( c_Suc @ SV18 )
!= ( c_Suc @ SY172 ) )
| ( SV18 = SY172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(218,plain,
! [SV19: $i] :
( ( ! [SY173: $i,SY174: $i,SY175: $i,SY176: $i] :
( ( c_Natural_Oevaln @ SV19 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SY173 @ SV19 @ SY174 @ SY175 @ SY176 ) @ SY174 @ SY176 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SY173 @ SV19 ) @ SY175 @ SY174 @ SY176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(219,plain,
! [SV20: $i] :
( ( ! [SY177: $i,SY178: $i,SY179: $i,SY180: $i] :
( ( c_Natural_Oevaln @ SV20 @ SY177 @ SY178 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV20 @ SY179 @ SY178 @ SY177 @ SY180 ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV20 @ SY179 ) @ SY177 @ SY178 @ SY180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(220,plain,
! [SV21: $i] :
( ( ! [SY181: $i,SY182: $i,SY183: $i] :
( ( c_Natural_Oevaln @ SV21 @ SY181 @ ( c_Suc @ SY182 ) @ SY183 )
| ~ ( c_Natural_Oevaln @ SV21 @ SY181 @ SY182 @ SY183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(221,plain,
! [SV22: $i] :
( ( ! [SY184: $i] :
( ( SV22
= ( c_Option_Ooption_ONone @ SY184 ) )
| ( SV22
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xnot__Some__eq__1__1 @ SV22 @ SY184 ) @ SY184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(222,plain,
! [SV23: $i] :
( ( ! [SY185: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV23 @ SY185 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(223,plain,
! [SV24: $i] :
( ( ( c_Com_OWT @ SV24 )
| ! [SY186: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SY186 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(224,plain,
! [SV25: $i] :
( ( ( c_Com_OWT @ SV25 )
| ! [SY187: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV25 @ SY187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(225,plain,
! [SV26: $i] :
( ( ! [SY188: $i] :
( ( c_Com_Ocom_OSemi @ SV26 @ SY188 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(226,plain,
! [SV27: $i] :
( ( ! [SY189: $i,SY190: $i] :
( ( c_Natural_Oevaln @ SV27 @ SY189 @ ( c_Natural_Osko__Natural__Xevalc__evaln__1__1 @ SV27 @ SY189 @ SY190 ) @ SY190 )
| ~ ( c_Natural_Oevalc @ SV27 @ SY189 @ SY190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(227,plain,
! [SV28: $i] :
( ( ! [SY191: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV28 @ SY191 ) )
| ~ ( c_Com_OWT @ SY191 )
| ~ ( c_Com_OWT @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(228,plain,
! [SV29: $i] :
( ( ! [SY192: $i] :
( ( ( c_Com_Obody @ SV29 )
!= ( c_Option_Ooption_OSome @ SY192 @ tc_Com_Ocom ) )
| ~ c_Com_OWT__bodies
| ( c_Com_OWT @ SY192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(229,plain,
! [SV30: $i] :
( ( ( ( c_Suc @ SV30 )
!= SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(230,plain,
! [SV31: $i] :
( ( ( SV31
!= ( c_Suc @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(231,plain,
! [SV32: $i] :
( ( ! [SY193: $i] :
( ( SV32
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xoption__Xexhaust__1__1 @ SV32 @ SY193 ) @ SY193 ) )
| ( SV32
= ( c_Option_Ooption_ONone @ SY193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(232,plain,
! [SV33: $i] :
( ( ! [SY194: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ SV33 @ SY194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(233,plain,
! [SV34: $i] :
( ( ! [SY195: $i] :
( ( c_Option_Othe @ ( c_Option_Ooption_OSome @ SV34 @ SY195 ) @ SY195 )
= SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(234,plain,
! [SV35: $i] :
( ( ( ( c_Com_Obody @ SV35 )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) )
| ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(235,plain,
! [SV36: $i] :
( ( ( ( c_Com_Ocom_OBODY @ SV36 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(236,plain,
! [SV37: $i] :
( ( ! [SY196: $i,SY197: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV37 ) @ SY196 @ SY197 )
| ~ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ SV37 ) @ tc_Com_Ocom ) @ SY196 @ SY197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(237,plain,
! [SV38: $i] :
( ( ! [SY198: $i,SY199: $i] :
( ( c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ SV38 ) @ tc_Com_Ocom ) @ SY198 @ SY199 )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV38 ) @ SY198 @ SY199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(238,plain,
! [SV39: $i] :
( ( ! [SY200: $i] :
( ( SV39 = SY200 )
| ! [SY201: $i,SY202: $i] :
( ~ ( c_Natural_Oevalc @ SY201 @ SY202 @ SV39 )
| ~ ( c_Natural_Oevalc @ SY201 @ SY202 @ SY200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(239,plain,
! [SV40: $i] :
( ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ SV40 @ SV40 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(240,plain,
! [SV41: $i] :
( ( ! [SY203: $i,SY204: $i,SY205: $i] :
( ( c_Natural_Oevaln @ ( c_Option_Othe @ ( c_Com_Obody @ SV41 ) @ tc_Com_Ocom ) @ SY203 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SV41 @ SY204 @ SY203 @ SY205 ) @ SY205 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV41 ) @ SY203 @ SY204 @ SY205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(241,plain,
! [SV42: $i] :
( ( ( ( c_Com_Obody @ SV42 )
= ( c_Option_Ooption_OSome @ ( c_Com_Osko__Com__XWTs__elim__cases__7__1 @ SV42 ) @ tc_Com_Ocom ) )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(242,plain,
! [SV43: $i] :
( ( ! [SY206: $i,SY207: $i] :
( ( c_Com_Ocom_OBODY @ SV43 )
!= ( c_Com_Ocom_OSemi @ SY206 @ SY207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(243,plain,
! [SV44: $i] :
( ( ! [SY208: $i,SY209: $i] :
( ( c_Com_Ocom_OSemi @ SV44 @ SY208 )
!= ( c_Com_Ocom_OBODY @ SY209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(244,plain,
! [SV45: $i] :
( ( ! [SY210: $i,SY211: $i,SY212: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV45 @ SY210 ) @ SY211 @ SY212 )
| ! [SY213: $i] :
( ~ ( c_Natural_Oevalc @ SY210 @ SY213 @ SY212 )
| ~ ( c_Natural_Oevalc @ SV45 @ SY211 @ SY213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(245,plain,
! [SV46: $i] :
( ( ! [SY214: $i,SY215: $i,SY216: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV46 ) @ SY214 @ ( c_Suc @ SY215 ) @ SY216 )
| ~ ( c_Natural_Oevaln @ ( c_Option_Othe @ ( c_Com_Obody @ SV46 ) @ tc_Com_Ocom ) @ SY214 @ SY215 @ SY216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(246,plain,
! [SV47: $i] :
( ( ! [SY217: $i] :
( ( ( c_Com_Ocom_OBODY @ SV47 )
!= ( c_Com_Ocom_OBODY @ SY217 ) )
| ( SV47 = SY217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(247,plain,
