TSTP Solution File: SWV370+1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SWV370+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 : n032.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 20:12:08 EDT 2022
% Result : Theorem 2.35s 2.56s
% Output : CNFRefutation 3.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 123
% Syntax : Number of formulae : 1406 ( 918 unt; 60 typ; 0 def)
% Number of atoms : 7345 (2604 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 16726 (2202 ~;2122 |; 121 &;12181 @)
% ( 42 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 76 ( 76 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 60 usr; 17 con; 0-3 aty)
% Number of variables : 4299 ( 0 ^4293 !; 6 ?;4299 :)
% 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_sK10_SY197,type,
sK10_SY197: $i ).
thf(tp_sK11_SY199,type,
sK11_SY199: $i ).
thf(tp_sK12_V,type,
sK12_V: $i > $i ).
thf(tp_sK13_V,type,
sK13_V: $i > $i ).
thf(tp_sK14_V,type,
sK14_V: $i > $i ).
thf(tp_sK15_W,type,
sK15_W: $i > $i > $i ).
thf(tp_sK1_U,type,
sK1_U: $i ).
thf(tp_sK2_SY175,type,
sK2_SY175: $i ).
thf(tp_sK3_SY180,type,
sK3_SY180: $i ).
thf(tp_sK4_SY184,type,
sK4_SY184: $i ).
thf(tp_sK5_SY187,type,
sK5_SY187: $i ).
thf(tp_sK6_SY189,type,
sK6_SY189: $i ).
thf(tp_sK7_SY175,type,
sK7_SY175: $i ).
thf(tp_sK8_SY190,type,
sK8_SY190: $i ).
thf(tp_sK9_SY194,type,
sK9_SY194: $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/sandbox2/benchmark/theBenchmark.p',ax62) ).
thf(2,axiom,
! [U: $i] :
( ( pi_removemin @ U )
<=> ? [V: $i] : ( pi_sharp_find_min @ ( i @ U ) @ V ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax58) ).
thf(6,axiom,
! [U: $i,V: $i] :
( ( pi_remove @ U @ V )
<=> ( pi_sharp_remove @ ( i @ U ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).
thf(7,axiom,
! [U: $i,V: $i] :
( ( pi_sharp_remove @ U @ V )
<=> ( contains_pq @ U @ V ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax55) ).
thf(9,axiom,
! [U: $i,V: $i] :
( ( i @ ( triple @ U @ create_slb @ V ) )
= create_pq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax54) ).
thf(10,axiom,
! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax51) ).
thf(13,axiom,
! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax42) ).
thf(22,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ( W = bad ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).
thf(23,axiom,
! [U: $i,V: $i] :
( ( ok @ ( triple @ U @ V @ bad ) )
<=> $false ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax37) ).
thf(27,axiom,
! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax32) ).
thf(32,axiom,
! [U: $i] : ( succ_cpq @ U @ U ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax29) ).
thf(35,axiom,
! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax23) ).
thf(41,axiom,
! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax21) ).
thf(43,axiom,
! [U: $i] :
~ ( contains_slb @ create_slb @ U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
thf(44,axiom,
! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).
thf(45,axiom,
~ ( isnonempty_slb @ create_slb ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax12) ).
thf(52,axiom,
! [U: $i,V: $i] :
( ( remove_pq @ ( insert_pq @ U @ V ) @ V )
= U ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax9) ).
thf(55,axiom,
! [U: $i] :
~ ( contains_pq @ create_pq @ U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8) ).
thf(56,axiom,
! [U: $i,V: $i] : ( isnonempty_pq @ ( insert_pq @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
thf(57,axiom,
~ ( isnonempty_pq @ create_pq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
thf(58,axiom,
! [U: $i] : ( less_than @ bottom @ U ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',stricly_smaller_definition) ).
thf(60,axiom,
! [U: $i] : ( less_than @ U @ U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(61,axiom,
! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(63,conjecture,
! [U: $i] :
( ! [V: $i,W: $i,X: $i] :
( ( contains_cpq @ ( triple @ V @ U @ W ) @ X )
<=> ( contains_pq @ ( i @ ( triple @ V @ U @ W ) ) @ X ) )
=> ! [Y: $i,Z: $i,X1: $i,X2: $i,X3: $i] :
( ( contains_cpq @ ( triple @ Y @ ( insert_slb @ U @ ( pair @ X1 @ X2 ) ) @ Z ) @ X3 )
<=> ( contains_pq @ ( i @ ( triple @ Y @ ( insert_slb @ U @ ( pair @ X1 @ X2 ) ) @ Z ) ) @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l6_co) ).
thf(64,negated_conjecture,
( ( ! [U: $i] :
( ! [V: $i,W: $i,X: $i] :
( ( contains_cpq @ ( triple @ V @ U @ W ) @ X )
<=> ( contains_pq @ ( i @ ( triple @ V @ U @ W ) ) @ X ) )
=> ! [Y: $i,Z: $i,X1: $i,X2: $i,X3: $i] :
( ( contains_cpq @ ( triple @ Y @ ( insert_slb @ U @ ( pair @ X1 @ X2 ) ) @ Z ) @ X3 )
<=> ( contains_pq @ ( i @ ( triple @ Y @ ( insert_slb @ U @ ( pair @ X1 @ X2 ) ) @ Z ) ) @ X3 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[63]) ).
thf(65,plain,
( ( ! [U: $i] :
( ! [V: $i,W: $i,X: $i] :
( ( contains_cpq @ ( triple @ V @ U @ W ) @ X )
<=> ( contains_pq @ ( i @ ( triple @ V @ U @ W ) ) @ X ) )
=> ! [Y: $i,Z: $i,X1: $i,X2: $i,X3: $i] :
( ( contains_cpq @ ( triple @ Y @ ( insert_slb @ U @ ( pair @ X1 @ X2 ) ) @ Z ) @ X3 )
<=> ( contains_pq @ ( i @ ( triple @ Y @ ( insert_slb @ U @ ( pair @ X1 @ X2 ) ) @ Z ) ) @ X3 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[64]) ).
thf(66,plain,
( ( ! [U: $i] :
( ( phi @ U )
<=> ? [V: $i] :
( ( succ_cpq @ U @ V )
& ( ok @ V )
& ( check_cpq @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(67,plain,
( ( ! [U: $i] :
( ( pi_removemin @ U )
<=> ? [V: $i] : ( pi_sharp_find_min @ ( i @ U ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(68,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(69,plain,
( ( ! [U: $i] :
( ( pi_find_min @ U )
<=> ? [V: $i] : ( pi_sharp_find_min @ ( i @ U ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(70,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(71,plain,
( ( ! [U: $i,V: $i] :
( ( pi_remove @ U @ V )
<=> ( pi_sharp_remove @ ( i @ U ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(72,plain,
( ( ! [U: $i,V: $i] :
( ( pi_sharp_remove @ U @ V )
<=> ( contains_pq @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(73,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(74,plain,
( ( ! [U: $i,V: $i] :
( ( i @ ( triple @ U @ create_slb @ V ) )
= create_pq ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(75,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(76,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(77,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(78,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(79,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(80,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(81,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(82,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(83,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(84,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(85,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(86,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(87,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ( W = bad ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(88,plain,
( ( ! [U: $i,V: $i] :
( ( ok @ ( triple @ U @ V @ bad ) )
<=> $false ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(89,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(90,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(91,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(92,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(93,plain,
( ( ! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(94,plain,
( ( ! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(95,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(96,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(97,plain,
( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(98,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(99,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(100,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(101,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(102,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(103,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(104,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(105,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(106,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(107,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(108,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(109,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(110,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(111,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(112,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(113,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(114,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(115,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(116,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(117,plain,
( ( ! [U: $i,V: $i] :
( ( remove_pq @ ( insert_pq @ U @ V ) @ V )
= U ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(118,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(119,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(120,plain,
( ( ! [U: $i] :
~ ( contains_pq @ create_pq @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(121,plain,
( ( ! [U: $i,V: $i] : ( isnonempty_pq @ ( insert_pq @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(122,plain,
( ( ~ ( isnonempty_pq @ create_pq ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(123,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(124,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(125,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(126,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(127,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(128,plain,
( ( ! [SY172: $i,SY173: $i,SY174: $i] :
( ( contains_cpq @ ( triple @ SY172 @ sK1_U @ SY173 ) @ SY174 )
<=> ( contains_pq @ ( i @ ( triple @ SY172 @ sK1_U @ SY173 ) ) @ SY174 ) )
=> ! [SY175: $i,SY176: $i,SY177: $i,SY178: $i,SY179: $i] :
( ( contains_cpq @ ( triple @ SY175 @ ( insert_slb @ sK1_U @ ( pair @ SY177 @ SY178 ) ) @ SY176 ) @ SY179 )
<=> ( contains_pq @ ( i @ ( triple @ SY175 @ ( insert_slb @ sK1_U @ ( pair @ SY177 @ SY178 ) ) @ SY176 ) ) @ SY179 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[65]) ).
thf(129,plain,
( ( ! [SY172: $i,SY173: $i,SY174: $i] :
( ( contains_cpq @ ( triple @ SY172 @ sK1_U @ SY173 ) @ SY174 )
<=> ( contains_pq @ ( i @ ( triple @ SY172 @ sK1_U @ SY173 ) ) @ SY174 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[128]) ).
thf(130,plain,
( ( ! [SY175: $i,SY176: $i,SY177: $i,SY178: $i,SY179: $i] :
( ( contains_cpq @ ( triple @ SY175 @ ( insert_slb @ sK1_U @ ( pair @ SY177 @ SY178 ) ) @ SY176 ) @ SY179 )
<=> ( contains_pq @ ( i @ ( triple @ SY175 @ ( insert_slb @ sK1_U @ ( pair @ SY177 @ SY178 ) ) @ SY176 ) ) @ SY179 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[128]) ).
thf(131,plain,
( ( ! [SY175: $i,SY176: $i,SY177: $i,SY178: $i,SY179: $i] :
( ( contains_cpq @ ( triple @ SY175 @ ( insert_slb @ sK1_U @ ( pair @ SY177 @ SY178 ) ) @ SY176 ) @ SY179 )
=> ( contains_pq @ ( i @ ( triple @ SY175 @ ( insert_slb @ sK1_U @ ( pair @ SY177 @ SY178 ) ) @ SY176 ) ) @ SY179 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[130]) ).
thf(132,plain,
( ( ! [SY175: $i,SY176: $i,SY177: $i,SY178: $i,SY179: $i] :
( ( contains_pq @ ( i @ ( triple @ SY175 @ ( insert_slb @ sK1_U @ ( pair @ SY177 @ SY178 ) ) @ SY176 ) ) @ SY179 )
=> ( contains_cpq @ ( triple @ SY175 @ ( insert_slb @ sK1_U @ ( pair @ SY177 @ SY178 ) ) @ SY176 ) @ SY179 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[130]) ).
thf(133,plain,
( ( ~ ! [SY175: $i,SY176: $i,SY177: $i,SY178: $i,SY179: $i] :
( ( contains_cpq @ ( triple @ SY175 @ ( insert_slb @ sK1_U @ ( pair @ SY177 @ SY178 ) ) @ SY176 ) @ SY179 )
=> ( contains_pq @ ( i @ ( triple @ SY175 @ ( insert_slb @ sK1_U @ ( pair @ SY177 @ SY178 ) ) @ SY176 ) ) @ SY179 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[131]) ).
thf(134,plain,
( ( ~ ! [SY175: $i,SY176: $i,SY177: $i,SY178: $i,SY179: $i] :
( ( contains_pq @ ( i @ ( triple @ SY175 @ ( insert_slb @ sK1_U @ ( pair @ SY177 @ SY178 ) ) @ SY176 ) ) @ SY179 )
=> ( contains_cpq @ ( triple @ SY175 @ ( insert_slb @ sK1_U @ ( pair @ SY177 @ SY178 ) ) @ SY176 ) @ SY179 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[132]) ).
thf(135,plain,
( ( ( contains_cpq @ ( triple @ sK2_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY184 @ sK5_SY187 ) ) @ sK3_SY180 ) @ sK6_SY189 )
& ~ ( contains_pq @ ( i @ ( triple @ sK2_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY184 @ sK5_SY187 ) ) @ sK3_SY180 ) ) @ sK6_SY189 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[133]) ).
thf(136,plain,
( ( ( contains_pq @ ( i @ ( triple @ sK7_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK9_SY194 @ sK10_SY197 ) ) @ sK8_SY190 ) ) @ sK11_SY199 )
& ~ ( contains_cpq @ ( triple @ sK7_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK9_SY194 @ sK10_SY197 ) ) @ sK8_SY190 ) @ sK11_SY199 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[134]) ).
thf(137,plain,
( ( ! [SY172: $i] :
( ! [SY173: $i,SY174: $i] :
( ~ ( contains_cpq @ ( triple @ SY172 @ sK1_U @ SY173 ) @ SY174 )
| ( contains_pq @ ( i @ ( triple @ SY172 @ sK1_U @ SY173 ) ) @ SY174 ) )
& ! [SY173: $i,SY174: $i] :
( ~ ( contains_pq @ ( i @ ( triple @ SY172 @ sK1_U @ SY173 ) ) @ SY174 )
| ( contains_cpq @ ( triple @ SY172 @ sK1_U @ SY173 ) @ SY174 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[129]) ).
thf(138,plain,
( ( ! [U: $i] :
( ! [V: $i] :
( ~ ( ok @ V )
| ~ ( succ_cpq @ U @ V )
| ~ ( check_cpq @ V ) )
| ( phi @ U ) )
& ! [U: $i] :
( ~ ( phi @ U )
| ( ( ok @ ( sK12_V @ U ) )
& ( succ_cpq @ U @ ( sK12_V @ U ) )
& ( check_cpq @ ( sK12_V @ U ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
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 ) @ ( sK13_V @ U ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
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)],[68]) ).
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 ) @ ( sK14_V @ U ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
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)],[70]) ).
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)],[71]) ).
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)],[72]) ).
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)],[77]) ).
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)],[79]) ).
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)],[80]) ).
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)],[81]) ).
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)],[83]) ).
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)],[84]) ).
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)],[85]) ).
thf(152,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( triple @ U @ V @ W ) )
| ( W = bad ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(153,plain,
( ( ! [U: $i,V: $i] :
~ ( ok @ ( triple @ U @ V @ bad ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[88]) ).
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)],[89]) ).
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)],[90]) ).
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)],[91]) ).
thf(157,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[93]) ).
thf(158,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[94]) ).
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)],[95]) ).
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)],[96]) ).
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)],[98]) ).
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)],[99]) ).
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)],[101]) ).
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)],[103]) ).
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)],[105]) ).
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)],[107]) ).
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)],[112]) ).
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)],[113]) ).
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)],[114]) ).
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)],[115]) ).
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)],[116]) ).
thf(172,plain,
( ( ! [U: $i,V: $i] :
( ( ( contains_pq @ U @ ( sK15_W @ V @ U ) )
& ~ ( less_than @ V @ ( sK15_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)],[118]) ).
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)],[119]) ).
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)],[124]) ).
