TSTP Solution File: SWV374+1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SWV374+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n013.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 20:12:10 EDT 2022
% Result : Theorem 1.02s 1.42s
% Output : CNFRefutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 72
% Syntax : Number of formulae : 1105 ( 752 unt; 30 typ; 0 def)
% Number of atoms : 5855 (2313 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 14574 (1591 ~;1708 |; 74 &;11143 @)
% ( 14 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 30 usr; 8 con; 0-3 aty)
% Number of variables : 3971 ( 0 ^3971 !; 0 ?;3971 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_bad,type,
bad: $i ).
thf(tp_bottom,type,
bottom: $i ).
thf(tp_check_cpq,type,
check_cpq: $i > $o ).
thf(tp_contains_cpq,type,
contains_cpq: $i > $i > $o ).
thf(tp_contains_slb,type,
contains_slb: $i > $i > $o ).
thf(tp_create_slb,type,
create_slb: $i ).
thf(tp_findmin_cpq_eff,type,
findmin_cpq_eff: $i > $i ).
thf(tp_findmin_cpq_res,type,
findmin_cpq_res: $i > $i ).
thf(tp_findmin_pqp_res,type,
findmin_pqp_res: $i > $i ).
thf(tp_insert_cpq,type,
insert_cpq: $i > $i > $i ).
thf(tp_insert_pqp,type,
insert_pqp: $i > $i > $i ).
thf(tp_insert_slb,type,
insert_slb: $i > $i > $i ).
thf(tp_isnonempty_slb,type,
isnonempty_slb: $i > $o ).
thf(tp_less_than,type,
less_than: $i > $i > $o ).
thf(tp_lookup_slb,type,
lookup_slb: $i > $i > $i ).
thf(tp_ok,type,
ok: $i > $o ).
thf(tp_pair,type,
pair: $i > $i > $i ).
thf(tp_pair_in_list,type,
pair_in_list: $i > $i > $i > $o ).
thf(tp_remove_cpq,type,
remove_cpq: $i > $i > $i ).
thf(tp_remove_pqp,type,
remove_pqp: $i > $i > $i ).
thf(tp_remove_slb,type,
remove_slb: $i > $i > $i ).
thf(tp_removemin_cpq_eff,type,
removemin_cpq_eff: $i > $i ).
thf(tp_removemin_cpq_res,type,
removemin_cpq_res: $i > $i ).
thf(tp_sK1_U,type,
sK1_U: $i ).
thf(tp_sK2_SY120,type,
sK2_SY120: $i ).
thf(tp_sK3_SY122,type,
sK3_SY122: $i ).
thf(tp_strictly_less_than,type,
strictly_less_than: $i > $i > $o ).
thf(tp_succ_cpq,type,
succ_cpq: $i > $i > $o ).
thf(tp_triple,type,
triple: $i > $i > $i > $i ).
thf(tp_update_slb,type,
update_slb: $i > $i > $i ).
thf(1,axiom,
! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).
thf(2,axiom,
! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
thf(3,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( V != create_slb )
=> ( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
= ( findmin_pqp_res @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).
thf(4,axiom,
! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax50) ).
thf(5,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != create_slb )
& ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
& ( less_than @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) @ ( findmin_pqp_res @ U ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).
thf(6,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != create_slb )
& ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
& ( strictly_less_than @ ( findmin_pqp_res @ U ) @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax48) ).
thf(7,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != create_slb )
& ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax47) ).
thf(8,axiom,
! [U: $i,V: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ create_slb @ V ) )
= ( triple @ U @ create_slb @ bad ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).
thf(9,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( contains_slb @ V @ X )
& ( strictly_less_than @ X @ ( lookup_slb @ V @ X ) ) )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ bad ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).
thf(10,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( contains_slb @ V @ X )
& ( less_than @ ( lookup_slb @ V @ X ) @ X ) )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax44) ).
thf(11,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ U @ V @ bad ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax43) ).
thf(12,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( insert_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( insert_pqp @ U @ X ) @ ( insert_slb @ V @ ( pair @ X @ bottom ) ) @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).
thf(13,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ( W = bad ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax41) ).
thf(14,axiom,
! [U: $i,V: $i] :
( ( ok @ ( triple @ U @ V @ bad ) )
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax40) ).
thf(15,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
<=> ( contains_slb @ V @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
thf(16,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( strictly_less_than @ X @ Y )
=> ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
<=> $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
thf(17,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( less_than @ Y @ X )
=> ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
<=> ( check_cpq @ ( triple @ U @ V @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax37) ).
thf(18,axiom,
! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).
thf(19,axiom,
! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax35) ).
thf(20,axiom,
! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax34) ).
thf(21,axiom,
! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax33) ).
thf(22,axiom,
! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax32) ).
thf(23,axiom,
! [U: $i] : ( succ_cpq @ U @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).
thf(24,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( less_than @ W @ X )
=> ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax30) ).
thf(25,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( strictly_less_than @ X @ W )
=> ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax29) ).
thf(26,axiom,
! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
thf(27,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != W )
& ( contains_slb @ U @ W ) )
=> ( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( lookup_slb @ U @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax27) ).
thf(28,axiom,
! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
thf(29,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != W )
& ( contains_slb @ U @ W ) )
=> ( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( remove_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).
thf(30,axiom,
! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
thf(31,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
<=> ( ( pair_in_list @ U @ W @ Y )
| ( ( V = W )
& ( X = Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
thf(32,axiom,
! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
thf(33,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
<=> ( ( contains_slb @ U @ W )
| ( V = W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
thf(34,axiom,
! [U: $i] :
~ ( contains_slb @ create_slb @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
thf(35,axiom,
! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax19) ).
thf(36,axiom,
~ ( isnonempty_slb @ create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
thf(37,axiom,
! [U: $i] : ( less_than @ bottom @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bottom_smallest) ).
thf(38,axiom,
! [U: $i,V: $i] :
( ( strictly_less_than @ U @ V )
<=> ( ( less_than @ U @ V )
& ~ ( less_than @ V @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).
thf(39,axiom,
! [U: $i] : ( less_than @ U @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(40,axiom,
! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
thf(41,axiom,
! [U: $i,V: $i,W: $i] :
( ( ( less_than @ U @ V )
& ( less_than @ V @ W ) )
=> ( less_than @ U @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(42,conjecture,
! [U: $i,V: $i,W: $i] :
( ( ok @ ( findmin_cpq_eff @ ( triple @ U @ V @ W ) ) )
=> ( ( V != create_slb )
& ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
& ( less_than @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) @ ( findmin_pqp_res @ U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l10_co) ).
thf(43,negated_conjecture,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( findmin_cpq_eff @ ( triple @ U @ V @ W ) ) )
=> ( ( V != create_slb )
& ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
& ( less_than @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) @ ( findmin_pqp_res @ U ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[42]) ).
thf(44,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( findmin_cpq_eff @ ( triple @ U @ V @ W ) ) )
=> ( ( V != create_slb )
& ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
& ( less_than @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) @ ( findmin_pqp_res @ U ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[43]) ).
thf(45,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(46,plain,
( ( ! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(47,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( V != create_slb )
=> ( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
= ( findmin_pqp_res @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(48,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(49,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != create_slb )
& ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
& ( less_than @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) @ ( findmin_pqp_res @ U ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(50,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != create_slb )
& ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
& ( strictly_less_than @ ( findmin_pqp_res @ U ) @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(51,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != create_slb )
& ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(52,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ create_slb @ V ) )
= ( triple @ U @ create_slb @ bad ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(53,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( contains_slb @ V @ X )
& ( strictly_less_than @ X @ ( lookup_slb @ V @ X ) ) )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ bad ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(54,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( contains_slb @ V @ X )
& ( less_than @ ( lookup_slb @ V @ X ) @ X ) )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(55,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ U @ V @ bad ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(56,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( insert_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( insert_pqp @ U @ X ) @ ( insert_slb @ V @ ( pair @ X @ bottom ) ) @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(57,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ( W = bad ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(58,plain,
( ( ! [U: $i,V: $i] :
( ( ok @ ( triple @ U @ V @ bad ) )
<=> $false ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(59,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
<=> ( contains_slb @ V @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(60,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( strictly_less_than @ X @ Y )
=> ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
<=> $false ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(61,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( less_than @ Y @ X )
=> ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
<=> ( check_cpq @ ( triple @ U @ V @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(62,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(63,plain,
( ( ! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(64,plain,
( ( ! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(65,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(66,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(67,plain,
( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(68,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( less_than @ W @ X )
=> ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(69,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( strictly_less_than @ X @ W )
=> ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(70,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(71,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != W )
& ( contains_slb @ U @ W ) )
=> ( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( lookup_slb @ U @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(72,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(73,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != W )
& ( contains_slb @ U @ W ) )
=> ( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( remove_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(74,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(75,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
<=> ( ( pair_in_list @ U @ W @ Y )
| ( ( V = W )
& ( X = Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(76,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(77,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
<=> ( ( contains_slb @ U @ W )
| ( V = W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(78,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(79,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(80,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(81,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(82,plain,
( ( ! [U: $i,V: $i] :
( ( strictly_less_than @ U @ V )
<=> ( ( less_than @ U @ V )
& ~ ( less_than @ V @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(83,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(84,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(85,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( less_than @ U @ V )
& ( less_than @ V @ W ) )
=> ( less_than @ U @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(86,plain,
( ( ! [SY120: $i,SY121: $i] :
( ( ok @ ( findmin_cpq_eff @ ( triple @ sK1_U @ SY120 @ SY121 ) ) )
=> ( ( SY120 != create_slb )
& ( contains_slb @ SY120 @ ( findmin_pqp_res @ sK1_U ) )
& ( less_than @ ( lookup_slb @ SY120 @ ( findmin_pqp_res @ sK1_U ) ) @ ( findmin_pqp_res @ sK1_U ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(87,plain,
( ( ! [SY122: $i] :
( ( ok @ ( findmin_cpq_eff @ ( triple @ sK1_U @ sK2_SY120 @ SY122 ) ) )
=> ( ( sK2_SY120 != create_slb )
& ( contains_slb @ sK2_SY120 @ ( findmin_pqp_res @ sK1_U ) )
& ( less_than @ ( lookup_slb @ sK2_SY120 @ ( findmin_pqp_res @ sK1_U ) ) @ ( findmin_pqp_res @ sK1_U ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[86]) ).
thf(88,plain,
( ( ( ok @ ( findmin_cpq_eff @ ( triple @ sK1_U @ sK2_SY120 @ sK3_SY122 ) ) )
=> ( ( sK2_SY120 != create_slb )
& ( contains_slb @ sK2_SY120 @ ( findmin_pqp_res @ sK1_U ) )
& ( less_than @ ( lookup_slb @ sK2_SY120 @ ( findmin_pqp_res @ sK1_U ) ) @ ( findmin_pqp_res @ sK1_U ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[87]) ).
thf(89,plain,
( ( ok @ ( findmin_cpq_eff @ ( triple @ sK1_U @ sK2_SY120 @ sK3_SY122 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[88]) ).
thf(90,plain,
( ( ( sK2_SY120 != create_slb )
& ( contains_slb @ sK2_SY120 @ ( findmin_pqp_res @ sK1_U ) )
& ( less_than @ ( lookup_slb @ sK2_SY120 @ ( findmin_pqp_res @ sK1_U ) ) @ ( findmin_pqp_res @ sK1_U ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[88]) ).
thf(91,plain,
( ( ( sK2_SY120 != create_slb ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[90]) ).
thf(92,plain,
( ( contains_slb @ sK2_SY120 @ ( findmin_pqp_res @ sK1_U ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[90]) ).
thf(93,plain,
( ( less_than @ ( lookup_slb @ sK2_SY120 @ ( findmin_pqp_res @ sK1_U ) ) @ ( findmin_pqp_res @ sK1_U ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[90]) ).
thf(94,plain,
( ( ~ ( ( sK2_SY120 != create_slb ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[91]) ).
thf(95,plain,
( ( ~ ( contains_slb @ sK2_SY120 @ ( findmin_pqp_res @ sK1_U ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[92]) ).
thf(96,plain,
( ( ~ ( less_than @ ( lookup_slb @ sK2_SY120 @ ( findmin_pqp_res @ sK1_U ) ) @ ( findmin_pqp_res @ sK1_U ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[93]) ).
thf(97,plain,
( ( sK2_SY120 = create_slb )
= $true ),
inference(extcnf_combined,[status(esa)],[94]) ).
thf(98,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ! [W: $i] :
( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
= ( findmin_pqp_res @ U ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(99,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
| ~ ( less_than @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) @ ( findmin_pqp_res @ U ) )
| ! [W: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(100,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ U ) @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) )
| ! [W: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(101,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
| ! [W: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(102,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
| ~ ( strictly_less_than @ X @ ( lookup_slb @ V @ X ) )
| ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ bad ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(103,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
| ~ ( less_than @ ( lookup_slb @ V @ X ) @ X )
| ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(104,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_slb @ V @ X )
| ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ U @ V @ bad ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(105,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( triple @ U @ V @ W ) )
| ( W = bad ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(106,plain,
( ( ! [U: $i,V: $i] :
~ ( ok @ ( triple @ U @ V @ bad ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(107,plain,
( ( ! [U: $i,V: $i] :
( ! [W: $i,X: $i] :
( ~ ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
| ( contains_slb @ V @ X ) )
& ! [W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
| ( contains_cpq @ ( triple @ U @ V @ W ) @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(108,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ~ ( strictly_less_than @ X @ Y )
| ~ ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(109,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ! [X: $i,Y: $i] :
( ~ ( less_than @ Y @ X )
| ~ ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
| ( check_cpq @ ( triple @ U @ V @ W ) ) )
& ! [X: $i,Y: $i] :
( ~ ( less_than @ Y @ X )
| ~ ( check_cpq @ ( triple @ U @ V @ W ) )
| ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(110,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[63]) ).
thf(111,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(112,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(113,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(114,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( less_than @ W @ X )
| ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[68]) ).
thf(115,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( strictly_less_than @ X @ W )
| ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(116,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( V = W )
| ~ ( contains_slb @ U @ W )
| ! [X: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( lookup_slb @ U @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[71]) ).
thf(117,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( V = W )
| ~ ( contains_slb @ U @ W )
| ! [X: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( remove_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[73]) ).
thf(118,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
| ( V = W )
| ( pair_in_list @ U @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
| ( X = Y )
| ( pair_in_list @ U @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ( V != W )
| ( X != Y )
| ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ U @ W @ Y )
| ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[75]) ).
thf(119,plain,
( ( ! [U: $i,V: $i] :
( ! [W: $i] :
( ! [X: $i] :
~ ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
| ( V = W )
| ( contains_slb @ U @ W ) )
& ! [W: $i] :
( ( V != W )
| ! [X: $i] : ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W ) )
& ! [W: $i] :
( ~ ( contains_slb @ U @ W )
| ! [X: $i] : ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[77]) ).
thf(120,plain,
( ( ! [U: $i,V: $i] :
( ~ ( less_than @ U @ V )
| ( less_than @ V @ U )
| ( strictly_less_than @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( strictly_less_than @ U @ V )
| ( less_than @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( strictly_less_than @ U @ V )
| ~ ( less_than @ V @ U ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[82]) ).
thf(121,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( less_than @ U @ V )
| ~ ( less_than @ V @ W )
| ( less_than @ U @ W ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[85]) ).
thf(122,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( less_than @ U @ V )
| ~ ( less_than @ V @ W )
| ( less_than @ U @ W ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(123,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(124,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(125,plain,
( ( ! [U: $i,V: $i] :
( ~ ( less_than @ U @ V )
| ( less_than @ V @ U )
| ( strictly_less_than @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( strictly_less_than @ U @ V )
| ( less_than @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( strictly_less_than @ U @ V )
| ~ ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(126,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(127,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(128,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(129,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(130,plain,
( ( ! [U: $i,V: $i] :
( ! [W: $i] :
( ! [X: $i] :
~ ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
| ( V = W )
| ( contains_slb @ U @ W ) )
& ! [W: $i] :
( ( V != W )
| ! [X: $i] : ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W ) )
& ! [W: $i] :
( ~ ( contains_slb @ U @ W )
| ! [X: $i] : ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(131,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(132,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
| ( V = W )
| ( pair_in_list @ U @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
| ( X = Y )
| ( pair_in_list @ U @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ( V != W )
| ( X != Y )
| ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ U @ W @ Y )
| ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(133,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(134,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( V = W )
| ~ ( contains_slb @ U @ W )
| ! [X: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( remove_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(135,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(136,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( V = W )
| ~ ( contains_slb @ U @ W )
| ! [X: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( lookup_slb @ U @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(137,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(138,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( strictly_less_than @ X @ W )
| ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(139,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( less_than @ W @ X )
| ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(140,plain,
( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(141,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(142,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(143,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(144,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(145,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(146,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ! [X: $i,Y: $i] :
( ~ ( less_than @ Y @ X )
| ~ ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
| ( check_cpq @ ( triple @ U @ V @ W ) ) )
& ! [X: $i,Y: $i] :
( ~ ( less_than @ Y @ X )
| ~ ( check_cpq @ ( triple @ U @ V @ W ) )
| ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(147,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ~ ( strictly_less_than @ X @ Y )
| ~ ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(148,plain,
( ( ! [U: $i,V: $i] :
( ! [W: $i,X: $i] :
( ~ ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
| ( contains_slb @ V @ X ) )
& ! [W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
| ( contains_cpq @ ( triple @ U @ V @ W ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(149,plain,
( ( ! [U: $i,V: $i] :
~ ( ok @ ( triple @ U @ V @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(150,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( triple @ U @ V @ W ) )
| ( W = bad ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(151,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( insert_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( insert_pqp @ U @ X ) @ ( insert_slb @ V @ ( pair @ X @ bottom ) ) @ W ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(152,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_slb @ V @ X )
| ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ U @ V @ bad ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(153,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
| ~ ( less_than @ ( lookup_slb @ V @ X ) @ X )
| ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(154,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
| ~ ( strictly_less_than @ X @ ( lookup_slb @ V @ X ) )
| ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ bad ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(155,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ create_slb @ V ) )
= ( triple @ U @ create_slb @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(156,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
| ! [W: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(157,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ U ) @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) )
| ! [W: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(158,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
| ~ ( less_than @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) @ ( findmin_pqp_res @ U ) )
| ! [W: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(159,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(160,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ! [W: $i] :
( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
= ( findmin_pqp_res @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(161,plain,
( ( ! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(162,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(163,plain,
( ( ok @ ( findmin_cpq_eff @ ( triple @ sK1_U @ sK2_SY120 @ sK3_SY122 ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(164,plain,
( ( sK2_SY120 = create_slb )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(165,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 )
| ( SX1 = SX2 )
| ( pair_in_list @ SX0 @ SX2 @ SX4 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 )
| ( SX3 = SX4 )
| ( pair_in_list @ SX0 @ SX2 @ SX4 ) ) )
| ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ( SX1 != SX2 )
| ( SX3 != SX4 )
| ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( pair_in_list @ SX0 @ SX2 @ SX4 )
| ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(166,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( less_than @ SX4 @ SX3 )
| ~ ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ SX1 @ ( pair @ SX3 @ SX4 ) ) @ SX2 ) )
| ( check_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( less_than @ SX4 @ SX3 )
| ~ ( check_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ SX1 @ ( pair @ SX3 @ SX4 ) ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(167,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 )
| ( SX1 = SX2 )
| ( contains_slb @ SX0 @ SX2 ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ( SX1 != SX2 )
| ! [SX3: $i] : ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 ) )
| ~ ! [SX2: $i] :
( ~ ( contains_slb @ SX0 @ SX2 )
| ! [SX3: $i] : ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(168,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( contains_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ SX3 )
| ( contains_slb @ SX1 @ SX3 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( contains_slb @ SX1 @ SX3 )
| ( contains_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(169,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( less_than @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 )
| ( strictly_less_than @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(170,plain,
! [SV1: $i] :
( ( ! [SY123: $i,SY124: $i] :
( ~ ( less_than @ SV1 @ SY123 )
| ~ ( less_than @ SY123 @ SY124 )
| ( less_than @ SV1 @ SY124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(171,plain,
! [SV2: $i] :
( ( ! [SY125: $i] :
( ( less_than @ SV2 @ SY125 )
| ( less_than @ SY125 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(172,plain,
! [SV3: $i] :
( ( less_than @ SV3 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(173,plain,
! [SV4: $i] :
( ( less_than @ bottom @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(174,plain,
( ( isnonempty_slb @ create_slb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(175,plain,
! [SV5: $i] :
( ( ! [SY126: $i,SY127: $i] : ( isnonempty_slb @ ( insert_slb @ SV5 @ ( pair @ SY126 @ SY127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(176,plain,
! [SV6: $i] :
( ( ~ ( contains_slb @ create_slb @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(177,plain,
! [SV7: $i] :
( ( ! [SY128: $i] :
~ ( pair_in_list @ create_slb @ SV7 @ SY128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(178,plain,
! [SV8: $i] :
( ( ! [SY129: $i,SY130: $i] :
( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SY129 @ SY130 ) ) @ SY129 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(179,plain,
! [SV9: $i] :
( ( ! [SY131: $i,SY132: $i] :
( ( SY131 = SY132 )
| ~ ( contains_slb @ SV9 @ SY132 )
| ! [SY133: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SY131 @ SY133 ) ) @ SY132 )
= ( insert_slb @ ( remove_slb @ SV9 @ SY132 ) @ ( pair @ SY131 @ SY133 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(180,plain,
! [SV10: $i] :
( ( ! [SY134: $i,SY135: $i] :
( ( lookup_slb @ ( insert_slb @ SV10 @ ( pair @ SY134 @ SY135 ) ) @ SY134 )
= SY135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(181,plain,
! [SV11: $i] :
( ( ! [SY136: $i,SY137: $i] :
( ( SY136 = SY137 )
| ~ ( contains_slb @ SV11 @ SY137 )
| ! [SY138: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SY136 @ SY138 ) ) @ SY137 )
= ( lookup_slb @ SV11 @ SY137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(182,plain,
! [SV12: $i] :
( ( ( update_slb @ create_slb @ SV12 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(183,plain,
! [SV13: $i] :
( ( ! [SY139: $i,SY140: $i,SY141: $i] :
( ~ ( strictly_less_than @ SY141 @ SY140 )
| ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SY139 @ SY141 ) ) @ SY140 )
= ( insert_slb @ ( update_slb @ SV13 @ SY140 ) @ ( pair @ SY139 @ SY140 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(184,plain,
! [SV14: $i] :
( ( ! [SY142: $i,SY143: $i,SY144: $i] :
( ~ ( less_than @ SY143 @ SY144 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SY142 @ SY144 ) ) @ SY143 )
= ( insert_slb @ ( update_slb @ SV14 @ SY143 ) @ ( pair @ SY142 @ SY144 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(185,plain,
! [SV15: $i] :
( ( succ_cpq @ SV15 @ SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(186,plain,
! [SV16: $i] :
( ( ! [SY145: $i] :
( ~ ( succ_cpq @ SV16 @ SY145 )
| ! [SY146: $i] : ( succ_cpq @ SV16 @ ( insert_cpq @ SY145 @ SY146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(187,plain,
! [SV17: $i] :
( ( ! [SY147: $i] :
( ~ ( succ_cpq @ SV17 @ SY147 )
| ! [SY148: $i] : ( succ_cpq @ SV17 @ ( remove_cpq @ SY147 @ SY148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(188,plain,
! [SV18: $i] :
( ( ! [SY149: $i] :
( ~ ( succ_cpq @ SV18 @ SY149 )
| ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SY149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(189,plain,
! [SV19: $i] :
( ( ! [SY150: $i] :
( ~ ( succ_cpq @ SV19 @ SY150 )
| ( succ_cpq @ SV19 @ ( removemin_cpq_eff @ SY150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(190,plain,
! [SV20: $i] :
( ( ! [SY151: $i] : ( check_cpq @ ( triple @ SV20 @ create_slb @ SY151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(191,plain,
! [SV21: $i] :
( ( ! [SY152: $i,SY153: $i,SY154: $i,SY155: $i] :
( ~ ( strictly_less_than @ SY154 @ SY155 )
| ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SY152 @ ( pair @ SY154 @ SY155 ) ) @ SY153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(192,plain,
! [SV22: $i] :
( ( ! [SY156: $i] :
~ ( ok @ ( triple @ SV22 @ SY156 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(193,plain,
! [SV23: $i] :
( ( ! [SY157: $i,SY158: $i] :
( ( ok @ ( triple @ SV23 @ SY157 @ SY158 ) )
| ( SY158 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(194,plain,
! [SV24: $i] :
( ( ! [SY159: $i,SY160: $i,SY161: $i] :
( ( insert_cpq @ ( triple @ SV24 @ SY159 @ SY160 ) @ SY161 )
= ( triple @ ( insert_pqp @ SV24 @ SY161 ) @ ( insert_slb @ SY159 @ ( pair @ SY161 @ bottom ) ) @ SY160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(195,plain,
! [SV25: $i] :
( ( ! [SY162: $i,SY163: $i,SY164: $i] :
( ( contains_slb @ SY162 @ SY164 )
| ( ( remove_cpq @ ( triple @ SV25 @ SY162 @ SY163 ) @ SY164 )
= ( triple @ SV25 @ SY162 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(196,plain,
! [SV26: $i] :
( ( ! [SY165: $i,SY166: $i,SY167: $i] :
( ~ ( contains_slb @ SY165 @ SY167 )
| ~ ( less_than @ ( lookup_slb @ SY165 @ SY167 ) @ SY167 )
| ( ( remove_cpq @ ( triple @ SV26 @ SY165 @ SY166 ) @ SY167 )
= ( triple @ ( remove_pqp @ SV26 @ SY167 ) @ ( remove_slb @ SY165 @ SY167 ) @ SY166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(197,plain,
! [SV27: $i] :
( ( ! [SY168: $i,SY169: $i,SY170: $i] :
( ~ ( contains_slb @ SY168 @ SY170 )
| ~ ( strictly_less_than @ SY170 @ ( lookup_slb @ SY168 @ SY170 ) )
| ( ( remove_cpq @ ( triple @ SV27 @ SY168 @ SY169 ) @ SY170 )
= ( triple @ ( remove_pqp @ SV27 @ SY170 ) @ ( remove_slb @ SY168 @ SY170 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(198,plain,
! [SV28: $i] :
( ( ! [SY171: $i] :
( ( findmin_cpq_eff @ ( triple @ SV28 @ create_slb @ SY171 ) )
= ( triple @ SV28 @ create_slb @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(199,plain,
! [SV29: $i] :
( ( ! [SY172: $i] :
( ( SY172 = create_slb )
| ( contains_slb @ SY172 @ ( findmin_pqp_res @ SV29 ) )
| ! [SY173: $i] :
( ( findmin_cpq_eff @ ( triple @ SV29 @ SY172 @ SY173 ) )
= ( triple @ SV29 @ ( update_slb @ SY172 @ ( findmin_pqp_res @ SV29 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(200,plain,
! [SV30: $i] :
( ( ! [SY174: $i] :
( ( SY174 = create_slb )
| ~ ( contains_slb @ SY174 @ ( findmin_pqp_res @ SV30 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SY174 @ ( findmin_pqp_res @ SV30 ) ) )
| ! [SY175: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SY174 @ SY175 ) )
= ( triple @ SV30 @ ( update_slb @ SY174 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(201,plain,
! [SV31: $i] :
( ( ! [SY176: $i] :
( ( SY176 = create_slb )
| ~ ( contains_slb @ SY176 @ ( findmin_pqp_res @ SV31 ) )
| ~ ( less_than @ ( lookup_slb @ SY176 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) )
| ! [SY177: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SY176 @ SY177 ) )
= ( triple @ SV31 @ ( update_slb @ SY176 @ ( findmin_pqp_res @ SV31 ) ) @ SY177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(202,plain,
! [SV32: $i] :
( ( ! [SY178: $i] :
( ( findmin_cpq_res @ ( triple @ SV32 @ create_slb @ SY178 ) )
= bottom ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(203,plain,
! [SV33: $i] :
( ( ! [SY179: $i] :
( ( SY179 = create_slb )
| ! [SY180: $i] :
( ( findmin_cpq_res @ ( triple @ SV33 @ SY179 @ SY180 ) )
= ( findmin_pqp_res @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(204,plain,
! [SV34: $i] :
( ( ( removemin_cpq_eff @ SV34 )
= ( remove_cpq @ ( findmin_cpq_eff @ SV34 ) @ ( findmin_cpq_res @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(205,plain,
! [SV35: $i] :
( ( ( removemin_cpq_res @ SV35 )
= ( findmin_cpq_res @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(206,plain,
! [SV36: $i] :
( ( ! [SY181: $i,SY182: $i] :
~ ( ~ ~ ( ~ ! [SY183: $i,SY184: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SY181 @ SY183 ) ) @ SY182 @ SY184 )
| ( SY181 = SY182 )
| ( pair_in_list @ SV36 @ SY182 @ SY184 ) )
| ~ ! [SY185: $i,SY186: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SY181 @ SY185 ) ) @ SY182 @ SY186 )
| ( SY185 = SY186 )
| ( pair_in_list @ SV36 @ SY182 @ SY186 ) ) )
| ~ ~ ( ~ ! [SY187: $i,SY188: $i] :
( ( SY181 != SY182 )
| ( SY187 != SY188 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SY181 @ SY187 ) ) @ SY182 @ SY188 ) )
