TSTP Solution File: SWV406+1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SWV406+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 : n009.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 0.98s 1.18s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 83
% Syntax : Number of formulae : 878 ( 573 unt; 41 typ; 0 def)
% Number of atoms : 4567 (1712 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 11386 (1322 ~;1317 |; 66 &;8594 @)
% ( 24 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 41 usr; 19 con; 0-3 aty)
% Number of variables : 3002 ( 0 ^3002 !; 0 ?;3002 :)
% 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_sK10_SY158,type,
sK10_SY158: $i ).
thf(tp_sK11_SY162,type,
sK11_SY162: $i ).
thf(tp_sK12_SY130,type,
sK12_SY130: $i ).
thf(tp_sK13_SY167,type,
sK13_SY167: $i ).
thf(tp_sK14_REN,type,
sK14_REN: $o ).
thf(tp_sK1_U,type,
sK1_U: $i ).
thf(tp_sK2_SY132,type,
sK2_SY132: $i ).
thf(tp_sK3_SY138,type,
sK3_SY138: $i ).
thf(tp_sK4_SY143,type,
sK4_SY143: $i ).
thf(tp_sK5_SY147,type,
sK5_SY147: $i ).
thf(tp_sK6_SY150,type,
sK6_SY150: $i ).
thf(tp_sK7_SY152,type,
sK7_SY152: $i ).
thf(tp_sK8_SY132,type,
sK8_SY132: $i ).
thf(tp_sK9_SY153,type,
sK9_SY153: $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,W: $i] :
( ( check_cpq @ ( triple @ V @ U @ W ) )
<=> ! [X: $i,Y: $i] :
( ( pair_in_list @ U @ X @ Y )
=> ( less_than @ Y @ X ) ) )
=> ! [Z: $i,X1: $i,X2: $i,X3: $i] :
( ( check_cpq @ ( triple @ Z @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ X1 ) )
<=> ! [X4: $i,X5: $i] :
( ( pair_in_list @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ X4 @ X5 )
=> ( less_than @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l42_co) ).
thf(43,negated_conjecture,
( ( ! [U: $i] :
( ! [V: $i,W: $i] :
( ( check_cpq @ ( triple @ V @ U @ W ) )
<=> ! [X: $i,Y: $i] :
( ( pair_in_list @ U @ X @ Y )
=> ( less_than @ Y @ X ) ) )
=> ! [Z: $i,X1: $i,X2: $i,X3: $i] :
( ( check_cpq @ ( triple @ Z @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ X1 ) )
<=> ! [X4: $i,X5: $i] :
( ( pair_in_list @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ X4 @ X5 )
=> ( less_than @ X5 @ X4 ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[42]) ).
thf(44,plain,
( ( ! [U: $i] :
( ! [V: $i,W: $i] :
( ( check_cpq @ ( triple @ V @ U @ W ) )
<=> ! [X: $i,Y: $i] :
( ( pair_in_list @ U @ X @ Y )
=> ( less_than @ Y @ X ) ) )
=> ! [Z: $i,X1: $i,X2: $i,X3: $i] :
( ( check_cpq @ ( triple @ Z @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ X1 ) )
<=> ! [X4: $i,X5: $i] :
( ( pair_in_list @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ X4 @ X5 )
=> ( less_than @ X5 @ X4 ) ) ) ) )
= $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,
( ( ! [SY128: $i,SY129: $i] :
( ( check_cpq @ ( triple @ SY128 @ sK1_U @ SY129 ) )
<=> ! [SY130: $i,SY131: $i] :
( ( pair_in_list @ sK1_U @ SY130 @ SY131 )
=> ( less_than @ SY131 @ SY130 ) ) )
=> ! [SY132: $i,SY133: $i,SY134: $i,SY135: $i] :
( ( check_cpq @ ( triple @ SY132 @ ( insert_slb @ sK1_U @ ( pair @ SY134 @ SY135 ) ) @ SY133 ) )
<=> ! [SY136: $i,SY137: $i] :
( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY134 @ SY135 ) ) @ SY136 @ SY137 )
=> ( less_than @ SY137 @ SY136 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(87,plain,
( ( ! [SY128: $i,SY129: $i] :
( ( check_cpq @ ( triple @ SY128 @ sK1_U @ SY129 ) )
<=> ! [SY130: $i,SY131: $i] :
( ( pair_in_list @ sK1_U @ SY130 @ SY131 )
=> ( less_than @ SY131 @ SY130 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[86]) ).
thf(88,plain,
( ( ! [SY132: $i,SY133: $i,SY134: $i,SY135: $i] :
( ( check_cpq @ ( triple @ SY132 @ ( insert_slb @ sK1_U @ ( pair @ SY134 @ SY135 ) ) @ SY133 ) )
<=> ! [SY136: $i,SY137: $i] :
( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY134 @ SY135 ) ) @ SY136 @ SY137 )
=> ( less_than @ SY137 @ SY136 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[86]) ).
thf(89,plain,
( ( ! [SY132: $i,SY133: $i,SY134: $i,SY135: $i] :
( ( check_cpq @ ( triple @ SY132 @ ( insert_slb @ sK1_U @ ( pair @ SY134 @ SY135 ) ) @ SY133 ) )
=> ! [SY136: $i,SY137: $i] :
( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY134 @ SY135 ) ) @ SY136 @ SY137 )
=> ( less_than @ SY137 @ SY136 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[88]) ).
thf(90,plain,
( ( ! [SY132: $i,SY133: $i,SY134: $i,SY135: $i] :
( ! [SY136: $i,SY137: $i] :
( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY134 @ SY135 ) ) @ SY136 @ SY137 )
=> ( less_than @ SY137 @ SY136 ) )
=> ( check_cpq @ ( triple @ SY132 @ ( insert_slb @ sK1_U @ ( pair @ SY134 @ SY135 ) ) @ SY133 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[88]) ).
thf(91,plain,
( ( ~ ! [SY132: $i,SY133: $i,SY134: $i,SY135: $i] :
( ( check_cpq @ ( triple @ SY132 @ ( insert_slb @ sK1_U @ ( pair @ SY134 @ SY135 ) ) @ SY133 ) )
=> ! [SY136: $i,SY137: $i] :
( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY134 @ SY135 ) ) @ SY136 @ SY137 )
=> ( less_than @ SY137 @ SY136 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[89]) ).
thf(92,plain,
( ( ~ ! [SY132: $i,SY133: $i,SY134: $i,SY135: $i] :
( ! [SY136: $i,SY137: $i] :
( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY134 @ SY135 ) ) @ SY136 @ SY137 )
=> ( less_than @ SY137 @ SY136 ) )
=> ( check_cpq @ ( triple @ SY132 @ ( insert_slb @ sK1_U @ ( pair @ SY134 @ SY135 ) ) @ SY133 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[90]) ).
thf(93,plain,
( ( ( check_cpq @ ( triple @ sK2_SY132 @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY143 @ sK5_SY147 ) ) @ sK3_SY138 ) )
& ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY143 @ sK5_SY147 ) ) @ sK6_SY150 @ sK7_SY152 )
& ~ ( less_than @ sK7_SY152 @ sK6_SY150 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[91]) ).
thf(94,plain,
( ( ! [SY165: $i,SY166: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK10_SY158 @ sK11_SY162 ) ) @ SY165 @ SY166 )
| ( less_than @ SY166 @ SY165 ) )
& ~ ( check_cpq @ ( triple @ sK8_SY132 @ ( insert_slb @ sK1_U @ ( pair @ sK10_SY158 @ sK11_SY162 ) ) @ sK9_SY153 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[92]) ).
thf(95,plain,
( ( ( sK14_REN
| ! [SY128: $i,SY129: $i] : ( check_cpq @ ( triple @ SY128 @ sK1_U @ SY129 ) ) )
& ( sK14_REN
=> ( ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
& ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) ) )
& ( ! [SY128: $i,SY129: $i] :
~ ( check_cpq @ ( triple @ SY128 @ sK1_U @ SY129 ) )
| ! [SY130: $i,SY131: $i] :
( ~ ( pair_in_list @ sK1_U @ SY130 @ SY131 )
| ( less_than @ SY131 @ SY130 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(96,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(97,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(98,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(99,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(100,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(101,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(102,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(103,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( triple @ U @ V @ W ) )
| ( W = bad ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(104,plain,
( ( ! [U: $i,V: $i] :
~ ( ok @ ( triple @ U @ V @ bad ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(105,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(106,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(107,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(108,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[63]) ).
thf(109,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(110,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(111,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(112,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(113,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(114,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(115,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(116,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(117,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(118,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(119,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(120,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( less_than @ U @ V )
| ~ ( less_than @ V @ W )
| ( less_than @ U @ W ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(121,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(122,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(123,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)],[118]) ).
thf(124,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(125,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(126,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(127,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(128,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)],[117]) ).
thf(129,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(130,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)],[116]) ).
thf(131,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(132,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)],[115]) ).
thf(133,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(134,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)],[114]) ).
thf(135,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(136,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)],[113]) ).
thf(137,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)],[112]) ).
thf(138,plain,
( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(139,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(140,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(141,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(142,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(143,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(144,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)],[107]) ).
thf(145,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)],[106]) ).
thf(146,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)],[105]) ).
thf(147,plain,
( ( ! [U: $i,V: $i] :
~ ( ok @ ( triple @ U @ V @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(148,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( triple @ U @ V @ W ) )
| ( W = bad ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(149,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(150,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)],[102]) ).
thf(151,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)],[101]) ).
thf(152,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)],[100]) ).
thf(153,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(154,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)],[99]) ).
thf(155,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)],[98]) ).
thf(156,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)],[97]) ).
thf(157,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(158,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)],[96]) ).
thf(159,plain,
( ( ! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(160,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(161,plain,
( ( ( sK14_REN
| ! [SY128: $i,SY129: $i] : ( check_cpq @ ( triple @ SY128 @ sK1_U @ SY129 ) ) )
& ( sK14_REN
=> ( ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
& ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) ) )
& ( ! [SY128: $i,SY129: $i] :
~ ( check_cpq @ ( triple @ SY128 @ sK1_U @ SY129 ) )
| ! [SY130: $i,SY131: $i] :
( ~ ( pair_in_list @ sK1_U @ SY130 @ SY131 )
| ( less_than @ SY131 @ SY130 ) ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(162,plain,
( ( ( check_cpq @ ( triple @ sK2_SY132 @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY143 @ sK5_SY147 ) ) @ sK3_SY138 ) )
& ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY143 @ sK5_SY147 ) ) @ sK6_SY150 @ sK7_SY152 )
& ~ ( less_than @ sK7_SY152 @ sK6_SY150 ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(163,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)],[123]) ).
thf(164,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)],[146]) ).
thf(165,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)],[128]) ).
thf(166,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)],[130]) ).
thf(167,plain,
( ( ~ ( ~ ( check_cpq @ ( triple @ sK2_SY132 @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY143 @ sK5_SY147 ) ) @ sK3_SY138 ) )
| ~ ~ ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY143 @ sK5_SY147 ) ) @ sK6_SY150 @ sK7_SY152 )
| ~ ~ ( less_than @ sK7_SY152 @ sK6_SY150 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(168,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)],[144]) ).
thf(169,plain,
( ( ~ ( ~ ~ ( ~ ( sK14_REN
| ! [SX0: $i,SX1: $i] : ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) ) )
| ~ ( ~ sK14_REN
| ~ ( ~ ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
| ~ ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) ) ) )
| ~ ( ! [SX0: $i,SX1: $i] :
~ ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ sK1_U @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(170,plain,
! [SV1: $i] :
( ( ! [SY168: $i,SY169: $i] :
( ~ ( less_than @ SV1 @ SY168 )
| ~ ( less_than @ SY168 @ SY169 )
| ( less_than @ SV1 @ SY169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(171,plain,
! [SV2: $i] :
( ( ! [SY170: $i] :
( ( less_than @ SV2 @ SY170 )
| ( less_than @ SY170 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(172,plain,
! [SV3: $i] :
( ( less_than @ SV3 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(173,plain,
! [SV4: $i] :
( ( less_than @ bottom @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(174,plain,
( ( isnonempty_slb @ create_slb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(175,plain,
! [SV5: $i] :
( ( ! [SY171: $i,SY172: $i] : ( isnonempty_slb @ ( insert_slb @ SV5 @ ( pair @ SY171 @ SY172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(176,plain,
! [SV6: $i] :
( ( ~ ( contains_slb @ create_slb @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(177,plain,
! [SV7: $i] :
( ( ! [SY173: $i] :
~ ( pair_in_list @ create_slb @ SV7 @ SY173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(178,plain,
! [SV8: $i] :
( ( ! [SY174: $i,SY175: $i] :
( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SY174 @ SY175 ) ) @ SY174 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(179,plain,
! [SV9: $i] :
( ( ! [SY176: $i,SY177: $i] :
( ( SY176 = SY177 )
| ~ ( contains_slb @ SV9 @ SY177 )
| ! [SY178: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SY176 @ SY178 ) ) @ SY177 )
= ( insert_slb @ ( remove_slb @ SV9 @ SY177 ) @ ( pair @ SY176 @ SY178 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(180,plain,
! [SV10: $i] :
( ( ! [SY179: $i,SY180: $i] :
( ( lookup_slb @ ( insert_slb @ SV10 @ ( pair @ SY179 @ SY180 ) ) @ SY179 )
= SY180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(181,plain,
! [SV11: $i] :
( ( ! [SY181: $i,SY182: $i] :
( ( SY181 = SY182 )
| ~ ( contains_slb @ SV11 @ SY182 )
| ! [SY183: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SY181 @ SY183 ) ) @ SY182 )
= ( lookup_slb @ SV11 @ SY182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(182,plain,
! [SV12: $i] :
( ( ( update_slb @ create_slb @ SV12 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(183,plain,
! [SV13: $i] :
( ( ! [SY184: $i,SY185: $i,SY186: $i] :
( ~ ( strictly_less_than @ SY186 @ SY185 )
| ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SY184 @ SY186 ) ) @ SY185 )
= ( insert_slb @ ( update_slb @ SV13 @ SY185 ) @ ( pair @ SY184 @ SY185 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(184,plain,
! [SV14: $i] :
( ( ! [SY187: $i,SY188: $i,SY189: $i] :
( ~ ( less_than @ SY188 @ SY189 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SY187 @ SY189 ) ) @ SY188 )
= ( insert_slb @ ( update_slb @ SV14 @ SY188 ) @ ( pair @ SY187 @ SY189 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(185,plain,
! [SV15: $i] :
( ( succ_cpq @ SV15 @ SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(186,plain,
! [SV16: $i] :
( ( ! [SY190: $i] :
( ~ ( succ_cpq @ SV16 @ SY190 )
| ! [SY191: $i] : ( succ_cpq @ SV16 @ ( insert_cpq @ SY190 @ SY191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(187,plain,
! [SV17: $i] :
( ( ! [SY192: $i] :
( ~ ( succ_cpq @ SV17 @ SY192 )
| ! [SY193: $i] : ( succ_cpq @ SV17 @ ( remove_cpq @ SY192 @ SY193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(188,plain,
! [SV18: $i] :
( ( ! [SY194: $i] :
( ~ ( succ_cpq @ SV18 @ SY194 )
| ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SY194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(189,plain,
! [SV19: $i] :
( ( ! [SY195: $i] :
( ~ ( succ_cpq @ SV19 @ SY195 )
| ( succ_cpq @ SV19 @ ( removemin_cpq_eff @ SY195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(190,plain,
! [SV20: $i] :
( ( ! [SY196: $i] : ( check_cpq @ ( triple @ SV20 @ create_slb @ SY196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(191,plain,
! [SV21: $i] :
( ( ! [SY197: $i,SY198: $i,SY199: $i,SY200: $i] :
( ~ ( strictly_less_than @ SY199 @ SY200 )
| ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SY197 @ ( pair @ SY199 @ SY200 ) ) @ SY198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(192,plain,
! [SV22: $i] :
( ( ! [SY201: $i] :
~ ( ok @ ( triple @ SV22 @ SY201 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(193,plain,
! [SV23: $i] :
( ( ! [SY202: $i,SY203: $i] :
( ( ok @ ( triple @ SV23 @ SY202 @ SY203 ) )
| ( SY203 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(194,plain,
! [SV24: $i] :
( ( ! [SY204: $i,SY205: $i,SY206: $i] :
( ( insert_cpq @ ( triple @ SV24 @ SY204 @ SY205 ) @ SY206 )
= ( triple @ ( insert_pqp @ SV24 @ SY206 ) @ ( insert_slb @ SY204 @ ( pair @ SY206 @ bottom ) ) @ SY205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(195,plain,
! [SV25: $i] :
( ( ! [SY207: $i,SY208: $i,SY209: $i] :
( ( contains_slb @ SY207 @ SY209 )
| ( ( remove_cpq @ ( triple @ SV25 @ SY207 @ SY208 ) @ SY209 )
= ( triple @ SV25 @ SY207 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(196,plain,
! [SV26: $i] :
( ( ! [SY210: $i,SY211: $i,SY212: $i] :
( ~ ( contains_slb @ SY210 @ SY212 )
| ~ ( less_than @ ( lookup_slb @ SY210 @ SY212 ) @ SY212 )
| ( ( remove_cpq @ ( triple @ SV26 @ SY210 @ SY211 ) @ SY212 )
= ( triple @ ( remove_pqp @ SV26 @ SY212 ) @ ( remove_slb @ SY210 @ SY212 ) @ SY211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(197,plain,
! [SV27: $i] :
( ( ! [SY213: $i,SY214: $i,SY215: $i] :
( ~ ( contains_slb @ SY213 @ SY215 )
| ~ ( strictly_less_than @ SY215 @ ( lookup_slb @ SY213 @ SY215 ) )
| ( ( remove_cpq @ ( triple @ SV27 @ SY213 @ SY214 ) @ SY215 )
= ( triple @ ( remove_pqp @ SV27 @ SY215 ) @ ( remove_slb @ SY213 @ SY215 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(198,plain,
! [SV28: $i] :
( ( ! [SY216: $i] :
( ( findmin_cpq_eff @ ( triple @ SV28 @ create_slb @ SY216 ) )
= ( triple @ SV28 @ create_slb @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(199,plain,
! [SV29: $i] :
( ( ! [SY217: $i] :
( ( SY217 = create_slb )
| ( contains_slb @ SY217 @ ( findmin_pqp_res @ SV29 ) )
| ! [SY218: $i] :
( ( findmin_cpq_eff @ ( triple @ SV29 @ SY217 @ SY218 ) )
= ( triple @ SV29 @ ( update_slb @ SY217 @ ( findmin_pqp_res @ SV29 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(200,plain,
! [SV30: $i] :
( ( ! [SY219: $i] :
( ( SY219 = create_slb )
| ~ ( contains_slb @ SY219 @ ( findmin_pqp_res @ SV30 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SY219 @ ( findmin_pqp_res @ SV30 ) ) )
| ! [SY220: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SY219 @ SY220 ) )
= ( triple @ SV30 @ ( update_slb @ SY219 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(201,plain,
! [SV31: $i] :
( ( ! [SY221: $i] :
( ( SY221 = create_slb )
| ~ ( contains_slb @ SY221 @ ( findmin_pqp_res @ SV31 ) )
| ~ ( less_than @ ( lookup_slb @ SY221 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) )
| ! [SY222: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SY221 @ SY222 ) )
= ( triple @ SV31 @ ( update_slb @ SY221 @ ( findmin_pqp_res @ SV31 ) ) @ SY222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(202,plain,
! [SV32: $i] :
( ( ! [SY223: $i] :
( ( findmin_cpq_res @ ( triple @ SV32 @ create_slb @ SY223 ) )
= bottom ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(203,plain,
! [SV33: $i] :
( ( ! [SY224: $i] :
( ( SY224 = create_slb )
| ! [SY225: $i] :
( ( findmin_cpq_res @ ( triple @ SV33 @ SY224 @ SY225 ) )
= ( findmin_pqp_res @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(204,plain,
! [SV34: $i] :
( ( ( removemin_cpq_eff @ SV34 )
= ( remove_cpq @ ( findmin_cpq_eff @ SV34 ) @ ( findmin_cpq_res @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(205,plain,
! [SV35: $i] :
( ( ( removemin_cpq_res @ SV35 )
= ( findmin_cpq_res @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(206,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)],[163]) ).
