TSTP Solution File: SWV371+1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SWV371+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 : n006.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 20:12:09 EDT 2022
% Result : Theorem 1.66s 1.87s
% Output : CNFRefutation 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 117
% Syntax : Number of formulae : 806 ( 518 unt; 52 typ; 0 def)
% Number of atoms : 3954 (1405 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 9100 (1125 ~;1096 |; 90 &;6697 @)
% ( 32 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 76 ( 76 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 52 usr; 9 con; 0-3 aty)
% Number of variables : 2365 ( 0 ^2359 !; 6 ?;2365 :)
% 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_pq,type,
contains_pq: $i > $i > $o ).
thf(tp_contains_slb,type,
contains_slb: $i > $i > $o ).
thf(tp_create_pq,type,
create_pq: $i ).
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_pq_eff,type,
findmin_pq_eff: $i > $i > $i ).
thf(tp_findmin_pq_res,type,
findmin_pq_res: $i > $i > $i ).
thf(tp_findmin_pqp_res,type,
findmin_pqp_res: $i > $i ).
thf(tp_i,type,
i: $i > $i ).
thf(tp_insert_cpq,type,
insert_cpq: $i > $i > $i ).
thf(tp_insert_pq,type,
insert_pq: $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_pq,type,
isnonempty_pq: $i > $o ).
thf(tp_isnonempty_slb,type,
isnonempty_slb: $i > $o ).
thf(tp_issmallestelement_pq,type,
issmallestelement_pq: $i > $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_phi,type,
phi: $i > $o ).
thf(tp_pi_find_min,type,
pi_find_min: $i > $o ).
thf(tp_pi_remove,type,
pi_remove: $i > $i > $o ).
thf(tp_pi_removemin,type,
pi_removemin: $i > $o ).
thf(tp_pi_sharp_find_min,type,
pi_sharp_find_min: $i > $i > $o ).
thf(tp_pi_sharp_remove,type,
pi_sharp_remove: $i > $i > $o ).
thf(tp_pi_sharp_removemin,type,
pi_sharp_removemin: $i > $i > $o ).
thf(tp_remove_cpq,type,
remove_cpq: $i > $i > $i ).
thf(tp_remove_pq,type,
remove_pq: $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_removemin_pq_eff,type,
removemin_pq_eff: $i > $i > $i ).
thf(tp_removemin_pq_res,type,
removemin_pq_res: $i > $i > $i ).
thf(tp_sK1_U,type,
sK1_U: $i ).
thf(tp_sK2_SY172,type,
sK2_SY172: $i ).
thf(tp_sK3_SY174,type,
sK3_SY174: $i ).
thf(tp_sK4_V,type,
sK4_V: $i > $i ).
thf(tp_sK5_V,type,
sK5_V: $i > $i ).
thf(tp_sK6_V,type,
sK6_V: $i > $i ).
thf(tp_sK7_W,type,
sK7_W: $i > $i > $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] :
( ( phi @ U )
<=> ? [V: $i] :
( ( succ_cpq @ U @ V )
& ( ok @ V )
& ( check_cpq @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax62) ).
thf(2,axiom,
! [U: $i] :
( ( pi_removemin @ U )
<=> ? [V: $i] : ( pi_sharp_find_min @ ( i @ U ) @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax61) ).
thf(3,axiom,
! [U: $i,V: $i] :
( ( pi_sharp_removemin @ U @ V )
<=> ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60) ).
thf(4,axiom,
! [U: $i] :
( ( pi_find_min @ U )
<=> ? [V: $i] : ( pi_sharp_find_min @ ( i @ U ) @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax59) ).
thf(5,axiom,
! [U: $i,V: $i] :
( ( pi_sharp_find_min @ U @ V )
<=> ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
thf(6,axiom,
! [U: $i,V: $i] :
( ( pi_remove @ U @ V )
<=> ( pi_sharp_remove @ ( i @ U ) @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
thf(7,axiom,
! [U: $i,V: $i] :
( ( pi_sharp_remove @ U @ V )
<=> ( contains_pq @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax56) ).
thf(8,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( i @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
= ( insert_pq @ ( i @ ( triple @ U @ V @ W ) ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
thf(9,axiom,
! [U: $i,V: $i] :
( ( i @ ( triple @ U @ create_slb @ V ) )
= create_pq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax54) ).
thf(10,axiom,
! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).
thf(11,axiom,
! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
thf(12,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( V != create_slb )
=> ( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
= ( findmin_pqp_res @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).
thf(13,axiom,
! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax50) ).
thf(14,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != create_slb )
& ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
& ( less_than @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) @ ( findmin_pqp_res @ U ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).
thf(15,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != create_slb )
& ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
& ( strictly_less_than @ ( findmin_pqp_res @ U ) @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax48) ).
thf(16,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != create_slb )
& ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax47) ).
thf(17,axiom,
! [U: $i,V: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ create_slb @ V ) )
= ( triple @ U @ create_slb @ bad ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).
thf(18,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( contains_slb @ V @ X )
& ( strictly_less_than @ X @ ( lookup_slb @ V @ X ) ) )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ bad ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).
thf(19,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( contains_slb @ V @ X )
& ( less_than @ ( lookup_slb @ V @ X ) @ X ) )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax44) ).
thf(20,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ U @ V @ bad ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax43) ).
thf(21,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( insert_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( insert_pqp @ U @ X ) @ ( insert_slb @ V @ ( pair @ X @ bottom ) ) @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).
thf(22,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ( W = bad ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax41) ).
thf(23,axiom,
! [U: $i,V: $i] :
( ( ok @ ( triple @ U @ V @ bad ) )
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax40) ).
thf(24,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
<=> ( contains_slb @ V @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
thf(25,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( strictly_less_than @ X @ Y )
=> ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
<=> $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
thf(26,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( less_than @ Y @ X )
=> ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
<=> ( check_cpq @ ( triple @ U @ V @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax37) ).
thf(27,axiom,
! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).
thf(28,axiom,
! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax35) ).
thf(29,axiom,
! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax34) ).
thf(30,axiom,
! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax33) ).
thf(31,axiom,
! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax32) ).
thf(32,axiom,
! [U: $i] : ( succ_cpq @ U @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).
thf(33,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( less_than @ W @ X )
=> ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax30) ).
thf(34,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( strictly_less_than @ X @ W )
=> ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax29) ).
thf(35,axiom,
! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
thf(36,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != W )
& ( contains_slb @ U @ W ) )
=> ( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( lookup_slb @ U @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax27) ).
thf(37,axiom,
! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
thf(38,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != W )
& ( contains_slb @ U @ W ) )
=> ( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( remove_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).
thf(39,axiom,
! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
thf(40,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
<=> ( ( pair_in_list @ U @ W @ Y )
| ( ( V = W )
& ( X = Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
thf(41,axiom,
! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
thf(42,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
<=> ( ( contains_slb @ U @ W )
| ( V = W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
thf(43,axiom,
! [U: $i] :
~ ( contains_slb @ create_slb @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
thf(44,axiom,
! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax19) ).
thf(45,axiom,
~ ( isnonempty_slb @ create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
thf(46,axiom,
! [U: $i,V: $i,W: $i] :
( ( insert_pq @ ( insert_pq @ U @ V ) @ W )
= ( insert_pq @ ( insert_pq @ U @ W ) @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
thf(47,axiom,
! [U: $i,V: $i] :
( ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) )
=> ( ( removemin_pq_res @ U @ V )
= V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
thf(48,axiom,
! [U: $i,V: $i] :
( ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) )
=> ( ( removemin_pq_eff @ U @ V )
= ( remove_pq @ U @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
thf(49,axiom,
! [U: $i,V: $i] :
( ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) )
=> ( ( findmin_pq_res @ U @ V )
= V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax14) ).
thf(50,axiom,
! [U: $i,V: $i] :
( ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) )
=> ( ( findmin_pq_eff @ U @ V )
= U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax13) ).
thf(51,axiom,
! [U: $i,V: $i,W: $i] :
( ( ( contains_pq @ U @ W )
& ( V != W ) )
=> ( ( remove_pq @ ( insert_pq @ U @ V ) @ W )
= ( insert_pq @ ( remove_pq @ U @ W ) @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax12) ).
thf(52,axiom,
! [U: $i,V: $i] :
( ( remove_pq @ ( insert_pq @ U @ V ) @ V )
= U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11) ).
thf(53,axiom,
! [U: $i,V: $i] :
( ( issmallestelement_pq @ U @ V )
<=> ! [W: $i] :
( ( contains_pq @ U @ W )
=> ( less_than @ V @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10) ).
thf(54,axiom,
! [U: $i,V: $i,W: $i] :
( ( contains_pq @ ( insert_pq @ U @ V ) @ W )
<=> ( ( contains_pq @ U @ W )
| ( V = W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax9) ).
thf(55,axiom,
! [U: $i] :
~ ( contains_pq @ create_pq @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8) ).
thf(56,axiom,
! [U: $i,V: $i] : ( isnonempty_pq @ ( insert_pq @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).
thf(57,axiom,
~ ( isnonempty_pq @ create_pq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
thf(58,axiom,
! [U: $i] : ( less_than @ bottom @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bottom_smallest) ).
thf(59,axiom,
! [U: $i,V: $i] :
( ( strictly_less_than @ U @ V )
<=> ( ( less_than @ U @ V )
& ~ ( less_than @ V @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).
thf(60,axiom,
! [U: $i] : ( less_than @ U @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(61,axiom,
! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
thf(62,axiom,
! [U: $i,V: $i,W: $i] :
( ( ( less_than @ U @ V )
& ( less_than @ V @ W ) )
=> ( less_than @ U @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(63,axiom,
! [U: $i,V: $i,W: $i] :
( ( phi @ ( findmin_cpq_eff @ ( triple @ U @ V @ W ) ) )
=> ( issmallestelement_pq @ ( i @ ( triple @ U @ V @ W ) ) @ ( findmin_cpq_res @ ( triple @ U @ V @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l7_lX) ).
thf(64,axiom,
! [U: $i,V: $i,W: $i] :
( ( phi @ ( findmin_cpq_eff @ ( triple @ U @ V @ W ) ) )
=> ( contains_pq @ ( i @ ( triple @ U @ V @ W ) ) @ ( findmin_cpq_res @ ( triple @ U @ V @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l7_l8) ).
thf(65,conjecture,
! [U: $i,V: $i,W: $i] :
( ( phi @ ( findmin_cpq_eff @ ( triple @ U @ V @ W ) ) )
=> ( pi_sharp_find_min @ ( i @ ( triple @ U @ V @ W ) ) @ ( findmin_cpq_res @ ( triple @ U @ V @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l7_co) ).
thf(66,negated_conjecture,
( ( ! [U: $i,V: $i,W: $i] :
( ( phi @ ( findmin_cpq_eff @ ( triple @ U @ V @ W ) ) )
=> ( pi_sharp_find_min @ ( i @ ( triple @ U @ V @ W ) ) @ ( findmin_cpq_res @ ( triple @ U @ V @ W ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[65]) ).
thf(67,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( phi @ ( findmin_cpq_eff @ ( triple @ U @ V @ W ) ) )
=> ( pi_sharp_find_min @ ( i @ ( triple @ U @ V @ W ) ) @ ( findmin_cpq_res @ ( triple @ U @ V @ W ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[66]) ).
thf(68,plain,
( ( ! [U: $i] :
( ( phi @ U )
<=> ? [V: $i] :
( ( succ_cpq @ U @ V )
& ( ok @ V )
& ( check_cpq @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(69,plain,
( ( ! [U: $i] :
( ( pi_removemin @ U )
<=> ? [V: $i] : ( pi_sharp_find_min @ ( i @ U ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(70,plain,
( ( ! [U: $i,V: $i] :
( ( pi_sharp_removemin @ U @ V )
<=> ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(71,plain,
( ( ! [U: $i] :
( ( pi_find_min @ U )
<=> ? [V: $i] : ( pi_sharp_find_min @ ( i @ U ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(72,plain,
( ( ! [U: $i,V: $i] :
( ( pi_sharp_find_min @ U @ V )
<=> ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(73,plain,
( ( ! [U: $i,V: $i] :
( ( pi_remove @ U @ V )
<=> ( pi_sharp_remove @ ( i @ U ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(74,plain,
( ( ! [U: $i,V: $i] :
( ( pi_sharp_remove @ U @ V )
<=> ( contains_pq @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(75,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( i @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
= ( insert_pq @ ( i @ ( triple @ U @ V @ W ) ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(76,plain,
( ( ! [U: $i,V: $i] :
( ( i @ ( triple @ U @ create_slb @ V ) )
= create_pq ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(77,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(78,plain,
( ( ! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(79,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)],[12]) ).
thf(80,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(81,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)],[14]) ).
thf(82,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)],[15]) ).
thf(83,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)],[16]) ).
thf(84,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ create_slb @ V ) )
= ( triple @ U @ create_slb @ bad ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(85,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)],[18]) ).
thf(86,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)],[19]) ).
thf(87,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)],[20]) ).
thf(88,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)],[21]) ).
thf(89,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ( W = bad ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(90,plain,
( ( ! [U: $i,V: $i] :
( ( ok @ ( triple @ U @ V @ bad ) )
<=> $false ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(91,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)],[24]) ).
thf(92,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)],[25]) ).
thf(93,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)],[26]) ).
thf(94,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(95,plain,
( ( ! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(96,plain,
( ( ! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(97,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(98,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(99,plain,
( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(100,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)],[33]) ).
thf(101,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)],[34]) ).
thf(102,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(103,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)],[36]) ).
thf(104,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(105,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)],[38]) ).
thf(106,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(107,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)],[40]) ).
thf(108,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(109,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)],[42]) ).
thf(110,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(111,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(112,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(113,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( insert_pq @ ( insert_pq @ U @ V ) @ W )
= ( insert_pq @ ( insert_pq @ U @ W ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(114,plain,
( ( ! [U: $i,V: $i] :
( ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) )
=> ( ( removemin_pq_res @ U @ V )
= V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(115,plain,
( ( ! [U: $i,V: $i] :
( ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) )
=> ( ( removemin_pq_eff @ U @ V )
= ( remove_pq @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(116,plain,
( ( ! [U: $i,V: $i] :
( ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) )
=> ( ( findmin_pq_res @ U @ V )
= V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(117,plain,
( ( ! [U: $i,V: $i] :
( ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) )
=> ( ( findmin_pq_eff @ U @ V )
= U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(118,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( contains_pq @ U @ W )
& ( V != W ) )
=> ( ( remove_pq @ ( insert_pq @ U @ V ) @ W )
= ( insert_pq @ ( remove_pq @ U @ W ) @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(119,plain,
( ( ! [U: $i,V: $i] :
( ( remove_pq @ ( insert_pq @ U @ V ) @ V )
= U ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(120,plain,
( ( ! [U: $i,V: $i] :
( ( issmallestelement_pq @ U @ V )
<=> ! [W: $i] :
( ( contains_pq @ U @ W )
=> ( less_than @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(121,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( contains_pq @ ( insert_pq @ U @ V ) @ W )
<=> ( ( contains_pq @ U @ W )
| ( V = W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(122,plain,
( ( ! [U: $i] :
~ ( contains_pq @ create_pq @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(123,plain,
( ( ! [U: $i,V: $i] : ( isnonempty_pq @ ( insert_pq @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(124,plain,
( ( ~ ( isnonempty_pq @ create_pq ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(125,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(126,plain,
( ( ! [U: $i,V: $i] :
( ( strictly_less_than @ U @ V )
<=> ( ( less_than @ U @ V )
& ~ ( less_than @ V @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(127,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(128,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(129,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)],[62]) ).
thf(130,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( phi @ ( findmin_cpq_eff @ ( triple @ U @ V @ W ) ) )
=> ( issmallestelement_pq @ ( i @ ( triple @ U @ V @ W ) ) @ ( findmin_cpq_res @ ( triple @ U @ V @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(131,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( phi @ ( findmin_cpq_eff @ ( triple @ U @ V @ W ) ) )
=> ( contains_pq @ ( i @ ( triple @ U @ V @ W ) ) @ ( findmin_cpq_res @ ( triple @ U @ V @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(132,plain,
( ( ! [SY172: $i,SY173: $i] :
( ( phi @ ( findmin_cpq_eff @ ( triple @ sK1_U @ SY172 @ SY173 ) ) )
=> ( pi_sharp_find_min @ ( i @ ( triple @ sK1_U @ SY172 @ SY173 ) ) @ ( findmin_cpq_res @ ( triple @ sK1_U @ SY172 @ SY173 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[67]) ).
thf(133,plain,
( ( ! [SY174: $i] :
( ( phi @ ( findmin_cpq_eff @ ( triple @ sK1_U @ sK2_SY172 @ SY174 ) ) )
=> ( pi_sharp_find_min @ ( i @ ( triple @ sK1_U @ sK2_SY172 @ SY174 ) ) @ ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY172 @ SY174 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[132]) ).
thf(134,plain,
( ( ( phi @ ( findmin_cpq_eff @ ( triple @ sK1_U @ sK2_SY172 @ sK3_SY174 ) ) )
=> ( pi_sharp_find_min @ ( i @ ( triple @ sK1_U @ sK2_SY172 @ sK3_SY174 ) ) @ ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY172 @ sK3_SY174 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[133]) ).
thf(135,plain,
( ( phi @ ( findmin_cpq_eff @ ( triple @ sK1_U @ sK2_SY172 @ sK3_SY174 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[134]) ).
thf(136,plain,
( ( pi_sharp_find_min @ ( i @ ( triple @ sK1_U @ sK2_SY172 @ sK3_SY174 ) ) @ ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY172 @ sK3_SY174 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[134]) ).
thf(137,plain,
( ( ~ ( pi_sharp_find_min @ ( i @ ( triple @ sK1_U @ sK2_SY172 @ sK3_SY174 ) ) @ ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY172 @ sK3_SY174 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[136]) ).
thf(138,plain,
( ( ! [U: $i] :
( ! [V: $i] :
( ~ ( ok @ V )
| ~ ( succ_cpq @ U @ V )
| ~ ( check_cpq @ V ) )
| ( phi @ U ) )
& ! [U: $i] :
( ~ ( phi @ U )
| ( ( ok @ ( sK4_V @ U ) )
& ( succ_cpq @ U @ ( sK4_V @ U ) )
& ( check_cpq @ ( sK4_V @ U ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[68]) ).
thf(139,plain,
( ( ! [U: $i] :
( ! [V: $i] :
~ ( pi_sharp_find_min @ ( i @ U ) @ V )
| ( pi_removemin @ U ) )
& ! [U: $i] :
( ~ ( pi_removemin @ U )
| ( pi_sharp_find_min @ ( i @ U ) @ ( sK5_V @ U ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(140,plain,
( ( ! [U: $i,V: $i] :
( ~ ( contains_pq @ U @ V )
| ~ ( issmallestelement_pq @ U @ V )
| ( pi_sharp_removemin @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( pi_sharp_removemin @ U @ V )
| ( contains_pq @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( pi_sharp_removemin @ U @ V )
| ( issmallestelement_pq @ U @ V ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(141,plain,
( ( ! [U: $i] :
( ! [V: $i] :
~ ( pi_sharp_find_min @ ( i @ U ) @ V )
| ( pi_find_min @ U ) )
& ! [U: $i] :
( ~ ( pi_find_min @ U )
| ( pi_sharp_find_min @ ( i @ U ) @ ( sK6_V @ U ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[71]) ).
thf(142,plain,
( ( ! [U: $i,V: $i] :
( ~ ( contains_pq @ U @ V )
| ~ ( issmallestelement_pq @ U @ V )
| ( pi_sharp_find_min @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( pi_sharp_find_min @ U @ V )
| ( contains_pq @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( pi_sharp_find_min @ U @ V )
| ( issmallestelement_pq @ U @ V ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[72]) ).
thf(143,plain,
( ( ! [U: $i,V: $i] :
( ~ ( pi_remove @ U @ V )
| ( pi_sharp_remove @ ( i @ U ) @ V ) )
& ! [U: $i,V: $i] :
( ~ ( pi_sharp_remove @ ( i @ U ) @ V )
| ( pi_remove @ U @ V ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[73]) ).
thf(144,plain,
( ( ! [U: $i,V: $i] :
( ~ ( contains_pq @ U @ V )
| ( pi_sharp_remove @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( pi_sharp_remove @ U @ V )
| ( contains_pq @ U @ V ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(145,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)],[79]) ).
thf(146,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)],[81]) ).
thf(147,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)],[82]) ).
thf(148,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)],[83]) ).
thf(149,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)],[85]) ).
thf(150,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)],[86]) ).
thf(151,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)],[87]) ).
thf(152,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( triple @ U @ V @ W ) )
| ( W = bad ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[89]) ).
thf(153,plain,
( ( ! [U: $i,V: $i] :
~ ( ok @ ( triple @ U @ V @ bad ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[90]) ).
thf(154,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)],[91]) ).
thf(155,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)],[92]) ).
thf(156,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)],[93]) ).
thf(157,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[95]) ).
thf(158,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[96]) ).
thf(159,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[97]) ).
thf(160,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[98]) ).
thf(161,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)],[100]) ).
thf(162,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)],[101]) ).
thf(163,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)],[103]) ).
thf(164,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)],[105]) ).
thf(165,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)],[107]) ).
thf(166,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)],[109]) ).
thf(167,plain,
( ( ! [U: $i,V: $i] :
( ~ ( contains_pq @ U @ V )
| ~ ( issmallestelement_pq @ U @ V )
| ( ( removemin_pq_res @ U @ V )
= V ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[114]) ).
thf(168,plain,
( ( ! [U: $i,V: $i] :
( ~ ( contains_pq @ U @ V )
| ~ ( issmallestelement_pq @ U @ V )
| ( ( removemin_pq_eff @ U @ V )
= ( remove_pq @ U @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[115]) ).
thf(169,plain,
( ( ! [U: $i,V: $i] :
( ~ ( contains_pq @ U @ V )
| ~ ( issmallestelement_pq @ U @ V )
| ( ( findmin_pq_res @ U @ V )
= V ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[116]) ).