| ~ ! [SY189: $i,SY190: $i] :
( ~ ( pair_in_list @ SV36 @ SY182 @ SY190 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SY181 @ SY189 ) ) @ SY182 @ SY190 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(207,plain,
! [SV37: $i] :
( ( ! [SY191: $i,SY192: $i] :
~ ( ~ ! [SY193: $i,SY194: $i] :
( ~ ( less_than @ SY194 @ SY193 )
| ~ ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SY191 @ ( pair @ SY193 @ SY194 ) ) @ SY192 ) )
| ( check_cpq @ ( triple @ SV37 @ SY191 @ SY192 ) ) )
| ~ ! [SY195: $i,SY196: $i] :
( ~ ( less_than @ SY196 @ SY195 )
| ~ ( check_cpq @ ( triple @ SV37 @ SY191 @ SY192 ) )
| ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SY191 @ ( pair @ SY195 @ SY196 ) ) @ SY192 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(208,plain,
! [SV38: $i] :
( ( ! [SY197: $i] :
~ ( ~ ! [SY198: $i] :
( ! [SY199: $i] :
~ ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SY197 @ SY199 ) ) @ SY198 )
| ( SY197 = SY198 )
| ( contains_slb @ SV38 @ SY198 ) )
| ~ ~ ( ~ ! [SY200: $i] :
( ( SY197 != SY200 )
| ! [SY201: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SY197 @ SY201 ) ) @ SY200 ) )
| ~ ! [SY202: $i] :
( ~ ( contains_slb @ SV38 @ SY202 )
| ! [SY203: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SY197 @ SY203 ) ) @ SY202 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(209,plain,
! [SV39: $i] :
( ( ! [SY204: $i] :
~ ( ~ ! [SY205: $i,SY206: $i] :
( ~ ( contains_cpq @ ( triple @ SV39 @ SY204 @ SY205 ) @ SY206 )
| ( contains_slb @ SY204 @ SY206 ) )
| ~ ! [SY207: $i,SY208: $i] :
( ~ ( contains_slb @ SY204 @ SY208 )
| ( contains_cpq @ ( triple @ SV39 @ SY204 @ SY207 ) @ SY208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(210,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( less_than @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 )
| ( strictly_less_than @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(211,plain,
! [SV40: $i,SV1: $i] :
( ( ! [SY209: $i] :
( ~ ( less_than @ SV1 @ SV40 )
| ~ ( less_than @ SV40 @ SY209 )
| ( less_than @ SV1 @ SY209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(212,plain,
! [SV41: $i,SV2: $i] :
( ( ( less_than @ SV2 @ SV41 )
| ( less_than @ SV41 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(213,plain,
! [SV42: $i,SV5: $i] :
( ( ! [SY210: $i] : ( isnonempty_slb @ ( insert_slb @ SV5 @ ( pair @ SV42 @ SY210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(214,plain,
! [SV6: $i] :
( ( contains_slb @ create_slb @ SV6 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(215,plain,
! [SV43: $i,SV7: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV7 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(216,plain,
! [SV44: $i,SV8: $i] :
( ( ! [SY211: $i] :
( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SV44 @ SY211 ) ) @ SV44 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(217,plain,
! [SV9: $i,SV45: $i] :
( ( ! [SY212: $i] :
( ( SV45 = SY212 )
| ~ ( contains_slb @ SV9 @ SY212 )
| ! [SY213: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV45 @ SY213 ) ) @ SY212 )
= ( insert_slb @ ( remove_slb @ SV9 @ SY212 ) @ ( pair @ SV45 @ SY213 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(218,plain,
! [SV46: $i,SV10: $i] :
( ( ! [SY214: $i] :
( ( lookup_slb @ ( insert_slb @ SV10 @ ( pair @ SV46 @ SY214 ) ) @ SV46 )
= SY214 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(219,plain,
! [SV11: $i,SV47: $i] :
( ( ! [SY215: $i] :
( ( SV47 = SY215 )
| ~ ( contains_slb @ SV11 @ SY215 )
| ! [SY216: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV47 @ SY216 ) ) @ SY215 )
= ( lookup_slb @ SV11 @ SY215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(220,plain,
! [SV48: $i,SV13: $i] :
( ( ! [SY217: $i,SY218: $i] :
( ~ ( strictly_less_than @ SY218 @ SY217 )
| ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV48 @ SY218 ) ) @ SY217 )
= ( insert_slb @ ( update_slb @ SV13 @ SY217 ) @ ( pair @ SV48 @ SY217 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(221,plain,
! [SV49: $i,SV14: $i] :
( ( ! [SY219: $i,SY220: $i] :
( ~ ( less_than @ SY219 @ SY220 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV49 @ SY220 ) ) @ SY219 )
= ( insert_slb @ ( update_slb @ SV14 @ SY219 ) @ ( pair @ SV49 @ SY220 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(222,plain,
! [SV50: $i,SV16: $i] :
( ( ~ ( succ_cpq @ SV16 @ SV50 )
| ! [SY221: $i] : ( succ_cpq @ SV16 @ ( insert_cpq @ SV50 @ SY221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(223,plain,
! [SV51: $i,SV17: $i] :
( ( ~ ( succ_cpq @ SV17 @ SV51 )
| ! [SY222: $i] : ( succ_cpq @ SV17 @ ( remove_cpq @ SV51 @ SY222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(224,plain,
! [SV52: $i,SV18: $i] :
( ( ~ ( succ_cpq @ SV18 @ SV52 )
| ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(225,plain,
! [SV53: $i,SV19: $i] :
( ( ~ ( succ_cpq @ SV19 @ SV53 )
| ( succ_cpq @ SV19 @ ( removemin_cpq_eff @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(226,plain,
! [SV54: $i,SV20: $i] :
( ( check_cpq @ ( triple @ SV20 @ create_slb @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(227,plain,
! [SV55: $i,SV21: $i] :
( ( ! [SY223: $i,SY224: $i,SY225: $i] :
( ~ ( strictly_less_than @ SY224 @ SY225 )
| ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV55 @ ( pair @ SY224 @ SY225 ) ) @ SY223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(228,plain,
! [SV56: $i,SV22: $i] :
( ( ~ ( ok @ ( triple @ SV22 @ SV56 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(229,plain,
! [SV57: $i,SV23: $i] :
( ( ! [SY226: $i] :
( ( ok @ ( triple @ SV23 @ SV57 @ SY226 ) )
| ( SY226 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(230,plain,
! [SV58: $i,SV24: $i] :
( ( ! [SY227: $i,SY228: $i] :
( ( insert_cpq @ ( triple @ SV24 @ SV58 @ SY227 ) @ SY228 )
= ( triple @ ( insert_pqp @ SV24 @ SY228 ) @ ( insert_slb @ SV58 @ ( pair @ SY228 @ bottom ) ) @ SY227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(231,plain,
! [SV25: $i,SV59: $i] :
( ( ! [SY229: $i,SY230: $i] :
( ( contains_slb @ SV59 @ SY230 )
| ( ( remove_cpq @ ( triple @ SV25 @ SV59 @ SY229 ) @ SY230 )
= ( triple @ SV25 @ SV59 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(232,plain,
! [SV26: $i,SV60: $i] :
( ( ! [SY231: $i,SY232: $i] :
( ~ ( contains_slb @ SV60 @ SY232 )
| ~ ( less_than @ ( lookup_slb @ SV60 @ SY232 ) @ SY232 )
| ( ( remove_cpq @ ( triple @ SV26 @ SV60 @ SY231 ) @ SY232 )
= ( triple @ ( remove_pqp @ SV26 @ SY232 ) @ ( remove_slb @ SV60 @ SY232 ) @ SY231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(233,plain,
! [SV27: $i,SV61: $i] :
( ( ! [SY233: $i,SY234: $i] :
( ~ ( contains_slb @ SV61 @ SY234 )
| ~ ( strictly_less_than @ SY234 @ ( lookup_slb @ SV61 @ SY234 ) )
| ( ( remove_cpq @ ( triple @ SV27 @ SV61 @ SY233 ) @ SY234 )
= ( triple @ ( remove_pqp @ SV27 @ SY234 ) @ ( remove_slb @ SV61 @ SY234 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(234,plain,
! [SV62: $i,SV28: $i] :
( ( ( findmin_cpq_eff @ ( triple @ SV28 @ create_slb @ SV62 ) )
= ( triple @ SV28 @ create_slb @ bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(235,plain,
! [SV29: $i,SV63: $i] :
( ( ( SV63 = create_slb )
| ( contains_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) )
| ! [SY235: $i] :
( ( findmin_cpq_eff @ ( triple @ SV29 @ SV63 @ SY235 ) )
= ( triple @ SV29 @ ( update_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(236,plain,
! [SV30: $i,SV64: $i] :
( ( ( SV64 = create_slb )
| ~ ( contains_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) )
| ! [SY236: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY236 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(237,plain,
! [SV31: $i,SV65: $i] :
( ( ( SV65 = create_slb )
| ~ ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) )
| ~ ( less_than @ ( lookup_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) )
| ! [SY237: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY237 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(238,plain,
! [SV66: $i,SV32: $i] :
( ( ( findmin_cpq_res @ ( triple @ SV32 @ create_slb @ SV66 ) )
= bottom )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(239,plain,
! [SV33: $i,SV67: $i] :
( ( ( SV67 = create_slb )
| ! [SY238: $i] :
( ( findmin_cpq_res @ ( triple @ SV33 @ SV67 @ SY238 ) )
= ( findmin_pqp_res @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(240,plain,
! [SV68: $i,SV36: $i] :
( ( ! [SY239: $i] :
~ ( ~ ~ ( ~ ! [SY240: $i,SY241: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY240 ) ) @ SY239 @ SY241 )
| ( SV68 = SY239 )
| ( pair_in_list @ SV36 @ SY239 @ SY241 ) )
| ~ ! [SY242: $i,SY243: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY242 ) ) @ SY239 @ SY243 )
| ( SY242 = SY243 )
| ( pair_in_list @ SV36 @ SY239 @ SY243 ) ) )
| ~ ~ ( ~ ! [SY244: $i,SY245: $i] :
( ( SV68 != SY239 )
| ( SY244 != SY245 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY244 ) ) @ SY239 @ SY245 ) )
| ~ ! [SY246: $i,SY247: $i] :
( ~ ( pair_in_list @ SV36 @ SY239 @ SY247 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY246 ) ) @ SY239 @ SY247 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(241,plain,
! [SV69: $i,SV37: $i] :
( ( ! [SY248: $i] :
~ ( ~ ! [SY249: $i,SY250: $i] :
( ~ ( less_than @ SY250 @ SY249 )
| ~ ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SV69 @ ( pair @ SY249 @ SY250 ) ) @ SY248 ) )
| ( check_cpq @ ( triple @ SV37 @ SV69 @ SY248 ) ) )
| ~ ! [SY251: $i,SY252: $i] :
( ~ ( less_than @ SY252 @ SY251 )
| ~ ( check_cpq @ ( triple @ SV37 @ SV69 @ SY248 ) )
| ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SV69 @ ( pair @ SY251 @ SY252 ) ) @ SY248 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(242,plain,
! [SV70: $i,SV38: $i] :
( ( ~ ( ~ ! [SY253: $i] :
( ! [SY254: $i] :
~ ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY254 ) ) @ SY253 )
| ( SV70 = SY253 )
| ( contains_slb @ SV38 @ SY253 ) )
| ~ ~ ( ~ ! [SY255: $i] :
( ( SV70 != SY255 )
| ! [SY256: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY256 ) ) @ SY255 ) )
| ~ ! [SY257: $i] :
( ~ ( contains_slb @ SV38 @ SY257 )
| ! [SY258: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY258 ) ) @ SY257 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(243,plain,
! [SV71: $i,SV39: $i] :
( ( ~ ( ~ ! [SY259: $i,SY260: $i] :
( ~ ( contains_cpq @ ( triple @ SV39 @ SV71 @ SY259 ) @ SY260 )
| ( contains_slb @ SV71 @ SY260 ) )
| ~ ! [SY261: $i,SY262: $i] :
( ~ ( contains_slb @ SV71 @ SY262 )
| ( contains_cpq @ ( triple @ SV39 @ SV71 @ SY261 ) @ SY262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(244,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( less_than @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 )
| ( strictly_less_than @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(245,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(246,plain,
! [SV72: $i,SV40: $i,SV1: $i] :
( ( ~ ( less_than @ SV1 @ SV40 )
| ~ ( less_than @ SV40 @ SV72 )
| ( less_than @ SV1 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(247,plain,
! [SV41: $i,SV2: $i] :
( ( ( less_than @ SV2 @ SV41 )
= $true )
| ( ( less_than @ SV41 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(248,plain,
! [SV73: $i,SV42: $i,SV5: $i] :
( ( isnonempty_slb @ ( insert_slb @ SV5 @ ( pair @ SV42 @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(249,plain,
! [SV43: $i,SV7: $i] :
( ( pair_in_list @ create_slb @ SV7 @ SV43 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(250,plain,
! [SV74: $i,SV44: $i,SV8: $i] :
( ( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SV44 @ SV74 ) ) @ SV44 )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(251,plain,
! [SV9: $i,SV75: $i,SV45: $i] :
( ( ( SV45 = SV75 )
| ~ ( contains_slb @ SV9 @ SV75 )
| ! [SY263: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV45 @ SY263 ) ) @ SV75 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV75 ) @ ( pair @ SV45 @ SY263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(252,plain,
! [SV76: $i,SV46: $i,SV10: $i] :
( ( ( lookup_slb @ ( insert_slb @ SV10 @ ( pair @ SV46 @ SV76 ) ) @ SV46 )
= SV76 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(253,plain,
! [SV11: $i,SV77: $i,SV47: $i] :
( ( ( SV47 = SV77 )
| ~ ( contains_slb @ SV11 @ SV77 )
| ! [SY264: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV47 @ SY264 ) ) @ SV77 )
= ( lookup_slb @ SV11 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(254,plain,
! [SV48: $i,SV13: $i,SV78: $i] :
( ( ! [SY265: $i] :
( ~ ( strictly_less_than @ SY265 @ SV78 )
| ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV48 @ SY265 ) ) @ SV78 )
= ( insert_slb @ ( update_slb @ SV13 @ SV78 ) @ ( pair @ SV48 @ SV78 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(255,plain,
! [SV49: $i,SV14: $i,SV79: $i] :
( ( ! [SY266: $i] :
( ~ ( less_than @ SV79 @ SY266 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV49 @ SY266 ) ) @ SV79 )
= ( insert_slb @ ( update_slb @ SV14 @ SV79 ) @ ( pair @ SV49 @ SY266 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(256,plain,
! [SV50: $i,SV16: $i] :
( ( ( ~ ( succ_cpq @ SV16 @ SV50 ) )
= $true )
| ( ( ! [SY221: $i] : ( succ_cpq @ SV16 @ ( insert_cpq @ SV50 @ SY221 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(257,plain,
! [SV51: $i,SV17: $i] :
( ( ( ~ ( succ_cpq @ SV17 @ SV51 ) )
= $true )
| ( ( ! [SY222: $i] : ( succ_cpq @ SV17 @ ( remove_cpq @ SV51 @ SY222 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(258,plain,
! [SV52: $i,SV18: $i] :
( ( ( ~ ( succ_cpq @ SV18 @ SV52 ) )
= $true )
| ( ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(259,plain,
! [SV53: $i,SV19: $i] :
( ( ( ~ ( succ_cpq @ SV19 @ SV53 ) )
= $true )
| ( ( succ_cpq @ SV19 @ ( removemin_cpq_eff @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(260,plain,
! [SV80: $i,SV55: $i,SV21: $i] :
( ( ! [SY267: $i,SY268: $i] :
( ~ ( strictly_less_than @ SY267 @ SY268 )
| ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV55 @ ( pair @ SY267 @ SY268 ) ) @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(261,plain,
! [SV56: $i,SV22: $i] :
( ( ok @ ( triple @ SV22 @ SV56 @ bad ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(262,plain,
! [SV81: $i,SV57: $i,SV23: $i] :
( ( ( ok @ ( triple @ SV23 @ SV57 @ SV81 ) )
| ( SV81 = bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(263,plain,
! [SV82: $i,SV58: $i,SV24: $i] :
( ( ! [SY269: $i] :
( ( insert_cpq @ ( triple @ SV24 @ SV58 @ SV82 ) @ SY269 )
= ( triple @ ( insert_pqp @ SV24 @ SY269 ) @ ( insert_slb @ SV58 @ ( pair @ SY269 @ bottom ) ) @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(264,plain,
! [SV83: $i,SV25: $i,SV59: $i] :
( ( ! [SY270: $i] :
( ( contains_slb @ SV59 @ SY270 )
| ( ( remove_cpq @ ( triple @ SV25 @ SV59 @ SV83 ) @ SY270 )
= ( triple @ SV25 @ SV59 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(265,plain,
! [SV84: $i,SV26: $i,SV60: $i] :
( ( ! [SY271: $i] :
( ~ ( contains_slb @ SV60 @ SY271 )
| ~ ( less_than @ ( lookup_slb @ SV60 @ SY271 ) @ SY271 )
| ( ( remove_cpq @ ( triple @ SV26 @ SV60 @ SV84 ) @ SY271 )
= ( triple @ ( remove_pqp @ SV26 @ SY271 ) @ ( remove_slb @ SV60 @ SY271 ) @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(266,plain,
! [SV85: $i,SV27: $i,SV61: $i] :
( ( ! [SY272: $i] :
( ~ ( contains_slb @ SV61 @ SY272 )
| ~ ( strictly_less_than @ SY272 @ ( lookup_slb @ SV61 @ SY272 ) )
| ( ( remove_cpq @ ( triple @ SV27 @ SV61 @ SV85 ) @ SY272 )
= ( triple @ ( remove_pqp @ SV27 @ SY272 ) @ ( remove_slb @ SV61 @ SY272 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(267,plain,
! [SV29: $i,SV63: $i] :
( ( ( ( SV63 = create_slb )
| ( contains_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) ) )
= $true )
| ( ( ! [SY235: $i] :
( ( findmin_cpq_eff @ ( triple @ SV29 @ SV63 @ SY235 ) )
= ( triple @ SV29 @ ( update_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(268,plain,
! [SV30: $i,SV64: $i] :
( ( ( ( SV64 = create_slb )
| ~ ( contains_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) ) )
= $true )
| ( ( ! [SY236: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY236 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(269,plain,
! [SV31: $i,SV65: $i] :
( ( ( ( SV65 = create_slb )
| ~ ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) )
| ~ ( less_than @ ( lookup_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) ) )
= $true )
| ( ( ! [SY237: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY237 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY237 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(270,plain,
! [SV33: $i,SV67: $i] :
( ( ( SV67 = create_slb )
= $true )
| ( ( ! [SY238: $i] :
( ( findmin_cpq_res @ ( triple @ SV33 @ SV67 @ SY238 ) )
= ( findmin_pqp_res @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(271,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY273: $i,SY274: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY273 ) ) @ SV86 @ SY274 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY274 ) )
| ~ ! [SY275: $i,SY276: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY275 ) ) @ SV86 @ SY276 )
| ( SY275 = SY276 )
| ( pair_in_list @ SV36 @ SV86 @ SY276 ) ) )
| ~ ~ ( ~ ! [SY277: $i,SY278: $i] :
( ( SV68 != SV86 )
| ( SY277 != SY278 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY277 ) ) @ SV86 @ SY278 ) )
| ~ ! [SY279: $i,SY280: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY280 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY279 ) ) @ SV86 @ SY280 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(272,plain,
! [SV87: $i,SV69: $i,SV37: $i] :
( ( ~ ( ~ ! [SY281: $i,SY282: $i] :
( ~ ( less_than @ SY282 @ SY281 )
| ~ ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SV69 @ ( pair @ SY281 @ SY282 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV37 @ SV69 @ SV87 ) ) )
| ~ ! [SY283: $i,SY284: $i] :
( ~ ( less_than @ SY284 @ SY283 )
| ~ ( check_cpq @ ( triple @ SV37 @ SV69 @ SV87 ) )
| ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SV69 @ ( pair @ SY283 @ SY284 ) ) @ SV87 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(273,plain,
! [SV70: $i,SV38: $i] :
( ( ~ ! [SY253: $i] :
( ! [SY254: $i] :
~ ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY254 ) ) @ SY253 )
| ( SV70 = SY253 )
| ( contains_slb @ SV38 @ SY253 ) )
| ~ ~ ( ~ ! [SY255: $i] :
( ( SV70 != SY255 )
| ! [SY256: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY256 ) ) @ SY255 ) )
| ~ ! [SY257: $i] :
( ~ ( contains_slb @ SV38 @ SY257 )
| ! [SY258: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY258 ) ) @ SY257 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(274,plain,
! [SV71: $i,SV39: $i] :
( ( ~ ! [SY259: $i,SY260: $i] :
( ~ ( contains_cpq @ ( triple @ SV39 @ SV71 @ SY259 ) @ SY260 )
| ( contains_slb @ SV71 @ SY260 ) )
| ~ ! [SY261: $i,SY262: $i] :
( ~ ( contains_slb @ SV71 @ SY262 )
| ( contains_cpq @ ( triple @ SV39 @ SV71 @ SY261 ) @ SY262 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(275,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( less_than @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 )
| ( strictly_less_than @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(276,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(277,plain,
! [SV72: $i,SV40: $i,SV1: $i] :
( ( ( ~ ( less_than @ SV1 @ SV40 )
| ~ ( less_than @ SV40 @ SV72 ) )
= $true )
| ( ( less_than @ SV1 @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(278,plain,
! [SV9: $i,SV75: $i,SV45: $i] :
( ( ( ( SV45 = SV75 )
| ~ ( contains_slb @ SV9 @ SV75 ) )
= $true )
| ( ( ! [SY263: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV45 @ SY263 ) ) @ SV75 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV75 ) @ ( pair @ SV45 @ SY263 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(279,plain,
! [SV11: $i,SV77: $i,SV47: $i] :
( ( ( ( SV47 = SV77 )
| ~ ( contains_slb @ SV11 @ SV77 ) )
= $true )
| ( ( ! [SY264: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV47 @ SY264 ) ) @ SV77 )
= ( lookup_slb @ SV11 @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(280,plain,
! [SV48: $i,SV13: $i,SV78: $i,SV88: $i] :
( ( ~ ( strictly_less_than @ SV88 @ SV78 )
| ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV48 @ SV88 ) ) @ SV78 )
= ( insert_slb @ ( update_slb @ SV13 @ SV78 ) @ ( pair @ SV48 @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(281,plain,
! [SV49: $i,SV14: $i,SV89: $i,SV79: $i] :
( ( ~ ( less_than @ SV79 @ SV89 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV49 @ SV89 ) ) @ SV79 )
= ( insert_slb @ ( update_slb @ SV14 @ SV79 ) @ ( pair @ SV49 @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(282,plain,
! [SV50: $i,SV16: $i] :
( ( ( succ_cpq @ SV16 @ SV50 )
= $false )
| ( ( ! [SY221: $i] : ( succ_cpq @ SV16 @ ( insert_cpq @ SV50 @ SY221 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(283,plain,
! [SV51: $i,SV17: $i] :
( ( ( succ_cpq @ SV17 @ SV51 )
= $false )
| ( ( ! [SY222: $i] : ( succ_cpq @ SV17 @ ( remove_cpq @ SV51 @ SY222 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(284,plain,
! [SV52: $i,SV18: $i] :
( ( ( succ_cpq @ SV18 @ SV52 )
= $false )
| ( ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(285,plain,
! [SV53: $i,SV19: $i] :
( ( ( succ_cpq @ SV19 @ SV53 )
= $false )
| ( ( succ_cpq @ SV19 @ ( removemin_cpq_eff @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(286,plain,
! [SV80: $i,SV55: $i,SV21: $i,SV90: $i] :
( ( ! [SY285: $i] :
( ~ ( strictly_less_than @ SV90 @ SY285 )
| ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV55 @ ( pair @ SV90 @ SY285 ) ) @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(287,plain,
! [SV81: $i,SV57: $i,SV23: $i] :
( ( ( ok @ ( triple @ SV23 @ SV57 @ SV81 ) )
= $true )
| ( ( SV81 = bad )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(288,plain,
! [SV91: $i,SV82: $i,SV58: $i,SV24: $i] :
( ( ( insert_cpq @ ( triple @ SV24 @ SV58 @ SV82 ) @ SV91 )
= ( triple @ ( insert_pqp @ SV24 @ SV91 ) @ ( insert_slb @ SV58 @ ( pair @ SV91 @ bottom ) ) @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(289,plain,
! [SV83: $i,SV25: $i,SV92: $i,SV59: $i] :
( ( ( contains_slb @ SV59 @ SV92 )
| ( ( remove_cpq @ ( triple @ SV25 @ SV59 @ SV83 ) @ SV92 )
= ( triple @ SV25 @ SV59 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(290,plain,
! [SV84: $i,SV26: $i,SV93: $i,SV60: $i] :
( ( ~ ( contains_slb @ SV60 @ SV93 )
| ~ ( less_than @ ( lookup_slb @ SV60 @ SV93 ) @ SV93 )
| ( ( remove_cpq @ ( triple @ SV26 @ SV60 @ SV84 ) @ SV93 )
= ( triple @ ( remove_pqp @ SV26 @ SV93 ) @ ( remove_slb @ SV60 @ SV93 ) @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(291,plain,
! [SV85: $i,SV27: $i,SV94: $i,SV61: $i] :
( ( ~ ( contains_slb @ SV61 @ SV94 )
| ~ ( strictly_less_than @ SV94 @ ( lookup_slb @ SV61 @ SV94 ) )
| ( ( remove_cpq @ ( triple @ SV27 @ SV61 @ SV85 ) @ SV94 )
= ( triple @ ( remove_pqp @ SV27 @ SV94 ) @ ( remove_slb @ SV61 @ SV94 ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(292,plain,
! [SV29: $i,SV63: $i] :
( ( ( SV63 = create_slb )
= $true )
| ( ( contains_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) )
= $true )
| ( ( ! [SY235: $i] :
( ( findmin_cpq_eff @ ( triple @ SV29 @ SV63 @ SY235 ) )
= ( triple @ SV29 @ ( update_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(293,plain,
! [SV30: $i,SV64: $i] :
( ( ( ( SV64 = create_slb )
| ~ ( contains_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) ) )
= $true )
| ( ( ! [SY236: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY236 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(294,plain,
! [SV31: $i,SV65: $i] :
( ( ( ( SV65 = create_slb )
| ~ ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) ) )
= $true )
| ( ( ! [SY237: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY237 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY237 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(295,plain,
! [SV95: $i,SV67: $i,SV33: $i] :
( ( ( ( findmin_cpq_res @ ( triple @ SV33 @ SV67 @ SV95 ) )
= ( findmin_pqp_res @ SV33 ) )
= $true )
| ( ( SV67 = create_slb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(296,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ~ ~ ( ~ ! [SY273: $i,SY274: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY273 ) ) @ SV86 @ SY274 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY274 ) )
| ~ ! [SY275: $i,SY276: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY275 ) ) @ SV86 @ SY276 )
| ( SY275 = SY276 )
| ( pair_in_list @ SV36 @ SV86 @ SY276 ) ) )
| ~ ~ ( ~ ! [SY277: $i,SY278: $i] :
( ( SV68 != SV86 )
| ( SY277 != SY278 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY277 ) ) @ SV86 @ SY278 ) )
| ~ ! [SY279: $i,SY280: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY280 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY279 ) ) @ SV86 @ SY280 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(297,plain,
! [SV87: $i,SV69: $i,SV37: $i] :
( ( ~ ! [SY281: $i,SY282: $i] :
( ~ ( less_than @ SY282 @ SY281 )
| ~ ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SV69 @ ( pair @ SY281 @ SY282 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV37 @ SV69 @ SV87 ) ) )
| ~ ! [SY283: $i,SY284: $i] :
( ~ ( less_than @ SY284 @ SY283 )
| ~ ( check_cpq @ ( triple @ SV37 @ SV69 @ SV87 ) )
| ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SV69 @ ( pair @ SY283 @ SY284 ) ) @ SV87 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(298,plain,
! [SV70: $i,SV38: $i] :
( ( ~ ! [SY253: $i] :
( ! [SY254: $i] :
~ ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY254 ) ) @ SY253 )
| ( SV70 = SY253 )
| ( contains_slb @ SV38 @ SY253 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(299,plain,
! [SV38: $i,SV70: $i] :
( ( ~ ~ ( ~ ! [SY255: $i] :
( ( SV70 != SY255 )
| ! [SY256: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY256 ) ) @ SY255 ) )
| ~ ! [SY257: $i] :
( ~ ( contains_slb @ SV38 @ SY257 )
| ! [SY258: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY258 ) ) @ SY257 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(300,plain,
! [SV71: $i,SV39: $i] :
( ( ~ ! [SY259: $i,SY260: $i] :
( ~ ( contains_cpq @ ( triple @ SV39 @ SV71 @ SY259 ) @ SY260 )
| ( contains_slb @ SV71 @ SY260 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[274]) ).
thf(301,plain,
! [SV39: $i,SV71: $i] :
( ( ~ ! [SY261: $i,SY262: $i] :
( ~ ( contains_slb @ SV71 @ SY262 )
| ( contains_cpq @ ( triple @ SV39 @ SV71 @ SY261 ) @ SY262 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[274]) ).
thf(302,plain,
! [SV96: $i] :
( ( ! [SY286: $i] :
( ~ ( less_than @ SV96 @ SY286 )
| ( less_than @ SY286 @ SV96 )
| ( strictly_less_than @ SV96 @ SY286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(303,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(304,plain,
! [SV72: $i,SV40: $i,SV1: $i] :
( ( ( ~ ( less_than @ SV1 @ SV40 ) )
= $true )
| ( ( ~ ( less_than @ SV40 @ SV72 ) )
= $true )
| ( ( less_than @ SV1 @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(305,plain,
! [SV9: $i,SV75: $i,SV45: $i] :
( ( ( SV45 = SV75 )
= $true )
| ( ( ~ ( contains_slb @ SV9 @ SV75 ) )
= $true )
| ( ( ! [SY263: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV45 @ SY263 ) ) @ SV75 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV75 ) @ ( pair @ SV45 @ SY263 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(306,plain,
! [SV11: $i,SV77: $i,SV47: $i] :
( ( ( SV47 = SV77 )
= $true )
| ( ( ~ ( contains_slb @ SV11 @ SV77 ) )
= $true )
| ( ( ! [SY264: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV47 @ SY264 ) ) @ SV77 )
= ( lookup_slb @ SV11 @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(307,plain,
! [SV48: $i,SV13: $i,SV78: $i,SV88: $i] :
( ( ( ~ ( strictly_less_than @ SV88 @ SV78 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV48 @ SV88 ) ) @ SV78 )
= ( insert_slb @ ( update_slb @ SV13 @ SV78 ) @ ( pair @ SV48 @ SV78 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(308,plain,
! [SV49: $i,SV14: $i,SV89: $i,SV79: $i] :
( ( ( ~ ( less_than @ SV79 @ SV89 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV49 @ SV89 ) ) @ SV79 )
= ( insert_slb @ ( update_slb @ SV14 @ SV79 ) @ ( pair @ SV49 @ SV89 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(309,plain,
! [SV97: $i,SV50: $i,SV16: $i] :
( ( ( succ_cpq @ SV16 @ ( insert_cpq @ SV50 @ SV97 ) )
= $true )
| ( ( succ_cpq @ SV16 @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(310,plain,
! [SV98: $i,SV51: $i,SV17: $i] :
( ( ( succ_cpq @ SV17 @ ( remove_cpq @ SV51 @ SV98 ) )
= $true )
| ( ( succ_cpq @ SV17 @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(311,plain,
! [SV80: $i,SV55: $i,SV21: $i,SV99: $i,SV90: $i] :
( ( ~ ( strictly_less_than @ SV90 @ SV99 )
| ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV55 @ ( pair @ SV90 @ SV99 ) ) @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(312,plain,
! [SV83: $i,SV25: $i,SV92: $i,SV59: $i] :
( ( ( contains_slb @ SV59 @ SV92 )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV25 @ SV59 @ SV83 ) @ SV92 )
= ( triple @ SV25 @ SV59 @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(313,plain,
! [SV84: $i,SV26: $i,SV93: $i,SV60: $i] :
( ( ( ~ ( contains_slb @ SV60 @ SV93 )
| ~ ( less_than @ ( lookup_slb @ SV60 @ SV93 ) @ SV93 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV26 @ SV60 @ SV84 ) @ SV93 )
= ( triple @ ( remove_pqp @ SV26 @ SV93 ) @ ( remove_slb @ SV60 @ SV93 ) @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(314,plain,
! [SV85: $i,SV27: $i,SV94: $i,SV61: $i] :
( ( ( ~ ( contains_slb @ SV61 @ SV94 )
| ~ ( strictly_less_than @ SV94 @ ( lookup_slb @ SV61 @ SV94 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV27 @ SV61 @ SV85 ) @ SV94 )
= ( triple @ ( remove_pqp @ SV27 @ SV94 ) @ ( remove_slb @ SV61 @ SV94 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(315,plain,
! [SV100: $i,SV63: $i,SV29: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV29 @ SV63 @ SV100 ) )
= ( triple @ SV29 @ ( update_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) ) @ bad ) )
= $true )
| ( ( contains_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) )
= $true )
| ( ( SV63 = create_slb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(316,plain,
! [SV30: $i,SV64: $i] :
( ( ( SV64 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) ) )
= $true )
| ( ( ! [SY236: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY236 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(317,plain,
! [SV31: $i,SV65: $i] :
( ( ( SV65 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) ) )
= $true )
| ( ( ! [SY237: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY237 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY237 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(318,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ~ ~ ( ~ ! [SY273: $i,SY274: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY273 ) ) @ SV86 @ SY274 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY274 ) )
| ~ ! [SY275: $i,SY276: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY275 ) ) @ SV86 @ SY276 )
| ( SY275 = SY276 )
| ( pair_in_list @ SV36 @ SV86 @ SY276 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(319,plain,
! [SV36: $i,SV86: $i,SV68: $i] :
( ( ~ ~ ( ~ ! [SY277: $i,SY278: $i] :
( ( SV68 != SV86 )
| ( SY277 != SY278 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY277 ) ) @ SV86 @ SY278 ) )
| ~ ! [SY279: $i,SY280: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY280 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY279 ) ) @ SV86 @ SY280 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(320,plain,
! [SV87: $i,SV69: $i,SV37: $i] :
( ( ~ ! [SY281: $i,SY282: $i] :
( ~ ( less_than @ SY282 @ SY281 )
| ~ ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SV69 @ ( pair @ SY281 @ SY282 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV37 @ SV69 @ SV87 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(321,plain,
! [SV87: $i,SV69: $i,SV37: $i] :
( ( ~ ! [SY283: $i,SY284: $i] :
( ~ ( less_than @ SY284 @ SY283 )
| ~ ( check_cpq @ ( triple @ SV37 @ SV69 @ SV87 ) )
| ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SV69 @ ( pair @ SY283 @ SY284 ) ) @ SV87 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(322,plain,
! [SV70: $i,SV38: $i] :
( ( ! [SY253: $i] :
( ! [SY254: $i] :
~ ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY254 ) ) @ SY253 )
| ( SV70 = SY253 )
| ( contains_slb @ SV38 @ SY253 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(323,plain,
! [SV38: $i,SV70: $i] :
( ( ~ ( ~ ! [SY255: $i] :
( ( SV70 != SY255 )
| ! [SY256: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY256 ) ) @ SY255 ) )
| ~ ! [SY257: $i] :
( ~ ( contains_slb @ SV38 @ SY257 )
| ! [SY258: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY258 ) ) @ SY257 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(324,plain,
! [SV71: $i,SV39: $i] :
( ( ! [SY259: $i,SY260: $i] :
( ~ ( contains_cpq @ ( triple @ SV39 @ SV71 @ SY259 ) @ SY260 )
| ( contains_slb @ SV71 @ SY260 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(325,plain,
! [SV39: $i,SV71: $i] :
( ( ! [SY261: $i,SY262: $i] :
( ~ ( contains_slb @ SV71 @ SY262 )
| ( contains_cpq @ ( triple @ SV39 @ SV71 @ SY261 ) @ SY262 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(326,plain,
! [SV101: $i,SV96: $i] :
( ( ~ ( less_than @ SV96 @ SV101 )
| ( less_than @ SV101 @ SV96 )
| ( strictly_less_than @ SV96 @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(327,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(328,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(329,plain,
! [SV72: $i,SV40: $i,SV1: $i] :
( ( ( less_than @ SV1 @ SV40 )
= $false )
| ( ( ~ ( less_than @ SV40 @ SV72 ) )
= $true )
| ( ( less_than @ SV1 @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(330,plain,
! [SV45: $i,SV75: $i,SV9: $i] :
( ( ( contains_slb @ SV9 @ SV75 )
= $false )
| ( ( SV45 = SV75 )
= $true )
| ( ( ! [SY263: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV45 @ SY263 ) ) @ SV75 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV75 ) @ ( pair @ SV45 @ SY263 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(331,plain,
! [SV47: $i,SV77: $i,SV11: $i] :
( ( ( contains_slb @ SV11 @ SV77 )
= $false )
| ( ( SV47 = SV77 )
= $true )
| ( ( ! [SY264: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV47 @ SY264 ) ) @ SV77 )
= ( lookup_slb @ SV11 @ SV77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(332,plain,
! [SV48: $i,SV13: $i,SV78: $i,SV88: $i] :
( ( ( strictly_less_than @ SV88 @ SV78 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV48 @ SV88 ) ) @ SV78 )
= ( insert_slb @ ( update_slb @ SV13 @ SV78 ) @ ( pair @ SV48 @ SV78 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(333,plain,
! [SV49: $i,SV14: $i,SV89: $i,SV79: $i] :
( ( ( less_than @ SV79 @ SV89 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV49 @ SV89 ) ) @ SV79 )
= ( insert_slb @ ( update_slb @ SV14 @ SV79 ) @ ( pair @ SV49 @ SV89 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(334,plain,
! [SV80: $i,SV55: $i,SV21: $i,SV99: $i,SV90: $i] :
( ( ( ~ ( strictly_less_than @ SV90 @ SV99 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV55 @ ( pair @ SV90 @ SV99 ) ) @ SV80 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(335,plain,
! [SV84: $i,SV26: $i,SV93: $i,SV60: $i] :
( ( ( ~ ( contains_slb @ SV60 @ SV93 ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV60 @ SV93 ) @ SV93 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV26 @ SV60 @ SV84 ) @ SV93 )
= ( triple @ ( remove_pqp @ SV26 @ SV93 ) @ ( remove_slb @ SV60 @ SV93 ) @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(336,plain,
! [SV85: $i,SV27: $i,SV94: $i,SV61: $i] :
( ( ( ~ ( contains_slb @ SV61 @ SV94 ) )
= $true )
| ( ( ~ ( strictly_less_than @ SV94 @ ( lookup_slb @ SV61 @ SV94 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV27 @ SV61 @ SV85 ) @ SV94 )
= ( triple @ ( remove_pqp @ SV27 @ SV94 ) @ ( remove_slb @ SV61 @ SV94 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(337,plain,
! [SV30: $i,SV64: $i] :
( ( ( contains_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) )
= $false )
| ( ( SV64 = create_slb )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) ) )
= $true )
| ( ( ! [SY236: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY236 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(338,plain,
! [SV31: $i,SV65: $i] :
( ( ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) )
= $false )
| ( ( SV65 = create_slb )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) ) )
= $true )
| ( ( ! [SY237: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY237 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY237 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(339,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ~ ( ~ ! [SY273: $i,SY274: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY273 ) ) @ SV86 @ SY274 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY274 ) )
| ~ ! [SY275: $i,SY276: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY275 ) ) @ SV86 @ SY276 )
| ( SY275 = SY276 )
| ( pair_in_list @ SV36 @ SV86 @ SY276 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[318]) ).
thf(340,plain,
! [SV36: $i,SV86: $i,SV68: $i] :
( ( ~ ( ~ ! [SY277: $i,SY278: $i] :
( ( SV68 != SV86 )
| ( SY277 != SY278 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY277 ) ) @ SV86 @ SY278 ) )
| ~ ! [SY279: $i,SY280: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY280 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY279 ) ) @ SV86 @ SY280 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[319]) ).