thf(207,plain,
! [SV36: $i] :
( ( ! [SY226: $i] :
~ ( ~ ! [SY227: $i,SY228: $i] :
( ~ ( contains_cpq @ ( triple @ SV36 @ SY226 @ SY227 ) @ SY228 )
| ( contains_slb @ SY226 @ SY228 ) )
| ~ ! [SY229: $i,SY230: $i] :
( ~ ( contains_slb @ SY226 @ SY230 )
| ( contains_cpq @ ( triple @ SV36 @ SY226 @ SY229 ) @ SY230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(208,plain,
! [SV37: $i] :
( ( ! [SY231: $i] :
~ ( ~ ! [SY232: $i] :
( ! [SY233: $i] :
~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SY231 @ SY233 ) ) @ SY232 )
| ( SY231 = SY232 )
| ( contains_slb @ SV37 @ SY232 ) )
| ~ ~ ( ~ ! [SY234: $i] :
( ( SY231 != SY234 )
| ! [SY235: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SY231 @ SY235 ) ) @ SY234 ) )
| ~ ! [SY236: $i] :
( ~ ( contains_slb @ SV37 @ SY236 )
| ! [SY237: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SY231 @ SY237 ) ) @ SY236 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(209,plain,
! [SV38: $i] :
( ( ! [SY238: $i,SY239: $i] :
~ ( ~ ~ ( ~ ! [SY240: $i,SY241: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SY238 @ SY240 ) ) @ SY239 @ SY241 )
| ( SY238 = SY239 )
| ( pair_in_list @ SV38 @ SY239 @ SY241 ) )
| ~ ! [SY242: $i,SY243: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SY238 @ SY242 ) ) @ SY239 @ SY243 )
| ( SY242 = SY243 )
| ( pair_in_list @ SV38 @ SY239 @ SY243 ) ) )
| ~ ~ ( ~ ! [SY244: $i,SY245: $i] :
( ( SY238 != SY239 )
| ( SY244 != SY245 )
| ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SY238 @ SY244 ) ) @ SY239 @ SY245 ) )
| ~ ! [SY246: $i,SY247: $i] :
( ~ ( pair_in_list @ SV38 @ SY239 @ SY247 )
| ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SY238 @ SY246 ) ) @ SY239 @ SY247 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(210,plain,
( ( ~ ( check_cpq @ ( triple @ sK2_SY132 @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY143 @ sK5_SY147 ) ) @ sK3_SY138 ) )
| ~ ~ ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY143 @ sK5_SY147 ) ) @ sK6_SY150 @ sK7_SY152 )
| ~ ~ ( less_than @ sK7_SY152 @ sK6_SY150 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(211,plain,
! [SV39: $i] :
( ( ! [SY248: $i,SY249: $i] :
~ ( ~ ! [SY250: $i,SY251: $i] :
( ~ ( less_than @ SY251 @ SY250 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SY248 @ ( pair @ SY250 @ SY251 ) ) @ SY249 ) )
| ( check_cpq @ ( triple @ SV39 @ SY248 @ SY249 ) ) )
| ~ ! [SY252: $i,SY253: $i] :
( ~ ( less_than @ SY253 @ SY252 )
| ~ ( check_cpq @ ( triple @ SV39 @ SY248 @ SY249 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SY248 @ ( pair @ SY252 @ SY253 ) ) @ SY249 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(212,plain,
( ( ~ ~ ( ~ ( sK14_REN
| ! [SX0: $i,SX1: $i] : ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) ) )
| ~ ( ~ sK14_REN
| ~ ( ~ ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
| ~ ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) ) ) )
| ~ ( ! [SX0: $i,SX1: $i] :
~ ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ sK1_U @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(213,plain,
! [SV40: $i,SV1: $i] :
( ( ! [SY254: $i] :
( ~ ( less_than @ SV1 @ SV40 )
| ~ ( less_than @ SV40 @ SY254 )
| ( less_than @ SV1 @ SY254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(214,plain,
! [SV41: $i,SV2: $i] :
( ( ( less_than @ SV2 @ SV41 )
| ( less_than @ SV41 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(215,plain,
! [SV42: $i,SV5: $i] :
( ( ! [SY255: $i] : ( isnonempty_slb @ ( insert_slb @ SV5 @ ( pair @ SV42 @ SY255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(216,plain,
! [SV6: $i] :
( ( contains_slb @ create_slb @ SV6 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(217,plain,
! [SV43: $i,SV7: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV7 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(218,plain,
! [SV44: $i,SV8: $i] :
( ( ! [SY256: $i] :
( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SV44 @ SY256 ) ) @ SV44 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(219,plain,
! [SV9: $i,SV45: $i] :
( ( ! [SY257: $i] :
( ( SV45 = SY257 )
| ~ ( contains_slb @ SV9 @ SY257 )
| ! [SY258: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV45 @ SY258 ) ) @ SY257 )
= ( insert_slb @ ( remove_slb @ SV9 @ SY257 ) @ ( pair @ SV45 @ SY258 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(220,plain,
! [SV46: $i,SV10: $i] :
( ( ! [SY259: $i] :
( ( lookup_slb @ ( insert_slb @ SV10 @ ( pair @ SV46 @ SY259 ) ) @ SV46 )
= SY259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(221,plain,
! [SV11: $i,SV47: $i] :
( ( ! [SY260: $i] :
( ( SV47 = SY260 )
| ~ ( contains_slb @ SV11 @ SY260 )
| ! [SY261: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV47 @ SY261 ) ) @ SY260 )
= ( lookup_slb @ SV11 @ SY260 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(222,plain,
! [SV48: $i,SV13: $i] :
( ( ! [SY262: $i,SY263: $i] :
( ~ ( strictly_less_than @ SY263 @ SY262 )
| ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV48 @ SY263 ) ) @ SY262 )
= ( insert_slb @ ( update_slb @ SV13 @ SY262 ) @ ( pair @ SV48 @ SY262 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(223,plain,
! [SV49: $i,SV14: $i] :
( ( ! [SY264: $i,SY265: $i] :
( ~ ( less_than @ SY264 @ SY265 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV49 @ SY265 ) ) @ SY264 )
= ( insert_slb @ ( update_slb @ SV14 @ SY264 ) @ ( pair @ SV49 @ SY265 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(224,plain,
! [SV50: $i,SV16: $i] :
( ( ~ ( succ_cpq @ SV16 @ SV50 )
| ! [SY266: $i] : ( succ_cpq @ SV16 @ ( insert_cpq @ SV50 @ SY266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(225,plain,
! [SV51: $i,SV17: $i] :
( ( ~ ( succ_cpq @ SV17 @ SV51 )
| ! [SY267: $i] : ( succ_cpq @ SV17 @ ( remove_cpq @ SV51 @ SY267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(226,plain,
! [SV52: $i,SV18: $i] :
( ( ~ ( succ_cpq @ SV18 @ SV52 )
| ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(227,plain,
! [SV53: $i,SV19: $i] :
( ( ~ ( succ_cpq @ SV19 @ SV53 )
| ( succ_cpq @ SV19 @ ( removemin_cpq_eff @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(228,plain,
! [SV54: $i,SV20: $i] :
( ( check_cpq @ ( triple @ SV20 @ create_slb @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(229,plain,
! [SV55: $i,SV21: $i] :
( ( ! [SY268: $i,SY269: $i,SY270: $i] :
( ~ ( strictly_less_than @ SY269 @ SY270 )
| ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV55 @ ( pair @ SY269 @ SY270 ) ) @ SY268 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(230,plain,
! [SV56: $i,SV22: $i] :
( ( ~ ( ok @ ( triple @ SV22 @ SV56 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(231,plain,
! [SV57: $i,SV23: $i] :
( ( ! [SY271: $i] :
( ( ok @ ( triple @ SV23 @ SV57 @ SY271 ) )
| ( SY271 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(232,plain,
! [SV58: $i,SV24: $i] :
( ( ! [SY272: $i,SY273: $i] :
( ( insert_cpq @ ( triple @ SV24 @ SV58 @ SY272 ) @ SY273 )
= ( triple @ ( insert_pqp @ SV24 @ SY273 ) @ ( insert_slb @ SV58 @ ( pair @ SY273 @ bottom ) ) @ SY272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(233,plain,
! [SV25: $i,SV59: $i] :
( ( ! [SY274: $i,SY275: $i] :
( ( contains_slb @ SV59 @ SY275 )
| ( ( remove_cpq @ ( triple @ SV25 @ SV59 @ SY274 ) @ SY275 )
= ( triple @ SV25 @ SV59 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(234,plain,
! [SV26: $i,SV60: $i] :
( ( ! [SY276: $i,SY277: $i] :
( ~ ( contains_slb @ SV60 @ SY277 )
| ~ ( less_than @ ( lookup_slb @ SV60 @ SY277 ) @ SY277 )
| ( ( remove_cpq @ ( triple @ SV26 @ SV60 @ SY276 ) @ SY277 )
= ( triple @ ( remove_pqp @ SV26 @ SY277 ) @ ( remove_slb @ SV60 @ SY277 ) @ SY276 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(235,plain,
! [SV27: $i,SV61: $i] :
( ( ! [SY278: $i,SY279: $i] :
( ~ ( contains_slb @ SV61 @ SY279 )
| ~ ( strictly_less_than @ SY279 @ ( lookup_slb @ SV61 @ SY279 ) )
| ( ( remove_cpq @ ( triple @ SV27 @ SV61 @ SY278 ) @ SY279 )
= ( triple @ ( remove_pqp @ SV27 @ SY279 ) @ ( remove_slb @ SV61 @ SY279 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(236,plain,
! [SV62: $i,SV28: $i] :
( ( ( findmin_cpq_eff @ ( triple @ SV28 @ create_slb @ SV62 ) )
= ( triple @ SV28 @ create_slb @ bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(237,plain,
! [SV29: $i,SV63: $i] :
( ( ( SV63 = create_slb )
| ( contains_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) )
| ! [SY280: $i] :
( ( findmin_cpq_eff @ ( triple @ SV29 @ SV63 @ SY280 ) )
= ( triple @ SV29 @ ( update_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(238,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 ) ) )
| ! [SY281: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY281 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(239,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 ) )
| ! [SY282: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY282 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(240,plain,
! [SV66: $i,SV32: $i] :
( ( ( findmin_cpq_res @ ( triple @ SV32 @ create_slb @ SV66 ) )
= bottom )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(241,plain,
! [SV33: $i,SV67: $i] :
( ( ( SV67 = create_slb )
| ! [SY283: $i] :
( ( findmin_cpq_res @ ( triple @ SV33 @ SV67 @ SY283 ) )
= ( findmin_pqp_res @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(242,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)],[206]) ).
thf(243,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)],[206]) ).
thf(244,plain,
! [SV68: $i,SV36: $i] :
( ( ~ ( ~ ! [SY284: $i,SY285: $i] :
( ~ ( contains_cpq @ ( triple @ SV36 @ SV68 @ SY284 ) @ SY285 )
| ( contains_slb @ SV68 @ SY285 ) )
| ~ ! [SY286: $i,SY287: $i] :
( ~ ( contains_slb @ SV68 @ SY287 )
| ( contains_cpq @ ( triple @ SV36 @ SV68 @ SY286 ) @ SY287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(245,plain,
! [SV69: $i,SV37: $i] :
( ( ~ ( ~ ! [SY288: $i] :
( ! [SY289: $i] :
~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY289 ) ) @ SY288 )
| ( SV69 = SY288 )
| ( contains_slb @ SV37 @ SY288 ) )
| ~ ~ ( ~ ! [SY290: $i] :
( ( SV69 != SY290 )
| ! [SY291: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY291 ) ) @ SY290 ) )
| ~ ! [SY292: $i] :
( ~ ( contains_slb @ SV37 @ SY292 )
| ! [SY293: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY293 ) ) @ SY292 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(246,plain,
! [SV70: $i,SV38: $i] :
( ( ! [SY294: $i] :
~ ( ~ ~ ( ~ ! [SY295: $i,SY296: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY295 ) ) @ SY294 @ SY296 )
| ( SV70 = SY294 )
| ( pair_in_list @ SV38 @ SY294 @ SY296 ) )
| ~ ! [SY297: $i,SY298: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY297 ) ) @ SY294 @ SY298 )
| ( SY297 = SY298 )
| ( pair_in_list @ SV38 @ SY294 @ SY298 ) ) )
| ~ ~ ( ~ ! [SY299: $i,SY300: $i] :
( ( SV70 != SY294 )
| ( SY299 != SY300 )
| ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY299 ) ) @ SY294 @ SY300 ) )
| ~ ! [SY301: $i,SY302: $i] :
( ~ ( pair_in_list @ SV38 @ SY294 @ SY302 )
| ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY301 ) ) @ SY294 @ SY302 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(247,plain,
( ( ~ ( check_cpq @ ( triple @ sK2_SY132 @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY143 @ sK5_SY147 ) ) @ sK3_SY138 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(248,plain,
( ( ~ ~ ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY143 @ sK5_SY147 ) ) @ sK6_SY150 @ sK7_SY152 )
| ~ ~ ( less_than @ sK7_SY152 @ sK6_SY150 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(249,plain,
! [SV71: $i,SV39: $i] :
( ( ! [SY303: $i] :
~ ( ~ ! [SY304: $i,SY305: $i] :
( ~ ( less_than @ SY305 @ SY304 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY304 @ SY305 ) ) @ SY303 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SY303 ) ) )
| ~ ! [SY306: $i,SY307: $i] :
( ~ ( less_than @ SY307 @ SY306 )
| ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SY303 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY306 @ SY307 ) ) @ SY303 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(250,plain,
( ( ~ ~ ( ~ ( sK14_REN
| ! [SX0: $i,SX1: $i] : ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) ) )
| ~ ( ~ sK14_REN
| ~ ( ~ ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
| ~ ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(251,plain,
( ( ~ ( ! [SX0: $i,SX1: $i] :
~ ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ sK1_U @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(252,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)],[213]) ).
thf(253,plain,
! [SV41: $i,SV2: $i] :
( ( ( less_than @ SV2 @ SV41 )
= $true )
| ( ( less_than @ SV41 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(254,plain,
! [SV73: $i,SV42: $i,SV5: $i] :
( ( isnonempty_slb @ ( insert_slb @ SV5 @ ( pair @ SV42 @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(255,plain,
! [SV43: $i,SV7: $i] :
( ( pair_in_list @ create_slb @ SV7 @ SV43 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(256,plain,
! [SV74: $i,SV44: $i,SV8: $i] :
( ( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SV44 @ SV74 ) ) @ SV44 )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(257,plain,
! [SV9: $i,SV75: $i,SV45: $i] :
( ( ( SV45 = SV75 )
| ~ ( contains_slb @ SV9 @ SV75 )
| ! [SY308: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV45 @ SY308 ) ) @ SV75 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV75 ) @ ( pair @ SV45 @ SY308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(258,plain,
! [SV76: $i,SV46: $i,SV10: $i] :
( ( ( lookup_slb @ ( insert_slb @ SV10 @ ( pair @ SV46 @ SV76 ) ) @ SV46 )
= SV76 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(259,plain,
! [SV11: $i,SV77: $i,SV47: $i] :
( ( ( SV47 = SV77 )
| ~ ( contains_slb @ SV11 @ SV77 )
| ! [SY309: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV47 @ SY309 ) ) @ SV77 )
= ( lookup_slb @ SV11 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(260,plain,
! [SV48: $i,SV13: $i,SV78: $i] :
( ( ! [SY310: $i] :
( ~ ( strictly_less_than @ SY310 @ SV78 )
| ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV48 @ SY310 ) ) @ SV78 )
= ( insert_slb @ ( update_slb @ SV13 @ SV78 ) @ ( pair @ SV48 @ SV78 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(261,plain,
! [SV49: $i,SV14: $i,SV79: $i] :
( ( ! [SY311: $i] :
( ~ ( less_than @ SV79 @ SY311 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV49 @ SY311 ) ) @ SV79 )
= ( insert_slb @ ( update_slb @ SV14 @ SV79 ) @ ( pair @ SV49 @ SY311 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(262,plain,
! [SV50: $i,SV16: $i] :
( ( ( ~ ( succ_cpq @ SV16 @ SV50 ) )
= $true )
| ( ( ! [SY266: $i] : ( succ_cpq @ SV16 @ ( insert_cpq @ SV50 @ SY266 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(263,plain,
! [SV51: $i,SV17: $i] :
( ( ( ~ ( succ_cpq @ SV17 @ SV51 ) )
= $true )
| ( ( ! [SY267: $i] : ( succ_cpq @ SV17 @ ( remove_cpq @ SV51 @ SY267 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(264,plain,
! [SV52: $i,SV18: $i] :
( ( ( ~ ( succ_cpq @ SV18 @ SV52 ) )
= $true )
| ( ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(265,plain,
! [SV53: $i,SV19: $i] :
( ( ( ~ ( succ_cpq @ SV19 @ SV53 ) )
= $true )
| ( ( succ_cpq @ SV19 @ ( removemin_cpq_eff @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(266,plain,
! [SV80: $i,SV55: $i,SV21: $i] :
( ( ! [SY312: $i,SY313: $i] :
( ~ ( strictly_less_than @ SY312 @ SY313 )
| ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV55 @ ( pair @ SY312 @ SY313 ) ) @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(267,plain,
! [SV56: $i,SV22: $i] :
( ( ok @ ( triple @ SV22 @ SV56 @ bad ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(268,plain,
! [SV81: $i,SV57: $i,SV23: $i] :
( ( ( ok @ ( triple @ SV23 @ SV57 @ SV81 ) )
| ( SV81 = bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(269,plain,
! [SV82: $i,SV58: $i,SV24: $i] :
( ( ! [SY314: $i] :
( ( insert_cpq @ ( triple @ SV24 @ SV58 @ SV82 ) @ SY314 )
= ( triple @ ( insert_pqp @ SV24 @ SY314 ) @ ( insert_slb @ SV58 @ ( pair @ SY314 @ bottom ) ) @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(270,plain,
! [SV83: $i,SV25: $i,SV59: $i] :
( ( ! [SY315: $i] :
( ( contains_slb @ SV59 @ SY315 )
| ( ( remove_cpq @ ( triple @ SV25 @ SV59 @ SV83 ) @ SY315 )
= ( triple @ SV25 @ SV59 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(271,plain,
! [SV84: $i,SV26: $i,SV60: $i] :
( ( ! [SY316: $i] :
( ~ ( contains_slb @ SV60 @ SY316 )
| ~ ( less_than @ ( lookup_slb @ SV60 @ SY316 ) @ SY316 )
| ( ( remove_cpq @ ( triple @ SV26 @ SV60 @ SV84 ) @ SY316 )
= ( triple @ ( remove_pqp @ SV26 @ SY316 ) @ ( remove_slb @ SV60 @ SY316 ) @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(272,plain,
! [SV85: $i,SV27: $i,SV61: $i] :
( ( ! [SY317: $i] :
( ~ ( contains_slb @ SV61 @ SY317 )
| ~ ( strictly_less_than @ SY317 @ ( lookup_slb @ SV61 @ SY317 ) )
| ( ( remove_cpq @ ( triple @ SV27 @ SV61 @ SV85 ) @ SY317 )
= ( triple @ ( remove_pqp @ SV27 @ SY317 ) @ ( remove_slb @ SV61 @ SY317 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(273,plain,
! [SV29: $i,SV63: $i] :
( ( ( ( SV63 = create_slb )
| ( contains_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) ) )
= $true )
| ( ( ! [SY280: $i] :
( ( findmin_cpq_eff @ ( triple @ SV29 @ SV63 @ SY280 ) )
= ( triple @ SV29 @ ( update_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(274,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 )
| ( ( ! [SY281: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY281 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(275,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 )
| ( ( ! [SY282: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY282 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY282 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(276,plain,
! [SV33: $i,SV67: $i] :
( ( ( SV67 = create_slb )
= $true )
| ( ( ! [SY283: $i] :
( ( findmin_cpq_res @ ( triple @ SV33 @ SV67 @ SY283 ) )
= ( findmin_pqp_res @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(277,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)],[242]) ).
thf(278,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)],[243]) ).
thf(279,plain,
! [SV68: $i,SV36: $i] :
( ( ~ ! [SY284: $i,SY285: $i] :
( ~ ( contains_cpq @ ( triple @ SV36 @ SV68 @ SY284 ) @ SY285 )
| ( contains_slb @ SV68 @ SY285 ) )
| ~ ! [SY286: $i,SY287: $i] :
( ~ ( contains_slb @ SV68 @ SY287 )
| ( contains_cpq @ ( triple @ SV36 @ SV68 @ SY286 ) @ SY287 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(280,plain,
! [SV69: $i,SV37: $i] :
( ( ~ ! [SY288: $i] :
( ! [SY289: $i] :
~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY289 ) ) @ SY288 )
| ( SV69 = SY288 )
| ( contains_slb @ SV37 @ SY288 ) )
| ~ ~ ( ~ ! [SY290: $i] :
( ( SV69 != SY290 )
| ! [SY291: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY291 ) ) @ SY290 ) )
| ~ ! [SY292: $i] :
( ~ ( contains_slb @ SV37 @ SY292 )
| ! [SY293: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY293 ) ) @ SY292 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(281,plain,
! [SV86: $i,SV70: $i,SV38: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY318: $i,SY319: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY318 ) ) @ SV86 @ SY319 )
| ( SV70 = SV86 )
| ( pair_in_list @ SV38 @ SV86 @ SY319 ) )
| ~ ! [SY320: $i,SY321: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY320 ) ) @ SV86 @ SY321 )
| ( SY320 = SY321 )
| ( pair_in_list @ SV38 @ SV86 @ SY321 ) ) )
| ~ ~ ( ~ ! [SY322: $i,SY323: $i] :
( ( SV70 != SV86 )
| ( SY322 != SY323 )
| ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY322 ) ) @ SV86 @ SY323 ) )
| ~ ! [SY324: $i,SY325: $i] :
( ~ ( pair_in_list @ SV38 @ SV86 @ SY325 )
| ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY324 ) ) @ SV86 @ SY325 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(282,plain,
( ( check_cpq @ ( triple @ sK2_SY132 @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY143 @ sK5_SY147 ) ) @ sK3_SY138 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(283,plain,
( ( ~ ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY143 @ sK5_SY147 ) ) @ sK6_SY150 @ sK7_SY152 )
| ~ ~ ( less_than @ sK7_SY152 @ sK6_SY150 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(284,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ~ ( ~ ! [SY326: $i,SY327: $i] :
( ~ ( less_than @ SY327 @ SY326 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY326 @ SY327 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) )
| ~ ! [SY328: $i,SY329: $i] :
( ~ ( less_than @ SY329 @ SY328 )
| ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY328 @ SY329 ) ) @ SV87 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(285,plain,
( ( ~ ( ~ ( sK14_REN
| ! [SX0: $i,SX1: $i] : ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) ) )
| ~ ( ~ sK14_REN
| ~ ( ~ ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
| ~ ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(286,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ sK1_U @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(287,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)],[252]) ).
thf(288,plain,
! [SV9: $i,SV75: $i,SV45: $i] :
( ( ( ( SV45 = SV75 )
| ~ ( contains_slb @ SV9 @ SV75 ) )
= $true )
| ( ( ! [SY308: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV45 @ SY308 ) ) @ SV75 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV75 ) @ ( pair @ SV45 @ SY308 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(289,plain,
! [SV11: $i,SV77: $i,SV47: $i] :
( ( ( ( SV47 = SV77 )
| ~ ( contains_slb @ SV11 @ SV77 ) )
= $true )
| ( ( ! [SY309: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV47 @ SY309 ) ) @ SV77 )
= ( lookup_slb @ SV11 @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(290,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)],[260]) ).
thf(291,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)],[261]) ).
thf(292,plain,
! [SV50: $i,SV16: $i] :
( ( ( succ_cpq @ SV16 @ SV50 )
= $false )
| ( ( ! [SY266: $i] : ( succ_cpq @ SV16 @ ( insert_cpq @ SV50 @ SY266 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(293,plain,
! [SV51: $i,SV17: $i] :
( ( ( succ_cpq @ SV17 @ SV51 )
= $false )
| ( ( ! [SY267: $i] : ( succ_cpq @ SV17 @ ( remove_cpq @ SV51 @ SY267 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(294,plain,
! [SV52: $i,SV18: $i] :
( ( ( succ_cpq @ SV18 @ SV52 )
= $false )
| ( ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(295,plain,
! [SV53: $i,SV19: $i] :
( ( ( succ_cpq @ SV19 @ SV53 )
= $false )
| ( ( succ_cpq @ SV19 @ ( removemin_cpq_eff @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(296,plain,
! [SV80: $i,SV55: $i,SV21: $i,SV90: $i] :
( ( ! [SY330: $i] :
( ~ ( strictly_less_than @ SV90 @ SY330 )
| ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV55 @ ( pair @ SV90 @ SY330 ) ) @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(297,plain,
! [SV81: $i,SV57: $i,SV23: $i] :
( ( ( ok @ ( triple @ SV23 @ SV57 @ SV81 ) )
= $true )
| ( ( SV81 = bad )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(298,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)],[269]) ).
