TSTP Solution File: SWV405+1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SWV405+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 : n026.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 20:12:21 EDT 2022
% Result : Theorem 0.59s 0.77s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 73
% Syntax : Number of formulae : 804 ( 547 unt; 31 typ; 0 def)
% Number of atoms : 4124 (1606 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 10307 (1129 ~;1176 |; 57 &;7875 @)
% ( 19 <=>; 51 =>; 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 : 34 ( 31 usr; 9 con; 0-3 aty)
% Number of variables : 2796 ( 0 ^2796 !; 0 ?;2796 :)
% 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_SY121,type,
sK2_SY121: $i ).
thf(tp_sK3_W,type,
sK3_W: $i ).
thf(tp_sK4_SY126,type,
sK4_SY126: $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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax51) ).
thf(4,axiom,
! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax42) ).
thf(13,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ( W = bad ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).
thf(14,axiom,
! [U: $i,V: $i] :
( ( ok @ ( triple @ U @ V @ bad ) )
<=> $false ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax37) ).
thf(18,axiom,
! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax32) ).
thf(23,axiom,
! [U: $i] : ( succ_cpq @ U @ U ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax29) ).
thf(26,axiom,
! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax23) ).
thf(32,axiom,
! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax21) ).
thf(34,axiom,
! [U: $i] :
~ ( contains_slb @ create_slb @ U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
thf(35,axiom,
! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).
thf(36,axiom,
~ ( isnonempty_slb @ create_slb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
thf(37,axiom,
! [U: $i] : ( less_than @ bottom @ U ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',stricly_smaller_definition) ).
thf(39,axiom,
! [U: $i] : ( less_than @ U @ U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(40,axiom,
! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(42,conjecture,
! [U: $i,V: $i] :
( ( check_cpq @ ( triple @ U @ create_slb @ V ) )
<=> ! [W: $i,X: $i] :
( ( pair_in_list @ create_slb @ W @ X )
=> ( less_than @ X @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l41_co) ).
thf(43,negated_conjecture,
( ( ! [U: $i,V: $i] :
( ( check_cpq @ ( triple @ U @ create_slb @ V ) )
<=> ! [W: $i,X: $i] :
( ( pair_in_list @ create_slb @ W @ X )
=> ( less_than @ X @ W ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[42]) ).
thf(44,plain,
( ( ! [U: $i,V: $i] :
( ( check_cpq @ ( triple @ U @ create_slb @ V ) )
<=> ! [W: $i,X: $i] :
( ( pair_in_list @ create_slb @ W @ X )
=> ( less_than @ X @ W ) ) ) )
= $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,
( ( ! [SY121: $i] :
( ( check_cpq @ ( triple @ sK1_U @ create_slb @ SY121 ) )
<=> ! [W: $i,X: $i] :
( ( pair_in_list @ create_slb @ W @ X )
=> ( less_than @ X @ W ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(87,plain,
( ( ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY121 ) )
<=> ! [W: $i,X: $i] :
( ( pair_in_list @ create_slb @ W @ X )
=> ( less_than @ X @ W ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[86]) ).
thf(88,plain,
( ( ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY121 ) )
=> ! [W: $i,X: $i] :
( ( pair_in_list @ create_slb @ W @ X )
=> ( less_than @ X @ W ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[87]) ).
thf(89,plain,
( ( ! [W: $i,X: $i] :
( ( pair_in_list @ create_slb @ W @ X )
=> ( less_than @ X @ W ) )
=> ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY121 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[87]) ).
thf(90,plain,
( ( ~ ( ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY121 ) )
=> ! [W: $i,X: $i] :
( ( pair_in_list @ create_slb @ W @ X )
=> ( less_than @ X @ W ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[88]) ).
thf(91,plain,
( ( ~ ( ! [W: $i,X: $i] :
( ( pair_in_list @ create_slb @ W @ X )
=> ( less_than @ X @ W ) )
=> ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY121 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[89]) ).
thf(92,plain,
( ( ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY121 ) )
& ( pair_in_list @ create_slb @ sK3_W @ sK4_SY126 )
& ~ ( less_than @ sK4_SY126 @ sK3_W ) )
= $true ),
inference(extcnf_combined,[status(esa)],[90]) ).
thf(93,plain,
( ( ! [W: $i,X: $i] :
( ~ ( pair_in_list @ create_slb @ W @ X )
| ( less_than @ X @ W ) )
& ~ ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY121 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[91]) ).
thf(94,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(95,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(96,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(97,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(98,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(99,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(100,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(101,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( triple @ U @ V @ W ) )
| ( W = bad ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(102,plain,
( ( ! [U: $i,V: $i] :
~ ( ok @ ( triple @ U @ V @ bad ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(103,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(104,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(105,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(106,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[63]) ).
thf(107,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(108,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(109,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(110,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(111,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(112,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(113,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(114,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(115,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(116,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(117,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(118,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( less_than @ U @ V )
| ~ ( less_than @ V @ W )
| ( less_than @ U @ W ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(119,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(120,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(121,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)],[116]) ).
thf(122,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(123,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(124,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(125,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(126,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)],[115]) ).
thf(127,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(128,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)],[114]) ).
thf(129,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(130,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)],[113]) ).
thf(131,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(132,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)],[112]) ).
thf(133,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(134,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)],[111]) ).
thf(135,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)],[110]) ).
thf(136,plain,
( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(137,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(138,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(139,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(140,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(141,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(142,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)],[105]) ).
thf(143,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)],[104]) ).
thf(144,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)],[103]) ).
thf(145,plain,
( ( ! [U: $i,V: $i] :
~ ( ok @ ( triple @ U @ V @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(146,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( triple @ U @ V @ W ) )
| ( W = bad ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(147,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(148,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)],[100]) ).
thf(149,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)],[99]) ).
thf(150,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)],[98]) ).
thf(151,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(152,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)],[97]) ).
thf(153,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)],[96]) ).
thf(154,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)],[95]) ).
thf(155,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(156,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)],[94]) ).
thf(157,plain,
( ( ! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(158,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(159,plain,
( ( ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY121 ) )
& ( pair_in_list @ create_slb @ sK3_W @ sK4_SY126 )
& ~ ( less_than @ sK4_SY126 @ sK3_W ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(160,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)],[128]) ).
thf(161,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)],[126]) ).
thf(162,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)],[144]) ).
thf(163,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)],[142]) ).
thf(164,plain,
( ( ~ ( ~ ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY121 ) )
| ~ ~ ( ~ ( pair_in_list @ create_slb @ sK3_W @ sK4_SY126 )
| ~ ~ ( less_than @ sK4_SY126 @ sK3_W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(165,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)],[121]) ).
thf(166,plain,
! [SV1: $i] :
( ( ! [SY127: $i,SY128: $i] :
( ~ ( less_than @ SV1 @ SY127 )
| ~ ( less_than @ SY127 @ SY128 )
| ( less_than @ SV1 @ SY128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(167,plain,
! [SV2: $i] :
( ( ! [SY129: $i] :
( ( less_than @ SV2 @ SY129 )
| ( less_than @ SY129 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(168,plain,
! [SV3: $i] :
( ( less_than @ SV3 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(169,plain,
! [SV4: $i] :
( ( less_than @ bottom @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(170,plain,
( ( isnonempty_slb @ create_slb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(171,plain,
! [SV5: $i] :
( ( ! [SY130: $i,SY131: $i] : ( isnonempty_slb @ ( insert_slb @ SV5 @ ( pair @ SY130 @ SY131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(172,plain,
! [SV6: $i] :
( ( ~ ( contains_slb @ create_slb @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(173,plain,
! [SV7: $i] :
( ( ! [SY132: $i] :
~ ( pair_in_list @ create_slb @ SV7 @ SY132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(174,plain,
! [SV8: $i] :
( ( ! [SY133: $i,SY134: $i] :
( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SY133 @ SY134 ) ) @ SY133 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(175,plain,
! [SV9: $i] :
( ( ! [SY135: $i,SY136: $i] :
( ( SY135 = SY136 )
| ~ ( contains_slb @ SV9 @ SY136 )
| ! [SY137: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SY135 @ SY137 ) ) @ SY136 )
= ( insert_slb @ ( remove_slb @ SV9 @ SY136 ) @ ( pair @ SY135 @ SY137 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(176,plain,
! [SV10: $i] :
( ( ! [SY138: $i,SY139: $i] :
( ( lookup_slb @ ( insert_slb @ SV10 @ ( pair @ SY138 @ SY139 ) ) @ SY138 )
= SY139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(177,plain,
! [SV11: $i] :
( ( ! [SY140: $i,SY141: $i] :
( ( SY140 = SY141 )
| ~ ( contains_slb @ SV11 @ SY141 )
| ! [SY142: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SY140 @ SY142 ) ) @ SY141 )
= ( lookup_slb @ SV11 @ SY141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(178,plain,
! [SV12: $i] :
( ( ( update_slb @ create_slb @ SV12 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(179,plain,
! [SV13: $i] :
( ( ! [SY143: $i,SY144: $i,SY145: $i] :
( ~ ( strictly_less_than @ SY145 @ SY144 )
| ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SY143 @ SY145 ) ) @ SY144 )
= ( insert_slb @ ( update_slb @ SV13 @ SY144 ) @ ( pair @ SY143 @ SY144 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(180,plain,
! [SV14: $i] :
( ( ! [SY146: $i,SY147: $i,SY148: $i] :
( ~ ( less_than @ SY147 @ SY148 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SY146 @ SY148 ) ) @ SY147 )
= ( insert_slb @ ( update_slb @ SV14 @ SY147 ) @ ( pair @ SY146 @ SY148 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(181,plain,
! [SV15: $i] :
( ( succ_cpq @ SV15 @ SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(182,plain,
! [SV16: $i] :
( ( ! [SY149: $i] :
( ~ ( succ_cpq @ SV16 @ SY149 )
| ! [SY150: $i] : ( succ_cpq @ SV16 @ ( insert_cpq @ SY149 @ SY150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(183,plain,
! [SV17: $i] :
( ( ! [SY151: $i] :
( ~ ( succ_cpq @ SV17 @ SY151 )
| ! [SY152: $i] : ( succ_cpq @ SV17 @ ( remove_cpq @ SY151 @ SY152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(184,plain,
! [SV18: $i] :
( ( ! [SY153: $i] :
( ~ ( succ_cpq @ SV18 @ SY153 )
| ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SY153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(185,plain,
! [SV19: $i] :
( ( ! [SY154: $i] :
( ~ ( succ_cpq @ SV19 @ SY154 )
| ( succ_cpq @ SV19 @ ( removemin_cpq_eff @ SY154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(186,plain,
! [SV20: $i] :
( ( ! [SY155: $i] : ( check_cpq @ ( triple @ SV20 @ create_slb @ SY155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(187,plain,
! [SV21: $i] :
( ( ! [SY156: $i,SY157: $i,SY158: $i,SY159: $i] :
( ~ ( strictly_less_than @ SY158 @ SY159 )
| ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SY156 @ ( pair @ SY158 @ SY159 ) ) @ SY157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(188,plain,
! [SV22: $i] :
( ( ! [SY160: $i] :
~ ( ok @ ( triple @ SV22 @ SY160 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(189,plain,
! [SV23: $i] :
( ( ! [SY161: $i,SY162: $i] :
( ( ok @ ( triple @ SV23 @ SY161 @ SY162 ) )
| ( SY162 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(190,plain,
! [SV24: $i] :
( ( ! [SY163: $i,SY164: $i,SY165: $i] :
( ( insert_cpq @ ( triple @ SV24 @ SY163 @ SY164 ) @ SY165 )
= ( triple @ ( insert_pqp @ SV24 @ SY165 ) @ ( insert_slb @ SY163 @ ( pair @ SY165 @ bottom ) ) @ SY164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(191,plain,
! [SV25: $i] :
( ( ! [SY166: $i,SY167: $i,SY168: $i] :
( ( contains_slb @ SY166 @ SY168 )
| ( ( remove_cpq @ ( triple @ SV25 @ SY166 @ SY167 ) @ SY168 )
= ( triple @ SV25 @ SY166 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(192,plain,
! [SV26: $i] :
( ( ! [SY169: $i,SY170: $i,SY171: $i] :
( ~ ( contains_slb @ SY169 @ SY171 )
| ~ ( less_than @ ( lookup_slb @ SY169 @ SY171 ) @ SY171 )
| ( ( remove_cpq @ ( triple @ SV26 @ SY169 @ SY170 ) @ SY171 )
= ( triple @ ( remove_pqp @ SV26 @ SY171 ) @ ( remove_slb @ SY169 @ SY171 ) @ SY170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(193,plain,
! [SV27: $i] :
( ( ! [SY172: $i,SY173: $i,SY174: $i] :
( ~ ( contains_slb @ SY172 @ SY174 )
| ~ ( strictly_less_than @ SY174 @ ( lookup_slb @ SY172 @ SY174 ) )
| ( ( remove_cpq @ ( triple @ SV27 @ SY172 @ SY173 ) @ SY174 )
= ( triple @ ( remove_pqp @ SV27 @ SY174 ) @ ( remove_slb @ SY172 @ SY174 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(194,plain,
! [SV28: $i] :
( ( ! [SY175: $i] :
( ( findmin_cpq_eff @ ( triple @ SV28 @ create_slb @ SY175 ) )
= ( triple @ SV28 @ create_slb @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(195,plain,
! [SV29: $i] :
( ( ! [SY176: $i] :
( ( SY176 = create_slb )
| ( contains_slb @ SY176 @ ( findmin_pqp_res @ SV29 ) )
| ! [SY177: $i] :
( ( findmin_cpq_eff @ ( triple @ SV29 @ SY176 @ SY177 ) )
= ( triple @ SV29 @ ( update_slb @ SY176 @ ( findmin_pqp_res @ SV29 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(196,plain,
! [SV30: $i] :
( ( ! [SY178: $i] :
( ( SY178 = create_slb )
| ~ ( contains_slb @ SY178 @ ( findmin_pqp_res @ SV30 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SY178 @ ( findmin_pqp_res @ SV30 ) ) )
| ! [SY179: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SY178 @ SY179 ) )
= ( triple @ SV30 @ ( update_slb @ SY178 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(197,plain,
! [SV31: $i] :
( ( ! [SY180: $i] :
( ( SY180 = create_slb )
| ~ ( contains_slb @ SY180 @ ( findmin_pqp_res @ SV31 ) )
| ~ ( less_than @ ( lookup_slb @ SY180 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) )
| ! [SY181: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SY180 @ SY181 ) )
= ( triple @ SV31 @ ( update_slb @ SY180 @ ( findmin_pqp_res @ SV31 ) ) @ SY181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(198,plain,
! [SV32: $i] :
( ( ! [SY182: $i] :
( ( findmin_cpq_res @ ( triple @ SV32 @ create_slb @ SY182 ) )
= bottom ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(199,plain,
! [SV33: $i] :
( ( ! [SY183: $i] :
( ( SY183 = create_slb )
| ! [SY184: $i] :
( ( findmin_cpq_res @ ( triple @ SV33 @ SY183 @ SY184 ) )
= ( findmin_pqp_res @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(200,plain,
! [SV34: $i] :
( ( ( removemin_cpq_eff @ SV34 )
= ( remove_cpq @ ( findmin_cpq_eff @ SV34 ) @ ( findmin_cpq_res @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(201,plain,
! [SV35: $i] :
( ( ( removemin_cpq_res @ SV35 )
= ( findmin_cpq_res @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(202,plain,
! [SV36: $i] :
( ( ! [SY185: $i,SY186: $i] :
~ ( ~ ~ ( ~ ! [SY187: $i,SY188: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SY185 @ SY187 ) ) @ SY186 @ SY188 )
| ( SY185 = SY186 )
| ( pair_in_list @ SV36 @ SY186 @ SY188 ) )
| ~ ! [SY189: $i,SY190: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SY185 @ SY189 ) ) @ SY186 @ SY190 )
| ( SY189 = SY190 )
| ( pair_in_list @ SV36 @ SY186 @ SY190 ) ) )
| ~ ~ ( ~ ! [SY191: $i,SY192: $i] :
( ( SY185 != SY186 )
| ( SY191 != SY192 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SY185 @ SY191 ) ) @ SY186 @ SY192 ) )
| ~ ! [SY193: $i,SY194: $i] :
( ~ ( pair_in_list @ SV36 @ SY186 @ SY194 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SY185 @ SY193 ) ) @ SY186 @ SY194 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(203,plain,
! [SV37: $i] :
( ( ! [SY195: $i] :
~ ( ~ ! [SY196: $i] :
( ! [SY197: $i] :
~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SY195 @ SY197 ) ) @ SY196 )
| ( SY195 = SY196 )
| ( contains_slb @ SV37 @ SY196 ) )
| ~ ~ ( ~ ! [SY198: $i] :
( ( SY195 != SY198 )
| ! [SY199: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SY195 @ SY199 ) ) @ SY198 ) )
| ~ ! [SY200: $i] :
( ~ ( contains_slb @ SV37 @ SY200 )
| ! [SY201: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SY195 @ SY201 ) ) @ SY200 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(204,plain,
! [SV38: $i] :
( ( ! [SY202: $i] :
~ ( ~ ! [SY203: $i,SY204: $i] :
( ~ ( contains_cpq @ ( triple @ SV38 @ SY202 @ SY203 ) @ SY204 )
| ( contains_slb @ SY202 @ SY204 ) )
| ~ ! [SY205: $i,SY206: $i] :
( ~ ( contains_slb @ SY202 @ SY206 )
| ( contains_cpq @ ( triple @ SV38 @ SY202 @ SY205 ) @ SY206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(205,plain,
! [SV39: $i] :
( ( ! [SY207: $i,SY208: $i] :
~ ( ~ ! [SY209: $i,SY210: $i] :
( ~ ( less_than @ SY210 @ SY209 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SY207 @ ( pair @ SY209 @ SY210 ) ) @ SY208 ) )
| ( check_cpq @ ( triple @ SV39 @ SY207 @ SY208 ) ) )
| ~ ! [SY211: $i,SY212: $i] :
( ~ ( less_than @ SY212 @ SY211 )
| ~ ( check_cpq @ ( triple @ SV39 @ SY207 @ SY208 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SY207 @ ( pair @ SY211 @ SY212 ) ) @ SY208 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(206,plain,
( ( ~ ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY121 ) )
| ~ ~ ( ~ ( pair_in_list @ create_slb @ sK3_W @ sK4_SY126 )
| ~ ~ ( less_than @ sK4_SY126 @ sK3_W ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(207,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)],[165]) ).