thf(341,plain,
! [SV87: $i,SV69: $i,SV37: $i] :
( ( ! [SY281: $i,SY282: $i] :
( ~ ( less_than @ SY282 @ SY281 )
| ~ ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SV69 @ ( pair @ SY281 @ SY282 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV37 @ SV69 @ SV87 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(342,plain,
! [SV87: $i,SV69: $i,SV37: $i] :
( ( ! [SY283: $i,SY284: $i] :
( ~ ( less_than @ SY284 @ SY283 )
| ~ ( check_cpq @ ( triple @ SV37 @ SV69 @ SV87 ) )
| ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SV69 @ ( pair @ SY283 @ SY284 ) ) @ SV87 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(343,plain,
! [SV102: $i,SV70: $i,SV38: $i] :
( ( ! [SY287: $i] :
~ ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY287 ) ) @ SV102 )
| ( SV70 = SV102 )
| ( contains_slb @ SV38 @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(344,plain,
! [SV38: $i,SV70: $i] :
( ( ~ ! [SY255: $i] :
( ( SV70 != SY255 )
| ! [SY256: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY256 ) ) @ SY255 ) )
| ~ ! [SY257: $i] :
( ~ ( contains_slb @ SV38 @ SY257 )
| ! [SY258: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY258 ) ) @ SY257 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(345,plain,
! [SV103: $i,SV71: $i,SV39: $i] :
( ( ! [SY288: $i] :
( ~ ( contains_cpq @ ( triple @ SV39 @ SV71 @ SV103 ) @ SY288 )
| ( contains_slb @ SV71 @ SY288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(346,plain,
! [SV104: $i,SV39: $i,SV71: $i] :
( ( ! [SY289: $i] :
( ~ ( contains_slb @ SV71 @ SY289 )
| ( contains_cpq @ ( triple @ SV39 @ SV71 @ SV104 ) @ SY289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(347,plain,
! [SV101: $i,SV96: $i] :
( ( ( ~ ( less_than @ SV96 @ SV101 )
| ( less_than @ SV101 @ SV96 ) )
= $true )
| ( ( strictly_less_than @ SV96 @ SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(348,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[327]) ).
thf(349,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(350,plain,
! [SV1: $i,SV72: $i,SV40: $i] :
( ( ( less_than @ SV40 @ SV72 )
= $false )
| ( ( less_than @ SV1 @ SV40 )
= $false )
| ( ( less_than @ SV1 @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(351,plain,
! [SV75: $i,SV105: $i,SV45: $i,SV9: $i] :
( ( ( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV45 @ SV105 ) ) @ SV75 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV75 ) @ ( pair @ SV45 @ SV105 ) ) )
= $true )
| ( ( SV45 = SV75 )
= $true )
| ( ( contains_slb @ SV9 @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(352,plain,
! [SV77: $i,SV106: $i,SV47: $i,SV11: $i] :
( ( ( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV47 @ SV106 ) ) @ SV77 )
= ( lookup_slb @ SV11 @ SV77 ) )
= $true )
| ( ( SV47 = SV77 )
= $true )
| ( ( contains_slb @ SV11 @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(353,plain,
! [SV80: $i,SV55: $i,SV21: $i,SV99: $i,SV90: $i] :
( ( ( strictly_less_than @ SV90 @ SV99 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV55 @ ( pair @ SV90 @ SV99 ) ) @ SV80 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(354,plain,
! [SV84: $i,SV26: $i,SV93: $i,SV60: $i] :
( ( ( contains_slb @ SV60 @ SV93 )
= $false )
| ( ( ~ ( less_than @ ( lookup_slb @ SV60 @ SV93 ) @ SV93 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV26 @ SV60 @ SV84 ) @ SV93 )
= ( triple @ ( remove_pqp @ SV26 @ SV93 ) @ ( remove_slb @ SV60 @ SV93 ) @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(355,plain,
! [SV85: $i,SV27: $i,SV94: $i,SV61: $i] :
( ( ( contains_slb @ SV61 @ SV94 )
= $false )
| ( ( ~ ( strictly_less_than @ SV94 @ ( lookup_slb @ SV61 @ SV94 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV27 @ SV61 @ SV85 ) @ SV94 )
= ( triple @ ( remove_pqp @ SV27 @ SV94 ) @ ( remove_slb @ SV61 @ SV94 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(356,plain,
! [SV64: $i,SV30: $i] :
( ( ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) )
= $false )
| ( ( SV64 = create_slb )
= $true )
| ( ( contains_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) )
= $false )
| ( ( ! [SY236: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY236 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(357,plain,
! [SV31: $i,SV65: $i] :
( ( ( less_than @ ( lookup_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) )
= $false )
| ( ( SV65 = create_slb )
= $true )
| ( ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) )
= $false )
| ( ( ! [SY237: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY237 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY237 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(358,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ~ ! [SY273: $i,SY274: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY273 ) ) @ SV86 @ SY274 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY274 ) )
| ~ ! [SY275: $i,SY276: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY275 ) ) @ SV86 @ SY276 )
| ( SY275 = SY276 )
| ( pair_in_list @ SV36 @ SV86 @ SY276 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(359,plain,
! [SV36: $i,SV86: $i,SV68: $i] :
( ( ~ ! [SY277: $i,SY278: $i] :
( ( SV68 != SV86 )
| ( SY277 != SY278 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY277 ) ) @ SV86 @ SY278 ) )
| ~ ! [SY279: $i,SY280: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY280 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY279 ) ) @ SV86 @ SY280 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(360,plain,
! [SV87: $i,SV69: $i,SV37: $i,SV107: $i] :
( ( ! [SY290: $i] :
( ~ ( less_than @ SY290 @ SV107 )
| ~ ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SV69 @ ( pair @ SV107 @ SY290 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV37 @ SV69 @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(361,plain,
! [SV87: $i,SV69: $i,SV37: $i,SV108: $i] :
( ( ! [SY291: $i] :
( ~ ( less_than @ SY291 @ SV108 )
| ~ ( check_cpq @ ( triple @ SV37 @ SV69 @ SV87 ) )
| ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SV69 @ ( pair @ SV108 @ SY291 ) ) @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(362,plain,
! [SV102: $i,SV70: $i,SV38: $i] :
( ( ( ! [SY287: $i] :
~ ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY287 ) ) @ SV102 ) )
= $true )
| ( ( ( SV70 = SV102 )
| ( contains_slb @ SV38 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(363,plain,
! [SV38: $i,SV70: $i] :
( ( ~ ! [SY255: $i] :
( ( SV70 != SY255 )
| ! [SY256: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY256 ) ) @ SY255 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(364,plain,
! [SV70: $i,SV38: $i] :
( ( ~ ! [SY257: $i] :
( ~ ( contains_slb @ SV38 @ SY257 )
| ! [SY258: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY258 ) ) @ SY257 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(365,plain,
! [SV109: $i,SV103: $i,SV71: $i,SV39: $i] :
( ( ~ ( contains_cpq @ ( triple @ SV39 @ SV71 @ SV103 ) @ SV109 )
| ( contains_slb @ SV71 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(366,plain,
! [SV104: $i,SV39: $i,SV110: $i,SV71: $i] :
( ( ~ ( contains_slb @ SV71 @ SV110 )
| ( contains_cpq @ ( triple @ SV39 @ SV71 @ SV104 ) @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(367,plain,
! [SV101: $i,SV96: $i] :
( ( ( ~ ( less_than @ SV96 @ SV101 ) )
= $true )
| ( ( less_than @ SV101 @ SV96 )
= $true )
| ( ( strictly_less_than @ SV96 @ SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(368,plain,
! [SV111: $i] :
( ( ! [SY292: $i] :
( ~ ( strictly_less_than @ SV111 @ SY292 )
| ( less_than @ SV111 @ SY292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(369,plain,
! [SV112: $i] :
( ( ! [SY293: $i] :
( ~ ( strictly_less_than @ SV112 @ SY293 )
| ~ ( less_than @ SY293 @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(370,plain,
! [SV80: $i,SV99: $i,SV90: $i,SV55: $i,SV21: $i] :
( ( ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV55 @ ( pair @ SV90 @ SV99 ) ) @ SV80 ) )
= $false )
| ( ( strictly_less_than @ SV90 @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(371,plain,
! [SV84: $i,SV26: $i,SV93: $i,SV60: $i] :
( ( ( less_than @ ( lookup_slb @ SV60 @ SV93 ) @ SV93 )
= $false )
| ( ( contains_slb @ SV60 @ SV93 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV26 @ SV60 @ SV84 ) @ SV93 )
= ( triple @ ( remove_pqp @ SV26 @ SV93 ) @ ( remove_slb @ SV60 @ SV93 ) @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(372,plain,
! [SV85: $i,SV27: $i,SV61: $i,SV94: $i] :
( ( ( strictly_less_than @ SV94 @ ( lookup_slb @ SV61 @ SV94 ) )
= $false )
| ( ( contains_slb @ SV61 @ SV94 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV27 @ SV61 @ SV85 ) @ SV94 )
= ( triple @ ( remove_pqp @ SV27 @ SV94 ) @ ( remove_slb @ SV61 @ SV94 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(373,plain,
! [SV113: $i,SV64: $i,SV30: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SV113 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) )
= $true )
| ( ( contains_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) )
= $false )
| ( ( SV64 = create_slb )
= $true )
| ( ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(374,plain,
! [SV114: $i,SV65: $i,SV31: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SV114 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SV114 ) )
= $true )
| ( ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) )
= $false )
| ( ( SV65 = create_slb )
= $true )
| ( ( less_than @ ( lookup_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(375,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ~ ! [SY273: $i,SY274: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY273 ) ) @ SV86 @ SY274 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY274 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(376,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ~ ! [SY275: $i,SY276: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY275 ) ) @ SV86 @ SY276 )
| ( SY275 = SY276 )
| ( pair_in_list @ SV36 @ SV86 @ SY276 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(377,plain,
! [SV36: $i,SV86: $i,SV68: $i] :
( ( ~ ! [SY277: $i,SY278: $i] :
( ( SV68 != SV86 )
| ( SY277 != SY278 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY277 ) ) @ SV86 @ SY278 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(378,plain,
! [SV68: $i,SV86: $i,SV36: $i] :
( ( ~ ! [SY279: $i,SY280: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY280 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY279 ) ) @ SV86 @ SY280 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(379,plain,
! [SV87: $i,SV69: $i,SV37: $i,SV107: $i,SV115: $i] :
( ( ~ ( less_than @ SV115 @ SV107 )
| ~ ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SV69 @ ( pair @ SV107 @ SV115 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV37 @ SV69 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(380,plain,
! [SV87: $i,SV69: $i,SV37: $i,SV108: $i,SV116: $i] :
( ( ~ ( less_than @ SV116 @ SV108 )
| ~ ( check_cpq @ ( triple @ SV37 @ SV69 @ SV87 ) )
| ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SV69 @ ( pair @ SV108 @ SV116 ) ) @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(381,plain,
! [SV102: $i,SV117: $i,SV70: $i,SV38: $i] :
( ( ( ~ ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV117 ) ) @ SV102 ) )
= $true )
| ( ( ( SV70 = SV102 )
| ( contains_slb @ SV38 @ SV102 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(382,plain,
! [SV38: $i,SV70: $i] :
( ( ! [SY255: $i] :
( ( SV70 != SY255 )
| ! [SY256: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY256 ) ) @ SY255 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[363]) ).
thf(383,plain,
! [SV70: $i,SV38: $i] :
( ( ! [SY257: $i] :
( ~ ( contains_slb @ SV38 @ SY257 )
| ! [SY258: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY258 ) ) @ SY257 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[364]) ).
thf(384,plain,
! [SV109: $i,SV103: $i,SV71: $i,SV39: $i] :
( ( ( ~ ( contains_cpq @ ( triple @ SV39 @ SV71 @ SV103 ) @ SV109 ) )
= $true )
| ( ( contains_slb @ SV71 @ SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(385,plain,
! [SV104: $i,SV39: $i,SV110: $i,SV71: $i] :
( ( ( ~ ( contains_slb @ SV71 @ SV110 ) )
= $true )
| ( ( contains_cpq @ ( triple @ SV39 @ SV71 @ SV104 ) @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(386,plain,
! [SV101: $i,SV96: $i] :
( ( ( less_than @ SV96 @ SV101 )
= $false )
| ( ( less_than @ SV101 @ SV96 )
= $true )
| ( ( strictly_less_than @ SV96 @ SV101 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(387,plain,
! [SV118: $i,SV111: $i] :
( ( ~ ( strictly_less_than @ SV111 @ SV118 )
| ( less_than @ SV111 @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(388,plain,
! [SV119: $i,SV112: $i] :
( ( ~ ( strictly_less_than @ SV112 @ SV119 )
| ~ ( less_than @ SV119 @ SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(389,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ! [SY273: $i,SY274: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY273 ) ) @ SV86 @ SY274 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY274 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[375]) ).
thf(390,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ! [SY275: $i,SY276: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY275 ) ) @ SV86 @ SY276 )
| ( SY275 = SY276 )
| ( pair_in_list @ SV36 @ SV86 @ SY276 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[376]) ).
thf(391,plain,
! [SV36: $i,SV86: $i,SV68: $i] :
( ( ! [SY277: $i,SY278: $i] :
( ( SV68 != SV86 )
| ( SY277 != SY278 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY277 ) ) @ SV86 @ SY278 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(392,plain,
! [SV68: $i,SV86: $i,SV36: $i] :
( ( ! [SY279: $i,SY280: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY280 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY279 ) ) @ SV86 @ SY280 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[378]) ).
thf(393,plain,
! [SV87: $i,SV69: $i,SV37: $i,SV107: $i,SV115: $i] :
( ( ( ~ ( less_than @ SV115 @ SV107 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SV69 @ ( pair @ SV107 @ SV115 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV37 @ SV69 @ SV87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(394,plain,
! [SV87: $i,SV69: $i,SV37: $i,SV108: $i,SV116: $i] :
( ( ( ~ ( less_than @ SV116 @ SV108 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV37 @ SV69 @ SV87 ) )
| ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SV69 @ ( pair @ SV108 @ SV116 ) ) @ SV87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(395,plain,
! [SV102: $i,SV117: $i,SV70: $i,SV38: $i] :
( ( ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV117 ) ) @ SV102 )
= $false )
| ( ( ( SV70 = SV102 )
| ( contains_slb @ SV38 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(396,plain,
! [SV38: $i,SV120: $i,SV70: $i] :
( ( ( SV70 != SV120 )
| ! [SY294: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY294 ) ) @ SV120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(397,plain,
! [SV70: $i,SV121: $i,SV38: $i] :
( ( ~ ( contains_slb @ SV38 @ SV121 )
| ! [SY295: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY295 ) ) @ SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(398,plain,
! [SV109: $i,SV103: $i,SV71: $i,SV39: $i] :
( ( ( contains_cpq @ ( triple @ SV39 @ SV71 @ SV103 ) @ SV109 )
= $false )
| ( ( contains_slb @ SV71 @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(399,plain,
! [SV104: $i,SV39: $i,SV110: $i,SV71: $i] :
( ( ( contains_slb @ SV71 @ SV110 )
= $false )
| ( ( contains_cpq @ ( triple @ SV39 @ SV71 @ SV104 ) @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(400,plain,
! [SV118: $i,SV111: $i] :
( ( ( ~ ( strictly_less_than @ SV111 @ SV118 ) )
= $true )
| ( ( less_than @ SV111 @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(401,plain,
! [SV119: $i,SV112: $i] :
( ( ( ~ ( strictly_less_than @ SV112 @ SV119 ) )
= $true )
| ( ( ~ ( less_than @ SV119 @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(402,plain,
! [SV86: $i,SV122: $i,SV68: $i,SV36: $i] :
( ( ! [SY296: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV122 ) ) @ SV86 @ SY296 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(403,plain,
! [SV86: $i,SV123: $i,SV68: $i,SV36: $i] :
( ( ! [SY297: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV123 ) ) @ SV86 @ SY297 )
| ( SV123 = SY297 )
| ( pair_in_list @ SV36 @ SV86 @ SY297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(404,plain,
! [SV36: $i,SV124: $i,SV86: $i,SV68: $i] :
( ( ! [SY298: $i] :
( ( SV68 != SV86 )
| ( SV124 != SY298 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV124 ) ) @ SV86 @ SY298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(405,plain,
! [SV125: $i,SV68: $i,SV86: $i,SV36: $i] :
( ( ! [SY299: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY299 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV125 ) ) @ SV86 @ SY299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(406,plain,
! [SV87: $i,SV69: $i,SV37: $i,SV107: $i,SV115: $i] :
( ( ( less_than @ SV115 @ SV107 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SV69 @ ( pair @ SV107 @ SV115 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV37 @ SV69 @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(407,plain,
! [SV87: $i,SV69: $i,SV37: $i,SV108: $i,SV116: $i] :
( ( ( less_than @ SV116 @ SV108 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV37 @ SV69 @ SV87 ) )
| ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SV69 @ ( pair @ SV108 @ SV116 ) ) @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(408,plain,
! [SV117: $i,SV38: $i,SV102: $i,SV70: $i] :
( ( ( SV70 = SV102 )
= $true )
| ( ( contains_slb @ SV38 @ SV102 )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV117 ) ) @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(409,plain,
! [SV38: $i,SV120: $i,SV70: $i] :
( ( ( ( SV70 != SV120 ) )
= $true )
| ( ( ! [SY294: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY294 ) ) @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(410,plain,
! [SV70: $i,SV121: $i,SV38: $i] :
( ( ( ~ ( contains_slb @ SV38 @ SV121 ) )
= $true )
| ( ( ! [SY295: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY295 ) ) @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[397]) ).
thf(411,plain,
! [SV118: $i,SV111: $i] :
( ( ( strictly_less_than @ SV111 @ SV118 )
= $false )
| ( ( less_than @ SV111 @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(412,plain,
! [SV119: $i,SV112: $i] :
( ( ( strictly_less_than @ SV112 @ SV119 )
= $false )
| ( ( ~ ( less_than @ SV119 @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(413,plain,
! [SV126: $i,SV86: $i,SV122: $i,SV68: $i,SV36: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV122 ) ) @ SV86 @ SV126 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(414,plain,
! [SV127: $i,SV86: $i,SV123: $i,SV68: $i,SV36: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV123 ) ) @ SV86 @ SV127 )
| ( SV123 = SV127 )
| ( pair_in_list @ SV36 @ SV86 @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(415,plain,
! [SV36: $i,SV128: $i,SV124: $i,SV86: $i,SV68: $i] :
( ( ( SV68 != SV86 )
| ( SV124 != SV128 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV124 ) ) @ SV86 @ SV128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(416,plain,
! [SV125: $i,SV68: $i,SV129: $i,SV86: $i,SV36: $i] :
( ( ~ ( pair_in_list @ SV36 @ SV86 @ SV129 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV125 ) ) @ SV86 @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(417,plain,
! [SV87: $i,SV115: $i,SV107: $i,SV69: $i,SV37: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SV69 @ ( pair @ SV107 @ SV115 ) ) @ SV87 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV37 @ SV69 @ SV87 ) )
= $true )
| ( ( less_than @ SV115 @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[406]) ).
thf(418,plain,
! [SV116: $i,SV108: $i,SV87: $i,SV69: $i,SV37: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV37 @ SV69 @ SV87 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SV69 @ ( pair @ SV108 @ SV116 ) ) @ SV87 ) )
= $true )
| ( ( less_than @ SV116 @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(419,plain,
! [SV38: $i,SV120: $i,SV70: $i] :
( ( ( SV70 = SV120 )
= $false )
| ( ( ! [SY294: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY294 ) ) @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(420,plain,
! [SV70: $i,SV121: $i,SV38: $i] :
( ( ( contains_slb @ SV38 @ SV121 )
= $false )
| ( ( ! [SY295: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY295 ) ) @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(421,plain,
! [SV112: $i,SV119: $i] :
( ( ( less_than @ SV119 @ SV112 )
= $false )
| ( ( strictly_less_than @ SV112 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(422,plain,
! [SV126: $i,SV86: $i,SV122: $i,SV68: $i,SV36: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV122 ) ) @ SV86 @ SV126 ) )
= $true )
| ( ( ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(423,plain,
! [SV127: $i,SV86: $i,SV123: $i,SV68: $i,SV36: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV123 ) ) @ SV86 @ SV127 ) )
= $true )
| ( ( ( SV123 = SV127 )
| ( pair_in_list @ SV36 @ SV86 @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(424,plain,
! [SV36: $i,SV128: $i,SV124: $i,SV86: $i,SV68: $i] :
( ( ( ( SV68 != SV86 )
| ( SV124 != SV128 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV124 ) ) @ SV86 @ SV128 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(425,plain,
! [SV125: $i,SV68: $i,SV129: $i,SV86: $i,SV36: $i] :
( ( ( ~ ( pair_in_list @ SV36 @ SV86 @ SV129 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV125 ) ) @ SV86 @ SV129 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(426,plain,
! [SV87: $i,SV115: $i,SV107: $i,SV69: $i,SV37: $i] :
( ( ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SV69 @ ( pair @ SV107 @ SV115 ) ) @ SV87 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV37 @ SV69 @ SV87 ) )
= $true )
| ( ( less_than @ SV115 @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(427,plain,
! [SV116: $i,SV108: $i,SV87: $i,SV69: $i,SV37: $i] :
( ( ( check_cpq @ ( triple @ SV37 @ SV69 @ SV87 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV37 @ ( insert_slb @ SV69 @ ( pair @ SV108 @ SV116 ) ) @ SV87 ) )
= $true )
| ( ( less_than @ SV116 @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(428,plain,
! [SV120: $i,SV130: $i,SV70: $i,SV38: $i] :
( ( ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV130 ) ) @ SV120 )
= $true )
| ( ( SV70 = SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(429,plain,
! [SV121: $i,SV131: $i,SV70: $i,SV38: $i] :
( ( ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV131 ) ) @ SV121 )
= $true )
| ( ( contains_slb @ SV38 @ SV121 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(430,plain,
! [SV126: $i,SV86: $i,SV122: $i,SV68: $i,SV36: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV122 ) ) @ SV86 @ SV126 )
= $false )
| ( ( ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(431,plain,
! [SV127: $i,SV86: $i,SV123: $i,SV68: $i,SV36: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV123 ) ) @ SV86 @ SV127 )
= $false )
| ( ( ( SV123 = SV127 )
| ( pair_in_list @ SV36 @ SV86 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(432,plain,
! [SV36: $i,SV128: $i,SV124: $i,SV86: $i,SV68: $i] :
( ( ( ( SV68 != SV86 ) )
= $true )
| ( ( ( SV124 != SV128 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV124 ) ) @ SV86 @ SV128 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(433,plain,
! [SV125: $i,SV68: $i,SV129: $i,SV86: $i,SV36: $i] :
( ( ( pair_in_list @ SV36 @ SV86 @ SV129 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV125 ) ) @ SV86 @ SV129 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(434,plain,
! [SV122: $i,SV126: $i,SV36: $i,SV86: $i,SV68: $i] :
( ( ( SV68 = SV86 )
= $true )
| ( ( pair_in_list @ SV36 @ SV86 @ SV126 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV122 ) ) @ SV86 @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(435,plain,
! [SV68: $i,SV86: $i,SV36: $i,SV127: $i,SV123: $i] :
( ( ( SV123 = SV127 )
= $true )
| ( ( pair_in_list @ SV36 @ SV86 @ SV127 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV123 ) ) @ SV86 @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(436,plain,
! [SV36: $i,SV128: $i,SV124: $i,SV86: $i,SV68: $i] :
( ( ( SV68 = SV86 )
= $false )
| ( ( ( SV124 != SV128 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV124 ) ) @ SV86 @ SV128 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(437,plain,
! [SV36: $i,SV86: $i,SV68: $i,SV128: $i,SV124: $i] :
( ( ( SV124 = SV128 )
= $false )
| ( ( SV68 = SV86 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV124 ) ) @ SV86 @ SV128 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(438,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[163,437,435,434,433,429,428,427,426,421,411,408,399,398,386,374,373,372,371,370,352,351,350,333,332,315,312,310,309,295,288,287,285,284,261,252,250,249,248,247,238,234,226,214,205,204,185,182,174,173,172,164]) ).
thf(439,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( less_than @ U @ V )
| ~ ( less_than @ V @ W )
| ( less_than @ U @ W ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(440,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(441,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(442,plain,
( ( ! [U: $i,V: $i] :
( ~ ( less_than @ U @ V )
| ( less_than @ V @ U )
| ( strictly_less_than @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( strictly_less_than @ U @ V )
| ( less_than @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( strictly_less_than @ U @ V )
| ~ ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(443,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(444,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(445,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(446,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(447,plain,
( ( ! [U: $i,V: $i] :
( ! [W: $i] :
( ! [X: $i] :
~ ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
| ( V = W )
| ( contains_slb @ U @ W ) )
& ! [W: $i] :
( ( V != W )
| ! [X: $i] : ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W ) )
& ! [W: $i] :
( ~ ( contains_slb @ U @ W )
| ! [X: $i] : ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(448,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(449,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
| ( V = W )
| ( pair_in_list @ U @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
| ( X = Y )
| ( pair_in_list @ U @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ( V != W )
| ( X != Y )
| ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ U @ W @ Y )
| ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(450,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(451,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( V = W )
| ~ ( contains_slb @ U @ W )
| ! [X: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( remove_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(452,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(453,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( V = W )
| ~ ( contains_slb @ U @ W )
| ! [X: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( lookup_slb @ U @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(454,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(455,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( strictly_less_than @ X @ W )
| ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(456,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( less_than @ W @ X )
| ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(457,plain,
( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(458,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(459,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(460,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(461,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(462,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(463,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ! [X: $i,Y: $i] :
( ~ ( less_than @ Y @ X )
| ~ ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
| ( check_cpq @ ( triple @ U @ V @ W ) ) )
& ! [X: $i,Y: $i] :
( ~ ( less_than @ Y @ X )
| ~ ( check_cpq @ ( triple @ U @ V @ W ) )
| ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(464,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ~ ( strictly_less_than @ X @ Y )
| ~ ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(465,plain,
( ( ! [U: $i,V: $i] :
( ! [W: $i,X: $i] :
( ~ ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
| ( contains_slb @ V @ X ) )
& ! [W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
| ( contains_cpq @ ( triple @ U @ V @ W ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(466,plain,
( ( ! [U: $i,V: $i] :
~ ( ok @ ( triple @ U @ V @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(467,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( triple @ U @ V @ W ) )
| ( W = bad ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(468,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( insert_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( insert_pqp @ U @ X ) @ ( insert_slb @ V @ ( pair @ X @ bottom ) ) @ W ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(469,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_slb @ V @ X )
| ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ U @ V @ bad ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(470,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
| ~ ( less_than @ ( lookup_slb @ V @ X ) @ X )
| ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(471,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
| ~ ( strictly_less_than @ X @ ( lookup_slb @ V @ X ) )
| ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ bad ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(472,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ create_slb @ V ) )
= ( triple @ U @ create_slb @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(473,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
| ! [W: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(474,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ U ) @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) )
| ! [W: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(475,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
| ~ ( less_than @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) @ ( findmin_pqp_res @ U ) )
| ! [W: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(476,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(477,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ! [W: $i] :
( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
= ( findmin_pqp_res @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(478,plain,
( ( ! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(479,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(480,plain,
( ( ok @ ( findmin_cpq_eff @ ( triple @ sK1_U @ sK2_SY120 @ sK3_SY122 ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(481,plain,
( ( ~ ( contains_slb @ sK2_SY120 @ ( findmin_pqp_res @ sK1_U ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(482,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( less_than @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 )
| ( strictly_less_than @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[442]) ).