thf(299,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)],[270]) ).
thf(300,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)],[271]) ).
thf(301,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)],[272]) ).
thf(302,plain,
! [SV29: $i,SV63: $i] :
( ( ( SV63 = create_slb )
= $true )
| ( ( contains_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) )
= $true )
| ( ( ! [SY280: $i] :
( ( findmin_cpq_eff @ ( triple @ SV29 @ SV63 @ SY280 ) )
= ( triple @ SV29 @ ( update_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(303,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 )
| ( ( ! [SY281: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY281 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(304,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 )
| ( ( ! [SY282: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY282 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY282 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(305,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)],[276]) ).
thf(306,plain,
! [SV96: $i] :
( ( ! [SY331: $i] :
( ~ ( less_than @ SV96 @ SY331 )
| ( less_than @ SY331 @ SV96 )
| ( strictly_less_than @ SV96 @ SY331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(307,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)],[278]) ).
thf(308,plain,
! [SV68: $i,SV36: $i] :
( ( ~ ! [SY284: $i,SY285: $i] :
( ~ ( contains_cpq @ ( triple @ SV36 @ SV68 @ SY284 ) @ SY285 )
| ( contains_slb @ SV68 @ SY285 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(309,plain,
! [SV36: $i,SV68: $i] :
( ( ~ ! [SY286: $i,SY287: $i] :
( ~ ( contains_slb @ SV68 @ SY287 )
| ( contains_cpq @ ( triple @ SV36 @ SV68 @ SY286 ) @ SY287 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(310,plain,
! [SV69: $i,SV37: $i] :
( ( ~ ! [SY288: $i] :
( ! [SY289: $i] :
~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY289 ) ) @ SY288 )
| ( SV69 = SY288 )
| ( contains_slb @ SV37 @ SY288 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(311,plain,
! [SV37: $i,SV69: $i] :
( ( ~ ~ ( ~ ! [SY290: $i] :
( ( SV69 != SY290 )
| ! [SY291: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY291 ) ) @ SY290 ) )
| ~ ! [SY292: $i] :
( ~ ( contains_slb @ SV37 @ SY292 )
| ! [SY293: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY293 ) ) @ SY292 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(312,plain,
! [SV86: $i,SV70: $i,SV38: $i] :
( ( ~ ~ ( ~ ! [SY318: $i,SY319: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY318 ) ) @ SV86 @ SY319 )
| ( SV70 = SV86 )
| ( pair_in_list @ SV38 @ SV86 @ SY319 ) )
| ~ ! [SY320: $i,SY321: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY320 ) ) @ SV86 @ SY321 )
| ( SY320 = SY321 )
| ( pair_in_list @ SV38 @ SV86 @ SY321 ) ) )
| ~ ~ ( ~ ! [SY322: $i,SY323: $i] :
( ( SV70 != SV86 )
| ( SY322 != SY323 )
| ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY322 ) ) @ SV86 @ SY323 ) )
| ~ ! [SY324: $i,SY325: $i] :
( ~ ( pair_in_list @ SV38 @ SV86 @ SY325 )
| ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY324 ) ) @ SV86 @ SY325 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(313,plain,
( ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY143 @ sK5_SY147 ) ) @ sK6_SY150 @ sK7_SY152 )
| ~ ~ ( less_than @ sK7_SY152 @ sK6_SY150 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(314,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ~ ! [SY326: $i,SY327: $i] :
( ~ ( less_than @ SY327 @ SY326 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY326 @ SY327 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) )
| ~ ! [SY328: $i,SY329: $i] :
( ~ ( less_than @ SY329 @ SY328 )
| ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY328 @ SY329 ) ) @ SV87 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(315,plain,
( ( ~ ( sK14_REN
| ! [SX0: $i,SX1: $i] : ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) ) )
| ~ ( ~ sK14_REN
| ~ ( ~ ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
| ~ ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(316,plain,
( ( ( ! [SX0: $i,SX1: $i] :
~ ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) ) )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ sK1_U @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(317,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)],[287]) ).
thf(318,plain,
! [SV9: $i,SV75: $i,SV45: $i] :
( ( ( SV45 = SV75 )
= $true )
| ( ( ~ ( contains_slb @ SV9 @ SV75 ) )
= $true )
| ( ( ! [SY308: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV45 @ SY308 ) ) @ SV75 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV75 ) @ ( pair @ SV45 @ SY308 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(319,plain,
! [SV11: $i,SV77: $i,SV47: $i] :
( ( ( SV47 = SV77 )
= $true )
| ( ( ~ ( contains_slb @ SV11 @ SV77 ) )
= $true )
| ( ( ! [SY309: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV47 @ SY309 ) ) @ SV77 )
= ( lookup_slb @ SV11 @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(320,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)],[290]) ).
thf(321,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)],[291]) ).
thf(322,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)],[292]) ).
thf(323,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)],[293]) ).
thf(324,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)],[296]) ).
thf(325,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)],[299]) ).
thf(326,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)],[300]) ).
thf(327,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)],[301]) ).
thf(328,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)],[302]) ).
thf(329,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 )
| ( ( ! [SY281: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY281 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(330,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 )
| ( ( ! [SY282: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY282 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY282 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(331,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)],[306]) ).
thf(332,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(333,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(334,plain,
! [SV68: $i,SV36: $i] :
( ( ! [SY284: $i,SY285: $i] :
( ~ ( contains_cpq @ ( triple @ SV36 @ SV68 @ SY284 ) @ SY285 )
| ( contains_slb @ SV68 @ SY285 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(335,plain,
! [SV36: $i,SV68: $i] :
( ( ! [SY286: $i,SY287: $i] :
( ~ ( contains_slb @ SV68 @ SY287 )
| ( contains_cpq @ ( triple @ SV36 @ SV68 @ SY286 ) @ SY287 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(336,plain,
! [SV69: $i,SV37: $i] :
( ( ! [SY288: $i] :
( ! [SY289: $i] :
~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY289 ) ) @ SY288 )
| ( SV69 = SY288 )
| ( contains_slb @ SV37 @ SY288 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(337,plain,
! [SV37: $i,SV69: $i] :
( ( ~ ( ~ ! [SY290: $i] :
( ( SV69 != SY290 )
| ! [SY291: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY291 ) ) @ SY290 ) )
| ~ ! [SY292: $i] :
( ~ ( contains_slb @ SV37 @ SY292 )
| ! [SY293: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY293 ) ) @ SY292 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(338,plain,
! [SV86: $i,SV70: $i,SV38: $i] :
( ( ~ ~ ( ~ ! [SY318: $i,SY319: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY318 ) ) @ SV86 @ SY319 )
| ( SV70 = SV86 )
| ( pair_in_list @ SV38 @ SV86 @ SY319 ) )
| ~ ! [SY320: $i,SY321: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY320 ) ) @ SV86 @ SY321 )
| ( SY320 = SY321 )
| ( pair_in_list @ SV38 @ SV86 @ SY321 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[312]) ).
thf(339,plain,
! [SV38: $i,SV86: $i,SV70: $i] :
( ( ~ ~ ( ~ ! [SY322: $i,SY323: $i] :
( ( SV70 != SV86 )
| ( SY322 != SY323 )
| ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY322 ) ) @ SV86 @ SY323 ) )
| ~ ! [SY324: $i,SY325: $i] :
( ~ ( pair_in_list @ SV38 @ SV86 @ SY325 )
| ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY324 ) ) @ SV86 @ SY325 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[312]) ).
thf(340,plain,
( ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY143 @ sK5_SY147 ) ) @ sK6_SY150 @ sK7_SY152 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(341,plain,
( ( ~ ~ ( less_than @ sK7_SY152 @ sK6_SY150 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(342,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ~ ! [SY326: $i,SY327: $i] :
( ~ ( less_than @ SY327 @ SY326 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY326 @ SY327 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[314]) ).
thf(343,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ~ ! [SY328: $i,SY329: $i] :
( ~ ( less_than @ SY329 @ SY328 )
| ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY328 @ SY329 ) ) @ SV87 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[314]) ).
thf(344,plain,
( ( ~ ( sK14_REN
| ! [SX0: $i,SX1: $i] : ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[315]) ).
thf(345,plain,
( ( ~ ( ~ sK14_REN
| ~ ( ~ ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
| ~ ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[315]) ).
thf(346,plain,
! [SV102: $i] :
( ( ( ! [SY332: $i] :
~ ( check_cpq @ ( triple @ SV102 @ sK1_U @ SY332 ) ) )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ sK1_U @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(347,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)],[317]) ).
thf(348,plain,
! [SV45: $i,SV75: $i,SV9: $i] :
( ( ( contains_slb @ SV9 @ SV75 )
= $false )
| ( ( SV45 = SV75 )
= $true )
| ( ( ! [SY308: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV45 @ SY308 ) ) @ SV75 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV75 ) @ ( pair @ SV45 @ SY308 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(349,plain,
! [SV47: $i,SV77: $i,SV11: $i] :
( ( ( contains_slb @ SV11 @ SV77 )
= $false )
| ( ( SV47 = SV77 )
= $true )
| ( ( ! [SY309: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV47 @ SY309 ) ) @ SV77 )
= ( lookup_slb @ SV11 @ SV77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(350,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)],[320]) ).
thf(351,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)],[321]) ).
thf(352,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)],[324]) ).
thf(353,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)],[326]) ).
thf(354,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)],[327]) ).
thf(355,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 )
| ( ( ! [SY281: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY281 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(356,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 )
| ( ( ! [SY282: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY282 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY282 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(357,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)],[331]) ).
thf(358,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(359,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[333]) ).
thf(360,plain,
! [SV103: $i,SV68: $i,SV36: $i] :
( ( ! [SY333: $i] :
( ~ ( contains_cpq @ ( triple @ SV36 @ SV68 @ SV103 ) @ SY333 )
| ( contains_slb @ SV68 @ SY333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(361,plain,
! [SV104: $i,SV36: $i,SV68: $i] :
( ( ! [SY334: $i] :
( ~ ( contains_slb @ SV68 @ SY334 )
| ( contains_cpq @ ( triple @ SV36 @ SV68 @ SV104 ) @ SY334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(362,plain,
! [SV105: $i,SV69: $i,SV37: $i] :
( ( ! [SY335: $i] :
~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY335 ) ) @ SV105 )
| ( SV69 = SV105 )
| ( contains_slb @ SV37 @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(363,plain,
! [SV37: $i,SV69: $i] :
( ( ~ ! [SY290: $i] :
( ( SV69 != SY290 )
| ! [SY291: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY291 ) ) @ SY290 ) )
| ~ ! [SY292: $i] :
( ~ ( contains_slb @ SV37 @ SY292 )
| ! [SY293: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY293 ) ) @ SY292 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(364,plain,
! [SV86: $i,SV70: $i,SV38: $i] :
( ( ~ ( ~ ! [SY318: $i,SY319: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY318 ) ) @ SV86 @ SY319 )
| ( SV70 = SV86 )
| ( pair_in_list @ SV38 @ SV86 @ SY319 ) )
| ~ ! [SY320: $i,SY321: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY320 ) ) @ SV86 @ SY321 )
| ( SY320 = SY321 )
| ( pair_in_list @ SV38 @ SV86 @ SY321 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(365,plain,
! [SV38: $i,SV86: $i,SV70: $i] :
( ( ~ ( ~ ! [SY322: $i,SY323: $i] :
( ( SV70 != SV86 )
| ( SY322 != SY323 )
| ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY322 ) ) @ SV86 @ SY323 ) )
| ~ ! [SY324: $i,SY325: $i] :
( ~ ( pair_in_list @ SV38 @ SV86 @ SY325 )
| ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY324 ) ) @ SV86 @ SY325 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(366,plain,
( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY143 @ sK5_SY147 ) ) @ sK6_SY150 @ sK7_SY152 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(367,plain,
( ( ~ ( less_than @ sK7_SY152 @ sK6_SY150 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(368,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ! [SY326: $i,SY327: $i] :
( ~ ( less_than @ SY327 @ SY326 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY326 @ SY327 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(369,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ! [SY328: $i,SY329: $i] :
( ~ ( less_than @ SY329 @ SY328 )
| ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY328 @ SY329 ) ) @ SV87 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[343]) ).
thf(370,plain,
( ( sK14_REN
| ! [SX0: $i,SX1: $i] : ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[344]) ).
thf(371,plain,
( ( ~ sK14_REN
| ~ ( ~ ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
| ~ ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[345]) ).
thf(372,plain,
! [SV106: $i,SV102: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV102 @ sK1_U @ SV106 ) ) )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ sK1_U @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(373,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)],[347]) ).
thf(374,plain,
! [SV75: $i,SV107: $i,SV45: $i,SV9: $i] :
( ( ( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV45 @ SV107 ) ) @ SV75 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV75 ) @ ( pair @ SV45 @ SV107 ) ) )
= $true )
| ( ( SV45 = SV75 )
= $true )
| ( ( contains_slb @ SV9 @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(375,plain,
! [SV77: $i,SV108: $i,SV47: $i,SV11: $i] :
( ( ( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV47 @ SV108 ) ) @ SV77 )
= ( lookup_slb @ SV11 @ SV77 ) )
= $true )
| ( ( SV47 = SV77 )
= $true )
| ( ( contains_slb @ SV11 @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(376,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)],[352]) ).
thf(377,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)],[353]) ).
thf(378,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)],[354]) ).
thf(379,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 )
| ( ( ! [SY281: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY281 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(380,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 )
| ( ( ! [SY282: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY282 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY282 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(381,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)],[357]) ).
thf(382,plain,
! [SV109: $i] :
( ( ! [SY336: $i] :
( ~ ( strictly_less_than @ SV109 @ SY336 )
| ( less_than @ SV109 @ SY336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(383,plain,
! [SV110: $i] :
( ( ! [SY337: $i] :
( ~ ( strictly_less_than @ SV110 @ SY337 )
| ~ ( less_than @ SY337 @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(384,plain,
! [SV111: $i,SV103: $i,SV68: $i,SV36: $i] :
( ( ~ ( contains_cpq @ ( triple @ SV36 @ SV68 @ SV103 ) @ SV111 )
| ( contains_slb @ SV68 @ SV111 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(385,plain,
! [SV104: $i,SV36: $i,SV112: $i,SV68: $i] :
( ( ~ ( contains_slb @ SV68 @ SV112 )
| ( contains_cpq @ ( triple @ SV36 @ SV68 @ SV104 ) @ SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(386,plain,
! [SV105: $i,SV69: $i,SV37: $i] :
( ( ( ! [SY335: $i] :
~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY335 ) ) @ SV105 ) )
= $true )
| ( ( ( SV69 = SV105 )
| ( contains_slb @ SV37 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(387,plain,
! [SV37: $i,SV69: $i] :
( ( ~ ! [SY290: $i] :
( ( SV69 != SY290 )
| ! [SY291: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY291 ) ) @ SY290 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[363]) ).
thf(388,plain,
! [SV69: $i,SV37: $i] :
( ( ~ ! [SY292: $i] :
( ~ ( contains_slb @ SV37 @ SY292 )
| ! [SY293: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY293 ) ) @ SY292 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[363]) ).
thf(389,plain,
! [SV86: $i,SV70: $i,SV38: $i] :
( ( ~ ! [SY318: $i,SY319: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY318 ) ) @ SV86 @ SY319 )
| ( SV70 = SV86 )
| ( pair_in_list @ SV38 @ SV86 @ SY319 ) )
| ~ ! [SY320: $i,SY321: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY320 ) ) @ SV86 @ SY321 )
| ( SY320 = SY321 )
| ( pair_in_list @ SV38 @ SV86 @ SY321 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(390,plain,
! [SV38: $i,SV86: $i,SV70: $i] :
( ( ~ ! [SY322: $i,SY323: $i] :
( ( SV70 != SV86 )
| ( SY322 != SY323 )
| ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY322 ) ) @ SV86 @ SY323 ) )
| ~ ! [SY324: $i,SY325: $i] :
( ~ ( pair_in_list @ SV38 @ SV86 @ SY325 )
| ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY324 ) ) @ SV86 @ SY325 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(391,plain,
( ( less_than @ sK7_SY152 @ sK6_SY150 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(392,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV113: $i] :
( ( ! [SY338: $i] :
( ~ ( less_than @ SY338 @ SV113 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV113 @ SY338 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(393,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV114: $i] :
( ( ! [SY339: $i] :
( ~ ( less_than @ SY339 @ SV114 )
| ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV114 @ SY339 ) ) @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(394,plain,
( ( sK14_REN = $true )
| ( ( ! [SX0: $i,SX1: $i] : ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(395,plain,
( ( ( ~ sK14_REN )
= $true )
| ( ( ~ ( ~ ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
| ~ ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(396,plain,
! [SV106: $i,SV102: $i] :
( ( ( check_cpq @ ( triple @ SV102 @ sK1_U @ SV106 ) )
= $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ sK1_U @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(397,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)],[376]) ).
thf(398,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)],[377]) ).
thf(399,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)],[378]) ).
thf(400,plain,
! [SV115: $i,SV64: $i,SV30: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SV115 ) )
= ( 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)],[379]) ).
thf(401,plain,
! [SV116: $i,SV65: $i,SV31: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SV116 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SV116 ) )
= $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)],[380]) ).
thf(402,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)],[381]) ).
thf(403,plain,
! [SV117: $i,SV109: $i] :
( ( ~ ( strictly_less_than @ SV109 @ SV117 )
| ( less_than @ SV109 @ SV117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(404,plain,
! [SV118: $i,SV110: $i] :
( ( ~ ( strictly_less_than @ SV110 @ SV118 )
| ~ ( less_than @ SV118 @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(405,plain,
! [SV111: $i,SV103: $i,SV68: $i,SV36: $i] :
( ( ( ~ ( contains_cpq @ ( triple @ SV36 @ SV68 @ SV103 ) @ SV111 ) )
= $true )
| ( ( contains_slb @ SV68 @ SV111 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(406,plain,
! [SV104: $i,SV36: $i,SV112: $i,SV68: $i] :
( ( ( ~ ( contains_slb @ SV68 @ SV112 ) )
= $true )
| ( ( contains_cpq @ ( triple @ SV36 @ SV68 @ SV104 ) @ SV112 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(407,plain,
! [SV105: $i,SV119: $i,SV69: $i,SV37: $i] :
( ( ( ~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SV119 ) ) @ SV105 ) )
= $true )
| ( ( ( SV69 = SV105 )
| ( contains_slb @ SV37 @ SV105 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(408,plain,
! [SV37: $i,SV69: $i] :
( ( ! [SY290: $i] :
( ( SV69 != SY290 )
| ! [SY291: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY291 ) ) @ SY290 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[387]) ).
thf(409,plain,
! [SV69: $i,SV37: $i] :
( ( ! [SY292: $i] :
( ~ ( contains_slb @ SV37 @ SY292 )
| ! [SY293: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY293 ) ) @ SY292 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(410,plain,
! [SV86: $i,SV70: $i,SV38: $i] :
( ( ~ ! [SY318: $i,SY319: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY318 ) ) @ SV86 @ SY319 )
| ( SV70 = SV86 )
| ( pair_in_list @ SV38 @ SV86 @ SY319 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(411,plain,
! [SV86: $i,SV70: $i,SV38: $i] :
( ( ~ ! [SY320: $i,SY321: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY320 ) ) @ SV86 @ SY321 )
| ( SY320 = SY321 )
| ( pair_in_list @ SV38 @ SV86 @ SY321 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(412,plain,
! [SV38: $i,SV86: $i,SV70: $i] :
( ( ~ ! [SY322: $i,SY323: $i] :
( ( SV70 != SV86 )
| ( SY322 != SY323 )
| ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY322 ) ) @ SV86 @ SY323 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[390]) ).
thf(413,plain,
! [SV70: $i,SV86: $i,SV38: $i] :
( ( ~ ! [SY324: $i,SY325: $i] :
( ~ ( pair_in_list @ SV38 @ SV86 @ SY325 )
| ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY324 ) ) @ SV86 @ SY325 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[390]) ).
thf(414,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV113: $i,SV120: $i] :
( ( ~ ( less_than @ SV120 @ SV113 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV113 @ SV120 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(415,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV114: $i,SV121: $i] :
( ( ~ ( less_than @ SV121 @ SV114 )
| ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV114 @ SV121 ) ) @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(416,plain,
! [SV122: $i] :
( ( ( ! [SY340: $i] : ( check_cpq @ ( triple @ SV122 @ sK1_U @ SY340 ) ) )
= $true )
| ( sK14_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(417,plain,
( ( sK14_REN = $false )
| ( ( ~ ( ~ ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
| ~ ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(418,plain,
! [SV106: $i,SV102: $i,SV123: $i] :
( ( ( ! [SY341: $i] :
( ~ ( pair_in_list @ sK1_U @ SV123 @ SY341 )
| ( less_than @ SY341 @ SV123 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV102 @ sK1_U @ SV106 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(419,plain,
! [SV117: $i,SV109: $i] :
( ( ( ~ ( strictly_less_than @ SV109 @ SV117 ) )
= $true )
| ( ( less_than @ SV109 @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(420,plain,
! [SV118: $i,SV110: $i] :
( ( ( ~ ( strictly_less_than @ SV110 @ SV118 ) )
= $true )
| ( ( ~ ( less_than @ SV118 @ SV110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(421,plain,
! [SV111: $i,SV103: $i,SV68: $i,SV36: $i] :
( ( ( contains_cpq @ ( triple @ SV36 @ SV68 @ SV103 ) @ SV111 )
= $false )
| ( ( contains_slb @ SV68 @ SV111 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(422,plain,
! [SV104: $i,SV36: $i,SV112: $i,SV68: $i] :
( ( ( contains_slb @ SV68 @ SV112 )
= $false )
| ( ( contains_cpq @ ( triple @ SV36 @ SV68 @ SV104 ) @ SV112 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(423,plain,
! [SV105: $i,SV119: $i,SV69: $i,SV37: $i] :
( ( ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SV119 ) ) @ SV105 )
= $false )
| ( ( ( SV69 = SV105 )
| ( contains_slb @ SV37 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(424,plain,
! [SV37: $i,SV124: $i,SV69: $i] :
( ( ( SV69 != SV124 )
| ! [SY342: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY342 ) ) @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(425,plain,
! [SV69: $i,SV125: $i,SV37: $i] :
( ( ~ ( contains_slb @ SV37 @ SV125 )
| ! [SY343: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY343 ) ) @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(426,plain,
! [SV86: $i,SV70: $i,SV38: $i] :
( ( ! [SY318: $i,SY319: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY318 ) ) @ SV86 @ SY319 )
| ( SV70 = SV86 )
| ( pair_in_list @ SV38 @ SV86 @ SY319 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[410]) ).