! [SV48: $i] :
( ( ( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(248,plain,
! [SV49: $i] :
( ( ! [SY218: $i] :
( ( SV49 = SY218 )
| ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ SY218 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(249,plain,
! [SV50: $i] :
( ( ! [SY219: $i,SY220: $i] :
( ( c_Natural_Oevalc @ SV50 @ SY219 @ SY220 )
| ! [SY221: $i] :
~ ( c_Natural_Oevaln @ SV50 @ SY219 @ SY221 @ SY220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(250,plain,
! [SV51: $i] :
( ( ! [SY222: $i,SY223: $i] :
( ( c_Natural_Oevalc @ SV51 @ SY222 @ SY223 )
| ! [SY224: $i] :
~ ( c_Natural_Oevaln @ SV51 @ SY222 @ SY224 @ SY223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(251,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(252,plain,
! [SV52: $i,SV1: $i] :
( ( ( c_Fun_Oid @ SV1 @ SV52 )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(253,plain,
! [SV53: $i,SV2: $i] :
( ( ( SV2 = SV53 )
| ! [SY225: $i] :
~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV53 @ SY225 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(254,plain,
! [SV54: $i,SV3: $i] :
( ( ( SV3
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xoption__Xnchotomy__1__1 @ SV3 @ SV54 ) @ SV54 ) )
| ( SV3
= ( c_Option_Ooption_ONone @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(255,plain,
! [SV55: $i,SV4: $i] :
( ( ! [SY226: $i,SY227: $i] :
( ( SV4
= ( c_Suc @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SV55 @ SV4 @ SY226 @ SY227 ) ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV55 ) @ SY226 @ SV4 @ SY227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(256,plain,
! [SV56: $i,SV5: $i] :
( ( ! [SY228: $i,SY229: $i] :
( ( c_Natural_Oevalc @ SV5 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV56 @ SV5 @ SY228 @ SY229 ) @ SY229 )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV56 @ SV5 ) @ SY228 @ SY229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(257,plain,
! [SV57: $i,SV6: $i] :
( ( ! [SY230: $i,SY231: $i] :
( ( c_Natural_Oevalc @ SV6 @ SV57 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV6 @ SY230 @ SV57 @ SY231 ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV6 @ SY230 ) @ SV57 @ SY231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(258,plain,
! [SV58: $i,SV7: $i] :
( ( ! [SY232: $i,SY233: $i,SY234: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV7 @ SV58 ) @ SY232 @ SY233 @ SY234 )
| ! [SY235: $i] :
( ~ ( c_Natural_Oevaln @ SV58 @ SY235 @ SY233 @ SY234 )
| ~ ( c_Natural_Oevaln @ SV7 @ SY232 @ SY233 @ SY235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(259,plain,
! [SV59: $i,SV8: $i] :
( ( ( ( c_Option_Ooption_ONone @ SV8 )
!= ( c_Option_Ooption_OSome @ SV59 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(260,plain,
! [SV60: $i,SV9: $i] :
( ( ( ( c_Option_Ooption_ONone @ SV9 )
!= ( c_Option_Ooption_OSome @ SV60 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(261,plain,
! [SV61: $i,SV10: $i] :
( ( ! [SY236: $i] :
( ( c_Natural_Oevaln @ SV10 @ SV61 @ ( c_Natural_Osko__Natural__Xeval__eq__1__1 @ SV10 @ SV61 @ SY236 ) @ SY236 )
| ~ ( c_Natural_Oevalc @ SV10 @ SV61 @ SY236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(262,plain,
! [SV62: $i,SV11: $i] :
( ( ( SV11
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xnot__None__eq__1__1 @ SV11 @ SV62 ) @ SV62 ) )
| ( SV11
= ( c_Option_Ooption_ONone @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(263,plain,
! [SV63: $i,SV12: $i] :
( ( ! [SY237: $i,SY238: $i] :
( ( ( c_Com_Ocom_OSemi @ SV12 @ SV63 )
!= ( c_Com_Ocom_OSemi @ SY237 @ SY238 ) )
| ( SV63 = SY238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(264,plain,
! [SV64: $i,SV13: $i] :
( ( ! [SY239: $i] :
( ! [SY240: $i] :
( ( c_Com_Ocom_OSemi @ SV13 @ SV64 )
!= ( c_Com_Ocom_OSemi @ SY239 @ SY240 ) )
| ( SV13 = SY239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(265,plain,
! [SV65: $i,SV14: $i] :
( ( ( ( c_Option_Ooption_OSome @ SV14 @ SV65 )
!= ( c_Option_Ooption_ONone @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(266,plain,
! [SV66: $i,SV15: $i] :
( ( ( ( c_Option_Ooption_OSome @ SV15 @ SV66 )
!= ( c_Option_Ooption_ONone @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(267,plain,
! [SV67: $i,SV16: $i] :
( ( ! [SY241: $i] :
( ( ( c_Option_Ooption_OSome @ SV16 @ SV67 )
!= ( c_Option_Ooption_OSome @ SY241 @ SV67 ) )
| ( SV16 = SY241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(268,plain,
! [SV68: $i,SV17: $i] :
( ( ( ( c_Suc @ SV17 )
!= ( c_Suc @ SV68 ) )
| ( SV17 = SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(269,plain,
! [SV69: $i,SV18: $i] :
( ( ( ( c_Suc @ SV18 )
!= ( c_Suc @ SV69 ) )
| ( SV18 = SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(270,plain,
! [SV70: $i,SV19: $i] :
( ( ! [SY242: $i,SY243: $i,SY244: $i] :
( ( c_Natural_Oevaln @ SV19 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV70 @ SV19 @ SY242 @ SY243 @ SY244 ) @ SY242 @ SY244 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV70 @ SV19 ) @ SY243 @ SY242 @ SY244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(271,plain,
! [SV71: $i,SV20: $i] :
( ( ! [SY245: $i,SY246: $i,SY247: $i] :
( ( c_Natural_Oevaln @ SV20 @ SV71 @ SY245 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV20 @ SY246 @ SY245 @ SV71 @ SY247 ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV20 @ SY246 ) @ SV71 @ SY245 @ SY247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(272,plain,
! [SV72: $i,SV21: $i] :
( ( ! [SY248: $i,SY249: $i] :
( ( c_Natural_Oevaln @ SV21 @ SV72 @ ( c_Suc @ SY248 ) @ SY249 )
| ~ ( c_Natural_Oevaln @ SV21 @ SV72 @ SY248 @ SY249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(273,plain,
! [SV73: $i,SV22: $i] :
( ( ( SV22
= ( c_Option_Ooption_ONone @ SV73 ) )
| ( SV22
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xnot__Some__eq__1__1 @ SV22 @ SV73 ) @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(274,plain,
! [SV74: $i,SV23: $i] :
( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV23 @ SV74 @ SV23 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(275,plain,
! [SV24: $i] :
( ( ( c_Com_OWT @ SV24 )
= $true )
| ( ( ! [SY186: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SY186 @ SV24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(276,plain,
! [SV25: $i] :
( ( ( c_Com_OWT @ SV25 )
= $true )
| ( ( ! [SY187: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV25 @ SY187 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(277,plain,