thf(483,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( less_than @ SX4 @ SX3 )
| ~ ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ SX1 @ ( pair @ SX3 @ SX4 ) ) @ SX2 ) )
| ( check_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( less_than @ SX4 @ SX3 )
| ~ ( check_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ SX1 @ ( pair @ SX3 @ SX4 ) ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(484,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 )
| ( SX1 = SX2 )
| ( contains_slb @ SX0 @ SX2 ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ( SX1 != SX2 )
| ! [SX3: $i] : ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 ) )
| ~ ! [SX2: $i] :
( ~ ( contains_slb @ SX0 @ SX2 )
| ! [SX3: $i] : ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(485,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 )
| ( SX1 = SX2 )
| ( pair_in_list @ SX0 @ SX2 @ SX4 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 )
| ( SX3 = SX4 )
| ( pair_in_list @ SX0 @ SX2 @ SX4 ) ) )
| ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ( SX1 != SX2 )
| ( SX3 != SX4 )
| ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( pair_in_list @ SX0 @ SX2 @ SX4 )
| ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(486,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( contains_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ SX3 )
| ( contains_slb @ SX1 @ SX3 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( contains_slb @ SX1 @ SX3 )
| ( contains_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(487,plain,
! [SV132: $i] :
( ( ! [SY300: $i,SY301: $i] :
( ~ ( less_than @ SV132 @ SY300 )
| ~ ( less_than @ SY300 @ SY301 )
| ( less_than @ SV132 @ SY301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(488,plain,
! [SV133: $i] :
( ( ! [SY302: $i] :
( ( less_than @ SV133 @ SY302 )
| ( less_than @ SY302 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(489,plain,
! [SV134: $i] :
( ( less_than @ SV134 @ SV134 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(490,plain,
! [SV135: $i] :
( ( less_than @ bottom @ SV135 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(491,plain,
( ( isnonempty_slb @ create_slb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(492,plain,
! [SV136: $i] :
( ( ! [SY303: $i,SY304: $i] : ( isnonempty_slb @ ( insert_slb @ SV136 @ ( pair @ SY303 @ SY304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(493,plain,
! [SV137: $i] :
( ( ~ ( contains_slb @ create_slb @ SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(494,plain,
! [SV138: $i] :
( ( ! [SY305: $i] :
~ ( pair_in_list @ create_slb @ SV138 @ SY305 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(495,plain,
! [SV139: $i] :
( ( ! [SY306: $i,SY307: $i] :
( ( remove_slb @ ( insert_slb @ SV139 @ ( pair @ SY306 @ SY307 ) ) @ SY306 )
= SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(496,plain,
! [SV140: $i] :
( ( ! [SY308: $i,SY309: $i] :
( ( SY308 = SY309 )
| ~ ( contains_slb @ SV140 @ SY309 )
| ! [SY310: $i] :
( ( remove_slb @ ( insert_slb @ SV140 @ ( pair @ SY308 @ SY310 ) ) @ SY309 )
= ( insert_slb @ ( remove_slb @ SV140 @ SY309 ) @ ( pair @ SY308 @ SY310 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(497,plain,
! [SV141: $i] :
( ( ! [SY311: $i,SY312: $i] :
( ( lookup_slb @ ( insert_slb @ SV141 @ ( pair @ SY311 @ SY312 ) ) @ SY311 )
= SY312 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(498,plain,
! [SV142: $i] :
( ( ! [SY313: $i,SY314: $i] :
( ( SY313 = SY314 )
| ~ ( contains_slb @ SV142 @ SY314 )
| ! [SY315: $i] :
( ( lookup_slb @ ( insert_slb @ SV142 @ ( pair @ SY313 @ SY315 ) ) @ SY314 )
= ( lookup_slb @ SV142 @ SY314 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(499,plain,
! [SV143: $i] :
( ( ( update_slb @ create_slb @ SV143 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(500,plain,
! [SV144: $i] :
( ( ! [SY316: $i,SY317: $i,SY318: $i] :
( ~ ( strictly_less_than @ SY318 @ SY317 )
| ( ( update_slb @ ( insert_slb @ SV144 @ ( pair @ SY316 @ SY318 ) ) @ SY317 )
= ( insert_slb @ ( update_slb @ SV144 @ SY317 ) @ ( pair @ SY316 @ SY317 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(501,plain,
! [SV145: $i] :
( ( ! [SY319: $i,SY320: $i,SY321: $i] :
( ~ ( less_than @ SY320 @ SY321 )
| ( ( update_slb @ ( insert_slb @ SV145 @ ( pair @ SY319 @ SY321 ) ) @ SY320 )
= ( insert_slb @ ( update_slb @ SV145 @ SY320 ) @ ( pair @ SY319 @ SY321 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(502,plain,
! [SV146: $i] :
( ( succ_cpq @ SV146 @ SV146 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(503,plain,
! [SV147: $i] :
( ( ! [SY322: $i] :
( ~ ( succ_cpq @ SV147 @ SY322 )
| ! [SY323: $i] : ( succ_cpq @ SV147 @ ( insert_cpq @ SY322 @ SY323 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(504,plain,
! [SV148: $i] :
( ( ! [SY324: $i] :
( ~ ( succ_cpq @ SV148 @ SY324 )
| ! [SY325: $i] : ( succ_cpq @ SV148 @ ( remove_cpq @ SY324 @ SY325 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(505,plain,
! [SV149: $i] :
( ( ! [SY326: $i] :
( ~ ( succ_cpq @ SV149 @ SY326 )
| ( succ_cpq @ SV149 @ ( findmin_cpq_eff @ SY326 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(506,plain,
! [SV150: $i] :
( ( ! [SY327: $i] :
( ~ ( succ_cpq @ SV150 @ SY327 )
| ( succ_cpq @ SV150 @ ( removemin_cpq_eff @ SY327 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(507,plain,
! [SV151: $i] :
( ( ! [SY328: $i] : ( check_cpq @ ( triple @ SV151 @ create_slb @ SY328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(508,plain,
! [SV152: $i] :
( ( ! [SY329: $i,SY330: $i,SY331: $i,SY332: $i] :
( ~ ( strictly_less_than @ SY331 @ SY332 )
| ~ ( check_cpq @ ( triple @ SV152 @ ( insert_slb @ SY329 @ ( pair @ SY331 @ SY332 ) ) @ SY330 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(509,plain,
! [SV153: $i] :
( ( ! [SY333: $i] :
~ ( ok @ ( triple @ SV153 @ SY333 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(510,plain,
! [SV154: $i] :
( ( ! [SY334: $i,SY335: $i] :
( ( ok @ ( triple @ SV154 @ SY334 @ SY335 ) )
| ( SY335 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(511,plain,
! [SV155: $i] :
( ( ! [SY336: $i,SY337: $i,SY338: $i] :
( ( insert_cpq @ ( triple @ SV155 @ SY336 @ SY337 ) @ SY338 )
= ( triple @ ( insert_pqp @ SV155 @ SY338 ) @ ( insert_slb @ SY336 @ ( pair @ SY338 @ bottom ) ) @ SY337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(512,plain,
! [SV156: $i] :
( ( ! [SY339: $i,SY340: $i,SY341: $i] :
( ( contains_slb @ SY339 @ SY341 )
| ( ( remove_cpq @ ( triple @ SV156 @ SY339 @ SY340 ) @ SY341 )
= ( triple @ SV156 @ SY339 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(513,plain,
! [SV157: $i] :
( ( ! [SY342: $i,SY343: $i,SY344: $i] :
( ~ ( contains_slb @ SY342 @ SY344 )
| ~ ( less_than @ ( lookup_slb @ SY342 @ SY344 ) @ SY344 )
| ( ( remove_cpq @ ( triple @ SV157 @ SY342 @ SY343 ) @ SY344 )
= ( triple @ ( remove_pqp @ SV157 @ SY344 ) @ ( remove_slb @ SY342 @ SY344 ) @ SY343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(514,plain,
! [SV158: $i] :
( ( ! [SY345: $i,SY346: $i,SY347: $i] :
( ~ ( contains_slb @ SY345 @ SY347 )
| ~ ( strictly_less_than @ SY347 @ ( lookup_slb @ SY345 @ SY347 ) )
| ( ( remove_cpq @ ( triple @ SV158 @ SY345 @ SY346 ) @ SY347 )
= ( triple @ ( remove_pqp @ SV158 @ SY347 ) @ ( remove_slb @ SY345 @ SY347 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(515,plain,
! [SV159: $i] :
( ( ! [SY348: $i] :
( ( findmin_cpq_eff @ ( triple @ SV159 @ create_slb @ SY348 ) )
= ( triple @ SV159 @ create_slb @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(516,plain,
! [SV160: $i] :
( ( ! [SY349: $i] :
( ( SY349 = create_slb )
| ( contains_slb @ SY349 @ ( findmin_pqp_res @ SV160 ) )
| ! [SY350: $i] :
( ( findmin_cpq_eff @ ( triple @ SV160 @ SY349 @ SY350 ) )
= ( triple @ SV160 @ ( update_slb @ SY349 @ ( findmin_pqp_res @ SV160 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(517,plain,
! [SV161: $i] :
( ( ! [SY351: $i] :
( ( SY351 = create_slb )
| ~ ( contains_slb @ SY351 @ ( findmin_pqp_res @ SV161 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV161 ) @ ( lookup_slb @ SY351 @ ( findmin_pqp_res @ SV161 ) ) )
| ! [SY352: $i] :
( ( findmin_cpq_eff @ ( triple @ SV161 @ SY351 @ SY352 ) )
= ( triple @ SV161 @ ( update_slb @ SY351 @ ( findmin_pqp_res @ SV161 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(518,plain,
! [SV162: $i] :
( ( ! [SY353: $i] :
( ( SY353 = create_slb )
| ~ ( contains_slb @ SY353 @ ( findmin_pqp_res @ SV162 ) )
| ~ ( less_than @ ( lookup_slb @ SY353 @ ( findmin_pqp_res @ SV162 ) ) @ ( findmin_pqp_res @ SV162 ) )
| ! [SY354: $i] :
( ( findmin_cpq_eff @ ( triple @ SV162 @ SY353 @ SY354 ) )
= ( triple @ SV162 @ ( update_slb @ SY353 @ ( findmin_pqp_res @ SV162 ) ) @ SY354 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(519,plain,
! [SV163: $i] :
( ( ! [SY355: $i] :
( ( findmin_cpq_res @ ( triple @ SV163 @ create_slb @ SY355 ) )
= bottom ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(520,plain,
! [SV164: $i] :
( ( ! [SY356: $i] :
( ( SY356 = create_slb )
| ! [SY357: $i] :
( ( findmin_cpq_res @ ( triple @ SV164 @ SY356 @ SY357 ) )
= ( findmin_pqp_res @ SV164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(521,plain,
! [SV165: $i] :
( ( ( removemin_cpq_eff @ SV165 )
= ( remove_cpq @ ( findmin_cpq_eff @ SV165 ) @ ( findmin_cpq_res @ SV165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(522,plain,
! [SV166: $i] :
( ( ( removemin_cpq_res @ SV166 )
= ( findmin_cpq_res @ SV166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(523,plain,
( ( contains_slb @ sK2_SY120 @ ( findmin_pqp_res @ sK1_U ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(524,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( less_than @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 )
| ( strictly_less_than @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(525,plain,
! [SV167: $i] :
( ( ! [SY358: $i,SY359: $i] :
~ ( ~ ! [SY360: $i,SY361: $i] :
( ~ ( less_than @ SY361 @ SY360 )
| ~ ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SY358 @ ( pair @ SY360 @ SY361 ) ) @ SY359 ) )
| ( check_cpq @ ( triple @ SV167 @ SY358 @ SY359 ) ) )
| ~ ! [SY362: $i,SY363: $i] :
( ~ ( less_than @ SY363 @ SY362 )
| ~ ( check_cpq @ ( triple @ SV167 @ SY358 @ SY359 ) )
| ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SY358 @ ( pair @ SY362 @ SY363 ) ) @ SY359 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(526,plain,
! [SV168: $i] :
( ( ! [SY364: $i] :
~ ( ~ ! [SY365: $i] :
( ! [SY366: $i] :
~ ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SY364 @ SY366 ) ) @ SY365 )
| ( SY364 = SY365 )
| ( contains_slb @ SV168 @ SY365 ) )
| ~ ~ ( ~ ! [SY367: $i] :
( ( SY364 != SY367 )
| ! [SY368: $i] : ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SY364 @ SY368 ) ) @ SY367 ) )
| ~ ! [SY369: $i] :
( ~ ( contains_slb @ SV168 @ SY369 )
| ! [SY370: $i] : ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SY364 @ SY370 ) ) @ SY369 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(527,plain,
! [SV169: $i] :
( ( ! [SY371: $i,SY372: $i] :
~ ( ~ ~ ( ~ ! [SY373: $i,SY374: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SY371 @ SY373 ) ) @ SY372 @ SY374 )
| ( SY371 = SY372 )
| ( pair_in_list @ SV169 @ SY372 @ SY374 ) )
| ~ ! [SY375: $i,SY376: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SY371 @ SY375 ) ) @ SY372 @ SY376 )
| ( SY375 = SY376 )
| ( pair_in_list @ SV169 @ SY372 @ SY376 ) ) )
| ~ ~ ( ~ ! [SY377: $i,SY378: $i] :
( ( SY371 != SY372 )
| ( SY377 != SY378 )
| ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SY371 @ SY377 ) ) @ SY372 @ SY378 ) )
| ~ ! [SY379: $i,SY380: $i] :
( ~ ( pair_in_list @ SV169 @ SY372 @ SY380 )
| ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SY371 @ SY379 ) ) @ SY372 @ SY380 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(528,plain,
! [SV170: $i] :
( ( ! [SY381: $i] :
~ ( ~ ! [SY382: $i,SY383: $i] :
( ~ ( contains_cpq @ ( triple @ SV170 @ SY381 @ SY382 ) @ SY383 )
| ( contains_slb @ SY381 @ SY383 ) )
| ~ ! [SY384: $i,SY385: $i] :
( ~ ( contains_slb @ SY381 @ SY385 )
| ( contains_cpq @ ( triple @ SV170 @ SY381 @ SY384 ) @ SY385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(529,plain,
! [SV171: $i,SV132: $i] :
( ( ! [SY386: $i] :
( ~ ( less_than @ SV132 @ SV171 )
| ~ ( less_than @ SV171 @ SY386 )
| ( less_than @ SV132 @ SY386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(530,plain,
! [SV172: $i,SV133: $i] :
( ( ( less_than @ SV133 @ SV172 )
| ( less_than @ SV172 @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(531,plain,
! [SV173: $i,SV136: $i] :
( ( ! [SY387: $i] : ( isnonempty_slb @ ( insert_slb @ SV136 @ ( pair @ SV173 @ SY387 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(532,plain,
! [SV137: $i] :
( ( contains_slb @ create_slb @ SV137 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(533,plain,
! [SV174: $i,SV138: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV138 @ SV174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(534,plain,
! [SV175: $i,SV139: $i] :
( ( ! [SY388: $i] :
( ( remove_slb @ ( insert_slb @ SV139 @ ( pair @ SV175 @ SY388 ) ) @ SV175 )
= SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(535,plain,
! [SV140: $i,SV176: $i] :
( ( ! [SY389: $i] :
( ( SV176 = SY389 )
| ~ ( contains_slb @ SV140 @ SY389 )
| ! [SY390: $i] :
( ( remove_slb @ ( insert_slb @ SV140 @ ( pair @ SV176 @ SY390 ) ) @ SY389 )
= ( insert_slb @ ( remove_slb @ SV140 @ SY389 ) @ ( pair @ SV176 @ SY390 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(536,plain,
! [SV177: $i,SV141: $i] :
( ( ! [SY391: $i] :
( ( lookup_slb @ ( insert_slb @ SV141 @ ( pair @ SV177 @ SY391 ) ) @ SV177 )
= SY391 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(537,plain,
! [SV142: $i,SV178: $i] :
( ( ! [SY392: $i] :
( ( SV178 = SY392 )
| ~ ( contains_slb @ SV142 @ SY392 )
| ! [SY393: $i] :
( ( lookup_slb @ ( insert_slb @ SV142 @ ( pair @ SV178 @ SY393 ) ) @ SY392 )
= ( lookup_slb @ SV142 @ SY392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(538,plain,
! [SV179: $i,SV144: $i] :
( ( ! [SY394: $i,SY395: $i] :
( ~ ( strictly_less_than @ SY395 @ SY394 )
| ( ( update_slb @ ( insert_slb @ SV144 @ ( pair @ SV179 @ SY395 ) ) @ SY394 )
= ( insert_slb @ ( update_slb @ SV144 @ SY394 ) @ ( pair @ SV179 @ SY394 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(539,plain,
! [SV180: $i,SV145: $i] :
( ( ! [SY396: $i,SY397: $i] :
( ~ ( less_than @ SY396 @ SY397 )
| ( ( update_slb @ ( insert_slb @ SV145 @ ( pair @ SV180 @ SY397 ) ) @ SY396 )
= ( insert_slb @ ( update_slb @ SV145 @ SY396 ) @ ( pair @ SV180 @ SY397 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(540,plain,
! [SV181: $i,SV147: $i] :
( ( ~ ( succ_cpq @ SV147 @ SV181 )
| ! [SY398: $i] : ( succ_cpq @ SV147 @ ( insert_cpq @ SV181 @ SY398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(541,plain,
! [SV182: $i,SV148: $i] :
( ( ~ ( succ_cpq @ SV148 @ SV182 )
| ! [SY399: $i] : ( succ_cpq @ SV148 @ ( remove_cpq @ SV182 @ SY399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(542,plain,
! [SV183: $i,SV149: $i] :
( ( ~ ( succ_cpq @ SV149 @ SV183 )
| ( succ_cpq @ SV149 @ ( findmin_cpq_eff @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(543,plain,
! [SV184: $i,SV150: $i] :
( ( ~ ( succ_cpq @ SV150 @ SV184 )
| ( succ_cpq @ SV150 @ ( removemin_cpq_eff @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(544,plain,
! [SV185: $i,SV151: $i] :
( ( check_cpq @ ( triple @ SV151 @ create_slb @ SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(545,plain,
! [SV186: $i,SV152: $i] :
( ( ! [SY400: $i,SY401: $i,SY402: $i] :
( ~ ( strictly_less_than @ SY401 @ SY402 )
| ~ ( check_cpq @ ( triple @ SV152 @ ( insert_slb @ SV186 @ ( pair @ SY401 @ SY402 ) ) @ SY400 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(546,plain,
! [SV187: $i,SV153: $i] :
( ( ~ ( ok @ ( triple @ SV153 @ SV187 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(547,plain,
! [SV188: $i,SV154: $i] :
( ( ! [SY403: $i] :
( ( ok @ ( triple @ SV154 @ SV188 @ SY403 ) )
| ( SY403 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(548,plain,
! [SV189: $i,SV155: $i] :
( ( ! [SY404: $i,SY405: $i] :
( ( insert_cpq @ ( triple @ SV155 @ SV189 @ SY404 ) @ SY405 )
= ( triple @ ( insert_pqp @ SV155 @ SY405 ) @ ( insert_slb @ SV189 @ ( pair @ SY405 @ bottom ) ) @ SY404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(549,plain,
! [SV156: $i,SV190: $i] :
( ( ! [SY406: $i,SY407: $i] :
( ( contains_slb @ SV190 @ SY407 )
| ( ( remove_cpq @ ( triple @ SV156 @ SV190 @ SY406 ) @ SY407 )
= ( triple @ SV156 @ SV190 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(550,plain,
! [SV157: $i,SV191: $i] :
( ( ! [SY408: $i,SY409: $i] :
( ~ ( contains_slb @ SV191 @ SY409 )
| ~ ( less_than @ ( lookup_slb @ SV191 @ SY409 ) @ SY409 )
| ( ( remove_cpq @ ( triple @ SV157 @ SV191 @ SY408 ) @ SY409 )
= ( triple @ ( remove_pqp @ SV157 @ SY409 ) @ ( remove_slb @ SV191 @ SY409 ) @ SY408 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(551,plain,
! [SV158: $i,SV192: $i] :
( ( ! [SY410: $i,SY411: $i] :
( ~ ( contains_slb @ SV192 @ SY411 )
| ~ ( strictly_less_than @ SY411 @ ( lookup_slb @ SV192 @ SY411 ) )
| ( ( remove_cpq @ ( triple @ SV158 @ SV192 @ SY410 ) @ SY411 )
= ( triple @ ( remove_pqp @ SV158 @ SY411 ) @ ( remove_slb @ SV192 @ SY411 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(552,plain,
! [SV193: $i,SV159: $i] :
( ( ( findmin_cpq_eff @ ( triple @ SV159 @ create_slb @ SV193 ) )
= ( triple @ SV159 @ create_slb @ bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(553,plain,
! [SV160: $i,SV194: $i] :
( ( ( SV194 = create_slb )
| ( contains_slb @ SV194 @ ( findmin_pqp_res @ SV160 ) )
| ! [SY412: $i] :
( ( findmin_cpq_eff @ ( triple @ SV160 @ SV194 @ SY412 ) )
= ( triple @ SV160 @ ( update_slb @ SV194 @ ( findmin_pqp_res @ SV160 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(554,plain,
! [SV161: $i,SV195: $i] :
( ( ( SV195 = create_slb )
| ~ ( contains_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV161 ) @ ( lookup_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) ) )
| ! [SY413: $i] :
( ( findmin_cpq_eff @ ( triple @ SV161 @ SV195 @ SY413 ) )
= ( triple @ SV161 @ ( update_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(555,plain,
! [SV162: $i,SV196: $i] :
( ( ( SV196 = create_slb )
| ~ ( contains_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) )
| ~ ( less_than @ ( lookup_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) ) @ ( findmin_pqp_res @ SV162 ) )
| ! [SY414: $i] :
( ( findmin_cpq_eff @ ( triple @ SV162 @ SV196 @ SY414 ) )
= ( triple @ SV162 @ ( update_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) ) @ SY414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(556,plain,
! [SV197: $i,SV163: $i] :
( ( ( findmin_cpq_res @ ( triple @ SV163 @ create_slb @ SV197 ) )
= bottom )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(557,plain,
! [SV164: $i,SV198: $i] :
( ( ( SV198 = create_slb )
| ! [SY415: $i] :
( ( findmin_cpq_res @ ( triple @ SV164 @ SV198 @ SY415 ) )
= ( findmin_pqp_res @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(558,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( less_than @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 )
| ( strictly_less_than @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[524]) ).
thf(559,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[524]) ).
thf(560,plain,
! [SV199: $i,SV167: $i] :
( ( ! [SY416: $i] :
~ ( ~ ! [SY417: $i,SY418: $i] :
( ~ ( less_than @ SY418 @ SY417 )
| ~ ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SV199 @ ( pair @ SY417 @ SY418 ) ) @ SY416 ) )
| ( check_cpq @ ( triple @ SV167 @ SV199 @ SY416 ) ) )
| ~ ! [SY419: $i,SY420: $i] :
( ~ ( less_than @ SY420 @ SY419 )
| ~ ( check_cpq @ ( triple @ SV167 @ SV199 @ SY416 ) )
| ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SV199 @ ( pair @ SY419 @ SY420 ) ) @ SY416 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(561,plain,
! [SV200: $i,SV168: $i] :
( ( ~ ( ~ ! [SY421: $i] :
( ! [SY422: $i] :
~ ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY422 ) ) @ SY421 )
| ( SV200 = SY421 )
| ( contains_slb @ SV168 @ SY421 ) )
| ~ ~ ( ~ ! [SY423: $i] :
( ( SV200 != SY423 )
| ! [SY424: $i] : ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY424 ) ) @ SY423 ) )
| ~ ! [SY425: $i] :
( ~ ( contains_slb @ SV168 @ SY425 )
| ! [SY426: $i] : ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY426 ) ) @ SY425 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(562,plain,
! [SV201: $i,SV169: $i] :
( ( ! [SY427: $i] :
~ ( ~ ~ ( ~ ! [SY428: $i,SY429: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY428 ) ) @ SY427 @ SY429 )
| ( SV201 = SY427 )
| ( pair_in_list @ SV169 @ SY427 @ SY429 ) )
| ~ ! [SY430: $i,SY431: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY430 ) ) @ SY427 @ SY431 )
| ( SY430 = SY431 )
| ( pair_in_list @ SV169 @ SY427 @ SY431 ) ) )
| ~ ~ ( ~ ! [SY432: $i,SY433: $i] :
( ( SV201 != SY427 )
| ( SY432 != SY433 )
| ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY432 ) ) @ SY427 @ SY433 ) )
| ~ ! [SY434: $i,SY435: $i] :
( ~ ( pair_in_list @ SV169 @ SY427 @ SY435 )
| ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY434 ) ) @ SY427 @ SY435 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(563,plain,
! [SV202: $i,SV170: $i] :
( ( ~ ( ~ ! [SY436: $i,SY437: $i] :
( ~ ( contains_cpq @ ( triple @ SV170 @ SV202 @ SY436 ) @ SY437 )
| ( contains_slb @ SV202 @ SY437 ) )
| ~ ! [SY438: $i,SY439: $i] :
( ~ ( contains_slb @ SV202 @ SY439 )
| ( contains_cpq @ ( triple @ SV170 @ SV202 @ SY438 ) @ SY439 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(564,plain,
! [SV203: $i,SV171: $i,SV132: $i] :
( ( ~ ( less_than @ SV132 @ SV171 )
| ~ ( less_than @ SV171 @ SV203 )
| ( less_than @ SV132 @ SV203 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(565,plain,
! [SV172: $i,SV133: $i] :
( ( ( less_than @ SV133 @ SV172 )
= $true )
| ( ( less_than @ SV172 @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[530]) ).
thf(566,plain,
! [SV204: $i,SV173: $i,SV136: $i] :
( ( isnonempty_slb @ ( insert_slb @ SV136 @ ( pair @ SV173 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(567,plain,
! [SV174: $i,SV138: $i] :
( ( pair_in_list @ create_slb @ SV138 @ SV174 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(568,plain,
! [SV205: $i,SV175: $i,SV139: $i] :
( ( ( remove_slb @ ( insert_slb @ SV139 @ ( pair @ SV175 @ SV205 ) ) @ SV175 )
= SV139 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(569,plain,
! [SV140: $i,SV206: $i,SV176: $i] :
( ( ( SV176 = SV206 )
| ~ ( contains_slb @ SV140 @ SV206 )
| ! [SY440: $i] :
( ( remove_slb @ ( insert_slb @ SV140 @ ( pair @ SV176 @ SY440 ) ) @ SV206 )
= ( insert_slb @ ( remove_slb @ SV140 @ SV206 ) @ ( pair @ SV176 @ SY440 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(570,plain,
! [SV207: $i,SV177: $i,SV141: $i] :
( ( ( lookup_slb @ ( insert_slb @ SV141 @ ( pair @ SV177 @ SV207 ) ) @ SV177 )
= SV207 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(571,plain,
! [SV142: $i,SV208: $i,SV178: $i] :
( ( ( SV178 = SV208 )
| ~ ( contains_slb @ SV142 @ SV208 )
| ! [SY441: $i] :
( ( lookup_slb @ ( insert_slb @ SV142 @ ( pair @ SV178 @ SY441 ) ) @ SV208 )
= ( lookup_slb @ SV142 @ SV208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(572,plain,
! [SV179: $i,SV144: $i,SV209: $i] :
( ( ! [SY442: $i] :
( ~ ( strictly_less_than @ SY442 @ SV209 )
| ( ( update_slb @ ( insert_slb @ SV144 @ ( pair @ SV179 @ SY442 ) ) @ SV209 )
= ( insert_slb @ ( update_slb @ SV144 @ SV209 ) @ ( pair @ SV179 @ SV209 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(573,plain,
! [SV180: $i,SV145: $i,SV210: $i] :
( ( ! [SY443: $i] :
( ~ ( less_than @ SV210 @ SY443 )
| ( ( update_slb @ ( insert_slb @ SV145 @ ( pair @ SV180 @ SY443 ) ) @ SV210 )
= ( insert_slb @ ( update_slb @ SV145 @ SV210 ) @ ( pair @ SV180 @ SY443 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(574,plain,
! [SV181: $i,SV147: $i] :
( ( ( ~ ( succ_cpq @ SV147 @ SV181 ) )
= $true )
| ( ( ! [SY398: $i] : ( succ_cpq @ SV147 @ ( insert_cpq @ SV181 @ SY398 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[540]) ).
thf(575,plain,
! [SV182: $i,SV148: $i] :
( ( ( ~ ( succ_cpq @ SV148 @ SV182 ) )
= $true )
| ( ( ! [SY399: $i] : ( succ_cpq @ SV148 @ ( remove_cpq @ SV182 @ SY399 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[541]) ).
thf(576,plain,
! [SV183: $i,SV149: $i] :
( ( ( ~ ( succ_cpq @ SV149 @ SV183 ) )
= $true )
| ( ( succ_cpq @ SV149 @ ( findmin_cpq_eff @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[542]) ).
thf(577,plain,
! [SV184: $i,SV150: $i] :
( ( ( ~ ( succ_cpq @ SV150 @ SV184 ) )
= $true )
| ( ( succ_cpq @ SV150 @ ( removemin_cpq_eff @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(578,plain,
! [SV211: $i,SV186: $i,SV152: $i] :
( ( ! [SY444: $i,SY445: $i] :
( ~ ( strictly_less_than @ SY444 @ SY445 )
| ~ ( check_cpq @ ( triple @ SV152 @ ( insert_slb @ SV186 @ ( pair @ SY444 @ SY445 ) ) @ SV211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(579,plain,
! [SV187: $i,SV153: $i] :
( ( ok @ ( triple @ SV153 @ SV187 @ bad ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(580,plain,
! [SV212: $i,SV188: $i,SV154: $i] :
( ( ( ok @ ( triple @ SV154 @ SV188 @ SV212 ) )
| ( SV212 = bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(581,plain,
! [SV213: $i,SV189: $i,SV155: $i] :
( ( ! [SY446: $i] :
( ( insert_cpq @ ( triple @ SV155 @ SV189 @ SV213 ) @ SY446 )
= ( triple @ ( insert_pqp @ SV155 @ SY446 ) @ ( insert_slb @ SV189 @ ( pair @ SY446 @ bottom ) ) @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(582,plain,
! [SV214: $i,SV156: $i,SV190: $i] :
( ( ! [SY447: $i] :
( ( contains_slb @ SV190 @ SY447 )
| ( ( remove_cpq @ ( triple @ SV156 @ SV190 @ SV214 ) @ SY447 )
= ( triple @ SV156 @ SV190 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(583,plain,
! [SV215: $i,SV157: $i,SV191: $i] :
( ( ! [SY448: $i] :
( ~ ( contains_slb @ SV191 @ SY448 )
| ~ ( less_than @ ( lookup_slb @ SV191 @ SY448 ) @ SY448 )
| ( ( remove_cpq @ ( triple @ SV157 @ SV191 @ SV215 ) @ SY448 )
= ( triple @ ( remove_pqp @ SV157 @ SY448 ) @ ( remove_slb @ SV191 @ SY448 ) @ SV215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(584,plain,
! [SV216: $i,SV158: $i,SV192: $i] :
( ( ! [SY449: $i] :
( ~ ( contains_slb @ SV192 @ SY449 )
| ~ ( strictly_less_than @ SY449 @ ( lookup_slb @ SV192 @ SY449 ) )
| ( ( remove_cpq @ ( triple @ SV158 @ SV192 @ SV216 ) @ SY449 )
= ( triple @ ( remove_pqp @ SV158 @ SY449 ) @ ( remove_slb @ SV192 @ SY449 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(585,plain,
! [SV160: $i,SV194: $i] :
( ( ( ( SV194 = create_slb )
| ( contains_slb @ SV194 @ ( findmin_pqp_res @ SV160 ) ) )
= $true )
| ( ( ! [SY412: $i] :
( ( findmin_cpq_eff @ ( triple @ SV160 @ SV194 @ SY412 ) )
= ( triple @ SV160 @ ( update_slb @ SV194 @ ( findmin_pqp_res @ SV160 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(586,plain,
! [SV161: $i,SV195: $i] :
( ( ( ( SV195 = create_slb )
| ~ ( contains_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV161 ) @ ( lookup_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) ) ) )
= $true )
| ( ( ! [SY413: $i] :
( ( findmin_cpq_eff @ ( triple @ SV161 @ SV195 @ SY413 ) )
= ( triple @ SV161 @ ( update_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(587,plain,
! [SV162: $i,SV196: $i] :
( ( ( ( SV196 = create_slb )
| ~ ( contains_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) )
| ~ ( less_than @ ( lookup_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) ) @ ( findmin_pqp_res @ SV162 ) ) )
= $true )
| ( ( ! [SY414: $i] :
( ( findmin_cpq_eff @ ( triple @ SV162 @ SV196 @ SY414 ) )
= ( triple @ SV162 @ ( update_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) ) @ SY414 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[555]) ).
thf(588,plain,
! [SV164: $i,SV198: $i] :
( ( ( SV198 = create_slb )
= $true )
| ( ( ! [SY415: $i] :
( ( findmin_cpq_res @ ( triple @ SV164 @ SV198 @ SY415 ) )
= ( findmin_pqp_res @ SV164 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(589,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( less_than @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 )
| ( strictly_less_than @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[558]) ).
thf(590,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[559]) ).
thf(591,plain,
! [SV217: $i,SV199: $i,SV167: $i] :
( ( ~ ( ~ ! [SY450: $i,SY451: $i] :
( ~ ( less_than @ SY451 @ SY450 )
| ~ ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SV199 @ ( pair @ SY450 @ SY451 ) ) @ SV217 ) )
| ( check_cpq @ ( triple @ SV167 @ SV199 @ SV217 ) ) )
| ~ ! [SY452: $i,SY453: $i] :
( ~ ( less_than @ SY453 @ SY452 )
| ~ ( check_cpq @ ( triple @ SV167 @ SV199 @ SV217 ) )
| ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SV199 @ ( pair @ SY452 @ SY453 ) ) @ SV217 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(592,plain,
! [SV200: $i,SV168: $i] :
( ( ~ ! [SY421: $i] :
( ! [SY422: $i] :
~ ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY422 ) ) @ SY421 )
| ( SV200 = SY421 )
| ( contains_slb @ SV168 @ SY421 ) )
| ~ ~ ( ~ ! [SY423: $i] :
( ( SV200 != SY423 )
| ! [SY424: $i] : ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY424 ) ) @ SY423 ) )
| ~ ! [SY425: $i] :
( ~ ( contains_slb @ SV168 @ SY425 )
| ! [SY426: $i] : ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY426 ) ) @ SY425 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(593,plain,
! [SV218: $i,SV201: $i,SV169: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY454: $i,SY455: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY454 ) ) @ SV218 @ SY455 )
| ( SV201 = SV218 )
| ( pair_in_list @ SV169 @ SV218 @ SY455 ) )
| ~ ! [SY456: $i,SY457: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY456 ) ) @ SV218 @ SY457 )
| ( SY456 = SY457 )
| ( pair_in_list @ SV169 @ SV218 @ SY457 ) ) )
| ~ ~ ( ~ ! [SY458: $i,SY459: $i] :
( ( SV201 != SV218 )
| ( SY458 != SY459 )
| ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY458 ) ) @ SV218 @ SY459 ) )
| ~ ! [SY460: $i,SY461: $i] :
( ~ ( pair_in_list @ SV169 @ SV218 @ SY461 )
| ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY460 ) ) @ SV218 @ SY461 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(594,plain,
! [SV202: $i,SV170: $i] :
( ( ~ ! [SY436: $i,SY437: $i] :
( ~ ( contains_cpq @ ( triple @ SV170 @ SV202 @ SY436 ) @ SY437 )
| ( contains_slb @ SV202 @ SY437 ) )
| ~ ! [SY438: $i,SY439: $i] :
( ~ ( contains_slb @ SV202 @ SY439 )
| ( contains_cpq @ ( triple @ SV170 @ SV202 @ SY438 ) @ SY439 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(595,plain,
! [SV203: $i,SV171: $i,SV132: $i] :
( ( ( ~ ( less_than @ SV132 @ SV171 )
| ~ ( less_than @ SV171 @ SV203 ) )
= $true )
| ( ( less_than @ SV132 @ SV203 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[564]) ).
thf(596,plain,
! [SV140: $i,SV206: $i,SV176: $i] :
( ( ( ( SV176 = SV206 )
| ~ ( contains_slb @ SV140 @ SV206 ) )
= $true )
| ( ( ! [SY440: $i] :
( ( remove_slb @ ( insert_slb @ SV140 @ ( pair @ SV176 @ SY440 ) ) @ SV206 )
= ( insert_slb @ ( remove_slb @ SV140 @ SV206 ) @ ( pair @ SV176 @ SY440 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[569]) ).
thf(597,plain,
! [SV142: $i,SV208: $i,SV178: $i] :
( ( ( ( SV178 = SV208 )
| ~ ( contains_slb @ SV142 @ SV208 ) )
= $true )
| ( ( ! [SY441: $i] :
( ( lookup_slb @ ( insert_slb @ SV142 @ ( pair @ SV178 @ SY441 ) ) @ SV208 )
= ( lookup_slb @ SV142 @ SV208 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(598,plain,
! [SV179: $i,SV144: $i,SV209: $i,SV219: $i] :
( ( ~ ( strictly_less_than @ SV219 @ SV209 )
| ( ( update_slb @ ( insert_slb @ SV144 @ ( pair @ SV179 @ SV219 ) ) @ SV209 )
= ( insert_slb @ ( update_slb @ SV144 @ SV209 ) @ ( pair @ SV179 @ SV209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(599,plain,
! [SV180: $i,SV145: $i,SV220: $i,SV210: $i] :
( ( ~ ( less_than @ SV210 @ SV220 )
| ( ( update_slb @ ( insert_slb @ SV145 @ ( pair @ SV180 @ SV220 ) ) @ SV210 )
= ( insert_slb @ ( update_slb @ SV145 @ SV210 ) @ ( pair @ SV180 @ SV220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(600,plain,
! [SV181: $i,SV147: $i] :
( ( ( succ_cpq @ SV147 @ SV181 )
= $false )
| ( ( ! [SY398: $i] : ( succ_cpq @ SV147 @ ( insert_cpq @ SV181 @ SY398 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(601,plain,
! [SV182: $i,SV148: $i] :
( ( ( succ_cpq @ SV148 @ SV182 )
= $false )
| ( ( ! [SY399: $i] : ( succ_cpq @ SV148 @ ( remove_cpq @ SV182 @ SY399 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(602,plain,
! [SV183: $i,SV149: $i] :
( ( ( succ_cpq @ SV149 @ SV183 )
= $false )
| ( ( succ_cpq @ SV149 @ ( findmin_cpq_eff @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(603,plain,
! [SV184: $i,SV150: $i] :
( ( ( succ_cpq @ SV150 @ SV184 )
= $false )
| ( ( succ_cpq @ SV150 @ ( removemin_cpq_eff @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(604,plain,
! [SV211: $i,SV186: $i,SV152: $i,SV221: $i] :
( ( ! [SY462: $i] :
( ~ ( strictly_less_than @ SV221 @ SY462 )
| ~ ( check_cpq @ ( triple @ SV152 @ ( insert_slb @ SV186 @ ( pair @ SV221 @ SY462 ) ) @ SV211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(605,plain,
! [SV212: $i,SV188: $i,SV154: $i] :
( ( ( ok @ ( triple @ SV154 @ SV188 @ SV212 ) )
= $true )
| ( ( SV212 = bad )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[580]) ).
thf(606,plain,
! [SV222: $i,SV213: $i,SV189: $i,SV155: $i] :
( ( ( insert_cpq @ ( triple @ SV155 @ SV189 @ SV213 ) @ SV222 )
= ( triple @ ( insert_pqp @ SV155 @ SV222 ) @ ( insert_slb @ SV189 @ ( pair @ SV222 @ bottom ) ) @ SV213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(607,plain,
! [SV214: $i,SV156: $i,SV223: $i,SV190: $i] :
( ( ( contains_slb @ SV190 @ SV223 )
| ( ( remove_cpq @ ( triple @ SV156 @ SV190 @ SV214 ) @ SV223 )
= ( triple @ SV156 @ SV190 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(608,plain,
! [SV215: $i,SV157: $i,SV224: $i,SV191: $i] :
( ( ~ ( contains_slb @ SV191 @ SV224 )
| ~ ( less_than @ ( lookup_slb @ SV191 @ SV224 ) @ SV224 )
| ( ( remove_cpq @ ( triple @ SV157 @ SV191 @ SV215 ) @ SV224 )
= ( triple @ ( remove_pqp @ SV157 @ SV224 ) @ ( remove_slb @ SV191 @ SV224 ) @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(609,plain,
! [SV216: $i,SV158: $i,SV225: $i,SV192: $i] :
( ( ~ ( contains_slb @ SV192 @ SV225 )
| ~ ( strictly_less_than @ SV225 @ ( lookup_slb @ SV192 @ SV225 ) )
| ( ( remove_cpq @ ( triple @ SV158 @ SV192 @ SV216 ) @ SV225 )
= ( triple @ ( remove_pqp @ SV158 @ SV225 ) @ ( remove_slb @ SV192 @ SV225 ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(610,plain,
! [SV160: $i,SV194: $i] :
( ( ( SV194 = create_slb )
= $true )
| ( ( contains_slb @ SV194 @ ( findmin_pqp_res @ SV160 ) )
= $true )
| ( ( ! [SY412: $i] :
( ( findmin_cpq_eff @ ( triple @ SV160 @ SV194 @ SY412 ) )
= ( triple @ SV160 @ ( update_slb @ SV194 @ ( findmin_pqp_res @ SV160 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[585]) ).
thf(611,plain,
! [SV161: $i,SV195: $i] :
( ( ( ( SV195 = create_slb )
| ~ ( contains_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV161 ) @ ( lookup_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) ) ) )
= $true )
| ( ( ! [SY413: $i] :
( ( findmin_cpq_eff @ ( triple @ SV161 @ SV195 @ SY413 ) )
= ( triple @ SV161 @ ( update_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[586]) ).
thf(612,plain,
! [SV162: $i,SV196: $i] :
( ( ( ( SV196 = create_slb )
| ~ ( contains_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) ) @ ( findmin_pqp_res @ SV162 ) ) )
= $true )
| ( ( ! [SY414: $i] :
( ( findmin_cpq_eff @ ( triple @ SV162 @ SV196 @ SY414 ) )
= ( triple @ SV162 @ ( update_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) ) @ SY414 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[587]) ).
thf(613,plain,
! [SV226: $i,SV198: $i,SV164: $i] :
( ( ( ( findmin_cpq_res @ ( triple @ SV164 @ SV198 @ SV226 ) )
= ( findmin_pqp_res @ SV164 ) )
= $true )
| ( ( SV198 = create_slb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(614,plain,
! [SV227: $i] :
( ( ! [SY463: $i] :
( ~ ( less_than @ SV227 @ SY463 )
| ( less_than @ SY463 @ SV227 )
| ( strictly_less_than @ SV227 @ SY463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(615,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(616,plain,
! [SV217: $i,SV199: $i,SV167: $i] :
( ( ~ ! [SY450: $i,SY451: $i] :
( ~ ( less_than @ SY451 @ SY450 )
| ~ ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SV199 @ ( pair @ SY450 @ SY451 ) ) @ SV217 ) )
| ( check_cpq @ ( triple @ SV167 @ SV199 @ SV217 ) ) )
| ~ ! [SY452: $i,SY453: $i] :
( ~ ( less_than @ SY453 @ SY452 )
| ~ ( check_cpq @ ( triple @ SV167 @ SV199 @ SV217 ) )
| ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SV199 @ ( pair @ SY452 @ SY453 ) ) @ SV217 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[591]) ).