thf(427,plain,
! [SV86: $i,SV70: $i,SV38: $i] :
( ( ! [SY320: $i,SY321: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY320 ) ) @ SV86 @ SY321 )
| ( SY320 = SY321 )
| ( pair_in_list @ SV38 @ SV86 @ SY321 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[411]) ).
thf(428,plain,
! [SV38: $i,SV86: $i,SV70: $i] :
( ( ! [SY322: $i,SY323: $i] :
( ( SV70 != SV86 )
| ( SY322 != SY323 )
| ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY322 ) ) @ SV86 @ SY323 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[412]) ).
thf(429,plain,
! [SV70: $i,SV86: $i,SV38: $i] :
( ( ! [SY324: $i,SY325: $i] :
( ~ ( pair_in_list @ SV38 @ SV86 @ SY325 )
| ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY324 ) ) @ SV86 @ SY325 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[413]) ).
thf(430,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV113: $i,SV120: $i] :
( ( ( ~ ( less_than @ SV120 @ SV113 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV113 @ SV120 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(431,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV114: $i,SV121: $i] :
( ( ( ~ ( less_than @ SV121 @ SV114 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV114 @ SV121 ) ) @ SV87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(432,plain,
! [SV126: $i,SV122: $i] :
( ( ( check_cpq @ ( triple @ SV122 @ sK1_U @ SV126 ) )
= $true )
| ( sK14_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(433,plain,
( ( ( ~ ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
| ~ ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) )
= $false )
| ( sK14_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(434,plain,
! [SV106: $i,SV102: $i,SV127: $i,SV123: $i] :
( ( ( ~ ( pair_in_list @ sK1_U @ SV123 @ SV127 )
| ( less_than @ SV127 @ SV123 ) )
= $true )
| ( ( check_cpq @ ( triple @ SV102 @ sK1_U @ SV106 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(435,plain,
! [SV117: $i,SV109: $i] :
( ( ( strictly_less_than @ SV109 @ SV117 )
= $false )
| ( ( less_than @ SV109 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(436,plain,
! [SV118: $i,SV110: $i] :
( ( ( strictly_less_than @ SV110 @ SV118 )
= $false )
| ( ( ~ ( less_than @ SV118 @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(437,plain,
! [SV119: $i,SV37: $i,SV105: $i,SV69: $i] :
( ( ( SV69 = SV105 )
= $true )
| ( ( contains_slb @ SV37 @ SV105 )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SV119 ) ) @ SV105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(438,plain,
! [SV37: $i,SV124: $i,SV69: $i] :
( ( ( ( SV69 != SV124 ) )
= $true )
| ( ( ! [SY342: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY342 ) ) @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(439,plain,
! [SV69: $i,SV125: $i,SV37: $i] :
( ( ( ~ ( contains_slb @ SV37 @ SV125 ) )
= $true )
| ( ( ! [SY343: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY343 ) ) @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[425]) ).
thf(440,plain,
! [SV86: $i,SV128: $i,SV70: $i,SV38: $i] :
( ( ! [SY344: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV128 ) ) @ SV86 @ SY344 )
| ( SV70 = SV86 )
| ( pair_in_list @ SV38 @ SV86 @ SY344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(441,plain,
! [SV86: $i,SV129: $i,SV70: $i,SV38: $i] :
( ( ! [SY345: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV129 ) ) @ SV86 @ SY345 )
| ( SV129 = SY345 )
| ( pair_in_list @ SV38 @ SV86 @ SY345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(442,plain,
! [SV38: $i,SV130: $i,SV86: $i,SV70: $i] :
( ( ! [SY346: $i] :
( ( SV70 != SV86 )
| ( SV130 != SY346 )
| ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV130 ) ) @ SV86 @ SY346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(443,plain,
! [SV131: $i,SV70: $i,SV86: $i,SV38: $i] :
( ( ! [SY347: $i] :
( ~ ( pair_in_list @ SV38 @ SV86 @ SY347 )
| ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV131 ) ) @ SV86 @ SY347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(444,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV113: $i,SV120: $i] :
( ( ( less_than @ SV120 @ SV113 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV113 @ SV120 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(445,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV114: $i,SV121: $i] :
( ( ( less_than @ SV121 @ SV114 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV114 @ SV121 ) ) @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(446,plain,
( ( ( ~ ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 ) )
= $false )
| ( sK14_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(447,plain,
( ( ( ~ ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) )
= $false )
| ( sK14_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(448,plain,
! [SV106: $i,SV102: $i,SV127: $i,SV123: $i] :
( ( ( ~ ( pair_in_list @ sK1_U @ SV123 @ SV127 ) )
= $true )
| ( ( less_than @ SV127 @ SV123 )
= $true )
| ( ( check_cpq @ ( triple @ SV102 @ sK1_U @ SV106 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(449,plain,
! [SV110: $i,SV118: $i] :
( ( ( less_than @ SV118 @ SV110 )
= $false )
| ( ( strictly_less_than @ SV110 @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(450,plain,
! [SV37: $i,SV124: $i,SV69: $i] :
( ( ( SV69 = SV124 )
= $false )
| ( ( ! [SY342: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY342 ) ) @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(451,plain,
! [SV69: $i,SV125: $i,SV37: $i] :
( ( ( contains_slb @ SV37 @ SV125 )
= $false )
| ( ( ! [SY343: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SY343 ) ) @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(452,plain,
! [SV132: $i,SV86: $i,SV128: $i,SV70: $i,SV38: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV128 ) ) @ SV86 @ SV132 )
| ( SV70 = SV86 )
| ( pair_in_list @ SV38 @ SV86 @ SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(453,plain,
! [SV133: $i,SV86: $i,SV129: $i,SV70: $i,SV38: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV129 ) ) @ SV86 @ SV133 )
| ( SV129 = SV133 )
| ( pair_in_list @ SV38 @ SV86 @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(454,plain,
! [SV38: $i,SV134: $i,SV130: $i,SV86: $i,SV70: $i] :
( ( ( SV70 != SV86 )
| ( SV130 != SV134 )
| ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV130 ) ) @ SV86 @ SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(455,plain,
! [SV131: $i,SV70: $i,SV135: $i,SV86: $i,SV38: $i] :
( ( ~ ( pair_in_list @ SV38 @ SV86 @ SV135 )
| ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV131 ) ) @ SV86 @ SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(456,plain,
! [SV87: $i,SV120: $i,SV113: $i,SV71: $i,SV39: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV113 @ SV120 ) ) @ SV87 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
= $true )
| ( ( less_than @ SV120 @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(457,plain,
! [SV121: $i,SV114: $i,SV87: $i,SV71: $i,SV39: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV114 @ SV121 ) ) @ SV87 ) )
= $true )
| ( ( less_than @ SV121 @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(458,plain,
( ( ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
= $true )
| ( sK14_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(459,plain,
( ( ( ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) )
= $true )
| ( sK14_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(460,plain,
! [SV106: $i,SV102: $i,SV127: $i,SV123: $i] :
( ( ( pair_in_list @ sK1_U @ SV123 @ SV127 )
= $false )
| ( ( less_than @ SV127 @ SV123 )
= $true )
| ( ( check_cpq @ ( triple @ SV102 @ sK1_U @ SV106 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(461,plain,
! [SV124: $i,SV136: $i,SV69: $i,SV37: $i] :
( ( ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SV136 ) ) @ SV124 )
= $true )
| ( ( SV69 = SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(462,plain,
! [SV125: $i,SV137: $i,SV69: $i,SV37: $i] :
( ( ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV69 @ SV137 ) ) @ SV125 )
= $true )
| ( ( contains_slb @ SV37 @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(463,plain,
! [SV132: $i,SV86: $i,SV128: $i,SV70: $i,SV38: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV128 ) ) @ SV86 @ SV132 ) )
= $true )
| ( ( ( SV70 = SV86 )
| ( pair_in_list @ SV38 @ SV86 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[452]) ).
thf(464,plain,
! [SV133: $i,SV86: $i,SV129: $i,SV70: $i,SV38: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV129 ) ) @ SV86 @ SV133 ) )
= $true )
| ( ( ( SV129 = SV133 )
| ( pair_in_list @ SV38 @ SV86 @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[453]) ).
thf(465,plain,
! [SV38: $i,SV134: $i,SV130: $i,SV86: $i,SV70: $i] :
( ( ( ( SV70 != SV86 )
| ( SV130 != SV134 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV130 ) ) @ SV86 @ SV134 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(466,plain,
! [SV131: $i,SV70: $i,SV135: $i,SV86: $i,SV38: $i] :
( ( ( ~ ( pair_in_list @ SV38 @ SV86 @ SV135 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV131 ) ) @ SV86 @ SV135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(467,plain,
! [SV87: $i,SV120: $i,SV113: $i,SV71: $i,SV39: $i] :
( ( ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV113 @ SV120 ) ) @ SV87 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
= $true )
| ( ( less_than @ SV120 @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(468,plain,
! [SV121: $i,SV114: $i,SV87: $i,SV71: $i,SV39: $i] :
( ( ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV114 @ SV121 ) ) @ SV87 ) )
= $true )
| ( ( less_than @ SV121 @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(469,plain,
( ( ( less_than @ sK13_SY167 @ sK12_SY130 )
= $false )
| ( sK14_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(470,plain,
! [SV132: $i,SV86: $i,SV128: $i,SV70: $i,SV38: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV128 ) ) @ SV86 @ SV132 )
= $false )
| ( ( ( SV70 = SV86 )
| ( pair_in_list @ SV38 @ SV86 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(471,plain,
! [SV133: $i,SV86: $i,SV129: $i,SV70: $i,SV38: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV129 ) ) @ SV86 @ SV133 )
= $false )
| ( ( ( SV129 = SV133 )
| ( pair_in_list @ SV38 @ SV86 @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(472,plain,
! [SV38: $i,SV134: $i,SV130: $i,SV86: $i,SV70: $i] :
( ( ( ( SV70 != SV86 ) )
= $true )
| ( ( ( SV130 != SV134 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV130 ) ) @ SV86 @ SV134 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(473,plain,
! [SV131: $i,SV70: $i,SV135: $i,SV86: $i,SV38: $i] :
( ( ( pair_in_list @ SV38 @ SV86 @ SV135 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV131 ) ) @ SV86 @ SV135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(474,plain,
! [SV128: $i,SV132: $i,SV38: $i,SV86: $i,SV70: $i] :
( ( ( SV70 = SV86 )
= $true )
| ( ( pair_in_list @ SV38 @ SV86 @ SV132 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV128 ) ) @ SV86 @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(475,plain,
! [SV70: $i,SV86: $i,SV38: $i,SV133: $i,SV129: $i] :
( ( ( SV129 = SV133 )
= $true )
| ( ( pair_in_list @ SV38 @ SV86 @ SV133 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV129 ) ) @ SV86 @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(476,plain,
! [SV38: $i,SV134: $i,SV130: $i,SV86: $i,SV70: $i] :
( ( ( SV70 = SV86 )
= $false )
| ( ( ( SV130 != SV134 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV130 ) ) @ SV86 @ SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(477,plain,
! [SV38: $i,SV86: $i,SV70: $i,SV134: $i,SV130: $i] :
( ( ( SV130 = SV134 )
= $false )
| ( ( SV70 = SV86 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV130 ) ) @ SV86 @ SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(478,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[172,477,475,474,473,469,468,467,462,461,460,458,449,437,435,432,422,421,402,401,400,399,398,397,391,375,374,373,366,351,350,328,325,323,322,305,298,297,295,294,282,267,258,256,255,254,253,240,236,228,216,205,204,185,182,174,173]) ).
thf(479,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( less_than @ U @ V )
| ~ ( less_than @ V @ W )
| ( less_than @ U @ W ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(480,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(481,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(482,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)],[118]) ).
thf(483,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(484,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(485,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(486,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(487,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)],[117]) ).
thf(488,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(489,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)],[116]) ).
thf(490,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(491,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)],[115]) ).
thf(492,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(493,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)],[114]) ).
thf(494,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(495,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)],[113]) ).
thf(496,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)],[112]) ).
thf(497,plain,
( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(498,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(499,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(500,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(501,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(502,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(503,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)],[107]) ).
thf(504,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)],[106]) ).
thf(505,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)],[105]) ).
thf(506,plain,
( ( ! [U: $i,V: $i] :
~ ( ok @ ( triple @ U @ V @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(507,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( triple @ U @ V @ W ) )
| ( W = bad ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(508,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(509,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)],[102]) ).
thf(510,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)],[101]) ).
thf(511,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)],[100]) ).
thf(512,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(513,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)],[99]) ).
thf(514,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)],[98]) ).
thf(515,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)],[97]) ).
thf(516,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(517,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)],[96]) ).
thf(518,plain,
( ( ! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(519,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(520,plain,
( ( ( sK14_REN
| ! [SY128: $i,SY129: $i] : ( check_cpq @ ( triple @ SY128 @ sK1_U @ SY129 ) ) )
& ( sK14_REN
=> ( ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
& ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) ) )
& ( ! [SY128: $i,SY129: $i] :
~ ( check_cpq @ ( triple @ SY128 @ sK1_U @ SY129 ) )
| ! [SY130: $i,SY131: $i] :
( ~ ( pair_in_list @ sK1_U @ SY130 @ SY131 )
| ( less_than @ SY131 @ SY130 ) ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(521,plain,
( ( ! [SY165: $i,SY166: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK10_SY158 @ sK11_SY162 ) ) @ SY165 @ SY166 )
| ( less_than @ SY166 @ SY165 ) )
& ~ ( check_cpq @ ( triple @ sK8_SY132 @ ( insert_slb @ sK1_U @ ( pair @ sK10_SY158 @ sK11_SY162 ) ) @ sK9_SY153 ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(522,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)],[489]) ).
thf(523,plain,
( ( ~ ( ~ ~ ( ~ ( sK14_REN
| ! [SX0: $i,SX1: $i] : ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) ) )
| ~ ( ~ sK14_REN
| ~ ( ~ ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
| ~ ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) ) ) )
| ~ ( ! [SX0: $i,SX1: $i] :
~ ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ sK1_U @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[520]) ).
thf(524,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)],[505]) ).
thf(525,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)],[503]) ).
thf(526,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)],[487]) ).
thf(527,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)],[482]) ).
thf(528,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK10_SY158 @ sK11_SY162 ) ) @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) )
| ~ ~ ( check_cpq @ ( triple @ sK8_SY132 @ ( insert_slb @ sK1_U @ ( pair @ sK10_SY158 @ sK11_SY162 ) ) @ sK9_SY153 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[521]) ).
thf(529,plain,
! [SV138: $i] :
( ( ! [SY348: $i,SY349: $i] :
( ~ ( less_than @ SV138 @ SY348 )
| ~ ( less_than @ SY348 @ SY349 )
| ( less_than @ SV138 @ SY349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(530,plain,
! [SV139: $i] :
( ( ! [SY350: $i] :
( ( less_than @ SV139 @ SY350 )
| ( less_than @ SY350 @ SV139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(531,plain,
! [SV140: $i] :
( ( less_than @ SV140 @ SV140 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(532,plain,
! [SV141: $i] :
( ( less_than @ bottom @ SV141 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(533,plain,
( ( isnonempty_slb @ create_slb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(534,plain,
! [SV142: $i] :
( ( ! [SY351: $i,SY352: $i] : ( isnonempty_slb @ ( insert_slb @ SV142 @ ( pair @ SY351 @ SY352 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(535,plain,
! [SV143: $i] :
( ( ~ ( contains_slb @ create_slb @ SV143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(536,plain,
! [SV144: $i] :
( ( ! [SY353: $i] :
~ ( pair_in_list @ create_slb @ SV144 @ SY353 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(537,plain,
! [SV145: $i] :
( ( ! [SY354: $i,SY355: $i] :
( ( remove_slb @ ( insert_slb @ SV145 @ ( pair @ SY354 @ SY355 ) ) @ SY354 )
= SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(538,plain,
! [SV146: $i] :
( ( ! [SY356: $i,SY357: $i] :
( ( SY356 = SY357 )
| ~ ( contains_slb @ SV146 @ SY357 )
| ! [SY358: $i] :
( ( remove_slb @ ( insert_slb @ SV146 @ ( pair @ SY356 @ SY358 ) ) @ SY357 )
= ( insert_slb @ ( remove_slb @ SV146 @ SY357 ) @ ( pair @ SY356 @ SY358 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(539,plain,
! [SV147: $i] :
( ( ! [SY359: $i,SY360: $i] :
( ( lookup_slb @ ( insert_slb @ SV147 @ ( pair @ SY359 @ SY360 ) ) @ SY359 )
= SY360 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(540,plain,
! [SV148: $i] :
( ( ! [SY361: $i,SY362: $i] :
( ( SY361 = SY362 )
| ~ ( contains_slb @ SV148 @ SY362 )
| ! [SY363: $i] :
( ( lookup_slb @ ( insert_slb @ SV148 @ ( pair @ SY361 @ SY363 ) ) @ SY362 )
= ( lookup_slb @ SV148 @ SY362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(541,plain,
! [SV149: $i] :
( ( ( update_slb @ create_slb @ SV149 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(542,plain,
! [SV150: $i] :
( ( ! [SY364: $i,SY365: $i,SY366: $i] :
( ~ ( strictly_less_than @ SY366 @ SY365 )
| ( ( update_slb @ ( insert_slb @ SV150 @ ( pair @ SY364 @ SY366 ) ) @ SY365 )
= ( insert_slb @ ( update_slb @ SV150 @ SY365 ) @ ( pair @ SY364 @ SY365 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(543,plain,
! [SV151: $i] :
( ( ! [SY367: $i,SY368: $i,SY369: $i] :
( ~ ( less_than @ SY368 @ SY369 )
| ( ( update_slb @ ( insert_slb @ SV151 @ ( pair @ SY367 @ SY369 ) ) @ SY368 )
= ( insert_slb @ ( update_slb @ SV151 @ SY368 ) @ ( pair @ SY367 @ SY369 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(544,plain,
! [SV152: $i] :
( ( succ_cpq @ SV152 @ SV152 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(545,plain,
! [SV153: $i] :
( ( ! [SY370: $i] :
( ~ ( succ_cpq @ SV153 @ SY370 )
| ! [SY371: $i] : ( succ_cpq @ SV153 @ ( insert_cpq @ SY370 @ SY371 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(546,plain,
! [SV154: $i] :
( ( ! [SY372: $i] :
( ~ ( succ_cpq @ SV154 @ SY372 )
| ! [SY373: $i] : ( succ_cpq @ SV154 @ ( remove_cpq @ SY372 @ SY373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(547,plain,
! [SV155: $i] :
( ( ! [SY374: $i] :
( ~ ( succ_cpq @ SV155 @ SY374 )
| ( succ_cpq @ SV155 @ ( findmin_cpq_eff @ SY374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(548,plain,
! [SV156: $i] :
( ( ! [SY375: $i] :
( ~ ( succ_cpq @ SV156 @ SY375 )
| ( succ_cpq @ SV156 @ ( removemin_cpq_eff @ SY375 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(549,plain,
! [SV157: $i] :
( ( ! [SY376: $i] : ( check_cpq @ ( triple @ SV157 @ create_slb @ SY376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(550,plain,
! [SV158: $i] :
( ( ! [SY377: $i,SY378: $i,SY379: $i,SY380: $i] :
( ~ ( strictly_less_than @ SY379 @ SY380 )
| ~ ( check_cpq @ ( triple @ SV158 @ ( insert_slb @ SY377 @ ( pair @ SY379 @ SY380 ) ) @ SY378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(551,plain,
! [SV159: $i] :
( ( ! [SY381: $i] :
~ ( ok @ ( triple @ SV159 @ SY381 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(552,plain,
! [SV160: $i] :
( ( ! [SY382: $i,SY383: $i] :
( ( ok @ ( triple @ SV160 @ SY382 @ SY383 ) )
| ( SY383 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(553,plain,
! [SV161: $i] :
( ( ! [SY384: $i,SY385: $i,SY386: $i] :
( ( insert_cpq @ ( triple @ SV161 @ SY384 @ SY385 ) @ SY386 )
= ( triple @ ( insert_pqp @ SV161 @ SY386 ) @ ( insert_slb @ SY384 @ ( pair @ SY386 @ bottom ) ) @ SY385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(554,plain,
! [SV162: $i] :
( ( ! [SY387: $i,SY388: $i,SY389: $i] :
( ( contains_slb @ SY387 @ SY389 )
| ( ( remove_cpq @ ( triple @ SV162 @ SY387 @ SY388 ) @ SY389 )
= ( triple @ SV162 @ SY387 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(555,plain,
! [SV163: $i] :
( ( ! [SY390: $i,SY391: $i,SY392: $i] :
( ~ ( contains_slb @ SY390 @ SY392 )
| ~ ( less_than @ ( lookup_slb @ SY390 @ SY392 ) @ SY392 )
| ( ( remove_cpq @ ( triple @ SV163 @ SY390 @ SY391 ) @ SY392 )
= ( triple @ ( remove_pqp @ SV163 @ SY392 ) @ ( remove_slb @ SY390 @ SY392 ) @ SY391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(556,plain,
! [SV164: $i] :
( ( ! [SY393: $i,SY394: $i,SY395: $i] :
( ~ ( contains_slb @ SY393 @ SY395 )
| ~ ( strictly_less_than @ SY395 @ ( lookup_slb @ SY393 @ SY395 ) )
| ( ( remove_cpq @ ( triple @ SV164 @ SY393 @ SY394 ) @ SY395 )
= ( triple @ ( remove_pqp @ SV164 @ SY395 ) @ ( remove_slb @ SY393 @ SY395 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(557,plain,
! [SV165: $i] :
( ( ! [SY396: $i] :
( ( findmin_cpq_eff @ ( triple @ SV165 @ create_slb @ SY396 ) )
= ( triple @ SV165 @ create_slb @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(558,plain,
! [SV166: $i] :
( ( ! [SY397: $i] :
( ( SY397 = create_slb )
| ( contains_slb @ SY397 @ ( findmin_pqp_res @ SV166 ) )
| ! [SY398: $i] :
( ( findmin_cpq_eff @ ( triple @ SV166 @ SY397 @ SY398 ) )
= ( triple @ SV166 @ ( update_slb @ SY397 @ ( findmin_pqp_res @ SV166 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(559,plain,
! [SV167: $i] :
( ( ! [SY399: $i] :
( ( SY399 = create_slb )
| ~ ( contains_slb @ SY399 @ ( findmin_pqp_res @ SV167 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV167 ) @ ( lookup_slb @ SY399 @ ( findmin_pqp_res @ SV167 ) ) )
| ! [SY400: $i] :
( ( findmin_cpq_eff @ ( triple @ SV167 @ SY399 @ SY400 ) )
= ( triple @ SV167 @ ( update_slb @ SY399 @ ( findmin_pqp_res @ SV167 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(560,plain,
! [SV168: $i] :
( ( ! [SY401: $i] :
( ( SY401 = create_slb )
| ~ ( contains_slb @ SY401 @ ( findmin_pqp_res @ SV168 ) )
| ~ ( less_than @ ( lookup_slb @ SY401 @ ( findmin_pqp_res @ SV168 ) ) @ ( findmin_pqp_res @ SV168 ) )
| ! [SY402: $i] :
( ( findmin_cpq_eff @ ( triple @ SV168 @ SY401 @ SY402 ) )
= ( triple @ SV168 @ ( update_slb @ SY401 @ ( findmin_pqp_res @ SV168 ) ) @ SY402 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(561,plain,
! [SV169: $i] :
( ( ! [SY403: $i] :
( ( findmin_cpq_res @ ( triple @ SV169 @ create_slb @ SY403 ) )
= bottom ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(562,plain,
! [SV170: $i] :
( ( ! [SY404: $i] :
( ( SY404 = create_slb )
| ! [SY405: $i] :
( ( findmin_cpq_res @ ( triple @ SV170 @ SY404 @ SY405 ) )
= ( findmin_pqp_res @ SV170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(563,plain,
! [SV171: $i] :
( ( ( removemin_cpq_eff @ SV171 )
= ( remove_cpq @ ( findmin_cpq_eff @ SV171 ) @ ( findmin_cpq_res @ SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(564,plain,
! [SV172: $i] :
( ( ( removemin_cpq_res @ SV172 )
= ( findmin_cpq_res @ SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(565,plain,
! [SV173: $i] :
( ( ! [SY406: $i,SY407: $i] :
~ ( ~ ~ ( ~ ! [SY408: $i,SY409: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SY406 @ SY408 ) ) @ SY407 @ SY409 )
| ( SY406 = SY407 )
| ( pair_in_list @ SV173 @ SY407 @ SY409 ) )
| ~ ! [SY410: $i,SY411: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SY406 @ SY410 ) ) @ SY407 @ SY411 )
| ( SY410 = SY411 )
| ( pair_in_list @ SV173 @ SY407 @ SY411 ) ) )
| ~ ~ ( ~ ! [SY412: $i,SY413: $i] :
( ( SY406 != SY407 )
| ( SY412 != SY413 )
| ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SY406 @ SY412 ) ) @ SY407 @ SY413 ) )
| ~ ! [SY414: $i,SY415: $i] :
( ~ ( pair_in_list @ SV173 @ SY407 @ SY415 )
| ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SY406 @ SY414 ) ) @ SY407 @ SY415 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(566,plain,
( ( ~ ~ ( ~ ( sK14_REN
| ! [SX0: $i,SX1: $i] : ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) ) )
| ~ ( ~ sK14_REN
| ~ ( ~ ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
| ~ ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) ) ) )
| ~ ( ! [SX0: $i,SX1: $i] :
~ ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ sK1_U @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(567,plain,
! [SV174: $i] :
( ( ! [SY416: $i] :
~ ( ~ ! [SY417: $i,SY418: $i] :
( ~ ( contains_cpq @ ( triple @ SV174 @ SY416 @ SY417 ) @ SY418 )
| ( contains_slb @ SY416 @ SY418 ) )
| ~ ! [SY419: $i,SY420: $i] :
( ~ ( contains_slb @ SY416 @ SY420 )
| ( contains_cpq @ ( triple @ SV174 @ SY416 @ SY419 ) @ SY420 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(568,plain,
! [SV175: $i] :
( ( ! [SY421: $i,SY422: $i] :
~ ( ~ ! [SY423: $i,SY424: $i] :
( ~ ( less_than @ SY424 @ SY423 )
| ~ ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SY421 @ ( pair @ SY423 @ SY424 ) ) @ SY422 ) )
| ( check_cpq @ ( triple @ SV175 @ SY421 @ SY422 ) ) )
| ~ ! [SY425: $i,SY426: $i] :
( ~ ( less_than @ SY426 @ SY425 )
| ~ ( check_cpq @ ( triple @ SV175 @ SY421 @ SY422 ) )
| ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SY421 @ ( pair @ SY425 @ SY426 ) ) @ SY422 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(569,plain,
! [SV176: $i] :
( ( ! [SY427: $i] :
~ ( ~ ! [SY428: $i] :
( ! [SY429: $i] :
~ ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SY427 @ SY429 ) ) @ SY428 )
| ( SY427 = SY428 )
| ( contains_slb @ SV176 @ SY428 ) )
| ~ ~ ( ~ ! [SY430: $i] :
( ( SY427 != SY430 )
| ! [SY431: $i] : ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SY427 @ SY431 ) ) @ SY430 ) )
| ~ ! [SY432: $i] :
( ~ ( contains_slb @ SV176 @ SY432 )
| ! [SY433: $i] : ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SY427 @ SY433 ) ) @ SY432 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(570,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)],[527]) ).