! [SV75: $i,SV26: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV26 @ SV75 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(278,plain,
! [SV76: $i,SV27: $i] :
( ( ! [SY250: $i] :
( ( c_Natural_Oevaln @ SV27 @ SV76 @ ( c_Natural_Osko__Natural__Xevalc__evaln__1__1 @ SV27 @ SV76 @ SY250 ) @ SY250 )
| ~ ( c_Natural_Oevalc @ SV27 @ SV76 @ SY250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(279,plain,
! [SV77: $i,SV28: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV28 @ SV77 ) )
| ~ ( c_Com_OWT @ SV77 )
| ~ ( c_Com_OWT @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(280,plain,
! [SV78: $i,SV29: $i] :
( ( ( ( c_Com_Obody @ SV29 )
!= ( c_Option_Ooption_OSome @ SV78 @ tc_Com_Ocom ) )
| ~ c_Com_OWT__bodies
| ( c_Com_OWT @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(281,plain,
! [SV30: $i] :
( ( ( c_Suc @ SV30 )
= SV30 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(282,plain,
! [SV31: $i] :
( ( SV31
= ( c_Suc @ SV31 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(283,plain,
! [SV79: $i,SV32: $i] :
( ( ( SV32
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xoption__Xexhaust__1__1 @ SV32 @ SV79 ) @ SV79 ) )
| ( SV32
= ( c_Option_Ooption_ONone @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(284,plain,
! [SV80: $i,SV33: $i] :
( ( ( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ SV33 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(285,plain,
! [SV81: $i,SV34: $i] :
( ( ( c_Option_Othe @ ( c_Option_Ooption_OSome @ SV34 @ SV81 ) @ SV81 )
= SV34 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(286,plain,
! [SV35: $i] :
( ( ( ( c_Com_Obody @ SV35 )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) )
= $true )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(287,plain,
! [SV36: $i] :
( ( ( c_Com_Ocom_OBODY @ SV36 )
= c_Com_Ocom_OSKIP )
= $false ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(288,plain,
! [SV82: $i,SV37: $i] :
( ( ! [SY251: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV37 ) @ SV82 @ SY251 )
| ~ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ SV37 ) @ tc_Com_Ocom ) @ SV82 @ SY251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(289,plain,
! [SV83: $i,SV38: $i] :
( ( ! [SY252: $i] :
( ( c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ SV38 ) @ tc_Com_Ocom ) @ SV83 @ SY252 )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV38 ) @ SV83 @ SY252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(290,plain,
! [SV84: $i,SV39: $i] :
( ( ( SV39 = SV84 )
| ! [SY253: $i,SY254: $i] :
( ~ ( c_Natural_Oevalc @ SY253 @ SY254 @ SV39 )
| ~ ( c_Natural_Oevalc @ SY253 @ SY254 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(291,plain,
! [SV85: $i,SV41: $i] :
( ( ! [SY255: $i,SY256: $i] :
( ( c_Natural_Oevaln @ ( c_Option_Othe @ ( c_Com_Obody @ SV41 ) @ tc_Com_Ocom ) @ SV85 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SV41 @ SY255 @ SV85 @ SY256 ) @ SY256 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV41 ) @ SV85 @ SY255 @ SY256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(292,plain,
! [SV42: $i] :
( ( ( ( c_Com_Obody @ SV42 )
= ( c_Option_Ooption_OSome @ ( c_Com_Osko__Com__XWTs__elim__cases__7__1 @ SV42 ) @ tc_Com_Ocom ) )
= $true )
| ( ( ~ ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(293,plain,
! [SV86: $i,SV43: $i] :
( ( ! [SY257: $i] :
( ( c_Com_Ocom_OBODY @ SV43 )
!= ( c_Com_Ocom_OSemi @ SV86 @ SY257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(294,plain,
! [SV87: $i,SV44: $i] :
( ( ! [SY258: $i] :
( ( c_Com_Ocom_OSemi @ SV44 @ SV87 )
!= ( c_Com_Ocom_OBODY @ SY258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(295,plain,
! [SV88: $i,SV45: $i] :
( ( ! [SY259: $i,SY260: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV45 @ SV88 ) @ SY259 @ SY260 )
| ! [SY261: $i] :
( ~ ( c_Natural_Oevalc @ SV88 @ SY261 @ SY260 )
| ~ ( c_Natural_Oevalc @ SV45 @ SY259 @ SY261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(296,plain,
! [SV89: $i,SV46: $i] :
( ( ! [SY262: $i,SY263: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV46 ) @ SV89 @ ( c_Suc @ SY262 ) @ SY263 )
| ~ ( c_Natural_Oevaln @ ( c_Option_Othe @ ( c_Com_Obody @ SV46 ) @ tc_Com_Ocom ) @ SV89 @ SY262 @ SY263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(297,plain,
! [SV90: $i,SV47: $i] :
( ( ( ( c_Com_Ocom_OBODY @ SV47 )
!= ( c_Com_Ocom_OBODY @ SV90 ) )
| ( SV47 = SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(298,plain,
! [SV48: $i] :
( ( c_Com_Ocom_OSKIP
= ( c_Com_Ocom_OBODY @ SV48 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(299,plain,
! [SV91: $i,SV49: $i] :
( ( ( SV49 = SV91 )
| ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ SV91 @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(300,plain,
! [SV92: $i,SV50: $i] :
( ( ! [SY264: $i] :
( ( c_Natural_Oevalc @ SV50 @ SV92 @ SY264 )
| ! [SY265: $i] :
~ ( c_Natural_Oevaln @ SV50 @ SV92 @ SY265 @ SY264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(301,plain,
! [SV93: $i,SV51: $i] :
( ( ! [SY266: $i] :
( ( c_Natural_Oevalc @ SV51 @ SV93 @ SY266 )
| ! [SY267: $i] :
~ ( c_Natural_Oevaln @ SV51 @ SV93 @ SY267 @ SY266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(302,plain,
! [SV53: $i,SV2: $i] :
( ( ( SV2 = SV53 )
= $true )
| ( ( ! [SY225: $i] :
~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV53 @ SY225 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(303,plain,
! [SV54: $i,SV3: $i] :
( ( ( SV3
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xoption__Xnchotomy__1__1 @ SV3 @ SV54 ) @ SV54 ) )
= $true )
| ( ( SV3
= ( c_Option_Ooption_ONone @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(304,plain,
! [SV94: $i,SV55: $i,SV4: $i] :
( ( ! [SY268: $i] :
( ( SV4
= ( c_Suc @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SV55 @ SV4 @ SV94 @ SY268 ) ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV55 ) @ SV94 @ SV4 @ SY268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(305,plain,
! [SV95: $i,SV56: $i,SV5: $i] :
( ( ! [SY269: $i] :
( ( c_Natural_Oevalc @ SV5 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV56 @ SV5 @ SV95 @ SY269 ) @ SY269 )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV56 @ SV5 ) @ SV95 @ SY269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(306,plain,
! [SV96: $i,SV57: $i,SV6: $i] :
( ( ! [SY270: $i] :
( ( c_Natural_Oevalc @ SV6 @ SV57 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV6 @ SV96 @ SV57 @ SY270 ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV6 @ SV96 ) @ SV57 @ SY270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(307,plain,