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)],[127]) ).
thf(176,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(177,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(178,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(179,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(180,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(181,plain,
( ( ~ ( isnonempty_pq @ create_pq ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(182,plain,
( ( ! [U: $i,V: $i] : ( isnonempty_pq @ ( insert_pq @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(183,plain,
( ( ! [U: $i] :
~ ( contains_pq @ create_pq @ U ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(184,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(185,plain,
( ( ! [U: $i,V: $i] :
( ( ( contains_pq @ U @ ( sK15_W @ V @ U ) )
& ~ ( less_than @ V @ ( sK15_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(186,plain,
( ( ! [U: $i,V: $i] :
( ( remove_pq @ ( insert_pq @ U @ V ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(187,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(188,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(189,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(190,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(191,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(192,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)],[111]) ).
thf(193,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(194,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(195,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(196,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(197,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(198,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(199,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(200,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(201,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(202,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(203,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(204,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(205,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(206,plain,
( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(207,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(208,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(209,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(210,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(211,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(212,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(213,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(214,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(215,plain,
( ( ! [U: $i,V: $i] :
~ ( ok @ ( triple @ U @ V @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(216,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( triple @ U @ V @ W ) )
| ( W = bad ) ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(217,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)],[86]) ).
thf(218,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(219,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(220,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(221,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ create_slb @ V ) )
= ( triple @ U @ create_slb @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(222,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(223,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(224,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(225,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(226,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(227,plain,
( ( ! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(228,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(229,plain,
( ( ! [U: $i,V: $i] :
( ( i @ ( triple @ U @ create_slb @ V ) )
= create_pq ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(230,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)],[73]) ).
thf(231,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(232,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(233,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(234,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 ) @ ( sK14_V @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(235,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(236,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 ) @ ( sK13_V @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(237,plain,
( ( ! [U: $i] :
( ! [V: $i] :
( ~ ( ok @ V )
| ~ ( succ_cpq @ U @ V )
| ~ ( check_cpq @ V ) )
| ( phi @ U ) )
& ! [U: $i] :
( ~ ( phi @ U )
| ( ( ok @ ( sK12_V @ U ) )
& ( succ_cpq @ U @ ( sK12_V @ U ) )
& ( check_cpq @ ( sK12_V @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(238,plain,
( ( ! [SY172: $i] :
( ! [SY173: $i,SY174: $i] :
( ~ ( contains_cpq @ ( triple @ SY172 @ sK1_U @ SY173 ) @ SY174 )
| ( contains_pq @ ( i @ ( triple @ SY172 @ sK1_U @ SY173 ) ) @ SY174 ) )
& ! [SY173: $i,SY174: $i] :
( ~ ( contains_pq @ ( i @ ( triple @ SY172 @ sK1_U @ SY173 ) ) @ SY174 )
| ( contains_cpq @ ( triple @ SY172 @ sK1_U @ SY173 ) @ SY174 ) ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(239,plain,
( ( ( contains_cpq @ ( triple @ sK2_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY184 @ sK5_SY187 ) ) @ sK3_SY180 ) @ sK6_SY189 )
& ~ ( contains_pq @ ( i @ ( triple @ sK2_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY184 @ sK5_SY187 ) ) @ sK3_SY180 ) ) @ sK6_SY189 ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(240,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( contains_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) @ SX2 )
| ( contains_pq @ ( i @ ( triple @ SX0 @ sK1_U @ SX1 ) ) @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( contains_pq @ ( i @ ( triple @ SX0 @ sK1_U @ SX1 ) ) @ SX2 )
| ( contains_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(241,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)],[232]) ).
thf(242,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)],[198]) ).
thf(243,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 ) @ ( sK14_V @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(244,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)],[196]) ).
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)],[214]) ).
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 ) @ ( sK13_V @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(247,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( contains_pq @ SX0 @ ( sK15_W @ SX1 @ SX0 ) )
| ~ ~ ( less_than @ SX1 @ ( sK15_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)],[185]) ).
thf(248,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)],[179]) ).
thf(249,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)],[233]) ).
thf(250,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)],[184]) ).
thf(251,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)],[212]) ).
thf(252,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( ok @ SX1 )
| ~ ( succ_cpq @ SX0 @ SX1 )
| ~ ( check_cpq @ SX1 ) )
| ( phi @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( phi @ SX0 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK12_V @ SX0 ) )
| ~ ( succ_cpq @ SX0 @ ( sK12_V @ SX0 ) ) )
| ~ ( check_cpq @ ( sK12_V @ SX0 ) ) ) ) ) )
= $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)],[231]) ).
thf(254,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)],[235]) ).
thf(255,plain,
( ( ~ ( ~ ( contains_cpq @ ( triple @ sK2_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY184 @ sK5_SY187 ) ) @ sK3_SY180 ) @ sK6_SY189 )
| ~ ~ ( contains_pq @ ( i @ ( triple @ sK2_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY184 @ sK5_SY187 ) ) @ sK3_SY180 ) ) @ sK6_SY189 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(256,plain,
! [SV1: $i] :
( ( ! [SY200: $i,SY201: $i] :
( ~ ( less_than @ SV1 @ SY200 )
| ~ ( less_than @ SY200 @ SY201 )
| ( less_than @ SV1 @ SY201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(257,plain,
! [SV2: $i] :
( ( ! [SY202: $i] :
( ( less_than @ SV2 @ SY202 )
| ( less_than @ SY202 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(258,plain,
! [SV3: $i] :
( ( less_than @ SV3 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(259,plain,
! [SV4: $i] :
( ( less_than @ bottom @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(260,plain,
( ( isnonempty_pq @ create_pq )
= $false ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(261,plain,
! [SV5: $i] :
( ( ! [SY203: $i] : ( isnonempty_pq @ ( insert_pq @ SV5 @ SY203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(262,plain,
! [SV6: $i] :
( ( ~ ( contains_pq @ create_pq @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(263,plain,
! [SV7: $i] :
( ( ! [SY204: $i] :
( ( remove_pq @ ( insert_pq @ SV7 @ SY204 ) @ SY204 )
= SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(264,plain,
! [SV8: $i] :
( ( ! [SY205: $i,SY206: $i] :
( ( SY205 = SY206 )
| ~ ( contains_pq @ SV8 @ SY206 )
| ( ( remove_pq @ ( insert_pq @ SV8 @ SY205 ) @ SY206 )
= ( insert_pq @ ( remove_pq @ SV8 @ SY206 ) @ SY205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(265,plain,
! [SV9: $i] :
( ( ! [SY207: $i] :
( ~ ( contains_pq @ SV9 @ SY207 )
| ~ ( issmallestelement_pq @ SV9 @ SY207 )
| ( ( findmin_pq_eff @ SV9 @ SY207 )
= SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(266,plain,
! [SV10: $i] :
( ( ! [SY208: $i] :
( ~ ( contains_pq @ SV10 @ SY208 )
| ~ ( issmallestelement_pq @ SV10 @ SY208 )
| ( ( findmin_pq_res @ SV10 @ SY208 )
= SY208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(267,plain,
! [SV11: $i] :
( ( ! [SY209: $i] :
( ~ ( contains_pq @ SV11 @ SY209 )
| ~ ( issmallestelement_pq @ SV11 @ SY209 )
| ( ( removemin_pq_eff @ SV11 @ SY209 )
= ( remove_pq @ SV11 @ SY209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(268,plain,
! [SV12: $i] :
( ( ! [SY210: $i] :
( ~ ( contains_pq @ SV12 @ SY210 )
| ~ ( issmallestelement_pq @ SV12 @ SY210 )
| ( ( removemin_pq_res @ SV12 @ SY210 )
= SY210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(269,plain,
! [SV13: $i] :
( ( ! [SY211: $i,SY212: $i] :
( ( insert_pq @ ( insert_pq @ SV13 @ SY211 ) @ SY212 )
= ( insert_pq @ ( insert_pq @ SV13 @ SY212 ) @ SY211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(270,plain,
( ( isnonempty_slb @ create_slb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(271,plain,
! [SV14: $i] :
( ( ! [SY213: $i,SY214: $i] : ( isnonempty_slb @ ( insert_slb @ SV14 @ ( pair @ SY213 @ SY214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(272,plain,
! [SV15: $i] :
( ( ~ ( contains_slb @ create_slb @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(273,plain,
! [SV16: $i] :
( ( ! [SY215: $i] :
~ ( pair_in_list @ create_slb @ SV16 @ SY215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(274,plain,
! [SV17: $i] :
( ( ! [SY216: $i,SY217: $i] :
( ( remove_slb @ ( insert_slb @ SV17 @ ( pair @ SY216 @ SY217 ) ) @ SY216 )
= SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(275,plain,
! [SV18: $i] :
( ( ! [SY218: $i,SY219: $i] :
( ( SY218 = SY219 )
| ~ ( contains_slb @ SV18 @ SY219 )
| ! [SY220: $i] :
( ( remove_slb @ ( insert_slb @ SV18 @ ( pair @ SY218 @ SY220 ) ) @ SY219 )
= ( insert_slb @ ( remove_slb @ SV18 @ SY219 ) @ ( pair @ SY218 @ SY220 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(276,plain,
! [SV19: $i] :
( ( ! [SY221: $i,SY222: $i] :
( ( lookup_slb @ ( insert_slb @ SV19 @ ( pair @ SY221 @ SY222 ) ) @ SY221 )
= SY222 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(277,plain,
! [SV20: $i] :
( ( ! [SY223: $i,SY224: $i] :
( ( SY223 = SY224 )
| ~ ( contains_slb @ SV20 @ SY224 )
| ! [SY225: $i] :
( ( lookup_slb @ ( insert_slb @ SV20 @ ( pair @ SY223 @ SY225 ) ) @ SY224 )
= ( lookup_slb @ SV20 @ SY224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(278,plain,
! [SV21: $i] :
( ( ( update_slb @ create_slb @ SV21 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(279,plain,
! [SV22: $i] :
( ( ! [SY226: $i,SY227: $i,SY228: $i] :
( ~ ( strictly_less_than @ SY228 @ SY227 )
| ( ( update_slb @ ( insert_slb @ SV22 @ ( pair @ SY226 @ SY228 ) ) @ SY227 )
= ( insert_slb @ ( update_slb @ SV22 @ SY227 ) @ ( pair @ SY226 @ SY227 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(280,plain,
! [SV23: $i] :
( ( ! [SY229: $i,SY230: $i,SY231: $i] :
( ~ ( less_than @ SY230 @ SY231 )
| ( ( update_slb @ ( insert_slb @ SV23 @ ( pair @ SY229 @ SY231 ) ) @ SY230 )
= ( insert_slb @ ( update_slb @ SV23 @ SY230 ) @ ( pair @ SY229 @ SY231 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(281,plain,
! [SV24: $i] :
( ( succ_cpq @ SV24 @ SV24 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(282,plain,
! [SV25: $i] :
( ( ! [SY232: $i] :
( ~ ( succ_cpq @ SV25 @ SY232 )
| ! [SY233: $i] : ( succ_cpq @ SV25 @ ( insert_cpq @ SY232 @ SY233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(283,plain,
! [SV26: $i] :
( ( ! [SY234: $i] :
( ~ ( succ_cpq @ SV26 @ SY234 )
| ! [SY235: $i] : ( succ_cpq @ SV26 @ ( remove_cpq @ SY234 @ SY235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(284,plain,
! [SV27: $i] :
( ( ! [SY236: $i] :
( ~ ( succ_cpq @ SV27 @ SY236 )
| ( succ_cpq @ SV27 @ ( findmin_cpq_eff @ SY236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(285,plain,
! [SV28: $i] :
( ( ! [SY237: $i] :
( ~ ( succ_cpq @ SV28 @ SY237 )
| ( succ_cpq @ SV28 @ ( removemin_cpq_eff @ SY237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(286,plain,
! [SV29: $i] :
( ( ! [SY238: $i] : ( check_cpq @ ( triple @ SV29 @ create_slb @ SY238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(287,plain,
! [SV30: $i] :
( ( ! [SY239: $i,SY240: $i,SY241: $i,SY242: $i] :
( ~ ( strictly_less_than @ SY241 @ SY242 )
| ~ ( check_cpq @ ( triple @ SV30 @ ( insert_slb @ SY239 @ ( pair @ SY241 @ SY242 ) ) @ SY240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(288,plain,
! [SV31: $i] :
( ( ! [SY243: $i] :
~ ( ok @ ( triple @ SV31 @ SY243 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(289,plain,
! [SV32: $i] :
( ( ! [SY244: $i,SY245: $i] :
( ( ok @ ( triple @ SV32 @ SY244 @ SY245 ) )
| ( SY245 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(290,plain,
! [SV33: $i] :
( ( ! [SY246: $i,SY247: $i,SY248: $i] :
( ( insert_cpq @ ( triple @ SV33 @ SY246 @ SY247 ) @ SY248 )
= ( triple @ ( insert_pqp @ SV33 @ SY248 ) @ ( insert_slb @ SY246 @ ( pair @ SY248 @ bottom ) ) @ SY247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(291,plain,
! [SV34: $i] :
( ( ! [SY249: $i,SY250: $i,SY251: $i] :
( ( contains_slb @ SY249 @ SY251 )
| ( ( remove_cpq @ ( triple @ SV34 @ SY249 @ SY250 ) @ SY251 )
= ( triple @ SV34 @ SY249 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(292,plain,
! [SV35: $i] :
( ( ! [SY252: $i,SY253: $i,SY254: $i] :
( ~ ( contains_slb @ SY252 @ SY254 )
| ~ ( less_than @ ( lookup_slb @ SY252 @ SY254 ) @ SY254 )
| ( ( remove_cpq @ ( triple @ SV35 @ SY252 @ SY253 ) @ SY254 )
= ( triple @ ( remove_pqp @ SV35 @ SY254 ) @ ( remove_slb @ SY252 @ SY254 ) @ SY253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(293,plain,
! [SV36: $i] :
( ( ! [SY255: $i,SY256: $i,SY257: $i] :
( ~ ( contains_slb @ SY255 @ SY257 )
| ~ ( strictly_less_than @ SY257 @ ( lookup_slb @ SY255 @ SY257 ) )
| ( ( remove_cpq @ ( triple @ SV36 @ SY255 @ SY256 ) @ SY257 )
= ( triple @ ( remove_pqp @ SV36 @ SY257 ) @ ( remove_slb @ SY255 @ SY257 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(294,plain,
! [SV37: $i] :
( ( ! [SY258: $i] :
( ( findmin_cpq_eff @ ( triple @ SV37 @ create_slb @ SY258 ) )
= ( triple @ SV37 @ create_slb @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(295,plain,
! [SV38: $i] :
( ( ! [SY259: $i] :
( ( SY259 = create_slb )
| ( contains_slb @ SY259 @ ( findmin_pqp_res @ SV38 ) )
| ! [SY260: $i] :
( ( findmin_cpq_eff @ ( triple @ SV38 @ SY259 @ SY260 ) )
= ( triple @ SV38 @ ( update_slb @ SY259 @ ( findmin_pqp_res @ SV38 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(296,plain,
! [SV39: $i] :
( ( ! [SY261: $i] :
( ( SY261 = create_slb )
| ~ ( contains_slb @ SY261 @ ( findmin_pqp_res @ SV39 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV39 ) @ ( lookup_slb @ SY261 @ ( findmin_pqp_res @ SV39 ) ) )
| ! [SY262: $i] :
( ( findmin_cpq_eff @ ( triple @ SV39 @ SY261 @ SY262 ) )
= ( triple @ SV39 @ ( update_slb @ SY261 @ ( findmin_pqp_res @ SV39 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(297,plain,
! [SV40: $i] :
( ( ! [SY263: $i] :
( ( SY263 = create_slb )
| ~ ( contains_slb @ SY263 @ ( findmin_pqp_res @ SV40 ) )
| ~ ( less_than @ ( lookup_slb @ SY263 @ ( findmin_pqp_res @ SV40 ) ) @ ( findmin_pqp_res @ SV40 ) )
| ! [SY264: $i] :
( ( findmin_cpq_eff @ ( triple @ SV40 @ SY263 @ SY264 ) )
= ( triple @ SV40 @ ( update_slb @ SY263 @ ( findmin_pqp_res @ SV40 ) ) @ SY264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(298,plain,
! [SV41: $i] :
( ( ! [SY265: $i] :
( ( findmin_cpq_res @ ( triple @ SV41 @ create_slb @ SY265 ) )
= bottom ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(299,plain,
! [SV42: $i] :
( ( ! [SY266: $i] :
( ( SY266 = create_slb )
| ! [SY267: $i] :
( ( findmin_cpq_res @ ( triple @ SV42 @ SY266 @ SY267 ) )
= ( findmin_pqp_res @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(300,plain,
! [SV43: $i] :
( ( ( removemin_cpq_eff @ SV43 )
= ( remove_cpq @ ( findmin_cpq_eff @ SV43 ) @ ( findmin_cpq_res @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(301,plain,
! [SV44: $i] :
( ( ( removemin_cpq_res @ SV44 )
= ( findmin_cpq_res @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(302,plain,
! [SV45: $i] :
( ( ! [SY268: $i] :
( ( i @ ( triple @ SV45 @ create_slb @ SY268 ) )
= create_pq ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(303,plain,
! [SV46: $i] :
( ( ! [SY269: $i,SY270: $i,SY271: $i,SY272: $i] :
( ( i @ ( triple @ SV46 @ ( insert_slb @ SY269 @ ( pair @ SY271 @ SY272 ) ) @ SY270 ) )
= ( insert_pq @ ( i @ ( triple @ SV46 @ SY269 @ SY270 ) ) @ SY271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(304,plain,
! [SV47: $i] :
( ( ~ ( ~ ! [SY273: $i,SY274: $i] :
( ~ ( contains_cpq @ ( triple @ SV47 @ sK1_U @ SY273 ) @ SY274 )
| ( contains_pq @ ( i @ ( triple @ SV47 @ sK1_U @ SY273 ) ) @ SY274 ) )
| ~ ! [SY275: $i,SY276: $i] :
( ~ ( contains_pq @ ( i @ ( triple @ SV47 @ sK1_U @ SY275 ) ) @ SY276 )
| ( contains_cpq @ ( triple @ SV47 @ sK1_U @ SY275 ) @ SY276 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(305,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)],[241]) ).