thf(571,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK10_SY158 @ sK11_SY162 ) ) @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) )
| ~ ~ ( check_cpq @ ( triple @ sK8_SY132 @ ( insert_slb @ sK1_U @ ( pair @ sK10_SY158 @ sK11_SY162 ) ) @ sK9_SY153 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(572,plain,
! [SV177: $i,SV138: $i] :
( ( ! [SY434: $i] :
( ~ ( less_than @ SV138 @ SV177 )
| ~ ( less_than @ SV177 @ SY434 )
| ( less_than @ SV138 @ SY434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(573,plain,
! [SV178: $i,SV139: $i] :
( ( ( less_than @ SV139 @ SV178 )
| ( less_than @ SV178 @ SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(574,plain,
! [SV179: $i,SV142: $i] :
( ( ! [SY435: $i] : ( isnonempty_slb @ ( insert_slb @ SV142 @ ( pair @ SV179 @ SY435 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(575,plain,
! [SV143: $i] :
( ( contains_slb @ create_slb @ SV143 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(576,plain,
! [SV180: $i,SV144: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV144 @ SV180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(577,plain,
! [SV181: $i,SV145: $i] :
( ( ! [SY436: $i] :
( ( remove_slb @ ( insert_slb @ SV145 @ ( pair @ SV181 @ SY436 ) ) @ SV181 )
= SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(578,plain,
! [SV146: $i,SV182: $i] :
( ( ! [SY437: $i] :
( ( SV182 = SY437 )
| ~ ( contains_slb @ SV146 @ SY437 )
| ! [SY438: $i] :
( ( remove_slb @ ( insert_slb @ SV146 @ ( pair @ SV182 @ SY438 ) ) @ SY437 )
= ( insert_slb @ ( remove_slb @ SV146 @ SY437 ) @ ( pair @ SV182 @ SY438 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(579,plain,
! [SV183: $i,SV147: $i] :
( ( ! [SY439: $i] :
( ( lookup_slb @ ( insert_slb @ SV147 @ ( pair @ SV183 @ SY439 ) ) @ SV183 )
= SY439 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(580,plain,
! [SV148: $i,SV184: $i] :
( ( ! [SY440: $i] :
( ( SV184 = SY440 )
| ~ ( contains_slb @ SV148 @ SY440 )
| ! [SY441: $i] :
( ( lookup_slb @ ( insert_slb @ SV148 @ ( pair @ SV184 @ SY441 ) ) @ SY440 )
= ( lookup_slb @ SV148 @ SY440 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(581,plain,
! [SV185: $i,SV150: $i] :
( ( ! [SY442: $i,SY443: $i] :
( ~ ( strictly_less_than @ SY443 @ SY442 )
| ( ( update_slb @ ( insert_slb @ SV150 @ ( pair @ SV185 @ SY443 ) ) @ SY442 )
= ( insert_slb @ ( update_slb @ SV150 @ SY442 ) @ ( pair @ SV185 @ SY442 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(582,plain,
! [SV186: $i,SV151: $i] :
( ( ! [SY444: $i,SY445: $i] :
( ~ ( less_than @ SY444 @ SY445 )
| ( ( update_slb @ ( insert_slb @ SV151 @ ( pair @ SV186 @ SY445 ) ) @ SY444 )
= ( insert_slb @ ( update_slb @ SV151 @ SY444 ) @ ( pair @ SV186 @ SY445 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(583,plain,
! [SV187: $i,SV153: $i] :
( ( ~ ( succ_cpq @ SV153 @ SV187 )
| ! [SY446: $i] : ( succ_cpq @ SV153 @ ( insert_cpq @ SV187 @ SY446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(584,plain,
! [SV188: $i,SV154: $i] :
( ( ~ ( succ_cpq @ SV154 @ SV188 )
| ! [SY447: $i] : ( succ_cpq @ SV154 @ ( remove_cpq @ SV188 @ SY447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(585,plain,
! [SV189: $i,SV155: $i] :
( ( ~ ( succ_cpq @ SV155 @ SV189 )
| ( succ_cpq @ SV155 @ ( findmin_cpq_eff @ SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(586,plain,
! [SV190: $i,SV156: $i] :
( ( ~ ( succ_cpq @ SV156 @ SV190 )
| ( succ_cpq @ SV156 @ ( removemin_cpq_eff @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(587,plain,
! [SV191: $i,SV157: $i] :
( ( check_cpq @ ( triple @ SV157 @ create_slb @ SV191 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(588,plain,
! [SV192: $i,SV158: $i] :
( ( ! [SY448: $i,SY449: $i,SY450: $i] :
( ~ ( strictly_less_than @ SY449 @ SY450 )
| ~ ( check_cpq @ ( triple @ SV158 @ ( insert_slb @ SV192 @ ( pair @ SY449 @ SY450 ) ) @ SY448 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(589,plain,
! [SV193: $i,SV159: $i] :
( ( ~ ( ok @ ( triple @ SV159 @ SV193 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(590,plain,
! [SV194: $i,SV160: $i] :
( ( ! [SY451: $i] :
( ( ok @ ( triple @ SV160 @ SV194 @ SY451 ) )
| ( SY451 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(591,plain,
! [SV195: $i,SV161: $i] :
( ( ! [SY452: $i,SY453: $i] :
( ( insert_cpq @ ( triple @ SV161 @ SV195 @ SY452 ) @ SY453 )
= ( triple @ ( insert_pqp @ SV161 @ SY453 ) @ ( insert_slb @ SV195 @ ( pair @ SY453 @ bottom ) ) @ SY452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(592,plain,
! [SV162: $i,SV196: $i] :
( ( ! [SY454: $i,SY455: $i] :
( ( contains_slb @ SV196 @ SY455 )
| ( ( remove_cpq @ ( triple @ SV162 @ SV196 @ SY454 ) @ SY455 )
= ( triple @ SV162 @ SV196 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(593,plain,
! [SV163: $i,SV197: $i] :
( ( ! [SY456: $i,SY457: $i] :
( ~ ( contains_slb @ SV197 @ SY457 )
| ~ ( less_than @ ( lookup_slb @ SV197 @ SY457 ) @ SY457 )
| ( ( remove_cpq @ ( triple @ SV163 @ SV197 @ SY456 ) @ SY457 )
= ( triple @ ( remove_pqp @ SV163 @ SY457 ) @ ( remove_slb @ SV197 @ SY457 ) @ SY456 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(594,plain,
! [SV164: $i,SV198: $i] :
( ( ! [SY458: $i,SY459: $i] :
( ~ ( contains_slb @ SV198 @ SY459 )
| ~ ( strictly_less_than @ SY459 @ ( lookup_slb @ SV198 @ SY459 ) )
| ( ( remove_cpq @ ( triple @ SV164 @ SV198 @ SY458 ) @ SY459 )
= ( triple @ ( remove_pqp @ SV164 @ SY459 ) @ ( remove_slb @ SV198 @ SY459 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(595,plain,
! [SV199: $i,SV165: $i] :
( ( ( findmin_cpq_eff @ ( triple @ SV165 @ create_slb @ SV199 ) )
= ( triple @ SV165 @ create_slb @ bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(596,plain,
! [SV166: $i,SV200: $i] :
( ( ( SV200 = create_slb )
| ( contains_slb @ SV200 @ ( findmin_pqp_res @ SV166 ) )
| ! [SY460: $i] :
( ( findmin_cpq_eff @ ( triple @ SV166 @ SV200 @ SY460 ) )
= ( triple @ SV166 @ ( update_slb @ SV200 @ ( findmin_pqp_res @ SV166 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(597,plain,
! [SV167: $i,SV201: $i] :
( ( ( SV201 = create_slb )
| ~ ( contains_slb @ SV201 @ ( findmin_pqp_res @ SV167 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV167 ) @ ( lookup_slb @ SV201 @ ( findmin_pqp_res @ SV167 ) ) )
| ! [SY461: $i] :
( ( findmin_cpq_eff @ ( triple @ SV167 @ SV201 @ SY461 ) )
= ( triple @ SV167 @ ( update_slb @ SV201 @ ( findmin_pqp_res @ SV167 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(598,plain,
! [SV168: $i,SV202: $i] :
( ( ( SV202 = create_slb )
| ~ ( contains_slb @ SV202 @ ( findmin_pqp_res @ SV168 ) )
| ~ ( less_than @ ( lookup_slb @ SV202 @ ( findmin_pqp_res @ SV168 ) ) @ ( findmin_pqp_res @ SV168 ) )
| ! [SY462: $i] :
( ( findmin_cpq_eff @ ( triple @ SV168 @ SV202 @ SY462 ) )
= ( triple @ SV168 @ ( update_slb @ SV202 @ ( findmin_pqp_res @ SV168 ) ) @ SY462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(599,plain,
! [SV203: $i,SV169: $i] :
( ( ( findmin_cpq_res @ ( triple @ SV169 @ create_slb @ SV203 ) )
= bottom )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(600,plain,
! [SV170: $i,SV204: $i] :
( ( ( SV204 = create_slb )
| ! [SY463: $i] :
( ( findmin_cpq_res @ ( triple @ SV170 @ SV204 @ SY463 ) )
= ( findmin_pqp_res @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(601,plain,
! [SV205: $i,SV173: $i] :
( ( ! [SY464: $i] :
~ ( ~ ~ ( ~ ! [SY465: $i,SY466: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY465 ) ) @ SY464 @ SY466 )
| ( SV205 = SY464 )
| ( pair_in_list @ SV173 @ SY464 @ SY466 ) )
| ~ ! [SY467: $i,SY468: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY467 ) ) @ SY464 @ SY468 )
| ( SY467 = SY468 )
| ( pair_in_list @ SV173 @ SY464 @ SY468 ) ) )
| ~ ~ ( ~ ! [SY469: $i,SY470: $i] :
( ( SV205 != SY464 )
| ( SY469 != SY470 )
| ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY469 ) ) @ SY464 @ SY470 ) )
| ~ ! [SY471: $i,SY472: $i] :
( ~ ( pair_in_list @ SV173 @ SY464 @ SY472 )
| ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY471 ) ) @ SY464 @ SY472 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(602,plain,
( ( ~ ~ ( ~ ( sK14_REN
| ! [SX0: $i,SX1: $i] : ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) ) )
| ~ ( ~ sK14_REN
| ~ ( ~ ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
| ~ ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[566]) ).
thf(603,plain,
( ( ~ ( ! [SX0: $i,SX1: $i] :
~ ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ sK1_U @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[566]) ).
thf(604,plain,
! [SV206: $i,SV174: $i] :
( ( ~ ( ~ ! [SY473: $i,SY474: $i] :
( ~ ( contains_cpq @ ( triple @ SV174 @ SV206 @ SY473 ) @ SY474 )
| ( contains_slb @ SV206 @ SY474 ) )
| ~ ! [SY475: $i,SY476: $i] :
( ~ ( contains_slb @ SV206 @ SY476 )
| ( contains_cpq @ ( triple @ SV174 @ SV206 @ SY475 ) @ SY476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(605,plain,
! [SV207: $i,SV175: $i] :
( ( ! [SY477: $i] :
~ ( ~ ! [SY478: $i,SY479: $i] :
( ~ ( less_than @ SY479 @ SY478 )
| ~ ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SV207 @ ( pair @ SY478 @ SY479 ) ) @ SY477 ) )
| ( check_cpq @ ( triple @ SV175 @ SV207 @ SY477 ) ) )
| ~ ! [SY480: $i,SY481: $i] :
( ~ ( less_than @ SY481 @ SY480 )
| ~ ( check_cpq @ ( triple @ SV175 @ SV207 @ SY477 ) )
| ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SV207 @ ( pair @ SY480 @ SY481 ) ) @ SY477 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(606,plain,
! [SV208: $i,SV176: $i] :
( ( ~ ( ~ ! [SY482: $i] :
( ! [SY483: $i] :
~ ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY483 ) ) @ SY482 )
| ( SV208 = SY482 )
| ( contains_slb @ SV176 @ SY482 ) )
| ~ ~ ( ~ ! [SY484: $i] :
( ( SV208 != SY484 )
| ! [SY485: $i] : ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY485 ) ) @ SY484 ) )
| ~ ! [SY486: $i] :
( ~ ( contains_slb @ SV176 @ SY486 )
| ! [SY487: $i] : ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY487 ) ) @ SY486 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(607,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)],[570]) ).
thf(608,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)],[570]) ).
thf(609,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK10_SY158 @ sK11_SY162 ) ) @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[571]) ).
thf(610,plain,
( ( ~ ~ ( check_cpq @ ( triple @ sK8_SY132 @ ( insert_slb @ sK1_U @ ( pair @ sK10_SY158 @ sK11_SY162 ) ) @ sK9_SY153 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[571]) ).
thf(611,plain,
! [SV209: $i,SV177: $i,SV138: $i] :
( ( ~ ( less_than @ SV138 @ SV177 )
| ~ ( less_than @ SV177 @ SV209 )
| ( less_than @ SV138 @ SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(612,plain,
! [SV178: $i,SV139: $i] :
( ( ( less_than @ SV139 @ SV178 )
= $true )
| ( ( less_than @ SV178 @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[573]) ).
thf(613,plain,
! [SV210: $i,SV179: $i,SV142: $i] :
( ( isnonempty_slb @ ( insert_slb @ SV142 @ ( pair @ SV179 @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(614,plain,
! [SV180: $i,SV144: $i] :
( ( pair_in_list @ create_slb @ SV144 @ SV180 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(615,plain,
! [SV211: $i,SV181: $i,SV145: $i] :
( ( ( remove_slb @ ( insert_slb @ SV145 @ ( pair @ SV181 @ SV211 ) ) @ SV181 )
= SV145 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(616,plain,
! [SV146: $i,SV212: $i,SV182: $i] :
( ( ( SV182 = SV212 )
| ~ ( contains_slb @ SV146 @ SV212 )
| ! [SY488: $i] :
( ( remove_slb @ ( insert_slb @ SV146 @ ( pair @ SV182 @ SY488 ) ) @ SV212 )
= ( insert_slb @ ( remove_slb @ SV146 @ SV212 ) @ ( pair @ SV182 @ SY488 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(617,plain,
! [SV213: $i,SV183: $i,SV147: $i] :
( ( ( lookup_slb @ ( insert_slb @ SV147 @ ( pair @ SV183 @ SV213 ) ) @ SV183 )
= SV213 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(618,plain,
! [SV148: $i,SV214: $i,SV184: $i] :
( ( ( SV184 = SV214 )
| ~ ( contains_slb @ SV148 @ SV214 )
| ! [SY489: $i] :
( ( lookup_slb @ ( insert_slb @ SV148 @ ( pair @ SV184 @ SY489 ) ) @ SV214 )
= ( lookup_slb @ SV148 @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(619,plain,
! [SV185: $i,SV150: $i,SV215: $i] :
( ( ! [SY490: $i] :
( ~ ( strictly_less_than @ SY490 @ SV215 )
| ( ( update_slb @ ( insert_slb @ SV150 @ ( pair @ SV185 @ SY490 ) ) @ SV215 )
= ( insert_slb @ ( update_slb @ SV150 @ SV215 ) @ ( pair @ SV185 @ SV215 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(620,plain,
! [SV186: $i,SV151: $i,SV216: $i] :
( ( ! [SY491: $i] :
( ~ ( less_than @ SV216 @ SY491 )
| ( ( update_slb @ ( insert_slb @ SV151 @ ( pair @ SV186 @ SY491 ) ) @ SV216 )
= ( insert_slb @ ( update_slb @ SV151 @ SV216 ) @ ( pair @ SV186 @ SY491 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(621,plain,
! [SV187: $i,SV153: $i] :
( ( ( ~ ( succ_cpq @ SV153 @ SV187 ) )
= $true )
| ( ( ! [SY446: $i] : ( succ_cpq @ SV153 @ ( insert_cpq @ SV187 @ SY446 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[583]) ).
thf(622,plain,
! [SV188: $i,SV154: $i] :
( ( ( ~ ( succ_cpq @ SV154 @ SV188 ) )
= $true )
| ( ( ! [SY447: $i] : ( succ_cpq @ SV154 @ ( remove_cpq @ SV188 @ SY447 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(623,plain,
! [SV189: $i,SV155: $i] :
( ( ( ~ ( succ_cpq @ SV155 @ SV189 ) )
= $true )
| ( ( succ_cpq @ SV155 @ ( findmin_cpq_eff @ SV189 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[585]) ).
thf(624,plain,
! [SV190: $i,SV156: $i] :
( ( ( ~ ( succ_cpq @ SV156 @ SV190 ) )
= $true )
| ( ( succ_cpq @ SV156 @ ( removemin_cpq_eff @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[586]) ).