! [SV97: $i,SV58: $i,SV7: $i] :
( ( ! [SY271: $i,SY272: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV7 @ SV58 ) @ SV97 @ SY271 @ SY272 )
| ! [SY273: $i] :
( ~ ( c_Natural_Oevaln @ SV58 @ SY273 @ SY271 @ SY272 )
| ~ ( c_Natural_Oevaln @ SV7 @ SV97 @ SY271 @ SY273 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(308,plain,
! [SV59: $i,SV8: $i] :
( ( ( c_Option_Ooption_ONone @ SV8 )
= ( c_Option_Ooption_OSome @ SV59 @ SV8 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(309,plain,
! [SV60: $i,SV9: $i] :
( ( ( c_Option_Ooption_ONone @ SV9 )
= ( c_Option_Ooption_OSome @ SV60 @ SV9 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(310,plain,
! [SV98: $i,SV61: $i,SV10: $i] :
( ( ( c_Natural_Oevaln @ SV10 @ SV61 @ ( c_Natural_Osko__Natural__Xeval__eq__1__1 @ SV10 @ SV61 @ SV98 ) @ SV98 )
| ~ ( c_Natural_Oevalc @ SV10 @ SV61 @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(311,plain,
! [SV62: $i,SV11: $i] :
( ( ( SV11
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xnot__None__eq__1__1 @ SV11 @ SV62 ) @ SV62 ) )
= $true )
| ( ( SV11
= ( c_Option_Ooption_ONone @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(312,plain,
! [SV99: $i,SV63: $i,SV12: $i] :
( ( ! [SY274: $i] :
( ( ( c_Com_Ocom_OSemi @ SV12 @ SV63 )
!= ( c_Com_Ocom_OSemi @ SV99 @ SY274 ) )
| ( SV63 = SY274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(313,plain,
! [SV100: $i,SV64: $i,SV13: $i] :
( ( ! [SY275: $i] :
( ( c_Com_Ocom_OSemi @ SV13 @ SV64 )
!= ( c_Com_Ocom_OSemi @ SV100 @ SY275 ) )
| ( SV13 = SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(314,plain,
! [SV65: $i,SV14: $i] :
( ( ( c_Option_Ooption_OSome @ SV14 @ SV65 )
= ( c_Option_Ooption_ONone @ SV65 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(315,plain,
! [SV66: $i,SV15: $i] :
( ( ( c_Option_Ooption_OSome @ SV15 @ SV66 )
= ( c_Option_Ooption_ONone @ SV66 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(316,plain,
! [SV101: $i,SV67: $i,SV16: $i] :
( ( ( ( c_Option_Ooption_OSome @ SV16 @ SV67 )
!= ( c_Option_Ooption_OSome @ SV101 @ SV67 ) )
| ( SV16 = SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(317,plain,
! [SV68: $i,SV17: $i] :
( ( ( ( ( c_Suc @ SV17 )
!= ( c_Suc @ SV68 ) ) )
= $true )
| ( ( SV17 = SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(318,plain,
! [SV69: $i,SV18: $i] :
( ( ( ( ( c_Suc @ SV18 )
!= ( c_Suc @ SV69 ) ) )
= $true )
| ( ( SV18 = SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(319,plain,
! [SV102: $i,SV70: $i,SV19: $i] :
( ( ! [SY276: $i,SY277: $i] :
( ( c_Natural_Oevaln @ SV19 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV70 @ SV19 @ SV102 @ SY276 @ SY277 ) @ SV102 @ SY277 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV70 @ SV19 ) @ SY276 @ SV102 @ SY277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(320,plain,
! [SV103: $i,SV71: $i,SV20: $i] :
( ( ! [SY278: $i,SY279: $i] :
( ( c_Natural_Oevaln @ SV20 @ SV71 @ SV103 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV20 @ SY278 @ SV103 @ SV71 @ SY279 ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV20 @ SY278 ) @ SV71 @ SV103 @ SY279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(321,plain,
! [SV104: $i,SV72: $i,SV21: $i] :
( ( ! [SY280: $i] :
( ( c_Natural_Oevaln @ SV21 @ SV72 @ ( c_Suc @ SV104 ) @ SY280 )
| ~ ( c_Natural_Oevaln @ SV21 @ SV72 @ SV104 @ SY280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(322,plain,
! [SV73: $i,SV22: $i] :
( ( ( SV22
= ( c_Option_Ooption_ONone @ SV73 ) )
= $true )
| ( ( SV22
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xnot__Some__eq__1__1 @ SV22 @ SV73 ) @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(323,plain,
! [SV24: $i,SV105: $i] :
( ( ( ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV105 @ SV24 ) ) )
= $true )
| ( ( c_Com_OWT @ SV24 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(324,plain,
! [SV106: $i,SV25: $i] :
( ( ( ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV25 @ SV106 ) ) )
= $true )
| ( ( c_Com_OWT @ SV25 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(325,plain,
! [SV75: $i,SV26: $i] :
( ( ( c_Com_Ocom_OSemi @ SV26 @ SV75 )
= c_Com_Ocom_OSKIP )
= $false ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(326,plain,
! [SV107: $i,SV76: $i,SV27: $i] :
( ( ( c_Natural_Oevaln @ SV27 @ SV76 @ ( c_Natural_Osko__Natural__Xevalc__evaln__1__1 @ SV27 @ SV76 @ SV107 ) @ SV107 )
| ~ ( c_Natural_Oevalc @ SV27 @ SV76 @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(327,plain,
! [SV77: $i,SV28: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV28 @ SV77 ) )
= $true )
| ( ( ~ ( c_Com_OWT @ SV77 )
| ~ ( c_Com_OWT @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(328,plain,
! [SV78: $i,SV29: $i] :
( ( ( ( ( c_Com_Obody @ SV29 )
!= ( c_Option_Ooption_OSome @ SV78 @ tc_Com_Ocom ) ) )
= $true )
| ( ( ~ c_Com_OWT__bodies
| ( c_Com_OWT @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(329,plain,
! [SV79: $i,SV32: $i] :
( ( ( SV32
= ( c_Option_Ooption_OSome @ ( c_ATP__Linkup_Osko__Option__Xoption__Xexhaust__1__1 @ SV32 @ SV79 ) @ SV79 ) )
= $true )
| ( ( SV32
= ( c_Option_Ooption_ONone @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(330,plain,
! [SV80: $i,SV33: $i] :
( ( c_Com_Ocom_OSKIP
= ( c_Com_Ocom_OSemi @ SV33 @ SV80 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(331,plain,
! [SV108: $i,SV82: $i,SV37: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV37 ) @ SV82 @ SV108 )
| ~ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ SV37 ) @ tc_Com_Ocom ) @ SV82 @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(332,plain,
! [SV109: $i,SV83: $i,SV38: $i] :
( ( ( c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ SV38 ) @ tc_Com_Ocom ) @ SV83 @ SV109 )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV38 ) @ SV83 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(333,plain,
! [SV84: $i,SV39: $i] :
( ( ( SV39 = SV84 )
= $true )
| ( ( ! [SY253: $i,SY254: $i] :
( ~ ( c_Natural_Oevalc @ SY253 @ SY254 @ SV39 )
| ~ ( c_Natural_Oevalc @ SY253 @ SY254 @ SV84 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(334,plain,
! [SV110: $i,SV85: $i,SV41: $i] :
( ( ! [SY281: $i] :
( ( c_Natural_Oevaln @ ( c_Option_Othe @ ( c_Com_Obody @ SV41 ) @ tc_Com_Ocom ) @ SV85 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SV41 @ SV110 @ SV85 @ SY281 ) @ SY281 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV41 ) @ SV85 @ SV110 @ SY281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(335,plain,