thf(170,plain,
( ( ! [U: $i,V: $i] :
( ~ ( contains_pq @ U @ V )
| ~ ( issmallestelement_pq @ U @ V )
| ( ( findmin_pq_eff @ U @ V )
= U ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[117]) ).
thf(171,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( V = W )
| ~ ( contains_pq @ U @ W )
| ( ( remove_pq @ ( insert_pq @ U @ V ) @ W )
= ( insert_pq @ ( remove_pq @ U @ W ) @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[118]) ).
thf(172,plain,
( ( ! [U: $i,V: $i] :
( ( ( contains_pq @ U @ ( sK7_W @ V @ U ) )
& ~ ( less_than @ V @ ( sK7_W @ V @ U ) ) )
| ( issmallestelement_pq @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( issmallestelement_pq @ U @ V )
| ! [W: $i] :
( ~ ( contains_pq @ U @ W )
| ( less_than @ V @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[120]) ).
thf(173,plain,
( ( ! [U: $i] :
( ! [V: $i,W: $i] :
( ~ ( contains_pq @ ( insert_pq @ U @ V ) @ W )
| ( V = W )
| ( contains_pq @ U @ W ) )
& ! [V: $i,W: $i] :
( ( V != W )
| ( contains_pq @ ( insert_pq @ U @ V ) @ W ) )
& ! [V: $i,W: $i] :
( ~ ( contains_pq @ U @ W )
| ( contains_pq @ ( insert_pq @ U @ V ) @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[121]) ).
thf(174,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)],[126]) ).
thf(175,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)],[129]) ).
thf(176,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( phi @ ( findmin_cpq_eff @ ( triple @ U @ V @ W ) ) )
| ( issmallestelement_pq @ ( i @ ( triple @ U @ V @ W ) ) @ ( findmin_cpq_res @ ( triple @ U @ V @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[130]) ).
thf(177,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( phi @ ( findmin_cpq_eff @ ( triple @ U @ V @ W ) ) )
| ( contains_pq @ ( i @ ( triple @ U @ V @ W ) ) @ ( findmin_cpq_res @ ( triple @ U @ V @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[131]) ).
thf(178,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( phi @ ( findmin_cpq_eff @ ( triple @ U @ V @ W ) ) )
| ( contains_pq @ ( i @ ( triple @ U @ V @ W ) ) @ ( findmin_cpq_res @ ( triple @ U @ V @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(179,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( phi @ ( findmin_cpq_eff @ ( triple @ U @ V @ W ) ) )
| ( issmallestelement_pq @ ( i @ ( triple @ U @ V @ W ) ) @ ( findmin_cpq_res @ ( triple @ U @ V @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(180,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( less_than @ U @ V )
| ~ ( less_than @ V @ W )
| ( less_than @ U @ W ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(181,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(182,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(183,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)],[174]) ).
thf(184,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(185,plain,
( ( ~ ( isnonempty_pq @ create_pq ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(186,plain,
( ( ! [U: $i,V: $i] : ( isnonempty_pq @ ( insert_pq @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(187,plain,
( ( ! [U: $i] :
~ ( contains_pq @ create_pq @ U ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(188,plain,
( ( ! [U: $i] :
( ! [V: $i,W: $i] :
( ~ ( contains_pq @ ( insert_pq @ U @ V ) @ W )
| ( V = W )
| ( contains_pq @ U @ W ) )
& ! [V: $i,W: $i] :
( ( V != W )
| ( contains_pq @ ( insert_pq @ U @ V ) @ W ) )
& ! [V: $i,W: $i] :
( ~ ( contains_pq @ U @ W )
| ( contains_pq @ ( insert_pq @ U @ V ) @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(189,plain,
( ( ! [U: $i,V: $i] :
( ( ( contains_pq @ U @ ( sK7_W @ V @ U ) )
& ~ ( less_than @ V @ ( sK7_W @ V @ U ) ) )
| ( issmallestelement_pq @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( issmallestelement_pq @ U @ V )
| ! [W: $i] :
( ~ ( contains_pq @ U @ W )
| ( less_than @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(190,plain,
( ( ! [U: $i,V: $i] :
( ( remove_pq @ ( insert_pq @ U @ V ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(191,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( V = W )
| ~ ( contains_pq @ U @ W )
| ( ( remove_pq @ ( insert_pq @ U @ V ) @ W )
= ( insert_pq @ ( remove_pq @ U @ W ) @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(192,plain,
( ( ! [U: $i,V: $i] :
( ~ ( contains_pq @ U @ V )
| ~ ( issmallestelement_pq @ U @ V )
| ( ( findmin_pq_eff @ U @ V )
= U ) ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(193,plain,
( ( ! [U: $i,V: $i] :
( ~ ( contains_pq @ U @ V )
| ~ ( issmallestelement_pq @ U @ V )
| ( ( findmin_pq_res @ U @ V )
= V ) ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(194,plain,
( ( ! [U: $i,V: $i] :
( ~ ( contains_pq @ U @ V )
| ~ ( issmallestelement_pq @ U @ V )
| ( ( removemin_pq_eff @ U @ V )
= ( remove_pq @ U @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(195,plain,
( ( ! [U: $i,V: $i] :
( ~ ( contains_pq @ U @ V )
| ~ ( issmallestelement_pq @ U @ V )
| ( ( removemin_pq_res @ U @ V )
= V ) ) )
= $true ),
inference(copy,[status(thm)],[167]) ).
thf(196,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( insert_pq @ ( insert_pq @ U @ V ) @ W )
= ( insert_pq @ ( insert_pq @ U @ W ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(197,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(198,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(199,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(200,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)],[166]) ).
thf(201,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(202,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)],[165]) ).
thf(203,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(204,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)],[164]) ).
thf(205,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(206,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)],[163]) ).
thf(207,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(208,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)],[162]) ).
thf(209,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)],[161]) ).
thf(210,plain,
( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(211,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(212,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(213,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(214,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(215,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(216,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)],[156]) ).
thf(217,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)],[155]) ).
thf(218,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)],[154]) ).
thf(219,plain,
( ( ! [U: $i,V: $i] :
~ ( ok @ ( triple @ U @ V @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(220,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( triple @ U @ V @ W ) )
| ( W = bad ) ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(221,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)],[88]) ).
thf(222,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)],[151]) ).
thf(223,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)],[150]) ).
thf(224,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)],[149]) ).
thf(225,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ create_slb @ V ) )
= ( triple @ U @ create_slb @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(226,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)],[148]) ).
thf(227,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)],[147]) ).
thf(228,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)],[146]) ).
thf(229,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(230,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)],[145]) ).
thf(231,plain,
( ( ! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(232,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(233,plain,
( ( ! [U: $i,V: $i] :
( ( i @ ( triple @ U @ create_slb @ V ) )
= create_pq ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(234,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( i @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
= ( insert_pq @ ( i @ ( triple @ U @ V @ W ) ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(235,plain,
( ( ! [U: $i,V: $i] :
( ~ ( contains_pq @ U @ V )
| ( pi_sharp_remove @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( pi_sharp_remove @ U @ V )
| ( contains_pq @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[144]) ).
thf(236,plain,
( ( ! [U: $i,V: $i] :
( ~ ( pi_remove @ U @ V )
| ( pi_sharp_remove @ ( i @ U ) @ V ) )
& ! [U: $i,V: $i] :
( ~ ( pi_sharp_remove @ ( i @ U ) @ V )
| ( pi_remove @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(237,plain,
( ( ! [U: $i,V: $i] :
( ~ ( contains_pq @ U @ V )
| ~ ( issmallestelement_pq @ U @ V )
| ( pi_sharp_find_min @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( pi_sharp_find_min @ U @ V )
| ( contains_pq @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( pi_sharp_find_min @ U @ V )
| ( issmallestelement_pq @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(238,plain,
( ( ! [U: $i] :
( ! [V: $i] :
~ ( pi_sharp_find_min @ ( i @ U ) @ V )
| ( pi_find_min @ U ) )
& ! [U: $i] :
( ~ ( pi_find_min @ U )
| ( pi_sharp_find_min @ ( i @ U ) @ ( sK6_V @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(239,plain,
( ( ! [U: $i,V: $i] :
( ~ ( contains_pq @ U @ V )
| ~ ( issmallestelement_pq @ U @ V )
| ( pi_sharp_removemin @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( pi_sharp_removemin @ U @ V )
| ( contains_pq @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( pi_sharp_removemin @ U @ V )
| ( issmallestelement_pq @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(240,plain,
( ( ! [U: $i] :
( ! [V: $i] :
~ ( pi_sharp_find_min @ ( i @ U ) @ V )
| ( pi_removemin @ U ) )
& ! [U: $i] :
( ~ ( pi_removemin @ U )
| ( pi_sharp_find_min @ ( i @ U ) @ ( sK5_V @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(241,plain,
( ( ! [U: $i] :
( ! [V: $i] :
( ~ ( ok @ V )
| ~ ( succ_cpq @ U @ V )
| ~ ( check_cpq @ V ) )
| ( phi @ U ) )
& ! [U: $i] :
( ~ ( phi @ U )
| ( ( ok @ ( sK4_V @ U ) )
& ( succ_cpq @ U @ ( sK4_V @ U ) )
& ( check_cpq @ ( sK4_V @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(242,plain,
( ( phi @ ( findmin_cpq_eff @ ( triple @ sK1_U @ sK2_SY172 @ sK3_SY174 ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(243,plain,
( ( ~ ( pi_sharp_find_min @ ( i @ ( triple @ sK1_U @ sK2_SY172 @ sK3_SY174 ) ) @ ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY172 @ sK3_SY174 ) ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(244,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_find_min @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( pi_find_min @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK6_V @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(245,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)],[218]) ).
thf(246,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_removemin @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( pi_removemin @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK5_V @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(247,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)],[202]) ).
thf(248,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_remove @ SX0 @ SX1 )
| ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 )
| ( pi_remove @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(249,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)],[200]) ).
thf(250,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( ok @ SX1 )
| ~ ( succ_cpq @ SX0 @ SX1 )
| ~ ( check_cpq @ SX1 ) )
| ( phi @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( phi @ SX0 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK4_V @ SX0 ) )
| ~ ( succ_cpq @ SX0 @ ( sK4_V @ SX0 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(251,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)],[183]) ).
thf(252,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( contains_pq @ SX0 @ SX1 )
| ~ ( issmallestelement_pq @ SX0 @ SX1 )
| ( pi_sharp_find_min @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(253,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( contains_pq @ SX0 @ SX1 )
| ( pi_sharp_remove @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(254,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)],[216]) ).
thf(255,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( contains_pq @ SX0 @ ( sK7_W @ SX1 @ SX0 ) )
| ~ ~ ( less_than @ SX1 @ ( sK7_W @ SX1 @ SX0 ) ) )
| ( issmallestelement_pq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( issmallestelement_pq @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( contains_pq @ SX0 @ SX2 )
| ( less_than @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(256,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( contains_pq @ ( insert_pq @ SX0 @ SX1 ) @ SX2 )
| ( SX1 = SX2 )
| ( contains_pq @ SX0 @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( SX1 != SX2 )
| ( contains_pq @ ( insert_pq @ SX0 @ SX1 ) @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( contains_pq @ SX0 @ SX2 )
| ( contains_pq @ ( insert_pq @ SX0 @ SX1 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(257,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( contains_pq @ SX0 @ SX1 )
| ~ ( issmallestelement_pq @ SX0 @ SX1 )
| ( pi_sharp_removemin @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(258,plain,
! [SV1: $i] :
( ( ! [SY175: $i,SY176: $i] :
( ~ ( phi @ ( findmin_cpq_eff @ ( triple @ SV1 @ SY175 @ SY176 ) ) )
| ( contains_pq @ ( i @ ( triple @ SV1 @ SY175 @ SY176 ) ) @ ( findmin_cpq_res @ ( triple @ SV1 @ SY175 @ SY176 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(259,plain,
! [SV2: $i] :
( ( ! [SY177: $i,SY178: $i] :
( ~ ( phi @ ( findmin_cpq_eff @ ( triple @ SV2 @ SY177 @ SY178 ) ) )
| ( issmallestelement_pq @ ( i @ ( triple @ SV2 @ SY177 @ SY178 ) ) @ ( findmin_cpq_res @ ( triple @ SV2 @ SY177 @ SY178 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(260,plain,
! [SV3: $i] :
( ( ! [SY179: $i,SY180: $i] :
( ~ ( less_than @ SV3 @ SY179 )
| ~ ( less_than @ SY179 @ SY180 )
| ( less_than @ SV3 @ SY180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(261,plain,
! [SV4: $i] :
( ( ! [SY181: $i] :
( ( less_than @ SV4 @ SY181 )
| ( less_than @ SY181 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(262,plain,
! [SV5: $i] :
( ( less_than @ SV5 @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(263,plain,
! [SV6: $i] :
( ( less_than @ bottom @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(264,plain,
( ( isnonempty_pq @ create_pq )
= $false ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(265,plain,
! [SV7: $i] :
( ( ! [SY182: $i] : ( isnonempty_pq @ ( insert_pq @ SV7 @ SY182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(266,plain,
! [SV8: $i] :
( ( ~ ( contains_pq @ create_pq @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(267,plain,
! [SV9: $i] :
( ( ! [SY183: $i] :
( ( remove_pq @ ( insert_pq @ SV9 @ SY183 ) @ SY183 )
= SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(268,plain,
! [SV10: $i] :
( ( ! [SY184: $i,SY185: $i] :
( ( SY184 = SY185 )
| ~ ( contains_pq @ SV10 @ SY185 )
| ( ( remove_pq @ ( insert_pq @ SV10 @ SY184 ) @ SY185 )
= ( insert_pq @ ( remove_pq @ SV10 @ SY185 ) @ SY184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(269,plain,
! [SV11: $i] :
( ( ! [SY186: $i] :
( ~ ( contains_pq @ SV11 @ SY186 )
| ~ ( issmallestelement_pq @ SV11 @ SY186 )
| ( ( findmin_pq_eff @ SV11 @ SY186 )
= SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(270,plain,
! [SV12: $i] :
( ( ! [SY187: $i] :
( ~ ( contains_pq @ SV12 @ SY187 )
| ~ ( issmallestelement_pq @ SV12 @ SY187 )
| ( ( findmin_pq_res @ SV12 @ SY187 )
= SY187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(271,plain,
! [SV13: $i] :
( ( ! [SY188: $i] :
( ~ ( contains_pq @ SV13 @ SY188 )
| ~ ( issmallestelement_pq @ SV13 @ SY188 )
| ( ( removemin_pq_eff @ SV13 @ SY188 )
= ( remove_pq @ SV13 @ SY188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(272,plain,
! [SV14: $i] :
( ( ! [SY189: $i] :
( ~ ( contains_pq @ SV14 @ SY189 )
| ~ ( issmallestelement_pq @ SV14 @ SY189 )
| ( ( removemin_pq_res @ SV14 @ SY189 )
= SY189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(273,plain,
! [SV15: $i] :
( ( ! [SY190: $i,SY191: $i] :
( ( insert_pq @ ( insert_pq @ SV15 @ SY190 ) @ SY191 )
= ( insert_pq @ ( insert_pq @ SV15 @ SY191 ) @ SY190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(274,plain,
( ( isnonempty_slb @ create_slb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(275,plain,
! [SV16: $i] :
( ( ! [SY192: $i,SY193: $i] : ( isnonempty_slb @ ( insert_slb @ SV16 @ ( pair @ SY192 @ SY193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(276,plain,
! [SV17: $i] :
( ( ~ ( contains_slb @ create_slb @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(277,plain,
! [SV18: $i] :
( ( ! [SY194: $i] :
~ ( pair_in_list @ create_slb @ SV18 @ SY194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(278,plain,
! [SV19: $i] :
( ( ! [SY195: $i,SY196: $i] :
( ( remove_slb @ ( insert_slb @ SV19 @ ( pair @ SY195 @ SY196 ) ) @ SY195 )
= SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(279,plain,
! [SV20: $i] :
( ( ! [SY197: $i,SY198: $i] :
( ( SY197 = SY198 )
| ~ ( contains_slb @ SV20 @ SY198 )
| ! [SY199: $i] :
( ( remove_slb @ ( insert_slb @ SV20 @ ( pair @ SY197 @ SY199 ) ) @ SY198 )
= ( insert_slb @ ( remove_slb @ SV20 @ SY198 ) @ ( pair @ SY197 @ SY199 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(280,plain,
! [SV21: $i] :
( ( ! [SY200: $i,SY201: $i] :
( ( lookup_slb @ ( insert_slb @ SV21 @ ( pair @ SY200 @ SY201 ) ) @ SY200 )
= SY201 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(281,plain,
! [SV22: $i] :
( ( ! [SY202: $i,SY203: $i] :
( ( SY202 = SY203 )
| ~ ( contains_slb @ SV22 @ SY203 )
| ! [SY204: $i] :
( ( lookup_slb @ ( insert_slb @ SV22 @ ( pair @ SY202 @ SY204 ) ) @ SY203 )
= ( lookup_slb @ SV22 @ SY203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(282,plain,
! [SV23: $i] :
( ( ( update_slb @ create_slb @ SV23 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(283,plain,
! [SV24: $i] :
( ( ! [SY205: $i,SY206: $i,SY207: $i] :
( ~ ( strictly_less_than @ SY207 @ SY206 )
| ( ( update_slb @ ( insert_slb @ SV24 @ ( pair @ SY205 @ SY207 ) ) @ SY206 )
= ( insert_slb @ ( update_slb @ SV24 @ SY206 ) @ ( pair @ SY205 @ SY206 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(284,plain,
! [SV25: $i] :
( ( ! [SY208: $i,SY209: $i,SY210: $i] :
( ~ ( less_than @ SY209 @ SY210 )
| ( ( update_slb @ ( insert_slb @ SV25 @ ( pair @ SY208 @ SY210 ) ) @ SY209 )
= ( insert_slb @ ( update_slb @ SV25 @ SY209 ) @ ( pair @ SY208 @ SY210 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(285,plain,
! [SV26: $i] :
( ( succ_cpq @ SV26 @ SV26 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(286,plain,
! [SV27: $i] :
( ( ! [SY211: $i] :
( ~ ( succ_cpq @ SV27 @ SY211 )
| ! [SY212: $i] : ( succ_cpq @ SV27 @ ( insert_cpq @ SY211 @ SY212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(287,plain,
! [SV28: $i] :
( ( ! [SY213: $i] :
( ~ ( succ_cpq @ SV28 @ SY213 )
| ! [SY214: $i] : ( succ_cpq @ SV28 @ ( remove_cpq @ SY213 @ SY214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(288,plain,
! [SV29: $i] :
( ( ! [SY215: $i] :
( ~ ( succ_cpq @ SV29 @ SY215 )
| ( succ_cpq @ SV29 @ ( findmin_cpq_eff @ SY215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(289,plain,
! [SV30: $i] :
( ( ! [SY216: $i] :
( ~ ( succ_cpq @ SV30 @ SY216 )
| ( succ_cpq @ SV30 @ ( removemin_cpq_eff @ SY216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(290,plain,
! [SV31: $i] :
( ( ! [SY217: $i] : ( check_cpq @ ( triple @ SV31 @ create_slb @ SY217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(291,plain,
! [SV32: $i] :
( ( ! [SY218: $i,SY219: $i,SY220: $i,SY221: $i] :
( ~ ( strictly_less_than @ SY220 @ SY221 )
| ~ ( check_cpq @ ( triple @ SV32 @ ( insert_slb @ SY218 @ ( pair @ SY220 @ SY221 ) ) @ SY219 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(292,plain,
! [SV33: $i] :
( ( ! [SY222: $i] :
~ ( ok @ ( triple @ SV33 @ SY222 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(293,plain,
! [SV34: $i] :
( ( ! [SY223: $i,SY224: $i] :
( ( ok @ ( triple @ SV34 @ SY223 @ SY224 ) )
| ( SY224 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(294,plain,
! [SV35: $i] :
( ( ! [SY225: $i,SY226: $i,SY227: $i] :
( ( insert_cpq @ ( triple @ SV35 @ SY225 @ SY226 ) @ SY227 )
= ( triple @ ( insert_pqp @ SV35 @ SY227 ) @ ( insert_slb @ SY225 @ ( pair @ SY227 @ bottom ) ) @ SY226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(295,plain,
! [SV36: $i] :
( ( ! [SY228: $i,SY229: $i,SY230: $i] :
( ( contains_slb @ SY228 @ SY230 )
| ( ( remove_cpq @ ( triple @ SV36 @ SY228 @ SY229 ) @ SY230 )
= ( triple @ SV36 @ SY228 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(296,plain,
! [SV37: $i] :
( ( ! [SY231: $i,SY232: $i,SY233: $i] :
( ~ ( contains_slb @ SY231 @ SY233 )
| ~ ( less_than @ ( lookup_slb @ SY231 @ SY233 ) @ SY233 )
| ( ( remove_cpq @ ( triple @ SV37 @ SY231 @ SY232 ) @ SY233 )
= ( triple @ ( remove_pqp @ SV37 @ SY233 ) @ ( remove_slb @ SY231 @ SY233 ) @ SY232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(297,plain,
! [SV38: $i] :
( ( ! [SY234: $i,SY235: $i,SY236: $i] :
( ~ ( contains_slb @ SY234 @ SY236 )
| ~ ( strictly_less_than @ SY236 @ ( lookup_slb @ SY234 @ SY236 ) )
| ( ( remove_cpq @ ( triple @ SV38 @ SY234 @ SY235 ) @ SY236 )
= ( triple @ ( remove_pqp @ SV38 @ SY236 ) @ ( remove_slb @ SY234 @ SY236 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(298,plain,
! [SV39: $i] :
( ( ! [SY237: $i] :
( ( findmin_cpq_eff @ ( triple @ SV39 @ create_slb @ SY237 ) )
= ( triple @ SV39 @ create_slb @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(299,plain,
! [SV40: $i] :
( ( ! [SY238: $i] :
( ( SY238 = create_slb )
| ( contains_slb @ SY238 @ ( findmin_pqp_res @ SV40 ) )
| ! [SY239: $i] :
( ( findmin_cpq_eff @ ( triple @ SV40 @ SY238 @ SY239 ) )
= ( triple @ SV40 @ ( update_slb @ SY238 @ ( findmin_pqp_res @ SV40 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(300,plain,
! [SV41: $i] :
( ( ! [SY240: $i] :
( ( SY240 = create_slb )
| ~ ( contains_slb @ SY240 @ ( findmin_pqp_res @ SV41 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV41 ) @ ( lookup_slb @ SY240 @ ( findmin_pqp_res @ SV41 ) ) )
| ! [SY241: $i] :
( ( findmin_cpq_eff @ ( triple @ SV41 @ SY240 @ SY241 ) )
= ( triple @ SV41 @ ( update_slb @ SY240 @ ( findmin_pqp_res @ SV41 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(301,plain,
! [SV42: $i] :
( ( ! [SY242: $i] :
( ( SY242 = create_slb )
| ~ ( contains_slb @ SY242 @ ( findmin_pqp_res @ SV42 ) )
| ~ ( less_than @ ( lookup_slb @ SY242 @ ( findmin_pqp_res @ SV42 ) ) @ ( findmin_pqp_res @ SV42 ) )
| ! [SY243: $i] :
( ( findmin_cpq_eff @ ( triple @ SV42 @ SY242 @ SY243 ) )
= ( triple @ SV42 @ ( update_slb @ SY242 @ ( findmin_pqp_res @ SV42 ) ) @ SY243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(302,plain,
! [SV43: $i] :
( ( ! [SY244: $i] :
( ( findmin_cpq_res @ ( triple @ SV43 @ create_slb @ SY244 ) )
= bottom ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(303,plain,
! [SV44: $i] :
( ( ! [SY245: $i] :
( ( SY245 = create_slb )
| ! [SY246: $i] :
( ( findmin_cpq_res @ ( triple @ SV44 @ SY245 @ SY246 ) )
= ( findmin_pqp_res @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(304,plain,
! [SV45: $i] :
( ( ( removemin_cpq_eff @ SV45 )
= ( remove_cpq @ ( findmin_cpq_eff @ SV45 ) @ ( findmin_cpq_res @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(305,plain,
! [SV46: $i] :
( ( ( removemin_cpq_res @ SV46 )
= ( findmin_cpq_res @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(306,plain,
! [SV47: $i] :
( ( ! [SY247: $i] :
( ( i @ ( triple @ SV47 @ create_slb @ SY247 ) )
= create_pq ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(307,plain,
! [SV48: $i] :
( ( ! [SY248: $i,SY249: $i,SY250: $i,SY251: $i] :
( ( i @ ( triple @ SV48 @ ( insert_slb @ SY248 @ ( pair @ SY250 @ SY251 ) ) @ SY249 ) )
= ( insert_pq @ ( i @ ( triple @ SV48 @ SY248 @ SY249 ) ) @ SY250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(308,plain,
( ( pi_sharp_find_min @ ( i @ ( triple @ sK1_U @ sK2_SY172 @ sK3_SY174 ) ) @ ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY172 @ sK3_SY174 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(309,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_find_min @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( pi_find_min @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK6_V @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(310,plain,
! [SV49: $i] :
( ( ! [SY252: $i] :
~ ( ~ ! [SY253: $i,SY254: $i] :
( ~ ( contains_cpq @ ( triple @ SV49 @ SY252 @ SY253 ) @ SY254 )
| ( contains_slb @ SY252 @ SY254 ) )
| ~ ! [SY255: $i,SY256: $i] :
( ~ ( contains_slb @ SY252 @ SY256 )
| ( contains_cpq @ ( triple @ SV49 @ SY252 @ SY255 ) @ SY256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(311,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_removemin @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( pi_removemin @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK5_V @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(312,plain,
! [SV50: $i] :
( ( ! [SY257: $i,SY258: $i] :
~ ( ~ ~ ( ~ ! [SY259: $i,SY260: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SY257 @ SY259 ) ) @ SY258 @ SY260 )
| ( SY257 = SY258 )
| ( pair_in_list @ SV50 @ SY258 @ SY260 ) )
| ~ ! [SY261: $i,SY262: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SY257 @ SY261 ) ) @ SY258 @ SY262 )
| ( SY261 = SY262 )
| ( pair_in_list @ SV50 @ SY258 @ SY262 ) ) )
| ~ ~ ( ~ ! [SY263: $i,SY264: $i] :
( ( SY257 != SY258 )
| ( SY263 != SY264 )
| ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SY257 @ SY263 ) ) @ SY258 @ SY264 ) )
| ~ ! [SY265: $i,SY266: $i] :
( ~ ( pair_in_list @ SV50 @ SY258 @ SY266 )
| ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SY257 @ SY265 ) ) @ SY258 @ SY266 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(313,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_remove @ SX0 @ SX1 )
| ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 )
| ( pi_remove @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(314,plain,
! [SV51: $i] :
( ( ! [SY267: $i] :
~ ( ~ ! [SY268: $i] :
( ! [SY269: $i] :
~ ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SY267 @ SY269 ) ) @ SY268 )
| ( SY267 = SY268 )
| ( contains_slb @ SV51 @ SY268 ) )
| ~ ~ ( ~ ! [SY270: $i] :
( ( SY267 != SY270 )
| ! [SY271: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SY267 @ SY271 ) ) @ SY270 ) )
| ~ ! [SY272: $i] :
( ~ ( contains_slb @ SV51 @ SY272 )
| ! [SY273: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SY267 @ SY273 ) ) @ SY272 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(315,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( ok @ SX1 )
| ~ ( succ_cpq @ SX0 @ SX1 )
| ~ ( check_cpq @ SX1 ) )
| ( phi @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( phi @ SX0 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK4_V @ SX0 ) )
| ~ ( succ_cpq @ SX0 @ ( sK4_V @ SX0 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(316,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)],[251]) ).