thf(208,plain,
! [SV40: $i,SV1: $i] :
( ( ! [SY213: $i] :
( ~ ( less_than @ SV1 @ SV40 )
| ~ ( less_than @ SV40 @ SY213 )
| ( less_than @ SV1 @ SY213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(209,plain,
! [SV41: $i,SV2: $i] :
( ( ( less_than @ SV2 @ SV41 )
| ( less_than @ SV41 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(210,plain,
! [SV42: $i,SV5: $i] :
( ( ! [SY214: $i] : ( isnonempty_slb @ ( insert_slb @ SV5 @ ( pair @ SV42 @ SY214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(211,plain,
! [SV6: $i] :
( ( contains_slb @ create_slb @ SV6 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(212,plain,
! [SV43: $i,SV7: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV7 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(213,plain,
! [SV44: $i,SV8: $i] :
( ( ! [SY215: $i] :
( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SV44 @ SY215 ) ) @ SV44 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(214,plain,
! [SV9: $i,SV45: $i] :
( ( ! [SY216: $i] :
( ( SV45 = SY216 )
| ~ ( contains_slb @ SV9 @ SY216 )
| ! [SY217: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV45 @ SY217 ) ) @ SY216 )
= ( insert_slb @ ( remove_slb @ SV9 @ SY216 ) @ ( pair @ SV45 @ SY217 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(215,plain,
! [SV46: $i,SV10: $i] :
( ( ! [SY218: $i] :
( ( lookup_slb @ ( insert_slb @ SV10 @ ( pair @ SV46 @ SY218 ) ) @ SV46 )
= SY218 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(216,plain,
! [SV11: $i,SV47: $i] :
( ( ! [SY219: $i] :
( ( SV47 = SY219 )
| ~ ( contains_slb @ SV11 @ SY219 )
| ! [SY220: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV47 @ SY220 ) ) @ SY219 )
= ( lookup_slb @ SV11 @ SY219 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(217,plain,
! [SV48: $i,SV13: $i] :
( ( ! [SY221: $i,SY222: $i] :
( ~ ( strictly_less_than @ SY222 @ SY221 )
| ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV48 @ SY222 ) ) @ SY221 )
= ( insert_slb @ ( update_slb @ SV13 @ SY221 ) @ ( pair @ SV48 @ SY221 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(218,plain,
! [SV49: $i,SV14: $i] :
( ( ! [SY223: $i,SY224: $i] :
( ~ ( less_than @ SY223 @ SY224 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV49 @ SY224 ) ) @ SY223 )
= ( insert_slb @ ( update_slb @ SV14 @ SY223 ) @ ( pair @ SV49 @ SY224 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(219,plain,
! [SV50: $i,SV16: $i] :
( ( ~ ( succ_cpq @ SV16 @ SV50 )
| ! [SY225: $i] : ( succ_cpq @ SV16 @ ( insert_cpq @ SV50 @ SY225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(220,plain,
! [SV51: $i,SV17: $i] :
( ( ~ ( succ_cpq @ SV17 @ SV51 )
| ! [SY226: $i] : ( succ_cpq @ SV17 @ ( remove_cpq @ SV51 @ SY226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(221,plain,
! [SV52: $i,SV18: $i] :
( ( ~ ( succ_cpq @ SV18 @ SV52 )
| ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(222,plain,
! [SV53: $i,SV19: $i] :
( ( ~ ( succ_cpq @ SV19 @ SV53 )
| ( succ_cpq @ SV19 @ ( removemin_cpq_eff @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(223,plain,
! [SV54: $i,SV20: $i] :
( ( check_cpq @ ( triple @ SV20 @ create_slb @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(224,plain,
! [SV55: $i,SV21: $i] :
( ( ! [SY227: $i,SY228: $i,SY229: $i] :
( ~ ( strictly_less_than @ SY228 @ SY229 )
| ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV55 @ ( pair @ SY228 @ SY229 ) ) @ SY227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(225,plain,
! [SV56: $i,SV22: $i] :
( ( ~ ( ok @ ( triple @ SV22 @ SV56 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(226,plain,
! [SV57: $i,SV23: $i] :
( ( ! [SY230: $i] :
( ( ok @ ( triple @ SV23 @ SV57 @ SY230 ) )
| ( SY230 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(227,plain,
! [SV58: $i,SV24: $i] :
( ( ! [SY231: $i,SY232: $i] :
( ( insert_cpq @ ( triple @ SV24 @ SV58 @ SY231 ) @ SY232 )
= ( triple @ ( insert_pqp @ SV24 @ SY232 ) @ ( insert_slb @ SV58 @ ( pair @ SY232 @ bottom ) ) @ SY231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(228,plain,
! [SV25: $i,SV59: $i] :
( ( ! [SY233: $i,SY234: $i] :
( ( contains_slb @ SV59 @ SY234 )
| ( ( remove_cpq @ ( triple @ SV25 @ SV59 @ SY233 ) @ SY234 )
= ( triple @ SV25 @ SV59 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(229,plain,
! [SV26: $i,SV60: $i] :
( ( ! [SY235: $i,SY236: $i] :
( ~ ( contains_slb @ SV60 @ SY236 )
| ~ ( less_than @ ( lookup_slb @ SV60 @ SY236 ) @ SY236 )
| ( ( remove_cpq @ ( triple @ SV26 @ SV60 @ SY235 ) @ SY236 )
= ( triple @ ( remove_pqp @ SV26 @ SY236 ) @ ( remove_slb @ SV60 @ SY236 ) @ SY235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(230,plain,
! [SV27: $i,SV61: $i] :
( ( ! [SY237: $i,SY238: $i] :
( ~ ( contains_slb @ SV61 @ SY238 )
| ~ ( strictly_less_than @ SY238 @ ( lookup_slb @ SV61 @ SY238 ) )
| ( ( remove_cpq @ ( triple @ SV27 @ SV61 @ SY237 ) @ SY238 )
= ( triple @ ( remove_pqp @ SV27 @ SY238 ) @ ( remove_slb @ SV61 @ SY238 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(231,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)],[194]) ).
thf(232,plain,
! [SV29: $i,SV63: $i] :
( ( ( SV63 = create_slb )
| ( contains_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) )
| ! [SY239: $i] :
( ( findmin_cpq_eff @ ( triple @ SV29 @ SV63 @ SY239 ) )
= ( triple @ SV29 @ ( update_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(233,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 ) ) )
| ! [SY240: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY240 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(234,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 ) )
| ! [SY241: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY241 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(235,plain,
! [SV66: $i,SV32: $i] :
( ( ( findmin_cpq_res @ ( triple @ SV32 @ create_slb @ SV66 ) )
= bottom )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(236,plain,
! [SV33: $i,SV67: $i] :
( ( ( SV67 = create_slb )
| ! [SY242: $i] :
( ( findmin_cpq_res @ ( triple @ SV33 @ SV67 @ SY242 ) )
= ( findmin_pqp_res @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(237,plain,
! [SV68: $i,SV36: $i] :
( ( ! [SY243: $i] :
~ ( ~ ~ ( ~ ! [SY244: $i,SY245: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY244 ) ) @ SY243 @ SY245 )
| ( SV68 = SY243 )
| ( pair_in_list @ SV36 @ SY243 @ SY245 ) )
| ~ ! [SY246: $i,SY247: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY246 ) ) @ SY243 @ SY247 )
| ( SY246 = SY247 )
| ( pair_in_list @ SV36 @ SY243 @ SY247 ) ) )
| ~ ~ ( ~ ! [SY248: $i,SY249: $i] :
( ( SV68 != SY243 )
| ( SY248 != SY249 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY248 ) ) @ SY243 @ SY249 ) )
| ~ ! [SY250: $i,SY251: $i] :
( ~ ( pair_in_list @ SV36 @ SY243 @ SY251 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY250 ) ) @ SY243 @ SY251 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(238,plain,
! [SV69: $i,SV37: $i] :
( ( ~ ( ~ ! [SY252: $i] :
( ! [SY253: $i] :
~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY253 ) ) @ SY252 )
| ( SV69 = SY252 )
| ( contains_slb @ SV37 @ SY252 ) )
| ~ ~ ( ~ ! [SY254: $i] :
( ( SV69 != SY254 )
| ! [SY255: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY255 ) ) @ SY254 ) )
| ~ ! [SY256: $i] :
( ~ ( contains_slb @ SV37 @ SY256 )
| ! [SY257: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY257 ) ) @ SY256 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(239,plain,
! [SV70: $i,SV38: $i] :
( ( ~ ( ~ ! [SY258: $i,SY259: $i] :
( ~ ( contains_cpq @ ( triple @ SV38 @ SV70 @ SY258 ) @ SY259 )
| ( contains_slb @ SV70 @ SY259 ) )
| ~ ! [SY260: $i,SY261: $i] :
( ~ ( contains_slb @ SV70 @ SY261 )
| ( contains_cpq @ ( triple @ SV38 @ SV70 @ SY260 ) @ SY261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(240,plain,
! [SV71: $i,SV39: $i] :
( ( ! [SY262: $i] :
~ ( ~ ! [SY263: $i,SY264: $i] :
( ~ ( less_than @ SY264 @ SY263 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY263 @ SY264 ) ) @ SY262 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SY262 ) ) )
| ~ ! [SY265: $i,SY266: $i] :
( ~ ( less_than @ SY266 @ SY265 )
| ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SY262 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY265 @ SY266 ) ) @ SY262 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(241,plain,
( ( ~ ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY121 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[206]) ).
thf(242,plain,
( ( ~ ~ ( ~ ( pair_in_list @ create_slb @ sK3_W @ sK4_SY126 )
| ~ ~ ( less_than @ sK4_SY126 @ sK3_W ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[206]) ).
thf(243,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)],[207]) ).
thf(244,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)],[207]) ).
thf(245,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)],[208]) ).
thf(246,plain,
! [SV41: $i,SV2: $i] :
( ( ( less_than @ SV2 @ SV41 )
= $true )
| ( ( less_than @ SV41 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(247,plain,
! [SV73: $i,SV42: $i,SV5: $i] :
( ( isnonempty_slb @ ( insert_slb @ SV5 @ ( pair @ SV42 @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(248,plain,
! [SV43: $i,SV7: $i] :
( ( pair_in_list @ create_slb @ SV7 @ SV43 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(249,plain,
! [SV74: $i,SV44: $i,SV8: $i] :
( ( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SV44 @ SV74 ) ) @ SV44 )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(250,plain,
! [SV9: $i,SV75: $i,SV45: $i] :
( ( ( SV45 = SV75 )
| ~ ( contains_slb @ SV9 @ SV75 )
| ! [SY267: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV45 @ SY267 ) ) @ SV75 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV75 ) @ ( pair @ SV45 @ SY267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(251,plain,
! [SV76: $i,SV46: $i,SV10: $i] :
( ( ( lookup_slb @ ( insert_slb @ SV10 @ ( pair @ SV46 @ SV76 ) ) @ SV46 )
= SV76 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(252,plain,
! [SV11: $i,SV77: $i,SV47: $i] :
( ( ( SV47 = SV77 )
| ~ ( contains_slb @ SV11 @ SV77 )
| ! [SY268: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV47 @ SY268 ) ) @ SV77 )
= ( lookup_slb @ SV11 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(253,plain,
! [SV48: $i,SV13: $i,SV78: $i] :
( ( ! [SY269: $i] :
( ~ ( strictly_less_than @ SY269 @ SV78 )
| ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV48 @ SY269 ) ) @ SV78 )
= ( insert_slb @ ( update_slb @ SV13 @ SV78 ) @ ( pair @ SV48 @ SV78 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(254,plain,
! [SV49: $i,SV14: $i,SV79: $i] :
( ( ! [SY270: $i] :
( ~ ( less_than @ SV79 @ SY270 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV49 @ SY270 ) ) @ SV79 )
= ( insert_slb @ ( update_slb @ SV14 @ SV79 ) @ ( pair @ SV49 @ SY270 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(255,plain,
! [SV50: $i,SV16: $i] :
( ( ( ~ ( succ_cpq @ SV16 @ SV50 ) )
= $true )
| ( ( ! [SY225: $i] : ( succ_cpq @ SV16 @ ( insert_cpq @ SV50 @ SY225 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(256,plain,
! [SV51: $i,SV17: $i] :
( ( ( ~ ( succ_cpq @ SV17 @ SV51 ) )
= $true )
| ( ( ! [SY226: $i] : ( succ_cpq @ SV17 @ ( remove_cpq @ SV51 @ SY226 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(257,plain,
! [SV52: $i,SV18: $i] :
( ( ( ~ ( succ_cpq @ SV18 @ SV52 ) )
= $true )
| ( ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(258,plain,
! [SV53: $i,SV19: $i] :
( ( ( ~ ( succ_cpq @ SV19 @ SV53 ) )
= $true )
| ( ( succ_cpq @ SV19 @ ( removemin_cpq_eff @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(259,plain,
! [SV80: $i,SV55: $i,SV21: $i] :
( ( ! [SY271: $i,SY272: $i] :
( ~ ( strictly_less_than @ SY271 @ SY272 )
| ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV55 @ ( pair @ SY271 @ SY272 ) ) @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(260,plain,
! [SV56: $i,SV22: $i] :
( ( ok @ ( triple @ SV22 @ SV56 @ bad ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(261,plain,
! [SV81: $i,SV57: $i,SV23: $i] :
( ( ( ok @ ( triple @ SV23 @ SV57 @ SV81 ) )
| ( SV81 = bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(262,plain,
! [SV82: $i,SV58: $i,SV24: $i] :
( ( ! [SY273: $i] :
( ( insert_cpq @ ( triple @ SV24 @ SV58 @ SV82 ) @ SY273 )
= ( triple @ ( insert_pqp @ SV24 @ SY273 ) @ ( insert_slb @ SV58 @ ( pair @ SY273 @ bottom ) ) @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(263,plain,
! [SV83: $i,SV25: $i,SV59: $i] :
( ( ! [SY274: $i] :
( ( contains_slb @ SV59 @ SY274 )
| ( ( remove_cpq @ ( triple @ SV25 @ SV59 @ SV83 ) @ SY274 )
= ( triple @ SV25 @ SV59 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(264,plain,
! [SV84: $i,SV26: $i,SV60: $i] :
( ( ! [SY275: $i] :
( ~ ( contains_slb @ SV60 @ SY275 )
| ~ ( less_than @ ( lookup_slb @ SV60 @ SY275 ) @ SY275 )
| ( ( remove_cpq @ ( triple @ SV26 @ SV60 @ SV84 ) @ SY275 )
= ( triple @ ( remove_pqp @ SV26 @ SY275 ) @ ( remove_slb @ SV60 @ SY275 ) @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(265,plain,
! [SV85: $i,SV27: $i,SV61: $i] :
( ( ! [SY276: $i] :
( ~ ( contains_slb @ SV61 @ SY276 )
| ~ ( strictly_less_than @ SY276 @ ( lookup_slb @ SV61 @ SY276 ) )
| ( ( remove_cpq @ ( triple @ SV27 @ SV61 @ SV85 ) @ SY276 )
= ( triple @ ( remove_pqp @ SV27 @ SY276 ) @ ( remove_slb @ SV61 @ SY276 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(266,plain,
! [SV29: $i,SV63: $i] :
( ( ( ( SV63 = create_slb )
| ( contains_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) ) )
= $true )
| ( ( ! [SY239: $i] :
( ( findmin_cpq_eff @ ( triple @ SV29 @ SV63 @ SY239 ) )
= ( triple @ SV29 @ ( update_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(267,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 )
| ( ( ! [SY240: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY240 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(268,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 )
| ( ( ! [SY241: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY241 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(269,plain,
! [SV33: $i,SV67: $i] :
( ( ( SV67 = create_slb )
= $true )
| ( ( ! [SY242: $i] :
( ( findmin_cpq_res @ ( triple @ SV33 @ SV67 @ SY242 ) )
= ( findmin_pqp_res @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(270,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY277: $i,SY278: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY277 ) ) @ SV86 @ SY278 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY278 ) )
| ~ ! [SY279: $i,SY280: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY279 ) ) @ SV86 @ SY280 )
| ( SY279 = SY280 )
| ( pair_in_list @ SV36 @ SV86 @ SY280 ) ) )
| ~ ~ ( ~ ! [SY281: $i,SY282: $i] :
( ( SV68 != SV86 )
| ( SY281 != SY282 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY281 ) ) @ SV86 @ SY282 ) )
| ~ ! [SY283: $i,SY284: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY284 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY283 ) ) @ SV86 @ SY284 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(271,plain,
! [SV69: $i,SV37: $i] :
( ( ~ ! [SY252: $i] :
( ! [SY253: $i] :
~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY253 ) ) @ SY252 )
| ( SV69 = SY252 )
| ( contains_slb @ SV37 @ SY252 ) )
| ~ ~ ( ~ ! [SY254: $i] :
( ( SV69 != SY254 )
| ! [SY255: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY255 ) ) @ SY254 ) )
| ~ ! [SY256: $i] :
( ~ ( contains_slb @ SV37 @ SY256 )
| ! [SY257: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY257 ) ) @ SY256 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(272,plain,
! [SV70: $i,SV38: $i] :
( ( ~ ! [SY258: $i,SY259: $i] :
( ~ ( contains_cpq @ ( triple @ SV38 @ SV70 @ SY258 ) @ SY259 )
| ( contains_slb @ SV70 @ SY259 ) )
| ~ ! [SY260: $i,SY261: $i] :
( ~ ( contains_slb @ SV70 @ SY261 )
| ( contains_cpq @ ( triple @ SV38 @ SV70 @ SY260 ) @ SY261 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(273,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ~ ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( less_than @ SY286 @ SY285 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY285 @ SY286 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) )
| ~ ! [SY287: $i,SY288: $i] :
( ~ ( less_than @ SY288 @ SY287 )
| ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY287 @ SY288 ) ) @ SV87 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(274,plain,
( ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY121 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(275,plain,
( ( ~ ( ~ ( pair_in_list @ create_slb @ sK3_W @ sK4_SY126 )
| ~ ~ ( less_than @ sK4_SY126 @ sK3_W ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(276,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)],[243]) ).