! [SV42: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ SV42 ) )
= $false )
| ( ( ( c_Com_Obody @ SV42 )
= ( c_Option_Ooption_OSome @ ( c_Com_Osko__Com__XWTs__elim__cases__7__1 @ SV42 ) @ tc_Com_Ocom ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(336,plain,
! [SV111: $i,SV86: $i,SV43: $i] :
( ( ( ( c_Com_Ocom_OBODY @ SV43 )
!= ( c_Com_Ocom_OSemi @ SV86 @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(337,plain,
! [SV112: $i,SV87: $i,SV44: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV44 @ SV87 )
!= ( c_Com_Ocom_OBODY @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(338,plain,
! [SV113: $i,SV88: $i,SV45: $i] :
( ( ! [SY282: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV45 @ SV88 ) @ SV113 @ SY282 )
| ! [SY283: $i] :
( ~ ( c_Natural_Oevalc @ SV88 @ SY283 @ SY282 )
| ~ ( c_Natural_Oevalc @ SV45 @ SV113 @ SY283 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(339,plain,
! [SV114: $i,SV89: $i,SV46: $i] :
( ( ! [SY284: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV46 ) @ SV89 @ ( c_Suc @ SV114 ) @ SY284 )
| ~ ( c_Natural_Oevaln @ ( c_Option_Othe @ ( c_Com_Obody @ SV46 ) @ tc_Com_Ocom ) @ SV89 @ SV114 @ SY284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(340,plain,
! [SV90: $i,SV47: $i] :
( ( ( ( ( c_Com_Ocom_OBODY @ SV47 )
!= ( c_Com_Ocom_OBODY @ SV90 ) ) )
= $true )
| ( ( SV47 = SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(341,plain,
! [SV91: $i,SV49: $i] :
( ( ( SV49 = SV91 )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ SV91 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(342,plain,
! [SV115: $i,SV92: $i,SV50: $i] :
( ( ( c_Natural_Oevalc @ SV50 @ SV92 @ SV115 )
| ! [SY285: $i] :
~ ( c_Natural_Oevaln @ SV50 @ SV92 @ SY285 @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(343,plain,
! [SV116: $i,SV93: $i,SV51: $i] :
( ( ( c_Natural_Oevalc @ SV51 @ SV93 @ SV116 )
| ! [SY286: $i] :
~ ( c_Natural_Oevaln @ SV51 @ SV93 @ SY286 @ SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(344,plain,
! [SV2: $i,SV117: $i,SV53: $i] :
( ( ( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV53 @ SV117 @ SV2 ) )
= $true )
| ( ( SV2 = SV53 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(345,plain,
! [SV118: $i,SV94: $i,SV55: $i,SV4: $i] :
( ( ( SV4
= ( c_Suc @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SV55 @ SV4 @ SV94 @ SV118 ) ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV55 ) @ SV94 @ SV4 @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(346,plain,
! [SV119: $i,SV95: $i,SV56: $i,SV5: $i] :
( ( ( c_Natural_Oevalc @ SV5 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV56 @ SV5 @ SV95 @ SV119 ) @ SV119 )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV56 @ SV5 ) @ SV95 @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(347,plain,
! [SV120: $i,SV96: $i,SV57: $i,SV6: $i] :
( ( ( c_Natural_Oevalc @ SV6 @ SV57 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV6 @ SV96 @ SV57 @ SV120 ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV6 @ SV96 ) @ SV57 @ SV120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(348,plain,
! [SV121: $i,SV97: $i,SV58: $i,SV7: $i] :
( ( ! [SY287: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV7 @ SV58 ) @ SV97 @ SV121 @ SY287 )
| ! [SY288: $i] :
( ~ ( c_Natural_Oevaln @ SV58 @ SY288 @ SV121 @ SY287 )
| ~ ( c_Natural_Oevaln @ SV7 @ SV97 @ SV121 @ SY288 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(349,plain,
! [SV98: $i,SV61: $i,SV10: $i] :
( ( ( c_Natural_Oevaln @ SV10 @ SV61 @ ( c_Natural_Osko__Natural__Xeval__eq__1__1 @ SV10 @ SV61 @ SV98 ) @ SV98 )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ SV10 @ SV61 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(350,plain,
! [SV122: $i,SV99: $i,SV63: $i,SV12: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV12 @ SV63 )
!= ( c_Com_Ocom_OSemi @ SV99 @ SV122 ) )
| ( SV63 = SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(351,plain,
! [SV100: $i,SV64: $i,SV13: $i] :
( ( ( ! [SY275: $i] :
( ( c_Com_Ocom_OSemi @ SV13 @ SV64 )
!= ( c_Com_Ocom_OSemi @ SV100 @ SY275 ) ) )
= $true )
| ( ( SV13 = SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(352,plain,
! [SV101: $i,SV67: $i,SV16: $i] :
( ( ( ( ( c_Option_Ooption_OSome @ SV16 @ SV67 )
!= ( c_Option_Ooption_OSome @ SV101 @ SV67 ) ) )
= $true )
| ( ( SV16 = SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(353,plain,
! [SV68: $i,SV17: $i] :
( ( ( ( c_Suc @ SV17 )
= ( c_Suc @ SV68 ) )
= $false )
| ( ( SV17 = SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(354,plain,
! [SV69: $i,SV18: $i] :
( ( ( ( c_Suc @ SV18 )
= ( c_Suc @ SV69 ) )
= $false )
| ( ( SV18 = SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(355,plain,
! [SV123: $i,SV102: $i,SV70: $i,SV19: $i] :
( ( ! [SY289: $i] :
( ( c_Natural_Oevaln @ SV19 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV70 @ SV19 @ SV102 @ SV123 @ SY289 ) @ SV102 @ SY289 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV70 @ SV19 ) @ SV123 @ SV102 @ SY289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(356,plain,
! [SV124: $i,SV103: $i,SV71: $i,SV20: $i] :
( ( ! [SY290: $i] :
( ( c_Natural_Oevaln @ SV20 @ SV71 @ SV103 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV20 @ SV124 @ SV103 @ SV71 @ SY290 ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV20 @ SV124 ) @ SV71 @ SV103 @ SY290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(357,plain,
! [SV125: $i,SV104: $i,SV72: $i,SV21: $i] :
( ( ( c_Natural_Oevaln @ SV21 @ SV72 @ ( c_Suc @ SV104 ) @ SV125 )
| ~ ( c_Natural_Oevaln @ SV21 @ SV72 @ SV104 @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(358,plain,
! [SV24: $i,SV105: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV105 @ SV24 ) )
= $false )
| ( ( c_Com_OWT @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(359,plain,
! [SV106: $i,SV25: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV25 @ SV106 ) )
= $false )
| ( ( c_Com_OWT @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(360,plain,
! [SV107: $i,SV76: $i,SV27: $i] :
( ( ( c_Natural_Oevaln @ SV27 @ SV76 @ ( c_Natural_Osko__Natural__Xevalc__evaln__1__1 @ SV27 @ SV76 @ SV107 ) @ SV107 )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ SV27 @ SV76 @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(361,plain,
! [SV28: $i,SV77: $i] :
( ( ( ~ ( c_Com_OWT @ SV77 ) )
= $true )
| ( ( ~ ( c_Com_OWT @ SV28 ) )
= $true )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV28 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(362,plain,