thf(317,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( contains_pq @ SX0 @ SX1 )
| ~ ( issmallestelement_pq @ SX0 @ SX1 )
| ( pi_sharp_find_min @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(318,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( contains_pq @ SX0 @ SX1 )
| ( pi_sharp_remove @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(319,plain,
! [SV52: $i] :
( ( ! [SY274: $i,SY275: $i] :
~ ( ~ ! [SY276: $i,SY277: $i] :
( ~ ( less_than @ SY277 @ SY276 )
| ~ ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SY274 @ ( pair @ SY276 @ SY277 ) ) @ SY275 ) )
| ( check_cpq @ ( triple @ SV52 @ SY274 @ SY275 ) ) )
| ~ ! [SY278: $i,SY279: $i] :
( ~ ( less_than @ SY279 @ SY278 )
| ~ ( check_cpq @ ( triple @ SV52 @ SY274 @ SY275 ) )
| ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SY274 @ ( pair @ SY278 @ SY279 ) ) @ SY275 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(320,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( contains_pq @ SX0 @ ( sK7_W @ SX1 @ SX0 ) )
| ~ ~ ( less_than @ SX1 @ ( sK7_W @ SX1 @ SX0 ) ) )
| ( issmallestelement_pq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( issmallestelement_pq @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( contains_pq @ SX0 @ SX2 )
| ( less_than @ SX1 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(321,plain,
! [SV53: $i] :
( ( ~ ( ~ ! [SY280: $i,SY281: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV53 @ SY280 ) @ SY281 )
| ( SY280 = SY281 )
| ( contains_pq @ SV53 @ SY281 ) )
| ~ ~ ( ~ ! [SY282: $i,SY283: $i] :
( ( SY282 != SY283 )
| ( contains_pq @ ( insert_pq @ SV53 @ SY282 ) @ SY283 ) )
| ~ ! [SY284: $i,SY285: $i] :
( ~ ( contains_pq @ SV53 @ SY285 )
| ( contains_pq @ ( insert_pq @ SV53 @ SY284 ) @ SY285 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(322,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( contains_pq @ SX0 @ SX1 )
| ~ ( issmallestelement_pq @ SX0 @ SX1 )
| ( pi_sharp_removemin @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(323,plain,
! [SV54: $i,SV1: $i] :
( ( ! [SY286: $i] :
( ~ ( phi @ ( findmin_cpq_eff @ ( triple @ SV1 @ SV54 @ SY286 ) ) )
| ( contains_pq @ ( i @ ( triple @ SV1 @ SV54 @ SY286 ) ) @ ( findmin_cpq_res @ ( triple @ SV1 @ SV54 @ SY286 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(324,plain,
! [SV55: $i,SV2: $i] :
( ( ! [SY287: $i] :
( ~ ( phi @ ( findmin_cpq_eff @ ( triple @ SV2 @ SV55 @ SY287 ) ) )
| ( issmallestelement_pq @ ( i @ ( triple @ SV2 @ SV55 @ SY287 ) ) @ ( findmin_cpq_res @ ( triple @ SV2 @ SV55 @ SY287 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(325,plain,
! [SV56: $i,SV3: $i] :
( ( ! [SY288: $i] :
( ~ ( less_than @ SV3 @ SV56 )
| ~ ( less_than @ SV56 @ SY288 )
| ( less_than @ SV3 @ SY288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(326,plain,
! [SV57: $i,SV4: $i] :
( ( ( less_than @ SV4 @ SV57 )
| ( less_than @ SV57 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(327,plain,
! [SV58: $i,SV7: $i] :
( ( isnonempty_pq @ ( insert_pq @ SV7 @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(328,plain,
! [SV8: $i] :
( ( contains_pq @ create_pq @ SV8 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(329,plain,
! [SV59: $i,SV9: $i] :
( ( ( remove_pq @ ( insert_pq @ SV9 @ SV59 ) @ SV59 )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(330,plain,
! [SV10: $i,SV60: $i] :
( ( ! [SY289: $i] :
( ( SV60 = SY289 )
| ~ ( contains_pq @ SV10 @ SY289 )
| ( ( remove_pq @ ( insert_pq @ SV10 @ SV60 ) @ SY289 )
= ( insert_pq @ ( remove_pq @ SV10 @ SY289 ) @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(331,plain,
! [SV61: $i,SV11: $i] :
( ( ~ ( contains_pq @ SV11 @ SV61 )
| ~ ( issmallestelement_pq @ SV11 @ SV61 )
| ( ( findmin_pq_eff @ SV11 @ SV61 )
= SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(332,plain,
! [SV62: $i,SV12: $i] :
( ( ~ ( contains_pq @ SV12 @ SV62 )
| ~ ( issmallestelement_pq @ SV12 @ SV62 )
| ( ( findmin_pq_res @ SV12 @ SV62 )
= SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(333,plain,
! [SV63: $i,SV13: $i] :
( ( ~ ( contains_pq @ SV13 @ SV63 )
| ~ ( issmallestelement_pq @ SV13 @ SV63 )
| ( ( removemin_pq_eff @ SV13 @ SV63 )
= ( remove_pq @ SV13 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(334,plain,
! [SV64: $i,SV14: $i] :
( ( ~ ( contains_pq @ SV14 @ SV64 )
| ~ ( issmallestelement_pq @ SV14 @ SV64 )
| ( ( removemin_pq_res @ SV14 @ SV64 )
= SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(335,plain,
! [SV65: $i,SV15: $i] :
( ( ! [SY290: $i] :
( ( insert_pq @ ( insert_pq @ SV15 @ SV65 ) @ SY290 )
= ( insert_pq @ ( insert_pq @ SV15 @ SY290 ) @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(336,plain,
! [SV66: $i,SV16: $i] :
( ( ! [SY291: $i] : ( isnonempty_slb @ ( insert_slb @ SV16 @ ( pair @ SV66 @ SY291 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(337,plain,
! [SV17: $i] :
( ( contains_slb @ create_slb @ SV17 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(338,plain,
! [SV67: $i,SV18: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV18 @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(339,plain,
! [SV68: $i,SV19: $i] :
( ( ! [SY292: $i] :
( ( remove_slb @ ( insert_slb @ SV19 @ ( pair @ SV68 @ SY292 ) ) @ SV68 )
= SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(340,plain,
! [SV20: $i,SV69: $i] :
( ( ! [SY293: $i] :
( ( SV69 = SY293 )
| ~ ( contains_slb @ SV20 @ SY293 )
| ! [SY294: $i] :
( ( remove_slb @ ( insert_slb @ SV20 @ ( pair @ SV69 @ SY294 ) ) @ SY293 )
= ( insert_slb @ ( remove_slb @ SV20 @ SY293 ) @ ( pair @ SV69 @ SY294 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(341,plain,
! [SV70: $i,SV21: $i] :
( ( ! [SY295: $i] :
( ( lookup_slb @ ( insert_slb @ SV21 @ ( pair @ SV70 @ SY295 ) ) @ SV70 )
= SY295 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(342,plain,
! [SV22: $i,SV71: $i] :
( ( ! [SY296: $i] :
( ( SV71 = SY296 )
| ~ ( contains_slb @ SV22 @ SY296 )
| ! [SY297: $i] :
( ( lookup_slb @ ( insert_slb @ SV22 @ ( pair @ SV71 @ SY297 ) ) @ SY296 )
= ( lookup_slb @ SV22 @ SY296 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(343,plain,
! [SV72: $i,SV24: $i] :
( ( ! [SY298: $i,SY299: $i] :
( ~ ( strictly_less_than @ SY299 @ SY298 )
| ( ( update_slb @ ( insert_slb @ SV24 @ ( pair @ SV72 @ SY299 ) ) @ SY298 )
= ( insert_slb @ ( update_slb @ SV24 @ SY298 ) @ ( pair @ SV72 @ SY298 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(344,plain,
! [SV73: $i,SV25: $i] :
( ( ! [SY300: $i,SY301: $i] :
( ~ ( less_than @ SY300 @ SY301 )
| ( ( update_slb @ ( insert_slb @ SV25 @ ( pair @ SV73 @ SY301 ) ) @ SY300 )
= ( insert_slb @ ( update_slb @ SV25 @ SY300 ) @ ( pair @ SV73 @ SY301 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(345,plain,
! [SV74: $i,SV27: $i] :
( ( ~ ( succ_cpq @ SV27 @ SV74 )
| ! [SY302: $i] : ( succ_cpq @ SV27 @ ( insert_cpq @ SV74 @ SY302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(346,plain,
! [SV75: $i,SV28: $i] :
( ( ~ ( succ_cpq @ SV28 @ SV75 )
| ! [SY303: $i] : ( succ_cpq @ SV28 @ ( remove_cpq @ SV75 @ SY303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(347,plain,
! [SV76: $i,SV29: $i] :
( ( ~ ( succ_cpq @ SV29 @ SV76 )
| ( succ_cpq @ SV29 @ ( findmin_cpq_eff @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(348,plain,
! [SV77: $i,SV30: $i] :
( ( ~ ( succ_cpq @ SV30 @ SV77 )
| ( succ_cpq @ SV30 @ ( removemin_cpq_eff @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(349,plain,
! [SV78: $i,SV31: $i] :
( ( check_cpq @ ( triple @ SV31 @ create_slb @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(350,plain,
! [SV79: $i,SV32: $i] :
( ( ! [SY304: $i,SY305: $i,SY306: $i] :
( ~ ( strictly_less_than @ SY305 @ SY306 )
| ~ ( check_cpq @ ( triple @ SV32 @ ( insert_slb @ SV79 @ ( pair @ SY305 @ SY306 ) ) @ SY304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(351,plain,
! [SV80: $i,SV33: $i] :
( ( ~ ( ok @ ( triple @ SV33 @ SV80 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(352,plain,
! [SV81: $i,SV34: $i] :
( ( ! [SY307: $i] :
( ( ok @ ( triple @ SV34 @ SV81 @ SY307 ) )
| ( SY307 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(353,plain,
! [SV82: $i,SV35: $i] :
( ( ! [SY308: $i,SY309: $i] :
( ( insert_cpq @ ( triple @ SV35 @ SV82 @ SY308 ) @ SY309 )
= ( triple @ ( insert_pqp @ SV35 @ SY309 ) @ ( insert_slb @ SV82 @ ( pair @ SY309 @ bottom ) ) @ SY308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(354,plain,
! [SV36: $i,SV83: $i] :
( ( ! [SY310: $i,SY311: $i] :
( ( contains_slb @ SV83 @ SY311 )
| ( ( remove_cpq @ ( triple @ SV36 @ SV83 @ SY310 ) @ SY311 )
= ( triple @ SV36 @ SV83 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(355,plain,
! [SV37: $i,SV84: $i] :
( ( ! [SY312: $i,SY313: $i] :
( ~ ( contains_slb @ SV84 @ SY313 )
| ~ ( less_than @ ( lookup_slb @ SV84 @ SY313 ) @ SY313 )
| ( ( remove_cpq @ ( triple @ SV37 @ SV84 @ SY312 ) @ SY313 )
= ( triple @ ( remove_pqp @ SV37 @ SY313 ) @ ( remove_slb @ SV84 @ SY313 ) @ SY312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(356,plain,
! [SV38: $i,SV85: $i] :
( ( ! [SY314: $i,SY315: $i] :
( ~ ( contains_slb @ SV85 @ SY315 )
| ~ ( strictly_less_than @ SY315 @ ( lookup_slb @ SV85 @ SY315 ) )
| ( ( remove_cpq @ ( triple @ SV38 @ SV85 @ SY314 ) @ SY315 )
= ( triple @ ( remove_pqp @ SV38 @ SY315 ) @ ( remove_slb @ SV85 @ SY315 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(357,plain,
! [SV86: $i,SV39: $i] :
( ( ( findmin_cpq_eff @ ( triple @ SV39 @ create_slb @ SV86 ) )
= ( triple @ SV39 @ create_slb @ bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(358,plain,
! [SV40: $i,SV87: $i] :
( ( ( SV87 = create_slb )
| ( contains_slb @ SV87 @ ( findmin_pqp_res @ SV40 ) )
| ! [SY316: $i] :
( ( findmin_cpq_eff @ ( triple @ SV40 @ SV87 @ SY316 ) )
= ( triple @ SV40 @ ( update_slb @ SV87 @ ( findmin_pqp_res @ SV40 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(359,plain,
! [SV41: $i,SV88: $i] :
( ( ( SV88 = create_slb )
| ~ ( contains_slb @ SV88 @ ( findmin_pqp_res @ SV41 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV41 ) @ ( lookup_slb @ SV88 @ ( findmin_pqp_res @ SV41 ) ) )
| ! [SY317: $i] :
( ( findmin_cpq_eff @ ( triple @ SV41 @ SV88 @ SY317 ) )
= ( triple @ SV41 @ ( update_slb @ SV88 @ ( findmin_pqp_res @ SV41 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(360,plain,
! [SV42: $i,SV89: $i] :
( ( ( SV89 = create_slb )
| ~ ( contains_slb @ SV89 @ ( findmin_pqp_res @ SV42 ) )
| ~ ( less_than @ ( lookup_slb @ SV89 @ ( findmin_pqp_res @ SV42 ) ) @ ( findmin_pqp_res @ SV42 ) )
| ! [SY318: $i] :
( ( findmin_cpq_eff @ ( triple @ SV42 @ SV89 @ SY318 ) )
= ( triple @ SV42 @ ( update_slb @ SV89 @ ( findmin_pqp_res @ SV42 ) ) @ SY318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(361,plain,
! [SV90: $i,SV43: $i] :
( ( ( findmin_cpq_res @ ( triple @ SV43 @ create_slb @ SV90 ) )
= bottom )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(362,plain,
! [SV44: $i,SV91: $i] :
( ( ( SV91 = create_slb )
| ! [SY319: $i] :
( ( findmin_cpq_res @ ( triple @ SV44 @ SV91 @ SY319 ) )
= ( findmin_pqp_res @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(363,plain,
! [SV92: $i,SV47: $i] :
( ( ( i @ ( triple @ SV47 @ create_slb @ SV92 ) )
= create_pq )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(364,plain,
! [SV93: $i,SV48: $i] :
( ( ! [SY320: $i,SY321: $i,SY322: $i] :
( ( i @ ( triple @ SV48 @ ( insert_slb @ SV93 @ ( pair @ SY321 @ SY322 ) ) @ SY320 ) )
= ( insert_pq @ ( i @ ( triple @ SV48 @ SV93 @ SY320 ) ) @ SY321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(365,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_find_min @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[309]) ).
thf(366,plain,
( ( ~ ! [SX0: $i] :
( ~ ( pi_find_min @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK6_V @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[309]) ).
thf(367,plain,
! [SV94: $i,SV49: $i] :
( ( ~ ( ~ ! [SY323: $i,SY324: $i] :
( ~ ( contains_cpq @ ( triple @ SV49 @ SV94 @ SY323 ) @ SY324 )
| ( contains_slb @ SV94 @ SY324 ) )
| ~ ! [SY325: $i,SY326: $i] :
( ~ ( contains_slb @ SV94 @ SY326 )
| ( contains_cpq @ ( triple @ SV49 @ SV94 @ SY325 ) @ SY326 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(368,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_removemin @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(369,plain,
( ( ~ ! [SX0: $i] :
( ~ ( pi_removemin @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK5_V @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(370,plain,
! [SV95: $i,SV50: $i] :
( ( ! [SY327: $i] :
~ ( ~ ~ ( ~ ! [SY328: $i,SY329: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY328 ) ) @ SY327 @ SY329 )
| ( SV95 = SY327 )
| ( pair_in_list @ SV50 @ SY327 @ SY329 ) )
| ~ ! [SY330: $i,SY331: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY330 ) ) @ SY327 @ SY331 )
| ( SY330 = SY331 )
| ( pair_in_list @ SV50 @ SY327 @ SY331 ) ) )
| ~ ~ ( ~ ! [SY332: $i,SY333: $i] :
( ( SV95 != SY327 )
| ( SY332 != SY333 )
| ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY332 ) ) @ SY327 @ SY333 ) )
| ~ ! [SY334: $i,SY335: $i] :
( ~ ( pair_in_list @ SV50 @ SY327 @ SY335 )
| ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY334 ) ) @ SY327 @ SY335 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(371,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_remove @ SX0 @ SX1 )
| ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(372,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 )
| ( pi_remove @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(373,plain,
! [SV96: $i,SV51: $i] :
( ( ~ ( ~ ! [SY336: $i] :
( ! [SY337: $i] :
~ ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY337 ) ) @ SY336 )
| ( SV96 = SY336 )
| ( contains_slb @ SV51 @ SY336 ) )
| ~ ~ ( ~ ! [SY338: $i] :
( ( SV96 != SY338 )
| ! [SY339: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY339 ) ) @ SY338 ) )
| ~ ! [SY340: $i] :
( ~ ( contains_slb @ SV51 @ SY340 )
| ! [SY341: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY341 ) ) @ SY340 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(374,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( ok @ SX1 )
| ~ ( succ_cpq @ SX0 @ SX1 )
| ~ ( check_cpq @ SX1 ) )
| ( phi @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[315]) ).