thf(306,plain,
! [SV48: $i] :
( ( ! [SY277: $i,SY278: $i] :
~ ( ~ ~ ( ~ ! [SY279: $i,SY280: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SY277 @ SY279 ) ) @ SY278 @ SY280 )
| ( SY277 = SY278 )
| ( pair_in_list @ SV48 @ SY278 @ SY280 ) )
| ~ ! [SY281: $i,SY282: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SY277 @ SY281 ) ) @ SY278 @ SY282 )
| ( SY281 = SY282 )
| ( pair_in_list @ SV48 @ SY278 @ SY282 ) ) )
| ~ ~ ( ~ ! [SY283: $i,SY284: $i] :
( ( SY277 != SY278 )
| ( SY283 != SY284 )
| ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SY277 @ SY283 ) ) @ SY278 @ SY284 ) )
| ~ ! [SY285: $i,SY286: $i] :
( ~ ( pair_in_list @ SV48 @ SY278 @ SY286 )
| ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SY277 @ SY285 ) ) @ SY278 @ SY286 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(307,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 ) @ ( sK14_V @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(308,plain,
! [SV49: $i] :
( ( ! [SY287: $i] :
~ ( ~ ! [SY288: $i] :
( ! [SY289: $i] :
~ ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SY287 @ SY289 ) ) @ SY288 )
| ( SY287 = SY288 )
| ( contains_slb @ SV49 @ SY288 ) )
| ~ ~ ( ~ ! [SY290: $i] :
( ( SY287 != SY290 )
| ! [SY291: $i] : ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SY287 @ SY291 ) ) @ SY290 ) )
| ~ ! [SY292: $i] :
( ~ ( contains_slb @ SV49 @ SY292 )
| ! [SY293: $i] : ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SY287 @ SY293 ) ) @ SY292 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(309,plain,
! [SV50: $i] :
( ( ! [SY294: $i] :
~ ( ~ ! [SY295: $i,SY296: $i] :
( ~ ( contains_cpq @ ( triple @ SV50 @ SY294 @ SY295 ) @ SY296 )
| ( contains_slb @ SY294 @ SY296 ) )
| ~ ! [SY297: $i,SY298: $i] :
( ~ ( contains_slb @ SY294 @ SY298 )
| ( contains_cpq @ ( triple @ SV50 @ SY294 @ SY297 ) @ SY298 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(310,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 ) @ ( sK13_V @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(311,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( contains_pq @ SX0 @ ( sK15_W @ SX1 @ SX0 ) )
| ~ ~ ( less_than @ SX1 @ ( sK15_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)],[247]) ).
thf(312,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)],[248]) ).
thf(313,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)],[249]) ).
thf(314,plain,
! [SV51: $i] :
( ( ~ ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV51 @ SY299 ) @ SY300 )
| ( SY299 = SY300 )
| ( contains_pq @ SV51 @ SY300 ) )
| ~ ~ ( ~ ! [SY301: $i,SY302: $i] :
( ( SY301 != SY302 )
| ( contains_pq @ ( insert_pq @ SV51 @ SY301 ) @ SY302 ) )
| ~ ! [SY303: $i,SY304: $i] :
( ~ ( contains_pq @ SV51 @ SY304 )
| ( contains_pq @ ( insert_pq @ SV51 @ SY303 ) @ SY304 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(315,plain,
! [SV52: $i] :
( ( ! [SY305: $i,SY306: $i] :
~ ( ~ ! [SY307: $i,SY308: $i] :
( ~ ( less_than @ SY308 @ SY307 )
| ~ ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SY305 @ ( pair @ SY307 @ SY308 ) ) @ SY306 ) )
| ( check_cpq @ ( triple @ SV52 @ SY305 @ SY306 ) ) )
| ~ ! [SY309: $i,SY310: $i] :
( ~ ( less_than @ SY310 @ SY309 )
| ~ ( check_cpq @ ( triple @ SV52 @ SY305 @ SY306 ) )
| ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SY305 @ ( pair @ SY309 @ SY310 ) ) @ SY306 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(316,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( ok @ SX1 )
| ~ ( succ_cpq @ SX0 @ SX1 )
| ~ ( check_cpq @ SX1 ) )
| ( phi @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( phi @ SX0 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK12_V @ SX0 ) )
| ~ ( succ_cpq @ SX0 @ ( sK12_V @ SX0 ) ) )
| ~ ( check_cpq @ ( sK12_V @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(317,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(318,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)],[254]) ).
thf(319,plain,
( ( ~ ( contains_cpq @ ( triple @ sK2_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY184 @ sK5_SY187 ) ) @ sK3_SY180 ) @ sK6_SY189 )
| ~ ~ ( contains_pq @ ( i @ ( triple @ sK2_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY184 @ sK5_SY187 ) ) @ sK3_SY180 ) ) @ sK6_SY189 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(320,plain,
! [SV53: $i,SV1: $i] :
( ( ! [SY311: $i] :
( ~ ( less_than @ SV1 @ SV53 )
| ~ ( less_than @ SV53 @ SY311 )
| ( less_than @ SV1 @ SY311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(321,plain,
! [SV54: $i,SV2: $i] :
( ( ( less_than @ SV2 @ SV54 )
| ( less_than @ SV54 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(322,plain,
! [SV55: $i,SV5: $i] :
( ( isnonempty_pq @ ( insert_pq @ SV5 @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(323,plain,
! [SV6: $i] :
( ( contains_pq @ create_pq @ SV6 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(324,plain,
! [SV56: $i,SV7: $i] :
( ( ( remove_pq @ ( insert_pq @ SV7 @ SV56 ) @ SV56 )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(325,plain,
! [SV8: $i,SV57: $i] :
( ( ! [SY312: $i] :
( ( SV57 = SY312 )
| ~ ( contains_pq @ SV8 @ SY312 )
| ( ( remove_pq @ ( insert_pq @ SV8 @ SV57 ) @ SY312 )
= ( insert_pq @ ( remove_pq @ SV8 @ SY312 ) @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(326,plain,
! [SV58: $i,SV9: $i] :
( ( ~ ( contains_pq @ SV9 @ SV58 )
| ~ ( issmallestelement_pq @ SV9 @ SV58 )
| ( ( findmin_pq_eff @ SV9 @ SV58 )
= SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(327,plain,
! [SV59: $i,SV10: $i] :
( ( ~ ( contains_pq @ SV10 @ SV59 )
| ~ ( issmallestelement_pq @ SV10 @ SV59 )
| ( ( findmin_pq_res @ SV10 @ SV59 )
= SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(328,plain,
! [SV60: $i,SV11: $i] :
( ( ~ ( contains_pq @ SV11 @ SV60 )
| ~ ( issmallestelement_pq @ SV11 @ SV60 )
| ( ( removemin_pq_eff @ SV11 @ SV60 )
= ( remove_pq @ SV11 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(329,plain,
! [SV61: $i,SV12: $i] :
( ( ~ ( contains_pq @ SV12 @ SV61 )
| ~ ( issmallestelement_pq @ SV12 @ SV61 )
| ( ( removemin_pq_res @ SV12 @ SV61 )
= SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(330,plain,
! [SV62: $i,SV13: $i] :
( ( ! [SY313: $i] :
( ( insert_pq @ ( insert_pq @ SV13 @ SV62 ) @ SY313 )
= ( insert_pq @ ( insert_pq @ SV13 @ SY313 ) @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(331,plain,
! [SV63: $i,SV14: $i] :
( ( ! [SY314: $i] : ( isnonempty_slb @ ( insert_slb @ SV14 @ ( pair @ SV63 @ SY314 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(332,plain,
! [SV15: $i] :
( ( contains_slb @ create_slb @ SV15 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(333,plain,
! [SV64: $i,SV16: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV16 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(334,plain,
! [SV65: $i,SV17: $i] :
( ( ! [SY315: $i] :
( ( remove_slb @ ( insert_slb @ SV17 @ ( pair @ SV65 @ SY315 ) ) @ SV65 )
= SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(335,plain,
! [SV18: $i,SV66: $i] :
( ( ! [SY316: $i] :
( ( SV66 = SY316 )
| ~ ( contains_slb @ SV18 @ SY316 )
| ! [SY317: $i] :
( ( remove_slb @ ( insert_slb @ SV18 @ ( pair @ SV66 @ SY317 ) ) @ SY316 )
= ( insert_slb @ ( remove_slb @ SV18 @ SY316 ) @ ( pair @ SV66 @ SY317 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(336,plain,
! [SV67: $i,SV19: $i] :
( ( ! [SY318: $i] :
( ( lookup_slb @ ( insert_slb @ SV19 @ ( pair @ SV67 @ SY318 ) ) @ SV67 )
= SY318 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(337,plain,
! [SV20: $i,SV68: $i] :
( ( ! [SY319: $i] :
( ( SV68 = SY319 )
| ~ ( contains_slb @ SV20 @ SY319 )
| ! [SY320: $i] :
( ( lookup_slb @ ( insert_slb @ SV20 @ ( pair @ SV68 @ SY320 ) ) @ SY319 )
= ( lookup_slb @ SV20 @ SY319 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(338,plain,
! [SV69: $i,SV22: $i] :
( ( ! [SY321: $i,SY322: $i] :
( ~ ( strictly_less_than @ SY322 @ SY321 )
| ( ( update_slb @ ( insert_slb @ SV22 @ ( pair @ SV69 @ SY322 ) ) @ SY321 )
= ( insert_slb @ ( update_slb @ SV22 @ SY321 ) @ ( pair @ SV69 @ SY321 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(339,plain,
! [SV70: $i,SV23: $i] :
( ( ! [SY323: $i,SY324: $i] :
( ~ ( less_than @ SY323 @ SY324 )
| ( ( update_slb @ ( insert_slb @ SV23 @ ( pair @ SV70 @ SY324 ) ) @ SY323 )
= ( insert_slb @ ( update_slb @ SV23 @ SY323 ) @ ( pair @ SV70 @ SY324 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(340,plain,
! [SV71: $i,SV25: $i] :
( ( ~ ( succ_cpq @ SV25 @ SV71 )
| ! [SY325: $i] : ( succ_cpq @ SV25 @ ( insert_cpq @ SV71 @ SY325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(341,plain,
! [SV72: $i,SV26: $i] :
( ( ~ ( succ_cpq @ SV26 @ SV72 )
| ! [SY326: $i] : ( succ_cpq @ SV26 @ ( remove_cpq @ SV72 @ SY326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(342,plain,
! [SV73: $i,SV27: $i] :
( ( ~ ( succ_cpq @ SV27 @ SV73 )
| ( succ_cpq @ SV27 @ ( findmin_cpq_eff @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(343,plain,
! [SV74: $i,SV28: $i] :
( ( ~ ( succ_cpq @ SV28 @ SV74 )
| ( succ_cpq @ SV28 @ ( removemin_cpq_eff @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(344,plain,
! [SV75: $i,SV29: $i] :
( ( check_cpq @ ( triple @ SV29 @ create_slb @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(345,plain,
! [SV76: $i,SV30: $i] :
( ( ! [SY327: $i,SY328: $i,SY329: $i] :
( ~ ( strictly_less_than @ SY328 @ SY329 )
| ~ ( check_cpq @ ( triple @ SV30 @ ( insert_slb @ SV76 @ ( pair @ SY328 @ SY329 ) ) @ SY327 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(346,plain,
! [SV77: $i,SV31: $i] :
( ( ~ ( ok @ ( triple @ SV31 @ SV77 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(347,plain,
! [SV78: $i,SV32: $i] :
( ( ! [SY330: $i] :
( ( ok @ ( triple @ SV32 @ SV78 @ SY330 ) )
| ( SY330 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(348,plain,
! [SV79: $i,SV33: $i] :
( ( ! [SY331: $i,SY332: $i] :
( ( insert_cpq @ ( triple @ SV33 @ SV79 @ SY331 ) @ SY332 )
= ( triple @ ( insert_pqp @ SV33 @ SY332 ) @ ( insert_slb @ SV79 @ ( pair @ SY332 @ bottom ) ) @ SY331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(349,plain,
! [SV34: $i,SV80: $i] :
( ( ! [SY333: $i,SY334: $i] :
( ( contains_slb @ SV80 @ SY334 )
| ( ( remove_cpq @ ( triple @ SV34 @ SV80 @ SY333 ) @ SY334 )
= ( triple @ SV34 @ SV80 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(350,plain,
! [SV35: $i,SV81: $i] :
( ( ! [SY335: $i,SY336: $i] :
( ~ ( contains_slb @ SV81 @ SY336 )
| ~ ( less_than @ ( lookup_slb @ SV81 @ SY336 ) @ SY336 )
| ( ( remove_cpq @ ( triple @ SV35 @ SV81 @ SY335 ) @ SY336 )
= ( triple @ ( remove_pqp @ SV35 @ SY336 ) @ ( remove_slb @ SV81 @ SY336 ) @ SY335 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(351,plain,
! [SV36: $i,SV82: $i] :
( ( ! [SY337: $i,SY338: $i] :
( ~ ( contains_slb @ SV82 @ SY338 )
| ~ ( strictly_less_than @ SY338 @ ( lookup_slb @ SV82 @ SY338 ) )
| ( ( remove_cpq @ ( triple @ SV36 @ SV82 @ SY337 ) @ SY338 )
= ( triple @ ( remove_pqp @ SV36 @ SY338 ) @ ( remove_slb @ SV82 @ SY338 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(352,plain,
! [SV83: $i,SV37: $i] :
( ( ( findmin_cpq_eff @ ( triple @ SV37 @ create_slb @ SV83 ) )
= ( triple @ SV37 @ create_slb @ bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(353,plain,
! [SV38: $i,SV84: $i] :
( ( ( SV84 = create_slb )
| ( contains_slb @ SV84 @ ( findmin_pqp_res @ SV38 ) )
| ! [SY339: $i] :
( ( findmin_cpq_eff @ ( triple @ SV38 @ SV84 @ SY339 ) )