thf(277,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)],[244]) ).
thf(278,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)],[245]) ).
thf(279,plain,
! [SV9: $i,SV75: $i,SV45: $i] :
( ( ( ( SV45 = SV75 )
| ~ ( contains_slb @ SV9 @ SV75 ) )
= $true )
| ( ( ! [SY267: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV45 @ SY267 ) ) @ SV75 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV75 ) @ ( pair @ SV45 @ SY267 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(280,plain,
! [SV11: $i,SV77: $i,SV47: $i] :
( ( ( ( SV47 = SV77 )
| ~ ( contains_slb @ SV11 @ SV77 ) )
= $true )
| ( ( ! [SY268: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV47 @ SY268 ) ) @ SV77 )
= ( lookup_slb @ SV11 @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(281,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)],[253]) ).
thf(282,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)],[254]) ).
thf(283,plain,
! [SV50: $i,SV16: $i] :
( ( ( succ_cpq @ SV16 @ SV50 )
= $false )
| ( ( ! [SY225: $i] : ( succ_cpq @ SV16 @ ( insert_cpq @ SV50 @ SY225 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(284,plain,
! [SV51: $i,SV17: $i] :
( ( ( succ_cpq @ SV17 @ SV51 )
= $false )
| ( ( ! [SY226: $i] : ( succ_cpq @ SV17 @ ( remove_cpq @ SV51 @ SY226 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(285,plain,
! [SV52: $i,SV18: $i] :
( ( ( succ_cpq @ SV18 @ SV52 )
= $false )
| ( ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(286,plain,
! [SV53: $i,SV19: $i] :
( ( ( succ_cpq @ SV19 @ SV53 )
= $false )
| ( ( succ_cpq @ SV19 @ ( removemin_cpq_eff @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(287,plain,
! [SV80: $i,SV55: $i,SV21: $i,SV90: $i] :
( ( ! [SY289: $i] :
( ~ ( strictly_less_than @ SV90 @ SY289 )
| ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV55 @ ( pair @ SV90 @ SY289 ) ) @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(288,plain,
! [SV81: $i,SV57: $i,SV23: $i] :
( ( ( ok @ ( triple @ SV23 @ SV57 @ SV81 ) )
= $true )
| ( ( SV81 = bad )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(289,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)],[262]) ).
thf(290,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)],[263]) ).
thf(291,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)],[264]) ).
thf(292,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)],[265]) ).
thf(293,plain,
! [SV29: $i,SV63: $i] :
( ( ( SV63 = create_slb )
= $true )
| ( ( contains_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) )
= $true )
| ( ( ! [SY239: $i] :
( ( findmin_cpq_eff @ ( triple @ SV29 @ SV63 @ SY239 ) )
= ( triple @ SV29 @ ( update_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(294,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 )
| ( ( ! [SY240: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY240 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(295,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 )
| ( ( ! [SY241: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY241 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(296,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)],[269]) ).
thf(297,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ~ ~ ( ~ ! [SY277: $i,SY278: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY277 ) ) @ SV86 @ SY278 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY278 ) )
| ~ ! [SY279: $i,SY280: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY279 ) ) @ SV86 @ SY280 )
| ( SY279 = SY280 )
| ( pair_in_list @ SV36 @ SV86 @ SY280 ) ) )
| ~ ~ ( ~ ! [SY281: $i,SY282: $i] :
( ( SV68 != SV86 )
| ( SY281 != SY282 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY281 ) ) @ SV86 @ SY282 ) )
| ~ ! [SY283: $i,SY284: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY284 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY283 ) ) @ SV86 @ SY284 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(298,plain,
! [SV69: $i,SV37: $i] :
( ( ~ ! [SY252: $i] :
( ! [SY253: $i] :
~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY253 ) ) @ SY252 )
| ( SV69 = SY252 )
| ( contains_slb @ SV37 @ SY252 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[271]) ).
thf(299,plain,
! [SV37: $i,SV69: $i] :
( ( ~ ~ ( ~ ! [SY254: $i] :
( ( SV69 != SY254 )
| ! [SY255: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY255 ) ) @ SY254 ) )
| ~ ! [SY256: $i] :
( ~ ( contains_slb @ SV37 @ SY256 )
| ! [SY257: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY257 ) ) @ SY256 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[271]) ).
thf(300,plain,
! [SV70: $i,SV38: $i] :
( ( ~ ! [SY258: $i,SY259: $i] :
( ~ ( contains_cpq @ ( triple @ SV38 @ SV70 @ SY258 ) @ SY259 )
| ( contains_slb @ SV70 @ SY259 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[272]) ).
thf(301,plain,
! [SV38: $i,SV70: $i] :
( ( ~ ! [SY260: $i,SY261: $i] :
( ~ ( contains_slb @ SV70 @ SY261 )
| ( contains_cpq @ ( triple @ SV38 @ SV70 @ SY260 ) @ SY261 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[272]) ).
thf(302,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( less_than @ SY286 @ SY285 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY285 @ SY286 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) )
| ~ ! [SY287: $i,SY288: $i] :
( ~ ( less_than @ SY288 @ SY287 )
| ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY287 @ SY288 ) ) @ SV87 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(303,plain,
( ( ~ ( pair_in_list @ create_slb @ sK3_W @ sK4_SY126 )
| ~ ~ ( less_than @ sK4_SY126 @ sK3_W ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(304,plain,
! [SV96: $i] :
( ( ! [SY290: $i] :
( ~ ( less_than @ SV96 @ SY290 )
| ( less_than @ SY290 @ SV96 )
| ( strictly_less_than @ SV96 @ SY290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(305,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)],[277]) ).
thf(306,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)],[278]) ).
thf(307,plain,
! [SV9: $i,SV75: $i,SV45: $i] :
( ( ( SV45 = SV75 )
= $true )
| ( ( ~ ( contains_slb @ SV9 @ SV75 ) )
= $true )
| ( ( ! [SY267: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV45 @ SY267 ) ) @ SV75 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV75 ) @ ( pair @ SV45 @ SY267 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(308,plain,
! [SV11: $i,SV77: $i,SV47: $i] :
( ( ( SV47 = SV77 )
= $true )
| ( ( ~ ( contains_slb @ SV11 @ SV77 ) )
= $true )
| ( ( ! [SY268: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV47 @ SY268 ) ) @ SV77 )
= ( lookup_slb @ SV11 @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(309,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)],[281]) ).
thf(310,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)],[282]) ).
thf(311,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)],[283]) ).
thf(312,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)],[284]) ).
thf(313,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)],[287]) ).
thf(314,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)],[290]) ).
thf(315,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)],[291]) ).
thf(316,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)],[292]) ).
thf(317,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)],[293]) ).
thf(318,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 )
| ( ( ! [SY240: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY240 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(319,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 )
| ( ( ! [SY241: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY241 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(320,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ~ ~ ( ~ ! [SY277: $i,SY278: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY277 ) ) @ SV86 @ SY278 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY278 ) )
| ~ ! [SY279: $i,SY280: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY279 ) ) @ SV86 @ SY280 )
| ( SY279 = SY280 )
| ( pair_in_list @ SV36 @ SV86 @ SY280 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(321,plain,
! [SV36: $i,SV86: $i,SV68: $i] :
( ( ~ ~ ( ~ ! [SY281: $i,SY282: $i] :
( ( SV68 != SV86 )
| ( SY281 != SY282 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY281 ) ) @ SV86 @ SY282 ) )
| ~ ! [SY283: $i,SY284: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY284 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY283 ) ) @ SV86 @ SY284 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(322,plain,
! [SV69: $i,SV37: $i] :
( ( ! [SY252: $i] :
( ! [SY253: $i] :
~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY253 ) ) @ SY252 )
| ( SV69 = SY252 )
| ( contains_slb @ SV37 @ SY252 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(323,plain,
! [SV37: $i,SV69: $i] :
( ( ~ ( ~ ! [SY254: $i] :
( ( SV69 != SY254 )
| ! [SY255: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY255 ) ) @ SY254 ) )
| ~ ! [SY256: $i] :
( ~ ( contains_slb @ SV37 @ SY256 )
| ! [SY257: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY257 ) ) @ SY256 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(324,plain,
! [SV70: $i,SV38: $i] :
( ( ! [SY258: $i,SY259: $i] :
( ~ ( contains_cpq @ ( triple @ SV38 @ SV70 @ SY258 ) @ SY259 )
| ( contains_slb @ SV70 @ SY259 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(325,plain,
! [SV38: $i,SV70: $i] :
( ( ! [SY260: $i,SY261: $i] :
( ~ ( contains_slb @ SV70 @ SY261 )
| ( contains_cpq @ ( triple @ SV38 @ SV70 @ SY260 ) @ SY261 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(326,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( less_than @ SY286 @ SY285 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY285 @ SY286 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[302]) ).
thf(327,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ~ ! [SY287: $i,SY288: $i] :
( ~ ( less_than @ SY288 @ SY287 )
| ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY287 @ SY288 ) ) @ SV87 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[302]) ).
thf(328,plain,
( ( ~ ( pair_in_list @ create_slb @ sK3_W @ sK4_SY126 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(329,plain,
( ( ~ ~ ( less_than @ sK4_SY126 @ sK3_W ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(330,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)],[304]) ).
thf(331,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(332,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(333,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)],[306]) ).
thf(334,plain,
! [SV45: $i,SV75: $i,SV9: $i] :
( ( ( contains_slb @ SV9 @ SV75 )
= $false )
| ( ( SV45 = SV75 )
= $true )
| ( ( ! [SY267: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV45 @ SY267 ) ) @ SV75 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV75 ) @ ( pair @ SV45 @ SY267 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(335,plain,
! [SV47: $i,SV77: $i,SV11: $i] :
( ( ( contains_slb @ SV11 @ SV77 )
= $false )
| ( ( SV47 = SV77 )
= $true )
| ( ( ! [SY268: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV47 @ SY268 ) ) @ SV77 )
= ( lookup_slb @ SV11 @ SV77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(336,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)],[309]) ).
thf(337,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)],[310]) ).
thf(338,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)],[313]) ).
thf(339,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)],[315]) ).
thf(340,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)],[316]) ).
thf(341,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 )
| ( ( ! [SY240: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY240 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(342,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 )
| ( ( ! [SY241: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY241 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY241 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(343,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ~ ( ~ ! [SY277: $i,SY278: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY277 ) ) @ SV86 @ SY278 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY278 ) )
| ~ ! [SY279: $i,SY280: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY279 ) ) @ SV86 @ SY280 )
| ( SY279 = SY280 )
| ( pair_in_list @ SV36 @ SV86 @ SY280 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(344,plain,
! [SV36: $i,SV86: $i,SV68: $i] :
( ( ~ ( ~ ! [SY281: $i,SY282: $i] :
( ( SV68 != SV86 )
| ( SY281 != SY282 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY281 ) ) @ SV86 @ SY282 ) )
| ~ ! [SY283: $i,SY284: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY284 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY283 ) ) @ SV86 @ SY284 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(345,plain,
! [SV102: $i,SV69: $i,SV37: $i] :
( ( ! [SY291: $i] :
~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY291 ) ) @ SV102 )
| ( SV69 = SV102 )
| ( contains_slb @ SV37 @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(346,plain,
! [SV37: $i,SV69: $i] :
( ( ~ ! [SY254: $i] :
( ( SV69 != SY254 )
| ! [SY255: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY255 ) ) @ SY254 ) )
| ~ ! [SY256: $i] :
( ~ ( contains_slb @ SV37 @ SY256 )
| ! [SY257: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY257 ) ) @ SY256 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(347,plain,
! [SV103: $i,SV70: $i,SV38: $i] :
( ( ! [SY292: $i] :
( ~ ( contains_cpq @ ( triple @ SV38 @ SV70 @ SV103 ) @ SY292 )
| ( contains_slb @ SV70 @ SY292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(348,plain,
! [SV104: $i,SV38: $i,SV70: $i] :
( ( ! [SY293: $i] :
( ~ ( contains_slb @ SV70 @ SY293 )
| ( contains_cpq @ ( triple @ SV38 @ SV70 @ SV104 ) @ SY293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(349,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ! [SY285: $i,SY286: $i] :
( ~ ( less_than @ SY286 @ SY285 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY285 @ SY286 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(350,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ! [SY287: $i,SY288: $i] :
( ~ ( less_than @ SY288 @ SY287 )
| ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY287 @ SY288 ) ) @ SV87 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[327]) ).
thf(351,plain,
( ( pair_in_list @ create_slb @ sK3_W @ sK4_SY126 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(352,plain,
( ( ~ ( less_than @ sK4_SY126 @ sK3_W ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(353,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)],[330]) ).
thf(354,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(355,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(356,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)],[333]) ).
thf(357,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)],[334]) ).
thf(358,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)],[335]) ).
thf(359,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)],[338]) ).
thf(360,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)],[339]) ).
thf(361,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)],[340]) ).
thf(362,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 )
| ( ( ! [SY240: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY240 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(363,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 )
| ( ( ! [SY241: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY241 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY241 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(364,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ~ ! [SY277: $i,SY278: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY277 ) ) @ SV86 @ SY278 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY278 ) )
| ~ ! [SY279: $i,SY280: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY279 ) ) @ SV86 @ SY280 )
| ( SY279 = SY280 )
| ( pair_in_list @ SV36 @ SV86 @ SY280 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(365,plain,
! [SV36: $i,SV86: $i,SV68: $i] :
( ( ~ ! [SY281: $i,SY282: $i] :
( ( SV68 != SV86 )
| ( SY281 != SY282 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY281 ) ) @ SV86 @ SY282 ) )
| ~ ! [SY283: $i,SY284: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY284 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY283 ) ) @ SV86 @ SY284 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(366,plain,
! [SV102: $i,SV69: $i,SV37: $i] :
( ( ( ! [SY291: $i] :
~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY291 ) ) @ SV102 ) )
= $true )
| ( ( ( SV69 = SV102 )
| ( contains_slb @ SV37 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(367,plain,
! [SV37: $i,SV69: $i] :
( ( ~ ! [SY254: $i] :
( ( SV69 != SY254 )
| ! [SY255: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY255 ) ) @ SY254 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[346]) ).
thf(368,plain,
! [SV69: $i,SV37: $i] :
( ( ~ ! [SY256: $i] :
( ~ ( contains_slb @ SV37 @ SY256 )
| ! [SY257: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY257 ) ) @ SY256 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[346]) ).
thf(369,plain,
! [SV107: $i,SV103: $i,SV70: $i,SV38: $i] :
( ( ~ ( contains_cpq @ ( triple @ SV38 @ SV70 @ SV103 ) @ SV107 )
| ( contains_slb @ SV70 @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(370,plain,
! [SV104: $i,SV38: $i,SV108: $i,SV70: $i] :
( ( ~ ( contains_slb @ SV70 @ SV108 )
| ( contains_cpq @ ( triple @ SV38 @ SV70 @ SV104 ) @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(371,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV109: $i] :
( ( ! [SY294: $i] :
( ~ ( less_than @ SY294 @ SV109 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV109 @ SY294 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(372,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV110: $i] :
( ( ! [SY295: $i] :
( ~ ( less_than @ SY295 @ SV110 )
| ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV110 @ SY295 ) ) @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(373,plain,
( ( less_than @ sK4_SY126 @ sK3_W )
= $false ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(374,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)],[353]) ).
thf(375,plain,
! [SV111: $i] :
( ( ! [SY296: $i] :
( ~ ( strictly_less_than @ SV111 @ SY296 )
| ( less_than @ SV111 @ SY296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(376,plain,
! [SV112: $i] :
( ( ! [SY297: $i] :
( ~ ( strictly_less_than @ SV112 @ SY297 )
| ~ ( less_than @ SY297 @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(377,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)],[359]) ).
thf(378,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)],[360]) ).
thf(379,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)],[361]) ).
thf(380,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)],[362]) ).
thf(381,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)],[363]) ).
thf(382,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ~ ! [SY277: $i,SY278: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY277 ) ) @ SV86 @ SY278 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY278 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[364]) ).
thf(383,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ~ ! [SY279: $i,SY280: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY279 ) ) @ SV86 @ SY280 )
| ( SY279 = SY280 )
| ( pair_in_list @ SV36 @ SV86 @ SY280 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[364]) ).
thf(384,plain,
! [SV36: $i,SV86: $i,SV68: $i] :
( ( ~ ! [SY281: $i,SY282: $i] :
( ( SV68 != SV86 )
| ( SY281 != SY282 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY281 ) ) @ SV86 @ SY282 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[365]) ).
thf(385,plain,
! [SV68: $i,SV86: $i,SV36: $i] :
( ( ~ ! [SY283: $i,SY284: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY284 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY283 ) ) @ SV86 @ SY284 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[365]) ).