thf(375,plain,
( ( ~ ! [SX0: $i] :
( ~ ( phi @ SX0 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK4_V @ SX0 ) )
| ~ ( succ_cpq @ SX0 @ ( sK4_V @ SX0 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[315]) ).
thf(376,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)],[316]) ).
thf(377,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)],[316]) ).
thf(378,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( contains_pq @ SX0 @ SX1 )
| ~ ( issmallestelement_pq @ SX0 @ SX1 )
| ( pi_sharp_find_min @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[317]) ).
thf(379,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[317]) ).
thf(380,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( contains_pq @ SX0 @ SX1 )
| ( pi_sharp_remove @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[318]) ).
thf(381,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[318]) ).
thf(382,plain,
! [SV97: $i,SV52: $i] :
( ( ! [SY342: $i] :
~ ( ~ ! [SY343: $i,SY344: $i] :
( ~ ( less_than @ SY344 @ SY343 )
| ~ ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV97 @ ( pair @ SY343 @ SY344 ) ) @ SY342 ) )
| ( check_cpq @ ( triple @ SV52 @ SV97 @ SY342 ) ) )
| ~ ! [SY345: $i,SY346: $i] :
( ~ ( less_than @ SY346 @ SY345 )
| ~ ( check_cpq @ ( triple @ SV52 @ SV97 @ SY342 ) )
| ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV97 @ ( pair @ SY345 @ SY346 ) ) @ SY342 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(383,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( contains_pq @ SX0 @ ( sK7_W @ SX1 @ SX0 ) )
| ~ ~ ( less_than @ SX1 @ ( sK7_W @ SX1 @ SX0 ) ) )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(384,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( issmallestelement_pq @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( contains_pq @ SX0 @ SX2 )
| ( less_than @ SX1 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(385,plain,
! [SV53: $i] :
( ( ~ ! [SY280: $i,SY281: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV53 @ SY280 ) @ SY281 )
| ( SY280 = SY281 )
| ( contains_pq @ SV53 @ SY281 ) )
| ~ ~ ( ~ ! [SY282: $i,SY283: $i] :
( ( SY282 != SY283 )
| ( contains_pq @ ( insert_pq @ SV53 @ SY282 ) @ SY283 ) )
| ~ ! [SY284: $i,SY285: $i] :
( ~ ( contains_pq @ SV53 @ SY285 )
| ( contains_pq @ ( insert_pq @ SV53 @ SY284 ) @ SY285 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(386,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( contains_pq @ SX0 @ SX1 )
| ~ ( issmallestelement_pq @ SX0 @ SX1 )
| ( pi_sharp_removemin @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(387,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(388,plain,
! [SV98: $i,SV54: $i,SV1: $i] :
( ( ~ ( phi @ ( findmin_cpq_eff @ ( triple @ SV1 @ SV54 @ SV98 ) ) )
| ( contains_pq @ ( i @ ( triple @ SV1 @ SV54 @ SV98 ) ) @ ( findmin_cpq_res @ ( triple @ SV1 @ SV54 @ SV98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(389,plain,
! [SV99: $i,SV55: $i,SV2: $i] :
( ( ~ ( phi @ ( findmin_cpq_eff @ ( triple @ SV2 @ SV55 @ SV99 ) ) )
| ( issmallestelement_pq @ ( i @ ( triple @ SV2 @ SV55 @ SV99 ) ) @ ( findmin_cpq_res @ ( triple @ SV2 @ SV55 @ SV99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(390,plain,
! [SV100: $i,SV56: $i,SV3: $i] :
( ( ~ ( less_than @ SV3 @ SV56 )
| ~ ( less_than @ SV56 @ SV100 )
| ( less_than @ SV3 @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(391,plain,
! [SV57: $i,SV4: $i] :
( ( ( less_than @ SV4 @ SV57 )
= $true )
| ( ( less_than @ SV57 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(392,plain,
! [SV10: $i,SV101: $i,SV60: $i] :
( ( ( SV60 = SV101 )
| ~ ( contains_pq @ SV10 @ SV101 )
| ( ( remove_pq @ ( insert_pq @ SV10 @ SV60 ) @ SV101 )
= ( insert_pq @ ( remove_pq @ SV10 @ SV101 ) @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(393,plain,
! [SV61: $i,SV11: $i] :
( ( ( ~ ( contains_pq @ SV11 @ SV61 )
| ~ ( issmallestelement_pq @ SV11 @ SV61 ) )
= $true )
| ( ( ( findmin_pq_eff @ SV11 @ SV61 )
= SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(394,plain,
! [SV62: $i,SV12: $i] :
( ( ( ~ ( contains_pq @ SV12 @ SV62 )
| ~ ( issmallestelement_pq @ SV12 @ SV62 ) )
= $true )
| ( ( ( findmin_pq_res @ SV12 @ SV62 )
= SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(395,plain,
! [SV63: $i,SV13: $i] :
( ( ( ~ ( contains_pq @ SV13 @ SV63 )
| ~ ( issmallestelement_pq @ SV13 @ SV63 ) )
= $true )
| ( ( ( removemin_pq_eff @ SV13 @ SV63 )
= ( remove_pq @ SV13 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(396,plain,
! [SV64: $i,SV14: $i] :
( ( ( ~ ( contains_pq @ SV14 @ SV64 )
| ~ ( issmallestelement_pq @ SV14 @ SV64 ) )
= $true )
| ( ( ( removemin_pq_res @ SV14 @ SV64 )
= SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(397,plain,
! [SV102: $i,SV65: $i,SV15: $i] :
( ( ( insert_pq @ ( insert_pq @ SV15 @ SV65 ) @ SV102 )
= ( insert_pq @ ( insert_pq @ SV15 @ SV102 ) @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(398,plain,
! [SV103: $i,SV66: $i,SV16: $i] :
( ( isnonempty_slb @ ( insert_slb @ SV16 @ ( pair @ SV66 @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(399,plain,
! [SV67: $i,SV18: $i] :
( ( pair_in_list @ create_slb @ SV18 @ SV67 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(400,plain,
! [SV104: $i,SV68: $i,SV19: $i] :
( ( ( remove_slb @ ( insert_slb @ SV19 @ ( pair @ SV68 @ SV104 ) ) @ SV68 )
= SV19 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(401,plain,
! [SV20: $i,SV105: $i,SV69: $i] :
( ( ( SV69 = SV105 )
| ~ ( contains_slb @ SV20 @ SV105 )
| ! [SY347: $i] :
( ( remove_slb @ ( insert_slb @ SV20 @ ( pair @ SV69 @ SY347 ) ) @ SV105 )
= ( insert_slb @ ( remove_slb @ SV20 @ SV105 ) @ ( pair @ SV69 @ SY347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(402,plain,
! [SV106: $i,SV70: $i,SV21: $i] :
( ( ( lookup_slb @ ( insert_slb @ SV21 @ ( pair @ SV70 @ SV106 ) ) @ SV70 )
= SV106 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(403,plain,
! [SV22: $i,SV107: $i,SV71: $i] :
( ( ( SV71 = SV107 )
| ~ ( contains_slb @ SV22 @ SV107 )
| ! [SY348: $i] :
( ( lookup_slb @ ( insert_slb @ SV22 @ ( pair @ SV71 @ SY348 ) ) @ SV107 )
= ( lookup_slb @ SV22 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(404,plain,
! [SV72: $i,SV24: $i,SV108: $i] :
( ( ! [SY349: $i] :
( ~ ( strictly_less_than @ SY349 @ SV108 )
| ( ( update_slb @ ( insert_slb @ SV24 @ ( pair @ SV72 @ SY349 ) ) @ SV108 )
= ( insert_slb @ ( update_slb @ SV24 @ SV108 ) @ ( pair @ SV72 @ SV108 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(405,plain,
! [SV73: $i,SV25: $i,SV109: $i] :
( ( ! [SY350: $i] :
( ~ ( less_than @ SV109 @ SY350 )
| ( ( update_slb @ ( insert_slb @ SV25 @ ( pair @ SV73 @ SY350 ) ) @ SV109 )
= ( insert_slb @ ( update_slb @ SV25 @ SV109 ) @ ( pair @ SV73 @ SY350 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(406,plain,
! [SV74: $i,SV27: $i] :
( ( ( ~ ( succ_cpq @ SV27 @ SV74 ) )
= $true )
| ( ( ! [SY302: $i] : ( succ_cpq @ SV27 @ ( insert_cpq @ SV74 @ SY302 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(407,plain,
! [SV75: $i,SV28: $i] :
( ( ( ~ ( succ_cpq @ SV28 @ SV75 ) )
= $true )
| ( ( ! [SY303: $i] : ( succ_cpq @ SV28 @ ( remove_cpq @ SV75 @ SY303 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(408,plain,
! [SV76: $i,SV29: $i] :
( ( ( ~ ( succ_cpq @ SV29 @ SV76 ) )
= $true )
| ( ( succ_cpq @ SV29 @ ( findmin_cpq_eff @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(409,plain,
! [SV77: $i,SV30: $i] :
( ( ( ~ ( succ_cpq @ SV30 @ SV77 ) )
= $true )
| ( ( succ_cpq @ SV30 @ ( removemin_cpq_eff @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(410,plain,
! [SV110: $i,SV79: $i,SV32: $i] :
( ( ! [SY351: $i,SY352: $i] :
( ~ ( strictly_less_than @ SY351 @ SY352 )
| ~ ( check_cpq @ ( triple @ SV32 @ ( insert_slb @ SV79 @ ( pair @ SY351 @ SY352 ) ) @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(411,plain,
! [SV80: $i,SV33: $i] :
( ( ok @ ( triple @ SV33 @ SV80 @ bad ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(412,plain,
! [SV111: $i,SV81: $i,SV34: $i] :
( ( ( ok @ ( triple @ SV34 @ SV81 @ SV111 ) )
| ( SV111 = bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(413,plain,
! [SV112: $i,SV82: $i,SV35: $i] :
( ( ! [SY353: $i] :
( ( insert_cpq @ ( triple @ SV35 @ SV82 @ SV112 ) @ SY353 )
= ( triple @ ( insert_pqp @ SV35 @ SY353 ) @ ( insert_slb @ SV82 @ ( pair @ SY353 @ bottom ) ) @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(414,plain,
! [SV113: $i,SV36: $i,SV83: $i] :
( ( ! [SY354: $i] :
( ( contains_slb @ SV83 @ SY354 )
| ( ( remove_cpq @ ( triple @ SV36 @ SV83 @ SV113 ) @ SY354 )
= ( triple @ SV36 @ SV83 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(415,plain,
! [SV114: $i,SV37: $i,SV84: $i] :
( ( ! [SY355: $i] :
( ~ ( contains_slb @ SV84 @ SY355 )
| ~ ( less_than @ ( lookup_slb @ SV84 @ SY355 ) @ SY355 )
| ( ( remove_cpq @ ( triple @ SV37 @ SV84 @ SV114 ) @ SY355 )
= ( triple @ ( remove_pqp @ SV37 @ SY355 ) @ ( remove_slb @ SV84 @ SY355 ) @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(416,plain,
! [SV115: $i,SV38: $i,SV85: $i] :
( ( ! [SY356: $i] :
( ~ ( contains_slb @ SV85 @ SY356 )
| ~ ( strictly_less_than @ SY356 @ ( lookup_slb @ SV85 @ SY356 ) )
| ( ( remove_cpq @ ( triple @ SV38 @ SV85 @ SV115 ) @ SY356 )
= ( triple @ ( remove_pqp @ SV38 @ SY356 ) @ ( remove_slb @ SV85 @ SY356 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(417,plain,
! [SV40: $i,SV87: $i] :
( ( ( ( SV87 = create_slb )
| ( contains_slb @ SV87 @ ( findmin_pqp_res @ SV40 ) ) )
= $true )
| ( ( ! [SY316: $i] :
( ( findmin_cpq_eff @ ( triple @ SV40 @ SV87 @ SY316 ) )
= ( triple @ SV40 @ ( update_slb @ SV87 @ ( findmin_pqp_res @ SV40 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(418,plain,
! [SV41: $i,SV88: $i] :
( ( ( ( SV88 = create_slb )
| ~ ( contains_slb @ SV88 @ ( findmin_pqp_res @ SV41 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV41 ) @ ( lookup_slb @ SV88 @ ( findmin_pqp_res @ SV41 ) ) ) )
= $true )
| ( ( ! [SY317: $i] :
( ( findmin_cpq_eff @ ( triple @ SV41 @ SV88 @ SY317 ) )
= ( triple @ SV41 @ ( update_slb @ SV88 @ ( findmin_pqp_res @ SV41 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[359]) ).
thf(419,plain,
! [SV42: $i,SV89: $i] :
( ( ( ( SV89 = create_slb )
| ~ ( contains_slb @ SV89 @ ( findmin_pqp_res @ SV42 ) )
| ~ ( less_than @ ( lookup_slb @ SV89 @ ( findmin_pqp_res @ SV42 ) ) @ ( findmin_pqp_res @ SV42 ) ) )
= $true )
| ( ( ! [SY318: $i] :
( ( findmin_cpq_eff @ ( triple @ SV42 @ SV89 @ SY318 ) )
= ( triple @ SV42 @ ( update_slb @ SV89 @ ( findmin_pqp_res @ SV42 ) ) @ SY318 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(420,plain,
! [SV44: $i,SV91: $i] :
( ( ( SV91 = create_slb )
= $true )
| ( ( ! [SY319: $i] :
( ( findmin_cpq_res @ ( triple @ SV44 @ SV91 @ SY319 ) )
= ( findmin_pqp_res @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(421,plain,
! [SV116: $i,SV93: $i,SV48: $i] :
( ( ! [SY357: $i,SY358: $i] :
( ( i @ ( triple @ SV48 @ ( insert_slb @ SV93 @ ( pair @ SY357 @ SY358 ) ) @ SV116 ) )
= ( insert_pq @ ( i @ ( triple @ SV48 @ SV93 @ SV116 ) ) @ SY357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(422,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_find_min @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[365]) ).
thf(423,plain,
( ( ! [SX0: $i] :
( ~ ( pi_find_min @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK6_V @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(424,plain,
! [SV94: $i,SV49: $i] :
( ( ~ ! [SY323: $i,SY324: $i] :
( ~ ( contains_cpq @ ( triple @ SV49 @ SV94 @ SY323 ) @ SY324 )
| ( contains_slb @ SV94 @ SY324 ) )
| ~ ! [SY325: $i,SY326: $i] :
( ~ ( contains_slb @ SV94 @ SY326 )
| ( contains_cpq @ ( triple @ SV49 @ SV94 @ SY325 ) @ SY326 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(425,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_removemin @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(426,plain,
( ( ! [SX0: $i] :
( ~ ( pi_removemin @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK5_V @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(427,plain,
! [SV117: $i,SV95: $i,SV50: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY359: $i,SY360: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY359 ) ) @ SV117 @ SY360 )
| ( SV95 = SV117 )
| ( pair_in_list @ SV50 @ SV117 @ SY360 ) )
| ~ ! [SY361: $i,SY362: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY361 ) ) @ SV117 @ SY362 )
| ( SY361 = SY362 )
| ( pair_in_list @ SV50 @ SV117 @ SY362 ) ) )
| ~ ~ ( ~ ! [SY363: $i,SY364: $i] :
( ( SV95 != SV117 )
| ( SY363 != SY364 )
| ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY363 ) ) @ SV117 @ SY364 ) )
| ~ ! [SY365: $i,SY366: $i] :
( ~ ( pair_in_list @ SV50 @ SV117 @ SY366 )
| ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY365 ) ) @ SV117 @ SY366 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(428,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_remove @ SX0 @ SX1 )
| ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[371]) ).
thf(429,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 )
| ( pi_remove @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(430,plain,
! [SV96: $i,SV51: $i] :
( ( ~ ! [SY336: $i] :
( ! [SY337: $i] :
~ ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY337 ) ) @ SY336 )
| ( SV96 = SY336 )
| ( contains_slb @ SV51 @ SY336 ) )
| ~ ~ ( ~ ! [SY338: $i] :
( ( SV96 != SY338 )
| ! [SY339: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY339 ) ) @ SY338 ) )
| ~ ! [SY340: $i] :
( ~ ( contains_slb @ SV51 @ SY340 )
| ! [SY341: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY341 ) ) @ SY340 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(431,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( ok @ SX1 )
| ~ ( succ_cpq @ SX0 @ SX1 )
| ~ ( check_cpq @ SX1 ) )
| ( phi @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[374]) ).
thf(432,plain,
( ( ! [SX0: $i] :
( ~ ( phi @ SX0 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK4_V @ SX0 ) )
| ~ ( succ_cpq @ SX0 @ ( sK4_V @ SX0 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[375]) ).
thf(433,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)],[376]) ).
thf(434,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)],[377]) ).
thf(435,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( contains_pq @ SX0 @ SX1 )
| ~ ( issmallestelement_pq @ SX0 @ SX1 )
| ( pi_sharp_find_min @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[378]) ).
thf(436,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[379]) ).
thf(437,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( contains_pq @ SX0 @ SX1 )
| ( pi_sharp_remove @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[380]) ).
thf(438,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[381]) ).
thf(439,plain,
! [SV118: $i,SV97: $i,SV52: $i] :
( ( ~ ( ~ ! [SY367: $i,SY368: $i] :
( ~ ( less_than @ SY368 @ SY367 )
| ~ ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV97 @ ( pair @ SY367 @ SY368 ) ) @ SV118 ) )
| ( check_cpq @ ( triple @ SV52 @ SV97 @ SV118 ) ) )
| ~ ! [SY369: $i,SY370: $i] :
( ~ ( less_than @ SY370 @ SY369 )
| ~ ( check_cpq @ ( triple @ SV52 @ SV97 @ SV118 ) )
| ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV97 @ ( pair @ SY369 @ SY370 ) ) @ SV118 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(440,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( contains_pq @ SX0 @ ( sK7_W @ SX1 @ SX0 ) )
| ~ ~ ( less_than @ SX1 @ ( sK7_W @ SX1 @ SX0 ) ) )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[383]) ).
thf(441,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( issmallestelement_pq @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( contains_pq @ SX0 @ SX2 )
| ( less_than @ SX1 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[384]) ).
thf(442,plain,
! [SV53: $i] :
( ( ~ ! [SY280: $i,SY281: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV53 @ SY280 ) @ SY281 )
| ( SY280 = SY281 )
| ( contains_pq @ SV53 @ SY281 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[385]) ).
thf(443,plain,
! [SV53: $i] :
( ( ~ ~ ( ~ ! [SY282: $i,SY283: $i] :
( ( SY282 != SY283 )
| ( contains_pq @ ( insert_pq @ SV53 @ SY282 ) @ SY283 ) )
| ~ ! [SY284: $i,SY285: $i] :
( ~ ( contains_pq @ SV53 @ SY285 )
| ( contains_pq @ ( insert_pq @ SV53 @ SY284 ) @ SY285 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[385]) ).
thf(444,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( contains_pq @ SX0 @ SX1 )
| ~ ( issmallestelement_pq @ SX0 @ SX1 )
| ( pi_sharp_removemin @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[386]) ).
thf(445,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[387]) ).
thf(446,plain,
! [SV98: $i,SV54: $i,SV1: $i] :
( ( ( ~ ( phi @ ( findmin_cpq_eff @ ( triple @ SV1 @ SV54 @ SV98 ) ) ) )
= $true )
| ( ( contains_pq @ ( i @ ( triple @ SV1 @ SV54 @ SV98 ) ) @ ( findmin_cpq_res @ ( triple @ SV1 @ SV54 @ SV98 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(447,plain,
! [SV99: $i,SV55: $i,SV2: $i] :
( ( ( ~ ( phi @ ( findmin_cpq_eff @ ( triple @ SV2 @ SV55 @ SV99 ) ) ) )
= $true )
| ( ( issmallestelement_pq @ ( i @ ( triple @ SV2 @ SV55 @ SV99 ) ) @ ( findmin_cpq_res @ ( triple @ SV2 @ SV55 @ SV99 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(448,plain,
! [SV100: $i,SV56: $i,SV3: $i] :
( ( ( ~ ( less_than @ SV3 @ SV56 )
| ~ ( less_than @ SV56 @ SV100 ) )
= $true )
| ( ( less_than @ SV3 @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[390]) ).