= ( triple @ SV38 @ ( update_slb @ SV84 @ ( findmin_pqp_res @ SV38 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(354,plain,
! [SV39: $i,SV85: $i] :
( ( ( SV85 = create_slb )
| ~ ( contains_slb @ SV85 @ ( findmin_pqp_res @ SV39 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV39 ) @ ( lookup_slb @ SV85 @ ( findmin_pqp_res @ SV39 ) ) )
| ! [SY340: $i] :
( ( findmin_cpq_eff @ ( triple @ SV39 @ SV85 @ SY340 ) )
= ( triple @ SV39 @ ( update_slb @ SV85 @ ( findmin_pqp_res @ SV39 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(355,plain,
! [SV40: $i,SV86: $i] :
( ( ( SV86 = create_slb )
| ~ ( contains_slb @ SV86 @ ( findmin_pqp_res @ SV40 ) )
| ~ ( less_than @ ( lookup_slb @ SV86 @ ( findmin_pqp_res @ SV40 ) ) @ ( findmin_pqp_res @ SV40 ) )
| ! [SY341: $i] :
( ( findmin_cpq_eff @ ( triple @ SV40 @ SV86 @ SY341 ) )
= ( triple @ SV40 @ ( update_slb @ SV86 @ ( findmin_pqp_res @ SV40 ) ) @ SY341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(356,plain,
! [SV87: $i,SV41: $i] :
( ( ( findmin_cpq_res @ ( triple @ SV41 @ create_slb @ SV87 ) )
= bottom )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(357,plain,
! [SV42: $i,SV88: $i] :
( ( ( SV88 = create_slb )
| ! [SY342: $i] :
( ( findmin_cpq_res @ ( triple @ SV42 @ SV88 @ SY342 ) )
= ( findmin_pqp_res @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(358,plain,
! [SV89: $i,SV45: $i] :
( ( ( i @ ( triple @ SV45 @ create_slb @ SV89 ) )
= create_pq )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(359,plain,
! [SV90: $i,SV46: $i] :
( ( ! [SY343: $i,SY344: $i,SY345: $i] :
( ( i @ ( triple @ SV46 @ ( insert_slb @ SV90 @ ( pair @ SY344 @ SY345 ) ) @ SY343 ) )
= ( insert_pq @ ( i @ ( triple @ SV46 @ SV90 @ SY343 ) ) @ SY344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(360,plain,
! [SV47: $i] :
( ( ~ ! [SY273: $i,SY274: $i] :
( ~ ( contains_cpq @ ( triple @ SV47 @ sK1_U @ SY273 ) @ SY274 )
| ( contains_pq @ ( i @ ( triple @ SV47 @ sK1_U @ SY273 ) ) @ SY274 ) )
| ~ ! [SY275: $i,SY276: $i] :
( ~ ( contains_pq @ ( i @ ( triple @ SV47 @ sK1_U @ SY275 ) ) @ SY276 )
| ( contains_cpq @ ( triple @ SV47 @ sK1_U @ SY275 ) @ SY276 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(361,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_remove @ SX0 @ SX1 )
| ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(362,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 )
| ( pi_remove @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(363,plain,
! [SV91: $i,SV48: $i] :
( ( ! [SY346: $i] :
~ ( ~ ~ ( ~ ! [SY347: $i,SY348: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY347 ) ) @ SY346 @ SY348 )
| ( SV91 = SY346 )
| ( pair_in_list @ SV48 @ SY346 @ SY348 ) )
| ~ ! [SY349: $i,SY350: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY349 ) ) @ SY346 @ SY350 )
| ( SY349 = SY350 )
| ( pair_in_list @ SV48 @ SY346 @ SY350 ) ) )
| ~ ~ ( ~ ! [SY351: $i,SY352: $i] :
( ( SV91 != SY346 )
| ( SY351 != SY352 )
| ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY351 ) ) @ SY346 @ SY352 ) )
| ~ ! [SY353: $i,SY354: $i] :
( ~ ( pair_in_list @ SV48 @ SY346 @ SY354 )
| ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY353 ) ) @ SY346 @ SY354 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(364,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_find_min @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(365,plain,
( ( ~ ! [SX0: $i] :
( ~ ( pi_find_min @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK14_V @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(366,plain,
! [SV92: $i,SV49: $i] :
( ( ~ ( ~ ! [SY355: $i] :
( ! [SY356: $i] :
~ ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY356 ) ) @ SY355 )
| ( SV92 = SY355 )
| ( contains_slb @ SV49 @ SY355 ) )
| ~ ~ ( ~ ! [SY357: $i] :
( ( SV92 != SY357 )
| ! [SY358: $i] : ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY358 ) ) @ SY357 ) )
| ~ ! [SY359: $i] :
( ~ ( contains_slb @ SV49 @ SY359 )
| ! [SY360: $i] : ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY360 ) ) @ SY359 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(367,plain,
! [SV93: $i,SV50: $i] :
( ( ~ ( ~ ! [SY361: $i,SY362: $i] :
( ~ ( contains_cpq @ ( triple @ SV50 @ SV93 @ SY361 ) @ SY362 )
| ( contains_slb @ SV93 @ SY362 ) )
| ~ ! [SY363: $i,SY364: $i] :
( ~ ( contains_slb @ SV93 @ SY364 )
| ( contains_cpq @ ( triple @ SV50 @ SV93 @ SY363 ) @ SY364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(368,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_removemin @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(369,plain,
( ( ~ ! [SX0: $i] :
( ~ ( pi_removemin @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK13_V @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(370,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( contains_pq @ SX0 @ ( sK15_W @ SX1 @ SX0 ) )
| ~ ~ ( less_than @ SX1 @ ( sK15_W @ SX1 @ SX0 ) ) )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(371,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)],[311]) ).
thf(372,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)],[312]) ).
thf(373,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)],[312]) ).
thf(374,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)],[313]) ).
thf(375,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)],[313]) ).
thf(376,plain,
! [SV51: $i] :
( ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV51 @ SY299 ) @ SY300 )
| ( SY299 = SY300 )
| ( contains_pq @ SV51 @ SY300 ) )
| ~ ~ ( ~ ! [SY301: $i,SY302: $i] :
( ( SY301 != SY302 )
| ( contains_pq @ ( insert_pq @ SV51 @ SY301 ) @ SY302 ) )
| ~ ! [SY303: $i,SY304: $i] :
( ~ ( contains_pq @ SV51 @ SY304 )
| ( contains_pq @ ( insert_pq @ SV51 @ SY303 ) @ SY304 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(377,plain,
! [SV94: $i,SV52: $i] :
( ( ! [SY365: $i] :
~ ( ~ ! [SY366: $i,SY367: $i] :
( ~ ( less_than @ SY367 @ SY366 )
| ~ ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV94 @ ( pair @ SY366 @ SY367 ) ) @ SY365 ) )
| ( check_cpq @ ( triple @ SV52 @ SV94 @ SY365 ) ) )
| ~ ! [SY368: $i,SY369: $i] :
( ~ ( less_than @ SY369 @ SY368 )
| ~ ( check_cpq @ ( triple @ SV52 @ SV94 @ SY365 ) )
| ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV94 @ ( pair @ SY368 @ SY369 ) ) @ SY365 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(378,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( ok @ SX1 )
| ~ ( succ_cpq @ SX0 @ SX1 )
| ~ ( check_cpq @ SX1 ) )
| ( phi @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[316]) ).
thf(379,plain,
( ( ~ ! [SX0: $i] :
( ~ ( phi @ SX0 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK12_V @ SX0 ) )
| ~ ( succ_cpq @ SX0 @ ( sK12_V @ SX0 ) ) )
| ~ ( check_cpq @ ( sK12_V @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[316]) ).
thf(380,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( contains_pq @ SX0 @ SX1 )
| ( pi_sharp_remove @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[317]) ).
thf(381,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[317]) ).
thf(382,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)],[318]) ).
thf(383,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)],[318]) ).
thf(384,plain,
( ( ~ ( contains_cpq @ ( triple @ sK2_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY184 @ sK5_SY187 ) ) @ sK3_SY180 ) @ sK6_SY189 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[319]) ).
thf(385,plain,
( ( ~ ~ ( contains_pq @ ( i @ ( triple @ sK2_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY184 @ sK5_SY187 ) ) @ sK3_SY180 ) ) @ sK6_SY189 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[319]) ).
thf(386,plain,
! [SV95: $i,SV53: $i,SV1: $i] :
( ( ~ ( less_than @ SV1 @ SV53 )
| ~ ( less_than @ SV53 @ SV95 )
| ( less_than @ SV1 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(387,plain,
! [SV54: $i,SV2: $i] :
( ( ( less_than @ SV2 @ SV54 )
= $true )
| ( ( less_than @ SV54 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(388,plain,
! [SV8: $i,SV96: $i,SV57: $i] :
( ( ( SV57 = SV96 )
| ~ ( contains_pq @ SV8 @ SV96 )
| ( ( remove_pq @ ( insert_pq @ SV8 @ SV57 ) @ SV96 )
= ( insert_pq @ ( remove_pq @ SV8 @ SV96 ) @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(389,plain,
! [SV58: $i,SV9: $i] :
( ( ( ~ ( contains_pq @ SV9 @ SV58 )
| ~ ( issmallestelement_pq @ SV9 @ SV58 ) )
= $true )
| ( ( ( findmin_pq_eff @ SV9 @ SV58 )
= SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(390,plain,
! [SV59: $i,SV10: $i] :
( ( ( ~ ( contains_pq @ SV10 @ SV59 )
| ~ ( issmallestelement_pq @ SV10 @ SV59 ) )
= $true )
| ( ( ( findmin_pq_res @ SV10 @ SV59 )
= SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(391,plain,
! [SV60: $i,SV11: $i] :
( ( ( ~ ( contains_pq @ SV11 @ SV60 )
| ~ ( issmallestelement_pq @ SV11 @ SV60 ) )
= $true )
| ( ( ( removemin_pq_eff @ SV11 @ SV60 )
= ( remove_pq @ SV11 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(392,plain,
! [SV61: $i,SV12: $i] :
( ( ( ~ ( contains_pq @ SV12 @ SV61 )
| ~ ( issmallestelement_pq @ SV12 @ SV61 ) )
= $true )
| ( ( ( removemin_pq_res @ SV12 @ SV61 )
= SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(393,plain,
! [SV97: $i,SV62: $i,SV13: $i] :
( ( ( insert_pq @ ( insert_pq @ SV13 @ SV62 ) @ SV97 )
= ( insert_pq @ ( insert_pq @ SV13 @ SV97 ) @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(394,plain,
! [SV98: $i,SV63: $i,SV14: $i] :
( ( isnonempty_slb @ ( insert_slb @ SV14 @ ( pair @ SV63 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(395,plain,
! [SV64: $i,SV16: $i] :
( ( pair_in_list @ create_slb @ SV16 @ SV64 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(396,plain,
! [SV99: $i,SV65: $i,SV17: $i] :
( ( ( remove_slb @ ( insert_slb @ SV17 @ ( pair @ SV65 @ SV99 ) ) @ SV65 )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(397,plain,
! [SV18: $i,SV100: $i,SV66: $i] :
( ( ( SV66 = SV100 )
| ~ ( contains_slb @ SV18 @ SV100 )
| ! [SY370: $i] :
( ( remove_slb @ ( insert_slb @ SV18 @ ( pair @ SV66 @ SY370 ) ) @ SV100 )
= ( insert_slb @ ( remove_slb @ SV18 @ SV100 ) @ ( pair @ SV66 @ SY370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(398,plain,
! [SV101: $i,SV67: $i,SV19: $i] :
( ( ( lookup_slb @ ( insert_slb @ SV19 @ ( pair @ SV67 @ SV101 ) ) @ SV67 )
= SV101 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(399,plain,
! [SV20: $i,SV102: $i,SV68: $i] :
( ( ( SV68 = SV102 )
| ~ ( contains_slb @ SV20 @ SV102 )
| ! [SY371: $i] :
( ( lookup_slb @ ( insert_slb @ SV20 @ ( pair @ SV68 @ SY371 ) ) @ SV102 )
= ( lookup_slb @ SV20 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(400,plain,
! [SV69: $i,SV22: $i,SV103: $i] :
( ( ! [SY372: $i] :
( ~ ( strictly_less_than @ SY372 @ SV103 )
| ( ( update_slb @ ( insert_slb @ SV22 @ ( pair @ SV69 @ SY372 ) ) @ SV103 )
= ( insert_slb @ ( update_slb @ SV22 @ SV103 ) @ ( pair @ SV69 @ SV103 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(401,plain,
! [SV70: $i,SV23: $i,SV104: $i] :
( ( ! [SY373: $i] :
( ~ ( less_than @ SV104 @ SY373 )
| ( ( update_slb @ ( insert_slb @ SV23 @ ( pair @ SV70 @ SY373 ) ) @ SV104 )
= ( insert_slb @ ( update_slb @ SV23 @ SV104 ) @ ( pair @ SV70 @ SY373 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(402,plain,
! [SV71: $i,SV25: $i] :
( ( ( ~ ( succ_cpq @ SV25 @ SV71 ) )
= $true )
| ( ( ! [SY325: $i] : ( succ_cpq @ SV25 @ ( insert_cpq @ SV71 @ SY325 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[340]) ).