thf(625,plain,
! [SV217: $i,SV192: $i,SV158: $i] :
( ( ! [SY492: $i,SY493: $i] :
( ~ ( strictly_less_than @ SY492 @ SY493 )
| ~ ( check_cpq @ ( triple @ SV158 @ ( insert_slb @ SV192 @ ( pair @ SY492 @ SY493 ) ) @ SV217 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(626,plain,
! [SV193: $i,SV159: $i] :
( ( ok @ ( triple @ SV159 @ SV193 @ bad ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(627,plain,
! [SV218: $i,SV194: $i,SV160: $i] :
( ( ( ok @ ( triple @ SV160 @ SV194 @ SV218 ) )
| ( SV218 = bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(628,plain,
! [SV219: $i,SV195: $i,SV161: $i] :
( ( ! [SY494: $i] :
( ( insert_cpq @ ( triple @ SV161 @ SV195 @ SV219 ) @ SY494 )
= ( triple @ ( insert_pqp @ SV161 @ SY494 ) @ ( insert_slb @ SV195 @ ( pair @ SY494 @ bottom ) ) @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(629,plain,
! [SV220: $i,SV162: $i,SV196: $i] :
( ( ! [SY495: $i] :
( ( contains_slb @ SV196 @ SY495 )
| ( ( remove_cpq @ ( triple @ SV162 @ SV196 @ SV220 ) @ SY495 )
= ( triple @ SV162 @ SV196 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(630,plain,
! [SV221: $i,SV163: $i,SV197: $i] :
( ( ! [SY496: $i] :
( ~ ( contains_slb @ SV197 @ SY496 )
| ~ ( less_than @ ( lookup_slb @ SV197 @ SY496 ) @ SY496 )
| ( ( remove_cpq @ ( triple @ SV163 @ SV197 @ SV221 ) @ SY496 )
= ( triple @ ( remove_pqp @ SV163 @ SY496 ) @ ( remove_slb @ SV197 @ SY496 ) @ SV221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(631,plain,
! [SV222: $i,SV164: $i,SV198: $i] :
( ( ! [SY497: $i] :
( ~ ( contains_slb @ SV198 @ SY497 )
| ~ ( strictly_less_than @ SY497 @ ( lookup_slb @ SV198 @ SY497 ) )
| ( ( remove_cpq @ ( triple @ SV164 @ SV198 @ SV222 ) @ SY497 )
= ( triple @ ( remove_pqp @ SV164 @ SY497 ) @ ( remove_slb @ SV198 @ SY497 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(632,plain,
! [SV166: $i,SV200: $i] :
( ( ( ( SV200 = create_slb )
| ( contains_slb @ SV200 @ ( findmin_pqp_res @ SV166 ) ) )
= $true )
| ( ( ! [SY460: $i] :
( ( findmin_cpq_eff @ ( triple @ SV166 @ SV200 @ SY460 ) )
= ( triple @ SV166 @ ( update_slb @ SV200 @ ( findmin_pqp_res @ SV166 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(633,plain,
! [SV167: $i,SV201: $i] :
( ( ( ( SV201 = create_slb )
| ~ ( contains_slb @ SV201 @ ( findmin_pqp_res @ SV167 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV167 ) @ ( lookup_slb @ SV201 @ ( findmin_pqp_res @ SV167 ) ) ) )
= $true )
| ( ( ! [SY461: $i] :
( ( findmin_cpq_eff @ ( triple @ SV167 @ SV201 @ SY461 ) )
= ( triple @ SV167 @ ( update_slb @ SV201 @ ( findmin_pqp_res @ SV167 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(634,plain,
! [SV168: $i,SV202: $i] :
( ( ( ( SV202 = create_slb )
| ~ ( contains_slb @ SV202 @ ( findmin_pqp_res @ SV168 ) )
| ~ ( less_than @ ( lookup_slb @ SV202 @ ( findmin_pqp_res @ SV168 ) ) @ ( findmin_pqp_res @ SV168 ) ) )
= $true )
| ( ( ! [SY462: $i] :
( ( findmin_cpq_eff @ ( triple @ SV168 @ SV202 @ SY462 ) )
= ( triple @ SV168 @ ( update_slb @ SV202 @ ( findmin_pqp_res @ SV168 ) ) @ SY462 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(635,plain,
! [SV170: $i,SV204: $i] :
( ( ( SV204 = create_slb )
= $true )
| ( ( ! [SY463: $i] :
( ( findmin_cpq_res @ ( triple @ SV170 @ SV204 @ SY463 ) )
= ( findmin_pqp_res @ SV170 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[600]) ).
thf(636,plain,
! [SV223: $i,SV205: $i,SV173: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY498: $i,SY499: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY498 ) ) @ SV223 @ SY499 )
| ( SV205 = SV223 )
| ( pair_in_list @ SV173 @ SV223 @ SY499 ) )
| ~ ! [SY500: $i,SY501: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY500 ) ) @ SV223 @ SY501 )
| ( SY500 = SY501 )
| ( pair_in_list @ SV173 @ SV223 @ SY501 ) ) )
| ~ ~ ( ~ ! [SY502: $i,SY503: $i] :
( ( SV205 != SV223 )
| ( SY502 != SY503 )
| ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY502 ) ) @ SV223 @ SY503 ) )
| ~ ! [SY504: $i,SY505: $i] :
( ~ ( pair_in_list @ SV173 @ SV223 @ SY505 )
| ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY504 ) ) @ SV223 @ SY505 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(637,plain,
( ( ~ ( ~ ( sK14_REN
| ! [SX0: $i,SX1: $i] : ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) ) )
| ~ ( ~ sK14_REN
| ~ ( ~ ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
| ~ ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[602]) ).
thf(638,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ sK1_U @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[603]) ).
thf(639,plain,
! [SV206: $i,SV174: $i] :
( ( ~ ! [SY473: $i,SY474: $i] :
( ~ ( contains_cpq @ ( triple @ SV174 @ SV206 @ SY473 ) @ SY474 )
| ( contains_slb @ SV206 @ SY474 ) )
| ~ ! [SY475: $i,SY476: $i] :
( ~ ( contains_slb @ SV206 @ SY476 )
| ( contains_cpq @ ( triple @ SV174 @ SV206 @ SY475 ) @ SY476 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(640,plain,
! [SV224: $i,SV207: $i,SV175: $i] :
( ( ~ ( ~ ! [SY506: $i,SY507: $i] :
( ~ ( less_than @ SY507 @ SY506 )
| ~ ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SV207 @ ( pair @ SY506 @ SY507 ) ) @ SV224 ) )
| ( check_cpq @ ( triple @ SV175 @ SV207 @ SV224 ) ) )
| ~ ! [SY508: $i,SY509: $i] :
( ~ ( less_than @ SY509 @ SY508 )
| ~ ( check_cpq @ ( triple @ SV175 @ SV207 @ SV224 ) )
| ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SV207 @ ( pair @ SY508 @ SY509 ) ) @ SV224 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(641,plain,
! [SV208: $i,SV176: $i] :
( ( ~ ! [SY482: $i] :
( ! [SY483: $i] :
~ ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY483 ) ) @ SY482 )
| ( SV208 = SY482 )
| ( contains_slb @ SV176 @ SY482 ) )
| ~ ~ ( ~ ! [SY484: $i] :
( ( SV208 != SY484 )
| ! [SY485: $i] : ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY485 ) ) @ SY484 ) )
| ~ ! [SY486: $i] :
( ~ ( contains_slb @ SV176 @ SY486 )
| ! [SY487: $i] : ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY487 ) ) @ SY486 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(642,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)],[607]) ).
thf(643,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)],[608]) ).
thf(644,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK10_SY158 @ sK11_SY162 ) ) @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[609]) ).
thf(645,plain,
( ( ~ ( check_cpq @ ( triple @ sK8_SY132 @ ( insert_slb @ sK1_U @ ( pair @ sK10_SY158 @ sK11_SY162 ) ) @ sK9_SY153 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[610]) ).
thf(646,plain,
! [SV209: $i,SV177: $i,SV138: $i] :
( ( ( ~ ( less_than @ SV138 @ SV177 )
| ~ ( less_than @ SV177 @ SV209 ) )
= $true )
| ( ( less_than @ SV138 @ SV209 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(647,plain,
! [SV146: $i,SV212: $i,SV182: $i] :
( ( ( ( SV182 = SV212 )
| ~ ( contains_slb @ SV146 @ SV212 ) )
= $true )
| ( ( ! [SY488: $i] :
( ( remove_slb @ ( insert_slb @ SV146 @ ( pair @ SV182 @ SY488 ) ) @ SV212 )
= ( insert_slb @ ( remove_slb @ SV146 @ SV212 ) @ ( pair @ SV182 @ SY488 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(648,plain,
! [SV148: $i,SV214: $i,SV184: $i] :
( ( ( ( SV184 = SV214 )
| ~ ( contains_slb @ SV148 @ SV214 ) )
= $true )
| ( ( ! [SY489: $i] :
( ( lookup_slb @ ( insert_slb @ SV148 @ ( pair @ SV184 @ SY489 ) ) @ SV214 )
= ( lookup_slb @ SV148 @ SV214 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(649,plain,
! [SV185: $i,SV150: $i,SV215: $i,SV225: $i] :
( ( ~ ( strictly_less_than @ SV225 @ SV215 )
| ( ( update_slb @ ( insert_slb @ SV150 @ ( pair @ SV185 @ SV225 ) ) @ SV215 )
= ( insert_slb @ ( update_slb @ SV150 @ SV215 ) @ ( pair @ SV185 @ SV215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(650,plain,
! [SV186: $i,SV151: $i,SV226: $i,SV216: $i] :
( ( ~ ( less_than @ SV216 @ SV226 )
| ( ( update_slb @ ( insert_slb @ SV151 @ ( pair @ SV186 @ SV226 ) ) @ SV216 )
= ( insert_slb @ ( update_slb @ SV151 @ SV216 ) @ ( pair @ SV186 @ SV226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(651,plain,
! [SV187: $i,SV153: $i] :
( ( ( succ_cpq @ SV153 @ SV187 )
= $false )
| ( ( ! [SY446: $i] : ( succ_cpq @ SV153 @ ( insert_cpq @ SV187 @ SY446 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(652,plain,
! [SV188: $i,SV154: $i] :
( ( ( succ_cpq @ SV154 @ SV188 )
= $false )
| ( ( ! [SY447: $i] : ( succ_cpq @ SV154 @ ( remove_cpq @ SV188 @ SY447 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(653,plain,
! [SV189: $i,SV155: $i] :
( ( ( succ_cpq @ SV155 @ SV189 )
= $false )
| ( ( succ_cpq @ SV155 @ ( findmin_cpq_eff @ SV189 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(654,plain,
! [SV190: $i,SV156: $i] :
( ( ( succ_cpq @ SV156 @ SV190 )
= $false )
| ( ( succ_cpq @ SV156 @ ( removemin_cpq_eff @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(655,plain,
! [SV217: $i,SV192: $i,SV158: $i,SV227: $i] :
( ( ! [SY510: $i] :
( ~ ( strictly_less_than @ SV227 @ SY510 )
| ~ ( check_cpq @ ( triple @ SV158 @ ( insert_slb @ SV192 @ ( pair @ SV227 @ SY510 ) ) @ SV217 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(656,plain,
! [SV218: $i,SV194: $i,SV160: $i] :
( ( ( ok @ ( triple @ SV160 @ SV194 @ SV218 ) )
= $true )
| ( ( SV218 = bad )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[627]) ).
thf(657,plain,
! [SV228: $i,SV219: $i,SV195: $i,SV161: $i] :
( ( ( insert_cpq @ ( triple @ SV161 @ SV195 @ SV219 ) @ SV228 )
= ( triple @ ( insert_pqp @ SV161 @ SV228 ) @ ( insert_slb @ SV195 @ ( pair @ SV228 @ bottom ) ) @ SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(658,plain,
! [SV220: $i,SV162: $i,SV229: $i,SV196: $i] :
( ( ( contains_slb @ SV196 @ SV229 )
| ( ( remove_cpq @ ( triple @ SV162 @ SV196 @ SV220 ) @ SV229 )
= ( triple @ SV162 @ SV196 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(659,plain,
! [SV221: $i,SV163: $i,SV230: $i,SV197: $i] :
( ( ~ ( contains_slb @ SV197 @ SV230 )
| ~ ( less_than @ ( lookup_slb @ SV197 @ SV230 ) @ SV230 )
| ( ( remove_cpq @ ( triple @ SV163 @ SV197 @ SV221 ) @ SV230 )
= ( triple @ ( remove_pqp @ SV163 @ SV230 ) @ ( remove_slb @ SV197 @ SV230 ) @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(660,plain,
! [SV222: $i,SV164: $i,SV231: $i,SV198: $i] :
( ( ~ ( contains_slb @ SV198 @ SV231 )
| ~ ( strictly_less_than @ SV231 @ ( lookup_slb @ SV198 @ SV231 ) )
| ( ( remove_cpq @ ( triple @ SV164 @ SV198 @ SV222 ) @ SV231 )
= ( triple @ ( remove_pqp @ SV164 @ SV231 ) @ ( remove_slb @ SV198 @ SV231 ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(661,plain,
! [SV166: $i,SV200: $i] :
( ( ( SV200 = create_slb )
= $true )
| ( ( contains_slb @ SV200 @ ( findmin_pqp_res @ SV166 ) )
= $true )
| ( ( ! [SY460: $i] :
( ( findmin_cpq_eff @ ( triple @ SV166 @ SV200 @ SY460 ) )
= ( triple @ SV166 @ ( update_slb @ SV200 @ ( findmin_pqp_res @ SV166 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[632]) ).
thf(662,plain,
! [SV167: $i,SV201: $i] :
( ( ( ( SV201 = create_slb )
| ~ ( contains_slb @ SV201 @ ( findmin_pqp_res @ SV167 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV167 ) @ ( lookup_slb @ SV201 @ ( findmin_pqp_res @ SV167 ) ) ) )
= $true )
| ( ( ! [SY461: $i] :
( ( findmin_cpq_eff @ ( triple @ SV167 @ SV201 @ SY461 ) )
= ( triple @ SV167 @ ( update_slb @ SV201 @ ( findmin_pqp_res @ SV167 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(663,plain,
! [SV168: $i,SV202: $i] :
( ( ( ( SV202 = create_slb )
| ~ ( contains_slb @ SV202 @ ( findmin_pqp_res @ SV168 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV202 @ ( findmin_pqp_res @ SV168 ) ) @ ( findmin_pqp_res @ SV168 ) ) )
= $true )
| ( ( ! [SY462: $i] :
( ( findmin_cpq_eff @ ( triple @ SV168 @ SV202 @ SY462 ) )
= ( triple @ SV168 @ ( update_slb @ SV202 @ ( findmin_pqp_res @ SV168 ) ) @ SY462 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[634]) ).
thf(664,plain,
! [SV232: $i,SV204: $i,SV170: $i] :
( ( ( ( findmin_cpq_res @ ( triple @ SV170 @ SV204 @ SV232 ) )
= ( findmin_pqp_res @ SV170 ) )
= $true )
| ( ( SV204 = create_slb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(665,plain,
! [SV223: $i,SV205: $i,SV173: $i] :
( ( ~ ~ ( ~ ! [SY498: $i,SY499: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY498 ) ) @ SV223 @ SY499 )
| ( SV205 = SV223 )
| ( pair_in_list @ SV173 @ SV223 @ SY499 ) )
| ~ ! [SY500: $i,SY501: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY500 ) ) @ SV223 @ SY501 )
| ( SY500 = SY501 )
| ( pair_in_list @ SV173 @ SV223 @ SY501 ) ) )
| ~ ~ ( ~ ! [SY502: $i,SY503: $i] :
( ( SV205 != SV223 )
| ( SY502 != SY503 )
| ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY502 ) ) @ SV223 @ SY503 ) )
| ~ ! [SY504: $i,SY505: $i] :
( ~ ( pair_in_list @ SV173 @ SV223 @ SY505 )
| ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY504 ) ) @ SV223 @ SY505 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(666,plain,
( ( ~ ( sK14_REN
| ! [SX0: $i,SX1: $i] : ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) ) )
| ~ ( ~ sK14_REN
| ~ ( ~ ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
| ~ ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(667,plain,
( ( ( ! [SX0: $i,SX1: $i] :
~ ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) ) )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ sK1_U @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[638]) ).
thf(668,plain,
! [SV206: $i,SV174: $i] :
( ( ~ ! [SY473: $i,SY474: $i] :
( ~ ( contains_cpq @ ( triple @ SV174 @ SV206 @ SY473 ) @ SY474 )
| ( contains_slb @ SV206 @ SY474 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[639]) ).
thf(669,plain,
! [SV174: $i,SV206: $i] :
( ( ~ ! [SY475: $i,SY476: $i] :
( ~ ( contains_slb @ SV206 @ SY476 )
| ( contains_cpq @ ( triple @ SV174 @ SV206 @ SY475 ) @ SY476 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[639]) ).
thf(670,plain,
! [SV224: $i,SV207: $i,SV175: $i] :
( ( ~ ! [SY506: $i,SY507: $i] :
( ~ ( less_than @ SY507 @ SY506 )
| ~ ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SV207 @ ( pair @ SY506 @ SY507 ) ) @ SV224 ) )
| ( check_cpq @ ( triple @ SV175 @ SV207 @ SV224 ) ) )
| ~ ! [SY508: $i,SY509: $i] :
( ~ ( less_than @ SY509 @ SY508 )
| ~ ( check_cpq @ ( triple @ SV175 @ SV207 @ SV224 ) )
| ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SV207 @ ( pair @ SY508 @ SY509 ) ) @ SV224 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(671,plain,
! [SV208: $i,SV176: $i] :
( ( ~ ! [SY482: $i] :
( ! [SY483: $i] :
~ ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY483 ) ) @ SY482 )
| ( SV208 = SY482 )
| ( contains_slb @ SV176 @ SY482 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[641]) ).
thf(672,plain,
! [SV176: $i,SV208: $i] :
( ( ~ ~ ( ~ ! [SY484: $i] :
( ( SV208 != SY484 )
| ! [SY485: $i] : ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY485 ) ) @ SY484 ) )
| ~ ! [SY486: $i] :
( ~ ( contains_slb @ SV176 @ SY486 )
| ! [SY487: $i] : ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY487 ) ) @ SY486 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[641]) ).
thf(673,plain,
! [SV233: $i] :
( ( ! [SY511: $i] :
( ~ ( less_than @ SV233 @ SY511 )
| ( less_than @ SY511 @ SV233 )
| ( strictly_less_than @ SV233 @ SY511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(674,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)],[643]) ).
thf(675,plain,
! [SV234: $i] :
( ( ! [SY512: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK10_SY158 @ sK11_SY162 ) ) @ SV234 @ SY512 )
| ( less_than @ SY512 @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(676,plain,
( ( check_cpq @ ( triple @ sK8_SY132 @ ( insert_slb @ sK1_U @ ( pair @ sK10_SY158 @ sK11_SY162 ) ) @ sK9_SY153 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(677,plain,
! [SV209: $i,SV177: $i,SV138: $i] :
( ( ( ~ ( less_than @ SV138 @ SV177 ) )
= $true )
| ( ( ~ ( less_than @ SV177 @ SV209 ) )
= $true )
| ( ( less_than @ SV138 @ SV209 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[646]) ).
thf(678,plain,
! [SV146: $i,SV212: $i,SV182: $i] :
( ( ( SV182 = SV212 )
= $true )
| ( ( ~ ( contains_slb @ SV146 @ SV212 ) )
= $true )
| ( ( ! [SY488: $i] :
( ( remove_slb @ ( insert_slb @ SV146 @ ( pair @ SV182 @ SY488 ) ) @ SV212 )
= ( insert_slb @ ( remove_slb @ SV146 @ SV212 ) @ ( pair @ SV182 @ SY488 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[647]) ).
thf(679,plain,
! [SV148: $i,SV214: $i,SV184: $i] :
( ( ( SV184 = SV214 )
= $true )
| ( ( ~ ( contains_slb @ SV148 @ SV214 ) )
= $true )
| ( ( ! [SY489: $i] :
( ( lookup_slb @ ( insert_slb @ SV148 @ ( pair @ SV184 @ SY489 ) ) @ SV214 )
= ( lookup_slb @ SV148 @ SV214 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[648]) ).
thf(680,plain,
! [SV185: $i,SV150: $i,SV215: $i,SV225: $i] :
( ( ( ~ ( strictly_less_than @ SV225 @ SV215 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV150 @ ( pair @ SV185 @ SV225 ) ) @ SV215 )
= ( insert_slb @ ( update_slb @ SV150 @ SV215 ) @ ( pair @ SV185 @ SV215 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(681,plain,
! [SV186: $i,SV151: $i,SV226: $i,SV216: $i] :
( ( ( ~ ( less_than @ SV216 @ SV226 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV151 @ ( pair @ SV186 @ SV226 ) ) @ SV216 )
= ( insert_slb @ ( update_slb @ SV151 @ SV216 ) @ ( pair @ SV186 @ SV226 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[650]) ).
thf(682,plain,
! [SV235: $i,SV187: $i,SV153: $i] :
( ( ( succ_cpq @ SV153 @ ( insert_cpq @ SV187 @ SV235 ) )
= $true )
| ( ( succ_cpq @ SV153 @ SV187 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(683,plain,
! [SV236: $i,SV188: $i,SV154: $i] :
( ( ( succ_cpq @ SV154 @ ( remove_cpq @ SV188 @ SV236 ) )
= $true )
| ( ( succ_cpq @ SV154 @ SV188 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(684,plain,
! [SV217: $i,SV192: $i,SV158: $i,SV237: $i,SV227: $i] :
( ( ~ ( strictly_less_than @ SV227 @ SV237 )
| ~ ( check_cpq @ ( triple @ SV158 @ ( insert_slb @ SV192 @ ( pair @ SV227 @ SV237 ) ) @ SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(685,plain,
! [SV220: $i,SV162: $i,SV229: $i,SV196: $i] :
( ( ( contains_slb @ SV196 @ SV229 )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV162 @ SV196 @ SV220 ) @ SV229 )
= ( triple @ SV162 @ SV196 @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[658]) ).
thf(686,plain,
! [SV221: $i,SV163: $i,SV230: $i,SV197: $i] :
( ( ( ~ ( contains_slb @ SV197 @ SV230 )
| ~ ( less_than @ ( lookup_slb @ SV197 @ SV230 ) @ SV230 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV163 @ SV197 @ SV221 ) @ SV230 )
= ( triple @ ( remove_pqp @ SV163 @ SV230 ) @ ( remove_slb @ SV197 @ SV230 ) @ SV221 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[659]) ).
thf(687,plain,
! [SV222: $i,SV164: $i,SV231: $i,SV198: $i] :
( ( ( ~ ( contains_slb @ SV198 @ SV231 )
| ~ ( strictly_less_than @ SV231 @ ( lookup_slb @ SV198 @ SV231 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV164 @ SV198 @ SV222 ) @ SV231 )
= ( triple @ ( remove_pqp @ SV164 @ SV231 ) @ ( remove_slb @ SV198 @ SV231 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[660]) ).