thf(449,plain,
! [SV10: $i,SV101: $i,SV60: $i] :
( ( ( ( SV60 = SV101 )
| ~ ( contains_pq @ SV10 @ SV101 ) )
= $true )
| ( ( ( remove_pq @ ( insert_pq @ SV10 @ SV60 ) @ SV101 )
= ( insert_pq @ ( remove_pq @ SV10 @ SV101 ) @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(450,plain,
! [SV61: $i,SV11: $i] :
( ( ( ~ ( contains_pq @ SV11 @ SV61 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV11 @ SV61 ) )
= $true )
| ( ( ( findmin_pq_eff @ SV11 @ SV61 )
= SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(451,plain,
! [SV62: $i,SV12: $i] :
( ( ( ~ ( contains_pq @ SV12 @ SV62 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV12 @ SV62 ) )
= $true )
| ( ( ( findmin_pq_res @ SV12 @ SV62 )
= SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(452,plain,
! [SV63: $i,SV13: $i] :
( ( ( ~ ( contains_pq @ SV13 @ SV63 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV13 @ SV63 ) )
= $true )
| ( ( ( removemin_pq_eff @ SV13 @ SV63 )
= ( remove_pq @ SV13 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(453,plain,
! [SV64: $i,SV14: $i] :
( ( ( ~ ( contains_pq @ SV14 @ SV64 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV14 @ SV64 ) )
= $true )
| ( ( ( removemin_pq_res @ SV14 @ SV64 )
= SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(454,plain,
! [SV20: $i,SV105: $i,SV69: $i] :
( ( ( ( SV69 = SV105 )
| ~ ( contains_slb @ SV20 @ SV105 ) )
= $true )
| ( ( ! [SY347: $i] :
( ( remove_slb @ ( insert_slb @ SV20 @ ( pair @ SV69 @ SY347 ) ) @ SV105 )
= ( insert_slb @ ( remove_slb @ SV20 @ SV105 ) @ ( pair @ SV69 @ SY347 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(455,plain,
! [SV22: $i,SV107: $i,SV71: $i] :
( ( ( ( SV71 = SV107 )
| ~ ( contains_slb @ SV22 @ SV107 ) )
= $true )
| ( ( ! [SY348: $i] :
( ( lookup_slb @ ( insert_slb @ SV22 @ ( pair @ SV71 @ SY348 ) ) @ SV107 )
= ( lookup_slb @ SV22 @ SV107 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(456,plain,
! [SV72: $i,SV24: $i,SV108: $i,SV119: $i] :
( ( ~ ( strictly_less_than @ SV119 @ SV108 )
| ( ( update_slb @ ( insert_slb @ SV24 @ ( pair @ SV72 @ SV119 ) ) @ SV108 )
= ( insert_slb @ ( update_slb @ SV24 @ SV108 ) @ ( pair @ SV72 @ SV108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(457,plain,
! [SV73: $i,SV25: $i,SV120: $i,SV109: $i] :
( ( ~ ( less_than @ SV109 @ SV120 )
| ( ( update_slb @ ( insert_slb @ SV25 @ ( pair @ SV73 @ SV120 ) ) @ SV109 )
= ( insert_slb @ ( update_slb @ SV25 @ SV109 ) @ ( pair @ SV73 @ SV120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(458,plain,
! [SV74: $i,SV27: $i] :
( ( ( succ_cpq @ SV27 @ SV74 )
= $false )
| ( ( ! [SY302: $i] : ( succ_cpq @ SV27 @ ( insert_cpq @ SV74 @ SY302 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(459,plain,
! [SV75: $i,SV28: $i] :
( ( ( succ_cpq @ SV28 @ SV75 )
= $false )
| ( ( ! [SY303: $i] : ( succ_cpq @ SV28 @ ( remove_cpq @ SV75 @ SY303 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(460,plain,
! [SV76: $i,SV29: $i] :
( ( ( succ_cpq @ SV29 @ SV76 )
= $false )
| ( ( succ_cpq @ SV29 @ ( findmin_cpq_eff @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(461,plain,
! [SV77: $i,SV30: $i] :
( ( ( succ_cpq @ SV30 @ SV77 )
= $false )
| ( ( succ_cpq @ SV30 @ ( removemin_cpq_eff @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(462,plain,
! [SV110: $i,SV79: $i,SV32: $i,SV121: $i] :
( ( ! [SY371: $i] :
( ~ ( strictly_less_than @ SV121 @ SY371 )
| ~ ( check_cpq @ ( triple @ SV32 @ ( insert_slb @ SV79 @ ( pair @ SV121 @ SY371 ) ) @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(463,plain,
! [SV111: $i,SV81: $i,SV34: $i] :
( ( ( ok @ ( triple @ SV34 @ SV81 @ SV111 ) )
= $true )
| ( ( SV111 = bad )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(464,plain,
! [SV122: $i,SV112: $i,SV82: $i,SV35: $i] :
( ( ( insert_cpq @ ( triple @ SV35 @ SV82 @ SV112 ) @ SV122 )
= ( triple @ ( insert_pqp @ SV35 @ SV122 ) @ ( insert_slb @ SV82 @ ( pair @ SV122 @ bottom ) ) @ SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(465,plain,
! [SV113: $i,SV36: $i,SV123: $i,SV83: $i] :
( ( ( contains_slb @ SV83 @ SV123 )
| ( ( remove_cpq @ ( triple @ SV36 @ SV83 @ SV113 ) @ SV123 )
= ( triple @ SV36 @ SV83 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(466,plain,
! [SV114: $i,SV37: $i,SV124: $i,SV84: $i] :
( ( ~ ( contains_slb @ SV84 @ SV124 )
| ~ ( less_than @ ( lookup_slb @ SV84 @ SV124 ) @ SV124 )
| ( ( remove_cpq @ ( triple @ SV37 @ SV84 @ SV114 ) @ SV124 )
= ( triple @ ( remove_pqp @ SV37 @ SV124 ) @ ( remove_slb @ SV84 @ SV124 ) @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(467,plain,
! [SV115: $i,SV38: $i,SV125: $i,SV85: $i] :
( ( ~ ( contains_slb @ SV85 @ SV125 )
| ~ ( strictly_less_than @ SV125 @ ( lookup_slb @ SV85 @ SV125 ) )
| ( ( remove_cpq @ ( triple @ SV38 @ SV85 @ SV115 ) @ SV125 )
= ( triple @ ( remove_pqp @ SV38 @ SV125 ) @ ( remove_slb @ SV85 @ SV125 ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(468,plain,
! [SV40: $i,SV87: $i] :
( ( ( SV87 = create_slb )
= $true )
| ( ( contains_slb @ SV87 @ ( findmin_pqp_res @ SV40 ) )
= $true )
| ( ( ! [SY316: $i] :
( ( findmin_cpq_eff @ ( triple @ SV40 @ SV87 @ SY316 ) )
= ( triple @ SV40 @ ( update_slb @ SV87 @ ( findmin_pqp_res @ SV40 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(469,plain,
! [SV41: $i,SV88: $i] :
( ( ( ( SV88 = create_slb )
| ~ ( contains_slb @ SV88 @ ( findmin_pqp_res @ SV41 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV41 ) @ ( lookup_slb @ SV88 @ ( findmin_pqp_res @ SV41 ) ) ) )
= $true )
| ( ( ! [SY317: $i] :
( ( findmin_cpq_eff @ ( triple @ SV41 @ SV88 @ SY317 ) )
= ( triple @ SV41 @ ( update_slb @ SV88 @ ( findmin_pqp_res @ SV41 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(470,plain,
! [SV42: $i,SV89: $i] :
( ( ( ( SV89 = create_slb )
| ~ ( contains_slb @ SV89 @ ( findmin_pqp_res @ SV42 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV89 @ ( findmin_pqp_res @ SV42 ) ) @ ( findmin_pqp_res @ SV42 ) ) )
= $true )
| ( ( ! [SY318: $i] :
( ( findmin_cpq_eff @ ( triple @ SV42 @ SV89 @ SY318 ) )
= ( triple @ SV42 @ ( update_slb @ SV89 @ ( findmin_pqp_res @ SV42 ) ) @ SY318 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(471,plain,
! [SV126: $i,SV91: $i,SV44: $i] :
( ( ( ( findmin_cpq_res @ ( triple @ SV44 @ SV91 @ SV126 ) )
= ( findmin_pqp_res @ SV44 ) )
= $true )
| ( ( SV91 = create_slb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(472,plain,
! [SV116: $i,SV127: $i,SV93: $i,SV48: $i] :
( ( ! [SY372: $i] :
( ( i @ ( triple @ SV48 @ ( insert_slb @ SV93 @ ( pair @ SV127 @ SY372 ) ) @ SV116 ) )
= ( insert_pq @ ( i @ ( triple @ SV48 @ SV93 @ SV116 ) ) @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(473,plain,
! [SV128: $i] :
( ( ! [SY373: $i] :
~ ( pi_sharp_find_min @ ( i @ SV128 ) @ SY373 )
| ( pi_find_min @ SV128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(474,plain,
! [SV129: $i] :
( ( ~ ( pi_find_min @ SV129 )
| ( pi_sharp_find_min @ ( i @ SV129 ) @ ( sK6_V @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(475,plain,
! [SV94: $i,SV49: $i] :
( ( ~ ! [SY323: $i,SY324: $i] :
( ~ ( contains_cpq @ ( triple @ SV49 @ SV94 @ SY323 ) @ SY324 )
| ( contains_slb @ SV94 @ SY324 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(476,plain,
! [SV49: $i,SV94: $i] :
( ( ~ ! [SY325: $i,SY326: $i] :
( ~ ( contains_slb @ SV94 @ SY326 )
| ( contains_cpq @ ( triple @ SV49 @ SV94 @ SY325 ) @ SY326 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(477,plain,
! [SV130: $i] :
( ( ! [SY374: $i] :
~ ( pi_sharp_find_min @ ( i @ SV130 ) @ SY374 )
| ( pi_removemin @ SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(478,plain,
! [SV131: $i] :
( ( ~ ( pi_removemin @ SV131 )
| ( pi_sharp_find_min @ ( i @ SV131 ) @ ( sK5_V @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(479,plain,
! [SV117: $i,SV95: $i,SV50: $i] :
( ( ~ ~ ( ~ ! [SY359: $i,SY360: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY359 ) ) @ SV117 @ SY360 )
| ( SV95 = SV117 )
| ( pair_in_list @ SV50 @ SV117 @ SY360 ) )
| ~ ! [SY361: $i,SY362: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY361 ) ) @ SV117 @ SY362 )
| ( SY361 = SY362 )
| ( pair_in_list @ SV50 @ SV117 @ SY362 ) ) )
| ~ ~ ( ~ ! [SY363: $i,SY364: $i] :
( ( SV95 != SV117 )
| ( SY363 != SY364 )
| ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY363 ) ) @ SV117 @ SY364 ) )
| ~ ! [SY365: $i,SY366: $i] :
( ~ ( pair_in_list @ SV50 @ SV117 @ SY366 )
| ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY365 ) ) @ SV117 @ SY366 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(480,plain,
! [SV132: $i] :
( ( ! [SY375: $i] :
( ~ ( pi_remove @ SV132 @ SY375 )
| ( pi_sharp_remove @ ( i @ SV132 ) @ SY375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(481,plain,
! [SV133: $i] :
( ( ! [SY376: $i] :
( ~ ( pi_sharp_remove @ ( i @ SV133 ) @ SY376 )
| ( pi_remove @ SV133 @ SY376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(482,plain,
! [SV96: $i,SV51: $i] :
( ( ~ ! [SY336: $i] :
( ! [SY337: $i] :
~ ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY337 ) ) @ SY336 )
| ( SV96 = SY336 )
| ( contains_slb @ SV51 @ SY336 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[430]) ).
thf(483,plain,
! [SV51: $i,SV96: $i] :
( ( ~ ~ ( ~ ! [SY338: $i] :
( ( SV96 != SY338 )
| ! [SY339: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY339 ) ) @ SY338 ) )
| ~ ! [SY340: $i] :
( ~ ( contains_slb @ SV51 @ SY340 )
| ! [SY341: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY341 ) ) @ SY340 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[430]) ).
thf(484,plain,
! [SV134: $i] :
( ( ! [SY377: $i] :
( ~ ( ok @ SY377 )
| ~ ( succ_cpq @ SV134 @ SY377 )
| ~ ( check_cpq @ SY377 ) )
| ( phi @ SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(485,plain,
! [SV135: $i] :
( ( ~ ( phi @ SV135 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK4_V @ SV135 ) )
| ~ ( succ_cpq @ SV135 @ ( sK4_V @ SV135 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SV135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(486,plain,
! [SV136: $i] :
( ( ! [SY378: $i] :
( ~ ( less_than @ SV136 @ SY378 )
| ( less_than @ SY378 @ SV136 )
| ( strictly_less_than @ SV136 @ SY378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(487,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)],[434]) ).
thf(488,plain,
! [SV137: $i] :
( ( ! [SY379: $i] :
( ~ ( contains_pq @ SV137 @ SY379 )
| ~ ( issmallestelement_pq @ SV137 @ SY379 )
| ( pi_sharp_find_min @ SV137 @ SY379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(489,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(490,plain,
! [SV138: $i] :
( ( ! [SY380: $i] :
( ~ ( contains_pq @ SV138 @ SY380 )
| ( pi_sharp_remove @ SV138 @ SY380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(491,plain,
! [SV139: $i] :
( ( ! [SY381: $i] :
( ~ ( pi_sharp_remove @ SV139 @ SY381 )
| ( contains_pq @ SV139 @ SY381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(492,plain,
! [SV118: $i,SV97: $i,SV52: $i] :
( ( ~ ! [SY367: $i,SY368: $i] :
( ~ ( less_than @ SY368 @ SY367 )
| ~ ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV97 @ ( pair @ SY367 @ SY368 ) ) @ SV118 ) )
| ( check_cpq @ ( triple @ SV52 @ SV97 @ SV118 ) ) )
| ~ ! [SY369: $i,SY370: $i] :
( ~ ( less_than @ SY370 @ SY369 )
| ~ ( check_cpq @ ( triple @ SV52 @ SV97 @ SV118 ) )
| ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV97 @ ( pair @ SY369 @ SY370 ) ) @ SV118 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(493,plain,
! [SV140: $i] :
( ( ! [SY382: $i] :
( ~ ( ~ ( contains_pq @ SV140 @ ( sK7_W @ SY382 @ SV140 ) )
| ~ ~ ( less_than @ SY382 @ ( sK7_W @ SY382 @ SV140 ) ) )
| ( issmallestelement_pq @ SV140 @ SY382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(494,plain,
! [SV141: $i] :
( ( ! [SY383: $i] :
( ~ ( issmallestelement_pq @ SV141 @ SY383 )
| ! [SY384: $i] :
( ~ ( contains_pq @ SV141 @ SY384 )
| ( less_than @ SY383 @ SY384 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(495,plain,
! [SV53: $i] :
( ( ! [SY280: $i,SY281: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV53 @ SY280 ) @ SY281 )
| ( SY280 = SY281 )
| ( contains_pq @ SV53 @ SY281 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(496,plain,
! [SV53: $i] :
( ( ~ ( ~ ! [SY282: $i,SY283: $i] :
( ( SY282 != SY283 )
| ( contains_pq @ ( insert_pq @ SV53 @ SY282 ) @ SY283 ) )
| ~ ! [SY284: $i,SY285: $i] :
( ~ ( contains_pq @ SV53 @ SY285 )
| ( contains_pq @ ( insert_pq @ SV53 @ SY284 ) @ SY285 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(497,plain,
! [SV142: $i] :
( ( ! [SY385: $i] :
( ~ ( contains_pq @ SV142 @ SY385 )
| ~ ( issmallestelement_pq @ SV142 @ SY385 )
| ( pi_sharp_removemin @ SV142 @ SY385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(498,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(499,plain,
! [SV98: $i,SV54: $i,SV1: $i] :
( ( ( phi @ ( findmin_cpq_eff @ ( triple @ SV1 @ SV54 @ SV98 ) ) )
= $false )
| ( ( contains_pq @ ( i @ ( triple @ SV1 @ SV54 @ SV98 ) ) @ ( findmin_cpq_res @ ( triple @ SV1 @ SV54 @ SV98 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(500,plain,
! [SV99: $i,SV55: $i,SV2: $i] :
( ( ( phi @ ( findmin_cpq_eff @ ( triple @ SV2 @ SV55 @ SV99 ) ) )
= $false )
| ( ( issmallestelement_pq @ ( i @ ( triple @ SV2 @ SV55 @ SV99 ) ) @ ( findmin_cpq_res @ ( triple @ SV2 @ SV55 @ SV99 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(501,plain,
! [SV100: $i,SV56: $i,SV3: $i] :
( ( ( ~ ( less_than @ SV3 @ SV56 ) )
= $true )
| ( ( ~ ( less_than @ SV56 @ SV100 ) )
= $true )
| ( ( less_than @ SV3 @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[448]) ).
thf(502,plain,
! [SV10: $i,SV101: $i,SV60: $i] :
( ( ( SV60 = SV101 )
= $true )
| ( ( ~ ( contains_pq @ SV10 @ SV101 ) )
= $true )
| ( ( ( remove_pq @ ( insert_pq @ SV10 @ SV60 ) @ SV101 )
= ( insert_pq @ ( remove_pq @ SV10 @ SV101 ) @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[449]) ).
thf(503,plain,
! [SV61: $i,SV11: $i] :
( ( ( contains_pq @ SV11 @ SV61 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV11 @ SV61 ) )
= $true )
| ( ( ( findmin_pq_eff @ SV11 @ SV61 )
= SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(504,plain,
! [SV62: $i,SV12: $i] :
( ( ( contains_pq @ SV12 @ SV62 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV12 @ SV62 ) )
= $true )
| ( ( ( findmin_pq_res @ SV12 @ SV62 )
= SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(505,plain,
! [SV63: $i,SV13: $i] :
( ( ( contains_pq @ SV13 @ SV63 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV13 @ SV63 ) )
= $true )
| ( ( ( removemin_pq_eff @ SV13 @ SV63 )
= ( remove_pq @ SV13 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(506,plain,
! [SV64: $i,SV14: $i] :
( ( ( contains_pq @ SV14 @ SV64 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV14 @ SV64 ) )
= $true )
| ( ( ( removemin_pq_res @ SV14 @ SV64 )
= SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(507,plain,
! [SV20: $i,SV105: $i,SV69: $i] :
( ( ( SV69 = SV105 )
= $true )
| ( ( ~ ( contains_slb @ SV20 @ SV105 ) )
= $true )
| ( ( ! [SY347: $i] :
( ( remove_slb @ ( insert_slb @ SV20 @ ( pair @ SV69 @ SY347 ) ) @ SV105 )
= ( insert_slb @ ( remove_slb @ SV20 @ SV105 ) @ ( pair @ SV69 @ SY347 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(508,plain,
! [SV22: $i,SV107: $i,SV71: $i] :
( ( ( SV71 = SV107 )
= $true )
| ( ( ~ ( contains_slb @ SV22 @ SV107 ) )
= $true )
| ( ( ! [SY348: $i] :
( ( lookup_slb @ ( insert_slb @ SV22 @ ( pair @ SV71 @ SY348 ) ) @ SV107 )
= ( lookup_slb @ SV22 @ SV107 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(509,plain,
! [SV72: $i,SV24: $i,SV108: $i,SV119: $i] :
( ( ( ~ ( strictly_less_than @ SV119 @ SV108 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV24 @ ( pair @ SV72 @ SV119 ) ) @ SV108 )
= ( insert_slb @ ( update_slb @ SV24 @ SV108 ) @ ( pair @ SV72 @ SV108 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[456]) ).
thf(510,plain,
! [SV73: $i,SV25: $i,SV120: $i,SV109: $i] :
( ( ( ~ ( less_than @ SV109 @ SV120 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV25 @ ( pair @ SV73 @ SV120 ) ) @ SV109 )
= ( insert_slb @ ( update_slb @ SV25 @ SV109 ) @ ( pair @ SV73 @ SV120 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(511,plain,
! [SV143: $i,SV74: $i,SV27: $i] :
( ( ( succ_cpq @ SV27 @ ( insert_cpq @ SV74 @ SV143 ) )
= $true )
| ( ( succ_cpq @ SV27 @ SV74 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(512,plain,
! [SV144: $i,SV75: $i,SV28: $i] :
( ( ( succ_cpq @ SV28 @ ( remove_cpq @ SV75 @ SV144 ) )
= $true )
| ( ( succ_cpq @ SV28 @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(513,plain,
! [SV110: $i,SV79: $i,SV32: $i,SV145: $i,SV121: $i] :
( ( ~ ( strictly_less_than @ SV121 @ SV145 )
| ~ ( check_cpq @ ( triple @ SV32 @ ( insert_slb @ SV79 @ ( pair @ SV121 @ SV145 ) ) @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(514,plain,
! [SV113: $i,SV36: $i,SV123: $i,SV83: $i] :
( ( ( contains_slb @ SV83 @ SV123 )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV36 @ SV83 @ SV113 ) @ SV123 )
= ( triple @ SV36 @ SV83 @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(515,plain,
! [SV114: $i,SV37: $i,SV124: $i,SV84: $i] :
( ( ( ~ ( contains_slb @ SV84 @ SV124 )
| ~ ( less_than @ ( lookup_slb @ SV84 @ SV124 ) @ SV124 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV37 @ SV84 @ SV114 ) @ SV124 )
= ( triple @ ( remove_pqp @ SV37 @ SV124 ) @ ( remove_slb @ SV84 @ SV124 ) @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(516,plain,
! [SV115: $i,SV38: $i,SV125: $i,SV85: $i] :
( ( ( ~ ( contains_slb @ SV85 @ SV125 )
| ~ ( strictly_less_than @ SV125 @ ( lookup_slb @ SV85 @ SV125 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV38 @ SV85 @ SV115 ) @ SV125 )
= ( triple @ ( remove_pqp @ SV38 @ SV125 ) @ ( remove_slb @ SV85 @ SV125 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(517,plain,
! [SV146: $i,SV87: $i,SV40: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV40 @ SV87 @ SV146 ) )
= ( triple @ SV40 @ ( update_slb @ SV87 @ ( findmin_pqp_res @ SV40 ) ) @ bad ) )
= $true )
| ( ( contains_slb @ SV87 @ ( findmin_pqp_res @ SV40 ) )
= $true )
| ( ( SV87 = create_slb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(518,plain,
! [SV41: $i,SV88: $i] :
( ( ( SV88 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV88 @ ( findmin_pqp_res @ SV41 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV41 ) @ ( lookup_slb @ SV88 @ ( findmin_pqp_res @ SV41 ) ) ) )
= $true )
| ( ( ! [SY317: $i] :
( ( findmin_cpq_eff @ ( triple @ SV41 @ SV88 @ SY317 ) )
= ( triple @ SV41 @ ( update_slb @ SV88 @ ( findmin_pqp_res @ SV41 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[469]) ).