thf(403,plain,
! [SV72: $i,SV26: $i] :
( ( ( ~ ( succ_cpq @ SV26 @ SV72 ) )
= $true )
| ( ( ! [SY326: $i] : ( succ_cpq @ SV26 @ ( remove_cpq @ SV72 @ SY326 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(404,plain,
! [SV73: $i,SV27: $i] :
( ( ( ~ ( succ_cpq @ SV27 @ SV73 ) )
= $true )
| ( ( succ_cpq @ SV27 @ ( findmin_cpq_eff @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(405,plain,
! [SV74: $i,SV28: $i] :
( ( ( ~ ( succ_cpq @ SV28 @ SV74 ) )
= $true )
| ( ( succ_cpq @ SV28 @ ( removemin_cpq_eff @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(406,plain,
! [SV105: $i,SV76: $i,SV30: $i] :
( ( ! [SY374: $i,SY375: $i] :
( ~ ( strictly_less_than @ SY374 @ SY375 )
| ~ ( check_cpq @ ( triple @ SV30 @ ( insert_slb @ SV76 @ ( pair @ SY374 @ SY375 ) ) @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(407,plain,
! [SV77: $i,SV31: $i] :
( ( ok @ ( triple @ SV31 @ SV77 @ bad ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(408,plain,
! [SV106: $i,SV78: $i,SV32: $i] :
( ( ( ok @ ( triple @ SV32 @ SV78 @ SV106 ) )
| ( SV106 = bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(409,plain,
! [SV107: $i,SV79: $i,SV33: $i] :
( ( ! [SY376: $i] :
( ( insert_cpq @ ( triple @ SV33 @ SV79 @ SV107 ) @ SY376 )
= ( triple @ ( insert_pqp @ SV33 @ SY376 ) @ ( insert_slb @ SV79 @ ( pair @ SY376 @ bottom ) ) @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(410,plain,
! [SV108: $i,SV34: $i,SV80: $i] :
( ( ! [SY377: $i] :
( ( contains_slb @ SV80 @ SY377 )
| ( ( remove_cpq @ ( triple @ SV34 @ SV80 @ SV108 ) @ SY377 )
= ( triple @ SV34 @ SV80 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(411,plain,
! [SV109: $i,SV35: $i,SV81: $i] :
( ( ! [SY378: $i] :
( ~ ( contains_slb @ SV81 @ SY378 )
| ~ ( less_than @ ( lookup_slb @ SV81 @ SY378 ) @ SY378 )
| ( ( remove_cpq @ ( triple @ SV35 @ SV81 @ SV109 ) @ SY378 )
= ( triple @ ( remove_pqp @ SV35 @ SY378 ) @ ( remove_slb @ SV81 @ SY378 ) @ SV109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(412,plain,
! [SV110: $i,SV36: $i,SV82: $i] :
( ( ! [SY379: $i] :
( ~ ( contains_slb @ SV82 @ SY379 )
| ~ ( strictly_less_than @ SY379 @ ( lookup_slb @ SV82 @ SY379 ) )
| ( ( remove_cpq @ ( triple @ SV36 @ SV82 @ SV110 ) @ SY379 )
= ( triple @ ( remove_pqp @ SV36 @ SY379 ) @ ( remove_slb @ SV82 @ SY379 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(413,plain,
! [SV38: $i,SV84: $i] :
( ( ( ( SV84 = create_slb )
| ( contains_slb @ SV84 @ ( findmin_pqp_res @ SV38 ) ) )
= $true )
| ( ( ! [SY339: $i] :
( ( findmin_cpq_eff @ ( triple @ SV38 @ SV84 @ SY339 ) )
= ( triple @ SV38 @ ( update_slb @ SV84 @ ( findmin_pqp_res @ SV38 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(414,plain,
! [SV39: $i,SV85: $i] :
( ( ( ( SV85 = create_slb )
| ~ ( contains_slb @ SV85 @ ( findmin_pqp_res @ SV39 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV39 ) @ ( lookup_slb @ SV85 @ ( findmin_pqp_res @ SV39 ) ) ) )
= $true )
| ( ( ! [SY340: $i] :
( ( findmin_cpq_eff @ ( triple @ SV39 @ SV85 @ SY340 ) )
= ( triple @ SV39 @ ( update_slb @ SV85 @ ( findmin_pqp_res @ SV39 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(415,plain,
! [SV40: $i,SV86: $i] :
( ( ( ( SV86 = create_slb )
| ~ ( contains_slb @ SV86 @ ( findmin_pqp_res @ SV40 ) )
| ~ ( less_than @ ( lookup_slb @ SV86 @ ( findmin_pqp_res @ SV40 ) ) @ ( findmin_pqp_res @ SV40 ) ) )
= $true )
| ( ( ! [SY341: $i] :
( ( findmin_cpq_eff @ ( triple @ SV40 @ SV86 @ SY341 ) )
= ( triple @ SV40 @ ( update_slb @ SV86 @ ( findmin_pqp_res @ SV40 ) ) @ SY341 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(416,plain,
! [SV42: $i,SV88: $i] :
( ( ( SV88 = create_slb )
= $true )
| ( ( ! [SY342: $i] :
( ( findmin_cpq_res @ ( triple @ SV42 @ SV88 @ SY342 ) )
= ( findmin_pqp_res @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(417,plain,
! [SV111: $i,SV90: $i,SV46: $i] :
( ( ! [SY380: $i,SY381: $i] :
( ( i @ ( triple @ SV46 @ ( insert_slb @ SV90 @ ( pair @ SY380 @ SY381 ) ) @ SV111 ) )
= ( insert_pq @ ( i @ ( triple @ SV46 @ SV90 @ SV111 ) ) @ SY380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(418,plain,
! [SV47: $i] :
( ( ~ ! [SY273: $i,SY274: $i] :
( ~ ( contains_cpq @ ( triple @ SV47 @ sK1_U @ SY273 ) @ SY274 )
| ( contains_pq @ ( i @ ( triple @ SV47 @ sK1_U @ SY273 ) ) @ SY274 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[360]) ).
thf(419,plain,
! [SV47: $i] :
( ( ~ ! [SY275: $i,SY276: $i] :
( ~ ( contains_pq @ ( i @ ( triple @ SV47 @ sK1_U @ SY275 ) ) @ SY276 )
| ( contains_cpq @ ( triple @ SV47 @ sK1_U @ SY275 ) @ SY276 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[360]) ).
thf(420,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_remove @ SX0 @ SX1 )
| ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[361]) ).
thf(421,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 )
| ( pi_remove @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[362]) ).
thf(422,plain,
! [SV112: $i,SV91: $i,SV48: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY382: $i,SY383: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY382 ) ) @ SV112 @ SY383 )
| ( SV91 = SV112 )
| ( pair_in_list @ SV48 @ SV112 @ SY383 ) )
| ~ ! [SY384: $i,SY385: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY384 ) ) @ SV112 @ SY385 )
| ( SY384 = SY385 )
| ( pair_in_list @ SV48 @ SV112 @ SY385 ) ) )
| ~ ~ ( ~ ! [SY386: $i,SY387: $i] :
( ( SV91 != SV112 )
| ( SY386 != SY387 )
| ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY386 ) ) @ SV112 @ SY387 ) )
| ~ ! [SY388: $i,SY389: $i] :
( ~ ( pair_in_list @ SV48 @ SV112 @ SY389 )
| ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY388 ) ) @ SV112 @ SY389 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(423,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_find_min @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[364]) ).
thf(424,plain,
( ( ! [SX0: $i] :
( ~ ( pi_find_min @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK14_V @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[365]) ).
thf(425,plain,
! [SV92: $i,SV49: $i] :
( ( ~ ! [SY355: $i] :
( ! [SY356: $i] :
~ ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY356 ) ) @ SY355 )
| ( SV92 = SY355 )
| ( contains_slb @ SV49 @ SY355 ) )
| ~ ~ ( ~ ! [SY357: $i] :
( ( SV92 != SY357 )
| ! [SY358: $i] : ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY358 ) ) @ SY357 ) )
| ~ ! [SY359: $i] :
( ~ ( contains_slb @ SV49 @ SY359 )
| ! [SY360: $i] : ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY360 ) ) @ SY359 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(426,plain,
! [SV93: $i,SV50: $i] :
( ( ~ ! [SY361: $i,SY362: $i] :
( ~ ( contains_cpq @ ( triple @ SV50 @ SV93 @ SY361 ) @ SY362 )
| ( contains_slb @ SV93 @ SY362 ) )
| ~ ! [SY363: $i,SY364: $i] :
( ~ ( contains_slb @ SV93 @ SY364 )
| ( contains_cpq @ ( triple @ SV50 @ SV93 @ SY363 ) @ SY364 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(427,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_removemin @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(428,plain,
( ( ! [SX0: $i] :
( ~ ( pi_removemin @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK13_V @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(429,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( contains_pq @ SX0 @ ( sK15_W @ SX1 @ SX0 ) )
| ~ ~ ( less_than @ SX1 @ ( sK15_W @ SX1 @ SX0 ) ) )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[370]) ).
thf(430,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)],[371]) ).
thf(431,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)],[372]) ).
thf(432,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)],[373]) ).
thf(433,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)],[374]) ).
thf(434,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)],[375]) ).
thf(435,plain,
! [SV51: $i] :
( ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV51 @ SY299 ) @ SY300 )
| ( SY299 = SY300 )
| ( contains_pq @ SV51 @ SY300 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[376]) ).
thf(436,plain,
! [SV51: $i] :
( ( ~ ~ ( ~ ! [SY301: $i,SY302: $i] :
( ( SY301 != SY302 )
| ( contains_pq @ ( insert_pq @ SV51 @ SY301 ) @ SY302 ) )
| ~ ! [SY303: $i,SY304: $i] :
( ~ ( contains_pq @ SV51 @ SY304 )
| ( contains_pq @ ( insert_pq @ SV51 @ SY303 ) @ SY304 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[376]) ).
thf(437,plain,
! [SV113: $i,SV94: $i,SV52: $i] :
( ( ~ ( ~ ! [SY390: $i,SY391: $i] :
( ~ ( less_than @ SY391 @ SY390 )
| ~ ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV94 @ ( pair @ SY390 @ SY391 ) ) @ SV113 ) )
| ( check_cpq @ ( triple @ SV52 @ SV94 @ SV113 ) ) )
| ~ ! [SY392: $i,SY393: $i] :
( ~ ( less_than @ SY393 @ SY392 )
| ~ ( check_cpq @ ( triple @ SV52 @ SV94 @ SV113 ) )
| ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV94 @ ( pair @ SY392 @ SY393 ) ) @ SV113 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(438,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( ok @ SX1 )
| ~ ( succ_cpq @ SX0 @ SX1 )
| ~ ( check_cpq @ SX1 ) )
| ( phi @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[378]) ).
thf(439,plain,
( ( ! [SX0: $i] :
( ~ ( phi @ SX0 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK12_V @ SX0 ) )
| ~ ( succ_cpq @ SX0 @ ( sK12_V @ SX0 ) ) )
| ~ ( check_cpq @ ( sK12_V @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[379]) ).
thf(440,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( contains_pq @ SX0 @ SX1 )
| ( pi_sharp_remove @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[380]) ).
thf(441,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[381]) ).
thf(442,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)],[382]) ).
thf(443,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)],[383]) ).
thf(444,plain,
( ( contains_cpq @ ( triple @ sK2_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY184 @ sK5_SY187 ) ) @ sK3_SY180 ) @ sK6_SY189 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[384]) ).
thf(445,plain,
( ( ~ ( contains_pq @ ( i @ ( triple @ sK2_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY184 @ sK5_SY187 ) ) @ sK3_SY180 ) ) @ sK6_SY189 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[385]) ).
thf(446,plain,
! [SV95: $i,SV53: $i,SV1: $i] :
( ( ( ~ ( less_than @ SV1 @ SV53 )
| ~ ( less_than @ SV53 @ SV95 ) )
= $true )
| ( ( less_than @ SV1 @ SV95 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(447,plain,
! [SV8: $i,SV96: $i,SV57: $i] :
( ( ( ( SV57 = SV96 )
| ~ ( contains_pq @ SV8 @ SV96 ) )
= $true )
| ( ( ( remove_pq @ ( insert_pq @ SV8 @ SV57 ) @ SV96 )
= ( insert_pq @ ( remove_pq @ SV8 @ SV96 ) @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(448,plain,
! [SV58: $i,SV9: $i] :
( ( ( ~ ( contains_pq @ SV9 @ SV58 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV9 @ SV58 ) )
= $true )
| ( ( ( findmin_pq_eff @ SV9 @ SV58 )
= SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(449,plain,
! [SV59: $i,SV10: $i] :
( ( ( ~ ( contains_pq @ SV10 @ SV59 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV10 @ SV59 ) )
= $true )
| ( ( ( findmin_pq_res @ SV10 @ SV59 )
= SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[390]) ).
thf(450,plain,
! [SV60: $i,SV11: $i] :
( ( ( ~ ( contains_pq @ SV11 @ SV60 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV11 @ SV60 ) )
= $true )
| ( ( ( removemin_pq_eff @ SV11 @ SV60 )
= ( remove_pq @ SV11 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(451,plain,
! [SV61: $i,SV12: $i] :
( ( ( ~ ( contains_pq @ SV12 @ SV61 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV12 @ SV61 ) )
= $true )
| ( ( ( removemin_pq_res @ SV12 @ SV61 )
= SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(452,plain,
! [SV18: $i,SV100: $i,SV66: $i] :
( ( ( ( SV66 = SV100 )
| ~ ( contains_slb @ SV18 @ SV100 ) )
= $true )
| ( ( ! [SY370: $i] :
( ( remove_slb @ ( insert_slb @ SV18 @ ( pair @ SV66 @ SY370 ) ) @ SV100 )
= ( insert_slb @ ( remove_slb @ SV18 @ SV100 ) @ ( pair @ SV66 @ SY370 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[397]) ).
thf(453,plain,
! [SV20: $i,SV102: $i,SV68: $i] :
( ( ( ( SV68 = SV102 )
| ~ ( contains_slb @ SV20 @ SV102 ) )
= $true )
| ( ( ! [SY371: $i] :
( ( lookup_slb @ ( insert_slb @ SV20 @ ( pair @ SV68 @ SY371 ) ) @ SV102 )
= ( lookup_slb @ SV20 @ SV102 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[399]) ).