thf(617,plain,
! [SV200: $i,SV168: $i] :
( ( ~ ! [SY421: $i] :
( ! [SY422: $i] :
~ ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY422 ) ) @ SY421 )
| ( SV200 = SY421 )
| ( contains_slb @ SV168 @ SY421 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[592]) ).
thf(618,plain,
! [SV168: $i,SV200: $i] :
( ( ~ ~ ( ~ ! [SY423: $i] :
( ( SV200 != SY423 )
| ! [SY424: $i] : ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY424 ) ) @ SY423 ) )
| ~ ! [SY425: $i] :
( ~ ( contains_slb @ SV168 @ SY425 )
| ! [SY426: $i] : ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY426 ) ) @ SY425 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[592]) ).
thf(619,plain,
! [SV218: $i,SV201: $i,SV169: $i] :
( ( ~ ~ ( ~ ! [SY454: $i,SY455: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY454 ) ) @ SV218 @ SY455 )
| ( SV201 = SV218 )
| ( pair_in_list @ SV169 @ SV218 @ SY455 ) )
| ~ ! [SY456: $i,SY457: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY456 ) ) @ SV218 @ SY457 )
| ( SY456 = SY457 )
| ( pair_in_list @ SV169 @ SV218 @ SY457 ) ) )
| ~ ~ ( ~ ! [SY458: $i,SY459: $i] :
( ( SV201 != SV218 )
| ( SY458 != SY459 )
| ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY458 ) ) @ SV218 @ SY459 ) )
| ~ ! [SY460: $i,SY461: $i] :
( ~ ( pair_in_list @ SV169 @ SV218 @ SY461 )
| ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY460 ) ) @ SV218 @ SY461 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(620,plain,
! [SV202: $i,SV170: $i] :
( ( ~ ! [SY436: $i,SY437: $i] :
( ~ ( contains_cpq @ ( triple @ SV170 @ SV202 @ SY436 ) @ SY437 )
| ( contains_slb @ SV202 @ SY437 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[594]) ).
thf(621,plain,
! [SV170: $i,SV202: $i] :
( ( ~ ! [SY438: $i,SY439: $i] :
( ~ ( contains_slb @ SV202 @ SY439 )
| ( contains_cpq @ ( triple @ SV170 @ SV202 @ SY438 ) @ SY439 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[594]) ).
thf(622,plain,
! [SV203: $i,SV171: $i,SV132: $i] :
( ( ( ~ ( less_than @ SV132 @ SV171 ) )
= $true )
| ( ( ~ ( less_than @ SV171 @ SV203 ) )
= $true )
| ( ( less_than @ SV132 @ SV203 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[595]) ).
thf(623,plain,
! [SV140: $i,SV206: $i,SV176: $i] :
( ( ( SV176 = SV206 )
= $true )
| ( ( ~ ( contains_slb @ SV140 @ SV206 ) )
= $true )
| ( ( ! [SY440: $i] :
( ( remove_slb @ ( insert_slb @ SV140 @ ( pair @ SV176 @ SY440 ) ) @ SV206 )
= ( insert_slb @ ( remove_slb @ SV140 @ SV206 ) @ ( pair @ SV176 @ SY440 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(624,plain,
! [SV142: $i,SV208: $i,SV178: $i] :
( ( ( SV178 = SV208 )
= $true )
| ( ( ~ ( contains_slb @ SV142 @ SV208 ) )
= $true )
| ( ( ! [SY441: $i] :
( ( lookup_slb @ ( insert_slb @ SV142 @ ( pair @ SV178 @ SY441 ) ) @ SV208 )
= ( lookup_slb @ SV142 @ SV208 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(625,plain,
! [SV179: $i,SV144: $i,SV209: $i,SV219: $i] :
( ( ( ~ ( strictly_less_than @ SV219 @ SV209 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV144 @ ( pair @ SV179 @ SV219 ) ) @ SV209 )
= ( insert_slb @ ( update_slb @ SV144 @ SV209 ) @ ( pair @ SV179 @ SV209 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(626,plain,
! [SV180: $i,SV145: $i,SV220: $i,SV210: $i] :
( ( ( ~ ( less_than @ SV210 @ SV220 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV145 @ ( pair @ SV180 @ SV220 ) ) @ SV210 )
= ( insert_slb @ ( update_slb @ SV145 @ SV210 ) @ ( pair @ SV180 @ SV220 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[599]) ).
thf(627,plain,
! [SV228: $i,SV181: $i,SV147: $i] :
( ( ( succ_cpq @ SV147 @ ( insert_cpq @ SV181 @ SV228 ) )
= $true )
| ( ( succ_cpq @ SV147 @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(628,plain,
! [SV229: $i,SV182: $i,SV148: $i] :
( ( ( succ_cpq @ SV148 @ ( remove_cpq @ SV182 @ SV229 ) )
= $true )
| ( ( succ_cpq @ SV148 @ SV182 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(629,plain,
! [SV211: $i,SV186: $i,SV152: $i,SV230: $i,SV221: $i] :
( ( ~ ( strictly_less_than @ SV221 @ SV230 )
| ~ ( check_cpq @ ( triple @ SV152 @ ( insert_slb @ SV186 @ ( pair @ SV221 @ SV230 ) ) @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(630,plain,
! [SV214: $i,SV156: $i,SV223: $i,SV190: $i] :
( ( ( contains_slb @ SV190 @ SV223 )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV156 @ SV190 @ SV214 ) @ SV223 )
= ( triple @ SV156 @ SV190 @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[607]) ).
thf(631,plain,
! [SV215: $i,SV157: $i,SV224: $i,SV191: $i] :
( ( ( ~ ( contains_slb @ SV191 @ SV224 )
| ~ ( less_than @ ( lookup_slb @ SV191 @ SV224 ) @ SV224 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV157 @ SV191 @ SV215 ) @ SV224 )
= ( triple @ ( remove_pqp @ SV157 @ SV224 ) @ ( remove_slb @ SV191 @ SV224 ) @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(632,plain,
! [SV216: $i,SV158: $i,SV225: $i,SV192: $i] :
( ( ( ~ ( contains_slb @ SV192 @ SV225 )
| ~ ( strictly_less_than @ SV225 @ ( lookup_slb @ SV192 @ SV225 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV158 @ SV192 @ SV216 ) @ SV225 )
= ( triple @ ( remove_pqp @ SV158 @ SV225 ) @ ( remove_slb @ SV192 @ SV225 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[609]) ).
thf(633,plain,
! [SV231: $i,SV194: $i,SV160: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV160 @ SV194 @ SV231 ) )
= ( triple @ SV160 @ ( update_slb @ SV194 @ ( findmin_pqp_res @ SV160 ) ) @ bad ) )
= $true )
| ( ( contains_slb @ SV194 @ ( findmin_pqp_res @ SV160 ) )
= $true )
| ( ( SV194 = create_slb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(634,plain,
! [SV161: $i,SV195: $i] :
( ( ( SV195 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV161 ) @ ( lookup_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) ) ) )
= $true )
| ( ( ! [SY413: $i] :
( ( findmin_cpq_eff @ ( triple @ SV161 @ SV195 @ SY413 ) )
= ( triple @ SV161 @ ( update_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(635,plain,
! [SV162: $i,SV196: $i] :
( ( ( SV196 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) ) @ ( findmin_pqp_res @ SV162 ) ) )
= $true )
| ( ( ! [SY414: $i] :
( ( findmin_cpq_eff @ ( triple @ SV162 @ SV196 @ SY414 ) )
= ( triple @ SV162 @ ( update_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) ) @ SY414 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(636,plain,
! [SV232: $i,SV227: $i] :
( ( ~ ( less_than @ SV227 @ SV232 )
| ( less_than @ SV232 @ SV227 )
| ( strictly_less_than @ SV227 @ SV232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(637,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[615]) ).
thf(638,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[615]) ).
thf(639,plain,
! [SV217: $i,SV199: $i,SV167: $i] :
( ( ~ ! [SY450: $i,SY451: $i] :
( ~ ( less_than @ SY451 @ SY450 )
| ~ ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SV199 @ ( pair @ SY450 @ SY451 ) ) @ SV217 ) )
| ( check_cpq @ ( triple @ SV167 @ SV199 @ SV217 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[616]) ).
thf(640,plain,
! [SV217: $i,SV199: $i,SV167: $i] :
( ( ~ ! [SY452: $i,SY453: $i] :
( ~ ( less_than @ SY453 @ SY452 )
| ~ ( check_cpq @ ( triple @ SV167 @ SV199 @ SV217 ) )
| ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SV199 @ ( pair @ SY452 @ SY453 ) ) @ SV217 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[616]) ).
thf(641,plain,
! [SV200: $i,SV168: $i] :
( ( ! [SY421: $i] :
( ! [SY422: $i] :
~ ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY422 ) ) @ SY421 )
| ( SV200 = SY421 )
| ( contains_slb @ SV168 @ SY421 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[617]) ).
thf(642,plain,
! [SV168: $i,SV200: $i] :
( ( ~ ( ~ ! [SY423: $i] :
( ( SV200 != SY423 )
| ! [SY424: $i] : ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY424 ) ) @ SY423 ) )
| ~ ! [SY425: $i] :
( ~ ( contains_slb @ SV168 @ SY425 )
| ! [SY426: $i] : ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY426 ) ) @ SY425 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[618]) ).
thf(643,plain,
! [SV218: $i,SV201: $i,SV169: $i] :
( ( ~ ~ ( ~ ! [SY454: $i,SY455: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY454 ) ) @ SV218 @ SY455 )
| ( SV201 = SV218 )
| ( pair_in_list @ SV169 @ SV218 @ SY455 ) )
| ~ ! [SY456: $i,SY457: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY456 ) ) @ SV218 @ SY457 )
| ( SY456 = SY457 )
| ( pair_in_list @ SV169 @ SV218 @ SY457 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[619]) ).
thf(644,plain,
! [SV169: $i,SV218: $i,SV201: $i] :
( ( ~ ~ ( ~ ! [SY458: $i,SY459: $i] :
( ( SV201 != SV218 )
| ( SY458 != SY459 )
| ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY458 ) ) @ SV218 @ SY459 ) )
| ~ ! [SY460: $i,SY461: $i] :
( ~ ( pair_in_list @ SV169 @ SV218 @ SY461 )
| ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY460 ) ) @ SV218 @ SY461 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[619]) ).
thf(645,plain,
! [SV202: $i,SV170: $i] :
( ( ! [SY436: $i,SY437: $i] :
( ~ ( contains_cpq @ ( triple @ SV170 @ SV202 @ SY436 ) @ SY437 )
| ( contains_slb @ SV202 @ SY437 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[620]) ).
thf(646,plain,
! [SV170: $i,SV202: $i] :
( ( ! [SY438: $i,SY439: $i] :
( ~ ( contains_slb @ SV202 @ SY439 )
| ( contains_cpq @ ( triple @ SV170 @ SV202 @ SY438 ) @ SY439 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[621]) ).
thf(647,plain,
! [SV203: $i,SV171: $i,SV132: $i] :
( ( ( less_than @ SV132 @ SV171 )
= $false )
| ( ( ~ ( less_than @ SV171 @ SV203 ) )
= $true )
| ( ( less_than @ SV132 @ SV203 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(648,plain,
! [SV176: $i,SV206: $i,SV140: $i] :
( ( ( contains_slb @ SV140 @ SV206 )
= $false )
| ( ( SV176 = SV206 )
= $true )
| ( ( ! [SY440: $i] :
( ( remove_slb @ ( insert_slb @ SV140 @ ( pair @ SV176 @ SY440 ) ) @ SV206 )
= ( insert_slb @ ( remove_slb @ SV140 @ SV206 ) @ ( pair @ SV176 @ SY440 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(649,plain,
! [SV178: $i,SV208: $i,SV142: $i] :
( ( ( contains_slb @ SV142 @ SV208 )
= $false )
| ( ( SV178 = SV208 )
= $true )
| ( ( ! [SY441: $i] :
( ( lookup_slb @ ( insert_slb @ SV142 @ ( pair @ SV178 @ SY441 ) ) @ SV208 )
= ( lookup_slb @ SV142 @ SV208 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(650,plain,
! [SV179: $i,SV144: $i,SV209: $i,SV219: $i] :
( ( ( strictly_less_than @ SV219 @ SV209 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV144 @ ( pair @ SV179 @ SV219 ) ) @ SV209 )
= ( insert_slb @ ( update_slb @ SV144 @ SV209 ) @ ( pair @ SV179 @ SV209 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(651,plain,
! [SV180: $i,SV145: $i,SV220: $i,SV210: $i] :
( ( ( less_than @ SV210 @ SV220 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV145 @ ( pair @ SV180 @ SV220 ) ) @ SV210 )
= ( insert_slb @ ( update_slb @ SV145 @ SV210 ) @ ( pair @ SV180 @ SV220 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(652,plain,
! [SV211: $i,SV186: $i,SV152: $i,SV230: $i,SV221: $i] :
( ( ( ~ ( strictly_less_than @ SV221 @ SV230 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV152 @ ( insert_slb @ SV186 @ ( pair @ SV221 @ SV230 ) ) @ SV211 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[629]) ).
thf(653,plain,
! [SV215: $i,SV157: $i,SV224: $i,SV191: $i] :
( ( ( ~ ( contains_slb @ SV191 @ SV224 ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV191 @ SV224 ) @ SV224 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV157 @ SV191 @ SV215 ) @ SV224 )
= ( triple @ ( remove_pqp @ SV157 @ SV224 ) @ ( remove_slb @ SV191 @ SV224 ) @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[631]) ).
thf(654,plain,
! [SV216: $i,SV158: $i,SV225: $i,SV192: $i] :
( ( ( ~ ( contains_slb @ SV192 @ SV225 ) )
= $true )
| ( ( ~ ( strictly_less_than @ SV225 @ ( lookup_slb @ SV192 @ SV225 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV158 @ SV192 @ SV216 ) @ SV225 )
= ( triple @ ( remove_pqp @ SV158 @ SV225 ) @ ( remove_slb @ SV192 @ SV225 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[632]) ).
thf(655,plain,
! [SV161: $i,SV195: $i] :
( ( ( contains_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) )
= $false )
| ( ( SV195 = create_slb )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV161 ) @ ( lookup_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) ) ) )
= $true )
| ( ( ! [SY413: $i] :
( ( findmin_cpq_eff @ ( triple @ SV161 @ SV195 @ SY413 ) )
= ( triple @ SV161 @ ( update_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[634]) ).
thf(656,plain,
! [SV162: $i,SV196: $i] :
( ( ( contains_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) )
= $false )
| ( ( SV196 = create_slb )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) ) @ ( findmin_pqp_res @ SV162 ) ) )
= $true )
| ( ( ! [SY414: $i] :
( ( findmin_cpq_eff @ ( triple @ SV162 @ SV196 @ SY414 ) )
= ( triple @ SV162 @ ( update_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) ) @ SY414 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(657,plain,
! [SV232: $i,SV227: $i] :
( ( ( ~ ( less_than @ SV227 @ SV232 )
| ( less_than @ SV232 @ SV227 ) )
= $true )
| ( ( strictly_less_than @ SV227 @ SV232 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[636]) ).
thf(658,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[637]) ).
thf(659,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[638]) ).
thf(660,plain,
! [SV217: $i,SV199: $i,SV167: $i] :
( ( ! [SY450: $i,SY451: $i] :
( ~ ( less_than @ SY451 @ SY450 )
| ~ ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SV199 @ ( pair @ SY450 @ SY451 ) ) @ SV217 ) )
| ( check_cpq @ ( triple @ SV167 @ SV199 @ SV217 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[639]) ).
thf(661,plain,
! [SV217: $i,SV199: $i,SV167: $i] :
( ( ! [SY452: $i,SY453: $i] :
( ~ ( less_than @ SY453 @ SY452 )
| ~ ( check_cpq @ ( triple @ SV167 @ SV199 @ SV217 ) )
| ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SV199 @ ( pair @ SY452 @ SY453 ) ) @ SV217 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[640]) ).
thf(662,plain,
! [SV233: $i,SV200: $i,SV168: $i] :
( ( ! [SY464: $i] :
~ ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY464 ) ) @ SV233 )
| ( SV200 = SV233 )
| ( contains_slb @ SV168 @ SV233 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(663,plain,
! [SV168: $i,SV200: $i] :
( ( ~ ! [SY423: $i] :
( ( SV200 != SY423 )
| ! [SY424: $i] : ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY424 ) ) @ SY423 ) )
| ~ ! [SY425: $i] :
( ~ ( contains_slb @ SV168 @ SY425 )
| ! [SY426: $i] : ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY426 ) ) @ SY425 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[642]) ).
thf(664,plain,
! [SV218: $i,SV201: $i,SV169: $i] :
( ( ~ ( ~ ! [SY454: $i,SY455: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY454 ) ) @ SV218 @ SY455 )
| ( SV201 = SV218 )
| ( pair_in_list @ SV169 @ SV218 @ SY455 ) )
| ~ ! [SY456: $i,SY457: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY456 ) ) @ SV218 @ SY457 )
| ( SY456 = SY457 )
| ( pair_in_list @ SV169 @ SV218 @ SY457 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[643]) ).
thf(665,plain,
! [SV169: $i,SV218: $i,SV201: $i] :
( ( ~ ( ~ ! [SY458: $i,SY459: $i] :
( ( SV201 != SV218 )
| ( SY458 != SY459 )
| ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY458 ) ) @ SV218 @ SY459 ) )
| ~ ! [SY460: $i,SY461: $i] :
( ~ ( pair_in_list @ SV169 @ SV218 @ SY461 )
| ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY460 ) ) @ SV218 @ SY461 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[644]) ).
thf(666,plain,
! [SV234: $i,SV202: $i,SV170: $i] :
( ( ! [SY465: $i] :
( ~ ( contains_cpq @ ( triple @ SV170 @ SV202 @ SV234 ) @ SY465 )
| ( contains_slb @ SV202 @ SY465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(667,plain,
! [SV235: $i,SV170: $i,SV202: $i] :
( ( ! [SY466: $i] :
( ~ ( contains_slb @ SV202 @ SY466 )
| ( contains_cpq @ ( triple @ SV170 @ SV202 @ SV235 ) @ SY466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(668,plain,
! [SV132: $i,SV203: $i,SV171: $i] :
( ( ( less_than @ SV171 @ SV203 )
= $false )
| ( ( less_than @ SV132 @ SV171 )
= $false )
| ( ( less_than @ SV132 @ SV203 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[647]) ).
thf(669,plain,
! [SV206: $i,SV236: $i,SV176: $i,SV140: $i] :
( ( ( ( remove_slb @ ( insert_slb @ SV140 @ ( pair @ SV176 @ SV236 ) ) @ SV206 )
= ( insert_slb @ ( remove_slb @ SV140 @ SV206 ) @ ( pair @ SV176 @ SV236 ) ) )
= $true )
| ( ( SV176 = SV206 )
= $true )
| ( ( contains_slb @ SV140 @ SV206 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(670,plain,
! [SV208: $i,SV237: $i,SV178: $i,SV142: $i] :
( ( ( ( lookup_slb @ ( insert_slb @ SV142 @ ( pair @ SV178 @ SV237 ) ) @ SV208 )
= ( lookup_slb @ SV142 @ SV208 ) )
= $true )
| ( ( SV178 = SV208 )
= $true )
| ( ( contains_slb @ SV142 @ SV208 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(671,plain,
! [SV211: $i,SV186: $i,SV152: $i,SV230: $i,SV221: $i] :
( ( ( strictly_less_than @ SV221 @ SV230 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV152 @ ( insert_slb @ SV186 @ ( pair @ SV221 @ SV230 ) ) @ SV211 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(672,plain,
! [SV215: $i,SV157: $i,SV224: $i,SV191: $i] :
( ( ( contains_slb @ SV191 @ SV224 )
= $false )
| ( ( ~ ( less_than @ ( lookup_slb @ SV191 @ SV224 ) @ SV224 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV157 @ SV191 @ SV215 ) @ SV224 )
= ( triple @ ( remove_pqp @ SV157 @ SV224 ) @ ( remove_slb @ SV191 @ SV224 ) @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[653]) ).
thf(673,plain,
! [SV216: $i,SV158: $i,SV225: $i,SV192: $i] :
( ( ( contains_slb @ SV192 @ SV225 )
= $false )
| ( ( ~ ( strictly_less_than @ SV225 @ ( lookup_slb @ SV192 @ SV225 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV158 @ SV192 @ SV216 ) @ SV225 )
= ( triple @ ( remove_pqp @ SV158 @ SV225 ) @ ( remove_slb @ SV192 @ SV225 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(674,plain,
! [SV195: $i,SV161: $i] :
( ( ( strictly_less_than @ ( findmin_pqp_res @ SV161 ) @ ( lookup_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) ) )
= $false )
| ( ( SV195 = create_slb )
= $true )
| ( ( contains_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) )
= $false )
| ( ( ! [SY413: $i] :
( ( findmin_cpq_eff @ ( triple @ SV161 @ SV195 @ SY413 ) )
= ( triple @ SV161 @ ( update_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(675,plain,
! [SV162: $i,SV196: $i] :
( ( ( less_than @ ( lookup_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) ) @ ( findmin_pqp_res @ SV162 ) )
= $false )
| ( ( SV196 = create_slb )
= $true )
| ( ( contains_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) )
= $false )
| ( ( ! [SY414: $i] :
( ( findmin_cpq_eff @ ( triple @ SV162 @ SV196 @ SY414 ) )
= ( triple @ SV162 @ ( update_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) ) @ SY414 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(676,plain,
! [SV232: $i,SV227: $i] :
( ( ( ~ ( less_than @ SV227 @ SV232 ) )
= $true )
| ( ( less_than @ SV232 @ SV227 )
= $true )
| ( ( strictly_less_than @ SV227 @ SV232 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[657]) ).
thf(677,plain,
! [SV238: $i] :
( ( ! [SY467: $i] :
( ~ ( strictly_less_than @ SV238 @ SY467 )
| ( less_than @ SV238 @ SY467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(678,plain,
! [SV239: $i] :
( ( ! [SY468: $i] :
( ~ ( strictly_less_than @ SV239 @ SY468 )
| ~ ( less_than @ SY468 @ SV239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(679,plain,
! [SV217: $i,SV199: $i,SV167: $i,SV240: $i] :
( ( ! [SY469: $i] :
( ~ ( less_than @ SY469 @ SV240 )
| ~ ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SV199 @ ( pair @ SV240 @ SY469 ) ) @ SV217 ) )
| ( check_cpq @ ( triple @ SV167 @ SV199 @ SV217 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(680,plain,
! [SV217: $i,SV199: $i,SV167: $i,SV241: $i] :
( ( ! [SY470: $i] :
( ~ ( less_than @ SY470 @ SV241 )
| ~ ( check_cpq @ ( triple @ SV167 @ SV199 @ SV217 ) )
| ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SV199 @ ( pair @ SV241 @ SY470 ) ) @ SV217 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(681,plain,
! [SV233: $i,SV200: $i,SV168: $i] :
( ( ( ! [SY464: $i] :
~ ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY464 ) ) @ SV233 ) )
= $true )
| ( ( ( SV200 = SV233 )
| ( contains_slb @ SV168 @ SV233 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[662]) ).
thf(682,plain,
! [SV168: $i,SV200: $i] :
( ( ~ ! [SY423: $i] :
( ( SV200 != SY423 )
| ! [SY424: $i] : ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY424 ) ) @ SY423 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[663]) ).
thf(683,plain,
! [SV200: $i,SV168: $i] :
( ( ~ ! [SY425: $i] :
( ~ ( contains_slb @ SV168 @ SY425 )
| ! [SY426: $i] : ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY426 ) ) @ SY425 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[663]) ).
thf(684,plain,
! [SV218: $i,SV201: $i,SV169: $i] :
( ( ~ ! [SY454: $i,SY455: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY454 ) ) @ SV218 @ SY455 )
| ( SV201 = SV218 )
| ( pair_in_list @ SV169 @ SV218 @ SY455 ) )
| ~ ! [SY456: $i,SY457: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY456 ) ) @ SV218 @ SY457 )
| ( SY456 = SY457 )
| ( pair_in_list @ SV169 @ SV218 @ SY457 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(685,plain,
! [SV169: $i,SV218: $i,SV201: $i] :
( ( ~ ! [SY458: $i,SY459: $i] :
( ( SV201 != SV218 )
| ( SY458 != SY459 )
| ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY458 ) ) @ SV218 @ SY459 ) )
| ~ ! [SY460: $i,SY461: $i] :
( ~ ( pair_in_list @ SV169 @ SV218 @ SY461 )
| ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY460 ) ) @ SV218 @ SY461 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(686,plain,
! [SV242: $i,SV234: $i,SV202: $i,SV170: $i] :
( ( ~ ( contains_cpq @ ( triple @ SV170 @ SV202 @ SV234 ) @ SV242 )
| ( contains_slb @ SV202 @ SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(687,plain,
! [SV235: $i,SV170: $i,SV243: $i,SV202: $i] :
( ( ~ ( contains_slb @ SV202 @ SV243 )
| ( contains_cpq @ ( triple @ SV170 @ SV202 @ SV235 ) @ SV243 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(688,plain,
! [SV211: $i,SV230: $i,SV221: $i,SV186: $i,SV152: $i] :
( ( ( check_cpq @ ( triple @ SV152 @ ( insert_slb @ SV186 @ ( pair @ SV221 @ SV230 ) ) @ SV211 ) )
= $false )
| ( ( strictly_less_than @ SV221 @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(689,plain,
! [SV215: $i,SV157: $i,SV224: $i,SV191: $i] :
( ( ( less_than @ ( lookup_slb @ SV191 @ SV224 ) @ SV224 )
= $false )
| ( ( contains_slb @ SV191 @ SV224 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV157 @ SV191 @ SV215 ) @ SV224 )
= ( triple @ ( remove_pqp @ SV157 @ SV224 ) @ ( remove_slb @ SV191 @ SV224 ) @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(690,plain,
! [SV216: $i,SV158: $i,SV192: $i,SV225: $i] :
( ( ( strictly_less_than @ SV225 @ ( lookup_slb @ SV192 @ SV225 ) )
= $false )
| ( ( contains_slb @ SV192 @ SV225 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV158 @ SV192 @ SV216 ) @ SV225 )
= ( triple @ ( remove_pqp @ SV158 @ SV225 ) @ ( remove_slb @ SV192 @ SV225 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(691,plain,
! [SV244: $i,SV195: $i,SV161: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV161 @ SV195 @ SV244 ) )
= ( triple @ SV161 @ ( update_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) ) @ bad ) )
= $true )
| ( ( contains_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) )
= $false )
| ( ( SV195 = create_slb )
= $true )
| ( ( strictly_less_than @ ( findmin_pqp_res @ SV161 ) @ ( lookup_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(692,plain,
! [SV245: $i,SV196: $i,SV162: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV162 @ SV196 @ SV245 ) )
= ( triple @ SV162 @ ( update_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) ) @ SV245 ) )
= $true )
| ( ( contains_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) )
= $false )
| ( ( SV196 = create_slb )
= $true )
| ( ( less_than @ ( lookup_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) ) @ ( findmin_pqp_res @ SV162 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(693,plain,
! [SV232: $i,SV227: $i] :
( ( ( less_than @ SV227 @ SV232 )
= $false )
| ( ( less_than @ SV232 @ SV227 )
= $true )
| ( ( strictly_less_than @ SV227 @ SV232 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(694,plain,
! [SV246: $i,SV238: $i] :
( ( ~ ( strictly_less_than @ SV238 @ SV246 )
| ( less_than @ SV238 @ SV246 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(695,plain,
! [SV247: $i,SV239: $i] :
( ( ~ ( strictly_less_than @ SV239 @ SV247 )
| ~ ( less_than @ SV247 @ SV239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(696,plain,
! [SV217: $i,SV199: $i,SV167: $i,SV240: $i,SV248: $i] :
( ( ~ ( less_than @ SV248 @ SV240 )
| ~ ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SV199 @ ( pair @ SV240 @ SV248 ) ) @ SV217 ) )
| ( check_cpq @ ( triple @ SV167 @ SV199 @ SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(697,plain,
! [SV217: $i,SV199: $i,SV167: $i,SV241: $i,SV249: $i] :
( ( ~ ( less_than @ SV249 @ SV241 )
| ~ ( check_cpq @ ( triple @ SV167 @ SV199 @ SV217 ) )
| ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SV199 @ ( pair @ SV241 @ SV249 ) ) @ SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(698,plain,
! [SV233: $i,SV250: $i,SV200: $i,SV168: $i] :
( ( ( ~ ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV250 ) ) @ SV233 ) )
= $true )
| ( ( ( SV200 = SV233 )
| ( contains_slb @ SV168 @ SV233 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(699,plain,
! [SV168: $i,SV200: $i] :
( ( ! [SY423: $i] :
( ( SV200 != SY423 )
| ! [SY424: $i] : ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY424 ) ) @ SY423 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[682]) ).
thf(700,plain,
! [SV200: $i,SV168: $i] :
( ( ! [SY425: $i] :
( ~ ( contains_slb @ SV168 @ SY425 )
| ! [SY426: $i] : ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY426 ) ) @ SY425 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[683]) ).
thf(701,plain,
! [SV218: $i,SV201: $i,SV169: $i] :
( ( ~ ! [SY454: $i,SY455: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY454 ) ) @ SV218 @ SY455 )
| ( SV201 = SV218 )
| ( pair_in_list @ SV169 @ SV218 @ SY455 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(702,plain,
! [SV218: $i,SV201: $i,SV169: $i] :
( ( ~ ! [SY456: $i,SY457: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY456 ) ) @ SV218 @ SY457 )
| ( SY456 = SY457 )
| ( pair_in_list @ SV169 @ SV218 @ SY457 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[684]) ).
thf(703,plain,
! [SV169: $i,SV218: $i,SV201: $i] :
( ( ~ ! [SY458: $i,SY459: $i] :
( ( SV201 != SV218 )
| ( SY458 != SY459 )
| ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY458 ) ) @ SV218 @ SY459 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(704,plain,
! [SV201: $i,SV218: $i,SV169: $i] :
( ( ~ ! [SY460: $i,SY461: $i] :
( ~ ( pair_in_list @ SV169 @ SV218 @ SY461 )
| ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY460 ) ) @ SV218 @ SY461 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(705,plain,
! [SV242: $i,SV234: $i,SV202: $i,SV170: $i] :
( ( ( ~ ( contains_cpq @ ( triple @ SV170 @ SV202 @ SV234 ) @ SV242 ) )
= $true )
| ( ( contains_slb @ SV202 @ SV242 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[686]) ).
thf(706,plain,
! [SV235: $i,SV170: $i,SV243: $i,SV202: $i] :
( ( ( ~ ( contains_slb @ SV202 @ SV243 ) )
= $true )
| ( ( contains_cpq @ ( triple @ SV170 @ SV202 @ SV235 ) @ SV243 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[687]) ).
thf(707,plain,
! [SV246: $i,SV238: $i] :
( ( ( ~ ( strictly_less_than @ SV238 @ SV246 ) )
= $true )
| ( ( less_than @ SV238 @ SV246 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[694]) ).
thf(708,plain,
! [SV247: $i,SV239: $i] :
( ( ( ~ ( strictly_less_than @ SV239 @ SV247 ) )
= $true )
| ( ( ~ ( less_than @ SV247 @ SV239 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[695]) ).
thf(709,plain,
! [SV217: $i,SV199: $i,SV167: $i,SV240: $i,SV248: $i] :
( ( ( ~ ( less_than @ SV248 @ SV240 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SV199 @ ( pair @ SV240 @ SV248 ) ) @ SV217 ) )
| ( check_cpq @ ( triple @ SV167 @ SV199 @ SV217 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[696]) ).
thf(710,plain,
! [SV217: $i,SV199: $i,SV167: $i,SV241: $i,SV249: $i] :
( ( ( ~ ( less_than @ SV249 @ SV241 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV167 @ SV199 @ SV217 ) )
| ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SV199 @ ( pair @ SV241 @ SV249 ) ) @ SV217 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[697]) ).
thf(711,plain,
! [SV233: $i,SV250: $i,SV200: $i,SV168: $i] :
( ( ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV250 ) ) @ SV233 )
= $false )
| ( ( ( SV200 = SV233 )
| ( contains_slb @ SV168 @ SV233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(712,plain,
! [SV168: $i,SV251: $i,SV200: $i] :
( ( ( SV200 != SV251 )
| ! [SY471: $i] : ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY471 ) ) @ SV251 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(713,plain,
! [SV200: $i,SV252: $i,SV168: $i] :
( ( ~ ( contains_slb @ SV168 @ SV252 )
| ! [SY472: $i] : ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY472 ) ) @ SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(714,plain,
! [SV218: $i,SV201: $i,SV169: $i] :
( ( ! [SY454: $i,SY455: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY454 ) ) @ SV218 @ SY455 )
| ( SV201 = SV218 )
| ( pair_in_list @ SV169 @ SV218 @ SY455 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[701]) ).
thf(715,plain,
! [SV218: $i,SV201: $i,SV169: $i] :
( ( ! [SY456: $i,SY457: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY456 ) ) @ SV218 @ SY457 )
| ( SY456 = SY457 )
| ( pair_in_list @ SV169 @ SV218 @ SY457 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[702]) ).
thf(716,plain,
! [SV169: $i,SV218: $i,SV201: $i] :
( ( ! [SY458: $i,SY459: $i] :
( ( SV201 != SV218 )
| ( SY458 != SY459 )
| ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY458 ) ) @ SV218 @ SY459 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[703]) ).
thf(717,plain,
! [SV201: $i,SV218: $i,SV169: $i] :
( ( ! [SY460: $i,SY461: $i] :
( ~ ( pair_in_list @ SV169 @ SV218 @ SY461 )
| ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY460 ) ) @ SV218 @ SY461 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[704]) ).
thf(718,plain,
! [SV242: $i,SV234: $i,SV202: $i,SV170: $i] :
( ( ( contains_cpq @ ( triple @ SV170 @ SV202 @ SV234 ) @ SV242 )
= $false )
| ( ( contains_slb @ SV202 @ SV242 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(719,plain,
! [SV235: $i,SV170: $i,SV243: $i,SV202: $i] :
( ( ( contains_slb @ SV202 @ SV243 )
= $false )
| ( ( contains_cpq @ ( triple @ SV170 @ SV202 @ SV235 ) @ SV243 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(720,plain,
! [SV246: $i,SV238: $i] :
( ( ( strictly_less_than @ SV238 @ SV246 )
= $false )
| ( ( less_than @ SV238 @ SV246 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(721,plain,
! [SV247: $i,SV239: $i] :
( ( ( strictly_less_than @ SV239 @ SV247 )
= $false )
| ( ( ~ ( less_than @ SV247 @ SV239 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(722,plain,
! [SV217: $i,SV199: $i,SV167: $i,SV240: $i,SV248: $i] :
( ( ( less_than @ SV248 @ SV240 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SV199 @ ( pair @ SV240 @ SV248 ) ) @ SV217 ) )
| ( check_cpq @ ( triple @ SV167 @ SV199 @ SV217 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[709]) ).