thf(386,plain,
! [SV102: $i,SV115: $i,SV69: $i,SV37: $i] :
( ( ( ~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SV115 ) ) @ SV102 ) )
= $true )
| ( ( ( SV69 = SV102 )
| ( contains_slb @ SV37 @ SV102 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(387,plain,
! [SV37: $i,SV69: $i] :
( ( ! [SY254: $i] :
( ( SV69 != SY254 )
| ! [SY255: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY255 ) ) @ SY254 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(388,plain,
! [SV69: $i,SV37: $i] :
( ( ! [SY256: $i] :
( ~ ( contains_slb @ SV37 @ SY256 )
| ! [SY257: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY257 ) ) @ SY256 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(389,plain,
! [SV107: $i,SV103: $i,SV70: $i,SV38: $i] :
( ( ( ~ ( contains_cpq @ ( triple @ SV38 @ SV70 @ SV103 ) @ SV107 ) )
= $true )
| ( ( contains_slb @ SV70 @ SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(390,plain,
! [SV104: $i,SV38: $i,SV108: $i,SV70: $i] :
( ( ( ~ ( contains_slb @ SV70 @ SV108 ) )
= $true )
| ( ( contains_cpq @ ( triple @ SV38 @ SV70 @ SV104 ) @ SV108 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(391,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV109: $i,SV116: $i] :
( ( ~ ( less_than @ SV116 @ SV109 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV109 @ SV116 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(392,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV110: $i,SV117: $i] :
( ( ~ ( less_than @ SV117 @ SV110 )
| ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV110 @ SV117 ) ) @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(393,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)],[374]) ).
thf(394,plain,
! [SV118: $i,SV111: $i] :
( ( ~ ( strictly_less_than @ SV111 @ SV118 )
| ( less_than @ SV111 @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(395,plain,
! [SV119: $i,SV112: $i] :
( ( ~ ( strictly_less_than @ SV112 @ SV119 )
| ~ ( less_than @ SV119 @ SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(396,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ! [SY277: $i,SY278: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY277 ) ) @ SV86 @ SY278 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY278 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[382]) ).
thf(397,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ! [SY279: $i,SY280: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY279 ) ) @ SV86 @ SY280 )
| ( SY279 = SY280 )
| ( pair_in_list @ SV36 @ SV86 @ SY280 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[383]) ).
thf(398,plain,
! [SV36: $i,SV86: $i,SV68: $i] :
( ( ! [SY281: $i,SY282: $i] :
( ( SV68 != SV86 )
| ( SY281 != SY282 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY281 ) ) @ SV86 @ SY282 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[384]) ).
thf(399,plain,
! [SV68: $i,SV86: $i,SV36: $i] :
( ( ! [SY283: $i,SY284: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY284 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY283 ) ) @ SV86 @ SY284 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[385]) ).
thf(400,plain,
! [SV102: $i,SV115: $i,SV69: $i,SV37: $i] :
( ( ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SV115 ) ) @ SV102 )
= $false )
| ( ( ( SV69 = SV102 )
| ( contains_slb @ SV37 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(401,plain,
! [SV37: $i,SV120: $i,SV69: $i] :
( ( ( SV69 != SV120 )
| ! [SY298: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY298 ) ) @ SV120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(402,plain,
! [SV69: $i,SV121: $i,SV37: $i] :
( ( ~ ( contains_slb @ SV37 @ SV121 )
| ! [SY299: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY299 ) ) @ SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(403,plain,
! [SV107: $i,SV103: $i,SV70: $i,SV38: $i] :
( ( ( contains_cpq @ ( triple @ SV38 @ SV70 @ SV103 ) @ SV107 )
= $false )
| ( ( contains_slb @ SV70 @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(404,plain,
! [SV104: $i,SV38: $i,SV108: $i,SV70: $i] :
( ( ( contains_slb @ SV70 @ SV108 )
= $false )
| ( ( contains_cpq @ ( triple @ SV38 @ SV70 @ SV104 ) @ SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(405,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV109: $i,SV116: $i] :
( ( ( ~ ( less_than @ SV116 @ SV109 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV109 @ SV116 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(406,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV110: $i,SV117: $i] :
( ( ( ~ ( less_than @ SV117 @ SV110 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV110 @ SV117 ) ) @ SV87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(407,plain,
! [SV118: $i,SV111: $i] :
( ( ( ~ ( strictly_less_than @ SV111 @ SV118 ) )
= $true )
| ( ( less_than @ SV111 @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(408,plain,
! [SV119: $i,SV112: $i] :
( ( ( ~ ( strictly_less_than @ SV112 @ SV119 ) )
= $true )
| ( ( ~ ( less_than @ SV119 @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(409,plain,
! [SV86: $i,SV122: $i,SV68: $i,SV36: $i] :
( ( ! [SY300: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV122 ) ) @ SV86 @ SY300 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(410,plain,
! [SV86: $i,SV123: $i,SV68: $i,SV36: $i] :
( ( ! [SY301: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV123 ) ) @ SV86 @ SY301 )
| ( SV123 = SY301 )
| ( pair_in_list @ SV36 @ SV86 @ SY301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(411,plain,
! [SV36: $i,SV124: $i,SV86: $i,SV68: $i] :
( ( ! [SY302: $i] :
( ( SV68 != SV86 )
| ( SV124 != SY302 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV124 ) ) @ SV86 @ SY302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(412,plain,
! [SV125: $i,SV68: $i,SV86: $i,SV36: $i] :
( ( ! [SY303: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY303 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV125 ) ) @ SV86 @ SY303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(413,plain,
! [SV115: $i,SV37: $i,SV102: $i,SV69: $i] :
( ( ( SV69 = SV102 )
= $true )
| ( ( contains_slb @ SV37 @ SV102 )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SV115 ) ) @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(414,plain,
! [SV37: $i,SV120: $i,SV69: $i] :
( ( ( ( SV69 != SV120 ) )
= $true )
| ( ( ! [SY298: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY298 ) ) @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(415,plain,
! [SV69: $i,SV121: $i,SV37: $i] :
( ( ( ~ ( contains_slb @ SV37 @ SV121 ) )
= $true )
| ( ( ! [SY299: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY299 ) ) @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(416,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV109: $i,SV116: $i] :
( ( ( less_than @ SV116 @ SV109 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV109 @ SV116 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(417,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV110: $i,SV117: $i] :
( ( ( less_than @ SV117 @ SV110 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV110 @ SV117 ) ) @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(418,plain,
! [SV118: $i,SV111: $i] :
( ( ( strictly_less_than @ SV111 @ SV118 )
= $false )
| ( ( less_than @ SV111 @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(419,plain,
! [SV119: $i,SV112: $i] :
( ( ( strictly_less_than @ SV112 @ SV119 )
= $false )
| ( ( ~ ( less_than @ SV119 @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(420,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)],[409]) ).
thf(421,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)],[410]) ).
thf(422,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)],[411]) ).
thf(423,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)],[412]) ).
thf(424,plain,
! [SV37: $i,SV120: $i,SV69: $i] :
( ( ( SV69 = SV120 )
= $false )
| ( ( ! [SY298: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY298 ) ) @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(425,plain,
! [SV69: $i,SV121: $i,SV37: $i] :
( ( ( contains_slb @ SV37 @ SV121 )
= $false )
| ( ( ! [SY299: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY299 ) ) @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(426,plain,
! [SV87: $i,SV116: $i,SV109: $i,SV71: $i,SV39: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV109 @ SV116 ) ) @ SV87 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
= $true )
| ( ( less_than @ SV116 @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(427,plain,
! [SV117: $i,SV110: $i,SV87: $i,SV71: $i,SV39: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV110 @ SV117 ) ) @ SV87 ) )
= $true )
| ( ( less_than @ SV117 @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(428,plain,
! [SV112: $i,SV119: $i] :
( ( ( less_than @ SV119 @ SV112 )
= $false )
| ( ( strictly_less_than @ SV112 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(429,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)],[420]) ).
thf(430,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)],[421]) ).
thf(431,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)],[422]) ).
thf(432,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)],[423]) ).
thf(433,plain,
! [SV120: $i,SV130: $i,SV69: $i,SV37: $i] :
( ( ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SV130 ) ) @ SV120 )
= $true )
| ( ( SV69 = SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(434,plain,
! [SV121: $i,SV131: $i,SV69: $i,SV37: $i] :
( ( ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SV131 ) ) @ SV121 )
= $true )
| ( ( contains_slb @ SV37 @ SV121 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(435,plain,
! [SV87: $i,SV116: $i,SV109: $i,SV71: $i,SV39: $i] :
( ( ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV109 @ SV116 ) ) @ SV87 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
= $true )
| ( ( less_than @ SV116 @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(436,plain,
! [SV117: $i,SV110: $i,SV87: $i,SV71: $i,SV39: $i] :
( ( ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV110 @ SV117 ) ) @ SV87 ) )
= $true )
| ( ( less_than @ SV117 @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(437,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)],[429]) ).
thf(438,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)],[430]) ).
thf(439,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)],[431]) ).
thf(440,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)],[432]) ).
thf(441,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)],[437]) ).
thf(442,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)],[438]) ).
thf(443,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)],[439]) ).
thf(444,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)],[443]) ).
thf(445,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[168,444,442,441,440,436,435,434,433,428,418,413,404,403,393,381,380,379,378,377,373,358,357,356,351,337,336,317,314,312,311,296,289,288,286,285,274,260,251,249,248,247,246,235,231,223,211,201,200,181,178,170,169]) ).
thf(446,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( less_than @ U @ V )
| ~ ( less_than @ V @ W )
| ( less_than @ U @ W ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(447,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(448,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(449,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)],[116]) ).
thf(450,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(451,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(452,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(453,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(454,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)],[115]) ).
thf(455,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(456,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)],[114]) ).
thf(457,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(458,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)],[113]) ).
thf(459,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(460,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)],[112]) ).
thf(461,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(462,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)],[111]) ).
thf(463,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)],[110]) ).
thf(464,plain,
( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(465,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(466,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(467,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(468,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(469,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(470,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)],[105]) ).
thf(471,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)],[104]) ).
thf(472,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)],[103]) ).
thf(473,plain,
( ( ! [U: $i,V: $i] :
~ ( ok @ ( triple @ U @ V @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(474,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( triple @ U @ V @ W ) )
| ( W = bad ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(475,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(476,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)],[100]) ).
thf(477,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)],[99]) ).
thf(478,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)],[98]) ).
thf(479,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(480,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)],[97]) ).
thf(481,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)],[96]) ).
thf(482,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)],[95]) ).
thf(483,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(484,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)],[94]) ).
thf(485,plain,
( ( ! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(486,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(487,plain,
( ( ! [W: $i,X: $i] :
( ~ ( pair_in_list @ create_slb @ W @ X )
| ( less_than @ X @ W ) )
& ~ ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY121 ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(488,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)],[472]) ).
thf(489,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)],[456]) ).
thf(490,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)],[454]) ).
thf(491,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)],[470]) ).
thf(492,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ create_slb @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) )
| ~ ~ ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY121 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[487]) ).
thf(493,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)],[449]) ).
thf(494,plain,
! [SV132: $i] :
( ( ! [SY304: $i,SY305: $i] :
( ~ ( less_than @ SV132 @ SY304 )
| ~ ( less_than @ SY304 @ SY305 )
| ( less_than @ SV132 @ SY305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(495,plain,
! [SV133: $i] :
( ( ! [SY306: $i] :
( ( less_than @ SV133 @ SY306 )
| ( less_than @ SY306 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(496,plain,
! [SV134: $i] :
( ( less_than @ SV134 @ SV134 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(497,plain,
! [SV135: $i] :
( ( less_than @ bottom @ SV135 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(498,plain,
( ( isnonempty_slb @ create_slb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(499,plain,
! [SV136: $i] :
( ( ! [SY307: $i,SY308: $i] : ( isnonempty_slb @ ( insert_slb @ SV136 @ ( pair @ SY307 @ SY308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(500,plain,
! [SV137: $i] :
( ( ~ ( contains_slb @ create_slb @ SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(501,plain,
! [SV138: $i] :
( ( ! [SY309: $i] :
~ ( pair_in_list @ create_slb @ SV138 @ SY309 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(502,plain,
! [SV139: $i] :
( ( ! [SY310: $i,SY311: $i] :
( ( remove_slb @ ( insert_slb @ SV139 @ ( pair @ SY310 @ SY311 ) ) @ SY310 )
= SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(503,plain,
! [SV140: $i] :
( ( ! [SY312: $i,SY313: $i] :
( ( SY312 = SY313 )
| ~ ( contains_slb @ SV140 @ SY313 )
| ! [SY314: $i] :
( ( remove_slb @ ( insert_slb @ SV140 @ ( pair @ SY312 @ SY314 ) ) @ SY313 )
= ( insert_slb @ ( remove_slb @ SV140 @ SY313 ) @ ( pair @ SY312 @ SY314 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(504,plain,
! [SV141: $i] :
( ( ! [SY315: $i,SY316: $i] :
( ( lookup_slb @ ( insert_slb @ SV141 @ ( pair @ SY315 @ SY316 ) ) @ SY315 )
= SY316 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(505,plain,
! [SV142: $i] :
( ( ! [SY317: $i,SY318: $i] :
( ( SY317 = SY318 )
| ~ ( contains_slb @ SV142 @ SY318 )
| ! [SY319: $i] :
( ( lookup_slb @ ( insert_slb @ SV142 @ ( pair @ SY317 @ SY319 ) ) @ SY318 )
= ( lookup_slb @ SV142 @ SY318 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(506,plain,
! [SV143: $i] :
( ( ( update_slb @ create_slb @ SV143 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(507,plain,
! [SV144: $i] :
( ( ! [SY320: $i,SY321: $i,SY322: $i] :
( ~ ( strictly_less_than @ SY322 @ SY321 )
| ( ( update_slb @ ( insert_slb @ SV144 @ ( pair @ SY320 @ SY322 ) ) @ SY321 )
= ( insert_slb @ ( update_slb @ SV144 @ SY321 ) @ ( pair @ SY320 @ SY321 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(508,plain,