thf(454,plain,
! [SV69: $i,SV22: $i,SV103: $i,SV114: $i] :
( ( ~ ( strictly_less_than @ SV114 @ SV103 )
| ( ( update_slb @ ( insert_slb @ SV22 @ ( pair @ SV69 @ SV114 ) ) @ SV103 )
= ( insert_slb @ ( update_slb @ SV22 @ SV103 ) @ ( pair @ SV69 @ SV103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(455,plain,
! [SV70: $i,SV23: $i,SV115: $i,SV104: $i] :
( ( ~ ( less_than @ SV104 @ SV115 )
| ( ( update_slb @ ( insert_slb @ SV23 @ ( pair @ SV70 @ SV115 ) ) @ SV104 )
= ( insert_slb @ ( update_slb @ SV23 @ SV104 ) @ ( pair @ SV70 @ SV115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(456,plain,
! [SV71: $i,SV25: $i] :
( ( ( succ_cpq @ SV25 @ SV71 )
= $false )
| ( ( ! [SY325: $i] : ( succ_cpq @ SV25 @ ( insert_cpq @ SV71 @ SY325 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(457,plain,
! [SV72: $i,SV26: $i] :
( ( ( succ_cpq @ SV26 @ SV72 )
= $false )
| ( ( ! [SY326: $i] : ( succ_cpq @ SV26 @ ( remove_cpq @ SV72 @ SY326 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(458,plain,
! [SV73: $i,SV27: $i] :
( ( ( succ_cpq @ SV27 @ SV73 )
= $false )
| ( ( succ_cpq @ SV27 @ ( findmin_cpq_eff @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(459,plain,
! [SV74: $i,SV28: $i] :
( ( ( succ_cpq @ SV28 @ SV74 )
= $false )
| ( ( succ_cpq @ SV28 @ ( removemin_cpq_eff @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(460,plain,
! [SV105: $i,SV76: $i,SV30: $i,SV116: $i] :
( ( ! [SY394: $i] :
( ~ ( strictly_less_than @ SV116 @ SY394 )
| ~ ( check_cpq @ ( triple @ SV30 @ ( insert_slb @ SV76 @ ( pair @ SV116 @ SY394 ) ) @ SV105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(461,plain,
! [SV106: $i,SV78: $i,SV32: $i] :
( ( ( ok @ ( triple @ SV32 @ SV78 @ SV106 ) )
= $true )
| ( ( SV106 = bad )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(462,plain,
! [SV117: $i,SV107: $i,SV79: $i,SV33: $i] :
( ( ( insert_cpq @ ( triple @ SV33 @ SV79 @ SV107 ) @ SV117 )
= ( triple @ ( insert_pqp @ SV33 @ SV117 ) @ ( insert_slb @ SV79 @ ( pair @ SV117 @ bottom ) ) @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(463,plain,
! [SV108: $i,SV34: $i,SV118: $i,SV80: $i] :
( ( ( contains_slb @ SV80 @ SV118 )
| ( ( remove_cpq @ ( triple @ SV34 @ SV80 @ SV108 ) @ SV118 )
= ( triple @ SV34 @ SV80 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(464,plain,
! [SV109: $i,SV35: $i,SV119: $i,SV81: $i] :
( ( ~ ( contains_slb @ SV81 @ SV119 )
| ~ ( less_than @ ( lookup_slb @ SV81 @ SV119 ) @ SV119 )
| ( ( remove_cpq @ ( triple @ SV35 @ SV81 @ SV109 ) @ SV119 )
= ( triple @ ( remove_pqp @ SV35 @ SV119 ) @ ( remove_slb @ SV81 @ SV119 ) @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(465,plain,
! [SV110: $i,SV36: $i,SV120: $i,SV82: $i] :
( ( ~ ( contains_slb @ SV82 @ SV120 )
| ~ ( strictly_less_than @ SV120 @ ( lookup_slb @ SV82 @ SV120 ) )
| ( ( remove_cpq @ ( triple @ SV36 @ SV82 @ SV110 ) @ SV120 )
= ( triple @ ( remove_pqp @ SV36 @ SV120 ) @ ( remove_slb @ SV82 @ SV120 ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(466,plain,
! [SV38: $i,SV84: $i] :
( ( ( SV84 = create_slb )
= $true )
| ( ( contains_slb @ SV84 @ ( findmin_pqp_res @ SV38 ) )
= $true )
| ( ( ! [SY339: $i] :
( ( findmin_cpq_eff @ ( triple @ SV38 @ SV84 @ SY339 ) )
= ( triple @ SV38 @ ( update_slb @ SV84 @ ( findmin_pqp_res @ SV38 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(467,plain,
! [SV39: $i,SV85: $i] :
( ( ( ( SV85 = create_slb )
| ~ ( contains_slb @ SV85 @ ( findmin_pqp_res @ SV39 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV39 ) @ ( lookup_slb @ SV85 @ ( findmin_pqp_res @ SV39 ) ) ) )
= $true )
| ( ( ! [SY340: $i] :
( ( findmin_cpq_eff @ ( triple @ SV39 @ SV85 @ SY340 ) )
= ( triple @ SV39 @ ( update_slb @ SV85 @ ( findmin_pqp_res @ SV39 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(468,plain,
! [SV40: $i,SV86: $i] :
( ( ( ( SV86 = create_slb )
| ~ ( contains_slb @ SV86 @ ( findmin_pqp_res @ SV40 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV86 @ ( findmin_pqp_res @ SV40 ) ) @ ( findmin_pqp_res @ SV40 ) ) )
= $true )
| ( ( ! [SY341: $i] :
( ( findmin_cpq_eff @ ( triple @ SV40 @ SV86 @ SY341 ) )
= ( triple @ SV40 @ ( update_slb @ SV86 @ ( findmin_pqp_res @ SV40 ) ) @ SY341 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(469,plain,
! [SV121: $i,SV88: $i,SV42: $i] :
( ( ( ( findmin_cpq_res @ ( triple @ SV42 @ SV88 @ SV121 ) )
= ( findmin_pqp_res @ SV42 ) )
= $true )
| ( ( SV88 = create_slb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(470,plain,
! [SV111: $i,SV122: $i,SV90: $i,SV46: $i] :
( ( ! [SY395: $i] :
( ( i @ ( triple @ SV46 @ ( insert_slb @ SV90 @ ( pair @ SV122 @ SY395 ) ) @ SV111 ) )
= ( insert_pq @ ( i @ ( triple @ SV46 @ SV90 @ SV111 ) ) @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(471,plain,
! [SV47: $i] :
( ( ! [SY273: $i,SY274: $i] :
( ~ ( contains_cpq @ ( triple @ SV47 @ sK1_U @ SY273 ) @ SY274 )
| ( contains_pq @ ( i @ ( triple @ SV47 @ sK1_U @ SY273 ) ) @ SY274 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[418]) ).
thf(472,plain,
! [SV47: $i] :
( ( ! [SY275: $i,SY276: $i] :
( ~ ( contains_pq @ ( i @ ( triple @ SV47 @ sK1_U @ SY275 ) ) @ SY276 )
| ( contains_cpq @ ( triple @ SV47 @ sK1_U @ SY275 ) @ SY276 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[419]) ).
thf(473,plain,
! [SV123: $i] :
( ( ! [SY396: $i] :
( ~ ( pi_remove @ SV123 @ SY396 )
| ( pi_sharp_remove @ ( i @ SV123 ) @ SY396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(474,plain,
! [SV124: $i] :
( ( ! [SY397: $i] :
( ~ ( pi_sharp_remove @ ( i @ SV124 ) @ SY397 )
| ( pi_remove @ SV124 @ SY397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(475,plain,
! [SV112: $i,SV91: $i,SV48: $i] :
( ( ~ ~ ( ~ ! [SY382: $i,SY383: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY382 ) ) @ SV112 @ SY383 )
| ( SV91 = SV112 )
| ( pair_in_list @ SV48 @ SV112 @ SY383 ) )
| ~ ! [SY384: $i,SY385: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY384 ) ) @ SV112 @ SY385 )
| ( SY384 = SY385 )
| ( pair_in_list @ SV48 @ SV112 @ SY385 ) ) )
| ~ ~ ( ~ ! [SY386: $i,SY387: $i] :
( ( SV91 != SV112 )
| ( SY386 != SY387 )
| ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY386 ) ) @ SV112 @ SY387 ) )
| ~ ! [SY388: $i,SY389: $i] :
( ~ ( pair_in_list @ SV48 @ SV112 @ SY389 )
| ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY388 ) ) @ SV112 @ SY389 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(476,plain,
! [SV125: $i] :
( ( ! [SY398: $i] :
~ ( pi_sharp_find_min @ ( i @ SV125 ) @ SY398 )
| ( pi_find_min @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(477,plain,
! [SV126: $i] :
( ( ~ ( pi_find_min @ SV126 )
| ( pi_sharp_find_min @ ( i @ SV126 ) @ ( sK14_V @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(478,plain,
! [SV92: $i,SV49: $i] :
( ( ~ ! [SY355: $i] :
( ! [SY356: $i] :
~ ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY356 ) ) @ SY355 )
| ( SV92 = SY355 )
| ( contains_slb @ SV49 @ SY355 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(479,plain,
! [SV49: $i,SV92: $i] :
( ( ~ ~ ( ~ ! [SY357: $i] :
( ( SV92 != SY357 )
| ! [SY358: $i] : ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY358 ) ) @ SY357 ) )
| ~ ! [SY359: $i] :
( ~ ( contains_slb @ SV49 @ SY359 )
| ! [SY360: $i] : ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY360 ) ) @ SY359 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(480,plain,
! [SV93: $i,SV50: $i] :
( ( ~ ! [SY361: $i,SY362: $i] :
( ~ ( contains_cpq @ ( triple @ SV50 @ SV93 @ SY361 ) @ SY362 )
| ( contains_slb @ SV93 @ SY362 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[426]) ).
thf(481,plain,
! [SV50: $i,SV93: $i] :
( ( ~ ! [SY363: $i,SY364: $i] :
( ~ ( contains_slb @ SV93 @ SY364 )
| ( contains_cpq @ ( triple @ SV50 @ SV93 @ SY363 ) @ SY364 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[426]) ).
thf(482,plain,
! [SV127: $i] :
( ( ! [SY399: $i] :
~ ( pi_sharp_find_min @ ( i @ SV127 ) @ SY399 )
| ( pi_removemin @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(483,plain,
! [SV128: $i] :
( ( ~ ( pi_removemin @ SV128 )
| ( pi_sharp_find_min @ ( i @ SV128 ) @ ( sK13_V @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(484,plain,
! [SV129: $i] :
( ( ! [SY400: $i] :
( ~ ( ~ ( contains_pq @ SV129 @ ( sK15_W @ SY400 @ SV129 ) )
| ~ ~ ( less_than @ SY400 @ ( sK15_W @ SY400 @ SV129 ) ) )
| ( issmallestelement_pq @ SV129 @ SY400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(485,plain,
! [SV130: $i] :
( ( ! [SY401: $i] :
( ~ ( issmallestelement_pq @ SV130 @ SY401 )
| ! [SY402: $i] :
( ~ ( contains_pq @ SV130 @ SY402 )
| ( less_than @ SY401 @ SY402 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(486,plain,
! [SV131: $i] :
( ( ! [SY403: $i] :
( ~ ( less_than @ SV131 @ SY403 )
| ( less_than @ SY403 @ SV131 )
| ( strictly_less_than @ SV131 @ SY403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
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)],[432]) ).
thf(488,plain,
! [SV132: $i] :
( ( ! [SY404: $i] :
( ~ ( contains_pq @ SV132 @ SY404 )
| ~ ( issmallestelement_pq @ SV132 @ SY404 )
| ( pi_sharp_find_min @ SV132 @ SY404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
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)],[434]) ).
thf(490,plain,
! [SV51: $i] :
( ( ! [SY299: $i,SY300: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV51 @ SY299 ) @ SY300 )
| ( SY299 = SY300 )
| ( contains_pq @ SV51 @ SY300 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(491,plain,
! [SV51: $i] :
( ( ~ ( ~ ! [SY301: $i,SY302: $i] :
( ( SY301 != SY302 )
| ( contains_pq @ ( insert_pq @ SV51 @ SY301 ) @ SY302 ) )
| ~ ! [SY303: $i,SY304: $i] :
( ~ ( contains_pq @ SV51 @ SY304 )
| ( contains_pq @ ( insert_pq @ SV51 @ SY303 ) @ SY304 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[436]) ).
thf(492,plain,
! [SV113: $i,SV94: $i,SV52: $i] :
( ( ~ ! [SY390: $i,SY391: $i] :
( ~ ( less_than @ SY391 @ SY390 )
| ~ ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV94 @ ( pair @ SY390 @ SY391 ) ) @ SV113 ) )
| ( check_cpq @ ( triple @ SV52 @ SV94 @ SV113 ) ) )
| ~ ! [SY392: $i,SY393: $i] :
( ~ ( less_than @ SY393 @ SY392 )
| ~ ( check_cpq @ ( triple @ SV52 @ SV94 @ SV113 ) )
| ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV94 @ ( pair @ SY392 @ SY393 ) ) @ SV113 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(493,plain,
! [SV133: $i] :
( ( ! [SY405: $i] :
( ~ ( ok @ SY405 )
| ~ ( succ_cpq @ SV133 @ SY405 )
| ~ ( check_cpq @ SY405 ) )
| ( phi @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(494,plain,
! [SV134: $i] :
( ( ~ ( phi @ SV134 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK12_V @ SV134 ) )
| ~ ( succ_cpq @ SV134 @ ( sK12_V @ SV134 ) ) )
| ~ ( check_cpq @ ( sK12_V @ SV134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(495,plain,
! [SV135: $i] :
( ( ! [SY406: $i] :
( ~ ( contains_pq @ SV135 @ SY406 )
| ( pi_sharp_remove @ SV135 @ SY406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(496,plain,
! [SV136: $i] :
( ( ! [SY407: $i] :
( ~ ( pi_sharp_remove @ SV136 @ SY407 )
| ( contains_pq @ SV136 @ SY407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(497,plain,
! [SV137: $i] :
( ( ! [SY408: $i] :
( ~ ( contains_pq @ SV137 @ SY408 )
| ~ ( issmallestelement_pq @ SV137 @ SY408 )
| ( pi_sharp_removemin @ SV137 @ SY408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
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)],[443]) ).
thf(499,plain,
( ( contains_pq @ ( i @ ( triple @ sK2_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY184 @ sK5_SY187 ) ) @ sK3_SY180 ) ) @ sK6_SY189 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(500,plain,
! [SV95: $i,SV53: $i,SV1: $i] :
( ( ( ~ ( less_than @ SV1 @ SV53 ) )
= $true )
| ( ( ~ ( less_than @ SV53 @ SV95 ) )
= $true )
| ( ( less_than @ SV1 @ SV95 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[446]) ).
thf(501,plain,
! [SV8: $i,SV96: $i,SV57: $i] :
( ( ( SV57 = SV96 )
= $true )
| ( ( ~ ( contains_pq @ SV8 @ SV96 ) )
= $true )
| ( ( ( remove_pq @ ( insert_pq @ SV8 @ SV57 ) @ SV96 )
= ( insert_pq @ ( remove_pq @ SV8 @ SV96 ) @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[447]) ).