thf(723,plain,
! [SV217: $i,SV199: $i,SV167: $i,SV241: $i,SV249: $i] :
( ( ( less_than @ SV249 @ SV241 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV167 @ SV199 @ SV217 ) )
| ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SV199 @ ( pair @ SV241 @ SV249 ) ) @ SV217 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(724,plain,
! [SV250: $i,SV168: $i,SV233: $i,SV200: $i] :
( ( ( SV200 = SV233 )
= $true )
| ( ( contains_slb @ SV168 @ SV233 )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV250 ) ) @ SV233 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[711]) ).
thf(725,plain,
! [SV168: $i,SV251: $i,SV200: $i] :
( ( ( ( SV200 != SV251 ) )
= $true )
| ( ( ! [SY471: $i] : ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY471 ) ) @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[712]) ).
thf(726,plain,
! [SV200: $i,SV252: $i,SV168: $i] :
( ( ( ~ ( contains_slb @ SV168 @ SV252 ) )
= $true )
| ( ( ! [SY472: $i] : ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY472 ) ) @ SV252 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[713]) ).
thf(727,plain,
! [SV218: $i,SV253: $i,SV201: $i,SV169: $i] :
( ( ! [SY473: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV253 ) ) @ SV218 @ SY473 )
| ( SV201 = SV218 )
| ( pair_in_list @ SV169 @ SV218 @ SY473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(728,plain,
! [SV218: $i,SV254: $i,SV201: $i,SV169: $i] :
( ( ! [SY474: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV254 ) ) @ SV218 @ SY474 )
| ( SV254 = SY474 )
| ( pair_in_list @ SV169 @ SV218 @ SY474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(729,plain,
! [SV169: $i,SV255: $i,SV218: $i,SV201: $i] :
( ( ! [SY475: $i] :
( ( SV201 != SV218 )
| ( SV255 != SY475 )
| ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV255 ) ) @ SV218 @ SY475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(730,plain,
! [SV256: $i,SV201: $i,SV218: $i,SV169: $i] :
( ( ! [SY476: $i] :
( ~ ( pair_in_list @ SV169 @ SV218 @ SY476 )
| ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV256 ) ) @ SV218 @ SY476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(731,plain,
! [SV239: $i,SV247: $i] :
( ( ( less_than @ SV247 @ SV239 )
= $false )
| ( ( strictly_less_than @ SV239 @ SV247 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(732,plain,
! [SV217: $i,SV248: $i,SV240: $i,SV199: $i,SV167: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SV199 @ ( pair @ SV240 @ SV248 ) ) @ SV217 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV167 @ SV199 @ SV217 ) )
= $true )
| ( ( less_than @ SV248 @ SV240 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[722]) ).
thf(733,plain,
! [SV249: $i,SV241: $i,SV217: $i,SV199: $i,SV167: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV167 @ SV199 @ SV217 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SV199 @ ( pair @ SV241 @ SV249 ) ) @ SV217 ) )
= $true )
| ( ( less_than @ SV249 @ SV241 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[723]) ).
thf(734,plain,
! [SV168: $i,SV251: $i,SV200: $i] :
( ( ( SV200 = SV251 )
= $false )
| ( ( ! [SY471: $i] : ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY471 ) ) @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(735,plain,
! [SV200: $i,SV252: $i,SV168: $i] :
( ( ( contains_slb @ SV168 @ SV252 )
= $false )
| ( ( ! [SY472: $i] : ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY472 ) ) @ SV252 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[726]) ).
thf(736,plain,
! [SV257: $i,SV218: $i,SV253: $i,SV201: $i,SV169: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV253 ) ) @ SV218 @ SV257 )
| ( SV201 = SV218 )
| ( pair_in_list @ SV169 @ SV218 @ SV257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(737,plain,
! [SV258: $i,SV218: $i,SV254: $i,SV201: $i,SV169: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV254 ) ) @ SV218 @ SV258 )
| ( SV254 = SV258 )
| ( pair_in_list @ SV169 @ SV218 @ SV258 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(738,plain,
! [SV169: $i,SV259: $i,SV255: $i,SV218: $i,SV201: $i] :
( ( ( SV201 != SV218 )
| ( SV255 != SV259 )
| ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV255 ) ) @ SV218 @ SV259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(739,plain,
! [SV256: $i,SV201: $i,SV260: $i,SV218: $i,SV169: $i] :
( ( ~ ( pair_in_list @ SV169 @ SV218 @ SV260 )
| ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV256 ) ) @ SV218 @ SV260 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(740,plain,
! [SV217: $i,SV248: $i,SV240: $i,SV199: $i,SV167: $i] :
( ( ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SV199 @ ( pair @ SV240 @ SV248 ) ) @ SV217 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV167 @ SV199 @ SV217 ) )
= $true )
| ( ( less_than @ SV248 @ SV240 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(741,plain,
! [SV249: $i,SV241: $i,SV217: $i,SV199: $i,SV167: $i] :
( ( ( check_cpq @ ( triple @ SV167 @ SV199 @ SV217 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV167 @ ( insert_slb @ SV199 @ ( pair @ SV241 @ SV249 ) ) @ SV217 ) )
= $true )
| ( ( less_than @ SV249 @ SV241 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[733]) ).
thf(742,plain,
! [SV251: $i,SV261: $i,SV200: $i,SV168: $i] :
( ( ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV261 ) ) @ SV251 )
= $true )
| ( ( SV200 = SV251 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(743,plain,
! [SV252: $i,SV262: $i,SV200: $i,SV168: $i] :
( ( ( contains_slb @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV262 ) ) @ SV252 )
= $true )
| ( ( contains_slb @ SV168 @ SV252 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(744,plain,
! [SV257: $i,SV218: $i,SV253: $i,SV201: $i,SV169: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV253 ) ) @ SV218 @ SV257 ) )
= $true )
| ( ( ( SV201 = SV218 )
| ( pair_in_list @ SV169 @ SV218 @ SV257 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(745,plain,
! [SV258: $i,SV218: $i,SV254: $i,SV201: $i,SV169: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV254 ) ) @ SV218 @ SV258 ) )
= $true )
| ( ( ( SV254 = SV258 )
| ( pair_in_list @ SV169 @ SV218 @ SV258 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[737]) ).
thf(746,plain,
! [SV169: $i,SV259: $i,SV255: $i,SV218: $i,SV201: $i] :
( ( ( ( SV201 != SV218 )
| ( SV255 != SV259 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV255 ) ) @ SV218 @ SV259 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[738]) ).
thf(747,plain,
! [SV256: $i,SV201: $i,SV260: $i,SV218: $i,SV169: $i] :
( ( ( ~ ( pair_in_list @ SV169 @ SV218 @ SV260 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV256 ) ) @ SV218 @ SV260 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[739]) ).
thf(748,plain,
! [SV257: $i,SV218: $i,SV253: $i,SV201: $i,SV169: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV253 ) ) @ SV218 @ SV257 )
= $false )
| ( ( ( SV201 = SV218 )
| ( pair_in_list @ SV169 @ SV218 @ SV257 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[744]) ).
thf(749,plain,
! [SV258: $i,SV218: $i,SV254: $i,SV201: $i,SV169: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV254 ) ) @ SV218 @ SV258 )
= $false )
| ( ( ( SV254 = SV258 )
| ( pair_in_list @ SV169 @ SV218 @ SV258 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[745]) ).
thf(750,plain,
! [SV169: $i,SV259: $i,SV255: $i,SV218: $i,SV201: $i] :
( ( ( ( SV201 != SV218 ) )
= $true )
| ( ( ( SV255 != SV259 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV255 ) ) @ SV218 @ SV259 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[746]) ).
thf(751,plain,
! [SV256: $i,SV201: $i,SV260: $i,SV218: $i,SV169: $i] :
( ( ( pair_in_list @ SV169 @ SV218 @ SV260 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV256 ) ) @ SV218 @ SV260 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(752,plain,
! [SV253: $i,SV257: $i,SV169: $i,SV218: $i,SV201: $i] :
( ( ( SV201 = SV218 )
= $true )
| ( ( pair_in_list @ SV169 @ SV218 @ SV257 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV253 ) ) @ SV218 @ SV257 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[748]) ).
thf(753,plain,
! [SV201: $i,SV218: $i,SV169: $i,SV258: $i,SV254: $i] :
( ( ( SV254 = SV258 )
= $true )
| ( ( pair_in_list @ SV169 @ SV218 @ SV258 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV254 ) ) @ SV218 @ SV258 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[749]) ).
thf(754,plain,
! [SV169: $i,SV259: $i,SV255: $i,SV218: $i,SV201: $i] :
( ( ( SV201 = SV218 )
= $false )
| ( ( ( SV255 != SV259 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV255 ) ) @ SV218 @ SV259 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(755,plain,
! [SV169: $i,SV218: $i,SV201: $i,SV259: $i,SV255: $i] :
( ( ( SV255 = SV259 )
= $false )
| ( ( SV201 = SV218 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV255 ) ) @ SV218 @ SV259 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[754]) ).
thf(756,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[480,755,753,752,751,743,742,741,740,731,724,720,719,718,693,692,691,690,689,688,670,669,668,651,650,633,630,628,627,613,606,605,603,602,579,570,568,567,566,565,556,552,544,532,523,522,521,502,499,491,490,489]) ).
thf(757,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( less_than @ U @ V )
| ~ ( less_than @ V @ W )
| ( less_than @ U @ W ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(758,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(759,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(760,plain,
( ( ! [U: $i,V: $i] :
( ~ ( less_than @ U @ V )
| ( less_than @ V @ U )
| ( strictly_less_than @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( strictly_less_than @ U @ V )
| ( less_than @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( strictly_less_than @ U @ V )
| ~ ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(761,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(762,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(763,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(764,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(765,plain,
( ( ! [U: $i,V: $i] :
( ! [W: $i] :
( ! [X: $i] :
~ ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
| ( V = W )
| ( contains_slb @ U @ W ) )
& ! [W: $i] :
( ( V != W )
| ! [X: $i] : ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W ) )
& ! [W: $i] :
( ~ ( contains_slb @ U @ W )
| ! [X: $i] : ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(766,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(767,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
| ( V = W )
| ( pair_in_list @ U @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
| ( X = Y )
| ( pair_in_list @ U @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ( V != W )
| ( X != Y )
| ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ U @ W @ Y )
| ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(768,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(769,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( V = W )
| ~ ( contains_slb @ U @ W )
| ! [X: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( remove_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(770,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(771,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( V = W )
| ~ ( contains_slb @ U @ W )
| ! [X: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( lookup_slb @ U @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(772,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(773,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( strictly_less_than @ X @ W )
| ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(774,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( less_than @ W @ X )
| ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(775,plain,
( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(776,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(777,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(778,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(779,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(780,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(781,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ! [X: $i,Y: $i] :
( ~ ( less_than @ Y @ X )
| ~ ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
| ( check_cpq @ ( triple @ U @ V @ W ) ) )
& ! [X: $i,Y: $i] :
( ~ ( less_than @ Y @ X )
| ~ ( check_cpq @ ( triple @ U @ V @ W ) )
| ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(782,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ~ ( strictly_less_than @ X @ Y )
| ~ ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(783,plain,
( ( ! [U: $i,V: $i] :
( ! [W: $i,X: $i] :
( ~ ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
| ( contains_slb @ V @ X ) )
& ! [W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
| ( contains_cpq @ ( triple @ U @ V @ W ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(784,plain,
( ( ! [U: $i,V: $i] :
~ ( ok @ ( triple @ U @ V @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(785,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( triple @ U @ V @ W ) )
| ( W = bad ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(786,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( insert_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( insert_pqp @ U @ X ) @ ( insert_slb @ V @ ( pair @ X @ bottom ) ) @ W ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(787,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_slb @ V @ X )
| ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ U @ V @ bad ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(788,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
| ~ ( less_than @ ( lookup_slb @ V @ X ) @ X )
| ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(789,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
| ~ ( strictly_less_than @ X @ ( lookup_slb @ V @ X ) )
| ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ bad ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(790,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ create_slb @ V ) )
= ( triple @ U @ create_slb @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(791,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
| ! [W: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(792,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ U ) @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) )
| ! [W: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(793,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
| ~ ( less_than @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) @ ( findmin_pqp_res @ U ) )
| ! [W: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(794,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(795,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ! [W: $i] :
( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
= ( findmin_pqp_res @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(796,plain,
( ( ! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(797,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(798,plain,
( ( ok @ ( findmin_cpq_eff @ ( triple @ sK1_U @ sK2_SY120 @ sK3_SY122 ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(799,plain,
( ( ~ ( less_than @ ( lookup_slb @ sK2_SY120 @ ( findmin_pqp_res @ sK1_U ) ) @ ( findmin_pqp_res @ sK1_U ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(800,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( less_than @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 )
| ( strictly_less_than @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[760]) ).
thf(801,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( contains_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ SX3 )
| ( contains_slb @ SX1 @ SX3 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( contains_slb @ SX1 @ SX3 )
| ( contains_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[783]) ).
thf(802,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 )
| ( SX1 = SX2 )
| ( contains_slb @ SX0 @ SX2 ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ( SX1 != SX2 )
| ! [SX3: $i] : ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 ) )
| ~ ! [SX2: $i] :
( ~ ( contains_slb @ SX0 @ SX2 )
| ! [SX3: $i] : ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[765]) ).
thf(803,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 )
| ( SX1 = SX2 )
| ( pair_in_list @ SX0 @ SX2 @ SX4 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 )
| ( SX3 = SX4 )
| ( pair_in_list @ SX0 @ SX2 @ SX4 ) ) )
| ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ( SX1 != SX2 )
| ( SX3 != SX4 )
| ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( pair_in_list @ SX0 @ SX2 @ SX4 )
| ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[767]) ).
thf(804,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( less_than @ SX4 @ SX3 )
| ~ ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ SX1 @ ( pair @ SX3 @ SX4 ) ) @ SX2 ) )
| ( check_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( less_than @ SX4 @ SX3 )
| ~ ( check_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ SX1 @ ( pair @ SX3 @ SX4 ) ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[781]) ).
thf(805,plain,
! [SV263: $i] :
( ( ! [SY477: $i,SY478: $i] :
( ~ ( less_than @ SV263 @ SY477 )
| ~ ( less_than @ SY477 @ SY478 )
| ( less_than @ SV263 @ SY478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(806,plain,
! [SV264: $i] :
( ( ! [SY479: $i] :
( ( less_than @ SV264 @ SY479 )
| ( less_than @ SY479 @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(807,plain,
! [SV265: $i] :
( ( less_than @ SV265 @ SV265 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(808,plain,
! [SV266: $i] :
( ( less_than @ bottom @ SV266 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(809,plain,
( ( isnonempty_slb @ create_slb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[762]) ).
thf(810,plain,
! [SV267: $i] :
( ( ! [SY480: $i,SY481: $i] : ( isnonempty_slb @ ( insert_slb @ SV267 @ ( pair @ SY480 @ SY481 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(811,plain,
! [SV268: $i] :
( ( ~ ( contains_slb @ create_slb @ SV268 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(812,plain,
! [SV269: $i] :
( ( ! [SY482: $i] :
~ ( pair_in_list @ create_slb @ SV269 @ SY482 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(813,plain,
! [SV270: $i] :
( ( ! [SY483: $i,SY484: $i] :
( ( remove_slb @ ( insert_slb @ SV270 @ ( pair @ SY483 @ SY484 ) ) @ SY483 )
= SV270 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(814,plain,
! [SV271: $i] :
( ( ! [SY485: $i,SY486: $i] :
( ( SY485 = SY486 )
| ~ ( contains_slb @ SV271 @ SY486 )
| ! [SY487: $i] :
( ( remove_slb @ ( insert_slb @ SV271 @ ( pair @ SY485 @ SY487 ) ) @ SY486 )
= ( insert_slb @ ( remove_slb @ SV271 @ SY486 ) @ ( pair @ SY485 @ SY487 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(815,plain,
! [SV272: $i] :
( ( ! [SY488: $i,SY489: $i] :
( ( lookup_slb @ ( insert_slb @ SV272 @ ( pair @ SY488 @ SY489 ) ) @ SY488 )
= SY489 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(816,plain,
! [SV273: $i] :
( ( ! [SY490: $i,SY491: $i] :
( ( SY490 = SY491 )
| ~ ( contains_slb @ SV273 @ SY491 )
| ! [SY492: $i] :
( ( lookup_slb @ ( insert_slb @ SV273 @ ( pair @ SY490 @ SY492 ) ) @ SY491 )
= ( lookup_slb @ SV273 @ SY491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(817,plain,
! [SV274: $i] :
( ( ( update_slb @ create_slb @ SV274 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(818,plain,
! [SV275: $i] :
( ( ! [SY493: $i,SY494: $i,SY495: $i] :
( ~ ( strictly_less_than @ SY495 @ SY494 )
| ( ( update_slb @ ( insert_slb @ SV275 @ ( pair @ SY493 @ SY495 ) ) @ SY494 )
= ( insert_slb @ ( update_slb @ SV275 @ SY494 ) @ ( pair @ SY493 @ SY494 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(819,plain,
! [SV276: $i] :
( ( ! [SY496: $i,SY497: $i,SY498: $i] :
( ~ ( less_than @ SY497 @ SY498 )
| ( ( update_slb @ ( insert_slb @ SV276 @ ( pair @ SY496 @ SY498 ) ) @ SY497 )
= ( insert_slb @ ( update_slb @ SV276 @ SY497 ) @ ( pair @ SY496 @ SY498 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(820,plain,
! [SV277: $i] :
( ( succ_cpq @ SV277 @ SV277 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(821,plain,
! [SV278: $i] :
( ( ! [SY499: $i] :
( ~ ( succ_cpq @ SV278 @ SY499 )
| ! [SY500: $i] : ( succ_cpq @ SV278 @ ( insert_cpq @ SY499 @ SY500 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(822,plain,
! [SV279: $i] :
( ( ! [SY501: $i] :
( ~ ( succ_cpq @ SV279 @ SY501 )
| ! [SY502: $i] : ( succ_cpq @ SV279 @ ( remove_cpq @ SY501 @ SY502 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(823,plain,
! [SV280: $i] :
( ( ! [SY503: $i] :
( ~ ( succ_cpq @ SV280 @ SY503 )
| ( succ_cpq @ SV280 @ ( findmin_cpq_eff @ SY503 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(824,plain,
! [SV281: $i] :
( ( ! [SY504: $i] :
( ~ ( succ_cpq @ SV281 @ SY504 )
| ( succ_cpq @ SV281 @ ( removemin_cpq_eff @ SY504 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(825,plain,
! [SV282: $i] :
( ( ! [SY505: $i] : ( check_cpq @ ( triple @ SV282 @ create_slb @ SY505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(826,plain,
! [SV283: $i] :
( ( ! [SY506: $i,SY507: $i,SY508: $i,SY509: $i] :
( ~ ( strictly_less_than @ SY508 @ SY509 )
| ~ ( check_cpq @ ( triple @ SV283 @ ( insert_slb @ SY506 @ ( pair @ SY508 @ SY509 ) ) @ SY507 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(827,plain,
! [SV284: $i] :
( ( ! [SY510: $i] :
~ ( ok @ ( triple @ SV284 @ SY510 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(828,plain,
! [SV285: $i] :
( ( ! [SY511: $i,SY512: $i] :
( ( ok @ ( triple @ SV285 @ SY511 @ SY512 ) )
| ( SY512 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(829,plain,
! [SV286: $i] :
( ( ! [SY513: $i,SY514: $i,SY515: $i] :
( ( insert_cpq @ ( triple @ SV286 @ SY513 @ SY514 ) @ SY515 )
= ( triple @ ( insert_pqp @ SV286 @ SY515 ) @ ( insert_slb @ SY513 @ ( pair @ SY515 @ bottom ) ) @ SY514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(830,plain,
! [SV287: $i] :
( ( ! [SY516: $i,SY517: $i,SY518: $i] :
( ( contains_slb @ SY516 @ SY518 )
| ( ( remove_cpq @ ( triple @ SV287 @ SY516 @ SY517 ) @ SY518 )
= ( triple @ SV287 @ SY516 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(831,plain,
! [SV288: $i] :
( ( ! [SY519: $i,SY520: $i,SY521: $i] :
( ~ ( contains_slb @ SY519 @ SY521 )
| ~ ( less_than @ ( lookup_slb @ SY519 @ SY521 ) @ SY521 )
| ( ( remove_cpq @ ( triple @ SV288 @ SY519 @ SY520 ) @ SY521 )
= ( triple @ ( remove_pqp @ SV288 @ SY521 ) @ ( remove_slb @ SY519 @ SY521 ) @ SY520 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(832,plain,
! [SV289: $i] :
( ( ! [SY522: $i,SY523: $i,SY524: $i] :
( ~ ( contains_slb @ SY522 @ SY524 )
| ~ ( strictly_less_than @ SY524 @ ( lookup_slb @ SY522 @ SY524 ) )
| ( ( remove_cpq @ ( triple @ SV289 @ SY522 @ SY523 ) @ SY524 )
= ( triple @ ( remove_pqp @ SV289 @ SY524 ) @ ( remove_slb @ SY522 @ SY524 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(833,plain,
! [SV290: $i] :
( ( ! [SY525: $i] :
( ( findmin_cpq_eff @ ( triple @ SV290 @ create_slb @ SY525 ) )
= ( triple @ SV290 @ create_slb @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(834,plain,
! [SV291: $i] :
( ( ! [SY526: $i] :
( ( SY526 = create_slb )
| ( contains_slb @ SY526 @ ( findmin_pqp_res @ SV291 ) )
| ! [SY527: $i] :
( ( findmin_cpq_eff @ ( triple @ SV291 @ SY526 @ SY527 ) )
= ( triple @ SV291 @ ( update_slb @ SY526 @ ( findmin_pqp_res @ SV291 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(835,plain,
! [SV292: $i] :
( ( ! [SY528: $i] :
( ( SY528 = create_slb )
| ~ ( contains_slb @ SY528 @ ( findmin_pqp_res @ SV292 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV292 ) @ ( lookup_slb @ SY528 @ ( findmin_pqp_res @ SV292 ) ) )
| ! [SY529: $i] :
( ( findmin_cpq_eff @ ( triple @ SV292 @ SY528 @ SY529 ) )
= ( triple @ SV292 @ ( update_slb @ SY528 @ ( findmin_pqp_res @ SV292 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(836,plain,
! [SV293: $i] :
( ( ! [SY530: $i] :
( ( SY530 = create_slb )
| ~ ( contains_slb @ SY530 @ ( findmin_pqp_res @ SV293 ) )
| ~ ( less_than @ ( lookup_slb @ SY530 @ ( findmin_pqp_res @ SV293 ) ) @ ( findmin_pqp_res @ SV293 ) )
| ! [SY531: $i] :
( ( findmin_cpq_eff @ ( triple @ SV293 @ SY530 @ SY531 ) )
= ( triple @ SV293 @ ( update_slb @ SY530 @ ( findmin_pqp_res @ SV293 ) ) @ SY531 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(837,plain,
! [SV294: $i] :
( ( ! [SY532: $i] :
( ( findmin_cpq_res @ ( triple @ SV294 @ create_slb @ SY532 ) )
= bottom ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(838,plain,
! [SV295: $i] :
( ( ! [SY533: $i] :
( ( SY533 = create_slb )
| ! [SY534: $i] :
( ( findmin_cpq_res @ ( triple @ SV295 @ SY533 @ SY534 ) )
= ( findmin_pqp_res @ SV295 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(839,plain,
! [SV296: $i] :
( ( ( removemin_cpq_eff @ SV296 )
= ( remove_cpq @ ( findmin_cpq_eff @ SV296 ) @ ( findmin_cpq_res @ SV296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(840,plain,
! [SV297: $i] :
( ( ( removemin_cpq_res @ SV297 )
= ( findmin_cpq_res @ SV297 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(841,plain,
( ( less_than @ ( lookup_slb @ sK2_SY120 @ ( findmin_pqp_res @ sK1_U ) ) @ ( findmin_pqp_res @ sK1_U ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(842,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( less_than @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 )
| ( strictly_less_than @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[800]) ).
thf(843,plain,
! [SV298: $i] :
( ( ! [SY535: $i] :
~ ( ~ ! [SY536: $i,SY537: $i] :
( ~ ( contains_cpq @ ( triple @ SV298 @ SY535 @ SY536 ) @ SY537 )
| ( contains_slb @ SY535 @ SY537 ) )
| ~ ! [SY538: $i,SY539: $i] :
( ~ ( contains_slb @ SY535 @ SY539 )
| ( contains_cpq @ ( triple @ SV298 @ SY535 @ SY538 ) @ SY539 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(844,plain,
! [SV299: $i] :
( ( ! [SY540: $i] :
~ ( ~ ! [SY541: $i] :
( ! [SY542: $i] :
~ ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SY540 @ SY542 ) ) @ SY541 )
| ( SY540 = SY541 )
| ( contains_slb @ SV299 @ SY541 ) )
| ~ ~ ( ~ ! [SY543: $i] :
( ( SY540 != SY543 )
| ! [SY544: $i] : ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SY540 @ SY544 ) ) @ SY543 ) )
| ~ ! [SY545: $i] :
( ~ ( contains_slb @ SV299 @ SY545 )
| ! [SY546: $i] : ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SY540 @ SY546 ) ) @ SY545 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(845,plain,
! [SV300: $i] :
( ( ! [SY547: $i,SY548: $i] :
~ ( ~ ~ ( ~ ! [SY549: $i,SY550: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SY547 @ SY549 ) ) @ SY548 @ SY550 )
| ( SY547 = SY548 )
| ( pair_in_list @ SV300 @ SY548 @ SY550 ) )
| ~ ! [SY551: $i,SY552: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SY547 @ SY551 ) ) @ SY548 @ SY552 )
| ( SY551 = SY552 )
| ( pair_in_list @ SV300 @ SY548 @ SY552 ) ) )
| ~ ~ ( ~ ! [SY553: $i,SY554: $i] :
( ( SY547 != SY548 )
| ( SY553 != SY554 )
| ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SY547 @ SY553 ) ) @ SY548 @ SY554 ) )
| ~ ! [SY555: $i,SY556: $i] :
( ~ ( pair_in_list @ SV300 @ SY548 @ SY556 )
| ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SY547 @ SY555 ) ) @ SY548 @ SY556 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(846,plain,
! [SV301: $i] :
( ( ! [SY557: $i,SY558: $i] :
~ ( ~ ! [SY559: $i,SY560: $i] :
( ~ ( less_than @ SY560 @ SY559 )
| ~ ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SY557 @ ( pair @ SY559 @ SY560 ) ) @ SY558 ) )
| ( check_cpq @ ( triple @ SV301 @ SY557 @ SY558 ) ) )
| ~ ! [SY561: $i,SY562: $i] :
( ~ ( less_than @ SY562 @ SY561 )
| ~ ( check_cpq @ ( triple @ SV301 @ SY557 @ SY558 ) )
| ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SY557 @ ( pair @ SY561 @ SY562 ) ) @ SY558 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(847,plain,
! [SV302: $i,SV263: $i] :
( ( ! [SY563: $i] :
( ~ ( less_than @ SV263 @ SV302 )
| ~ ( less_than @ SV302 @ SY563 )
| ( less_than @ SV263 @ SY563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(848,plain,
! [SV303: $i,SV264: $i] :
( ( ( less_than @ SV264 @ SV303 )
| ( less_than @ SV303 @ SV264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(849,plain,
! [SV304: $i,SV267: $i] :
( ( ! [SY564: $i] : ( isnonempty_slb @ ( insert_slb @ SV267 @ ( pair @ SV304 @ SY564 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(850,plain,
! [SV268: $i] :
( ( contains_slb @ create_slb @ SV268 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(851,plain,
! [SV305: $i,SV269: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV269 @ SV305 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(852,plain,
! [SV306: $i,SV270: $i] :
( ( ! [SY565: $i] :
( ( remove_slb @ ( insert_slb @ SV270 @ ( pair @ SV306 @ SY565 ) ) @ SV306 )
= SV270 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(853,plain,
! [SV271: $i,SV307: $i] :
( ( ! [SY566: $i] :
( ( SV307 = SY566 )
| ~ ( contains_slb @ SV271 @ SY566 )
| ! [SY567: $i] :
( ( remove_slb @ ( insert_slb @ SV271 @ ( pair @ SV307 @ SY567 ) ) @ SY566 )
= ( insert_slb @ ( remove_slb @ SV271 @ SY566 ) @ ( pair @ SV307 @ SY567 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(854,plain,
! [SV308: $i,SV272: $i] :
( ( ! [SY568: $i] :
( ( lookup_slb @ ( insert_slb @ SV272 @ ( pair @ SV308 @ SY568 ) ) @ SV308 )
= SY568 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(855,plain,
! [SV273: $i,SV309: $i] :
( ( ! [SY569: $i] :
( ( SV309 = SY569 )
| ~ ( contains_slb @ SV273 @ SY569 )
| ! [SY570: $i] :
( ( lookup_slb @ ( insert_slb @ SV273 @ ( pair @ SV309 @ SY570 ) ) @ SY569 )
= ( lookup_slb @ SV273 @ SY569 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(856,plain,
! [SV310: $i,SV275: $i] :
( ( ! [SY571: $i,SY572: $i] :
( ~ ( strictly_less_than @ SY572 @ SY571 )
| ( ( update_slb @ ( insert_slb @ SV275 @ ( pair @ SV310 @ SY572 ) ) @ SY571 )
= ( insert_slb @ ( update_slb @ SV275 @ SY571 ) @ ( pair @ SV310 @ SY571 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(857,plain,
! [SV311: $i,SV276: $i] :
( ( ! [SY573: $i,SY574: $i] :
( ~ ( less_than @ SY573 @ SY574 )
| ( ( update_slb @ ( insert_slb @ SV276 @ ( pair @ SV311 @ SY574 ) ) @ SY573 )
= ( insert_slb @ ( update_slb @ SV276 @ SY573 ) @ ( pair @ SV311 @ SY574 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(858,plain,
! [SV312: $i,SV278: $i] :
( ( ~ ( succ_cpq @ SV278 @ SV312 )
| ! [SY575: $i] : ( succ_cpq @ SV278 @ ( insert_cpq @ SV312 @ SY575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(859,plain,
! [SV313: $i,SV279: $i] :
( ( ~ ( succ_cpq @ SV279 @ SV313 )
| ! [SY576: $i] : ( succ_cpq @ SV279 @ ( remove_cpq @ SV313 @ SY576 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(860,plain,
! [SV314: $i,SV280: $i] :
( ( ~ ( succ_cpq @ SV280 @ SV314 )
| ( succ_cpq @ SV280 @ ( findmin_cpq_eff @ SV314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(861,plain,
! [SV315: $i,SV281: $i] :
( ( ~ ( succ_cpq @ SV281 @ SV315 )
| ( succ_cpq @ SV281 @ ( removemin_cpq_eff @ SV315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(862,plain,
! [SV316: $i,SV282: $i] :
( ( check_cpq @ ( triple @ SV282 @ create_slb @ SV316 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(863,plain,
! [SV317: $i,SV283: $i] :
( ( ! [SY577: $i,SY578: $i,SY579: $i] :
( ~ ( strictly_less_than @ SY578 @ SY579 )
| ~ ( check_cpq @ ( triple @ SV283 @ ( insert_slb @ SV317 @ ( pair @ SY578 @ SY579 ) ) @ SY577 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(864,plain,
! [SV318: $i,SV284: $i] :
( ( ~ ( ok @ ( triple @ SV284 @ SV318 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(865,plain,
! [SV319: $i,SV285: $i] :
( ( ! [SY580: $i] :
( ( ok @ ( triple @ SV285 @ SV319 @ SY580 ) )
| ( SY580 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(866,plain,
! [SV320: $i,SV286: $i] :
( ( ! [SY581: $i,SY582: $i] :
( ( insert_cpq @ ( triple @ SV286 @ SV320 @ SY581 ) @ SY582 )
= ( triple @ ( insert_pqp @ SV286 @ SY582 ) @ ( insert_slb @ SV320 @ ( pair @ SY582 @ bottom ) ) @ SY581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(867,plain,
! [SV287: $i,SV321: $i] :
( ( ! [SY583: $i,SY584: $i] :
( ( contains_slb @ SV321 @ SY584 )
| ( ( remove_cpq @ ( triple @ SV287 @ SV321 @ SY583 ) @ SY584 )
= ( triple @ SV287 @ SV321 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(868,plain,
! [SV288: $i,SV322: $i] :
( ( ! [SY585: $i,SY586: $i] :
( ~ ( contains_slb @ SV322 @ SY586 )
| ~ ( less_than @ ( lookup_slb @ SV322 @ SY586 ) @ SY586 )
| ( ( remove_cpq @ ( triple @ SV288 @ SV322 @ SY585 ) @ SY586 )
= ( triple @ ( remove_pqp @ SV288 @ SY586 ) @ ( remove_slb @ SV322 @ SY586 ) @ SY585 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(869,plain,
! [SV289: $i,SV323: $i] :
( ( ! [SY587: $i,SY588: $i] :
( ~ ( contains_slb @ SV323 @ SY588 )
| ~ ( strictly_less_than @ SY588 @ ( lookup_slb @ SV323 @ SY588 ) )
| ( ( remove_cpq @ ( triple @ SV289 @ SV323 @ SY587 ) @ SY588 )
= ( triple @ ( remove_pqp @ SV289 @ SY588 ) @ ( remove_slb @ SV323 @ SY588 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(870,plain,
! [SV324: $i,SV290: $i] :
( ( ( findmin_cpq_eff @ ( triple @ SV290 @ create_slb @ SV324 ) )
= ( triple @ SV290 @ create_slb @ bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(871,plain,
! [SV291: $i,SV325: $i] :
( ( ( SV325 = create_slb )
| ( contains_slb @ SV325 @ ( findmin_pqp_res @ SV291 ) )
| ! [SY589: $i] :
( ( findmin_cpq_eff @ ( triple @ SV291 @ SV325 @ SY589 ) )
= ( triple @ SV291 @ ( update_slb @ SV325 @ ( findmin_pqp_res @ SV291 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(872,plain,
! [SV292: $i,SV326: $i] :
( ( ( SV326 = create_slb )
| ~ ( contains_slb @ SV326 @ ( findmin_pqp_res @ SV292 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV292 ) @ ( lookup_slb @ SV326 @ ( findmin_pqp_res @ SV292 ) ) )
| ! [SY590: $i] :
( ( findmin_cpq_eff @ ( triple @ SV292 @ SV326 @ SY590 ) )
= ( triple @ SV292 @ ( update_slb @ SV326 @ ( findmin_pqp_res @ SV292 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(873,plain,
! [SV293: $i,SV327: $i] :
( ( ( SV327 = create_slb )
| ~ ( contains_slb @ SV327 @ ( findmin_pqp_res @ SV293 ) )
| ~ ( less_than @ ( lookup_slb @ SV327 @ ( findmin_pqp_res @ SV293 ) ) @ ( findmin_pqp_res @ SV293 ) )
| ! [SY591: $i] :
( ( findmin_cpq_eff @ ( triple @ SV293 @ SV327 @ SY591 ) )
= ( triple @ SV293 @ ( update_slb @ SV327 @ ( findmin_pqp_res @ SV293 ) ) @ SY591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(874,plain,
! [SV328: $i,SV294: $i] :
( ( ( findmin_cpq_res @ ( triple @ SV294 @ create_slb @ SV328 ) )
= bottom )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(875,plain,
! [SV295: $i,SV329: $i] :
( ( ( SV329 = create_slb )
| ! [SY592: $i] :
( ( findmin_cpq_res @ ( triple @ SV295 @ SV329 @ SY592 ) )
= ( findmin_pqp_res @ SV295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(876,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( less_than @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 )
| ( strictly_less_than @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[842]) ).