thf(519,plain,
! [SV42: $i,SV89: $i] :
( ( ( SV89 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV89 @ ( findmin_pqp_res @ SV42 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV89 @ ( findmin_pqp_res @ SV42 ) ) @ ( findmin_pqp_res @ SV42 ) ) )
= $true )
| ( ( ! [SY318: $i] :
( ( findmin_cpq_eff @ ( triple @ SV42 @ SV89 @ SY318 ) )
= ( triple @ SV42 @ ( update_slb @ SV89 @ ( findmin_pqp_res @ SV42 ) ) @ SY318 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(520,plain,
! [SV116: $i,SV147: $i,SV127: $i,SV93: $i,SV48: $i] :
( ( ( i @ ( triple @ SV48 @ ( insert_slb @ SV93 @ ( pair @ SV127 @ SV147 ) ) @ SV116 ) )
= ( insert_pq @ ( i @ ( triple @ SV48 @ SV93 @ SV116 ) ) @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(521,plain,
! [SV128: $i] :
( ( ( ! [SY373: $i] :
~ ( pi_sharp_find_min @ ( i @ SV128 ) @ SY373 ) )
= $true )
| ( ( pi_find_min @ SV128 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(522,plain,
! [SV129: $i] :
( ( ( ~ ( pi_find_min @ SV129 ) )
= $true )
| ( ( pi_sharp_find_min @ ( i @ SV129 ) @ ( sK6_V @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(523,plain,
! [SV94: $i,SV49: $i] :
( ( ! [SY323: $i,SY324: $i] :
( ~ ( contains_cpq @ ( triple @ SV49 @ SV94 @ SY323 ) @ SY324 )
| ( contains_slb @ SV94 @ SY324 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[475]) ).
thf(524,plain,
! [SV49: $i,SV94: $i] :
( ( ! [SY325: $i,SY326: $i] :
( ~ ( contains_slb @ SV94 @ SY326 )
| ( contains_cpq @ ( triple @ SV49 @ SV94 @ SY325 ) @ SY326 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[476]) ).
thf(525,plain,
! [SV130: $i] :
( ( ( ! [SY374: $i] :
~ ( pi_sharp_find_min @ ( i @ SV130 ) @ SY374 ) )
= $true )
| ( ( pi_removemin @ SV130 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(526,plain,
! [SV131: $i] :
( ( ( ~ ( pi_removemin @ SV131 ) )
= $true )
| ( ( pi_sharp_find_min @ ( i @ SV131 ) @ ( sK5_V @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[478]) ).
thf(527,plain,
! [SV117: $i,SV95: $i,SV50: $i] :
( ( ~ ~ ( ~ ! [SY359: $i,SY360: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY359 ) ) @ SV117 @ SY360 )
| ( SV95 = SV117 )
| ( pair_in_list @ SV50 @ SV117 @ SY360 ) )
| ~ ! [SY361: $i,SY362: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY361 ) ) @ SV117 @ SY362 )
| ( SY361 = SY362 )
| ( pair_in_list @ SV50 @ SV117 @ SY362 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[479]) ).
thf(528,plain,
! [SV50: $i,SV117: $i,SV95: $i] :
( ( ~ ~ ( ~ ! [SY363: $i,SY364: $i] :
( ( SV95 != SV117 )
| ( SY363 != SY364 )
| ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY363 ) ) @ SV117 @ SY364 ) )
| ~ ! [SY365: $i,SY366: $i] :
( ~ ( pair_in_list @ SV50 @ SV117 @ SY366 )
| ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY365 ) ) @ SV117 @ SY366 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[479]) ).
thf(529,plain,
! [SV148: $i,SV132: $i] :
( ( ~ ( pi_remove @ SV132 @ SV148 )
| ( pi_sharp_remove @ ( i @ SV132 ) @ SV148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(530,plain,
! [SV149: $i,SV133: $i] :
( ( ~ ( pi_sharp_remove @ ( i @ SV133 ) @ SV149 )
| ( pi_remove @ SV133 @ SV149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(531,plain,
! [SV96: $i,SV51: $i] :
( ( ! [SY336: $i] :
( ! [SY337: $i] :
~ ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY337 ) ) @ SY336 )
| ( SV96 = SY336 )
| ( contains_slb @ SV51 @ SY336 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[482]) ).
thf(532,plain,
! [SV51: $i,SV96: $i] :
( ( ~ ( ~ ! [SY338: $i] :
( ( SV96 != SY338 )
| ! [SY339: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY339 ) ) @ SY338 ) )
| ~ ! [SY340: $i] :
( ~ ( contains_slb @ SV51 @ SY340 )
| ! [SY341: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY341 ) ) @ SY340 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(533,plain,
! [SV134: $i] :
( ( ( ! [SY377: $i] :
( ~ ( ok @ SY377 )
| ~ ( succ_cpq @ SV134 @ SY377 )
| ~ ( check_cpq @ SY377 ) ) )
= $true )
| ( ( phi @ SV134 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[484]) ).
thf(534,plain,
! [SV135: $i] :
( ( ( ~ ( phi @ SV135 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ok @ ( sK4_V @ SV135 ) )
| ~ ( succ_cpq @ SV135 @ ( sK4_V @ SV135 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SV135 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(535,plain,
! [SV150: $i,SV136: $i] :
( ( ~ ( less_than @ SV136 @ SV150 )
| ( less_than @ SV150 @ SV136 )
| ( strictly_less_than @ SV136 @ SV150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(536,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[487]) ).
thf(537,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[487]) ).
thf(538,plain,
! [SV151: $i,SV137: $i] :
( ( ~ ( contains_pq @ SV137 @ SV151 )
| ~ ( issmallestelement_pq @ SV137 @ SV151 )
| ( pi_sharp_find_min @ SV137 @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(539,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[489]) ).
thf(540,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[489]) ).
thf(541,plain,
! [SV152: $i,SV138: $i] :
( ( ~ ( contains_pq @ SV138 @ SV152 )
| ( pi_sharp_remove @ SV138 @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(542,plain,
! [SV153: $i,SV139: $i] :
( ( ~ ( pi_sharp_remove @ SV139 @ SV153 )
| ( contains_pq @ SV139 @ SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(543,plain,
! [SV118: $i,SV97: $i,SV52: $i] :
( ( ~ ! [SY367: $i,SY368: $i] :
( ~ ( less_than @ SY368 @ SY367 )
| ~ ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV97 @ ( pair @ SY367 @ SY368 ) ) @ SV118 ) )
| ( check_cpq @ ( triple @ SV52 @ SV97 @ SV118 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[492]) ).
thf(544,plain,
! [SV118: $i,SV97: $i,SV52: $i] :
( ( ~ ! [SY369: $i,SY370: $i] :
( ~ ( less_than @ SY370 @ SY369 )
| ~ ( check_cpq @ ( triple @ SV52 @ SV97 @ SV118 ) )
| ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV97 @ ( pair @ SY369 @ SY370 ) ) @ SV118 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[492]) ).
thf(545,plain,
! [SV154: $i,SV140: $i] :
( ( ~ ( ~ ( contains_pq @ SV140 @ ( sK7_W @ SV154 @ SV140 ) )
| ~ ~ ( less_than @ SV154 @ ( sK7_W @ SV154 @ SV140 ) ) )
| ( issmallestelement_pq @ SV140 @ SV154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(546,plain,
! [SV155: $i,SV141: $i] :
( ( ~ ( issmallestelement_pq @ SV141 @ SV155 )
| ! [SY386: $i] :
( ~ ( contains_pq @ SV141 @ SY386 )
| ( less_than @ SV155 @ SY386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(547,plain,
! [SV156: $i,SV53: $i] :
( ( ! [SY387: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV53 @ SV156 ) @ SY387 )
| ( SV156 = SY387 )
| ( contains_pq @ SV53 @ SY387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(548,plain,
! [SV53: $i] :
( ( ~ ! [SY282: $i,SY283: $i] :
( ( SY282 != SY283 )
| ( contains_pq @ ( insert_pq @ SV53 @ SY282 ) @ SY283 ) )
| ~ ! [SY284: $i,SY285: $i] :
( ~ ( contains_pq @ SV53 @ SY285 )
| ( contains_pq @ ( insert_pq @ SV53 @ SY284 ) @ SY285 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(549,plain,
! [SV157: $i,SV142: $i] :
( ( ~ ( contains_pq @ SV142 @ SV157 )
| ~ ( issmallestelement_pq @ SV142 @ SV157 )
| ( pi_sharp_removemin @ SV142 @ SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(550,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[498]) ).
thf(551,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[498]) ).
thf(552,plain,
! [SV100: $i,SV56: $i,SV3: $i] :
( ( ( less_than @ SV3 @ SV56 )
= $false )
| ( ( ~ ( less_than @ SV56 @ SV100 ) )
= $true )
| ( ( less_than @ SV3 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(553,plain,
! [SV60: $i,SV101: $i,SV10: $i] :
( ( ( contains_pq @ SV10 @ SV101 )
= $false )
| ( ( SV60 = SV101 )
= $true )
| ( ( ( remove_pq @ ( insert_pq @ SV10 @ SV60 ) @ SV101 )
= ( insert_pq @ ( remove_pq @ SV10 @ SV101 ) @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(554,plain,
! [SV61: $i,SV11: $i] :
( ( ( issmallestelement_pq @ SV11 @ SV61 )
= $false )
| ( ( contains_pq @ SV11 @ SV61 )
= $false )
| ( ( ( findmin_pq_eff @ SV11 @ SV61 )
= SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(555,plain,
! [SV62: $i,SV12: $i] :
( ( ( issmallestelement_pq @ SV12 @ SV62 )
= $false )
| ( ( contains_pq @ SV12 @ SV62 )
= $false )
| ( ( ( findmin_pq_res @ SV12 @ SV62 )
= SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(556,plain,
! [SV63: $i,SV13: $i] :
( ( ( issmallestelement_pq @ SV13 @ SV63 )
= $false )
| ( ( contains_pq @ SV13 @ SV63 )
= $false )
| ( ( ( removemin_pq_eff @ SV13 @ SV63 )
= ( remove_pq @ SV13 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[505]) ).
thf(557,plain,
! [SV64: $i,SV14: $i] :
( ( ( issmallestelement_pq @ SV14 @ SV64 )
= $false )
| ( ( contains_pq @ SV14 @ SV64 )
= $false )
| ( ( ( removemin_pq_res @ SV14 @ SV64 )
= SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(558,plain,
! [SV69: $i,SV105: $i,SV20: $i] :
( ( ( contains_slb @ SV20 @ SV105 )
= $false )
| ( ( SV69 = SV105 )
= $true )
| ( ( ! [SY347: $i] :
( ( remove_slb @ ( insert_slb @ SV20 @ ( pair @ SV69 @ SY347 ) ) @ SV105 )
= ( insert_slb @ ( remove_slb @ SV20 @ SV105 ) @ ( pair @ SV69 @ SY347 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(559,plain,
! [SV71: $i,SV107: $i,SV22: $i] :
( ( ( contains_slb @ SV22 @ SV107 )
= $false )
| ( ( SV71 = SV107 )
= $true )
| ( ( ! [SY348: $i] :
( ( lookup_slb @ ( insert_slb @ SV22 @ ( pair @ SV71 @ SY348 ) ) @ SV107 )
= ( lookup_slb @ SV22 @ SV107 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(560,plain,
! [SV72: $i,SV24: $i,SV108: $i,SV119: $i] :
( ( ( strictly_less_than @ SV119 @ SV108 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV24 @ ( pair @ SV72 @ SV119 ) ) @ SV108 )
= ( insert_slb @ ( update_slb @ SV24 @ SV108 ) @ ( pair @ SV72 @ SV108 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[509]) ).
thf(561,plain,
! [SV73: $i,SV25: $i,SV120: $i,SV109: $i] :
( ( ( less_than @ SV109 @ SV120 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV25 @ ( pair @ SV73 @ SV120 ) ) @ SV109 )
= ( insert_slb @ ( update_slb @ SV25 @ SV109 ) @ ( pair @ SV73 @ SV120 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(562,plain,
! [SV110: $i,SV79: $i,SV32: $i,SV145: $i,SV121: $i] :
( ( ( ~ ( strictly_less_than @ SV121 @ SV145 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV32 @ ( insert_slb @ SV79 @ ( pair @ SV121 @ SV145 ) ) @ SV110 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(563,plain,
! [SV114: $i,SV37: $i,SV124: $i,SV84: $i] :
( ( ( ~ ( contains_slb @ SV84 @ SV124 ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV84 @ SV124 ) @ SV124 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV37 @ SV84 @ SV114 ) @ SV124 )
= ( triple @ ( remove_pqp @ SV37 @ SV124 ) @ ( remove_slb @ SV84 @ SV124 ) @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(564,plain,
! [SV115: $i,SV38: $i,SV125: $i,SV85: $i] :
( ( ( ~ ( contains_slb @ SV85 @ SV125 ) )
= $true )
| ( ( ~ ( strictly_less_than @ SV125 @ ( lookup_slb @ SV85 @ SV125 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV38 @ SV85 @ SV115 ) @ SV125 )
= ( triple @ ( remove_pqp @ SV38 @ SV125 ) @ ( remove_slb @ SV85 @ SV125 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(565,plain,
! [SV41: $i,SV88: $i] :
( ( ( contains_slb @ SV88 @ ( findmin_pqp_res @ SV41 ) )
= $false )
| ( ( SV88 = create_slb )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV41 ) @ ( lookup_slb @ SV88 @ ( findmin_pqp_res @ SV41 ) ) ) )
= $true )
| ( ( ! [SY317: $i] :
( ( findmin_cpq_eff @ ( triple @ SV41 @ SV88 @ SY317 ) )
= ( triple @ SV41 @ ( update_slb @ SV88 @ ( findmin_pqp_res @ SV41 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(566,plain,
! [SV42: $i,SV89: $i] :
( ( ( contains_slb @ SV89 @ ( findmin_pqp_res @ SV42 ) )
= $false )
| ( ( SV89 = create_slb )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV89 @ ( findmin_pqp_res @ SV42 ) ) @ ( findmin_pqp_res @ SV42 ) ) )
= $true )
| ( ( ! [SY318: $i] :
( ( findmin_cpq_eff @ ( triple @ SV42 @ SV89 @ SY318 ) )
= ( triple @ SV42 @ ( update_slb @ SV89 @ ( findmin_pqp_res @ SV42 ) ) @ SY318 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(567,plain,
! [SV158: $i,SV128: $i] :
( ( ( ~ ( pi_sharp_find_min @ ( i @ SV128 ) @ SV158 ) )
= $true )
| ( ( pi_find_min @ SV128 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(568,plain,
! [SV129: $i] :
( ( ( pi_find_min @ SV129 )
= $false )
| ( ( pi_sharp_find_min @ ( i @ SV129 ) @ ( sK6_V @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(569,plain,
! [SV159: $i,SV94: $i,SV49: $i] :
( ( ! [SY388: $i] :
( ~ ( contains_cpq @ ( triple @ SV49 @ SV94 @ SV159 ) @ SY388 )
| ( contains_slb @ SV94 @ SY388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(570,plain,
! [SV160: $i,SV49: $i,SV94: $i] :
( ( ! [SY389: $i] :
( ~ ( contains_slb @ SV94 @ SY389 )
| ( contains_cpq @ ( triple @ SV49 @ SV94 @ SV160 ) @ SY389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(571,plain,
! [SV161: $i,SV130: $i] :
( ( ( ~ ( pi_sharp_find_min @ ( i @ SV130 ) @ SV161 ) )
= $true )
| ( ( pi_removemin @ SV130 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(572,plain,
! [SV131: $i] :
( ( ( pi_removemin @ SV131 )
= $false )
| ( ( pi_sharp_find_min @ ( i @ SV131 ) @ ( sK5_V @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(573,plain,
! [SV117: $i,SV95: $i,SV50: $i] :
( ( ~ ( ~ ! [SY359: $i,SY360: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY359 ) ) @ SV117 @ SY360 )
| ( SV95 = SV117 )
| ( pair_in_list @ SV50 @ SV117 @ SY360 ) )
| ~ ! [SY361: $i,SY362: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY361 ) ) @ SV117 @ SY362 )
| ( SY361 = SY362 )
| ( pair_in_list @ SV50 @ SV117 @ SY362 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[527]) ).
thf(574,plain,
! [SV50: $i,SV117: $i,SV95: $i] :
( ( ~ ( ~ ! [SY363: $i,SY364: $i] :
( ( SV95 != SV117 )
| ( SY363 != SY364 )
| ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY363 ) ) @ SV117 @ SY364 ) )
| ~ ! [SY365: $i,SY366: $i] :
( ~ ( pair_in_list @ SV50 @ SV117 @ SY366 )
| ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY365 ) ) @ SV117 @ SY366 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[528]) ).
thf(575,plain,
! [SV148: $i,SV132: $i] :
( ( ( ~ ( pi_remove @ SV132 @ SV148 ) )
= $true )
| ( ( pi_sharp_remove @ ( i @ SV132 ) @ SV148 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[529]) ).
thf(576,plain,
! [SV149: $i,SV133: $i] :
( ( ( ~ ( pi_sharp_remove @ ( i @ SV133 ) @ SV149 ) )
= $true )
| ( ( pi_remove @ SV133 @ SV149 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[530]) ).
thf(577,plain,
! [SV162: $i,SV96: $i,SV51: $i] :
( ( ! [SY390: $i] :
~ ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY390 ) ) @ SV162 )
| ( SV96 = SV162 )
| ( contains_slb @ SV51 @ SV162 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(578,plain,
! [SV51: $i,SV96: $i] :
( ( ~ ! [SY338: $i] :
( ( SV96 != SY338 )
| ! [SY339: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY339 ) ) @ SY338 ) )
| ~ ! [SY340: $i] :
( ~ ( contains_slb @ SV51 @ SY340 )
| ! [SY341: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY341 ) ) @ SY340 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(579,plain,
! [SV134: $i,SV163: $i] :
( ( ( ~ ( ok @ SV163 )
| ~ ( succ_cpq @ SV134 @ SV163 )
| ~ ( check_cpq @ SV163 ) )
= $true )
| ( ( phi @ SV134 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(580,plain,
! [SV135: $i] :
( ( ( phi @ SV135 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( ok @ ( sK4_V @ SV135 ) )
| ~ ( succ_cpq @ SV135 @ ( sK4_V @ SV135 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SV135 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(581,plain,
! [SV150: $i,SV136: $i] :
( ( ( ~ ( less_than @ SV136 @ SV150 )
| ( less_than @ SV150 @ SV136 ) )
= $true )
| ( ( strictly_less_than @ SV136 @ SV150 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[535]) ).
thf(582,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[536]) ).
thf(583,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[537]) ).
thf(584,plain,
! [SV151: $i,SV137: $i] :
( ( ( ~ ( contains_pq @ SV137 @ SV151 )
| ~ ( issmallestelement_pq @ SV137 @ SV151 ) )
= $true )
| ( ( pi_sharp_find_min @ SV137 @ SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[538]) ).
thf(585,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[539]) ).
thf(586,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[540]) ).
thf(587,plain,
! [SV152: $i,SV138: $i] :
( ( ( ~ ( contains_pq @ SV138 @ SV152 ) )
= $true )
| ( ( pi_sharp_remove @ SV138 @ SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[541]) ).
thf(588,plain,
! [SV153: $i,SV139: $i] :
( ( ( ~ ( pi_sharp_remove @ SV139 @ SV153 ) )
= $true )
| ( ( contains_pq @ SV139 @ SV153 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[542]) ).
thf(589,plain,
! [SV118: $i,SV97: $i,SV52: $i] :
( ( ! [SY367: $i,SY368: $i] :
( ~ ( less_than @ SY368 @ SY367 )
| ~ ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV97 @ ( pair @ SY367 @ SY368 ) ) @ SV118 ) )
| ( check_cpq @ ( triple @ SV52 @ SV97 @ SV118 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[543]) ).
thf(590,plain,
! [SV118: $i,SV97: $i,SV52: $i] :
( ( ! [SY369: $i,SY370: $i] :
( ~ ( less_than @ SY370 @ SY369 )
| ~ ( check_cpq @ ( triple @ SV52 @ SV97 @ SV118 ) )
| ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV97 @ ( pair @ SY369 @ SY370 ) ) @ SV118 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[544]) ).
thf(591,plain,
! [SV154: $i,SV140: $i] :
( ( ( ~ ( ~ ( contains_pq @ SV140 @ ( sK7_W @ SV154 @ SV140 ) )
| ~ ~ ( less_than @ SV154 @ ( sK7_W @ SV154 @ SV140 ) ) ) )
= $true )
| ( ( issmallestelement_pq @ SV140 @ SV154 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(592,plain,
! [SV155: $i,SV141: $i] :
( ( ( ~ ( issmallestelement_pq @ SV141 @ SV155 ) )
= $true )
| ( ( ! [SY386: $i] :
( ~ ( contains_pq @ SV141 @ SY386 )
| ( less_than @ SV155 @ SY386 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[546]) ).
thf(593,plain,
! [SV164: $i,SV156: $i,SV53: $i] :
( ( ~ ( contains_pq @ ( insert_pq @ SV53 @ SV156 ) @ SV164 )
| ( SV156 = SV164 )
| ( contains_pq @ SV53 @ SV164 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(594,plain,
! [SV53: $i] :
( ( ~ ! [SY282: $i,SY283: $i] :
( ( SY282 != SY283 )
| ( contains_pq @ ( insert_pq @ SV53 @ SY282 ) @ SY283 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[548]) ).
thf(595,plain,
! [SV53: $i] :
( ( ~ ! [SY284: $i,SY285: $i] :
( ~ ( contains_pq @ SV53 @ SY285 )
| ( contains_pq @ ( insert_pq @ SV53 @ SY284 ) @ SY285 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[548]) ).
thf(596,plain,
! [SV157: $i,SV142: $i] :
( ( ( ~ ( contains_pq @ SV142 @ SV157 )
| ~ ( issmallestelement_pq @ SV142 @ SV157 ) )
= $true )
| ( ( pi_sharp_removemin @ SV142 @ SV157 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[549]) ).