! [SV78: $i,SV29: $i] :
( ( ( ( c_Com_Obody @ SV29 )
= ( c_Option_Ooption_OSome @ SV78 @ tc_Com_Ocom ) )
= $false )
| ( ( ~ c_Com_OWT__bodies
| ( c_Com_OWT @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(363,plain,
! [SV108: $i,SV82: $i,SV37: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV37 ) @ SV82 @ SV108 )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ SV37 ) @ tc_Com_Ocom ) @ SV82 @ SV108 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(364,plain,
! [SV109: $i,SV83: $i,SV38: $i] :
( ( ( c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ SV38 ) @ tc_Com_Ocom ) @ SV83 @ SV109 )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV38 ) @ SV83 @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(365,plain,
! [SV84: $i,SV39: $i,SV126: $i] :
( ( ( ! [SY291: $i] :
( ~ ( c_Natural_Oevalc @ SV126 @ SY291 @ SV39 )
| ~ ( c_Natural_Oevalc @ SV126 @ SY291 @ SV84 ) ) )
= $true )
| ( ( SV39 = SV84 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(366,plain,
! [SV127: $i,SV110: $i,SV85: $i,SV41: $i] :
( ( ( c_Natural_Oevaln @ ( c_Option_Othe @ ( c_Com_Obody @ SV41 ) @ tc_Com_Ocom ) @ SV85 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SV41 @ SV110 @ SV85 @ SV127 ) @ SV127 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV41 ) @ SV85 @ SV110 @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(367,plain,
! [SV111: $i,SV86: $i,SV43: $i] :
( ( ( c_Com_Ocom_OBODY @ SV43 )
= ( c_Com_Ocom_OSemi @ SV86 @ SV111 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(368,plain,
! [SV112: $i,SV87: $i,SV44: $i] :
( ( ( c_Com_Ocom_OSemi @ SV44 @ SV87 )
= ( c_Com_Ocom_OBODY @ SV112 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(369,plain,
! [SV128: $i,SV113: $i,SV88: $i,SV45: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV45 @ SV88 ) @ SV113 @ SV128 )
| ! [SY292: $i] :
( ~ ( c_Natural_Oevalc @ SV88 @ SY292 @ SV128 )
| ~ ( c_Natural_Oevalc @ SV45 @ SV113 @ SY292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(370,plain,
! [SV129: $i,SV114: $i,SV89: $i,SV46: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV46 ) @ SV89 @ ( c_Suc @ SV114 ) @ SV129 )
| ~ ( c_Natural_Oevaln @ ( c_Option_Othe @ ( c_Com_Obody @ SV46 ) @ tc_Com_Ocom ) @ SV89 @ SV114 @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(371,plain,
! [SV90: $i,SV47: $i] :
( ( ( ( c_Com_Ocom_OBODY @ SV47 )
= ( c_Com_Ocom_OBODY @ SV90 ) )
= $false )
| ( ( SV47 = SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(372,plain,
! [SV49: $i,SV91: $i] :
( ( ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ SV91 @ SV49 )
= $false )
| ( ( SV49 = SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(373,plain,
! [SV115: $i,SV92: $i,SV50: $i] :
( ( ( c_Natural_Oevalc @ SV50 @ SV92 @ SV115 )
= $true )
| ( ( ! [SY285: $i] :
~ ( c_Natural_Oevaln @ SV50 @ SV92 @ SY285 @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(374,plain,
! [SV116: $i,SV93: $i,SV51: $i] :
( ( ( c_Natural_Oevalc @ SV51 @ SV93 @ SV116 )
= $true )
| ( ( ! [SY286: $i] :
~ ( c_Natural_Oevaln @ SV51 @ SV93 @ SY286 @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(375,plain,
! [SV2: $i,SV117: $i,SV53: $i] :
( ( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV53 @ SV117 @ SV2 )
= $false )
| ( ( SV2 = SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(376,plain,
! [SV118: $i,SV94: $i,SV55: $i,SV4: $i] :
( ( ( SV4
= ( c_Suc @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SV55 @ SV4 @ SV94 @ SV118 ) ) )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV55 ) @ SV94 @ SV4 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(377,plain,
! [SV119: $i,SV95: $i,SV56: $i,SV5: $i] :
( ( ( c_Natural_Oevalc @ SV5 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV56 @ SV5 @ SV95 @ SV119 ) @ SV119 )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV56 @ SV5 ) @ SV95 @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(378,plain,
! [SV120: $i,SV96: $i,SV57: $i,SV6: $i] :
( ( ( c_Natural_Oevalc @ SV6 @ SV57 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV6 @ SV96 @ SV57 @ SV120 ) )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV6 @ SV96 ) @ SV57 @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(379,plain,
! [SV130: $i,SV121: $i,SV97: $i,SV58: $i,SV7: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV7 @ SV58 ) @ SV97 @ SV121 @ SV130 )
| ! [SY293: $i] :
( ~ ( c_Natural_Oevaln @ SV58 @ SY293 @ SV121 @ SV130 )
| ~ ( c_Natural_Oevaln @ SV7 @ SV97 @ SV121 @ SY293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(380,plain,
! [SV98: $i,SV61: $i,SV10: $i] :
( ( ( c_Natural_Oevalc @ SV10 @ SV61 @ SV98 )
= $false )
| ( ( c_Natural_Oevaln @ SV10 @ SV61 @ ( c_Natural_Osko__Natural__Xeval__eq__1__1 @ SV10 @ SV61 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(381,plain,
! [SV122: $i,SV99: $i,SV63: $i,SV12: $i] :
( ( ( ( ( c_Com_Ocom_OSemi @ SV12 @ SV63 )
!= ( c_Com_Ocom_OSemi @ SV99 @ SV122 ) ) )
= $true )
| ( ( SV63 = SV122 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(382,plain,
! [SV131: $i,SV100: $i,SV64: $i,SV13: $i] :
( ( ( ( ( c_Com_Ocom_OSemi @ SV13 @ SV64 )
!= ( c_Com_Ocom_OSemi @ SV100 @ SV131 ) ) )
= $true )
| ( ( SV13 = SV100 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(383,plain,
! [SV101: $i,SV67: $i,SV16: $i] :
( ( ( ( c_Option_Ooption_OSome @ SV16 @ SV67 )
= ( c_Option_Ooption_OSome @ SV101 @ SV67 ) )
= $false )
| ( ( SV16 = SV101 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(384,plain,
! [SV132: $i,SV123: $i,SV102: $i,SV70: $i,SV19: $i] :
( ( ( c_Natural_Oevaln @ SV19 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV70 @ SV19 @ SV102 @ SV123 @ SV132 ) @ SV102 @ SV132 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV70 @ SV19 ) @ SV123 @ SV102 @ SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(385,plain,
! [SV133: $i,SV124: $i,SV103: $i,SV71: $i,SV20: $i] :
( ( ( c_Natural_Oevaln @ SV20 @ SV71 @ SV103 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV20 @ SV124 @ SV103 @ SV71 @ SV133 ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV20 @ SV124 ) @ SV71 @ SV103 @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(386,plain,
! [SV125: $i,SV104: $i,SV72: $i,SV21: $i] :
( ( ( c_Natural_Oevaln @ SV21 @ SV72 @ ( c_Suc @ SV104 ) @ SV125 )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ SV21 @ SV72 @ SV104 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(387,plain,
! [SV107: $i,SV76: $i,SV27: $i] :
( ( ( c_Natural_Oevalc @ SV27 @ SV76 @ SV107 )