! [SV145: $i] :
( ( ! [SY323: $i,SY324: $i,SY325: $i] :
( ~ ( less_than @ SY324 @ SY325 )
| ( ( update_slb @ ( insert_slb @ SV145 @ ( pair @ SY323 @ SY325 ) ) @ SY324 )
= ( insert_slb @ ( update_slb @ SV145 @ SY324 ) @ ( pair @ SY323 @ SY325 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(509,plain,
! [SV146: $i] :
( ( succ_cpq @ SV146 @ SV146 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(510,plain,
! [SV147: $i] :
( ( ! [SY326: $i] :
( ~ ( succ_cpq @ SV147 @ SY326 )
| ! [SY327: $i] : ( succ_cpq @ SV147 @ ( insert_cpq @ SY326 @ SY327 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(511,plain,
! [SV148: $i] :
( ( ! [SY328: $i] :
( ~ ( succ_cpq @ SV148 @ SY328 )
| ! [SY329: $i] : ( succ_cpq @ SV148 @ ( remove_cpq @ SY328 @ SY329 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(512,plain,
! [SV149: $i] :
( ( ! [SY330: $i] :
( ~ ( succ_cpq @ SV149 @ SY330 )
| ( succ_cpq @ SV149 @ ( findmin_cpq_eff @ SY330 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(513,plain,
! [SV150: $i] :
( ( ! [SY331: $i] :
( ~ ( succ_cpq @ SV150 @ SY331 )
| ( succ_cpq @ SV150 @ ( removemin_cpq_eff @ SY331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(514,plain,
! [SV151: $i] :
( ( ! [SY332: $i] : ( check_cpq @ ( triple @ SV151 @ create_slb @ SY332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(515,plain,
! [SV152: $i] :
( ( ! [SY333: $i,SY334: $i,SY335: $i,SY336: $i] :
( ~ ( strictly_less_than @ SY335 @ SY336 )
| ~ ( check_cpq @ ( triple @ SV152 @ ( insert_slb @ SY333 @ ( pair @ SY335 @ SY336 ) ) @ SY334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(516,plain,
! [SV153: $i] :
( ( ! [SY337: $i] :
~ ( ok @ ( triple @ SV153 @ SY337 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(517,plain,
! [SV154: $i] :
( ( ! [SY338: $i,SY339: $i] :
( ( ok @ ( triple @ SV154 @ SY338 @ SY339 ) )
| ( SY339 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(518,plain,
! [SV155: $i] :
( ( ! [SY340: $i,SY341: $i,SY342: $i] :
( ( insert_cpq @ ( triple @ SV155 @ SY340 @ SY341 ) @ SY342 )
= ( triple @ ( insert_pqp @ SV155 @ SY342 ) @ ( insert_slb @ SY340 @ ( pair @ SY342 @ bottom ) ) @ SY341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(519,plain,
! [SV156: $i] :
( ( ! [SY343: $i,SY344: $i,SY345: $i] :
( ( contains_slb @ SY343 @ SY345 )
| ( ( remove_cpq @ ( triple @ SV156 @ SY343 @ SY344 ) @ SY345 )
= ( triple @ SV156 @ SY343 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(520,plain,
! [SV157: $i] :
( ( ! [SY346: $i,SY347: $i,SY348: $i] :
( ~ ( contains_slb @ SY346 @ SY348 )
| ~ ( less_than @ ( lookup_slb @ SY346 @ SY348 ) @ SY348 )
| ( ( remove_cpq @ ( triple @ SV157 @ SY346 @ SY347 ) @ SY348 )
= ( triple @ ( remove_pqp @ SV157 @ SY348 ) @ ( remove_slb @ SY346 @ SY348 ) @ SY347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(521,plain,
! [SV158: $i] :
( ( ! [SY349: $i,SY350: $i,SY351: $i] :
( ~ ( contains_slb @ SY349 @ SY351 )
| ~ ( strictly_less_than @ SY351 @ ( lookup_slb @ SY349 @ SY351 ) )
| ( ( remove_cpq @ ( triple @ SV158 @ SY349 @ SY350 ) @ SY351 )
= ( triple @ ( remove_pqp @ SV158 @ SY351 ) @ ( remove_slb @ SY349 @ SY351 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(522,plain,
! [SV159: $i] :
( ( ! [SY352: $i] :
( ( findmin_cpq_eff @ ( triple @ SV159 @ create_slb @ SY352 ) )
= ( triple @ SV159 @ create_slb @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(523,plain,
! [SV160: $i] :
( ( ! [SY353: $i] :
( ( SY353 = create_slb )
| ( contains_slb @ SY353 @ ( findmin_pqp_res @ SV160 ) )
| ! [SY354: $i] :
( ( findmin_cpq_eff @ ( triple @ SV160 @ SY353 @ SY354 ) )
= ( triple @ SV160 @ ( update_slb @ SY353 @ ( findmin_pqp_res @ SV160 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(524,plain,
! [SV161: $i] :
( ( ! [SY355: $i] :
( ( SY355 = create_slb )
| ~ ( contains_slb @ SY355 @ ( findmin_pqp_res @ SV161 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV161 ) @ ( lookup_slb @ SY355 @ ( findmin_pqp_res @ SV161 ) ) )
| ! [SY356: $i] :
( ( findmin_cpq_eff @ ( triple @ SV161 @ SY355 @ SY356 ) )
= ( triple @ SV161 @ ( update_slb @ SY355 @ ( findmin_pqp_res @ SV161 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(525,plain,
! [SV162: $i] :
( ( ! [SY357: $i] :
( ( SY357 = create_slb )
| ~ ( contains_slb @ SY357 @ ( findmin_pqp_res @ SV162 ) )
| ~ ( less_than @ ( lookup_slb @ SY357 @ ( findmin_pqp_res @ SV162 ) ) @ ( findmin_pqp_res @ SV162 ) )
| ! [SY358: $i] :
( ( findmin_cpq_eff @ ( triple @ SV162 @ SY357 @ SY358 ) )
= ( triple @ SV162 @ ( update_slb @ SY357 @ ( findmin_pqp_res @ SV162 ) ) @ SY358 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(526,plain,
! [SV163: $i] :
( ( ! [SY359: $i] :
( ( findmin_cpq_res @ ( triple @ SV163 @ create_slb @ SY359 ) )
= bottom ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(527,plain,
! [SV164: $i] :
( ( ! [SY360: $i] :
( ( SY360 = create_slb )
| ! [SY361: $i] :
( ( findmin_cpq_res @ ( triple @ SV164 @ SY360 @ SY361 ) )
= ( findmin_pqp_res @ SV164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(528,plain,
! [SV165: $i] :
( ( ( removemin_cpq_eff @ SV165 )
= ( remove_cpq @ ( findmin_cpq_eff @ SV165 ) @ ( findmin_cpq_res @ SV165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(529,plain,
! [SV166: $i] :
( ( ( removemin_cpq_res @ SV166 )
= ( findmin_cpq_res @ SV166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(530,plain,
! [SV167: $i] :
( ( ! [SY362: $i] :
~ ( ~ ! [SY363: $i,SY364: $i] :
( ~ ( contains_cpq @ ( triple @ SV167 @ SY362 @ SY363 ) @ SY364 )
| ( contains_slb @ SY362 @ SY364 ) )
| ~ ! [SY365: $i,SY366: $i] :
( ~ ( contains_slb @ SY362 @ SY366 )
| ( contains_cpq @ ( triple @ SV167 @ SY362 @ SY365 ) @ SY366 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(531,plain,
! [SV168: $i] :
( ( ! [SY367: $i,SY368: $i] :
~ ( ~ ~ ( ~ ! [SY369: $i,SY370: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SY367 @ SY369 ) ) @ SY368 @ SY370 )
| ( SY367 = SY368 )
| ( pair_in_list @ SV168 @ SY368 @ SY370 ) )
| ~ ! [SY371: $i,SY372: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SY367 @ SY371 ) ) @ SY368 @ SY372 )
| ( SY371 = SY372 )
| ( pair_in_list @ SV168 @ SY368 @ SY372 ) ) )
| ~ ~ ( ~ ! [SY373: $i,SY374: $i] :
( ( SY367 != SY368 )
| ( SY373 != SY374 )
| ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SY367 @ SY373 ) ) @ SY368 @ SY374 ) )
| ~ ! [SY375: $i,SY376: $i] :
( ~ ( pair_in_list @ SV168 @ SY368 @ SY376 )
| ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SY367 @ SY375 ) ) @ SY368 @ SY376 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(532,plain,
! [SV169: $i] :
( ( ! [SY377: $i] :
~ ( ~ ! [SY378: $i] :
( ! [SY379: $i] :
~ ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SY377 @ SY379 ) ) @ SY378 )
| ( SY377 = SY378 )
| ( contains_slb @ SV169 @ SY378 ) )
| ~ ~ ( ~ ! [SY380: $i] :
( ( SY377 != SY380 )
| ! [SY381: $i] : ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SY377 @ SY381 ) ) @ SY380 ) )
| ~ ! [SY382: $i] :
( ~ ( contains_slb @ SV169 @ SY382 )
| ! [SY383: $i] : ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SY377 @ SY383 ) ) @ SY382 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(533,plain,
! [SV170: $i] :
( ( ! [SY384: $i,SY385: $i] :
~ ( ~ ! [SY386: $i,SY387: $i] :
( ~ ( less_than @ SY387 @ SY386 )
| ~ ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SY384 @ ( pair @ SY386 @ SY387 ) ) @ SY385 ) )
| ( check_cpq @ ( triple @ SV170 @ SY384 @ SY385 ) ) )
| ~ ! [SY388: $i,SY389: $i] :
( ~ ( less_than @ SY389 @ SY388 )
| ~ ( check_cpq @ ( triple @ SV170 @ SY384 @ SY385 ) )
| ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SY384 @ ( pair @ SY388 @ SY389 ) ) @ SY385 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(534,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ create_slb @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) )
| ~ ~ ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY121 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(535,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)],[493]) ).
thf(536,plain,
! [SV171: $i,SV132: $i] :
( ( ! [SY390: $i] :
( ~ ( less_than @ SV132 @ SV171 )
| ~ ( less_than @ SV171 @ SY390 )
| ( less_than @ SV132 @ SY390 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(537,plain,
! [SV172: $i,SV133: $i] :
( ( ( less_than @ SV133 @ SV172 )
| ( less_than @ SV172 @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(538,plain,
! [SV173: $i,SV136: $i] :
( ( ! [SY391: $i] : ( isnonempty_slb @ ( insert_slb @ SV136 @ ( pair @ SV173 @ SY391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(539,plain,
! [SV137: $i] :
( ( contains_slb @ create_slb @ SV137 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(540,plain,
! [SV174: $i,SV138: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV138 @ SV174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(541,plain,
! [SV175: $i,SV139: $i] :
( ( ! [SY392: $i] :
( ( remove_slb @ ( insert_slb @ SV139 @ ( pair @ SV175 @ SY392 ) ) @ SV175 )
= SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(542,plain,
! [SV140: $i,SV176: $i] :
( ( ! [SY393: $i] :
( ( SV176 = SY393 )
| ~ ( contains_slb @ SV140 @ SY393 )
| ! [SY394: $i] :
( ( remove_slb @ ( insert_slb @ SV140 @ ( pair @ SV176 @ SY394 ) ) @ SY393 )
= ( insert_slb @ ( remove_slb @ SV140 @ SY393 ) @ ( pair @ SV176 @ SY394 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(543,plain,
! [SV177: $i,SV141: $i] :
( ( ! [SY395: $i] :
( ( lookup_slb @ ( insert_slb @ SV141 @ ( pair @ SV177 @ SY395 ) ) @ SV177 )
= SY395 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(544,plain,
! [SV142: $i,SV178: $i] :
( ( ! [SY396: $i] :
( ( SV178 = SY396 )
| ~ ( contains_slb @ SV142 @ SY396 )
| ! [SY397: $i] :
( ( lookup_slb @ ( insert_slb @ SV142 @ ( pair @ SV178 @ SY397 ) ) @ SY396 )
= ( lookup_slb @ SV142 @ SY396 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(545,plain,
! [SV179: $i,SV144: $i] :
( ( ! [SY398: $i,SY399: $i] :
( ~ ( strictly_less_than @ SY399 @ SY398 )
| ( ( update_slb @ ( insert_slb @ SV144 @ ( pair @ SV179 @ SY399 ) ) @ SY398 )
= ( insert_slb @ ( update_slb @ SV144 @ SY398 ) @ ( pair @ SV179 @ SY398 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(546,plain,
! [SV180: $i,SV145: $i] :
( ( ! [SY400: $i,SY401: $i] :
( ~ ( less_than @ SY400 @ SY401 )
| ( ( update_slb @ ( insert_slb @ SV145 @ ( pair @ SV180 @ SY401 ) ) @ SY400 )
= ( insert_slb @ ( update_slb @ SV145 @ SY400 ) @ ( pair @ SV180 @ SY401 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(547,plain,
! [SV181: $i,SV147: $i] :
( ( ~ ( succ_cpq @ SV147 @ SV181 )
| ! [SY402: $i] : ( succ_cpq @ SV147 @ ( insert_cpq @ SV181 @ SY402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(548,plain,
! [SV182: $i,SV148: $i] :
( ( ~ ( succ_cpq @ SV148 @ SV182 )
| ! [SY403: $i] : ( succ_cpq @ SV148 @ ( remove_cpq @ SV182 @ SY403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(549,plain,
! [SV183: $i,SV149: $i] :
( ( ~ ( succ_cpq @ SV149 @ SV183 )
| ( succ_cpq @ SV149 @ ( findmin_cpq_eff @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(550,plain,
! [SV184: $i,SV150: $i] :
( ( ~ ( succ_cpq @ SV150 @ SV184 )
| ( succ_cpq @ SV150 @ ( removemin_cpq_eff @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(551,plain,
! [SV185: $i,SV151: $i] :
( ( check_cpq @ ( triple @ SV151 @ create_slb @ SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(552,plain,
! [SV186: $i,SV152: $i] :
( ( ! [SY404: $i,SY405: $i,SY406: $i] :
( ~ ( strictly_less_than @ SY405 @ SY406 )
| ~ ( check_cpq @ ( triple @ SV152 @ ( insert_slb @ SV186 @ ( pair @ SY405 @ SY406 ) ) @ SY404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(553,plain,
! [SV187: $i,SV153: $i] :
( ( ~ ( ok @ ( triple @ SV153 @ SV187 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(554,plain,
! [SV188: $i,SV154: $i] :
( ( ! [SY407: $i] :
( ( ok @ ( triple @ SV154 @ SV188 @ SY407 ) )
| ( SY407 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(555,plain,
! [SV189: $i,SV155: $i] :
( ( ! [SY408: $i,SY409: $i] :
( ( insert_cpq @ ( triple @ SV155 @ SV189 @ SY408 ) @ SY409 )
= ( triple @ ( insert_pqp @ SV155 @ SY409 ) @ ( insert_slb @ SV189 @ ( pair @ SY409 @ bottom ) ) @ SY408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(556,plain,
! [SV156: $i,SV190: $i] :
( ( ! [SY410: $i,SY411: $i] :
( ( contains_slb @ SV190 @ SY411 )
| ( ( remove_cpq @ ( triple @ SV156 @ SV190 @ SY410 ) @ SY411 )
= ( triple @ SV156 @ SV190 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(557,plain,
! [SV157: $i,SV191: $i] :
( ( ! [SY412: $i,SY413: $i] :
( ~ ( contains_slb @ SV191 @ SY413 )
| ~ ( less_than @ ( lookup_slb @ SV191 @ SY413 ) @ SY413 )
| ( ( remove_cpq @ ( triple @ SV157 @ SV191 @ SY412 ) @ SY413 )
= ( triple @ ( remove_pqp @ SV157 @ SY413 ) @ ( remove_slb @ SV191 @ SY413 ) @ SY412 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(558,plain,
! [SV158: $i,SV192: $i] :
( ( ! [SY414: $i,SY415: $i] :
( ~ ( contains_slb @ SV192 @ SY415 )
| ~ ( strictly_less_than @ SY415 @ ( lookup_slb @ SV192 @ SY415 ) )
| ( ( remove_cpq @ ( triple @ SV158 @ SV192 @ SY414 ) @ SY415 )
= ( triple @ ( remove_pqp @ SV158 @ SY415 ) @ ( remove_slb @ SV192 @ SY415 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(559,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)],[522]) ).
thf(560,plain,
! [SV160: $i,SV194: $i] :
( ( ( SV194 = create_slb )
| ( contains_slb @ SV194 @ ( findmin_pqp_res @ SV160 ) )
| ! [SY416: $i] :
( ( findmin_cpq_eff @ ( triple @ SV160 @ SV194 @ SY416 ) )
= ( triple @ SV160 @ ( update_slb @ SV194 @ ( findmin_pqp_res @ SV160 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(561,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 ) ) )
| ! [SY417: $i] :
( ( findmin_cpq_eff @ ( triple @ SV161 @ SV195 @ SY417 ) )
= ( triple @ SV161 @ ( update_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(562,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 ) )
| ! [SY418: $i] :
( ( findmin_cpq_eff @ ( triple @ SV162 @ SV196 @ SY418 ) )
= ( triple @ SV162 @ ( update_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) ) @ SY418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(563,plain,
! [SV197: $i,SV163: $i] :
( ( ( findmin_cpq_res @ ( triple @ SV163 @ create_slb @ SV197 ) )
= bottom )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(564,plain,
! [SV164: $i,SV198: $i] :
( ( ( SV198 = create_slb )
| ! [SY419: $i] :
( ( findmin_cpq_res @ ( triple @ SV164 @ SV198 @ SY419 ) )
= ( findmin_pqp_res @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(565,plain,
! [SV199: $i,SV167: $i] :
( ( ~ ( ~ ! [SY420: $i,SY421: $i] :
( ~ ( contains_cpq @ ( triple @ SV167 @ SV199 @ SY420 ) @ SY421 )
| ( contains_slb @ SV199 @ SY421 ) )
| ~ ! [SY422: $i,SY423: $i] :
( ~ ( contains_slb @ SV199 @ SY423 )
| ( contains_cpq @ ( triple @ SV167 @ SV199 @ SY422 ) @ SY423 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(566,plain,
! [SV200: $i,SV168: $i] :
( ( ! [SY424: $i] :
~ ( ~ ~ ( ~ ! [SY425: $i,SY426: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY425 ) ) @ SY424 @ SY426 )
| ( SV200 = SY424 )
| ( pair_in_list @ SV168 @ SY424 @ SY426 ) )
| ~ ! [SY427: $i,SY428: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY427 ) ) @ SY424 @ SY428 )
| ( SY427 = SY428 )
| ( pair_in_list @ SV168 @ SY424 @ SY428 ) ) )
| ~ ~ ( ~ ! [SY429: $i,SY430: $i] :
( ( SV200 != SY424 )
| ( SY429 != SY430 )
| ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY429 ) ) @ SY424 @ SY430 ) )
| ~ ! [SY431: $i,SY432: $i] :
( ~ ( pair_in_list @ SV168 @ SY424 @ SY432 )
| ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY431 ) ) @ SY424 @ SY432 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(567,plain,
! [SV201: $i,SV169: $i] :
( ( ~ ( ~ ! [SY433: $i] :
( ! [SY434: $i] :
~ ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY434 ) ) @ SY433 )
| ( SV201 = SY433 )
| ( contains_slb @ SV169 @ SY433 ) )
| ~ ~ ( ~ ! [SY435: $i] :
( ( SV201 != SY435 )
| ! [SY436: $i] : ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY436 ) ) @ SY435 ) )
| ~ ! [SY437: $i] :
( ~ ( contains_slb @ SV169 @ SY437 )
| ! [SY438: $i] : ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY438 ) ) @ SY437 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(568,plain,
! [SV202: $i,SV170: $i] :
( ( ! [SY439: $i] :
~ ( ~ ! [SY440: $i,SY441: $i] :
( ~ ( less_than @ SY441 @ SY440 )
| ~ ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SV202 @ ( pair @ SY440 @ SY441 ) ) @ SY439 ) )
| ( check_cpq @ ( triple @ SV170 @ SV202 @ SY439 ) ) )
| ~ ! [SY442: $i,SY443: $i] :
( ~ ( less_than @ SY443 @ SY442 )
| ~ ( check_cpq @ ( triple @ SV170 @ SV202 @ SY439 ) )
| ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SV202 @ ( pair @ SY442 @ SY443 ) ) @ SY439 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(569,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ create_slb @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[534]) ).
thf(570,plain,
( ( ~ ~ ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY121 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[534]) ).
thf(571,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)],[535]) ).
thf(572,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)],[535]) ).
thf(573,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)],[536]) ).
thf(574,plain,
! [SV172: $i,SV133: $i] :
( ( ( less_than @ SV133 @ SV172 )
= $true )
| ( ( less_than @ SV172 @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[537]) ).