thf(597,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(598,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(599,plain,
! [SV3: $i,SV100: $i,SV56: $i] :
( ( ( less_than @ SV56 @ SV100 )
= $false )
| ( ( less_than @ SV3 @ SV56 )
= $false )
| ( ( less_than @ SV3 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(600,plain,
! [SV105: $i,SV165: $i,SV69: $i,SV20: $i] :
( ( ( ( remove_slb @ ( insert_slb @ SV20 @ ( pair @ SV69 @ SV165 ) ) @ SV105 )
= ( insert_slb @ ( remove_slb @ SV20 @ SV105 ) @ ( pair @ SV69 @ SV165 ) ) )
= $true )
| ( ( SV69 = SV105 )
= $true )
| ( ( contains_slb @ SV20 @ SV105 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(601,plain,
! [SV107: $i,SV166: $i,SV71: $i,SV22: $i] :
( ( ( ( lookup_slb @ ( insert_slb @ SV22 @ ( pair @ SV71 @ SV166 ) ) @ SV107 )
= ( lookup_slb @ SV22 @ SV107 ) )
= $true )
| ( ( SV71 = SV107 )
= $true )
| ( ( contains_slb @ SV22 @ SV107 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(602,plain,
! [SV110: $i,SV79: $i,SV32: $i,SV145: $i,SV121: $i] :
( ( ( strictly_less_than @ SV121 @ SV145 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV32 @ ( insert_slb @ SV79 @ ( pair @ SV121 @ SV145 ) ) @ SV110 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(603,plain,
! [SV114: $i,SV37: $i,SV124: $i,SV84: $i] :
( ( ( contains_slb @ SV84 @ SV124 )
= $false )
| ( ( ~ ( less_than @ ( lookup_slb @ SV84 @ SV124 ) @ SV124 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV37 @ SV84 @ SV114 ) @ SV124 )
= ( triple @ ( remove_pqp @ SV37 @ SV124 ) @ ( remove_slb @ SV84 @ SV124 ) @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(604,plain,
! [SV115: $i,SV38: $i,SV125: $i,SV85: $i] :
( ( ( contains_slb @ SV85 @ SV125 )
= $false )
| ( ( ~ ( strictly_less_than @ SV125 @ ( lookup_slb @ SV85 @ SV125 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV38 @ SV85 @ SV115 ) @ SV125 )
= ( triple @ ( remove_pqp @ SV38 @ SV125 ) @ ( remove_slb @ SV85 @ SV125 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(605,plain,
! [SV88: $i,SV41: $i] :
( ( ( strictly_less_than @ ( findmin_pqp_res @ SV41 ) @ ( lookup_slb @ SV88 @ ( findmin_pqp_res @ SV41 ) ) )
= $false )
| ( ( SV88 = create_slb )
= $true )
| ( ( contains_slb @ SV88 @ ( findmin_pqp_res @ SV41 ) )
= $false )
| ( ( ! [SY317: $i] :
( ( findmin_cpq_eff @ ( triple @ SV41 @ SV88 @ SY317 ) )
= ( triple @ SV41 @ ( update_slb @ SV88 @ ( findmin_pqp_res @ SV41 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(606,plain,
! [SV42: $i,SV89: $i] :
( ( ( less_than @ ( lookup_slb @ SV89 @ ( findmin_pqp_res @ SV42 ) ) @ ( findmin_pqp_res @ SV42 ) )
= $false )
| ( ( SV89 = create_slb )
= $true )
| ( ( contains_slb @ SV89 @ ( findmin_pqp_res @ SV42 ) )
= $false )
| ( ( ! [SY318: $i] :
( ( findmin_cpq_eff @ ( triple @ SV42 @ SV89 @ SY318 ) )
= ( triple @ SV42 @ ( update_slb @ SV89 @ ( findmin_pqp_res @ SV42 ) ) @ SY318 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(607,plain,
! [SV158: $i,SV128: $i] :
( ( ( pi_sharp_find_min @ ( i @ SV128 ) @ SV158 )
= $false )
| ( ( pi_find_min @ SV128 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(608,plain,
! [SV167: $i,SV159: $i,SV94: $i,SV49: $i] :
( ( ~ ( contains_cpq @ ( triple @ SV49 @ SV94 @ SV159 ) @ SV167 )
| ( contains_slb @ SV94 @ SV167 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(609,plain,
! [SV160: $i,SV49: $i,SV168: $i,SV94: $i] :
( ( ~ ( contains_slb @ SV94 @ SV168 )
| ( contains_cpq @ ( triple @ SV49 @ SV94 @ SV160 ) @ SV168 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(610,plain,
! [SV161: $i,SV130: $i] :
( ( ( pi_sharp_find_min @ ( i @ SV130 ) @ SV161 )
= $false )
| ( ( pi_removemin @ SV130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(611,plain,
! [SV117: $i,SV95: $i,SV50: $i] :
( ( ~ ! [SY359: $i,SY360: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY359 ) ) @ SV117 @ SY360 )
| ( SV95 = SV117 )
| ( pair_in_list @ SV50 @ SV117 @ SY360 ) )
| ~ ! [SY361: $i,SY362: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY361 ) ) @ SV117 @ SY362 )
| ( SY361 = SY362 )
| ( pair_in_list @ SV50 @ SV117 @ SY362 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(612,plain,
! [SV50: $i,SV117: $i,SV95: $i] :
( ( ~ ! [SY363: $i,SY364: $i] :
( ( SV95 != SV117 )
| ( SY363 != SY364 )
| ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY363 ) ) @ SV117 @ SY364 ) )
| ~ ! [SY365: $i,SY366: $i] :
( ~ ( pair_in_list @ SV50 @ SV117 @ SY366 )
| ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY365 ) ) @ SV117 @ SY366 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(613,plain,
! [SV148: $i,SV132: $i] :
( ( ( pi_remove @ SV132 @ SV148 )
= $false )
| ( ( pi_sharp_remove @ ( i @ SV132 ) @ SV148 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(614,plain,
! [SV149: $i,SV133: $i] :
( ( ( pi_sharp_remove @ ( i @ SV133 ) @ SV149 )
= $false )
| ( ( pi_remove @ SV133 @ SV149 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(615,plain,
! [SV162: $i,SV96: $i,SV51: $i] :
( ( ( ! [SY390: $i] :
~ ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY390 ) ) @ SV162 ) )
= $true )
| ( ( ( SV96 = SV162 )
| ( contains_slb @ SV51 @ SV162 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[577]) ).
thf(616,plain,
! [SV51: $i,SV96: $i] :
( ( ~ ! [SY338: $i] :
( ( SV96 != SY338 )
| ! [SY339: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY339 ) ) @ SY338 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[578]) ).
thf(617,plain,
! [SV96: $i,SV51: $i] :
( ( ~ ! [SY340: $i] :
( ~ ( contains_slb @ SV51 @ SY340 )
| ! [SY341: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY341 ) ) @ SY340 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[578]) ).
thf(618,plain,
! [SV134: $i,SV163: $i] :
( ( ( ~ ( ok @ SV163 )
| ~ ( succ_cpq @ SV134 @ SV163 ) )
= $true )
| ( ( ~ ( check_cpq @ SV163 ) )
= $true )
| ( ( phi @ SV134 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[579]) ).
thf(619,plain,
! [SV135: $i] :
( ( ( ~ ~ ( ~ ( ok @ ( sK4_V @ SV135 ) )
| ~ ( succ_cpq @ SV135 @ ( sK4_V @ SV135 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SV135 ) ) )
= $false )
| ( ( phi @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(620,plain,
! [SV150: $i,SV136: $i] :
( ( ( ~ ( less_than @ SV136 @ SV150 ) )
= $true )
| ( ( less_than @ SV150 @ SV136 )
= $true )
| ( ( strictly_less_than @ SV136 @ SV150 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[581]) ).
thf(621,plain,
! [SV169: $i] :
( ( ! [SY391: $i] :
( ~ ( strictly_less_than @ SV169 @ SY391 )
| ( less_than @ SV169 @ SY391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(622,plain,
! [SV170: $i] :
( ( ! [SY392: $i] :
( ~ ( strictly_less_than @ SV170 @ SY392 )
| ~ ( less_than @ SY392 @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(623,plain,
! [SV151: $i,SV137: $i] :
( ( ( ~ ( contains_pq @ SV137 @ SV151 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV137 @ SV151 ) )
= $true )
| ( ( pi_sharp_find_min @ SV137 @ SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(624,plain,
! [SV171: $i] :
( ( ! [SY393: $i] :
( ~ ( pi_sharp_find_min @ SV171 @ SY393 )
| ( contains_pq @ SV171 @ SY393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(625,plain,
! [SV172: $i] :
( ( ! [SY394: $i] :
( ~ ( pi_sharp_find_min @ SV172 @ SY394 )
| ( issmallestelement_pq @ SV172 @ SY394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(626,plain,
! [SV152: $i,SV138: $i] :
( ( ( contains_pq @ SV138 @ SV152 )
= $false )
| ( ( pi_sharp_remove @ SV138 @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(627,plain,
! [SV153: $i,SV139: $i] :
( ( ( pi_sharp_remove @ SV139 @ SV153 )
= $false )
| ( ( contains_pq @ SV139 @ SV153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[588]) ).
thf(628,plain,
! [SV118: $i,SV97: $i,SV52: $i,SV173: $i] :
( ( ! [SY395: $i] :
( ~ ( less_than @ SY395 @ SV173 )
| ~ ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV97 @ ( pair @ SV173 @ SY395 ) ) @ SV118 ) )
| ( check_cpq @ ( triple @ SV52 @ SV97 @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(629,plain,
! [SV118: $i,SV97: $i,SV52: $i,SV174: $i] :
( ( ! [SY396: $i] :
( ~ ( less_than @ SY396 @ SV174 )
| ~ ( check_cpq @ ( triple @ SV52 @ SV97 @ SV118 ) )
| ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV97 @ ( pair @ SV174 @ SY396 ) ) @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(630,plain,
! [SV154: $i,SV140: $i] :
( ( ( ~ ( contains_pq @ SV140 @ ( sK7_W @ SV154 @ SV140 ) )
| ~ ~ ( less_than @ SV154 @ ( sK7_W @ SV154 @ SV140 ) ) )
= $false )
| ( ( issmallestelement_pq @ SV140 @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[591]) ).
thf(631,plain,
! [SV155: $i,SV141: $i] :
( ( ( issmallestelement_pq @ SV141 @ SV155 )
= $false )
| ( ( ! [SY386: $i] :
( ~ ( contains_pq @ SV141 @ SY386 )
| ( less_than @ SV155 @ SY386 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(632,plain,
! [SV164: $i,SV156: $i,SV53: $i] :
( ( ( ~ ( contains_pq @ ( insert_pq @ SV53 @ SV156 ) @ SV164 ) )
= $true )
| ( ( ( SV156 = SV164 )
| ( contains_pq @ SV53 @ SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[593]) ).
thf(633,plain,
! [SV53: $i] :
( ( ! [SY282: $i,SY283: $i] :
( ( SY282 != SY283 )
| ( contains_pq @ ( insert_pq @ SV53 @ SY282 ) @ SY283 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[594]) ).
thf(634,plain,
! [SV53: $i] :
( ( ! [SY284: $i,SY285: $i] :
( ~ ( contains_pq @ SV53 @ SY285 )
| ( contains_pq @ ( insert_pq @ SV53 @ SY284 ) @ SY285 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[595]) ).
thf(635,plain,
! [SV157: $i,SV142: $i] :
( ( ( ~ ( contains_pq @ SV142 @ SV157 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV142 @ SV157 ) )
= $true )
| ( ( pi_sharp_removemin @ SV142 @ SV157 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(636,plain,
! [SV175: $i] :
( ( ! [SY397: $i] :
( ~ ( pi_sharp_removemin @ SV175 @ SY397 )
| ( contains_pq @ SV175 @ SY397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(637,plain,
! [SV176: $i] :
( ( ! [SY398: $i] :
( ~ ( pi_sharp_removemin @ SV176 @ SY398 )
| ( issmallestelement_pq @ SV176 @ SY398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(638,plain,
! [SV110: $i,SV145: $i,SV121: $i,SV79: $i,SV32: $i] :
( ( ( check_cpq @ ( triple @ SV32 @ ( insert_slb @ SV79 @ ( pair @ SV121 @ SV145 ) ) @ SV110 ) )
= $false )
| ( ( strictly_less_than @ SV121 @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(639,plain,
! [SV114: $i,SV37: $i,SV124: $i,SV84: $i] :
( ( ( less_than @ ( lookup_slb @ SV84 @ SV124 ) @ SV124 )
= $false )
| ( ( contains_slb @ SV84 @ SV124 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV37 @ SV84 @ SV114 ) @ SV124 )
= ( triple @ ( remove_pqp @ SV37 @ SV124 ) @ ( remove_slb @ SV84 @ SV124 ) @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(640,plain,
! [SV115: $i,SV38: $i,SV85: $i,SV125: $i] :
( ( ( strictly_less_than @ SV125 @ ( lookup_slb @ SV85 @ SV125 ) )
= $false )
| ( ( contains_slb @ SV85 @ SV125 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV38 @ SV85 @ SV115 ) @ SV125 )
= ( triple @ ( remove_pqp @ SV38 @ SV125 ) @ ( remove_slb @ SV85 @ SV125 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(641,plain,
! [SV177: $i,SV88: $i,SV41: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV41 @ SV88 @ SV177 ) )
= ( triple @ SV41 @ ( update_slb @ SV88 @ ( findmin_pqp_res @ SV41 ) ) @ bad ) )
= $true )
| ( ( contains_slb @ SV88 @ ( findmin_pqp_res @ SV41 ) )
= $false )
| ( ( SV88 = create_slb )
= $true )
| ( ( strictly_less_than @ ( findmin_pqp_res @ SV41 ) @ ( lookup_slb @ SV88 @ ( findmin_pqp_res @ SV41 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(642,plain,
! [SV178: $i,SV89: $i,SV42: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV42 @ SV89 @ SV178 ) )
= ( triple @ SV42 @ ( update_slb @ SV89 @ ( findmin_pqp_res @ SV42 ) ) @ SV178 ) )
= $true )
| ( ( contains_slb @ SV89 @ ( findmin_pqp_res @ SV42 ) )
= $false )
| ( ( SV89 = create_slb )
= $true )
| ( ( less_than @ ( lookup_slb @ SV89 @ ( findmin_pqp_res @ SV42 ) ) @ ( findmin_pqp_res @ SV42 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(643,plain,
! [SV167: $i,SV159: $i,SV94: $i,SV49: $i] :
( ( ( ~ ( contains_cpq @ ( triple @ SV49 @ SV94 @ SV159 ) @ SV167 ) )
= $true )
| ( ( contains_slb @ SV94 @ SV167 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(644,plain,
! [SV160: $i,SV49: $i,SV168: $i,SV94: $i] :
( ( ( ~ ( contains_slb @ SV94 @ SV168 ) )
= $true )
| ( ( contains_cpq @ ( triple @ SV49 @ SV94 @ SV160 ) @ SV168 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[609]) ).
thf(645,plain,
! [SV117: $i,SV95: $i,SV50: $i] :
( ( ~ ! [SY359: $i,SY360: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY359 ) ) @ SV117 @ SY360 )
| ( SV95 = SV117 )
| ( pair_in_list @ SV50 @ SV117 @ SY360 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[611]) ).
thf(646,plain,
! [SV117: $i,SV95: $i,SV50: $i] :
( ( ~ ! [SY361: $i,SY362: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY361 ) ) @ SV117 @ SY362 )
| ( SY361 = SY362 )
| ( pair_in_list @ SV50 @ SV117 @ SY362 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[611]) ).
thf(647,plain,
! [SV50: $i,SV117: $i,SV95: $i] :
( ( ~ ! [SY363: $i,SY364: $i] :
( ( SV95 != SV117 )
| ( SY363 != SY364 )
| ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY363 ) ) @ SV117 @ SY364 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[612]) ).
thf(648,plain,
! [SV95: $i,SV117: $i,SV50: $i] :
( ( ~ ! [SY365: $i,SY366: $i] :
( ~ ( pair_in_list @ SV50 @ SV117 @ SY366 )
| ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY365 ) ) @ SV117 @ SY366 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[612]) ).
thf(649,plain,
! [SV162: $i,SV179: $i,SV96: $i,SV51: $i] :
( ( ( ~ ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SV179 ) ) @ SV162 ) )
= $true )
| ( ( ( SV96 = SV162 )
| ( contains_slb @ SV51 @ SV162 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(650,plain,
! [SV51: $i,SV96: $i] :
( ( ! [SY338: $i] :
( ( SV96 != SY338 )
| ! [SY339: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY339 ) ) @ SY338 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[616]) ).
thf(651,plain,
! [SV96: $i,SV51: $i] :
( ( ! [SY340: $i] :
( ~ ( contains_slb @ SV51 @ SY340 )
| ! [SY341: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY341 ) ) @ SY340 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[617]) ).
thf(652,plain,
! [SV134: $i,SV163: $i] :
( ( ( ~ ( ok @ SV163 ) )
= $true )
| ( ( ~ ( succ_cpq @ SV134 @ SV163 ) )
= $true )
| ( ( ~ ( check_cpq @ SV163 ) )
= $true )
| ( ( phi @ SV134 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(653,plain,
! [SV135: $i] :
( ( ( ~ ~ ( ~ ( ok @ ( sK4_V @ SV135 ) )
| ~ ( succ_cpq @ SV135 @ ( sK4_V @ SV135 ) ) ) )
= $false )
| ( ( phi @ SV135 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[619]) ).
thf(654,plain,
! [SV135: $i] :
( ( ( ~ ( check_cpq @ ( sK4_V @ SV135 ) ) )
= $false )
| ( ( phi @ SV135 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[619]) ).
thf(655,plain,
! [SV150: $i,SV136: $i] :
( ( ( less_than @ SV136 @ SV150 )
= $false )
| ( ( less_than @ SV150 @ SV136 )
= $true )
| ( ( strictly_less_than @ SV136 @ SV150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[620]) ).
thf(656,plain,
! [SV180: $i,SV169: $i] :
( ( ~ ( strictly_less_than @ SV169 @ SV180 )
| ( less_than @ SV169 @ SV180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(657,plain,
! [SV181: $i,SV170: $i] :
( ( ~ ( strictly_less_than @ SV170 @ SV181 )
| ~ ( less_than @ SV181 @ SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(658,plain,
! [SV151: $i,SV137: $i] :
( ( ( contains_pq @ SV137 @ SV151 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV137 @ SV151 ) )
= $true )
| ( ( pi_sharp_find_min @ SV137 @ SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(659,plain,
! [SV182: $i,SV171: $i] :
( ( ~ ( pi_sharp_find_min @ SV171 @ SV182 )
| ( contains_pq @ SV171 @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(660,plain,
! [SV183: $i,SV172: $i] :
( ( ~ ( pi_sharp_find_min @ SV172 @ SV183 )
| ( issmallestelement_pq @ SV172 @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(661,plain,
! [SV118: $i,SV97: $i,SV52: $i,SV173: $i,SV184: $i] :
( ( ~ ( less_than @ SV184 @ SV173 )
| ~ ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV97 @ ( pair @ SV173 @ SV184 ) ) @ SV118 ) )
| ( check_cpq @ ( triple @ SV52 @ SV97 @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(662,plain,
! [SV118: $i,SV97: $i,SV52: $i,SV174: $i,SV185: $i] :
( ( ~ ( less_than @ SV185 @ SV174 )
| ~ ( check_cpq @ ( triple @ SV52 @ SV97 @ SV118 ) )
| ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV97 @ ( pair @ SV174 @ SV185 ) ) @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(663,plain,
! [SV154: $i,SV140: $i] :
( ( ( ~ ( contains_pq @ SV140 @ ( sK7_W @ SV154 @ SV140 ) ) )
= $false )
| ( ( issmallestelement_pq @ SV140 @ SV154 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[630]) ).
thf(664,plain,
! [SV140: $i,SV154: $i] :
( ( ( ~ ~ ( less_than @ SV154 @ ( sK7_W @ SV154 @ SV140 ) ) )
= $false )
| ( ( issmallestelement_pq @ SV140 @ SV154 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[630]) ).
thf(665,plain,
! [SV155: $i,SV186: $i,SV141: $i] :
( ( ( ~ ( contains_pq @ SV141 @ SV186 )
| ( less_than @ SV155 @ SV186 ) )
= $true )
| ( ( issmallestelement_pq @ SV141 @ SV155 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(666,plain,
! [SV164: $i,SV156: $i,SV53: $i] :
( ( ( contains_pq @ ( insert_pq @ SV53 @ SV156 ) @ SV164 )
= $false )
| ( ( ( SV156 = SV164 )
| ( contains_pq @ SV53 @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[632]) ).
thf(667,plain,
! [SV53: $i,SV187: $i] :
( ( ! [SY399: $i] :
( ( SV187 != SY399 )
| ( contains_pq @ ( insert_pq @ SV53 @ SV187 ) @ SY399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(668,plain,
! [SV188: $i,SV53: $i] :
( ( ! [SY400: $i] :
( ~ ( contains_pq @ SV53 @ SY400 )
| ( contains_pq @ ( insert_pq @ SV53 @ SV188 ) @ SY400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(669,plain,
! [SV157: $i,SV142: $i] :
( ( ( contains_pq @ SV142 @ SV157 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV142 @ SV157 ) )
= $true )
| ( ( pi_sharp_removemin @ SV142 @ SV157 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(670,plain,
! [SV189: $i,SV175: $i] :
( ( ~ ( pi_sharp_removemin @ SV175 @ SV189 )
| ( contains_pq @ SV175 @ SV189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(671,plain,
! [SV190: $i,SV176: $i] :
( ( ~ ( pi_sharp_removemin @ SV176 @ SV190 )
| ( issmallestelement_pq @ SV176 @ SV190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(672,plain,
! [SV167: $i,SV159: $i,SV94: $i,SV49: $i] :
( ( ( contains_cpq @ ( triple @ SV49 @ SV94 @ SV159 ) @ SV167 )
= $false )
| ( ( contains_slb @ SV94 @ SV167 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[643]) ).