thf(502,plain,
! [SV58: $i,SV9: $i] :
( ( ( contains_pq @ SV9 @ SV58 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV9 @ SV58 ) )
= $true )
| ( ( ( findmin_pq_eff @ SV9 @ SV58 )
= SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(503,plain,
! [SV59: $i,SV10: $i] :
( ( ( contains_pq @ SV10 @ SV59 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV10 @ SV59 ) )
= $true )
| ( ( ( findmin_pq_res @ SV10 @ SV59 )
= SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(504,plain,
! [SV60: $i,SV11: $i] :
( ( ( contains_pq @ SV11 @ SV60 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV11 @ SV60 ) )
= $true )
| ( ( ( removemin_pq_eff @ SV11 @ SV60 )
= ( remove_pq @ SV11 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(505,plain,
! [SV61: $i,SV12: $i] :
( ( ( contains_pq @ SV12 @ SV61 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV12 @ SV61 ) )
= $true )
| ( ( ( removemin_pq_res @ SV12 @ SV61 )
= SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(506,plain,
! [SV18: $i,SV100: $i,SV66: $i] :
( ( ( SV66 = SV100 )
= $true )
| ( ( ~ ( contains_slb @ SV18 @ SV100 ) )
= $true )
| ( ( ! [SY370: $i] :
( ( remove_slb @ ( insert_slb @ SV18 @ ( pair @ SV66 @ SY370 ) ) @ SV100 )
= ( insert_slb @ ( remove_slb @ SV18 @ SV100 ) @ ( pair @ SV66 @ SY370 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[452]) ).
thf(507,plain,
! [SV20: $i,SV102: $i,SV68: $i] :
( ( ( SV68 = SV102 )
= $true )
| ( ( ~ ( contains_slb @ SV20 @ SV102 ) )
= $true )
| ( ( ! [SY371: $i] :
( ( lookup_slb @ ( insert_slb @ SV20 @ ( pair @ SV68 @ SY371 ) ) @ SV102 )
= ( lookup_slb @ SV20 @ SV102 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[453]) ).
thf(508,plain,
! [SV69: $i,SV22: $i,SV103: $i,SV114: $i] :
( ( ( ~ ( strictly_less_than @ SV114 @ SV103 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV22 @ ( pair @ SV69 @ SV114 ) ) @ SV103 )
= ( insert_slb @ ( update_slb @ SV22 @ SV103 ) @ ( pair @ SV69 @ SV103 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(509,plain,
! [SV70: $i,SV23: $i,SV115: $i,SV104: $i] :
( ( ( ~ ( less_than @ SV104 @ SV115 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV23 @ ( pair @ SV70 @ SV115 ) ) @ SV104 )
= ( insert_slb @ ( update_slb @ SV23 @ SV104 ) @ ( pair @ SV70 @ SV115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(510,plain,
! [SV138: $i,SV71: $i,SV25: $i] :
( ( ( succ_cpq @ SV25 @ ( insert_cpq @ SV71 @ SV138 ) )
= $true )
| ( ( succ_cpq @ SV25 @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(511,plain,
! [SV139: $i,SV72: $i,SV26: $i] :
( ( ( succ_cpq @ SV26 @ ( remove_cpq @ SV72 @ SV139 ) )
= $true )
| ( ( succ_cpq @ SV26 @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(512,plain,
! [SV105: $i,SV76: $i,SV30: $i,SV140: $i,SV116: $i] :
( ( ~ ( strictly_less_than @ SV116 @ SV140 )
| ~ ( check_cpq @ ( triple @ SV30 @ ( insert_slb @ SV76 @ ( pair @ SV116 @ SV140 ) ) @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(513,plain,
! [SV108: $i,SV34: $i,SV118: $i,SV80: $i] :
( ( ( contains_slb @ SV80 @ SV118 )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV34 @ SV80 @ SV108 ) @ SV118 )
= ( triple @ SV34 @ SV80 @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(514,plain,
! [SV109: $i,SV35: $i,SV119: $i,SV81: $i] :
( ( ( ~ ( contains_slb @ SV81 @ SV119 )
| ~ ( less_than @ ( lookup_slb @ SV81 @ SV119 ) @ SV119 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV35 @ SV81 @ SV109 ) @ SV119 )
= ( triple @ ( remove_pqp @ SV35 @ SV119 ) @ ( remove_slb @ SV81 @ SV119 ) @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[464]) ).
thf(515,plain,
! [SV110: $i,SV36: $i,SV120: $i,SV82: $i] :
( ( ( ~ ( contains_slb @ SV82 @ SV120 )
| ~ ( strictly_less_than @ SV120 @ ( lookup_slb @ SV82 @ SV120 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV36 @ SV82 @ SV110 ) @ SV120 )
= ( triple @ ( remove_pqp @ SV36 @ SV120 ) @ ( remove_slb @ SV82 @ SV120 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(516,plain,
! [SV141: $i,SV84: $i,SV38: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV38 @ SV84 @ SV141 ) )
= ( triple @ SV38 @ ( update_slb @ SV84 @ ( findmin_pqp_res @ SV38 ) ) @ bad ) )
= $true )
| ( ( contains_slb @ SV84 @ ( findmin_pqp_res @ SV38 ) )
= $true )
| ( ( SV84 = create_slb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(517,plain,
! [SV39: $i,SV85: $i] :
( ( ( SV85 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV85 @ ( findmin_pqp_res @ SV39 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV39 ) @ ( lookup_slb @ SV85 @ ( findmin_pqp_res @ SV39 ) ) ) )
= $true )
| ( ( ! [SY340: $i] :
( ( findmin_cpq_eff @ ( triple @ SV39 @ SV85 @ SY340 ) )
= ( triple @ SV39 @ ( update_slb @ SV85 @ ( findmin_pqp_res @ SV39 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(518,plain,
! [SV40: $i,SV86: $i] :
( ( ( SV86 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV86 @ ( findmin_pqp_res @ SV40 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV86 @ ( findmin_pqp_res @ SV40 ) ) @ ( findmin_pqp_res @ SV40 ) ) )
= $true )
| ( ( ! [SY341: $i] :
( ( findmin_cpq_eff @ ( triple @ SV40 @ SV86 @ SY341 ) )
= ( triple @ SV40 @ ( update_slb @ SV86 @ ( findmin_pqp_res @ SV40 ) ) @ SY341 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(519,plain,
! [SV111: $i,SV142: $i,SV122: $i,SV90: $i,SV46: $i] :
( ( ( i @ ( triple @ SV46 @ ( insert_slb @ SV90 @ ( pair @ SV122 @ SV142 ) ) @ SV111 ) )
= ( insert_pq @ ( i @ ( triple @ SV46 @ SV90 @ SV111 ) ) @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(520,plain,
! [SV143: $i,SV47: $i] :
( ( ! [SY409: $i] :
( ~ ( contains_cpq @ ( triple @ SV47 @ sK1_U @ SV143 ) @ SY409 )
| ( contains_pq @ ( i @ ( triple @ SV47 @ sK1_U @ SV143 ) ) @ SY409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(521,plain,
! [SV144: $i,SV47: $i] :
( ( ! [SY410: $i] :
( ~ ( contains_pq @ ( i @ ( triple @ SV47 @ sK1_U @ SV144 ) ) @ SY410 )
| ( contains_cpq @ ( triple @ SV47 @ sK1_U @ SV144 ) @ SY410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(522,plain,
! [SV145: $i,SV123: $i] :
( ( ~ ( pi_remove @ SV123 @ SV145 )
| ( pi_sharp_remove @ ( i @ SV123 ) @ SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(523,plain,
! [SV146: $i,SV124: $i] :
( ( ~ ( pi_sharp_remove @ ( i @ SV124 ) @ SV146 )
| ( pi_remove @ SV124 @ SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(524,plain,
! [SV112: $i,SV91: $i,SV48: $i] :
( ( ~ ~ ( ~ ! [SY382: $i,SY383: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY382 ) ) @ SV112 @ SY383 )
| ( SV91 = SV112 )
| ( pair_in_list @ SV48 @ SV112 @ SY383 ) )
| ~ ! [SY384: $i,SY385: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY384 ) ) @ SV112 @ SY385 )
| ( SY384 = SY385 )
| ( pair_in_list @ SV48 @ SV112 @ SY385 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[475]) ).
thf(525,plain,
! [SV48: $i,SV112: $i,SV91: $i] :
( ( ~ ~ ( ~ ! [SY386: $i,SY387: $i] :
( ( SV91 != SV112 )
| ( SY386 != SY387 )
| ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY386 ) ) @ SV112 @ SY387 ) )
| ~ ! [SY388: $i,SY389: $i] :
( ~ ( pair_in_list @ SV48 @ SV112 @ SY389 )
| ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY388 ) ) @ SV112 @ SY389 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[475]) ).
thf(526,plain,
! [SV125: $i] :
( ( ( ! [SY398: $i] :
~ ( pi_sharp_find_min @ ( i @ SV125 ) @ SY398 ) )
= $true )
| ( ( pi_find_min @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(527,plain,
! [SV126: $i] :
( ( ( ~ ( pi_find_min @ SV126 ) )
= $true )
| ( ( pi_sharp_find_min @ ( i @ SV126 ) @ ( sK14_V @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(528,plain,
! [SV92: $i,SV49: $i] :
( ( ! [SY355: $i] :
( ! [SY356: $i] :
~ ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY356 ) ) @ SY355 )
| ( SV92 = SY355 )
| ( contains_slb @ SV49 @ SY355 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(529,plain,
! [SV49: $i,SV92: $i] :
( ( ~ ( ~ ! [SY357: $i] :
( ( SV92 != SY357 )
| ! [SY358: $i] : ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY358 ) ) @ SY357 ) )
| ~ ! [SY359: $i] :
( ~ ( contains_slb @ SV49 @ SY359 )
| ! [SY360: $i] : ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY360 ) ) @ SY359 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(530,plain,
! [SV93: $i,SV50: $i] :
( ( ! [SY361: $i,SY362: $i] :
( ~ ( contains_cpq @ ( triple @ SV50 @ SV93 @ SY361 ) @ SY362 )
| ( contains_slb @ SV93 @ SY362 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[480]) ).
thf(531,plain,
! [SV50: $i,SV93: $i] :
( ( ! [SY363: $i,SY364: $i] :
( ~ ( contains_slb @ SV93 @ SY364 )
| ( contains_cpq @ ( triple @ SV50 @ SV93 @ SY363 ) @ SY364 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[481]) ).
thf(532,plain,
! [SV127: $i] :
( ( ( ! [SY399: $i] :
~ ( pi_sharp_find_min @ ( i @ SV127 ) @ SY399 ) )
= $true )
| ( ( pi_removemin @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(533,plain,
! [SV128: $i] :
( ( ( ~ ( pi_removemin @ SV128 ) )
= $true )
| ( ( pi_sharp_find_min @ ( i @ SV128 ) @ ( sK13_V @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[483]) ).
thf(534,plain,
! [SV147: $i,SV129: $i] :
( ( ~ ( ~ ( contains_pq @ SV129 @ ( sK15_W @ SV147 @ SV129 ) )
| ~ ~ ( less_than @ SV147 @ ( sK15_W @ SV147 @ SV129 ) ) )
| ( issmallestelement_pq @ SV129 @ SV147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(535,plain,
! [SV148: $i,SV130: $i] :
( ( ~ ( issmallestelement_pq @ SV130 @ SV148 )
| ! [SY411: $i] :
( ~ ( contains_pq @ SV130 @ SY411 )
| ( less_than @ SV148 @ SY411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(536,plain,
! [SV149: $i,SV131: $i] :
( ( ~ ( less_than @ SV131 @ SV149 )
| ( less_than @ SV149 @ SV131 )
| ( strictly_less_than @ SV131 @ SV149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(537,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[487]) ).
thf(538,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[487]) ).
thf(539,plain,
! [SV150: $i,SV132: $i] :
( ( ~ ( contains_pq @ SV132 @ SV150 )
| ~ ( issmallestelement_pq @ SV132 @ SV150 )
| ( pi_sharp_find_min @ SV132 @ SV150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(540,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[489]) ).
thf(541,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[489]) ).
thf(542,plain,
! [SV151: $i,SV51: $i] :
( ( ! [SY412: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV51 @ SV151 ) @ SY412 )
| ( SV151 = SY412 )
| ( contains_pq @ SV51 @ SY412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(543,plain,
! [SV51: $i] :
( ( ~ ! [SY301: $i,SY302: $i] :
( ( SY301 != SY302 )
| ( contains_pq @ ( insert_pq @ SV51 @ SY301 ) @ SY302 ) )
| ~ ! [SY303: $i,SY304: $i] :
( ~ ( contains_pq @ SV51 @ SY304 )
| ( contains_pq @ ( insert_pq @ SV51 @ SY303 ) @ SY304 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(544,plain,
! [SV113: $i,SV94: $i,SV52: $i] :
( ( ~ ! [SY390: $i,SY391: $i] :
( ~ ( less_than @ SY391 @ SY390 )
| ~ ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV94 @ ( pair @ SY390 @ SY391 ) ) @ SV113 ) )
| ( check_cpq @ ( triple @ SV52 @ SV94 @ SV113 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[492]) ).
thf(545,plain,
! [SV113: $i,SV94: $i,SV52: $i] :
( ( ~ ! [SY392: $i,SY393: $i] :
( ~ ( less_than @ SY393 @ SY392 )
| ~ ( check_cpq @ ( triple @ SV52 @ SV94 @ SV113 ) )
| ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV94 @ ( pair @ SY392 @ SY393 ) ) @ SV113 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[492]) ).
thf(546,plain,
! [SV133: $i] :
( ( ( ! [SY405: $i] :
( ~ ( ok @ SY405 )
| ~ ( succ_cpq @ SV133 @ SY405 )
| ~ ( check_cpq @ SY405 ) ) )
= $true )
| ( ( phi @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(547,plain,
! [SV134: $i] :
( ( ( ~ ( phi @ SV134 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ok @ ( sK12_V @ SV134 ) )
| ~ ( succ_cpq @ SV134 @ ( sK12_V @ SV134 ) ) )
| ~ ( check_cpq @ ( sK12_V @ SV134 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(548,plain,
! [SV152: $i,SV135: $i] :
( ( ~ ( contains_pq @ SV135 @ SV152 )
| ( pi_sharp_remove @ SV135 @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(549,plain,
! [SV153: $i,SV136: $i] :
( ( ~ ( pi_sharp_remove @ SV136 @ SV153 )
| ( contains_pq @ SV136 @ SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(550,plain,
! [SV154: $i,SV137: $i] :
( ( ~ ( contains_pq @ SV137 @ SV154 )
| ~ ( issmallestelement_pq @ SV137 @ SV154 )
| ( pi_sharp_removemin @ SV137 @ SV154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(551,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[498]) ).
thf(552,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[498]) ).