thf(575,plain,
! [SV204: $i,SV173: $i,SV136: $i] :
( ( isnonempty_slb @ ( insert_slb @ SV136 @ ( pair @ SV173 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(576,plain,
! [SV174: $i,SV138: $i] :
( ( pair_in_list @ create_slb @ SV138 @ SV174 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(577,plain,
! [SV205: $i,SV175: $i,SV139: $i] :
( ( ( remove_slb @ ( insert_slb @ SV139 @ ( pair @ SV175 @ SV205 ) ) @ SV175 )
= SV139 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(578,plain,
! [SV140: $i,SV206: $i,SV176: $i] :
( ( ( SV176 = SV206 )
| ~ ( contains_slb @ SV140 @ SV206 )
| ! [SY444: $i] :
( ( remove_slb @ ( insert_slb @ SV140 @ ( pair @ SV176 @ SY444 ) ) @ SV206 )
= ( insert_slb @ ( remove_slb @ SV140 @ SV206 ) @ ( pair @ SV176 @ SY444 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(579,plain,
! [SV207: $i,SV177: $i,SV141: $i] :
( ( ( lookup_slb @ ( insert_slb @ SV141 @ ( pair @ SV177 @ SV207 ) ) @ SV177 )
= SV207 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(580,plain,
! [SV142: $i,SV208: $i,SV178: $i] :
( ( ( SV178 = SV208 )
| ~ ( contains_slb @ SV142 @ SV208 )
| ! [SY445: $i] :
( ( lookup_slb @ ( insert_slb @ SV142 @ ( pair @ SV178 @ SY445 ) ) @ SV208 )
= ( lookup_slb @ SV142 @ SV208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(581,plain,
! [SV179: $i,SV144: $i,SV209: $i] :
( ( ! [SY446: $i] :
( ~ ( strictly_less_than @ SY446 @ SV209 )
| ( ( update_slb @ ( insert_slb @ SV144 @ ( pair @ SV179 @ SY446 ) ) @ SV209 )
= ( insert_slb @ ( update_slb @ SV144 @ SV209 ) @ ( pair @ SV179 @ SV209 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(582,plain,
! [SV180: $i,SV145: $i,SV210: $i] :
( ( ! [SY447: $i] :
( ~ ( less_than @ SV210 @ SY447 )
| ( ( update_slb @ ( insert_slb @ SV145 @ ( pair @ SV180 @ SY447 ) ) @ SV210 )
= ( insert_slb @ ( update_slb @ SV145 @ SV210 ) @ ( pair @ SV180 @ SY447 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(583,plain,
! [SV181: $i,SV147: $i] :
( ( ( ~ ( succ_cpq @ SV147 @ SV181 ) )
= $true )
| ( ( ! [SY402: $i] : ( succ_cpq @ SV147 @ ( insert_cpq @ SV181 @ SY402 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[547]) ).
thf(584,plain,
! [SV182: $i,SV148: $i] :
( ( ( ~ ( succ_cpq @ SV148 @ SV182 ) )
= $true )
| ( ( ! [SY403: $i] : ( succ_cpq @ SV148 @ ( remove_cpq @ SV182 @ SY403 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(585,plain,
! [SV183: $i,SV149: $i] :
( ( ( ~ ( succ_cpq @ SV149 @ SV183 ) )
= $true )
| ( ( succ_cpq @ SV149 @ ( findmin_cpq_eff @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[549]) ).
thf(586,plain,
! [SV184: $i,SV150: $i] :
( ( ( ~ ( succ_cpq @ SV150 @ SV184 ) )
= $true )
| ( ( succ_cpq @ SV150 @ ( removemin_cpq_eff @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[550]) ).
thf(587,plain,
! [SV211: $i,SV186: $i,SV152: $i] :
( ( ! [SY448: $i,SY449: $i] :
( ~ ( strictly_less_than @ SY448 @ SY449 )
| ~ ( check_cpq @ ( triple @ SV152 @ ( insert_slb @ SV186 @ ( pair @ SY448 @ SY449 ) ) @ SV211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(588,plain,
! [SV187: $i,SV153: $i] :
( ( ok @ ( triple @ SV153 @ SV187 @ bad ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(589,plain,
! [SV212: $i,SV188: $i,SV154: $i] :
( ( ( ok @ ( triple @ SV154 @ SV188 @ SV212 ) )
| ( SV212 = bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(590,plain,
! [SV213: $i,SV189: $i,SV155: $i] :
( ( ! [SY450: $i] :
( ( insert_cpq @ ( triple @ SV155 @ SV189 @ SV213 ) @ SY450 )
= ( triple @ ( insert_pqp @ SV155 @ SY450 ) @ ( insert_slb @ SV189 @ ( pair @ SY450 @ bottom ) ) @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(591,plain,
! [SV214: $i,SV156: $i,SV190: $i] :
( ( ! [SY451: $i] :
( ( contains_slb @ SV190 @ SY451 )
| ( ( remove_cpq @ ( triple @ SV156 @ SV190 @ SV214 ) @ SY451 )
= ( triple @ SV156 @ SV190 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(592,plain,
! [SV215: $i,SV157: $i,SV191: $i] :
( ( ! [SY452: $i] :
( ~ ( contains_slb @ SV191 @ SY452 )
| ~ ( less_than @ ( lookup_slb @ SV191 @ SY452 ) @ SY452 )
| ( ( remove_cpq @ ( triple @ SV157 @ SV191 @ SV215 ) @ SY452 )
= ( triple @ ( remove_pqp @ SV157 @ SY452 ) @ ( remove_slb @ SV191 @ SY452 ) @ SV215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(593,plain,
! [SV216: $i,SV158: $i,SV192: $i] :
( ( ! [SY453: $i] :
( ~ ( contains_slb @ SV192 @ SY453 )
| ~ ( strictly_less_than @ SY453 @ ( lookup_slb @ SV192 @ SY453 ) )
| ( ( remove_cpq @ ( triple @ SV158 @ SV192 @ SV216 ) @ SY453 )
= ( triple @ ( remove_pqp @ SV158 @ SY453 ) @ ( remove_slb @ SV192 @ SY453 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(594,plain,
! [SV160: $i,SV194: $i] :
( ( ( ( SV194 = create_slb )
| ( contains_slb @ SV194 @ ( findmin_pqp_res @ SV160 ) ) )
= $true )
| ( ( ! [SY416: $i] :
( ( findmin_cpq_eff @ ( triple @ SV160 @ SV194 @ SY416 ) )
= ( triple @ SV160 @ ( update_slb @ SV194 @ ( findmin_pqp_res @ SV160 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[560]) ).
thf(595,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 )
| ( ( ! [SY417: $i] :
( ( findmin_cpq_eff @ ( triple @ SV161 @ SV195 @ SY417 ) )
= ( triple @ SV161 @ ( update_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[561]) ).
thf(596,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 )
| ( ( ! [SY418: $i] :
( ( findmin_cpq_eff @ ( triple @ SV162 @ SV196 @ SY418 ) )
= ( triple @ SV162 @ ( update_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) ) @ SY418 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(597,plain,
! [SV164: $i,SV198: $i] :
( ( ( SV198 = create_slb )
= $true )
| ( ( ! [SY419: $i] :
( ( findmin_cpq_res @ ( triple @ SV164 @ SV198 @ SY419 ) )
= ( findmin_pqp_res @ SV164 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[564]) ).
thf(598,plain,
! [SV199: $i,SV167: $i] :
( ( ~ ! [SY420: $i,SY421: $i] :
( ~ ( contains_cpq @ ( triple @ SV167 @ SV199 @ SY420 ) @ SY421 )
| ( contains_slb @ SV199 @ SY421 ) )
| ~ ! [SY422: $i,SY423: $i] :
( ~ ( contains_slb @ SV199 @ SY423 )
| ( contains_cpq @ ( triple @ SV167 @ SV199 @ SY422 ) @ SY423 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(599,plain,
! [SV217: $i,SV200: $i,SV168: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY454: $i,SY455: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY454 ) ) @ SV217 @ SY455 )
| ( SV200 = SV217 )
| ( pair_in_list @ SV168 @ SV217 @ SY455 ) )
| ~ ! [SY456: $i,SY457: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY456 ) ) @ SV217 @ SY457 )
| ( SY456 = SY457 )
| ( pair_in_list @ SV168 @ SV217 @ SY457 ) ) )
| ~ ~ ( ~ ! [SY458: $i,SY459: $i] :
( ( SV200 != SV217 )
| ( SY458 != SY459 )
| ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY458 ) ) @ SV217 @ SY459 ) )
| ~ ! [SY460: $i,SY461: $i] :
( ~ ( pair_in_list @ SV168 @ SV217 @ SY461 )
| ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY460 ) ) @ SV217 @ SY461 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(600,plain,
! [SV201: $i,SV169: $i] :
( ( ~ ! [SY433: $i] :
( ! [SY434: $i] :
~ ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY434 ) ) @ SY433 )
| ( SV201 = SY433 )
| ( contains_slb @ SV169 @ SY433 ) )
| ~ ~ ( ~ ! [SY435: $i] :
( ( SV201 != SY435 )
| ! [SY436: $i] : ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY436 ) ) @ SY435 ) )
| ~ ! [SY437: $i] :
( ~ ( contains_slb @ SV169 @ SY437 )
| ! [SY438: $i] : ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY438 ) ) @ SY437 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(601,plain,
! [SV218: $i,SV202: $i,SV170: $i] :
( ( ~ ( ~ ! [SY462: $i,SY463: $i] :
( ~ ( less_than @ SY463 @ SY462 )
| ~ ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SV202 @ ( pair @ SY462 @ SY463 ) ) @ SV218 ) )
| ( check_cpq @ ( triple @ SV170 @ SV202 @ SV218 ) ) )
| ~ ! [SY464: $i,SY465: $i] :
( ~ ( less_than @ SY465 @ SY464 )
| ~ ( check_cpq @ ( triple @ SV170 @ SV202 @ SV218 ) )
| ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SV202 @ ( pair @ SY464 @ SY465 ) ) @ SV218 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(602,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ create_slb @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[569]) ).
thf(603,plain,
( ( ~ ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY121 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[570]) ).
thf(604,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)],[571]) ).
thf(605,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)],[572]) ).
thf(606,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)],[573]) ).
thf(607,plain,
! [SV140: $i,SV206: $i,SV176: $i] :
( ( ( ( SV176 = SV206 )
| ~ ( contains_slb @ SV140 @ SV206 ) )
= $true )
| ( ( ! [SY444: $i] :
( ( remove_slb @ ( insert_slb @ SV140 @ ( pair @ SV176 @ SY444 ) ) @ SV206 )
= ( insert_slb @ ( remove_slb @ SV140 @ SV206 ) @ ( pair @ SV176 @ SY444 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[578]) ).
thf(608,plain,
! [SV142: $i,SV208: $i,SV178: $i] :
( ( ( ( SV178 = SV208 )
| ~ ( contains_slb @ SV142 @ SV208 ) )
= $true )
| ( ( ! [SY445: $i] :
( ( lookup_slb @ ( insert_slb @ SV142 @ ( pair @ SV178 @ SY445 ) ) @ SV208 )
= ( lookup_slb @ SV142 @ SV208 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[580]) ).
thf(609,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)],[581]) ).
thf(610,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)],[582]) ).
thf(611,plain,
! [SV181: $i,SV147: $i] :
( ( ( succ_cpq @ SV147 @ SV181 )
= $false )
| ( ( ! [SY402: $i] : ( succ_cpq @ SV147 @ ( insert_cpq @ SV181 @ SY402 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(612,plain,
! [SV182: $i,SV148: $i] :
( ( ( succ_cpq @ SV148 @ SV182 )
= $false )
| ( ( ! [SY403: $i] : ( succ_cpq @ SV148 @ ( remove_cpq @ SV182 @ SY403 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(613,plain,
! [SV183: $i,SV149: $i] :
( ( ( succ_cpq @ SV149 @ SV183 )
= $false )
| ( ( succ_cpq @ SV149 @ ( findmin_cpq_eff @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(614,plain,
! [SV184: $i,SV150: $i] :
( ( ( succ_cpq @ SV150 @ SV184 )
= $false )
| ( ( succ_cpq @ SV150 @ ( removemin_cpq_eff @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(615,plain,
! [SV211: $i,SV186: $i,SV152: $i,SV221: $i] :
( ( ! [SY466: $i] :
( ~ ( strictly_less_than @ SV221 @ SY466 )
| ~ ( check_cpq @ ( triple @ SV152 @ ( insert_slb @ SV186 @ ( pair @ SV221 @ SY466 ) ) @ SV211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(616,plain,
! [SV212: $i,SV188: $i,SV154: $i] :
( ( ( ok @ ( triple @ SV154 @ SV188 @ SV212 ) )
= $true )
| ( ( SV212 = bad )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[589]) ).
thf(617,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)],[590]) ).
thf(618,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)],[591]) ).
thf(619,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)],[592]) ).
thf(620,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)],[593]) ).
thf(621,plain,
! [SV160: $i,SV194: $i] :
( ( ( SV194 = create_slb )
= $true )
| ( ( contains_slb @ SV194 @ ( findmin_pqp_res @ SV160 ) )
= $true )
| ( ( ! [SY416: $i] :
( ( findmin_cpq_eff @ ( triple @ SV160 @ SV194 @ SY416 ) )
= ( triple @ SV160 @ ( update_slb @ SV194 @ ( findmin_pqp_res @ SV160 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[594]) ).
thf(622,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 )
| ( ( ! [SY417: $i] :
( ( findmin_cpq_eff @ ( triple @ SV161 @ SV195 @ SY417 ) )
= ( triple @ SV161 @ ( update_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[595]) ).
thf(623,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 )
| ( ( ! [SY418: $i] :
( ( findmin_cpq_eff @ ( triple @ SV162 @ SV196 @ SY418 ) )
= ( triple @ SV162 @ ( update_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) ) @ SY418 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(624,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)],[597]) ).
thf(625,plain,
! [SV199: $i,SV167: $i] :
( ( ~ ! [SY420: $i,SY421: $i] :
( ~ ( contains_cpq @ ( triple @ SV167 @ SV199 @ SY420 ) @ SY421 )
| ( contains_slb @ SV199 @ SY421 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[598]) ).
thf(626,plain,
! [SV167: $i,SV199: $i] :
( ( ~ ! [SY422: $i,SY423: $i] :
( ~ ( contains_slb @ SV199 @ SY423 )
| ( contains_cpq @ ( triple @ SV167 @ SV199 @ SY422 ) @ SY423 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[598]) ).
thf(627,plain,
! [SV217: $i,SV200: $i,SV168: $i] :
( ( ~ ~ ( ~ ! [SY454: $i,SY455: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY454 ) ) @ SV217 @ SY455 )
| ( SV200 = SV217 )
| ( pair_in_list @ SV168 @ SV217 @ SY455 ) )
| ~ ! [SY456: $i,SY457: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY456 ) ) @ SV217 @ SY457 )
| ( SY456 = SY457 )
| ( pair_in_list @ SV168 @ SV217 @ SY457 ) ) )
| ~ ~ ( ~ ! [SY458: $i,SY459: $i] :
( ( SV200 != SV217 )
| ( SY458 != SY459 )
| ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY458 ) ) @ SV217 @ SY459 ) )
| ~ ! [SY460: $i,SY461: $i] :
( ~ ( pair_in_list @ SV168 @ SV217 @ SY461 )
| ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY460 ) ) @ SV217 @ SY461 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(628,plain,
! [SV201: $i,SV169: $i] :
( ( ~ ! [SY433: $i] :
( ! [SY434: $i] :
~ ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY434 ) ) @ SY433 )
| ( SV201 = SY433 )
| ( contains_slb @ SV169 @ SY433 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[600]) ).
thf(629,plain,
! [SV169: $i,SV201: $i] :
( ( ~ ~ ( ~ ! [SY435: $i] :
( ( SV201 != SY435 )
| ! [SY436: $i] : ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY436 ) ) @ SY435 ) )
| ~ ! [SY437: $i] :
( ~ ( contains_slb @ SV169 @ SY437 )
| ! [SY438: $i] : ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY438 ) ) @ SY437 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[600]) ).
thf(630,plain,
! [SV218: $i,SV202: $i,SV170: $i] :
( ( ~ ! [SY462: $i,SY463: $i] :
( ~ ( less_than @ SY463 @ SY462 )
| ~ ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SV202 @ ( pair @ SY462 @ SY463 ) ) @ SV218 ) )
| ( check_cpq @ ( triple @ SV170 @ SV202 @ SV218 ) ) )
| ~ ! [SY464: $i,SY465: $i] :
( ~ ( less_than @ SY465 @ SY464 )
| ~ ( check_cpq @ ( triple @ SV170 @ SV202 @ SV218 ) )
| ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SV202 @ ( pair @ SY464 @ SY465 ) ) @ SV218 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(631,plain,
! [SV227: $i] :
( ( ! [SY467: $i] :
( ~ ( pair_in_list @ create_slb @ SV227 @ SY467 )
| ( less_than @ SY467 @ SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(632,plain,
( ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY121 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(633,plain,
! [SV228: $i] :
( ( ! [SY468: $i] :
( ~ ( less_than @ SV228 @ SY468 )
| ( less_than @ SY468 @ SV228 )
| ( strictly_less_than @ SV228 @ SY468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(634,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)],[605]) ).
thf(635,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)],[606]) ).
thf(636,plain,
! [SV140: $i,SV206: $i,SV176: $i] :
( ( ( SV176 = SV206 )
= $true )
| ( ( ~ ( contains_slb @ SV140 @ SV206 ) )
= $true )
| ( ( ! [SY444: $i] :
( ( remove_slb @ ( insert_slb @ SV140 @ ( pair @ SV176 @ SY444 ) ) @ SV206 )
= ( insert_slb @ ( remove_slb @ SV140 @ SV206 ) @ ( pair @ SV176 @ SY444 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[607]) ).
thf(637,plain,
! [SV142: $i,SV208: $i,SV178: $i] :
( ( ( SV178 = SV208 )
= $true )
| ( ( ~ ( contains_slb @ SV142 @ SV208 ) )
= $true )
| ( ( ! [SY445: $i] :
( ( lookup_slb @ ( insert_slb @ SV142 @ ( pair @ SV178 @ SY445 ) ) @ SV208 )
= ( lookup_slb @ SV142 @ SV208 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(638,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)],[609]) ).
thf(639,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)],[610]) ).