thf(673,plain,
! [SV160: $i,SV49: $i,SV168: $i,SV94: $i] :
( ( ( contains_slb @ SV94 @ SV168 )
= $false )
| ( ( contains_cpq @ ( triple @ SV49 @ SV94 @ SV160 ) @ SV168 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[644]) ).
thf(674,plain,
! [SV117: $i,SV95: $i,SV50: $i] :
( ( ! [SY359: $i,SY360: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY359 ) ) @ SV117 @ SY360 )
| ( SV95 = SV117 )
| ( pair_in_list @ SV50 @ SV117 @ SY360 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[645]) ).
thf(675,plain,
! [SV117: $i,SV95: $i,SV50: $i] :
( ( ! [SY361: $i,SY362: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY361 ) ) @ SV117 @ SY362 )
| ( SY361 = SY362 )
| ( pair_in_list @ SV50 @ SV117 @ SY362 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[646]) ).
thf(676,plain,
! [SV50: $i,SV117: $i,SV95: $i] :
( ( ! [SY363: $i,SY364: $i] :
( ( SV95 != SV117 )
| ( SY363 != SY364 )
| ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY363 ) ) @ SV117 @ SY364 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[647]) ).
thf(677,plain,
! [SV95: $i,SV117: $i,SV50: $i] :
( ( ! [SY365: $i,SY366: $i] :
( ~ ( pair_in_list @ SV50 @ SV117 @ SY366 )
| ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SY365 ) ) @ SV117 @ SY366 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[648]) ).
thf(678,plain,
! [SV162: $i,SV179: $i,SV96: $i,SV51: $i] :
( ( ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SV179 ) ) @ SV162 )
= $false )
| ( ( ( SV96 = SV162 )
| ( contains_slb @ SV51 @ SV162 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(679,plain,
! [SV51: $i,SV191: $i,SV96: $i] :
( ( ( SV96 != SV191 )
| ! [SY401: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY401 ) ) @ SV191 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(680,plain,
! [SV96: $i,SV192: $i,SV51: $i] :
( ( ~ ( contains_slb @ SV51 @ SV192 )
| ! [SY402: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY402 ) ) @ SV192 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(681,plain,
! [SV134: $i,SV163: $i] :
( ( ( ok @ SV163 )
= $false )
| ( ( ~ ( succ_cpq @ SV134 @ SV163 ) )
= $true )
| ( ( ~ ( check_cpq @ SV163 ) )
= $true )
| ( ( phi @ SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(682,plain,
! [SV135: $i] :
( ( ( ~ ( ~ ( ok @ ( sK4_V @ SV135 ) )
| ~ ( succ_cpq @ SV135 @ ( sK4_V @ SV135 ) ) ) )
= $true )
| ( ( phi @ SV135 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[653]) ).
thf(683,plain,
! [SV135: $i] :
( ( ( check_cpq @ ( sK4_V @ SV135 ) )
= $true )
| ( ( phi @ SV135 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[654]) ).
thf(684,plain,
! [SV180: $i,SV169: $i] :
( ( ( ~ ( strictly_less_than @ SV169 @ SV180 ) )
= $true )
| ( ( less_than @ SV169 @ SV180 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[656]) ).
thf(685,plain,
! [SV181: $i,SV170: $i] :
( ( ( ~ ( strictly_less_than @ SV170 @ SV181 ) )
= $true )
| ( ( ~ ( less_than @ SV181 @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[657]) ).
thf(686,plain,
! [SV151: $i,SV137: $i] :
( ( ( issmallestelement_pq @ SV137 @ SV151 )
= $false )
| ( ( contains_pq @ SV137 @ SV151 )
= $false )
| ( ( pi_sharp_find_min @ SV137 @ SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(687,plain,
! [SV182: $i,SV171: $i] :
( ( ( ~ ( pi_sharp_find_min @ SV171 @ SV182 ) )
= $true )
| ( ( contains_pq @ SV171 @ SV182 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[659]) ).
thf(688,plain,
! [SV183: $i,SV172: $i] :
( ( ( ~ ( pi_sharp_find_min @ SV172 @ SV183 ) )
= $true )
| ( ( issmallestelement_pq @ SV172 @ SV183 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[660]) ).
thf(689,plain,
! [SV118: $i,SV97: $i,SV52: $i,SV173: $i,SV184: $i] :
( ( ( ~ ( less_than @ SV184 @ SV173 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV97 @ ( pair @ SV173 @ SV184 ) ) @ SV118 ) )
| ( check_cpq @ ( triple @ SV52 @ SV97 @ SV118 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[661]) ).
thf(690,plain,
! [SV118: $i,SV97: $i,SV52: $i,SV174: $i,SV185: $i] :
( ( ( ~ ( less_than @ SV185 @ SV174 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV52 @ SV97 @ SV118 ) )
| ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV97 @ ( pair @ SV174 @ SV185 ) ) @ SV118 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[662]) ).
thf(691,plain,
! [SV154: $i,SV140: $i] :
( ( ( contains_pq @ SV140 @ ( sK7_W @ SV154 @ SV140 ) )
= $true )
| ( ( issmallestelement_pq @ SV140 @ SV154 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[663]) ).
thf(692,plain,
! [SV140: $i,SV154: $i] :
( ( ( ~ ( less_than @ SV154 @ ( sK7_W @ SV154 @ SV140 ) ) )
= $true )
| ( ( issmallestelement_pq @ SV140 @ SV154 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[664]) ).
thf(693,plain,
! [SV155: $i,SV186: $i,SV141: $i] :
( ( ( ~ ( contains_pq @ SV141 @ SV186 ) )
= $true )
| ( ( less_than @ SV155 @ SV186 )
= $true )
| ( ( issmallestelement_pq @ SV141 @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[665]) ).
thf(694,plain,
! [SV53: $i,SV164: $i,SV156: $i] :
( ( ( SV156 = SV164 )
= $true )
| ( ( contains_pq @ SV53 @ SV164 )
= $true )
| ( ( contains_pq @ ( insert_pq @ SV53 @ SV156 ) @ SV164 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[666]) ).
thf(695,plain,
! [SV53: $i,SV193: $i,SV187: $i] :
( ( ( SV187 != SV193 )
| ( contains_pq @ ( insert_pq @ SV53 @ SV187 ) @ SV193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(696,plain,
! [SV188: $i,SV194: $i,SV53: $i] :
( ( ~ ( contains_pq @ SV53 @ SV194 )
| ( contains_pq @ ( insert_pq @ SV53 @ SV188 ) @ SV194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(697,plain,
! [SV157: $i,SV142: $i] :
( ( ( issmallestelement_pq @ SV142 @ SV157 )
= $false )
| ( ( contains_pq @ SV142 @ SV157 )
= $false )
| ( ( pi_sharp_removemin @ SV142 @ SV157 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(698,plain,
! [SV189: $i,SV175: $i] :
( ( ( ~ ( pi_sharp_removemin @ SV175 @ SV189 ) )
= $true )
| ( ( contains_pq @ SV175 @ SV189 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[670]) ).
thf(699,plain,
! [SV190: $i,SV176: $i] :
( ( ( ~ ( pi_sharp_removemin @ SV176 @ SV190 ) )
= $true )
| ( ( issmallestelement_pq @ SV176 @ SV190 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[671]) ).
thf(700,plain,
! [SV117: $i,SV195: $i,SV95: $i,SV50: $i] :
( ( ! [SY403: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SV195 ) ) @ SV117 @ SY403 )
| ( SV95 = SV117 )
| ( pair_in_list @ SV50 @ SV117 @ SY403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(701,plain,
! [SV117: $i,SV196: $i,SV95: $i,SV50: $i] :
( ( ! [SY404: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SV196 ) ) @ SV117 @ SY404 )
| ( SV196 = SY404 )
| ( pair_in_list @ SV50 @ SV117 @ SY404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(702,plain,
! [SV50: $i,SV197: $i,SV117: $i,SV95: $i] :
( ( ! [SY405: $i] :
( ( SV95 != SV117 )
| ( SV197 != SY405 )
| ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SV197 ) ) @ SV117 @ SY405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(703,plain,
! [SV198: $i,SV95: $i,SV117: $i,SV50: $i] :
( ( ! [SY406: $i] :
( ~ ( pair_in_list @ SV50 @ SV117 @ SY406 )
| ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SV198 ) ) @ SV117 @ SY406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(704,plain,
! [SV179: $i,SV51: $i,SV162: $i,SV96: $i] :
( ( ( SV96 = SV162 )
= $true )
| ( ( contains_slb @ SV51 @ SV162 )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SV179 ) ) @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[678]) ).
thf(705,plain,
! [SV51: $i,SV191: $i,SV96: $i] :
( ( ( ( SV96 != SV191 ) )
= $true )
| ( ( ! [SY401: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY401 ) ) @ SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[679]) ).
thf(706,plain,
! [SV96: $i,SV192: $i,SV51: $i] :
( ( ( ~ ( contains_slb @ SV51 @ SV192 ) )
= $true )
| ( ( ! [SY402: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY402 ) ) @ SV192 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[680]) ).
thf(707,plain,
! [SV163: $i,SV134: $i] :
( ( ( succ_cpq @ SV134 @ SV163 )
= $false )
| ( ( ok @ SV163 )
= $false )
| ( ( ~ ( check_cpq @ SV163 ) )
= $true )
| ( ( phi @ SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[681]) ).
thf(708,plain,
! [SV135: $i] :
( ( ( ~ ( ok @ ( sK4_V @ SV135 ) )
| ~ ( succ_cpq @ SV135 @ ( sK4_V @ SV135 ) ) )
= $false )
| ( ( phi @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[682]) ).
thf(709,plain,
! [SV180: $i,SV169: $i] :
( ( ( strictly_less_than @ SV169 @ SV180 )
= $false )
| ( ( less_than @ SV169 @ SV180 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(710,plain,
! [SV181: $i,SV170: $i] :
( ( ( strictly_less_than @ SV170 @ SV181 )
= $false )
| ( ( ~ ( less_than @ SV181 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[685]) ).
thf(711,plain,
! [SV182: $i,SV171: $i] :
( ( ( pi_sharp_find_min @ SV171 @ SV182 )
= $false )
| ( ( contains_pq @ SV171 @ SV182 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(712,plain,
! [SV183: $i,SV172: $i] :
( ( ( pi_sharp_find_min @ SV172 @ SV183 )
= $false )
| ( ( issmallestelement_pq @ SV172 @ SV183 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[688]) ).
thf(713,plain,
! [SV118: $i,SV97: $i,SV52: $i,SV173: $i,SV184: $i] :
( ( ( less_than @ SV184 @ SV173 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV97 @ ( pair @ SV173 @ SV184 ) ) @ SV118 ) )
| ( check_cpq @ ( triple @ SV52 @ SV97 @ SV118 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[689]) ).
thf(714,plain,
! [SV118: $i,SV97: $i,SV52: $i,SV174: $i,SV185: $i] :
( ( ( less_than @ SV185 @ SV174 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV52 @ SV97 @ SV118 ) )
| ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV97 @ ( pair @ SV174 @ SV185 ) ) @ SV118 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(715,plain,
! [SV140: $i,SV154: $i] :
( ( ( less_than @ SV154 @ ( sK7_W @ SV154 @ SV140 ) )
= $false )
| ( ( issmallestelement_pq @ SV140 @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[692]) ).
thf(716,plain,
! [SV155: $i,SV186: $i,SV141: $i] :
( ( ( contains_pq @ SV141 @ SV186 )
= $false )
| ( ( less_than @ SV155 @ SV186 )
= $true )
| ( ( issmallestelement_pq @ SV141 @ SV155 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(717,plain,
! [SV53: $i,SV193: $i,SV187: $i] :
( ( ( ( SV187 != SV193 ) )
= $true )
| ( ( contains_pq @ ( insert_pq @ SV53 @ SV187 ) @ SV193 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[695]) ).
thf(718,plain,
! [SV188: $i,SV194: $i,SV53: $i] :
( ( ( ~ ( contains_pq @ SV53 @ SV194 ) )
= $true )
| ( ( contains_pq @ ( insert_pq @ SV53 @ SV188 ) @ SV194 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[696]) ).
thf(719,plain,
! [SV189: $i,SV175: $i] :
( ( ( pi_sharp_removemin @ SV175 @ SV189 )
= $false )
| ( ( contains_pq @ SV175 @ SV189 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(720,plain,
! [SV190: $i,SV176: $i] :
( ( ( pi_sharp_removemin @ SV176 @ SV190 )
= $false )
| ( ( issmallestelement_pq @ SV176 @ SV190 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(721,plain,
! [SV199: $i,SV117: $i,SV195: $i,SV95: $i,SV50: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SV195 ) ) @ SV117 @ SV199 )
| ( SV95 = SV117 )
| ( pair_in_list @ SV50 @ SV117 @ SV199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(722,plain,
! [SV200: $i,SV117: $i,SV196: $i,SV95: $i,SV50: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SV196 ) ) @ SV117 @ SV200 )
| ( SV196 = SV200 )
| ( pair_in_list @ SV50 @ SV117 @ SV200 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(723,plain,
! [SV50: $i,SV201: $i,SV197: $i,SV117: $i,SV95: $i] :
( ( ( SV95 != SV117 )
| ( SV197 != SV201 )
| ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SV197 ) ) @ SV117 @ SV201 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(724,plain,
! [SV198: $i,SV95: $i,SV202: $i,SV117: $i,SV50: $i] :
( ( ~ ( pair_in_list @ SV50 @ SV117 @ SV202 )
| ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SV198 ) ) @ SV117 @ SV202 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(725,plain,
! [SV51: $i,SV191: $i,SV96: $i] :
( ( ( SV96 = SV191 )
= $false )
| ( ( ! [SY401: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY401 ) ) @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(726,plain,
! [SV96: $i,SV192: $i,SV51: $i] :
( ( ( contains_slb @ SV51 @ SV192 )
= $false )
| ( ( ! [SY402: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SY402 ) ) @ SV192 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(727,plain,
! [SV134: $i,SV163: $i] :
( ( ( check_cpq @ SV163 )
= $false )
| ( ( ok @ SV163 )
= $false )
| ( ( succ_cpq @ SV134 @ SV163 )
= $false )
| ( ( phi @ SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(728,plain,
! [SV135: $i] :
( ( ( ~ ( ok @ ( sK4_V @ SV135 ) ) )
= $false )
| ( ( phi @ SV135 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[708]) ).
thf(729,plain,
! [SV135: $i] :
( ( ( ~ ( succ_cpq @ SV135 @ ( sK4_V @ SV135 ) ) )
= $false )
| ( ( phi @ SV135 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[708]) ).
thf(730,plain,
! [SV170: $i,SV181: $i] :
( ( ( less_than @ SV181 @ SV170 )
= $false )
| ( ( strictly_less_than @ SV170 @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(731,plain,
! [SV118: $i,SV184: $i,SV173: $i,SV97: $i,SV52: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV97 @ ( pair @ SV173 @ SV184 ) ) @ SV118 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV52 @ SV97 @ SV118 ) )
= $true )
| ( ( less_than @ SV184 @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[713]) ).
thf(732,plain,
! [SV185: $i,SV174: $i,SV118: $i,SV97: $i,SV52: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV52 @ SV97 @ SV118 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV97 @ ( pair @ SV174 @ SV185 ) ) @ SV118 ) )
= $true )
| ( ( less_than @ SV185 @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[714]) ).
thf(733,plain,
! [SV53: $i,SV193: $i,SV187: $i] :
( ( ( SV187 = SV193 )
= $false )
| ( ( contains_pq @ ( insert_pq @ SV53 @ SV187 ) @ SV193 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(734,plain,
! [SV188: $i,SV194: $i,SV53: $i] :
( ( ( contains_pq @ SV53 @ SV194 )
= $false )
| ( ( contains_pq @ ( insert_pq @ SV53 @ SV188 ) @ SV194 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(735,plain,
! [SV199: $i,SV117: $i,SV195: $i,SV95: $i,SV50: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SV195 ) ) @ SV117 @ SV199 ) )
= $true )
| ( ( ( SV95 = SV117 )
| ( pair_in_list @ SV50 @ SV117 @ SV199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[721]) ).
thf(736,plain,
! [SV200: $i,SV117: $i,SV196: $i,SV95: $i,SV50: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SV196 ) ) @ SV117 @ SV200 ) )
= $true )
| ( ( ( SV196 = SV200 )
| ( pair_in_list @ SV50 @ SV117 @ SV200 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[722]) ).
thf(737,plain,
! [SV50: $i,SV201: $i,SV197: $i,SV117: $i,SV95: $i] :
( ( ( ( SV95 != SV117 )
| ( SV197 != SV201 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SV197 ) ) @ SV117 @ SV201 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[723]) ).
thf(738,plain,
! [SV198: $i,SV95: $i,SV202: $i,SV117: $i,SV50: $i] :
( ( ( ~ ( pair_in_list @ SV50 @ SV117 @ SV202 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SV198 ) ) @ SV117 @ SV202 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[724]) ).
thf(739,plain,
! [SV191: $i,SV203: $i,SV96: $i,SV51: $i] :
( ( ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SV203 ) ) @ SV191 )
= $true )
| ( ( SV96 = SV191 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(740,plain,
! [SV192: $i,SV204: $i,SV96: $i,SV51: $i] :
( ( ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV96 @ SV204 ) ) @ SV192 )
= $true )
| ( ( contains_slb @ SV51 @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(741,plain,
! [SV135: $i] :
( ( ( ok @ ( sK4_V @ SV135 ) )
= $true )
| ( ( phi @ SV135 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[728]) ).
thf(742,plain,
! [SV135: $i] :
( ( ( succ_cpq @ SV135 @ ( sK4_V @ SV135 ) )
= $true )
| ( ( phi @ SV135 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[729]) ).
thf(743,plain,
! [SV118: $i,SV184: $i,SV173: $i,SV97: $i,SV52: $i] :
( ( ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV97 @ ( pair @ SV173 @ SV184 ) ) @ SV118 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV52 @ SV97 @ SV118 ) )
= $true )
| ( ( less_than @ SV184 @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[731]) ).
thf(744,plain,
! [SV185: $i,SV174: $i,SV118: $i,SV97: $i,SV52: $i] :
( ( ( check_cpq @ ( triple @ SV52 @ SV97 @ SV118 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV97 @ ( pair @ SV174 @ SV185 ) ) @ SV118 ) )
= $true )
| ( ( less_than @ SV185 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(745,plain,
! [SV199: $i,SV117: $i,SV195: $i,SV95: $i,SV50: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SV195 ) ) @ SV117 @ SV199 )
= $false )
| ( ( ( SV95 = SV117 )
| ( pair_in_list @ SV50 @ SV117 @ SV199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(746,plain,
! [SV200: $i,SV117: $i,SV196: $i,SV95: $i,SV50: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SV196 ) ) @ SV117 @ SV200 )
= $false )
| ( ( ( SV196 = SV200 )
| ( pair_in_list @ SV50 @ SV117 @ SV200 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[736]) ).
thf(747,plain,
! [SV50: $i,SV201: $i,SV197: $i,SV117: $i,SV95: $i] :
( ( ( ( SV95 != SV117 ) )
= $true )
| ( ( ( SV197 != SV201 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SV197 ) ) @ SV117 @ SV201 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[737]) ).
thf(748,plain,
! [SV198: $i,SV95: $i,SV202: $i,SV117: $i,SV50: $i] :
( ( ( pair_in_list @ SV50 @ SV117 @ SV202 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SV198 ) ) @ SV117 @ SV202 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(749,plain,
! [SV195: $i,SV199: $i,SV50: $i,SV117: $i,SV95: $i] :
( ( ( SV95 = SV117 )
= $true )
| ( ( pair_in_list @ SV50 @ SV117 @ SV199 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SV195 ) ) @ SV117 @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[745]) ).
thf(750,plain,
! [SV95: $i,SV117: $i,SV50: $i,SV200: $i,SV196: $i] :
( ( ( SV196 = SV200 )
= $true )
| ( ( pair_in_list @ SV50 @ SV117 @ SV200 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SV196 ) ) @ SV117 @ SV200 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[746]) ).
thf(751,plain,
! [SV50: $i,SV201: $i,SV197: $i,SV117: $i,SV95: $i] :
( ( ( SV95 = SV117 )
= $false )
| ( ( ( SV197 != SV201 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SV197 ) ) @ SV117 @ SV201 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(752,plain,
! [SV50: $i,SV117: $i,SV95: $i,SV201: $i,SV197: $i] :
( ( ( SV197 = SV201 )
= $false )
| ( ( SV95 = SV117 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV50 @ ( pair @ SV95 @ SV197 ) ) @ SV117 @ SV201 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(753,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[242,752,750,749,748,744,743,742,741,740,739,734,733,730,727,720,719,716,715,712,711,709,704,697,694,691,686,683,673,672,655,642,641,640,639,638,627,626,614,613,610,607,601,600,599,572,568,561,560,557,556,555,554,553,520,517,514,512,511,500,499,471,464,463,461,460,411,402,400,399,398,397,391,363,361,357,349,337,329,328,327,308,305,304,285,282,274,264,263,262]) ).
thf(754,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[753]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV371+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n006.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 : Tue Jun 14 15:34:56 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.38 .
% 0.19/0.40
% 0.19/0.40 No.of.Axioms: 64
% 0.19/0.40
% 0.19/0.40 Length.of.Defs: 0
% 0.19/0.40
% 0.19/0.40 Contains.Choice.Funs: false
% 0.19/0.43 ..
% 0.19/0.46 (rf:0,axioms:64,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:66,loop_count:0,foatp_calls:0,translation:fof_full)..................................................
% 1.66/1.87
% 1.66/1.87 ********************************
% 1.66/1.87 * All subproblems solved! *
% 1.66/1.87 ********************************
% 1.66/1.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:65,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:753,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.94/2.12
% 1.94/2.12 %**** Beginning of derivation protocol ****
% 1.94/2.12 % SZS output start CNFRefutation
% See solution above
% 1.94/2.12
% 1.94/2.12 %**** End of derivation protocol ****
% 1.94/2.12 %**** no. of clauses in derivation: 754 ****
% 1.94/2.12 %**** clause counter: 753 ****
% 1.94/2.12
% 1.94/2.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:65,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:753,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------