= $false )
| ( ( c_Natural_Oevaln @ SV27 @ SV76 @ ( c_Natural_Osko__Natural__Xevalc__evaln__1__1 @ SV27 @ SV76 @ SV107 ) @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(388,plain,
! [SV28: $i,SV77: $i] :
( ( ( c_Com_OWT @ SV77 )
= $false )
| ( ( ~ ( c_Com_OWT @ SV28 ) )
= $true )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV28 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(389,plain,
! [SV29: $i,SV78: $i] :
( ( ( ~ c_Com_OWT__bodies )
= $true )
| ( ( c_Com_OWT @ SV78 )
= $true )
| ( ( ( c_Com_Obody @ SV29 )
= ( c_Option_Ooption_OSome @ SV78 @ tc_Com_Ocom ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(390,plain,
! [SV108: $i,SV82: $i,SV37: $i] :
( ( ( c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ SV37 ) @ tc_Com_Ocom ) @ SV82 @ SV108 )
= $false )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV37 ) @ SV82 @ SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(391,plain,
! [SV109: $i,SV83: $i,SV38: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV38 ) @ SV83 @ SV109 )
= $false )
| ( ( c_Natural_Oevalc @ ( c_Option_Othe @ ( c_Com_Obody @ SV38 ) @ tc_Com_Ocom ) @ SV83 @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(392,plain,
! [SV84: $i,SV39: $i,SV134: $i,SV126: $i] :
( ( ( ~ ( c_Natural_Oevalc @ SV126 @ SV134 @ SV39 )
| ~ ( c_Natural_Oevalc @ SV126 @ SV134 @ SV84 ) )
= $true )
| ( ( SV39 = SV84 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(393,plain,
! [SV127: $i,SV110: $i,SV85: $i,SV41: $i] :
( ( ( c_Natural_Oevaln @ ( c_Option_Othe @ ( c_Com_Obody @ SV41 ) @ tc_Com_Ocom ) @ SV85 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SV41 @ SV110 @ SV85 @ SV127 ) @ SV127 )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV41 ) @ SV85 @ SV110 @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(394,plain,
! [SV128: $i,SV113: $i,SV88: $i,SV45: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV45 @ SV88 ) @ SV113 @ SV128 )
= $true )
| ( ( ! [SY292: $i] :
( ~ ( c_Natural_Oevalc @ SV88 @ SY292 @ SV128 )
| ~ ( c_Natural_Oevalc @ SV45 @ SV113 @ SY292 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(395,plain,
! [SV129: $i,SV114: $i,SV89: $i,SV46: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV46 ) @ SV89 @ ( c_Suc @ SV114 ) @ SV129 )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ ( c_Option_Othe @ ( c_Com_Obody @ SV46 ) @ tc_Com_Ocom ) @ SV89 @ SV114 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(396,plain,
! [SV115: $i,SV135: $i,SV92: $i,SV50: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV50 @ SV92 @ SV135 @ SV115 ) )
= $true )
| ( ( c_Natural_Oevalc @ SV50 @ SV92 @ SV115 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(397,plain,
! [SV116: $i,SV136: $i,SV93: $i,SV51: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV51 @ SV93 @ SV136 @ SV116 ) )
= $true )
| ( ( c_Natural_Oevalc @ SV51 @ SV93 @ SV116 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(398,plain,
! [SV118: $i,SV4: $i,SV94: $i,SV55: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV55 ) @ SV94 @ SV4 @ SV118 )
= $false )
| ( ( SV4
= ( c_Suc @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SV55 @ SV4 @ SV94 @ SV118 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(399,plain,
! [SV119: $i,SV95: $i,SV5: $i,SV56: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV56 @ SV5 ) @ SV95 @ SV119 )
= $false )
| ( ( c_Natural_Oevalc @ SV5 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV56 @ SV5 @ SV95 @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(400,plain,
! [SV120: $i,SV57: $i,SV96: $i,SV6: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV6 @ SV96 ) @ SV57 @ SV120 )
= $false )
| ( ( c_Natural_Oevalc @ SV6 @ SV57 @ ( c_Natural_Osko__Natural__Xevalc__elim__cases__4__1 @ SV6 @ SV96 @ SV57 @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(401,plain,
! [SV130: $i,SV121: $i,SV97: $i,SV58: $i,SV7: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV7 @ SV58 ) @ SV97 @ SV121 @ SV130 )
= $true )
| ( ( ! [SY293: $i] :
( ~ ( c_Natural_Oevaln @ SV58 @ SY293 @ SV121 @ SV130 )
| ~ ( c_Natural_Oevaln @ SV7 @ SV97 @ SV121 @ SY293 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(402,plain,
! [SV122: $i,SV99: $i,SV63: $i,SV12: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV12 @ SV63 )
= ( c_Com_Ocom_OSemi @ SV99 @ SV122 ) )
= $false )
| ( ( SV63 = SV122 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(403,plain,
! [SV131: $i,SV100: $i,SV64: $i,SV13: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV13 @ SV64 )
= ( c_Com_Ocom_OSemi @ SV100 @ SV131 ) )
= $false )
| ( ( SV13 = SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(404,plain,
! [SV132: $i,SV123: $i,SV102: $i,SV70: $i,SV19: $i] :
( ( ( c_Natural_Oevaln @ SV19 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV70 @ SV19 @ SV102 @ SV123 @ SV132 ) @ SV102 @ SV132 )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV70 @ SV19 ) @ SV123 @ SV102 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(405,plain,
! [SV133: $i,SV124: $i,SV103: $i,SV71: $i,SV20: $i] :
( ( ( c_Natural_Oevaln @ SV20 @ SV71 @ SV103 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV20 @ SV124 @ SV103 @ SV71 @ SV133 ) )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV20 @ SV124 ) @ SV71 @ SV103 @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(406,plain,
! [SV125: $i,SV104: $i,SV72: $i,SV21: $i] :
( ( ( c_Natural_Oevaln @ SV21 @ SV72 @ SV104 @ SV125 )
= $false )
| ( ( c_Natural_Oevaln @ SV21 @ SV72 @ ( c_Suc @ SV104 ) @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(407,plain,
! [SV77: $i,SV28: $i] :
( ( ( c_Com_OWT @ SV28 )
= $false )
| ( ( c_Com_OWT @ SV77 )
= $false )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV28 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(408,plain,
! [SV29: $i,SV78: $i] :
( ( c_Com_OWT__bodies = $false )
| ( ( c_Com_OWT @ SV78 )
= $true )
| ( ( ( c_Com_Obody @ SV29 )
= ( c_Option_Ooption_OSome @ SV78 @ tc_Com_Ocom ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(409,plain,
! [SV84: $i,SV39: $i,SV134: $i,SV126: $i] :
( ( ( ~ ( c_Natural_Oevalc @ SV126 @ SV134 @ SV39 ) )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ SV126 @ SV134 @ SV84 ) )
= $true )
| ( ( SV39 = SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(410,plain,
! [SV127: $i,SV110: $i,SV85: $i,SV41: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV41 ) @ SV85 @ SV110 @ SV127 )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Option_Othe @ ( c_Com_Obody @ SV41 ) @ tc_Com_Ocom ) @ SV85 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SV41 @ SV110 @ SV85 @ SV127 ) @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(411,plain,