thf(640,plain,
! [SV229: $i,SV181: $i,SV147: $i] :
( ( ( succ_cpq @ SV147 @ ( insert_cpq @ SV181 @ SV229 ) )
= $true )
| ( ( succ_cpq @ SV147 @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(641,plain,
! [SV230: $i,SV182: $i,SV148: $i] :
( ( ( succ_cpq @ SV148 @ ( remove_cpq @ SV182 @ SV230 ) )
= $true )
| ( ( succ_cpq @ SV148 @ SV182 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(642,plain,
! [SV211: $i,SV186: $i,SV152: $i,SV231: $i,SV221: $i] :
( ( ~ ( strictly_less_than @ SV221 @ SV231 )
| ~ ( check_cpq @ ( triple @ SV152 @ ( insert_slb @ SV186 @ ( pair @ SV221 @ SV231 ) ) @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(643,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)],[618]) ).
thf(644,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)],[619]) ).
thf(645,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)],[620]) ).
thf(646,plain,
! [SV232: $i,SV194: $i,SV160: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV160 @ SV194 @ SV232 ) )
= ( 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)],[621]) ).
thf(647,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 )
| ( ( ! [SY417: $i] :
( ( findmin_cpq_eff @ ( triple @ SV161 @ SV195 @ SY417 ) )
= ( triple @ SV161 @ ( update_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[622]) ).
thf(648,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 )
| ( ( ! [SY418: $i] :
( ( findmin_cpq_eff @ ( triple @ SV162 @ SV196 @ SY418 ) )
= ( triple @ SV162 @ ( update_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) ) @ SY418 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[623]) ).
thf(649,plain,
! [SV199: $i,SV167: $i] :
( ( ! [SY420: $i,SY421: $i] :
( ~ ( contains_cpq @ ( triple @ SV167 @ SV199 @ SY420 ) @ SY421 )
| ( contains_slb @ SV199 @ SY421 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[625]) ).
thf(650,plain,
! [SV167: $i,SV199: $i] :
( ( ! [SY422: $i,SY423: $i] :
( ~ ( contains_slb @ SV199 @ SY423 )
| ( contains_cpq @ ( triple @ SV167 @ SV199 @ SY422 ) @ SY423 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[626]) ).
thf(651,plain,
! [SV217: $i,SV200: $i,SV168: $i] :
( ( ~ ~ ( ~ ! [SY454: $i,SY455: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY454 ) ) @ SV217 @ SY455 )
| ( SV200 = SV217 )
| ( pair_in_list @ SV168 @ SV217 @ SY455 ) )
| ~ ! [SY456: $i,SY457: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY456 ) ) @ SV217 @ SY457 )
| ( SY456 = SY457 )
| ( pair_in_list @ SV168 @ SV217 @ SY457 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[627]) ).
thf(652,plain,
! [SV168: $i,SV217: $i,SV200: $i] :
( ( ~ ~ ( ~ ! [SY458: $i,SY459: $i] :
( ( SV200 != SV217 )
| ( SY458 != SY459 )
| ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY458 ) ) @ SV217 @ SY459 ) )
| ~ ! [SY460: $i,SY461: $i] :
( ~ ( pair_in_list @ SV168 @ SV217 @ SY461 )
| ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY460 ) ) @ SV217 @ SY461 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[627]) ).
thf(653,plain,
! [SV201: $i,SV169: $i] :
( ( ! [SY433: $i] :
( ! [SY434: $i] :
~ ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY434 ) ) @ SY433 )
| ( SV201 = SY433 )
| ( contains_slb @ SV169 @ SY433 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[628]) ).
thf(654,plain,
! [SV169: $i,SV201: $i] :
( ( ~ ( ~ ! [SY435: $i] :
( ( SV201 != SY435 )
| ! [SY436: $i] : ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY436 ) ) @ SY435 ) )
| ~ ! [SY437: $i] :
( ~ ( contains_slb @ SV169 @ SY437 )
| ! [SY438: $i] : ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY438 ) ) @ SY437 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[629]) ).
thf(655,plain,
! [SV218: $i,SV202: $i,SV170: $i] :
( ( ~ ! [SY462: $i,SY463: $i] :
( ~ ( less_than @ SY463 @ SY462 )
| ~ ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SV202 @ ( pair @ SY462 @ SY463 ) ) @ SV218 ) )
| ( check_cpq @ ( triple @ SV170 @ SV202 @ SV218 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[630]) ).
thf(656,plain,
! [SV218: $i,SV202: $i,SV170: $i] :
( ( ~ ! [SY464: $i,SY465: $i] :
( ~ ( less_than @ SY465 @ SY464 )
| ~ ( check_cpq @ ( triple @ SV170 @ SV202 @ SV218 ) )
| ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SV202 @ ( pair @ SY464 @ SY465 ) ) @ SV218 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[630]) ).
thf(657,plain,
! [SV233: $i,SV227: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV227 @ SV233 )
| ( less_than @ SV233 @ SV227 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(658,plain,
! [SV234: $i,SV228: $i] :
( ( ~ ( less_than @ SV228 @ SV234 )
| ( less_than @ SV234 @ SV228 )
| ( strictly_less_than @ SV228 @ SV234 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(659,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[634]) ).
thf(660,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[634]) ).
thf(661,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)],[635]) ).
thf(662,plain,
! [SV176: $i,SV206: $i,SV140: $i] :
( ( ( contains_slb @ SV140 @ SV206 )
= $false )
| ( ( SV176 = SV206 )
= $true )
| ( ( ! [SY444: $i] :
( ( remove_slb @ ( insert_slb @ SV140 @ ( pair @ SV176 @ SY444 ) ) @ SV206 )
= ( insert_slb @ ( remove_slb @ SV140 @ SV206 ) @ ( pair @ SV176 @ SY444 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(663,plain,
! [SV178: $i,SV208: $i,SV142: $i] :
( ( ( contains_slb @ SV142 @ SV208 )
= $false )
| ( ( SV178 = SV208 )
= $true )
| ( ( ! [SY445: $i] :
( ( lookup_slb @ ( insert_slb @ SV142 @ ( pair @ SV178 @ SY445 ) ) @ SV208 )
= ( lookup_slb @ SV142 @ SV208 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(664,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)],[638]) ).
thf(665,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)],[639]) ).
thf(666,plain,
! [SV211: $i,SV186: $i,SV152: $i,SV231: $i,SV221: $i] :
( ( ( ~ ( strictly_less_than @ SV221 @ SV231 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV152 @ ( insert_slb @ SV186 @ ( pair @ SV221 @ SV231 ) ) @ SV211 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[642]) ).
thf(667,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)],[644]) ).
thf(668,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)],[645]) ).
thf(669,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 )
| ( ( ! [SY417: $i] :
( ( findmin_cpq_eff @ ( triple @ SV161 @ SV195 @ SY417 ) )
= ( triple @ SV161 @ ( update_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[647]) ).
thf(670,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 )
| ( ( ! [SY418: $i] :
( ( findmin_cpq_eff @ ( triple @ SV162 @ SV196 @ SY418 ) )
= ( triple @ SV162 @ ( update_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) ) @ SY418 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[648]) ).
thf(671,plain,
! [SV235: $i,SV199: $i,SV167: $i] :
( ( ! [SY469: $i] :
( ~ ( contains_cpq @ ( triple @ SV167 @ SV199 @ SV235 ) @ SY469 )
| ( contains_slb @ SV199 @ SY469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(672,plain,
! [SV236: $i,SV167: $i,SV199: $i] :
( ( ! [SY470: $i] :
( ~ ( contains_slb @ SV199 @ SY470 )
| ( contains_cpq @ ( triple @ SV167 @ SV199 @ SV236 ) @ SY470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(673,plain,
! [SV217: $i,SV200: $i,SV168: $i] :
( ( ~ ( ~ ! [SY454: $i,SY455: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY454 ) ) @ SV217 @ SY455 )
| ( SV200 = SV217 )
| ( pair_in_list @ SV168 @ SV217 @ SY455 ) )
| ~ ! [SY456: $i,SY457: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY456 ) ) @ SV217 @ SY457 )
| ( SY456 = SY457 )
| ( pair_in_list @ SV168 @ SV217 @ SY457 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[651]) ).
thf(674,plain,
! [SV168: $i,SV217: $i,SV200: $i] :
( ( ~ ( ~ ! [SY458: $i,SY459: $i] :
( ( SV200 != SV217 )
| ( SY458 != SY459 )
| ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY458 ) ) @ SV217 @ SY459 ) )
| ~ ! [SY460: $i,SY461: $i] :
( ~ ( pair_in_list @ SV168 @ SV217 @ SY461 )
| ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY460 ) ) @ SV217 @ SY461 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[652]) ).
thf(675,plain,
! [SV237: $i,SV201: $i,SV169: $i] :
( ( ! [SY471: $i] :
~ ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY471 ) ) @ SV237 )
| ( SV201 = SV237 )
| ( contains_slb @ SV169 @ SV237 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(676,plain,
! [SV169: $i,SV201: $i] :
( ( ~ ! [SY435: $i] :
( ( SV201 != SY435 )
| ! [SY436: $i] : ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY436 ) ) @ SY435 ) )
| ~ ! [SY437: $i] :
( ~ ( contains_slb @ SV169 @ SY437 )
| ! [SY438: $i] : ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY438 ) ) @ SY437 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(677,plain,
! [SV218: $i,SV202: $i,SV170: $i] :
( ( ! [SY462: $i,SY463: $i] :
( ~ ( less_than @ SY463 @ SY462 )
| ~ ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SV202 @ ( pair @ SY462 @ SY463 ) ) @ SV218 ) )
| ( check_cpq @ ( triple @ SV170 @ SV202 @ SV218 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[655]) ).
thf(678,plain,
! [SV218: $i,SV202: $i,SV170: $i] :
( ( ! [SY464: $i,SY465: $i] :
( ~ ( less_than @ SY465 @ SY464 )
| ~ ( check_cpq @ ( triple @ SV170 @ SV202 @ SV218 ) )
| ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SV202 @ ( pair @ SY464 @ SY465 ) ) @ SV218 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[656]) ).
thf(679,plain,
! [SV233: $i,SV227: $i] :
( ( ( ~ ( pair_in_list @ create_slb @ SV227 @ SV233 ) )
= $true )
| ( ( less_than @ SV233 @ SV227 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[657]) ).
thf(680,plain,
! [SV234: $i,SV228: $i] :
( ( ( ~ ( less_than @ SV228 @ SV234 )
| ( less_than @ SV234 @ SV228 ) )
= $true )
| ( ( strictly_less_than @ SV228 @ SV234 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[658]) ).
thf(681,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[659]) ).
thf(682,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[660]) ).
thf(683,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)],[661]) ).
thf(684,plain,
! [SV206: $i,SV238: $i,SV176: $i,SV140: $i] :
( ( ( ( remove_slb @ ( insert_slb @ SV140 @ ( pair @ SV176 @ SV238 ) ) @ SV206 )
= ( insert_slb @ ( remove_slb @ SV140 @ SV206 ) @ ( pair @ SV176 @ SV238 ) ) )
= $true )
| ( ( SV176 = SV206 )
= $true )
| ( ( contains_slb @ SV140 @ SV206 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(685,plain,
! [SV208: $i,SV239: $i,SV178: $i,SV142: $i] :
( ( ( ( lookup_slb @ ( insert_slb @ SV142 @ ( pair @ SV178 @ SV239 ) ) @ SV208 )
= ( lookup_slb @ SV142 @ SV208 ) )
= $true )
| ( ( SV178 = SV208 )
= $true )
| ( ( contains_slb @ SV142 @ SV208 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(686,plain,
! [SV211: $i,SV186: $i,SV152: $i,SV231: $i,SV221: $i] :
( ( ( strictly_less_than @ SV221 @ SV231 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV152 @ ( insert_slb @ SV186 @ ( pair @ SV221 @ SV231 ) ) @ SV211 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[666]) ).
thf(687,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)],[667]) ).
thf(688,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)],[668]) ).
thf(689,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 )
| ( ( ! [SY417: $i] :
( ( findmin_cpq_eff @ ( triple @ SV161 @ SV195 @ SY417 ) )
= ( triple @ SV161 @ ( update_slb @ SV195 @ ( findmin_pqp_res @ SV161 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(690,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 )
| ( ( ! [SY418: $i] :
( ( findmin_cpq_eff @ ( triple @ SV162 @ SV196 @ SY418 ) )
= ( triple @ SV162 @ ( update_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) ) @ SY418 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(691,plain,
! [SV240: $i,SV235: $i,SV199: $i,SV167: $i] :
( ( ~ ( contains_cpq @ ( triple @ SV167 @ SV199 @ SV235 ) @ SV240 )
| ( contains_slb @ SV199 @ SV240 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(692,plain,
! [SV236: $i,SV167: $i,SV241: $i,SV199: $i] :
( ( ~ ( contains_slb @ SV199 @ SV241 )
| ( contains_cpq @ ( triple @ SV167 @ SV199 @ SV236 ) @ SV241 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(693,plain,
! [SV217: $i,SV200: $i,SV168: $i] :
( ( ~ ! [SY454: $i,SY455: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY454 ) ) @ SV217 @ SY455 )
| ( SV200 = SV217 )
| ( pair_in_list @ SV168 @ SV217 @ SY455 ) )
| ~ ! [SY456: $i,SY457: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY456 ) ) @ SV217 @ SY457 )
| ( SY456 = SY457 )
| ( pair_in_list @ SV168 @ SV217 @ SY457 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(694,plain,
! [SV168: $i,SV217: $i,SV200: $i] :
( ( ~ ! [SY458: $i,SY459: $i] :
( ( SV200 != SV217 )
| ( SY458 != SY459 )
| ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY458 ) ) @ SV217 @ SY459 ) )
| ~ ! [SY460: $i,SY461: $i] :
( ~ ( pair_in_list @ SV168 @ SV217 @ SY461 )
| ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY460 ) ) @ SV217 @ SY461 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(695,plain,
! [SV237: $i,SV201: $i,SV169: $i] :
( ( ( ! [SY471: $i] :
~ ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY471 ) ) @ SV237 ) )
= $true )
| ( ( ( SV201 = SV237 )
| ( contains_slb @ SV169 @ SV237 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[675]) ).
thf(696,plain,
! [SV169: $i,SV201: $i] :
( ( ~ ! [SY435: $i] :
( ( SV201 != SY435 )
| ! [SY436: $i] : ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY436 ) ) @ SY435 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[676]) ).
thf(697,plain,
! [SV201: $i,SV169: $i] :
( ( ~ ! [SY437: $i] :
( ~ ( contains_slb @ SV169 @ SY437 )
| ! [SY438: $i] : ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY438 ) ) @ SY437 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[676]) ).
thf(698,plain,
! [SV218: $i,SV202: $i,SV170: $i,SV242: $i] :
( ( ! [SY472: $i] :
( ~ ( less_than @ SY472 @ SV242 )
| ~ ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SV202 @ ( pair @ SV242 @ SY472 ) ) @ SV218 ) )
| ( check_cpq @ ( triple @ SV170 @ SV202 @ SV218 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(699,plain,
! [SV218: $i,SV202: $i,SV170: $i,SV243: $i] :
( ( ! [SY473: $i] :
( ~ ( less_than @ SY473 @ SV243 )
| ~ ( check_cpq @ ( triple @ SV170 @ SV202 @ SV218 ) )
| ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SV202 @ ( pair @ SV243 @ SY473 ) ) @ SV218 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(700,plain,
! [SV233: $i,SV227: $i] :
( ( ( pair_in_list @ create_slb @ SV227 @ SV233 )
= $false )
| ( ( less_than @ SV233 @ SV227 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(701,plain,
! [SV234: $i,SV228: $i] :
( ( ( ~ ( less_than @ SV228 @ SV234 ) )
= $true )
| ( ( less_than @ SV234 @ SV228 )
= $true )
| ( ( strictly_less_than @ SV228 @ SV234 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[680]) ).
thf(702,plain,
! [SV244: $i] :
( ( ! [SY474: $i] :
( ~ ( strictly_less_than @ SV244 @ SY474 )
| ( less_than @ SV244 @ SY474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(703,plain,
! [SV245: $i] :
( ( ! [SY475: $i] :
( ~ ( strictly_less_than @ SV245 @ SY475 )
| ~ ( less_than @ SY475 @ SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(704,plain,
! [SV211: $i,SV231: $i,SV221: $i,SV186: $i,SV152: $i] :
( ( ( check_cpq @ ( triple @ SV152 @ ( insert_slb @ SV186 @ ( pair @ SV221 @ SV231 ) ) @ SV211 ) )
= $false )
| ( ( strictly_less_than @ SV221 @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(705,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)],[687]) ).
thf(706,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)],[688]) ).
thf(707,plain,
! [SV246: $i,SV195: $i,SV161: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV161 @ SV195 @ SV246 ) )
= ( 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)],[689]) ).
thf(708,plain,
! [SV247: $i,SV196: $i,SV162: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV162 @ SV196 @ SV247 ) )
= ( triple @ SV162 @ ( update_slb @ SV196 @ ( findmin_pqp_res @ SV162 ) ) @ SV247 ) )
= $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)],[690]) ).
thf(709,plain,
! [SV240: $i,SV235: $i,SV199: $i,SV167: $i] :
( ( ( ~ ( contains_cpq @ ( triple @ SV167 @ SV199 @ SV235 ) @ SV240 ) )
= $true )
| ( ( contains_slb @ SV199 @ SV240 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[691]) ).
thf(710,plain,
! [SV236: $i,SV167: $i,SV241: $i,SV199: $i] :
( ( ( ~ ( contains_slb @ SV199 @ SV241 ) )
= $true )
| ( ( contains_cpq @ ( triple @ SV167 @ SV199 @ SV236 ) @ SV241 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[692]) ).