thf(877,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[842]) ).
thf(878,plain,
! [SV330: $i,SV298: $i] :
( ( ~ ( ~ ! [SY593: $i,SY594: $i] :
( ~ ( contains_cpq @ ( triple @ SV298 @ SV330 @ SY593 ) @ SY594 )
| ( contains_slb @ SV330 @ SY594 ) )
| ~ ! [SY595: $i,SY596: $i] :
( ~ ( contains_slb @ SV330 @ SY596 )
| ( contains_cpq @ ( triple @ SV298 @ SV330 @ SY595 ) @ SY596 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(879,plain,
! [SV331: $i,SV299: $i] :
( ( ~ ( ~ ! [SY597: $i] :
( ! [SY598: $i] :
~ ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY598 ) ) @ SY597 )
| ( SV331 = SY597 )
| ( contains_slb @ SV299 @ SY597 ) )
| ~ ~ ( ~ ! [SY599: $i] :
( ( SV331 != SY599 )
| ! [SY600: $i] : ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY600 ) ) @ SY599 ) )
| ~ ! [SY601: $i] :
( ~ ( contains_slb @ SV299 @ SY601 )
| ! [SY602: $i] : ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY602 ) ) @ SY601 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(880,plain,
! [SV332: $i,SV300: $i] :
( ( ! [SY603: $i] :
~ ( ~ ~ ( ~ ! [SY604: $i,SY605: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY604 ) ) @ SY603 @ SY605 )
| ( SV332 = SY603 )
| ( pair_in_list @ SV300 @ SY603 @ SY605 ) )
| ~ ! [SY606: $i,SY607: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY606 ) ) @ SY603 @ SY607 )
| ( SY606 = SY607 )
| ( pair_in_list @ SV300 @ SY603 @ SY607 ) ) )
| ~ ~ ( ~ ! [SY608: $i,SY609: $i] :
( ( SV332 != SY603 )
| ( SY608 != SY609 )
| ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY608 ) ) @ SY603 @ SY609 ) )
| ~ ! [SY610: $i,SY611: $i] :
( ~ ( pair_in_list @ SV300 @ SY603 @ SY611 )
| ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY610 ) ) @ SY603 @ SY611 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(881,plain,
! [SV333: $i,SV301: $i] :
( ( ! [SY612: $i] :
~ ( ~ ! [SY613: $i,SY614: $i] :
( ~ ( less_than @ SY614 @ SY613 )
| ~ ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SV333 @ ( pair @ SY613 @ SY614 ) ) @ SY612 ) )
| ( check_cpq @ ( triple @ SV301 @ SV333 @ SY612 ) ) )
| ~ ! [SY615: $i,SY616: $i] :
( ~ ( less_than @ SY616 @ SY615 )
| ~ ( check_cpq @ ( triple @ SV301 @ SV333 @ SY612 ) )
| ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SV333 @ ( pair @ SY615 @ SY616 ) ) @ SY612 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(882,plain,
! [SV334: $i,SV302: $i,SV263: $i] :
( ( ~ ( less_than @ SV263 @ SV302 )
| ~ ( less_than @ SV302 @ SV334 )
| ( less_than @ SV263 @ SV334 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(883,plain,
! [SV303: $i,SV264: $i] :
( ( ( less_than @ SV264 @ SV303 )
= $true )
| ( ( less_than @ SV303 @ SV264 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(884,plain,
! [SV335: $i,SV304: $i,SV267: $i] :
( ( isnonempty_slb @ ( insert_slb @ SV267 @ ( pair @ SV304 @ SV335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(885,plain,
! [SV305: $i,SV269: $i] :
( ( pair_in_list @ create_slb @ SV269 @ SV305 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[851]) ).
thf(886,plain,
! [SV336: $i,SV306: $i,SV270: $i] :
( ( ( remove_slb @ ( insert_slb @ SV270 @ ( pair @ SV306 @ SV336 ) ) @ SV306 )
= SV270 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(887,plain,
! [SV271: $i,SV337: $i,SV307: $i] :
( ( ( SV307 = SV337 )
| ~ ( contains_slb @ SV271 @ SV337 )
| ! [SY617: $i] :
( ( remove_slb @ ( insert_slb @ SV271 @ ( pair @ SV307 @ SY617 ) ) @ SV337 )
= ( insert_slb @ ( remove_slb @ SV271 @ SV337 ) @ ( pair @ SV307 @ SY617 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(888,plain,
! [SV338: $i,SV308: $i,SV272: $i] :
( ( ( lookup_slb @ ( insert_slb @ SV272 @ ( pair @ SV308 @ SV338 ) ) @ SV308 )
= SV338 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(889,plain,
! [SV273: $i,SV339: $i,SV309: $i] :
( ( ( SV309 = SV339 )
| ~ ( contains_slb @ SV273 @ SV339 )
| ! [SY618: $i] :
( ( lookup_slb @ ( insert_slb @ SV273 @ ( pair @ SV309 @ SY618 ) ) @ SV339 )
= ( lookup_slb @ SV273 @ SV339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(890,plain,
! [SV310: $i,SV275: $i,SV340: $i] :
( ( ! [SY619: $i] :
( ~ ( strictly_less_than @ SY619 @ SV340 )
| ( ( update_slb @ ( insert_slb @ SV275 @ ( pair @ SV310 @ SY619 ) ) @ SV340 )
= ( insert_slb @ ( update_slb @ SV275 @ SV340 ) @ ( pair @ SV310 @ SV340 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(891,plain,
! [SV311: $i,SV276: $i,SV341: $i] :
( ( ! [SY620: $i] :
( ~ ( less_than @ SV341 @ SY620 )
| ( ( update_slb @ ( insert_slb @ SV276 @ ( pair @ SV311 @ SY620 ) ) @ SV341 )
= ( insert_slb @ ( update_slb @ SV276 @ SV341 ) @ ( pair @ SV311 @ SY620 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(892,plain,
! [SV312: $i,SV278: $i] :
( ( ( ~ ( succ_cpq @ SV278 @ SV312 ) )
= $true )
| ( ( ! [SY575: $i] : ( succ_cpq @ SV278 @ ( insert_cpq @ SV312 @ SY575 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[858]) ).
thf(893,plain,
! [SV313: $i,SV279: $i] :
( ( ( ~ ( succ_cpq @ SV279 @ SV313 ) )
= $true )
| ( ( ! [SY576: $i] : ( succ_cpq @ SV279 @ ( remove_cpq @ SV313 @ SY576 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(894,plain,
! [SV314: $i,SV280: $i] :
( ( ( ~ ( succ_cpq @ SV280 @ SV314 ) )
= $true )
| ( ( succ_cpq @ SV280 @ ( findmin_cpq_eff @ SV314 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[860]) ).
thf(895,plain,
! [SV315: $i,SV281: $i] :
( ( ( ~ ( succ_cpq @ SV281 @ SV315 ) )
= $true )
| ( ( succ_cpq @ SV281 @ ( removemin_cpq_eff @ SV315 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[861]) ).
thf(896,plain,
! [SV342: $i,SV317: $i,SV283: $i] :
( ( ! [SY621: $i,SY622: $i] :
( ~ ( strictly_less_than @ SY621 @ SY622 )
| ~ ( check_cpq @ ( triple @ SV283 @ ( insert_slb @ SV317 @ ( pair @ SY621 @ SY622 ) ) @ SV342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(897,plain,
! [SV318: $i,SV284: $i] :
( ( ok @ ( triple @ SV284 @ SV318 @ bad ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[864]) ).
thf(898,plain,
! [SV343: $i,SV319: $i,SV285: $i] :
( ( ( ok @ ( triple @ SV285 @ SV319 @ SV343 ) )
| ( SV343 = bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(899,plain,
! [SV344: $i,SV320: $i,SV286: $i] :
( ( ! [SY623: $i] :
( ( insert_cpq @ ( triple @ SV286 @ SV320 @ SV344 ) @ SY623 )
= ( triple @ ( insert_pqp @ SV286 @ SY623 ) @ ( insert_slb @ SV320 @ ( pair @ SY623 @ bottom ) ) @ SV344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(900,plain,
! [SV345: $i,SV287: $i,SV321: $i] :
( ( ! [SY624: $i] :
( ( contains_slb @ SV321 @ SY624 )
| ( ( remove_cpq @ ( triple @ SV287 @ SV321 @ SV345 ) @ SY624 )
= ( triple @ SV287 @ SV321 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(901,plain,
! [SV346: $i,SV288: $i,SV322: $i] :
( ( ! [SY625: $i] :
( ~ ( contains_slb @ SV322 @ SY625 )
| ~ ( less_than @ ( lookup_slb @ SV322 @ SY625 ) @ SY625 )
| ( ( remove_cpq @ ( triple @ SV288 @ SV322 @ SV346 ) @ SY625 )
= ( triple @ ( remove_pqp @ SV288 @ SY625 ) @ ( remove_slb @ SV322 @ SY625 ) @ SV346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(902,plain,
! [SV347: $i,SV289: $i,SV323: $i] :
( ( ! [SY626: $i] :
( ~ ( contains_slb @ SV323 @ SY626 )
| ~ ( strictly_less_than @ SY626 @ ( lookup_slb @ SV323 @ SY626 ) )
| ( ( remove_cpq @ ( triple @ SV289 @ SV323 @ SV347 ) @ SY626 )
= ( triple @ ( remove_pqp @ SV289 @ SY626 ) @ ( remove_slb @ SV323 @ SY626 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(903,plain,
! [SV291: $i,SV325: $i] :
( ( ( ( SV325 = create_slb )
| ( contains_slb @ SV325 @ ( findmin_pqp_res @ SV291 ) ) )
= $true )
| ( ( ! [SY589: $i] :
( ( findmin_cpq_eff @ ( triple @ SV291 @ SV325 @ SY589 ) )
= ( triple @ SV291 @ ( update_slb @ SV325 @ ( findmin_pqp_res @ SV291 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(904,plain,
! [SV292: $i,SV326: $i] :
( ( ( ( SV326 = create_slb )
| ~ ( contains_slb @ SV326 @ ( findmin_pqp_res @ SV292 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV292 ) @ ( lookup_slb @ SV326 @ ( findmin_pqp_res @ SV292 ) ) ) )
= $true )
| ( ( ! [SY590: $i] :
( ( findmin_cpq_eff @ ( triple @ SV292 @ SV326 @ SY590 ) )
= ( triple @ SV292 @ ( update_slb @ SV326 @ ( findmin_pqp_res @ SV292 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(905,plain,
! [SV293: $i,SV327: $i] :
( ( ( ( SV327 = create_slb )
| ~ ( contains_slb @ SV327 @ ( findmin_pqp_res @ SV293 ) )
| ~ ( less_than @ ( lookup_slb @ SV327 @ ( findmin_pqp_res @ SV293 ) ) @ ( findmin_pqp_res @ SV293 ) ) )
= $true )
| ( ( ! [SY591: $i] :
( ( findmin_cpq_eff @ ( triple @ SV293 @ SV327 @ SY591 ) )
= ( triple @ SV293 @ ( update_slb @ SV327 @ ( findmin_pqp_res @ SV293 ) ) @ SY591 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(906,plain,
! [SV295: $i,SV329: $i] :
( ( ( SV329 = create_slb )
= $true )
| ( ( ! [SY592: $i] :
( ( findmin_cpq_res @ ( triple @ SV295 @ SV329 @ SY592 ) )
= ( findmin_pqp_res @ SV295 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[875]) ).
thf(907,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( less_than @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 )
| ( strictly_less_than @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[876]) ).
thf(908,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[877]) ).
thf(909,plain,
! [SV330: $i,SV298: $i] :
( ( ~ ! [SY593: $i,SY594: $i] :
( ~ ( contains_cpq @ ( triple @ SV298 @ SV330 @ SY593 ) @ SY594 )
| ( contains_slb @ SV330 @ SY594 ) )
| ~ ! [SY595: $i,SY596: $i] :
( ~ ( contains_slb @ SV330 @ SY596 )
| ( contains_cpq @ ( triple @ SV298 @ SV330 @ SY595 ) @ SY596 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(910,plain,
! [SV331: $i,SV299: $i] :
( ( ~ ! [SY597: $i] :
( ! [SY598: $i] :
~ ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY598 ) ) @ SY597 )
| ( SV331 = SY597 )
| ( contains_slb @ SV299 @ SY597 ) )
| ~ ~ ( ~ ! [SY599: $i] :
( ( SV331 != SY599 )
| ! [SY600: $i] : ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY600 ) ) @ SY599 ) )
| ~ ! [SY601: $i] :
( ~ ( contains_slb @ SV299 @ SY601 )
| ! [SY602: $i] : ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY602 ) ) @ SY601 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(911,plain,
! [SV348: $i,SV332: $i,SV300: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY627: $i,SY628: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY627 ) ) @ SV348 @ SY628 )
| ( SV332 = SV348 )
| ( pair_in_list @ SV300 @ SV348 @ SY628 ) )
| ~ ! [SY629: $i,SY630: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY629 ) ) @ SV348 @ SY630 )
| ( SY629 = SY630 )
| ( pair_in_list @ SV300 @ SV348 @ SY630 ) ) )
| ~ ~ ( ~ ! [SY631: $i,SY632: $i] :
( ( SV332 != SV348 )
| ( SY631 != SY632 )
| ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY631 ) ) @ SV348 @ SY632 ) )
| ~ ! [SY633: $i,SY634: $i] :
( ~ ( pair_in_list @ SV300 @ SV348 @ SY634 )
| ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY633 ) ) @ SV348 @ SY634 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(912,plain,
! [SV349: $i,SV333: $i,SV301: $i] :
( ( ~ ( ~ ! [SY635: $i,SY636: $i] :
( ~ ( less_than @ SY636 @ SY635 )
| ~ ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SV333 @ ( pair @ SY635 @ SY636 ) ) @ SV349 ) )
| ( check_cpq @ ( triple @ SV301 @ SV333 @ SV349 ) ) )
| ~ ! [SY637: $i,SY638: $i] :
( ~ ( less_than @ SY638 @ SY637 )
| ~ ( check_cpq @ ( triple @ SV301 @ SV333 @ SV349 ) )
| ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SV333 @ ( pair @ SY637 @ SY638 ) ) @ SV349 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(913,plain,
! [SV334: $i,SV302: $i,SV263: $i] :
( ( ( ~ ( less_than @ SV263 @ SV302 )
| ~ ( less_than @ SV302 @ SV334 ) )
= $true )
| ( ( less_than @ SV263 @ SV334 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[882]) ).
thf(914,plain,
! [SV271: $i,SV337: $i,SV307: $i] :
( ( ( ( SV307 = SV337 )
| ~ ( contains_slb @ SV271 @ SV337 ) )
= $true )
| ( ( ! [SY617: $i] :
( ( remove_slb @ ( insert_slb @ SV271 @ ( pair @ SV307 @ SY617 ) ) @ SV337 )
= ( insert_slb @ ( remove_slb @ SV271 @ SV337 ) @ ( pair @ SV307 @ SY617 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(915,plain,
! [SV273: $i,SV339: $i,SV309: $i] :
( ( ( ( SV309 = SV339 )
| ~ ( contains_slb @ SV273 @ SV339 ) )
= $true )
| ( ( ! [SY618: $i] :
( ( lookup_slb @ ( insert_slb @ SV273 @ ( pair @ SV309 @ SY618 ) ) @ SV339 )
= ( lookup_slb @ SV273 @ SV339 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[889]) ).
thf(916,plain,
! [SV310: $i,SV275: $i,SV340: $i,SV350: $i] :
( ( ~ ( strictly_less_than @ SV350 @ SV340 )
| ( ( update_slb @ ( insert_slb @ SV275 @ ( pair @ SV310 @ SV350 ) ) @ SV340 )
= ( insert_slb @ ( update_slb @ SV275 @ SV340 ) @ ( pair @ SV310 @ SV340 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(917,plain,
! [SV311: $i,SV276: $i,SV351: $i,SV341: $i] :
( ( ~ ( less_than @ SV341 @ SV351 )
| ( ( update_slb @ ( insert_slb @ SV276 @ ( pair @ SV311 @ SV351 ) ) @ SV341 )
= ( insert_slb @ ( update_slb @ SV276 @ SV341 ) @ ( pair @ SV311 @ SV351 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(918,plain,
! [SV312: $i,SV278: $i] :
( ( ( succ_cpq @ SV278 @ SV312 )
= $false )
| ( ( ! [SY575: $i] : ( succ_cpq @ SV278 @ ( insert_cpq @ SV312 @ SY575 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[892]) ).
thf(919,plain,
! [SV313: $i,SV279: $i] :
( ( ( succ_cpq @ SV279 @ SV313 )
= $false )
| ( ( ! [SY576: $i] : ( succ_cpq @ SV279 @ ( remove_cpq @ SV313 @ SY576 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(920,plain,
! [SV314: $i,SV280: $i] :
( ( ( succ_cpq @ SV280 @ SV314 )
= $false )
| ( ( succ_cpq @ SV280 @ ( findmin_cpq_eff @ SV314 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(921,plain,
! [SV315: $i,SV281: $i] :
( ( ( succ_cpq @ SV281 @ SV315 )
= $false )
| ( ( succ_cpq @ SV281 @ ( removemin_cpq_eff @ SV315 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[895]) ).
thf(922,plain,
! [SV342: $i,SV317: $i,SV283: $i,SV352: $i] :
( ( ! [SY639: $i] :
( ~ ( strictly_less_than @ SV352 @ SY639 )
| ~ ( check_cpq @ ( triple @ SV283 @ ( insert_slb @ SV317 @ ( pair @ SV352 @ SY639 ) ) @ SV342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(923,plain,
! [SV343: $i,SV319: $i,SV285: $i] :
( ( ( ok @ ( triple @ SV285 @ SV319 @ SV343 ) )
= $true )
| ( ( SV343 = bad )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[898]) ).
thf(924,plain,
! [SV353: $i,SV344: $i,SV320: $i,SV286: $i] :
( ( ( insert_cpq @ ( triple @ SV286 @ SV320 @ SV344 ) @ SV353 )
= ( triple @ ( insert_pqp @ SV286 @ SV353 ) @ ( insert_slb @ SV320 @ ( pair @ SV353 @ bottom ) ) @ SV344 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(925,plain,
! [SV345: $i,SV287: $i,SV354: $i,SV321: $i] :
( ( ( contains_slb @ SV321 @ SV354 )
| ( ( remove_cpq @ ( triple @ SV287 @ SV321 @ SV345 ) @ SV354 )
= ( triple @ SV287 @ SV321 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(926,plain,
! [SV346: $i,SV288: $i,SV355: $i,SV322: $i] :
( ( ~ ( contains_slb @ SV322 @ SV355 )
| ~ ( less_than @ ( lookup_slb @ SV322 @ SV355 ) @ SV355 )
| ( ( remove_cpq @ ( triple @ SV288 @ SV322 @ SV346 ) @ SV355 )
= ( triple @ ( remove_pqp @ SV288 @ SV355 ) @ ( remove_slb @ SV322 @ SV355 ) @ SV346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(927,plain,
! [SV347: $i,SV289: $i,SV356: $i,SV323: $i] :
( ( ~ ( contains_slb @ SV323 @ SV356 )
| ~ ( strictly_less_than @ SV356 @ ( lookup_slb @ SV323 @ SV356 ) )
| ( ( remove_cpq @ ( triple @ SV289 @ SV323 @ SV347 ) @ SV356 )
= ( triple @ ( remove_pqp @ SV289 @ SV356 ) @ ( remove_slb @ SV323 @ SV356 ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(928,plain,
! [SV291: $i,SV325: $i] :
( ( ( SV325 = create_slb )
= $true )
| ( ( contains_slb @ SV325 @ ( findmin_pqp_res @ SV291 ) )
= $true )
| ( ( ! [SY589: $i] :
( ( findmin_cpq_eff @ ( triple @ SV291 @ SV325 @ SY589 ) )
= ( triple @ SV291 @ ( update_slb @ SV325 @ ( findmin_pqp_res @ SV291 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[903]) ).
thf(929,plain,
! [SV292: $i,SV326: $i] :
( ( ( ( SV326 = create_slb )
| ~ ( contains_slb @ SV326 @ ( findmin_pqp_res @ SV292 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV292 ) @ ( lookup_slb @ SV326 @ ( findmin_pqp_res @ SV292 ) ) ) )
= $true )
| ( ( ! [SY590: $i] :
( ( findmin_cpq_eff @ ( triple @ SV292 @ SV326 @ SY590 ) )
= ( triple @ SV292 @ ( update_slb @ SV326 @ ( findmin_pqp_res @ SV292 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[904]) ).
thf(930,plain,
! [SV293: $i,SV327: $i] :
( ( ( ( SV327 = create_slb )
| ~ ( contains_slb @ SV327 @ ( findmin_pqp_res @ SV293 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV327 @ ( findmin_pqp_res @ SV293 ) ) @ ( findmin_pqp_res @ SV293 ) ) )
= $true )
| ( ( ! [SY591: $i] :
( ( findmin_cpq_eff @ ( triple @ SV293 @ SV327 @ SY591 ) )
= ( triple @ SV293 @ ( update_slb @ SV327 @ ( findmin_pqp_res @ SV293 ) ) @ SY591 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[905]) ).
thf(931,plain,
! [SV357: $i,SV329: $i,SV295: $i] :
( ( ( ( findmin_cpq_res @ ( triple @ SV295 @ SV329 @ SV357 ) )
= ( findmin_pqp_res @ SV295 ) )
= $true )
| ( ( SV329 = create_slb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(932,plain,
! [SV358: $i] :
( ( ! [SY640: $i] :
( ~ ( less_than @ SV358 @ SY640 )
| ( less_than @ SY640 @ SV358 )
| ( strictly_less_than @ SV358 @ SY640 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(933,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[908]) ).
thf(934,plain,
! [SV330: $i,SV298: $i] :
( ( ~ ! [SY593: $i,SY594: $i] :
( ~ ( contains_cpq @ ( triple @ SV298 @ SV330 @ SY593 ) @ SY594 )
| ( contains_slb @ SV330 @ SY594 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[909]) ).
thf(935,plain,
! [SV298: $i,SV330: $i] :
( ( ~ ! [SY595: $i,SY596: $i] :
( ~ ( contains_slb @ SV330 @ SY596 )
| ( contains_cpq @ ( triple @ SV298 @ SV330 @ SY595 ) @ SY596 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[909]) ).
thf(936,plain,
! [SV331: $i,SV299: $i] :
( ( ~ ! [SY597: $i] :
( ! [SY598: $i] :
~ ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY598 ) ) @ SY597 )
| ( SV331 = SY597 )
| ( contains_slb @ SV299 @ SY597 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[910]) ).
thf(937,plain,
! [SV299: $i,SV331: $i] :
( ( ~ ~ ( ~ ! [SY599: $i] :
( ( SV331 != SY599 )
| ! [SY600: $i] : ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY600 ) ) @ SY599 ) )
| ~ ! [SY601: $i] :
( ~ ( contains_slb @ SV299 @ SY601 )
| ! [SY602: $i] : ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY602 ) ) @ SY601 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[910]) ).
thf(938,plain,
! [SV348: $i,SV332: $i,SV300: $i] :
( ( ~ ~ ( ~ ! [SY627: $i,SY628: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY627 ) ) @ SV348 @ SY628 )
| ( SV332 = SV348 )
| ( pair_in_list @ SV300 @ SV348 @ SY628 ) )
| ~ ! [SY629: $i,SY630: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY629 ) ) @ SV348 @ SY630 )
| ( SY629 = SY630 )
| ( pair_in_list @ SV300 @ SV348 @ SY630 ) ) )
| ~ ~ ( ~ ! [SY631: $i,SY632: $i] :
( ( SV332 != SV348 )
| ( SY631 != SY632 )
| ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY631 ) ) @ SV348 @ SY632 ) )
| ~ ! [SY633: $i,SY634: $i] :
( ~ ( pair_in_list @ SV300 @ SV348 @ SY634 )
| ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY633 ) ) @ SV348 @ SY634 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(939,plain,
! [SV349: $i,SV333: $i,SV301: $i] :
( ( ~ ! [SY635: $i,SY636: $i] :
( ~ ( less_than @ SY636 @ SY635 )
| ~ ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SV333 @ ( pair @ SY635 @ SY636 ) ) @ SV349 ) )
| ( check_cpq @ ( triple @ SV301 @ SV333 @ SV349 ) ) )
| ~ ! [SY637: $i,SY638: $i] :
( ~ ( less_than @ SY638 @ SY637 )
| ~ ( check_cpq @ ( triple @ SV301 @ SV333 @ SV349 ) )
| ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SV333 @ ( pair @ SY637 @ SY638 ) ) @ SV349 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(940,plain,
! [SV334: $i,SV302: $i,SV263: $i] :
( ( ( ~ ( less_than @ SV263 @ SV302 ) )
= $true )
| ( ( ~ ( less_than @ SV302 @ SV334 ) )
= $true )
| ( ( less_than @ SV263 @ SV334 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[913]) ).
thf(941,plain,
! [SV271: $i,SV337: $i,SV307: $i] :
( ( ( SV307 = SV337 )
= $true )
| ( ( ~ ( contains_slb @ SV271 @ SV337 ) )
= $true )
| ( ( ! [SY617: $i] :
( ( remove_slb @ ( insert_slb @ SV271 @ ( pair @ SV307 @ SY617 ) ) @ SV337 )
= ( insert_slb @ ( remove_slb @ SV271 @ SV337 ) @ ( pair @ SV307 @ SY617 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[914]) ).
thf(942,plain,
! [SV273: $i,SV339: $i,SV309: $i] :
( ( ( SV309 = SV339 )
= $true )
| ( ( ~ ( contains_slb @ SV273 @ SV339 ) )
= $true )
| ( ( ! [SY618: $i] :
( ( lookup_slb @ ( insert_slb @ SV273 @ ( pair @ SV309 @ SY618 ) ) @ SV339 )
= ( lookup_slb @ SV273 @ SV339 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[915]) ).
thf(943,plain,
! [SV310: $i,SV275: $i,SV340: $i,SV350: $i] :
( ( ( ~ ( strictly_less_than @ SV350 @ SV340 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV275 @ ( pair @ SV310 @ SV350 ) ) @ SV340 )
= ( insert_slb @ ( update_slb @ SV275 @ SV340 ) @ ( pair @ SV310 @ SV340 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[916]) ).
thf(944,plain,
! [SV311: $i,SV276: $i,SV351: $i,SV341: $i] :
( ( ( ~ ( less_than @ SV341 @ SV351 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV276 @ ( pair @ SV311 @ SV351 ) ) @ SV341 )
= ( insert_slb @ ( update_slb @ SV276 @ SV341 ) @ ( pair @ SV311 @ SV351 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[917]) ).
thf(945,plain,
! [SV359: $i,SV312: $i,SV278: $i] :
( ( ( succ_cpq @ SV278 @ ( insert_cpq @ SV312 @ SV359 ) )
= $true )
| ( ( succ_cpq @ SV278 @ SV312 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(946,plain,
! [SV360: $i,SV313: $i,SV279: $i] :
( ( ( succ_cpq @ SV279 @ ( remove_cpq @ SV313 @ SV360 ) )
= $true )
| ( ( succ_cpq @ SV279 @ SV313 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(947,plain,
! [SV342: $i,SV317: $i,SV283: $i,SV361: $i,SV352: $i] :
( ( ~ ( strictly_less_than @ SV352 @ SV361 )
| ~ ( check_cpq @ ( triple @ SV283 @ ( insert_slb @ SV317 @ ( pair @ SV352 @ SV361 ) ) @ SV342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(948,plain,
! [SV345: $i,SV287: $i,SV354: $i,SV321: $i] :
( ( ( contains_slb @ SV321 @ SV354 )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV287 @ SV321 @ SV345 ) @ SV354 )
= ( triple @ SV287 @ SV321 @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[925]) ).
thf(949,plain,
! [SV346: $i,SV288: $i,SV355: $i,SV322: $i] :
( ( ( ~ ( contains_slb @ SV322 @ SV355 )
| ~ ( less_than @ ( lookup_slb @ SV322 @ SV355 ) @ SV355 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV288 @ SV322 @ SV346 ) @ SV355 )
= ( triple @ ( remove_pqp @ SV288 @ SV355 ) @ ( remove_slb @ SV322 @ SV355 ) @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[926]) ).
thf(950,plain,
! [SV347: $i,SV289: $i,SV356: $i,SV323: $i] :
( ( ( ~ ( contains_slb @ SV323 @ SV356 )
| ~ ( strictly_less_than @ SV356 @ ( lookup_slb @ SV323 @ SV356 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV289 @ SV323 @ SV347 ) @ SV356 )
= ( triple @ ( remove_pqp @ SV289 @ SV356 ) @ ( remove_slb @ SV323 @ SV356 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[927]) ).
thf(951,plain,
! [SV362: $i,SV325: $i,SV291: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV291 @ SV325 @ SV362 ) )
= ( triple @ SV291 @ ( update_slb @ SV325 @ ( findmin_pqp_res @ SV291 ) ) @ bad ) )
= $true )
| ( ( contains_slb @ SV325 @ ( findmin_pqp_res @ SV291 ) )
= $true )
| ( ( SV325 = create_slb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(952,plain,
! [SV292: $i,SV326: $i] :
( ( ( SV326 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV326 @ ( findmin_pqp_res @ SV292 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV292 ) @ ( lookup_slb @ SV326 @ ( findmin_pqp_res @ SV292 ) ) ) )
= $true )
| ( ( ! [SY590: $i] :
( ( findmin_cpq_eff @ ( triple @ SV292 @ SV326 @ SY590 ) )
= ( triple @ SV292 @ ( update_slb @ SV326 @ ( findmin_pqp_res @ SV292 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(953,plain,
! [SV293: $i,SV327: $i] :
( ( ( SV327 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV327 @ ( findmin_pqp_res @ SV293 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV327 @ ( findmin_pqp_res @ SV293 ) ) @ ( findmin_pqp_res @ SV293 ) ) )
= $true )
| ( ( ! [SY591: $i] :
( ( findmin_cpq_eff @ ( triple @ SV293 @ SV327 @ SY591 ) )
= ( triple @ SV293 @ ( update_slb @ SV327 @ ( findmin_pqp_res @ SV293 ) ) @ SY591 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[930]) ).
thf(954,plain,
! [SV363: $i,SV358: $i] :
( ( ~ ( less_than @ SV358 @ SV363 )
| ( less_than @ SV363 @ SV358 )
| ( strictly_less_than @ SV358 @ SV363 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(955,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[933]) ).
thf(956,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[933]) ).
thf(957,plain,
! [SV330: $i,SV298: $i] :
( ( ! [SY593: $i,SY594: $i] :
( ~ ( contains_cpq @ ( triple @ SV298 @ SV330 @ SY593 ) @ SY594 )
| ( contains_slb @ SV330 @ SY594 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[934]) ).
thf(958,plain,
! [SV298: $i,SV330: $i] :
( ( ! [SY595: $i,SY596: $i] :
( ~ ( contains_slb @ SV330 @ SY596 )
| ( contains_cpq @ ( triple @ SV298 @ SV330 @ SY595 ) @ SY596 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[935]) ).
thf(959,plain,
! [SV331: $i,SV299: $i] :
( ( ! [SY597: $i] :
( ! [SY598: $i] :
~ ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY598 ) ) @ SY597 )
| ( SV331 = SY597 )
| ( contains_slb @ SV299 @ SY597 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[936]) ).
thf(960,plain,
! [SV299: $i,SV331: $i] :
( ( ~ ( ~ ! [SY599: $i] :
( ( SV331 != SY599 )
| ! [SY600: $i] : ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY600 ) ) @ SY599 ) )
| ~ ! [SY601: $i] :
( ~ ( contains_slb @ SV299 @ SY601 )
| ! [SY602: $i] : ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY602 ) ) @ SY601 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[937]) ).
thf(961,plain,
! [SV348: $i,SV332: $i,SV300: $i] :
( ( ~ ~ ( ~ ! [SY627: $i,SY628: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY627 ) ) @ SV348 @ SY628 )
| ( SV332 = SV348 )
| ( pair_in_list @ SV300 @ SV348 @ SY628 ) )
| ~ ! [SY629: $i,SY630: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY629 ) ) @ SV348 @ SY630 )
| ( SY629 = SY630 )
| ( pair_in_list @ SV300 @ SV348 @ SY630 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(962,plain,
! [SV300: $i,SV348: $i,SV332: $i] :
( ( ~ ~ ( ~ ! [SY631: $i,SY632: $i] :
( ( SV332 != SV348 )
| ( SY631 != SY632 )
| ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY631 ) ) @ SV348 @ SY632 ) )
| ~ ! [SY633: $i,SY634: $i] :
( ~ ( pair_in_list @ SV300 @ SV348 @ SY634 )
| ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY633 ) ) @ SV348 @ SY634 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(963,plain,
! [SV349: $i,SV333: $i,SV301: $i] :
( ( ~ ! [SY635: $i,SY636: $i] :
( ~ ( less_than @ SY636 @ SY635 )
| ~ ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SV333 @ ( pair @ SY635 @ SY636 ) ) @ SV349 ) )
| ( check_cpq @ ( triple @ SV301 @ SV333 @ SV349 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[939]) ).
thf(964,plain,
! [SV349: $i,SV333: $i,SV301: $i] :
( ( ~ ! [SY637: $i,SY638: $i] :
( ~ ( less_than @ SY638 @ SY637 )
| ~ ( check_cpq @ ( triple @ SV301 @ SV333 @ SV349 ) )
| ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SV333 @ ( pair @ SY637 @ SY638 ) ) @ SV349 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[939]) ).
thf(965,plain,
! [SV334: $i,SV302: $i,SV263: $i] :
( ( ( less_than @ SV263 @ SV302 )
= $false )
| ( ( ~ ( less_than @ SV302 @ SV334 ) )
= $true )
| ( ( less_than @ SV263 @ SV334 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(966,plain,
! [SV307: $i,SV337: $i,SV271: $i] :
( ( ( contains_slb @ SV271 @ SV337 )
= $false )
| ( ( SV307 = SV337 )
= $true )
| ( ( ! [SY617: $i] :
( ( remove_slb @ ( insert_slb @ SV271 @ ( pair @ SV307 @ SY617 ) ) @ SV337 )
= ( insert_slb @ ( remove_slb @ SV271 @ SV337 ) @ ( pair @ SV307 @ SY617 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[941]) ).
thf(967,plain,
! [SV309: $i,SV339: $i,SV273: $i] :
( ( ( contains_slb @ SV273 @ SV339 )
= $false )
| ( ( SV309 = SV339 )
= $true )
| ( ( ! [SY618: $i] :
( ( lookup_slb @ ( insert_slb @ SV273 @ ( pair @ SV309 @ SY618 ) ) @ SV339 )
= ( lookup_slb @ SV273 @ SV339 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[942]) ).