! [SV113: $i,SV45: $i,SV128: $i,SV137: $i,SV88: $i] :
( ( ( ~ ( c_Natural_Oevalc @ SV88 @ SV137 @ SV128 )
| ~ ( c_Natural_Oevalc @ SV45 @ SV113 @ SV137 ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV45 @ SV88 ) @ SV113 @ SV128 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(412,plain,
! [SV129: $i,SV114: $i,SV89: $i,SV46: $i] :
( ( ( c_Natural_Oevaln @ ( c_Option_Othe @ ( c_Com_Obody @ SV46 ) @ tc_Com_Ocom ) @ SV89 @ SV114 @ SV129 )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ SV46 ) @ SV89 @ ( c_Suc @ SV114 ) @ SV129 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(413,plain,
! [SV115: $i,SV135: $i,SV92: $i,SV50: $i] :
( ( ( c_Natural_Oevaln @ SV50 @ SV92 @ SV135 @ SV115 )
= $false )
| ( ( c_Natural_Oevalc @ SV50 @ SV92 @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(414,plain,
! [SV116: $i,SV136: $i,SV93: $i,SV51: $i] :
( ( ( c_Natural_Oevaln @ SV51 @ SV93 @ SV136 @ SV116 )
= $false )
| ( ( c_Natural_Oevalc @ SV51 @ SV93 @ SV116 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(415,plain,
! [SV97: $i,SV7: $i,SV130: $i,SV121: $i,SV138: $i,SV58: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV58 @ SV138 @ SV121 @ SV130 )
| ~ ( c_Natural_Oevaln @ SV7 @ SV97 @ SV121 @ SV138 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV7 @ SV58 ) @ SV97 @ SV121 @ SV130 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(416,plain,
! [SV132: $i,SV102: $i,SV123: $i,SV19: $i,SV70: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV70 @ SV19 ) @ SV123 @ SV102 @ SV132 )
= $false )
| ( ( c_Natural_Oevaln @ SV19 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV70 @ SV19 @ SV102 @ SV123 @ SV132 ) @ SV102 @ SV132 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(417,plain,
! [SV133: $i,SV103: $i,SV71: $i,SV124: $i,SV20: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV20 @ SV124 ) @ SV71 @ SV103 @ SV133 )
= $false )
| ( ( c_Natural_Oevaln @ SV20 @ SV71 @ SV103 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__4__1 @ SV20 @ SV124 @ SV103 @ SV71 @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(418,plain,
! [SV84: $i,SV39: $i,SV134: $i,SV126: $i] :
( ( ( c_Natural_Oevalc @ SV126 @ SV134 @ SV39 )
= $false )
| ( ( ~ ( c_Natural_Oevalc @ SV126 @ SV134 @ SV84 ) )
= $true )
| ( ( SV39 = SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(419,plain,
! [SV113: $i,SV45: $i,SV128: $i,SV137: $i,SV88: $i] :
( ( ( ~ ( c_Natural_Oevalc @ SV88 @ SV137 @ SV128 ) )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ SV45 @ SV113 @ SV137 ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV45 @ SV88 ) @ SV113 @ SV128 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(420,plain,
! [SV97: $i,SV7: $i,SV130: $i,SV121: $i,SV138: $i,SV58: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV58 @ SV138 @ SV121 @ SV130 ) )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ SV7 @ SV97 @ SV121 @ SV138 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV7 @ SV58 ) @ SV97 @ SV121 @ SV130 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(421,plain,
! [SV39: $i,SV84: $i,SV134: $i,SV126: $i] :
( ( ( c_Natural_Oevalc @ SV126 @ SV134 @ SV84 )
= $false )
| ( ( c_Natural_Oevalc @ SV126 @ SV134 @ SV39 )
= $false )
| ( ( SV39 = SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(422,plain,
! [SV113: $i,SV45: $i,SV128: $i,SV137: $i,SV88: $i] :
( ( ( c_Natural_Oevalc @ SV88 @ SV137 @ SV128 )
= $false )
| ( ( ~ ( c_Natural_Oevalc @ SV45 @ SV113 @ SV137 ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV45 @ SV88 ) @ SV113 @ SV128 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(423,plain,
! [SV97: $i,SV7: $i,SV130: $i,SV121: $i,SV138: $i,SV58: $i] :
( ( ( c_Natural_Oevaln @ SV58 @ SV138 @ SV121 @ SV130 )
= $false )
| ( ( ~ ( c_Natural_Oevaln @ SV7 @ SV97 @ SV121 @ SV138 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV7 @ SV58 ) @ SV97 @ SV121 @ SV130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(424,plain,
! [SV128: $i,SV88: $i,SV137: $i,SV113: $i,SV45: $i] :
( ( ( c_Natural_Oevalc @ SV45 @ SV113 @ SV137 )
= $false )
| ( ( c_Natural_Oevalc @ SV88 @ SV137 @ SV128 )
= $false )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV45 @ SV88 ) @ SV113 @ SV128 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(425,plain,
! [SV130: $i,SV58: $i,SV138: $i,SV121: $i,SV97: $i,SV7: $i] :
( ( ( c_Natural_Oevaln @ SV7 @ SV97 @ SV121 @ SV138 )
= $false )
| ( ( c_Natural_Oevaln @ SV58 @ SV138 @ SV121 @ SV130 )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV7 @ SV58 ) @ SV97 @ SV121 @ SV130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(426,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[143,425,424,421,417,416,414,413,412,410,408,407,406,403,402,400,399,398,391,390,387,383,380,375,372,371,368,367,359,358,354,353,335,330,329,325,322,315,314,311,309,308,303,298,287,286,285,282,281,274,252,251,239,199,186,151]) ).
thf(427,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[426]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV888-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n004.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 : Wed Jun 15 03:17:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.38 .
% 0.19/0.39
% 0.19/0.39 No.of.Axioms: 55
% 0.19/0.39
% 0.19/0.39 Length.of.Defs: 0
% 0.19/0.39
% 0.19/0.39 Contains.Choice.Funs: false
% 0.19/0.41 .
% 0.19/0.43 (rf:0,axioms:55,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:57,loop_count:0,foatp_calls:0,translation:fof_full).....................
% 0.38/0.60
% 0.38/0.60 ********************************
% 0.38/0.60 * All subproblems solved! *
% 0.38/0.60 ********************************
% 0.38/0.60 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:55,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:426,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.48/0.66
% 0.48/0.66 %**** Beginning of derivation protocol ****
% 0.48/0.66 % SZS output start CNFRefutation
% See solution above
% 0.48/0.66
% 0.48/0.66 %**** End of derivation protocol ****
% 0.48/0.66 %**** no. of clauses in derivation: 427 ****
% 0.48/0.66 %**** clause counter: 426 ****
% 0.48/0.66
% 0.48/0.66 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:55,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:426,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------