thf(711,plain,
! [SV217: $i,SV200: $i,SV168: $i] :
( ( ~ ! [SY454: $i,SY455: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY454 ) ) @ SV217 @ SY455 )
| ( SV200 = SV217 )
| ( pair_in_list @ SV168 @ SV217 @ SY455 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[693]) ).
thf(712,plain,
! [SV217: $i,SV200: $i,SV168: $i] :
( ( ~ ! [SY456: $i,SY457: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY456 ) ) @ SV217 @ SY457 )
| ( SY456 = SY457 )
| ( pair_in_list @ SV168 @ SV217 @ SY457 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[693]) ).
thf(713,plain,
! [SV168: $i,SV217: $i,SV200: $i] :
( ( ~ ! [SY458: $i,SY459: $i] :
( ( SV200 != SV217 )
| ( SY458 != SY459 )
| ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY458 ) ) @ SV217 @ SY459 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[694]) ).
thf(714,plain,
! [SV200: $i,SV217: $i,SV168: $i] :
( ( ~ ! [SY460: $i,SY461: $i] :
( ~ ( pair_in_list @ SV168 @ SV217 @ SY461 )
| ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY460 ) ) @ SV217 @ SY461 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[694]) ).
thf(715,plain,
! [SV237: $i,SV248: $i,SV201: $i,SV169: $i] :
( ( ( ~ ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV248 ) ) @ SV237 ) )
= $true )
| ( ( ( SV201 = SV237 )
| ( contains_slb @ SV169 @ SV237 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(716,plain,
! [SV169: $i,SV201: $i] :
( ( ! [SY435: $i] :
( ( SV201 != SY435 )
| ! [SY436: $i] : ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY436 ) ) @ SY435 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[696]) ).
thf(717,plain,
! [SV201: $i,SV169: $i] :
( ( ! [SY437: $i] :
( ~ ( contains_slb @ SV169 @ SY437 )
| ! [SY438: $i] : ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY438 ) ) @ SY437 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[697]) ).
thf(718,plain,
! [SV218: $i,SV202: $i,SV170: $i,SV242: $i,SV249: $i] :
( ( ~ ( less_than @ SV249 @ SV242 )
| ~ ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SV202 @ ( pair @ SV242 @ SV249 ) ) @ SV218 ) )
| ( check_cpq @ ( triple @ SV170 @ SV202 @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(719,plain,
! [SV218: $i,SV202: $i,SV170: $i,SV243: $i,SV250: $i] :
( ( ~ ( less_than @ SV250 @ SV243 )
| ~ ( check_cpq @ ( triple @ SV170 @ SV202 @ SV218 ) )
| ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SV202 @ ( pair @ SV243 @ SV250 ) ) @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(720,plain,
! [SV234: $i,SV228: $i] :
( ( ( less_than @ SV228 @ SV234 )
= $false )
| ( ( less_than @ SV234 @ SV228 )
= $true )
| ( ( strictly_less_than @ SV228 @ SV234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[701]) ).
thf(721,plain,
! [SV251: $i,SV244: $i] :
( ( ~ ( strictly_less_than @ SV244 @ SV251 )
| ( less_than @ SV244 @ SV251 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(722,plain,
! [SV252: $i,SV245: $i] :
( ( ~ ( strictly_less_than @ SV245 @ SV252 )
| ~ ( less_than @ SV252 @ SV245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(723,plain,
! [SV240: $i,SV235: $i,SV199: $i,SV167: $i] :
( ( ( contains_cpq @ ( triple @ SV167 @ SV199 @ SV235 ) @ SV240 )
= $false )
| ( ( contains_slb @ SV199 @ SV240 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[709]) ).
thf(724,plain,
! [SV236: $i,SV167: $i,SV241: $i,SV199: $i] :
( ( ( contains_slb @ SV199 @ SV241 )
= $false )
| ( ( contains_cpq @ ( triple @ SV167 @ SV199 @ SV236 ) @ SV241 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(725,plain,
! [SV217: $i,SV200: $i,SV168: $i] :
( ( ! [SY454: $i,SY455: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY454 ) ) @ SV217 @ SY455 )
| ( SV200 = SV217 )
| ( pair_in_list @ SV168 @ SV217 @ SY455 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[711]) ).
thf(726,plain,
! [SV217: $i,SV200: $i,SV168: $i] :
( ( ! [SY456: $i,SY457: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY456 ) ) @ SV217 @ SY457 )
| ( SY456 = SY457 )
| ( pair_in_list @ SV168 @ SV217 @ SY457 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[712]) ).
thf(727,plain,
! [SV168: $i,SV217: $i,SV200: $i] :
( ( ! [SY458: $i,SY459: $i] :
( ( SV200 != SV217 )
| ( SY458 != SY459 )
| ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY458 ) ) @ SV217 @ SY459 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[713]) ).
thf(728,plain,
! [SV200: $i,SV217: $i,SV168: $i] :
( ( ! [SY460: $i,SY461: $i] :
( ~ ( pair_in_list @ SV168 @ SV217 @ SY461 )
| ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SY460 ) ) @ SV217 @ SY461 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[714]) ).
thf(729,plain,
! [SV237: $i,SV248: $i,SV201: $i,SV169: $i] :
( ( ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV248 ) ) @ SV237 )
= $false )
| ( ( ( SV201 = SV237 )
| ( contains_slb @ SV169 @ SV237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(730,plain,
! [SV169: $i,SV253: $i,SV201: $i] :
( ( ( SV201 != SV253 )
| ! [SY476: $i] : ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY476 ) ) @ SV253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(731,plain,
! [SV201: $i,SV254: $i,SV169: $i] :
( ( ~ ( contains_slb @ SV169 @ SV254 )
| ! [SY477: $i] : ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY477 ) ) @ SV254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(732,plain,
! [SV218: $i,SV202: $i,SV170: $i,SV242: $i,SV249: $i] :
( ( ( ~ ( less_than @ SV249 @ SV242 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SV202 @ ( pair @ SV242 @ SV249 ) ) @ SV218 ) )
| ( check_cpq @ ( triple @ SV170 @ SV202 @ SV218 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[718]) ).
thf(733,plain,
! [SV218: $i,SV202: $i,SV170: $i,SV243: $i,SV250: $i] :
( ( ( ~ ( less_than @ SV250 @ SV243 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV170 @ SV202 @ SV218 ) )
| ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SV202 @ ( pair @ SV243 @ SV250 ) ) @ SV218 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(734,plain,
! [SV251: $i,SV244: $i] :
( ( ( ~ ( strictly_less_than @ SV244 @ SV251 ) )
= $true )
| ( ( less_than @ SV244 @ SV251 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[721]) ).
thf(735,plain,
! [SV252: $i,SV245: $i] :
( ( ( ~ ( strictly_less_than @ SV245 @ SV252 ) )
= $true )
| ( ( ~ ( less_than @ SV252 @ SV245 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[722]) ).
thf(736,plain,
! [SV217: $i,SV255: $i,SV200: $i,SV168: $i] :
( ( ! [SY478: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV255 ) ) @ SV217 @ SY478 )
| ( SV200 = SV217 )
| ( pair_in_list @ SV168 @ SV217 @ SY478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(737,plain,
! [SV217: $i,SV256: $i,SV200: $i,SV168: $i] :
( ( ! [SY479: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV256 ) ) @ SV217 @ SY479 )
| ( SV256 = SY479 )
| ( pair_in_list @ SV168 @ SV217 @ SY479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(738,plain,
! [SV168: $i,SV257: $i,SV217: $i,SV200: $i] :
( ( ! [SY480: $i] :
( ( SV200 != SV217 )
| ( SV257 != SY480 )
| ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV257 ) ) @ SV217 @ SY480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(739,plain,
! [SV258: $i,SV200: $i,SV217: $i,SV168: $i] :
( ( ! [SY481: $i] :
( ~ ( pair_in_list @ SV168 @ SV217 @ SY481 )
| ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV258 ) ) @ SV217 @ SY481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(740,plain,
! [SV248: $i,SV169: $i,SV237: $i,SV201: $i] :
( ( ( SV201 = SV237 )
= $true )
| ( ( contains_slb @ SV169 @ SV237 )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV248 ) ) @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[729]) ).
thf(741,plain,
! [SV169: $i,SV253: $i,SV201: $i] :
( ( ( ( SV201 != SV253 ) )
= $true )
| ( ( ! [SY476: $i] : ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY476 ) ) @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[730]) ).
thf(742,plain,
! [SV201: $i,SV254: $i,SV169: $i] :
( ( ( ~ ( contains_slb @ SV169 @ SV254 ) )
= $true )
| ( ( ! [SY477: $i] : ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY477 ) ) @ SV254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[731]) ).
thf(743,plain,
! [SV218: $i,SV202: $i,SV170: $i,SV242: $i,SV249: $i] :
( ( ( less_than @ SV249 @ SV242 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SV202 @ ( pair @ SV242 @ SV249 ) ) @ SV218 ) )
| ( check_cpq @ ( triple @ SV170 @ SV202 @ SV218 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(744,plain,
! [SV218: $i,SV202: $i,SV170: $i,SV243: $i,SV250: $i] :
( ( ( less_than @ SV250 @ SV243 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV170 @ SV202 @ SV218 ) )
| ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SV202 @ ( pair @ SV243 @ SV250 ) ) @ SV218 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[733]) ).
thf(745,plain,
! [SV251: $i,SV244: $i] :
( ( ( strictly_less_than @ SV244 @ SV251 )
= $false )
| ( ( less_than @ SV244 @ SV251 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(746,plain,
! [SV252: $i,SV245: $i] :
( ( ( strictly_less_than @ SV245 @ SV252 )
= $false )
| ( ( ~ ( less_than @ SV252 @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(747,plain,
! [SV259: $i,SV217: $i,SV255: $i,SV200: $i,SV168: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV255 ) ) @ SV217 @ SV259 )
| ( SV200 = SV217 )
| ( pair_in_list @ SV168 @ SV217 @ SV259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(748,plain,
! [SV260: $i,SV217: $i,SV256: $i,SV200: $i,SV168: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV256 ) ) @ SV217 @ SV260 )
| ( SV256 = SV260 )
| ( pair_in_list @ SV168 @ SV217 @ SV260 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(749,plain,
! [SV168: $i,SV261: $i,SV257: $i,SV217: $i,SV200: $i] :
( ( ( SV200 != SV217 )
| ( SV257 != SV261 )
| ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV257 ) ) @ SV217 @ SV261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(750,plain,
! [SV258: $i,SV200: $i,SV262: $i,SV217: $i,SV168: $i] :
( ( ~ ( pair_in_list @ SV168 @ SV217 @ SV262 )
| ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV258 ) ) @ SV217 @ SV262 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(751,plain,
! [SV169: $i,SV253: $i,SV201: $i] :
( ( ( SV201 = SV253 )
= $false )
| ( ( ! [SY476: $i] : ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY476 ) ) @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[741]) ).
thf(752,plain,
! [SV201: $i,SV254: $i,SV169: $i] :
( ( ( contains_slb @ SV169 @ SV254 )
= $false )
| ( ( ! [SY477: $i] : ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SY477 ) ) @ SV254 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[742]) ).
thf(753,plain,
! [SV218: $i,SV249: $i,SV242: $i,SV202: $i,SV170: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SV202 @ ( pair @ SV242 @ SV249 ) ) @ SV218 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV170 @ SV202 @ SV218 ) )
= $true )
| ( ( less_than @ SV249 @ SV242 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[743]) ).
thf(754,plain,
! [SV250: $i,SV243: $i,SV218: $i,SV202: $i,SV170: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV170 @ SV202 @ SV218 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SV202 @ ( pair @ SV243 @ SV250 ) ) @ SV218 ) )
= $true )
| ( ( less_than @ SV250 @ SV243 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[744]) ).
thf(755,plain,
! [SV245: $i,SV252: $i] :
( ( ( less_than @ SV252 @ SV245 )
= $false )
| ( ( strictly_less_than @ SV245 @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[746]) ).
thf(756,plain,
! [SV259: $i,SV217: $i,SV255: $i,SV200: $i,SV168: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV255 ) ) @ SV217 @ SV259 ) )
= $true )
| ( ( ( SV200 = SV217 )
| ( pair_in_list @ SV168 @ SV217 @ SV259 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[747]) ).
thf(757,plain,
! [SV260: $i,SV217: $i,SV256: $i,SV200: $i,SV168: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV256 ) ) @ SV217 @ SV260 ) )
= $true )
| ( ( ( SV256 = SV260 )
| ( pair_in_list @ SV168 @ SV217 @ SV260 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[748]) ).
thf(758,plain,
! [SV168: $i,SV261: $i,SV257: $i,SV217: $i,SV200: $i] :
( ( ( ( SV200 != SV217 )
| ( SV257 != SV261 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV257 ) ) @ SV217 @ SV261 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[749]) ).
thf(759,plain,
! [SV258: $i,SV200: $i,SV262: $i,SV217: $i,SV168: $i] :
( ( ( ~ ( pair_in_list @ SV168 @ SV217 @ SV262 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV258 ) ) @ SV217 @ SV262 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(760,plain,
! [SV253: $i,SV263: $i,SV201: $i,SV169: $i] :
( ( ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV263 ) ) @ SV253 )
= $true )
| ( ( SV201 = SV253 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(761,plain,
! [SV254: $i,SV264: $i,SV201: $i,SV169: $i] :
( ( ( contains_slb @ ( insert_slb @ SV169 @ ( pair @ SV201 @ SV264 ) ) @ SV254 )
= $true )
| ( ( contains_slb @ SV169 @ SV254 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(762,plain,
! [SV218: $i,SV249: $i,SV242: $i,SV202: $i,SV170: $i] :
( ( ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SV202 @ ( pair @ SV242 @ SV249 ) ) @ SV218 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV170 @ SV202 @ SV218 ) )
= $true )
| ( ( less_than @ SV249 @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(763,plain,
! [SV250: $i,SV243: $i,SV218: $i,SV202: $i,SV170: $i] :
( ( ( check_cpq @ ( triple @ SV170 @ SV202 @ SV218 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV170 @ ( insert_slb @ SV202 @ ( pair @ SV243 @ SV250 ) ) @ SV218 ) )
= $true )
| ( ( less_than @ SV250 @ SV243 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[754]) ).
thf(764,plain,
! [SV259: $i,SV217: $i,SV255: $i,SV200: $i,SV168: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV255 ) ) @ SV217 @ SV259 )
= $false )
| ( ( ( SV200 = SV217 )
| ( pair_in_list @ SV168 @ SV217 @ SV259 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(765,plain,
! [SV260: $i,SV217: $i,SV256: $i,SV200: $i,SV168: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV256 ) ) @ SV217 @ SV260 )
= $false )
| ( ( ( SV256 = SV260 )
| ( pair_in_list @ SV168 @ SV217 @ SV260 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(766,plain,
! [SV168: $i,SV261: $i,SV257: $i,SV217: $i,SV200: $i] :
( ( ( ( SV200 != SV217 ) )
= $true )
| ( ( ( SV257 != SV261 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV257 ) ) @ SV217 @ SV261 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[758]) ).
thf(767,plain,
! [SV258: $i,SV200: $i,SV262: $i,SV217: $i,SV168: $i] :
( ( ( pair_in_list @ SV168 @ SV217 @ SV262 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV258 ) ) @ SV217 @ SV262 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[759]) ).
thf(768,plain,
! [SV255: $i,SV259: $i,SV168: $i,SV217: $i,SV200: $i] :
( ( ( SV200 = SV217 )
= $true )
| ( ( pair_in_list @ SV168 @ SV217 @ SV259 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV255 ) ) @ SV217 @ SV259 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[764]) ).
thf(769,plain,
! [SV200: $i,SV217: $i,SV168: $i,SV260: $i,SV256: $i] :
( ( ( SV256 = SV260 )
= $true )
| ( ( pair_in_list @ SV168 @ SV217 @ SV260 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV256 ) ) @ SV217 @ SV260 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[765]) ).
thf(770,plain,
! [SV168: $i,SV261: $i,SV257: $i,SV217: $i,SV200: $i] :
( ( ( SV200 = SV217 )
= $false )
| ( ( ( SV257 != SV261 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV257 ) ) @ SV217 @ SV261 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[766]) ).
thf(771,plain,
! [SV168: $i,SV217: $i,SV200: $i,SV261: $i,SV257: $i] :
( ( ( SV257 = SV261 )
= $false )
| ( ( SV200 = SV217 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV168 @ ( pair @ SV200 @ SV257 ) ) @ SV217 @ SV261 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[770]) ).
thf(772,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[496,771,769,768,767,763,762,761,760,755,745,740,724,723,720,708,707,706,705,704,700,685,684,683,665,664,646,643,641,640,632,624,617,616,614,613,588,579,577,576,575,574,563,559,551,539,529,528,509,506,498,497]) ).
thf(773,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[772,445]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWV405+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 15 12:05:52 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.22/0.40 .
% 0.22/0.40
% 0.22/0.40 No.of.Axioms: 41
% 0.22/0.40
% 0.22/0.40 Length.of.Defs: 0
% 0.22/0.40
% 0.22/0.40 Contains.Choice.Funs: false
% 0.22/0.44 .
% 0.22/0.44 (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)...................................................
% 0.59/0.77
% 0.59/0.77 ********************************
% 0.59/0.77 * All subproblems solved! *
% 0.59/0.77 ********************************
% 0.59/0.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:772,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.69/0.92
% 0.69/0.92 %**** Beginning of derivation protocol ****
% 0.69/0.92 % SZS output start CNFRefutation
% See solution above
% 0.69/0.92
% 0.69/0.92 %**** End of derivation protocol ****
% 0.69/0.92 %**** no. of clauses in derivation: 773 ****
% 0.69/0.92 %**** clause counter: 772 ****
% 0.69/0.92
% 0.69/0.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:772,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------