thf(688,plain,
! [SV238: $i,SV200: $i,SV166: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV166 @ SV200 @ SV238 ) )
= ( triple @ SV166 @ ( update_slb @ SV200 @ ( findmin_pqp_res @ SV166 ) ) @ bad ) )
= $true )
| ( ( contains_slb @ SV200 @ ( findmin_pqp_res @ SV166 ) )
= $true )
| ( ( SV200 = create_slb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(689,plain,
! [SV167: $i,SV201: $i] :
( ( ( SV201 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV201 @ ( findmin_pqp_res @ SV167 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV167 ) @ ( lookup_slb @ SV201 @ ( findmin_pqp_res @ SV167 ) ) ) )
= $true )
| ( ( ! [SY461: $i] :
( ( findmin_cpq_eff @ ( triple @ SV167 @ SV201 @ SY461 ) )
= ( triple @ SV167 @ ( update_slb @ SV201 @ ( findmin_pqp_res @ SV167 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[662]) ).
thf(690,plain,
! [SV168: $i,SV202: $i] :
( ( ( SV202 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV202 @ ( findmin_pqp_res @ SV168 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV202 @ ( findmin_pqp_res @ SV168 ) ) @ ( findmin_pqp_res @ SV168 ) ) )
= $true )
| ( ( ! [SY462: $i] :
( ( findmin_cpq_eff @ ( triple @ SV168 @ SV202 @ SY462 ) )
= ( triple @ SV168 @ ( update_slb @ SV202 @ ( findmin_pqp_res @ SV168 ) ) @ SY462 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[663]) ).
thf(691,plain,
! [SV223: $i,SV205: $i,SV173: $i] :
( ( ~ ~ ( ~ ! [SY498: $i,SY499: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY498 ) ) @ SV223 @ SY499 )
| ( SV205 = SV223 )
| ( pair_in_list @ SV173 @ SV223 @ SY499 ) )
| ~ ! [SY500: $i,SY501: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY500 ) ) @ SV223 @ SY501 )
| ( SY500 = SY501 )
| ( pair_in_list @ SV173 @ SV223 @ SY501 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[665]) ).
thf(692,plain,
! [SV173: $i,SV223: $i,SV205: $i] :
( ( ~ ~ ( ~ ! [SY502: $i,SY503: $i] :
( ( SV205 != SV223 )
| ( SY502 != SY503 )
| ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY502 ) ) @ SV223 @ SY503 ) )
| ~ ! [SY504: $i,SY505: $i] :
( ~ ( pair_in_list @ SV173 @ SV223 @ SY505 )
| ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY504 ) ) @ SV223 @ SY505 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[665]) ).
thf(693,plain,
( ( ~ ( sK14_REN
| ! [SX0: $i,SX1: $i] : ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[666]) ).
thf(694,plain,
( ( ~ ( ~ sK14_REN
| ~ ( ~ ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
| ~ ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[666]) ).
thf(695,plain,
! [SV239: $i] :
( ( ( ! [SY513: $i] :
~ ( check_cpq @ ( triple @ SV239 @ sK1_U @ SY513 ) ) )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ sK1_U @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(696,plain,
! [SV206: $i,SV174: $i] :
( ( ! [SY473: $i,SY474: $i] :
( ~ ( contains_cpq @ ( triple @ SV174 @ SV206 @ SY473 ) @ SY474 )
| ( contains_slb @ SV206 @ SY474 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[668]) ).
thf(697,plain,
! [SV174: $i,SV206: $i] :
( ( ! [SY475: $i,SY476: $i] :
( ~ ( contains_slb @ SV206 @ SY476 )
| ( contains_cpq @ ( triple @ SV174 @ SV206 @ SY475 ) @ SY476 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[669]) ).
thf(698,plain,
! [SV224: $i,SV207: $i,SV175: $i] :
( ( ~ ! [SY506: $i,SY507: $i] :
( ~ ( less_than @ SY507 @ SY506 )
| ~ ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SV207 @ ( pair @ SY506 @ SY507 ) ) @ SV224 ) )
| ( check_cpq @ ( triple @ SV175 @ SV207 @ SV224 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[670]) ).
thf(699,plain,
! [SV224: $i,SV207: $i,SV175: $i] :
( ( ~ ! [SY508: $i,SY509: $i] :
( ~ ( less_than @ SY509 @ SY508 )
| ~ ( check_cpq @ ( triple @ SV175 @ SV207 @ SV224 ) )
| ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SV207 @ ( pair @ SY508 @ SY509 ) ) @ SV224 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[670]) ).
thf(700,plain,
! [SV208: $i,SV176: $i] :
( ( ! [SY482: $i] :
( ! [SY483: $i] :
~ ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY483 ) ) @ SY482 )
| ( SV208 = SY482 )
| ( contains_slb @ SV176 @ SY482 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[671]) ).
thf(701,plain,
! [SV176: $i,SV208: $i] :
( ( ~ ( ~ ! [SY484: $i] :
( ( SV208 != SY484 )
| ! [SY485: $i] : ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY485 ) ) @ SY484 ) )
| ~ ! [SY486: $i] :
( ~ ( contains_slb @ SV176 @ SY486 )
| ! [SY487: $i] : ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY487 ) ) @ SY486 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[672]) ).
thf(702,plain,
! [SV240: $i,SV233: $i] :
( ( ~ ( less_than @ SV233 @ SV240 )
| ( less_than @ SV240 @ SV233 )
| ( strictly_less_than @ SV233 @ SV240 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(703,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(704,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(705,plain,
! [SV241: $i,SV234: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK10_SY158 @ sK11_SY162 ) ) @ SV234 @ SV241 )
| ( less_than @ SV241 @ SV234 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(706,plain,
! [SV209: $i,SV177: $i,SV138: $i] :
( ( ( less_than @ SV138 @ SV177 )
= $false )
| ( ( ~ ( less_than @ SV177 @ SV209 ) )
= $true )
| ( ( less_than @ SV138 @ SV209 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(707,plain,
! [SV182: $i,SV212: $i,SV146: $i] :
( ( ( contains_slb @ SV146 @ SV212 )
= $false )
| ( ( SV182 = SV212 )
= $true )
| ( ( ! [SY488: $i] :
( ( remove_slb @ ( insert_slb @ SV146 @ ( pair @ SV182 @ SY488 ) ) @ SV212 )
= ( insert_slb @ ( remove_slb @ SV146 @ SV212 ) @ ( pair @ SV182 @ SY488 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(708,plain,
! [SV184: $i,SV214: $i,SV148: $i] :
( ( ( contains_slb @ SV148 @ SV214 )
= $false )
| ( ( SV184 = SV214 )
= $true )
| ( ( ! [SY489: $i] :
( ( lookup_slb @ ( insert_slb @ SV148 @ ( pair @ SV184 @ SY489 ) ) @ SV214 )
= ( lookup_slb @ SV148 @ SV214 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(709,plain,
! [SV185: $i,SV150: $i,SV215: $i,SV225: $i] :
( ( ( strictly_less_than @ SV225 @ SV215 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV150 @ ( pair @ SV185 @ SV225 ) ) @ SV215 )
= ( insert_slb @ ( update_slb @ SV150 @ SV215 ) @ ( pair @ SV185 @ SV215 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[680]) ).
thf(710,plain,
! [SV186: $i,SV151: $i,SV226: $i,SV216: $i] :
( ( ( less_than @ SV216 @ SV226 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV151 @ ( pair @ SV186 @ SV226 ) ) @ SV216 )
= ( insert_slb @ ( update_slb @ SV151 @ SV216 ) @ ( pair @ SV186 @ SV226 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[681]) ).
thf(711,plain,
! [SV217: $i,SV192: $i,SV158: $i,SV237: $i,SV227: $i] :
( ( ( ~ ( strictly_less_than @ SV227 @ SV237 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV158 @ ( insert_slb @ SV192 @ ( pair @ SV227 @ SV237 ) ) @ SV217 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[684]) ).
thf(712,plain,
! [SV221: $i,SV163: $i,SV230: $i,SV197: $i] :
( ( ( ~ ( contains_slb @ SV197 @ SV230 ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV197 @ SV230 ) @ SV230 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV163 @ SV197 @ SV221 ) @ SV230 )
= ( triple @ ( remove_pqp @ SV163 @ SV230 ) @ ( remove_slb @ SV197 @ SV230 ) @ SV221 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[686]) ).
thf(713,plain,
! [SV222: $i,SV164: $i,SV231: $i,SV198: $i] :
( ( ( ~ ( contains_slb @ SV198 @ SV231 ) )
= $true )
| ( ( ~ ( strictly_less_than @ SV231 @ ( lookup_slb @ SV198 @ SV231 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV164 @ SV198 @ SV222 ) @ SV231 )
= ( triple @ ( remove_pqp @ SV164 @ SV231 ) @ ( remove_slb @ SV198 @ SV231 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[687]) ).
thf(714,plain,
! [SV167: $i,SV201: $i] :
( ( ( contains_slb @ SV201 @ ( findmin_pqp_res @ SV167 ) )
= $false )
| ( ( SV201 = create_slb )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV167 ) @ ( lookup_slb @ SV201 @ ( findmin_pqp_res @ SV167 ) ) ) )
= $true )
| ( ( ! [SY461: $i] :
( ( findmin_cpq_eff @ ( triple @ SV167 @ SV201 @ SY461 ) )
= ( triple @ SV167 @ ( update_slb @ SV201 @ ( findmin_pqp_res @ SV167 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[689]) ).
thf(715,plain,
! [SV168: $i,SV202: $i] :
( ( ( contains_slb @ SV202 @ ( findmin_pqp_res @ SV168 ) )
= $false )
| ( ( SV202 = create_slb )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV202 @ ( findmin_pqp_res @ SV168 ) ) @ ( findmin_pqp_res @ SV168 ) ) )
= $true )
| ( ( ! [SY462: $i] :
( ( findmin_cpq_eff @ ( triple @ SV168 @ SV202 @ SY462 ) )
= ( triple @ SV168 @ ( update_slb @ SV202 @ ( findmin_pqp_res @ SV168 ) ) @ SY462 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(716,plain,
! [SV223: $i,SV205: $i,SV173: $i] :
( ( ~ ( ~ ! [SY498: $i,SY499: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY498 ) ) @ SV223 @ SY499 )
| ( SV205 = SV223 )
| ( pair_in_list @ SV173 @ SV223 @ SY499 ) )
| ~ ! [SY500: $i,SY501: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY500 ) ) @ SV223 @ SY501 )
| ( SY500 = SY501 )
| ( pair_in_list @ SV173 @ SV223 @ SY501 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[691]) ).
thf(717,plain,
! [SV173: $i,SV223: $i,SV205: $i] :
( ( ~ ( ~ ! [SY502: $i,SY503: $i] :
( ( SV205 != SV223 )
| ( SY502 != SY503 )
| ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY502 ) ) @ SV223 @ SY503 ) )
| ~ ! [SY504: $i,SY505: $i] :
( ~ ( pair_in_list @ SV173 @ SV223 @ SY505 )
| ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY504 ) ) @ SV223 @ SY505 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[692]) ).
thf(718,plain,
( ( sK14_REN
| ! [SX0: $i,SX1: $i] : ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[693]) ).
thf(719,plain,
( ( ~ sK14_REN
| ~ ( ~ ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
| ~ ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[694]) ).
thf(720,plain,
! [SV242: $i,SV239: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV239 @ sK1_U @ SV242 ) ) )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ sK1_U @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(721,plain,
! [SV243: $i,SV206: $i,SV174: $i] :
( ( ! [SY514: $i] :
( ~ ( contains_cpq @ ( triple @ SV174 @ SV206 @ SV243 ) @ SY514 )
| ( contains_slb @ SV206 @ SY514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(722,plain,
! [SV244: $i,SV174: $i,SV206: $i] :
( ( ! [SY515: $i] :
( ~ ( contains_slb @ SV206 @ SY515 )
| ( contains_cpq @ ( triple @ SV174 @ SV206 @ SV244 ) @ SY515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(723,plain,
! [SV224: $i,SV207: $i,SV175: $i] :
( ( ! [SY506: $i,SY507: $i] :
( ~ ( less_than @ SY507 @ SY506 )
| ~ ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SV207 @ ( pair @ SY506 @ SY507 ) ) @ SV224 ) )
| ( check_cpq @ ( triple @ SV175 @ SV207 @ SV224 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[698]) ).
thf(724,plain,
! [SV224: $i,SV207: $i,SV175: $i] :
( ( ! [SY508: $i,SY509: $i] :
( ~ ( less_than @ SY509 @ SY508 )
| ~ ( check_cpq @ ( triple @ SV175 @ SV207 @ SV224 ) )
| ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SV207 @ ( pair @ SY508 @ SY509 ) ) @ SV224 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[699]) ).
thf(725,plain,
! [SV245: $i,SV208: $i,SV176: $i] :
( ( ! [SY516: $i] :
~ ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY516 ) ) @ SV245 )
| ( SV208 = SV245 )
| ( contains_slb @ SV176 @ SV245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(726,plain,
! [SV176: $i,SV208: $i] :
( ( ~ ! [SY484: $i] :
( ( SV208 != SY484 )
| ! [SY485: $i] : ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY485 ) ) @ SY484 ) )
| ~ ! [SY486: $i] :
( ~ ( contains_slb @ SV176 @ SY486 )
| ! [SY487: $i] : ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY487 ) ) @ SY486 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[701]) ).
thf(727,plain,
! [SV240: $i,SV233: $i] :
( ( ( ~ ( less_than @ SV233 @ SV240 )
| ( less_than @ SV240 @ SV233 ) )
= $true )
| ( ( strictly_less_than @ SV233 @ SV240 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[702]) ).
thf(728,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[703]) ).
thf(729,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[704]) ).
thf(730,plain,
! [SV241: $i,SV234: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK10_SY158 @ sK11_SY162 ) ) @ SV234 @ SV241 ) )
= $true )
| ( ( less_than @ SV241 @ SV234 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[705]) ).
thf(731,plain,
! [SV138: $i,SV209: $i,SV177: $i] :
( ( ( less_than @ SV177 @ SV209 )
= $false )
| ( ( less_than @ SV138 @ SV177 )
= $false )
| ( ( less_than @ SV138 @ SV209 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(732,plain,
! [SV212: $i,SV246: $i,SV182: $i,SV146: $i] :
( ( ( ( remove_slb @ ( insert_slb @ SV146 @ ( pair @ SV182 @ SV246 ) ) @ SV212 )
= ( insert_slb @ ( remove_slb @ SV146 @ SV212 ) @ ( pair @ SV182 @ SV246 ) ) )
= $true )
| ( ( SV182 = SV212 )
= $true )
| ( ( contains_slb @ SV146 @ SV212 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(733,plain,
! [SV214: $i,SV247: $i,SV184: $i,SV148: $i] :
( ( ( ( lookup_slb @ ( insert_slb @ SV148 @ ( pair @ SV184 @ SV247 ) ) @ SV214 )
= ( lookup_slb @ SV148 @ SV214 ) )
= $true )
| ( ( SV184 = SV214 )
= $true )
| ( ( contains_slb @ SV148 @ SV214 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(734,plain,
! [SV217: $i,SV192: $i,SV158: $i,SV237: $i,SV227: $i] :
( ( ( strictly_less_than @ SV227 @ SV237 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV158 @ ( insert_slb @ SV192 @ ( pair @ SV227 @ SV237 ) ) @ SV217 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[711]) ).
thf(735,plain,
! [SV221: $i,SV163: $i,SV230: $i,SV197: $i] :
( ( ( contains_slb @ SV197 @ SV230 )
= $false )
| ( ( ~ ( less_than @ ( lookup_slb @ SV197 @ SV230 ) @ SV230 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV163 @ SV197 @ SV221 ) @ SV230 )
= ( triple @ ( remove_pqp @ SV163 @ SV230 ) @ ( remove_slb @ SV197 @ SV230 ) @ SV221 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(736,plain,
! [SV222: $i,SV164: $i,SV231: $i,SV198: $i] :
( ( ( contains_slb @ SV198 @ SV231 )
= $false )
| ( ( ~ ( strictly_less_than @ SV231 @ ( lookup_slb @ SV198 @ SV231 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV164 @ SV198 @ SV222 ) @ SV231 )
= ( triple @ ( remove_pqp @ SV164 @ SV231 ) @ ( remove_slb @ SV198 @ SV231 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(737,plain,
! [SV201: $i,SV167: $i] :
( ( ( strictly_less_than @ ( findmin_pqp_res @ SV167 ) @ ( lookup_slb @ SV201 @ ( findmin_pqp_res @ SV167 ) ) )
= $false )
| ( ( SV201 = create_slb )
= $true )
| ( ( contains_slb @ SV201 @ ( findmin_pqp_res @ SV167 ) )
= $false )
| ( ( ! [SY461: $i] :
( ( findmin_cpq_eff @ ( triple @ SV167 @ SV201 @ SY461 ) )
= ( triple @ SV167 @ ( update_slb @ SV201 @ ( findmin_pqp_res @ SV167 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(738,plain,
! [SV168: $i,SV202: $i] :
( ( ( less_than @ ( lookup_slb @ SV202 @ ( findmin_pqp_res @ SV168 ) ) @ ( findmin_pqp_res @ SV168 ) )
= $false )
| ( ( SV202 = create_slb )
= $true )
| ( ( contains_slb @ SV202 @ ( findmin_pqp_res @ SV168 ) )
= $false )
| ( ( ! [SY462: $i] :
( ( findmin_cpq_eff @ ( triple @ SV168 @ SV202 @ SY462 ) )
= ( triple @ SV168 @ ( update_slb @ SV202 @ ( findmin_pqp_res @ SV168 ) ) @ SY462 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(739,plain,
! [SV223: $i,SV205: $i,SV173: $i] :
( ( ~ ! [SY498: $i,SY499: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY498 ) ) @ SV223 @ SY499 )
| ( SV205 = SV223 )
| ( pair_in_list @ SV173 @ SV223 @ SY499 ) )
| ~ ! [SY500: $i,SY501: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY500 ) ) @ SV223 @ SY501 )
| ( SY500 = SY501 )
| ( pair_in_list @ SV173 @ SV223 @ SY501 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[716]) ).
thf(740,plain,
! [SV173: $i,SV223: $i,SV205: $i] :
( ( ~ ! [SY502: $i,SY503: $i] :
( ( SV205 != SV223 )
| ( SY502 != SY503 )
| ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY502 ) ) @ SV223 @ SY503 ) )
| ~ ! [SY504: $i,SY505: $i] :
( ~ ( pair_in_list @ SV173 @ SV223 @ SY505 )
| ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY504 ) ) @ SV223 @ SY505 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(741,plain,
( ( sK14_REN = $true )
| ( ( ! [SX0: $i,SX1: $i] : ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[718]) ).
thf(742,plain,
( ( ( ~ sK14_REN )
= $true )
| ( ( ~ ( ~ ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
| ~ ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(743,plain,
! [SV242: $i,SV239: $i] :
( ( ( check_cpq @ ( triple @ SV239 @ sK1_U @ SV242 ) )
= $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ sK1_U @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(744,plain,
! [SV248: $i,SV243: $i,SV206: $i,SV174: $i] :
( ( ~ ( contains_cpq @ ( triple @ SV174 @ SV206 @ SV243 ) @ SV248 )
| ( contains_slb @ SV206 @ SV248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(745,plain,
! [SV244: $i,SV174: $i,SV249: $i,SV206: $i] :
( ( ~ ( contains_slb @ SV206 @ SV249 )
| ( contains_cpq @ ( triple @ SV174 @ SV206 @ SV244 ) @ SV249 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(746,plain,
! [SV224: $i,SV207: $i,SV175: $i,SV250: $i] :
( ( ! [SY517: $i] :
( ~ ( less_than @ SY517 @ SV250 )
| ~ ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SV207 @ ( pair @ SV250 @ SY517 ) ) @ SV224 ) )
| ( check_cpq @ ( triple @ SV175 @ SV207 @ SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(747,plain,
! [SV224: $i,SV207: $i,SV175: $i,SV251: $i] :
( ( ! [SY518: $i] :
( ~ ( less_than @ SY518 @ SV251 )
| ~ ( check_cpq @ ( triple @ SV175 @ SV207 @ SV224 ) )
| ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SV207 @ ( pair @ SV251 @ SY518 ) ) @ SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(748,plain,
! [SV245: $i,SV208: $i,SV176: $i] :
( ( ( ! [SY516: $i] :
~ ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY516 ) ) @ SV245 ) )
= $true )
| ( ( ( SV208 = SV245 )
| ( contains_slb @ SV176 @ SV245 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[725]) ).
thf(749,plain,
! [SV176: $i,SV208: $i] :
( ( ~ ! [SY484: $i] :
( ( SV208 != SY484 )
| ! [SY485: $i] : ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY485 ) ) @ SY484 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[726]) ).
thf(750,plain,
! [SV208: $i,SV176: $i] :
( ( ~ ! [SY486: $i] :
( ~ ( contains_slb @ SV176 @ SY486 )
| ! [SY487: $i] : ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY487 ) ) @ SY486 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[726]) ).
thf(751,plain,
! [SV240: $i,SV233: $i] :
( ( ( ~ ( less_than @ SV233 @ SV240 ) )
= $true )
| ( ( less_than @ SV240 @ SV233 )
= $true )
| ( ( strictly_less_than @ SV233 @ SV240 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(752,plain,
! [SV252: $i] :
( ( ! [SY519: $i] :
( ~ ( strictly_less_than @ SV252 @ SY519 )
| ( less_than @ SV252 @ SY519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(753,plain,
! [SV253: $i] :
( ( ! [SY520: $i] :
( ~ ( strictly_less_than @ SV253 @ SY520 )
| ~ ( less_than @ SY520 @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(754,plain,
! [SV241: $i,SV234: $i] :
( ( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK10_SY158 @ sK11_SY162 ) ) @ SV234 @ SV241 )
= $false )
| ( ( less_than @ SV241 @ SV234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(755,plain,
! [SV217: $i,SV237: $i,SV227: $i,SV192: $i,SV158: $i] :
( ( ( check_cpq @ ( triple @ SV158 @ ( insert_slb @ SV192 @ ( pair @ SV227 @ SV237 ) ) @ SV217 ) )
= $false )
| ( ( strictly_less_than @ SV227 @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(756,plain,
! [SV221: $i,SV163: $i,SV230: $i,SV197: $i] :
( ( ( less_than @ ( lookup_slb @ SV197 @ SV230 ) @ SV230 )
= $false )
| ( ( contains_slb @ SV197 @ SV230 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV163 @ SV197 @ SV221 ) @ SV230 )
= ( triple @ ( remove_pqp @ SV163 @ SV230 ) @ ( remove_slb @ SV197 @ SV230 ) @ SV221 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(757,plain,
! [SV222: $i,SV164: $i,SV198: $i,SV231: $i] :
( ( ( strictly_less_than @ SV231 @ ( lookup_slb @ SV198 @ SV231 ) )
= $false )
| ( ( contains_slb @ SV198 @ SV231 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV164 @ SV198 @ SV222 ) @ SV231 )
= ( triple @ ( remove_pqp @ SV164 @ SV231 ) @ ( remove_slb @ SV198 @ SV231 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[736]) ).