thf(968,plain,
! [SV310: $i,SV275: $i,SV340: $i,SV350: $i] :
( ( ( strictly_less_than @ SV350 @ SV340 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV275 @ ( pair @ SV310 @ SV350 ) ) @ SV340 )
= ( insert_slb @ ( update_slb @ SV275 @ SV340 ) @ ( pair @ SV310 @ SV340 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(969,plain,
! [SV311: $i,SV276: $i,SV351: $i,SV341: $i] :
( ( ( less_than @ SV341 @ SV351 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV276 @ ( pair @ SV311 @ SV351 ) ) @ SV341 )
= ( insert_slb @ ( update_slb @ SV276 @ SV341 ) @ ( pair @ SV311 @ SV351 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(970,plain,
! [SV342: $i,SV317: $i,SV283: $i,SV361: $i,SV352: $i] :
( ( ( ~ ( strictly_less_than @ SV352 @ SV361 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV283 @ ( insert_slb @ SV317 @ ( pair @ SV352 @ SV361 ) ) @ SV342 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[947]) ).
thf(971,plain,
! [SV346: $i,SV288: $i,SV355: $i,SV322: $i] :
( ( ( ~ ( contains_slb @ SV322 @ SV355 ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV322 @ SV355 ) @ SV355 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV288 @ SV322 @ SV346 ) @ SV355 )
= ( triple @ ( remove_pqp @ SV288 @ SV355 ) @ ( remove_slb @ SV322 @ SV355 ) @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[949]) ).
thf(972,plain,
! [SV347: $i,SV289: $i,SV356: $i,SV323: $i] :
( ( ( ~ ( contains_slb @ SV323 @ SV356 ) )
= $true )
| ( ( ~ ( strictly_less_than @ SV356 @ ( lookup_slb @ SV323 @ SV356 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV289 @ SV323 @ SV347 ) @ SV356 )
= ( triple @ ( remove_pqp @ SV289 @ SV356 ) @ ( remove_slb @ SV323 @ SV356 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[950]) ).
thf(973,plain,
! [SV292: $i,SV326: $i] :
( ( ( contains_slb @ SV326 @ ( findmin_pqp_res @ SV292 ) )
= $false )
| ( ( SV326 = create_slb )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV292 ) @ ( lookup_slb @ SV326 @ ( findmin_pqp_res @ SV292 ) ) ) )
= $true )
| ( ( ! [SY590: $i] :
( ( findmin_cpq_eff @ ( triple @ SV292 @ SV326 @ SY590 ) )
= ( triple @ SV292 @ ( update_slb @ SV326 @ ( findmin_pqp_res @ SV292 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(974,plain,
! [SV293: $i,SV327: $i] :
( ( ( contains_slb @ SV327 @ ( findmin_pqp_res @ SV293 ) )
= $false )
| ( ( SV327 = create_slb )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV327 @ ( findmin_pqp_res @ SV293 ) ) @ ( findmin_pqp_res @ SV293 ) ) )
= $true )
| ( ( ! [SY591: $i] :
( ( findmin_cpq_eff @ ( triple @ SV293 @ SV327 @ SY591 ) )
= ( triple @ SV293 @ ( update_slb @ SV327 @ ( findmin_pqp_res @ SV293 ) ) @ SY591 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(975,plain,
! [SV363: $i,SV358: $i] :
( ( ( ~ ( less_than @ SV358 @ SV363 )
| ( less_than @ SV363 @ SV358 ) )
= $true )
| ( ( strictly_less_than @ SV358 @ SV363 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[954]) ).
thf(976,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[955]) ).
thf(977,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[956]) ).
thf(978,plain,
! [SV364: $i,SV330: $i,SV298: $i] :
( ( ! [SY641: $i] :
( ~ ( contains_cpq @ ( triple @ SV298 @ SV330 @ SV364 ) @ SY641 )
| ( contains_slb @ SV330 @ SY641 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(979,plain,
! [SV365: $i,SV298: $i,SV330: $i] :
( ( ! [SY642: $i] :
( ~ ( contains_slb @ SV330 @ SY642 )
| ( contains_cpq @ ( triple @ SV298 @ SV330 @ SV365 ) @ SY642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(980,plain,
! [SV366: $i,SV331: $i,SV299: $i] :
( ( ! [SY643: $i] :
~ ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY643 ) ) @ SV366 )
| ( SV331 = SV366 )
| ( contains_slb @ SV299 @ SV366 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(981,plain,
! [SV299: $i,SV331: $i] :
( ( ~ ! [SY599: $i] :
( ( SV331 != SY599 )
| ! [SY600: $i] : ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY600 ) ) @ SY599 ) )
| ~ ! [SY601: $i] :
( ~ ( contains_slb @ SV299 @ SY601 )
| ! [SY602: $i] : ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY602 ) ) @ SY601 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(982,plain,
! [SV348: $i,SV332: $i,SV300: $i] :
( ( ~ ( ~ ! [SY627: $i,SY628: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY627 ) ) @ SV348 @ SY628 )
| ( SV332 = SV348 )
| ( pair_in_list @ SV300 @ SV348 @ SY628 ) )
| ~ ! [SY629: $i,SY630: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY629 ) ) @ SV348 @ SY630 )
| ( SY629 = SY630 )
| ( pair_in_list @ SV300 @ SV348 @ SY630 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[961]) ).
thf(983,plain,
! [SV300: $i,SV348: $i,SV332: $i] :
( ( ~ ( ~ ! [SY631: $i,SY632: $i] :
( ( SV332 != SV348 )
| ( SY631 != SY632 )
| ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY631 ) ) @ SV348 @ SY632 ) )
| ~ ! [SY633: $i,SY634: $i] :
( ~ ( pair_in_list @ SV300 @ SV348 @ SY634 )
| ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY633 ) ) @ SV348 @ SY634 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[962]) ).
thf(984,plain,
! [SV349: $i,SV333: $i,SV301: $i] :
( ( ! [SY635: $i,SY636: $i] :
( ~ ( less_than @ SY636 @ SY635 )
| ~ ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SV333 @ ( pair @ SY635 @ SY636 ) ) @ SV349 ) )
| ( check_cpq @ ( triple @ SV301 @ SV333 @ SV349 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[963]) ).
thf(985,plain,
! [SV349: $i,SV333: $i,SV301: $i] :
( ( ! [SY637: $i,SY638: $i] :
( ~ ( less_than @ SY638 @ SY637 )
| ~ ( check_cpq @ ( triple @ SV301 @ SV333 @ SV349 ) )
| ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SV333 @ ( pair @ SY637 @ SY638 ) ) @ SV349 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[964]) ).
thf(986,plain,
! [SV263: $i,SV334: $i,SV302: $i] :
( ( ( less_than @ SV302 @ SV334 )
= $false )
| ( ( less_than @ SV263 @ SV302 )
= $false )
| ( ( less_than @ SV263 @ SV334 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(987,plain,
! [SV337: $i,SV367: $i,SV307: $i,SV271: $i] :
( ( ( ( remove_slb @ ( insert_slb @ SV271 @ ( pair @ SV307 @ SV367 ) ) @ SV337 )
= ( insert_slb @ ( remove_slb @ SV271 @ SV337 ) @ ( pair @ SV307 @ SV367 ) ) )
= $true )
| ( ( SV307 = SV337 )
= $true )
| ( ( contains_slb @ SV271 @ SV337 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(988,plain,
! [SV339: $i,SV368: $i,SV309: $i,SV273: $i] :
( ( ( ( lookup_slb @ ( insert_slb @ SV273 @ ( pair @ SV309 @ SV368 ) ) @ SV339 )
= ( lookup_slb @ SV273 @ SV339 ) )
= $true )
| ( ( SV309 = SV339 )
= $true )
| ( ( contains_slb @ SV273 @ SV339 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(989,plain,
! [SV342: $i,SV317: $i,SV283: $i,SV361: $i,SV352: $i] :
( ( ( strictly_less_than @ SV352 @ SV361 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV283 @ ( insert_slb @ SV317 @ ( pair @ SV352 @ SV361 ) ) @ SV342 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[970]) ).
thf(990,plain,
! [SV346: $i,SV288: $i,SV355: $i,SV322: $i] :
( ( ( contains_slb @ SV322 @ SV355 )
= $false )
| ( ( ~ ( less_than @ ( lookup_slb @ SV322 @ SV355 ) @ SV355 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV288 @ SV322 @ SV346 ) @ SV355 )
= ( triple @ ( remove_pqp @ SV288 @ SV355 ) @ ( remove_slb @ SV322 @ SV355 ) @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(991,plain,
! [SV347: $i,SV289: $i,SV356: $i,SV323: $i] :
( ( ( contains_slb @ SV323 @ SV356 )
= $false )
| ( ( ~ ( strictly_less_than @ SV356 @ ( lookup_slb @ SV323 @ SV356 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV289 @ SV323 @ SV347 ) @ SV356 )
= ( triple @ ( remove_pqp @ SV289 @ SV356 ) @ ( remove_slb @ SV323 @ SV356 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(992,plain,
! [SV326: $i,SV292: $i] :
( ( ( strictly_less_than @ ( findmin_pqp_res @ SV292 ) @ ( lookup_slb @ SV326 @ ( findmin_pqp_res @ SV292 ) ) )
= $false )
| ( ( SV326 = create_slb )
= $true )
| ( ( contains_slb @ SV326 @ ( findmin_pqp_res @ SV292 ) )
= $false )
| ( ( ! [SY590: $i] :
( ( findmin_cpq_eff @ ( triple @ SV292 @ SV326 @ SY590 ) )
= ( triple @ SV292 @ ( update_slb @ SV326 @ ( findmin_pqp_res @ SV292 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[973]) ).
thf(993,plain,
! [SV293: $i,SV327: $i] :
( ( ( less_than @ ( lookup_slb @ SV327 @ ( findmin_pqp_res @ SV293 ) ) @ ( findmin_pqp_res @ SV293 ) )
= $false )
| ( ( SV327 = create_slb )
= $true )
| ( ( contains_slb @ SV327 @ ( findmin_pqp_res @ SV293 ) )
= $false )
| ( ( ! [SY591: $i] :
( ( findmin_cpq_eff @ ( triple @ SV293 @ SV327 @ SY591 ) )
= ( triple @ SV293 @ ( update_slb @ SV327 @ ( findmin_pqp_res @ SV293 ) ) @ SY591 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(994,plain,
! [SV363: $i,SV358: $i] :
( ( ( ~ ( less_than @ SV358 @ SV363 ) )
= $true )
| ( ( less_than @ SV363 @ SV358 )
= $true )
| ( ( strictly_less_than @ SV358 @ SV363 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[975]) ).
thf(995,plain,
! [SV369: $i] :
( ( ! [SY644: $i] :
( ~ ( strictly_less_than @ SV369 @ SY644 )
| ( less_than @ SV369 @ SY644 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(996,plain,
! [SV370: $i] :
( ( ! [SY645: $i] :
( ~ ( strictly_less_than @ SV370 @ SY645 )
| ~ ( less_than @ SY645 @ SV370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(997,plain,
! [SV371: $i,SV364: $i,SV330: $i,SV298: $i] :
( ( ~ ( contains_cpq @ ( triple @ SV298 @ SV330 @ SV364 ) @ SV371 )
| ( contains_slb @ SV330 @ SV371 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(998,plain,
! [SV365: $i,SV298: $i,SV372: $i,SV330: $i] :
( ( ~ ( contains_slb @ SV330 @ SV372 )
| ( contains_cpq @ ( triple @ SV298 @ SV330 @ SV365 ) @ SV372 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(999,plain,
! [SV366: $i,SV331: $i,SV299: $i] :
( ( ( ! [SY643: $i] :
~ ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY643 ) ) @ SV366 ) )
= $true )
| ( ( ( SV331 = SV366 )
| ( contains_slb @ SV299 @ SV366 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[980]) ).
thf(1000,plain,
! [SV299: $i,SV331: $i] :
( ( ~ ! [SY599: $i] :
( ( SV331 != SY599 )
| ! [SY600: $i] : ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY600 ) ) @ SY599 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[981]) ).
thf(1001,plain,
! [SV331: $i,SV299: $i] :
( ( ~ ! [SY601: $i] :
( ~ ( contains_slb @ SV299 @ SY601 )
| ! [SY602: $i] : ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY602 ) ) @ SY601 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[981]) ).
thf(1002,plain,
! [SV348: $i,SV332: $i,SV300: $i] :
( ( ~ ! [SY627: $i,SY628: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY627 ) ) @ SV348 @ SY628 )
| ( SV332 = SV348 )
| ( pair_in_list @ SV300 @ SV348 @ SY628 ) )
| ~ ! [SY629: $i,SY630: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY629 ) ) @ SV348 @ SY630 )
| ( SY629 = SY630 )
| ( pair_in_list @ SV300 @ SV348 @ SY630 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1003,plain,
! [SV300: $i,SV348: $i,SV332: $i] :
( ( ~ ! [SY631: $i,SY632: $i] :
( ( SV332 != SV348 )
| ( SY631 != SY632 )
| ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY631 ) ) @ SV348 @ SY632 ) )
| ~ ! [SY633: $i,SY634: $i] :
( ~ ( pair_in_list @ SV300 @ SV348 @ SY634 )
| ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY633 ) ) @ SV348 @ SY634 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1004,plain,
! [SV349: $i,SV333: $i,SV301: $i,SV373: $i] :
( ( ! [SY646: $i] :
( ~ ( less_than @ SY646 @ SV373 )
| ~ ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SV333 @ ( pair @ SV373 @ SY646 ) ) @ SV349 ) )
| ( check_cpq @ ( triple @ SV301 @ SV333 @ SV349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1005,plain,
! [SV349: $i,SV333: $i,SV301: $i,SV374: $i] :
( ( ! [SY647: $i] :
( ~ ( less_than @ SY647 @ SV374 )
| ~ ( check_cpq @ ( triple @ SV301 @ SV333 @ SV349 ) )
| ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SV333 @ ( pair @ SV374 @ SY647 ) ) @ SV349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1006,plain,
! [SV342: $i,SV361: $i,SV352: $i,SV317: $i,SV283: $i] :
( ( ( check_cpq @ ( triple @ SV283 @ ( insert_slb @ SV317 @ ( pair @ SV352 @ SV361 ) ) @ SV342 ) )
= $false )
| ( ( strictly_less_than @ SV352 @ SV361 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1007,plain,
! [SV346: $i,SV288: $i,SV355: $i,SV322: $i] :
( ( ( less_than @ ( lookup_slb @ SV322 @ SV355 ) @ SV355 )
= $false )
| ( ( contains_slb @ SV322 @ SV355 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV288 @ SV322 @ SV346 ) @ SV355 )
= ( triple @ ( remove_pqp @ SV288 @ SV355 ) @ ( remove_slb @ SV322 @ SV355 ) @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1008,plain,
! [SV347: $i,SV289: $i,SV323: $i,SV356: $i] :
( ( ( strictly_less_than @ SV356 @ ( lookup_slb @ SV323 @ SV356 ) )
= $false )
| ( ( contains_slb @ SV323 @ SV356 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV289 @ SV323 @ SV347 ) @ SV356 )
= ( triple @ ( remove_pqp @ SV289 @ SV356 ) @ ( remove_slb @ SV323 @ SV356 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1009,plain,
! [SV375: $i,SV326: $i,SV292: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV292 @ SV326 @ SV375 ) )
= ( triple @ SV292 @ ( update_slb @ SV326 @ ( findmin_pqp_res @ SV292 ) ) @ bad ) )
= $true )
| ( ( contains_slb @ SV326 @ ( findmin_pqp_res @ SV292 ) )
= $false )
| ( ( SV326 = create_slb )
= $true )
| ( ( strictly_less_than @ ( findmin_pqp_res @ SV292 ) @ ( lookup_slb @ SV326 @ ( findmin_pqp_res @ SV292 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1010,plain,
! [SV376: $i,SV327: $i,SV293: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV293 @ SV327 @ SV376 ) )
= ( triple @ SV293 @ ( update_slb @ SV327 @ ( findmin_pqp_res @ SV293 ) ) @ SV376 ) )
= $true )
| ( ( contains_slb @ SV327 @ ( findmin_pqp_res @ SV293 ) )
= $false )
| ( ( SV327 = create_slb )
= $true )
| ( ( less_than @ ( lookup_slb @ SV327 @ ( findmin_pqp_res @ SV293 ) ) @ ( findmin_pqp_res @ SV293 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1011,plain,
! [SV363: $i,SV358: $i] :
( ( ( less_than @ SV358 @ SV363 )
= $false )
| ( ( less_than @ SV363 @ SV358 )
= $true )
| ( ( strictly_less_than @ SV358 @ SV363 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1012,plain,
! [SV377: $i,SV369: $i] :
( ( ~ ( strictly_less_than @ SV369 @ SV377 )
| ( less_than @ SV369 @ SV377 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1013,plain,
! [SV378: $i,SV370: $i] :
( ( ~ ( strictly_less_than @ SV370 @ SV378 )
| ~ ( less_than @ SV378 @ SV370 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1014,plain,
! [SV371: $i,SV364: $i,SV330: $i,SV298: $i] :
( ( ( ~ ( contains_cpq @ ( triple @ SV298 @ SV330 @ SV364 ) @ SV371 ) )
= $true )
| ( ( contains_slb @ SV330 @ SV371 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[997]) ).
thf(1015,plain,
! [SV365: $i,SV298: $i,SV372: $i,SV330: $i] :
( ( ( ~ ( contains_slb @ SV330 @ SV372 ) )
= $true )
| ( ( contains_cpq @ ( triple @ SV298 @ SV330 @ SV365 ) @ SV372 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[998]) ).
thf(1016,plain,
! [SV366: $i,SV379: $i,SV331: $i,SV299: $i] :
( ( ( ~ ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SV379 ) ) @ SV366 ) )
= $true )
| ( ( ( SV331 = SV366 )
| ( contains_slb @ SV299 @ SV366 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1017,plain,
! [SV299: $i,SV331: $i] :
( ( ! [SY599: $i] :
( ( SV331 != SY599 )
| ! [SY600: $i] : ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY600 ) ) @ SY599 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1000]) ).
thf(1018,plain,
! [SV331: $i,SV299: $i] :
( ( ! [SY601: $i] :
( ~ ( contains_slb @ SV299 @ SY601 )
| ! [SY602: $i] : ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY602 ) ) @ SY601 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1001]) ).
thf(1019,plain,
! [SV348: $i,SV332: $i,SV300: $i] :
( ( ~ ! [SY627: $i,SY628: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY627 ) ) @ SV348 @ SY628 )
| ( SV332 = SV348 )
| ( pair_in_list @ SV300 @ SV348 @ SY628 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1002]) ).
thf(1020,plain,
! [SV348: $i,SV332: $i,SV300: $i] :
( ( ~ ! [SY629: $i,SY630: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY629 ) ) @ SV348 @ SY630 )
| ( SY629 = SY630 )
| ( pair_in_list @ SV300 @ SV348 @ SY630 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1002]) ).
thf(1021,plain,
! [SV300: $i,SV348: $i,SV332: $i] :
( ( ~ ! [SY631: $i,SY632: $i] :
( ( SV332 != SV348 )
| ( SY631 != SY632 )
| ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY631 ) ) @ SV348 @ SY632 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1003]) ).
thf(1022,plain,
! [SV332: $i,SV348: $i,SV300: $i] :
( ( ~ ! [SY633: $i,SY634: $i] :
( ~ ( pair_in_list @ SV300 @ SV348 @ SY634 )
| ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY633 ) ) @ SV348 @ SY634 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1003]) ).
thf(1023,plain,
! [SV349: $i,SV333: $i,SV301: $i,SV373: $i,SV380: $i] :
( ( ~ ( less_than @ SV380 @ SV373 )
| ~ ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SV333 @ ( pair @ SV373 @ SV380 ) ) @ SV349 ) )
| ( check_cpq @ ( triple @ SV301 @ SV333 @ SV349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1024,plain,
! [SV349: $i,SV333: $i,SV301: $i,SV374: $i,SV381: $i] :
( ( ~ ( less_than @ SV381 @ SV374 )
| ~ ( check_cpq @ ( triple @ SV301 @ SV333 @ SV349 ) )
| ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SV333 @ ( pair @ SV374 @ SV381 ) ) @ SV349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1025,plain,
! [SV377: $i,SV369: $i] :
( ( ( ~ ( strictly_less_than @ SV369 @ SV377 ) )
= $true )
| ( ( less_than @ SV369 @ SV377 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1026,plain,
! [SV378: $i,SV370: $i] :
( ( ( ~ ( strictly_less_than @ SV370 @ SV378 ) )
= $true )
| ( ( ~ ( less_than @ SV378 @ SV370 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1027,plain,
! [SV371: $i,SV364: $i,SV330: $i,SV298: $i] :
( ( ( contains_cpq @ ( triple @ SV298 @ SV330 @ SV364 ) @ SV371 )
= $false )
| ( ( contains_slb @ SV330 @ SV371 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1028,plain,
! [SV365: $i,SV298: $i,SV372: $i,SV330: $i] :
( ( ( contains_slb @ SV330 @ SV372 )
= $false )
| ( ( contains_cpq @ ( triple @ SV298 @ SV330 @ SV365 ) @ SV372 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1029,plain,
! [SV366: $i,SV379: $i,SV331: $i,SV299: $i] :
( ( ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SV379 ) ) @ SV366 )
= $false )
| ( ( ( SV331 = SV366 )
| ( contains_slb @ SV299 @ SV366 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1016]) ).
thf(1030,plain,
! [SV299: $i,SV382: $i,SV331: $i] :
( ( ( SV331 != SV382 )
| ! [SY648: $i] : ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY648 ) ) @ SV382 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1031,plain,
! [SV331: $i,SV383: $i,SV299: $i] :
( ( ~ ( contains_slb @ SV299 @ SV383 )
| ! [SY649: $i] : ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY649 ) ) @ SV383 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1032,plain,
! [SV348: $i,SV332: $i,SV300: $i] :
( ( ! [SY627: $i,SY628: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY627 ) ) @ SV348 @ SY628 )
| ( SV332 = SV348 )
| ( pair_in_list @ SV300 @ SV348 @ SY628 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1019]) ).
thf(1033,plain,
! [SV348: $i,SV332: $i,SV300: $i] :
( ( ! [SY629: $i,SY630: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY629 ) ) @ SV348 @ SY630 )
| ( SY629 = SY630 )
| ( pair_in_list @ SV300 @ SV348 @ SY630 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1020]) ).
thf(1034,plain,
! [SV300: $i,SV348: $i,SV332: $i] :
( ( ! [SY631: $i,SY632: $i] :
( ( SV332 != SV348 )
| ( SY631 != SY632 )
| ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY631 ) ) @ SV348 @ SY632 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1021]) ).
thf(1035,plain,
! [SV332: $i,SV348: $i,SV300: $i] :
( ( ! [SY633: $i,SY634: $i] :
( ~ ( pair_in_list @ SV300 @ SV348 @ SY634 )
| ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SY633 ) ) @ SV348 @ SY634 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1022]) ).
thf(1036,plain,
! [SV349: $i,SV333: $i,SV301: $i,SV373: $i,SV380: $i] :
( ( ( ~ ( less_than @ SV380 @ SV373 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SV333 @ ( pair @ SV373 @ SV380 ) ) @ SV349 ) )
| ( check_cpq @ ( triple @ SV301 @ SV333 @ SV349 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1023]) ).
thf(1037,plain,
! [SV349: $i,SV333: $i,SV301: $i,SV374: $i,SV381: $i] :
( ( ( ~ ( less_than @ SV381 @ SV374 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV301 @ SV333 @ SV349 ) )
| ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SV333 @ ( pair @ SV374 @ SV381 ) ) @ SV349 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1024]) ).
thf(1038,plain,
! [SV377: $i,SV369: $i] :
( ( ( strictly_less_than @ SV369 @ SV377 )
= $false )
| ( ( less_than @ SV369 @ SV377 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1025]) ).
thf(1039,plain,
! [SV378: $i,SV370: $i] :
( ( ( strictly_less_than @ SV370 @ SV378 )
= $false )
| ( ( ~ ( less_than @ SV378 @ SV370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1026]) ).
thf(1040,plain,
! [SV379: $i,SV299: $i,SV366: $i,SV331: $i] :
( ( ( SV331 = SV366 )
= $true )
| ( ( contains_slb @ SV299 @ SV366 )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SV379 ) ) @ SV366 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1029]) ).
thf(1041,plain,
! [SV299: $i,SV382: $i,SV331: $i] :
( ( ( ( SV331 != SV382 ) )
= $true )
| ( ( ! [SY648: $i] : ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY648 ) ) @ SV382 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1042,plain,
! [SV331: $i,SV383: $i,SV299: $i] :
( ( ( ~ ( contains_slb @ SV299 @ SV383 ) )
= $true )
| ( ( ! [SY649: $i] : ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY649 ) ) @ SV383 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1031]) ).
thf(1043,plain,
! [SV348: $i,SV384: $i,SV332: $i,SV300: $i] :
( ( ! [SY650: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SV384 ) ) @ SV348 @ SY650 )
| ( SV332 = SV348 )
| ( pair_in_list @ SV300 @ SV348 @ SY650 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1044,plain,
! [SV348: $i,SV385: $i,SV332: $i,SV300: $i] :
( ( ! [SY651: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SV385 ) ) @ SV348 @ SY651 )
| ( SV385 = SY651 )
| ( pair_in_list @ SV300 @ SV348 @ SY651 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1045,plain,
! [SV300: $i,SV386: $i,SV348: $i,SV332: $i] :
( ( ! [SY652: $i] :
( ( SV332 != SV348 )
| ( SV386 != SY652 )
| ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SV386 ) ) @ SV348 @ SY652 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1046,plain,
! [SV387: $i,SV332: $i,SV348: $i,SV300: $i] :
( ( ! [SY653: $i] :
( ~ ( pair_in_list @ SV300 @ SV348 @ SY653 )
| ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SV387 ) ) @ SV348 @ SY653 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1047,plain,
! [SV349: $i,SV333: $i,SV301: $i,SV373: $i,SV380: $i] :
( ( ( less_than @ SV380 @ SV373 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SV333 @ ( pair @ SV373 @ SV380 ) ) @ SV349 ) )
| ( check_cpq @ ( triple @ SV301 @ SV333 @ SV349 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1048,plain,
! [SV349: $i,SV333: $i,SV301: $i,SV374: $i,SV381: $i] :
( ( ( less_than @ SV381 @ SV374 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV301 @ SV333 @ SV349 ) )
| ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SV333 @ ( pair @ SV374 @ SV381 ) ) @ SV349 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1049,plain,
! [SV370: $i,SV378: $i] :
( ( ( less_than @ SV378 @ SV370 )
= $false )
| ( ( strictly_less_than @ SV370 @ SV378 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1050,plain,
! [SV299: $i,SV382: $i,SV331: $i] :
( ( ( SV331 = SV382 )
= $false )
| ( ( ! [SY648: $i] : ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY648 ) ) @ SV382 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1041]) ).
thf(1051,plain,
! [SV331: $i,SV383: $i,SV299: $i] :
( ( ( contains_slb @ SV299 @ SV383 )
= $false )
| ( ( ! [SY649: $i] : ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SY649 ) ) @ SV383 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1042]) ).
thf(1052,plain,
! [SV388: $i,SV348: $i,SV384: $i,SV332: $i,SV300: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SV384 ) ) @ SV348 @ SV388 )
| ( SV332 = SV348 )
| ( pair_in_list @ SV300 @ SV348 @ SV388 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1053,plain,
! [SV389: $i,SV348: $i,SV385: $i,SV332: $i,SV300: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SV385 ) ) @ SV348 @ SV389 )
| ( SV385 = SV389 )
| ( pair_in_list @ SV300 @ SV348 @ SV389 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1054,plain,
! [SV300: $i,SV390: $i,SV386: $i,SV348: $i,SV332: $i] :
( ( ( SV332 != SV348 )
| ( SV386 != SV390 )
| ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SV386 ) ) @ SV348 @ SV390 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1055,plain,
! [SV387: $i,SV332: $i,SV391: $i,SV348: $i,SV300: $i] :
( ( ~ ( pair_in_list @ SV300 @ SV348 @ SV391 )
| ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SV387 ) ) @ SV348 @ SV391 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1056,plain,
! [SV349: $i,SV380: $i,SV373: $i,SV333: $i,SV301: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SV333 @ ( pair @ SV373 @ SV380 ) ) @ SV349 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV301 @ SV333 @ SV349 ) )
= $true )
| ( ( less_than @ SV380 @ SV373 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1047]) ).
thf(1057,plain,
! [SV381: $i,SV374: $i,SV349: $i,SV333: $i,SV301: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV301 @ SV333 @ SV349 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SV333 @ ( pair @ SV374 @ SV381 ) ) @ SV349 ) )
= $true )
| ( ( less_than @ SV381 @ SV374 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1058,plain,
! [SV382: $i,SV392: $i,SV331: $i,SV299: $i] :
( ( ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SV392 ) ) @ SV382 )
= $true )
| ( ( SV331 = SV382 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1059,plain,
! [SV383: $i,SV393: $i,SV331: $i,SV299: $i] :
( ( ( contains_slb @ ( insert_slb @ SV299 @ ( pair @ SV331 @ SV393 ) ) @ SV383 )
= $true )
| ( ( contains_slb @ SV299 @ SV383 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1060,plain,
! [SV388: $i,SV348: $i,SV384: $i,SV332: $i,SV300: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SV384 ) ) @ SV348 @ SV388 ) )
= $true )
| ( ( ( SV332 = SV348 )
| ( pair_in_list @ SV300 @ SV348 @ SV388 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1052]) ).
thf(1061,plain,
! [SV389: $i,SV348: $i,SV385: $i,SV332: $i,SV300: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SV385 ) ) @ SV348 @ SV389 ) )
= $true )
| ( ( ( SV385 = SV389 )
| ( pair_in_list @ SV300 @ SV348 @ SV389 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1053]) ).
thf(1062,plain,
! [SV300: $i,SV390: $i,SV386: $i,SV348: $i,SV332: $i] :
( ( ( ( SV332 != SV348 )
| ( SV386 != SV390 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SV386 ) ) @ SV348 @ SV390 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1054]) ).
thf(1063,plain,
! [SV387: $i,SV332: $i,SV391: $i,SV348: $i,SV300: $i] :
( ( ( ~ ( pair_in_list @ SV300 @ SV348 @ SV391 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SV387 ) ) @ SV348 @ SV391 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1064,plain,
! [SV349: $i,SV380: $i,SV373: $i,SV333: $i,SV301: $i] :
( ( ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SV333 @ ( pair @ SV373 @ SV380 ) ) @ SV349 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV301 @ SV333 @ SV349 ) )
= $true )
| ( ( less_than @ SV380 @ SV373 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1056]) ).
thf(1065,plain,
! [SV381: $i,SV374: $i,SV349: $i,SV333: $i,SV301: $i] :
( ( ( check_cpq @ ( triple @ SV301 @ SV333 @ SV349 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV301 @ ( insert_slb @ SV333 @ ( pair @ SV374 @ SV381 ) ) @ SV349 ) )
= $true )
| ( ( less_than @ SV381 @ SV374 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1066,plain,
! [SV388: $i,SV348: $i,SV384: $i,SV332: $i,SV300: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SV384 ) ) @ SV348 @ SV388 )
= $false )
| ( ( ( SV332 = SV348 )
| ( pair_in_list @ SV300 @ SV348 @ SV388 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1060]) ).
thf(1067,plain,
! [SV389: $i,SV348: $i,SV385: $i,SV332: $i,SV300: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SV385 ) ) @ SV348 @ SV389 )
= $false )
| ( ( ( SV385 = SV389 )
| ( pair_in_list @ SV300 @ SV348 @ SV389 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1061]) ).
thf(1068,plain,
! [SV300: $i,SV390: $i,SV386: $i,SV348: $i,SV332: $i] :
( ( ( ( SV332 != SV348 ) )
= $true )
| ( ( ( SV386 != SV390 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SV386 ) ) @ SV348 @ SV390 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1062]) ).
thf(1069,plain,
! [SV387: $i,SV332: $i,SV391: $i,SV348: $i,SV300: $i] :
( ( ( pair_in_list @ SV300 @ SV348 @ SV391 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SV387 ) ) @ SV348 @ SV391 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1063]) ).
thf(1070,plain,
! [SV384: $i,SV388: $i,SV300: $i,SV348: $i,SV332: $i] :
( ( ( SV332 = SV348 )
= $true )
| ( ( pair_in_list @ SV300 @ SV348 @ SV388 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SV384 ) ) @ SV348 @ SV388 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1066]) ).
thf(1071,plain,
! [SV332: $i,SV348: $i,SV300: $i,SV389: $i,SV385: $i] :
( ( ( SV385 = SV389 )
= $true )
| ( ( pair_in_list @ SV300 @ SV348 @ SV389 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SV385 ) ) @ SV348 @ SV389 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1067]) ).
thf(1072,plain,
! [SV300: $i,SV390: $i,SV386: $i,SV348: $i,SV332: $i] :
( ( ( SV332 = SV348 )
= $false )
| ( ( ( SV386 != SV390 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SV386 ) ) @ SV348 @ SV390 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1068]) ).
thf(1073,plain,
! [SV300: $i,SV348: $i,SV332: $i,SV390: $i,SV386: $i] :
( ( ( SV386 = SV390 )
= $false )
| ( ( SV332 = SV348 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV300 @ ( pair @ SV332 @ SV386 ) ) @ SV348 @ SV390 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1074,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[798,1073,1071,1070,1069,1065,1064,1059,1058,1049,1040,1038,1028,1027,1011,1010,1009,1008,1007,1006,988,987,986,969,968,951,948,946,945,931,924,923,921,920,897,888,886,885,884,883,874,870,862,850,841,840,839,820,817,809,808,807]) ).
thf(1075,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1074,438,756]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV374+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.15/0.36 % Computer : n013.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Wed Jun 15 18:17:44 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.41 .
% 0.15/0.41
% 0.15/0.41 No.of.Axioms: 41
% 0.15/0.41
% 0.15/0.41 Length.of.Defs: 0
% 0.15/0.41
% 0.15/0.41 Contains.Choice.Funs: false
% 0.22/0.46 .
% 0.22/0.46 (rf:0,axioms:41,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:43,loop_count:0,foatp_calls:0,translation:fof_full)....................................................................
% 1.02/1.42
% 1.02/1.42 ********************************
% 1.02/1.42 * All subproblems solved! *
% 1.02/1.42 ********************************
% 1.02/1.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:42,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:1074,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.65/1.88
% 1.65/1.88 %**** Beginning of derivation protocol ****
% 1.65/1.88 % SZS output start CNFRefutation
% See solution above
% 1.65/1.89
% 1.65/1.89 %**** End of derivation protocol ****
% 1.65/1.89 %**** no. of clauses in derivation: 1075 ****
% 1.65/1.89 %**** clause counter: 1074 ****
% 1.65/1.89
% 1.65/1.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:42,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:1074,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------