thf(758,plain,
! [SV254: $i,SV201: $i,SV167: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV167 @ SV201 @ SV254 ) )
= ( triple @ SV167 @ ( update_slb @ SV201 @ ( findmin_pqp_res @ SV167 ) ) @ bad ) )
= $true )
| ( ( contains_slb @ SV201 @ ( findmin_pqp_res @ SV167 ) )
= $false )
| ( ( SV201 = create_slb )
= $true )
| ( ( strictly_less_than @ ( findmin_pqp_res @ SV167 ) @ ( lookup_slb @ SV201 @ ( findmin_pqp_res @ SV167 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(759,plain,
! [SV255: $i,SV202: $i,SV168: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV168 @ SV202 @ SV255 ) )
= ( triple @ SV168 @ ( update_slb @ SV202 @ ( findmin_pqp_res @ SV168 ) ) @ SV255 ) )
= $true )
| ( ( contains_slb @ SV202 @ ( findmin_pqp_res @ SV168 ) )
= $false )
| ( ( SV202 = create_slb )
= $true )
| ( ( less_than @ ( lookup_slb @ SV202 @ ( findmin_pqp_res @ SV168 ) ) @ ( findmin_pqp_res @ SV168 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(760,plain,
! [SV223: $i,SV205: $i,SV173: $i] :
( ( ~ ! [SY498: $i,SY499: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY498 ) ) @ SV223 @ SY499 )
| ( SV205 = SV223 )
| ( pair_in_list @ SV173 @ SV223 @ SY499 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[739]) ).
thf(761,plain,
! [SV223: $i,SV205: $i,SV173: $i] :
( ( ~ ! [SY500: $i,SY501: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY500 ) ) @ SV223 @ SY501 )
| ( SY500 = SY501 )
| ( pair_in_list @ SV173 @ SV223 @ SY501 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[739]) ).
thf(762,plain,
! [SV173: $i,SV223: $i,SV205: $i] :
( ( ~ ! [SY502: $i,SY503: $i] :
( ( SV205 != SV223 )
| ( SY502 != SY503 )
| ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY502 ) ) @ SV223 @ SY503 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[740]) ).
thf(763,plain,
! [SV205: $i,SV223: $i,SV173: $i] :
( ( ~ ! [SY504: $i,SY505: $i] :
( ~ ( pair_in_list @ SV173 @ SV223 @ SY505 )
| ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY504 ) ) @ SV223 @ SY505 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[740]) ).
thf(764,plain,
! [SV256: $i] :
( ( ( ! [SY521: $i] : ( check_cpq @ ( triple @ SV256 @ sK1_U @ SY521 ) ) )
= $true )
| ( sK14_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(765,plain,
( ( sK14_REN = $false )
| ( ( ~ ( ~ ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
| ~ ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[742]) ).
thf(766,plain,
! [SV242: $i,SV239: $i,SV257: $i] :
( ( ( ! [SY522: $i] :
( ~ ( pair_in_list @ sK1_U @ SV257 @ SY522 )
| ( less_than @ SY522 @ SV257 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV239 @ sK1_U @ SV242 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(767,plain,
! [SV248: $i,SV243: $i,SV206: $i,SV174: $i] :
( ( ( ~ ( contains_cpq @ ( triple @ SV174 @ SV206 @ SV243 ) @ SV248 ) )
= $true )
| ( ( contains_slb @ SV206 @ SV248 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[744]) ).
thf(768,plain,
! [SV244: $i,SV174: $i,SV249: $i,SV206: $i] :
( ( ( ~ ( contains_slb @ SV206 @ SV249 ) )
= $true )
| ( ( contains_cpq @ ( triple @ SV174 @ SV206 @ SV244 ) @ SV249 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[745]) ).
thf(769,plain,
! [SV224: $i,SV207: $i,SV175: $i,SV250: $i,SV258: $i] :
( ( ~ ( less_than @ SV258 @ SV250 )
| ~ ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SV207 @ ( pair @ SV250 @ SV258 ) ) @ SV224 ) )
| ( check_cpq @ ( triple @ SV175 @ SV207 @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(770,plain,
! [SV224: $i,SV207: $i,SV175: $i,SV251: $i,SV259: $i] :
( ( ~ ( less_than @ SV259 @ SV251 )
| ~ ( check_cpq @ ( triple @ SV175 @ SV207 @ SV224 ) )
| ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SV207 @ ( pair @ SV251 @ SV259 ) ) @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(771,plain,
! [SV245: $i,SV260: $i,SV208: $i,SV176: $i] :
( ( ( ~ ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SV260 ) ) @ SV245 ) )
= $true )
| ( ( ( SV208 = SV245 )
| ( contains_slb @ SV176 @ SV245 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(772,plain,
! [SV176: $i,SV208: $i] :
( ( ! [SY484: $i] :
( ( SV208 != SY484 )
| ! [SY485: $i] : ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY485 ) ) @ SY484 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[749]) ).
thf(773,plain,
! [SV208: $i,SV176: $i] :
( ( ! [SY486: $i] :
( ~ ( contains_slb @ SV176 @ SY486 )
| ! [SY487: $i] : ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY487 ) ) @ SY486 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[750]) ).
thf(774,plain,
! [SV240: $i,SV233: $i] :
( ( ( less_than @ SV233 @ SV240 )
= $false )
| ( ( less_than @ SV240 @ SV233 )
= $true )
| ( ( strictly_less_than @ SV233 @ SV240 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(775,plain,
! [SV261: $i,SV252: $i] :
( ( ~ ( strictly_less_than @ SV252 @ SV261 )
| ( less_than @ SV252 @ SV261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(776,plain,
! [SV262: $i,SV253: $i] :
( ( ~ ( strictly_less_than @ SV253 @ SV262 )
| ~ ( less_than @ SV262 @ SV253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(777,plain,
! [SV223: $i,SV205: $i,SV173: $i] :
( ( ! [SY498: $i,SY499: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY498 ) ) @ SV223 @ SY499 )
| ( SV205 = SV223 )
| ( pair_in_list @ SV173 @ SV223 @ SY499 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[760]) ).
thf(778,plain,
! [SV223: $i,SV205: $i,SV173: $i] :
( ( ! [SY500: $i,SY501: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY500 ) ) @ SV223 @ SY501 )
| ( SY500 = SY501 )
| ( pair_in_list @ SV173 @ SV223 @ SY501 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[761]) ).
thf(779,plain,
! [SV173: $i,SV223: $i,SV205: $i] :
( ( ! [SY502: $i,SY503: $i] :
( ( SV205 != SV223 )
| ( SY502 != SY503 )
| ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY502 ) ) @ SV223 @ SY503 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[762]) ).
thf(780,plain,
! [SV205: $i,SV223: $i,SV173: $i] :
( ( ! [SY504: $i,SY505: $i] :
( ~ ( pair_in_list @ SV173 @ SV223 @ SY505 )
| ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SY504 ) ) @ SV223 @ SY505 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[763]) ).
thf(781,plain,
! [SV263: $i,SV256: $i] :
( ( ( check_cpq @ ( triple @ SV256 @ sK1_U @ SV263 ) )
= $true )
| ( sK14_REN = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(782,plain,
( ( ( ~ ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
| ~ ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) )
= $false )
| ( sK14_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[765]) ).
thf(783,plain,
! [SV242: $i,SV239: $i,SV264: $i,SV257: $i] :
( ( ( ~ ( pair_in_list @ sK1_U @ SV257 @ SV264 )
| ( less_than @ SV264 @ SV257 ) )
= $true )
| ( ( check_cpq @ ( triple @ SV239 @ sK1_U @ SV242 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(784,plain,
! [SV248: $i,SV243: $i,SV206: $i,SV174: $i] :
( ( ( contains_cpq @ ( triple @ SV174 @ SV206 @ SV243 ) @ SV248 )
= $false )
| ( ( contains_slb @ SV206 @ SV248 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[767]) ).
thf(785,plain,
! [SV244: $i,SV174: $i,SV249: $i,SV206: $i] :
( ( ( contains_slb @ SV206 @ SV249 )
= $false )
| ( ( contains_cpq @ ( triple @ SV174 @ SV206 @ SV244 ) @ SV249 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(786,plain,
! [SV224: $i,SV207: $i,SV175: $i,SV250: $i,SV258: $i] :
( ( ( ~ ( less_than @ SV258 @ SV250 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SV207 @ ( pair @ SV250 @ SV258 ) ) @ SV224 ) )
| ( check_cpq @ ( triple @ SV175 @ SV207 @ SV224 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(787,plain,
! [SV224: $i,SV207: $i,SV175: $i,SV251: $i,SV259: $i] :
( ( ( ~ ( less_than @ SV259 @ SV251 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV175 @ SV207 @ SV224 ) )
| ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SV207 @ ( pair @ SV251 @ SV259 ) ) @ SV224 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(788,plain,
! [SV245: $i,SV260: $i,SV208: $i,SV176: $i] :
( ( ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SV260 ) ) @ SV245 )
= $false )
| ( ( ( SV208 = SV245 )
| ( contains_slb @ SV176 @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[771]) ).
thf(789,plain,
! [SV176: $i,SV265: $i,SV208: $i] :
( ( ( SV208 != SV265 )
| ! [SY523: $i] : ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY523 ) ) @ SV265 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(790,plain,
! [SV208: $i,SV266: $i,SV176: $i] :
( ( ~ ( contains_slb @ SV176 @ SV266 )
| ! [SY524: $i] : ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY524 ) ) @ SV266 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(791,plain,
! [SV261: $i,SV252: $i] :
( ( ( ~ ( strictly_less_than @ SV252 @ SV261 ) )
= $true )
| ( ( less_than @ SV252 @ SV261 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[775]) ).
thf(792,plain,
! [SV262: $i,SV253: $i] :
( ( ( ~ ( strictly_less_than @ SV253 @ SV262 ) )
= $true )
| ( ( ~ ( less_than @ SV262 @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[776]) ).
thf(793,plain,
! [SV223: $i,SV267: $i,SV205: $i,SV173: $i] :
( ( ! [SY525: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SV267 ) ) @ SV223 @ SY525 )
| ( SV205 = SV223 )
| ( pair_in_list @ SV173 @ SV223 @ SY525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(794,plain,
! [SV223: $i,SV268: $i,SV205: $i,SV173: $i] :
( ( ! [SY526: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SV268 ) ) @ SV223 @ SY526 )
| ( SV268 = SY526 )
| ( pair_in_list @ SV173 @ SV223 @ SY526 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(795,plain,
! [SV173: $i,SV269: $i,SV223: $i,SV205: $i] :
( ( ! [SY527: $i] :
( ( SV205 != SV223 )
| ( SV269 != SY527 )
| ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SV269 ) ) @ SV223 @ SY527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(796,plain,
! [SV270: $i,SV205: $i,SV223: $i,SV173: $i] :
( ( ! [SY528: $i] :
( ~ ( pair_in_list @ SV173 @ SV223 @ SY528 )
| ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SV270 ) ) @ SV223 @ SY528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(797,plain,
( ( ( ~ ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 ) )
= $false )
| ( sK14_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[782]) ).
thf(798,plain,
( ( ( ~ ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) )
= $false )
| ( sK14_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[782]) ).
thf(799,plain,
! [SV242: $i,SV239: $i,SV264: $i,SV257: $i] :
( ( ( ~ ( pair_in_list @ sK1_U @ SV257 @ SV264 ) )
= $true )
| ( ( less_than @ SV264 @ SV257 )
= $true )
| ( ( check_cpq @ ( triple @ SV239 @ sK1_U @ SV242 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[783]) ).
thf(800,plain,
! [SV224: $i,SV207: $i,SV175: $i,SV250: $i,SV258: $i] :
( ( ( less_than @ SV258 @ SV250 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SV207 @ ( pair @ SV250 @ SV258 ) ) @ SV224 ) )
| ( check_cpq @ ( triple @ SV175 @ SV207 @ SV224 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[786]) ).
thf(801,plain,
! [SV224: $i,SV207: $i,SV175: $i,SV251: $i,SV259: $i] :
( ( ( less_than @ SV259 @ SV251 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV175 @ SV207 @ SV224 ) )
| ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SV207 @ ( pair @ SV251 @ SV259 ) ) @ SV224 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(802,plain,
! [SV260: $i,SV176: $i,SV245: $i,SV208: $i] :
( ( ( SV208 = SV245 )
= $true )
| ( ( contains_slb @ SV176 @ SV245 )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SV260 ) ) @ SV245 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[788]) ).
thf(803,plain,
! [SV176: $i,SV265: $i,SV208: $i] :
( ( ( ( SV208 != SV265 ) )
= $true )
| ( ( ! [SY523: $i] : ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY523 ) ) @ SV265 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[789]) ).
thf(804,plain,
! [SV208: $i,SV266: $i,SV176: $i] :
( ( ( ~ ( contains_slb @ SV176 @ SV266 ) )
= $true )
| ( ( ! [SY524: $i] : ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY524 ) ) @ SV266 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[790]) ).
thf(805,plain,
! [SV261: $i,SV252: $i] :
( ( ( strictly_less_than @ SV252 @ SV261 )
= $false )
| ( ( less_than @ SV252 @ SV261 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[791]) ).
thf(806,plain,
! [SV262: $i,SV253: $i] :
( ( ( strictly_less_than @ SV253 @ SV262 )
= $false )
| ( ( ~ ( less_than @ SV262 @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[792]) ).
thf(807,plain,
! [SV271: $i,SV223: $i,SV267: $i,SV205: $i,SV173: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SV267 ) ) @ SV223 @ SV271 )
| ( SV205 = SV223 )
| ( pair_in_list @ SV173 @ SV223 @ SV271 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(808,plain,
! [SV272: $i,SV223: $i,SV268: $i,SV205: $i,SV173: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SV268 ) ) @ SV223 @ SV272 )
| ( SV268 = SV272 )
| ( pair_in_list @ SV173 @ SV223 @ SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(809,plain,
! [SV173: $i,SV273: $i,SV269: $i,SV223: $i,SV205: $i] :
( ( ( SV205 != SV223 )
| ( SV269 != SV273 )
| ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SV269 ) ) @ SV223 @ SV273 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(810,plain,
! [SV270: $i,SV205: $i,SV274: $i,SV223: $i,SV173: $i] :
( ( ~ ( pair_in_list @ SV173 @ SV223 @ SV274 )
| ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SV270 ) ) @ SV223 @ SV274 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(811,plain,
( ( ( pair_in_list @ sK1_U @ sK12_SY130 @ sK13_SY167 )
= $true )
| ( sK14_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[797]) ).
thf(812,plain,
( ( ( ~ ( less_than @ sK13_SY167 @ sK12_SY130 ) )
= $true )
| ( sK14_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[798]) ).
thf(813,plain,
! [SV242: $i,SV239: $i,SV264: $i,SV257: $i] :
( ( ( pair_in_list @ sK1_U @ SV257 @ SV264 )
= $false )
| ( ( less_than @ SV264 @ SV257 )
= $true )
| ( ( check_cpq @ ( triple @ SV239 @ sK1_U @ SV242 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(814,plain,
! [SV224: $i,SV258: $i,SV250: $i,SV207: $i,SV175: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SV207 @ ( pair @ SV250 @ SV258 ) ) @ SV224 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV175 @ SV207 @ SV224 ) )
= $true )
| ( ( less_than @ SV258 @ SV250 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[800]) ).
thf(815,plain,
! [SV259: $i,SV251: $i,SV224: $i,SV207: $i,SV175: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV175 @ SV207 @ SV224 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SV207 @ ( pair @ SV251 @ SV259 ) ) @ SV224 ) )
= $true )
| ( ( less_than @ SV259 @ SV251 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[801]) ).
thf(816,plain,
! [SV176: $i,SV265: $i,SV208: $i] :
( ( ( SV208 = SV265 )
= $false )
| ( ( ! [SY523: $i] : ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY523 ) ) @ SV265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[803]) ).
thf(817,plain,
! [SV208: $i,SV266: $i,SV176: $i] :
( ( ( contains_slb @ SV176 @ SV266 )
= $false )
| ( ( ! [SY524: $i] : ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SY524 ) ) @ SV266 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[804]) ).
thf(818,plain,
! [SV253: $i,SV262: $i] :
( ( ( less_than @ SV262 @ SV253 )
= $false )
| ( ( strictly_less_than @ SV253 @ SV262 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(819,plain,
! [SV271: $i,SV223: $i,SV267: $i,SV205: $i,SV173: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SV267 ) ) @ SV223 @ SV271 ) )
= $true )
| ( ( ( SV205 = SV223 )
| ( pair_in_list @ SV173 @ SV223 @ SV271 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[807]) ).
thf(820,plain,
! [SV272: $i,SV223: $i,SV268: $i,SV205: $i,SV173: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SV268 ) ) @ SV223 @ SV272 ) )
= $true )
| ( ( ( SV268 = SV272 )
| ( pair_in_list @ SV173 @ SV223 @ SV272 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[808]) ).
thf(821,plain,
! [SV173: $i,SV273: $i,SV269: $i,SV223: $i,SV205: $i] :
( ( ( ( SV205 != SV223 )
| ( SV269 != SV273 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SV269 ) ) @ SV223 @ SV273 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[809]) ).
thf(822,plain,
! [SV270: $i,SV205: $i,SV274: $i,SV223: $i,SV173: $i] :
( ( ( ~ ( pair_in_list @ SV173 @ SV223 @ SV274 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SV270 ) ) @ SV223 @ SV274 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[810]) ).
thf(823,plain,
( ( ( less_than @ sK13_SY167 @ sK12_SY130 )
= $false )
| ( sK14_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(824,plain,
! [SV224: $i,SV258: $i,SV250: $i,SV207: $i,SV175: $i] :
( ( ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SV207 @ ( pair @ SV250 @ SV258 ) ) @ SV224 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV175 @ SV207 @ SV224 ) )
= $true )
| ( ( less_than @ SV258 @ SV250 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[814]) ).
thf(825,plain,
! [SV259: $i,SV251: $i,SV224: $i,SV207: $i,SV175: $i] :
( ( ( check_cpq @ ( triple @ SV175 @ SV207 @ SV224 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV175 @ ( insert_slb @ SV207 @ ( pair @ SV251 @ SV259 ) ) @ SV224 ) )
= $true )
| ( ( less_than @ SV259 @ SV251 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[815]) ).
thf(826,plain,
! [SV265: $i,SV275: $i,SV208: $i,SV176: $i] :
( ( ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SV275 ) ) @ SV265 )
= $true )
| ( ( SV208 = SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(827,plain,
! [SV266: $i,SV276: $i,SV208: $i,SV176: $i] :
( ( ( contains_slb @ ( insert_slb @ SV176 @ ( pair @ SV208 @ SV276 ) ) @ SV266 )
= $true )
| ( ( contains_slb @ SV176 @ SV266 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(828,plain,
! [SV271: $i,SV223: $i,SV267: $i,SV205: $i,SV173: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SV267 ) ) @ SV223 @ SV271 )
= $false )
| ( ( ( SV205 = SV223 )
| ( pair_in_list @ SV173 @ SV223 @ SV271 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[819]) ).
thf(829,plain,
! [SV272: $i,SV223: $i,SV268: $i,SV205: $i,SV173: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SV268 ) ) @ SV223 @ SV272 )
= $false )
| ( ( ( SV268 = SV272 )
| ( pair_in_list @ SV173 @ SV223 @ SV272 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[820]) ).
thf(830,plain,
! [SV173: $i,SV273: $i,SV269: $i,SV223: $i,SV205: $i] :
( ( ( ( SV205 != SV223 ) )
= $true )
| ( ( ( SV269 != SV273 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SV269 ) ) @ SV223 @ SV273 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[821]) ).
thf(831,plain,
! [SV270: $i,SV205: $i,SV274: $i,SV223: $i,SV173: $i] :
( ( ( pair_in_list @ SV173 @ SV223 @ SV274 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SV270 ) ) @ SV223 @ SV274 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[822]) ).
thf(832,plain,
! [SV267: $i,SV271: $i,SV173: $i,SV223: $i,SV205: $i] :
( ( ( SV205 = SV223 )
= $true )
| ( ( pair_in_list @ SV173 @ SV223 @ SV271 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SV267 ) ) @ SV223 @ SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[828]) ).
thf(833,plain,
! [SV205: $i,SV223: $i,SV173: $i,SV272: $i,SV268: $i] :
( ( ( SV268 = SV272 )
= $true )
| ( ( pair_in_list @ SV173 @ SV223 @ SV272 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SV268 ) ) @ SV223 @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[829]) ).
thf(834,plain,
! [SV173: $i,SV273: $i,SV269: $i,SV223: $i,SV205: $i] :
( ( ( SV205 = SV223 )
= $false )
| ( ( ( SV269 != SV273 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SV269 ) ) @ SV223 @ SV273 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[830]) ).
thf(835,plain,
! [SV173: $i,SV223: $i,SV205: $i,SV273: $i,SV269: $i] :
( ( ( SV269 = SV273 )
= $false )
| ( ( SV205 = SV223 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV173 @ ( pair @ SV205 @ SV269 ) ) @ SV223 @ SV273 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(836,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[531,835,833,832,831,827,826,825,824,823,818,813,811,805,802,785,784,781,774,759,758,757,756,755,754,733,732,731,710,709,688,685,683,682,676,664,657,656,654,653,626,617,615,614,613,612,599,595,587,575,564,563,544,541,533,532]) ).
thf(837,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[836,478]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV406+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 15 09:37:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.39 .
% 0.13/0.39
% 0.13/0.39 No.of.Axioms: 41
% 0.13/0.39
% 0.13/0.39 Length.of.Defs: 0
% 0.13/0.39
% 0.13/0.39 Contains.Choice.Funs: false
% 0.19/0.44 .
% 0.19/0.44 (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).......................................................
% 0.98/1.18
% 0.98/1.18 ********************************
% 0.98/1.18 * All subproblems solved! *
% 0.98/1.18 ********************************
% 0.98/1.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:42,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:836,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.24/1.43
% 1.24/1.43 %**** Beginning of derivation protocol ****
% 1.24/1.43 % SZS output start CNFRefutation
% See solution above
% 1.24/1.43
% 1.24/1.43 %**** End of derivation protocol ****
% 1.24/1.43 %**** no. of clauses in derivation: 837 ****
% 1.24/1.43 %**** clause counter: 836 ****
% 1.24/1.43
% 1.24/1.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:42,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:836,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------