thf(553,plain,
! [SV95: $i,SV53: $i,SV1: $i] :
( ( ( less_than @ SV1 @ SV53 )
= $false )
| ( ( ~ ( less_than @ SV53 @ SV95 ) )
= $true )
| ( ( less_than @ SV1 @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(554,plain,
! [SV57: $i,SV96: $i,SV8: $i] :
( ( ( contains_pq @ SV8 @ SV96 )
= $false )
| ( ( SV57 = SV96 )
= $true )
| ( ( ( remove_pq @ ( insert_pq @ SV8 @ SV57 ) @ SV96 )
= ( insert_pq @ ( remove_pq @ SV8 @ SV96 ) @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(555,plain,
! [SV58: $i,SV9: $i] :
( ( ( issmallestelement_pq @ SV9 @ SV58 )
= $false )
| ( ( contains_pq @ SV9 @ SV58 )
= $false )
| ( ( ( findmin_pq_eff @ SV9 @ SV58 )
= SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(556,plain,
! [SV59: $i,SV10: $i] :
( ( ( issmallestelement_pq @ SV10 @ SV59 )
= $false )
| ( ( contains_pq @ SV10 @ SV59 )
= $false )
| ( ( ( findmin_pq_res @ SV10 @ SV59 )
= SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(557,plain,
! [SV60: $i,SV11: $i] :
( ( ( issmallestelement_pq @ SV11 @ SV60 )
= $false )
| ( ( contains_pq @ SV11 @ SV60 )
= $false )
| ( ( ( removemin_pq_eff @ SV11 @ SV60 )
= ( remove_pq @ SV11 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(558,plain,
! [SV61: $i,SV12: $i] :
( ( ( issmallestelement_pq @ SV12 @ SV61 )
= $false )
| ( ( contains_pq @ SV12 @ SV61 )
= $false )
| ( ( ( removemin_pq_res @ SV12 @ SV61 )
= SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[505]) ).
thf(559,plain,
! [SV66: $i,SV100: $i,SV18: $i] :
( ( ( contains_slb @ SV18 @ SV100 )
= $false )
| ( ( SV66 = SV100 )
= $true )
| ( ( ! [SY370: $i] :
( ( remove_slb @ ( insert_slb @ SV18 @ ( pair @ SV66 @ SY370 ) ) @ SV100 )
= ( insert_slb @ ( remove_slb @ SV18 @ SV100 ) @ ( pair @ SV66 @ SY370 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(560,plain,
! [SV68: $i,SV102: $i,SV20: $i] :
( ( ( contains_slb @ SV20 @ SV102 )
= $false )
| ( ( SV68 = SV102 )
= $true )
| ( ( ! [SY371: $i] :
( ( lookup_slb @ ( insert_slb @ SV20 @ ( pair @ SV68 @ SY371 ) ) @ SV102 )
= ( lookup_slb @ SV20 @ SV102 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(561,plain,
! [SV69: $i,SV22: $i,SV103: $i,SV114: $i] :
( ( ( strictly_less_than @ SV114 @ SV103 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV22 @ ( pair @ SV69 @ SV114 ) ) @ SV103 )
= ( insert_slb @ ( update_slb @ SV22 @ SV103 ) @ ( pair @ SV69 @ SV103 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(562,plain,
! [SV70: $i,SV23: $i,SV115: $i,SV104: $i] :
( ( ( less_than @ SV104 @ SV115 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV23 @ ( pair @ SV70 @ SV115 ) ) @ SV104 )
= ( insert_slb @ ( update_slb @ SV23 @ SV104 ) @ ( pair @ SV70 @ SV115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[509]) ).
thf(563,plain,
! [SV105: $i,SV76: $i,SV30: $i,SV140: $i,SV116: $i] :
( ( ( ~ ( strictly_less_than @ SV116 @ SV140 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV30 @ ( insert_slb @ SV76 @ ( pair @ SV116 @ SV140 ) ) @ SV105 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[512]) ).
thf(564,plain,
! [SV109: $i,SV35: $i,SV119: $i,SV81: $i] :
( ( ( ~ ( contains_slb @ SV81 @ SV119 ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV81 @ SV119 ) @ SV119 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV35 @ SV81 @ SV109 ) @ SV119 )
= ( triple @ ( remove_pqp @ SV35 @ SV119 ) @ ( remove_slb @ SV81 @ SV119 ) @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(565,plain,
! [SV110: $i,SV36: $i,SV120: $i,SV82: $i] :
( ( ( ~ ( contains_slb @ SV82 @ SV120 ) )
= $true )
| ( ( ~ ( strictly_less_than @ SV120 @ ( lookup_slb @ SV82 @ SV120 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV36 @ SV82 @ SV110 ) @ SV120 )
= ( triple @ ( remove_pqp @ SV36 @ SV120 ) @ ( remove_slb @ SV82 @ SV120 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(566,plain,
! [SV39: $i,SV85: $i] :
( ( ( contains_slb @ SV85 @ ( findmin_pqp_res @ SV39 ) )
= $false )
| ( ( SV85 = create_slb )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV39 ) @ ( lookup_slb @ SV85 @ ( findmin_pqp_res @ SV39 ) ) ) )
= $true )
| ( ( ! [SY340: $i] :
( ( findmin_cpq_eff @ ( triple @ SV39 @ SV85 @ SY340 ) )
= ( triple @ SV39 @ ( update_slb @ SV85 @ ( findmin_pqp_res @ SV39 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(567,plain,
! [SV40: $i,SV86: $i] :
( ( ( contains_slb @ SV86 @ ( findmin_pqp_res @ SV40 ) )
= $false )
| ( ( SV86 = create_slb )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV86 @ ( findmin_pqp_res @ SV40 ) ) @ ( findmin_pqp_res @ SV40 ) ) )
= $true )
| ( ( ! [SY341: $i] :
( ( findmin_cpq_eff @ ( triple @ SV40 @ SV86 @ SY341 ) )
= ( triple @ SV40 @ ( update_slb @ SV86 @ ( findmin_pqp_res @ SV40 ) ) @ SY341 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(568,plain,
! [SV155: $i,SV143: $i,SV47: $i] :
( ( ~ ( contains_cpq @ ( triple @ SV47 @ sK1_U @ SV143 ) @ SV155 )
| ( contains_pq @ ( i @ ( triple @ SV47 @ sK1_U @ SV143 ) ) @ SV155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(569,plain,
! [SV156: $i,SV144: $i,SV47: $i] :
( ( ~ ( contains_pq @ ( i @ ( triple @ SV47 @ sK1_U @ SV144 ) ) @ SV156 )
| ( contains_cpq @ ( triple @ SV47 @ sK1_U @ SV144 ) @ SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(570,plain,
! [SV145: $i,SV123: $i] :
( ( ( ~ ( pi_remove @ SV123 @ SV145 ) )
= $true )
| ( ( pi_sharp_remove @ ( i @ SV123 ) @ SV145 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[522]) ).
thf(571,plain,
! [SV146: $i,SV124: $i] :
( ( ( ~ ( pi_sharp_remove @ ( i @ SV124 ) @ SV146 ) )
= $true )
| ( ( pi_remove @ SV124 @ SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(572,plain,
! [SV112: $i,SV91: $i,SV48: $i] :
( ( ~ ( ~ ! [SY382: $i,SY383: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY382 ) ) @ SV112 @ SY383 )
| ( SV91 = SV112 )
| ( pair_in_list @ SV48 @ SV112 @ SY383 ) )
| ~ ! [SY384: $i,SY385: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY384 ) ) @ SV112 @ SY385 )
| ( SY384 = SY385 )
| ( pair_in_list @ SV48 @ SV112 @ SY385 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[524]) ).
thf(573,plain,
! [SV48: $i,SV112: $i,SV91: $i] :
( ( ~ ( ~ ! [SY386: $i,SY387: $i] :
( ( SV91 != SV112 )
| ( SY386 != SY387 )
| ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY386 ) ) @ SV112 @ SY387 ) )
| ~ ! [SY388: $i,SY389: $i] :
( ~ ( pair_in_list @ SV48 @ SV112 @ SY389 )
| ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY388 ) ) @ SV112 @ SY389 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[525]) ).
thf(574,plain,
! [SV157: $i,SV125: $i] :
( ( ( ~ ( pi_sharp_find_min @ ( i @ SV125 ) @ SV157 ) )
= $true )
| ( ( pi_find_min @ SV125 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(575,plain,
! [SV126: $i] :
( ( ( pi_find_min @ SV126 )
= $false )
| ( ( pi_sharp_find_min @ ( i @ SV126 ) @ ( sK14_V @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(576,plain,
! [SV158: $i,SV92: $i,SV49: $i] :
( ( ! [SY413: $i] :
~ ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY413 ) ) @ SV158 )
| ( SV92 = SV158 )
| ( contains_slb @ SV49 @ SV158 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(577,plain,
! [SV49: $i,SV92: $i] :
( ( ~ ! [SY357: $i] :
( ( SV92 != SY357 )
| ! [SY358: $i] : ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY358 ) ) @ SY357 ) )
| ~ ! [SY359: $i] :
( ~ ( contains_slb @ SV49 @ SY359 )
| ! [SY360: $i] : ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY360 ) ) @ SY359 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(578,plain,
! [SV159: $i,SV93: $i,SV50: $i] :
( ( ! [SY414: $i] :
( ~ ( contains_cpq @ ( triple @ SV50 @ SV93 @ SV159 ) @ SY414 )
| ( contains_slb @ SV93 @ SY414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(579,plain,
! [SV160: $i,SV50: $i,SV93: $i] :
( ( ! [SY415: $i] :
( ~ ( contains_slb @ SV93 @ SY415 )
| ( contains_cpq @ ( triple @ SV50 @ SV93 @ SV160 ) @ SY415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(580,plain,
! [SV161: $i,SV127: $i] :
( ( ( ~ ( pi_sharp_find_min @ ( i @ SV127 ) @ SV161 ) )
= $true )
| ( ( pi_removemin @ SV127 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(581,plain,
! [SV128: $i] :
( ( ( pi_removemin @ SV128 )
= $false )
| ( ( pi_sharp_find_min @ ( i @ SV128 ) @ ( sK13_V @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(582,plain,
! [SV147: $i,SV129: $i] :
( ( ( ~ ( ~ ( contains_pq @ SV129 @ ( sK15_W @ SV147 @ SV129 ) )
| ~ ~ ( less_than @ SV147 @ ( sK15_W @ SV147 @ SV129 ) ) ) )
= $true )
| ( ( issmallestelement_pq @ SV129 @ SV147 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[534]) ).
thf(583,plain,
! [SV148: $i,SV130: $i] :
( ( ( ~ ( issmallestelement_pq @ SV130 @ SV148 ) )
= $true )
| ( ( ! [SY411: $i] :
( ~ ( contains_pq @ SV130 @ SY411 )
| ( less_than @ SV148 @ SY411 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[535]) ).
thf(584,plain,
! [SV149: $i,SV131: $i] :
( ( ( ~ ( less_than @ SV131 @ SV149 )
| ( less_than @ SV149 @ SV131 ) )
= $true )
| ( ( strictly_less_than @ SV131 @ SV149 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[536]) ).
thf(585,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[537]) ).
thf(586,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[538]) ).
thf(587,plain,
! [SV150: $i,SV132: $i] :
( ( ( ~ ( contains_pq @ SV132 @ SV150 )
| ~ ( issmallestelement_pq @ SV132 @ SV150 ) )
= $true )
| ( ( pi_sharp_find_min @ SV132 @ SV150 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[539]) ).
thf(588,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[540]) ).
thf(589,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[541]) ).
thf(590,plain,
! [SV162: $i,SV151: $i,SV51: $i] :
( ( ~ ( contains_pq @ ( insert_pq @ SV51 @ SV151 ) @ SV162 )
| ( SV151 = SV162 )
| ( contains_pq @ SV51 @ SV162 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(591,plain,
! [SV51: $i] :
( ( ~ ! [SY301: $i,SY302: $i] :
( ( SY301 != SY302 )
| ( contains_pq @ ( insert_pq @ SV51 @ SY301 ) @ SY302 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[543]) ).
thf(592,plain,
! [SV51: $i] :
( ( ~ ! [SY303: $i,SY304: $i] :
( ~ ( contains_pq @ SV51 @ SY304 )
| ( contains_pq @ ( insert_pq @ SV51 @ SY303 ) @ SY304 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[543]) ).
thf(593,plain,
! [SV113: $i,SV94: $i,SV52: $i] :
( ( ! [SY390: $i,SY391: $i] :
( ~ ( less_than @ SY391 @ SY390 )
| ~ ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV94 @ ( pair @ SY390 @ SY391 ) ) @ SV113 ) )
| ( check_cpq @ ( triple @ SV52 @ SV94 @ SV113 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[544]) ).
thf(594,plain,
! [SV113: $i,SV94: $i,SV52: $i] :
( ( ! [SY392: $i,SY393: $i] :
( ~ ( less_than @ SY393 @ SY392 )
| ~ ( check_cpq @ ( triple @ SV52 @ SV94 @ SV113 ) )
| ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV94 @ ( pair @ SY392 @ SY393 ) ) @ SV113 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[545]) ).
thf(595,plain,
! [SV133: $i,SV163: $i] :
( ( ( ~ ( ok @ SV163 )
| ~ ( succ_cpq @ SV133 @ SV163 )
| ~ ( check_cpq @ SV163 ) )
= $true )
| ( ( phi @ SV133 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(596,plain,
! [SV134: $i] :
( ( ( phi @ SV134 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( ok @ ( sK12_V @ SV134 ) )
| ~ ( succ_cpq @ SV134 @ ( sK12_V @ SV134 ) ) )
| ~ ( check_cpq @ ( sK12_V @ SV134 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(597,plain,
! [SV152: $i,SV135: $i] :
( ( ( ~ ( contains_pq @ SV135 @ SV152 ) )
= $true )
| ( ( pi_sharp_remove @ SV135 @ SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(598,plain,
! [SV153: $i,SV136: $i] :
( ( ( ~ ( pi_sharp_remove @ SV136 @ SV153 ) )
= $true )
| ( ( contains_pq @ SV136 @ SV153 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[549]) ).
thf(599,plain,
! [SV154: $i,SV137: $i] :
( ( ( ~ ( contains_pq @ SV137 @ SV154 )
| ~ ( issmallestelement_pq @ SV137 @ SV154 ) )
= $true )
| ( ( pi_sharp_removemin @ SV137 @ SV154 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[550]) ).
thf(600,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(601,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(602,plain,
! [SV1: $i,SV95: $i,SV53: $i] :
( ( ( less_than @ SV53 @ SV95 )
= $false )
| ( ( less_than @ SV1 @ SV53 )
= $false )
| ( ( less_than @ SV1 @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(603,plain,
! [SV100: $i,SV164: $i,SV66: $i,SV18: $i] :
( ( ( ( remove_slb @ ( insert_slb @ SV18 @ ( pair @ SV66 @ SV164 ) ) @ SV100 )
= ( insert_slb @ ( remove_slb @ SV18 @ SV100 ) @ ( pair @ SV66 @ SV164 ) ) )
= $true )
| ( ( SV66 = SV100 )
= $true )
| ( ( contains_slb @ SV18 @ SV100 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(604,plain,
! [SV102: $i,SV165: $i,SV68: $i,SV20: $i] :
( ( ( ( lookup_slb @ ( insert_slb @ SV20 @ ( pair @ SV68 @ SV165 ) ) @ SV102 )
= ( lookup_slb @ SV20 @ SV102 ) )
= $true )
| ( ( SV68 = SV102 )
= $true )
| ( ( contains_slb @ SV20 @ SV102 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(605,plain,
! [SV105: $i,SV76: $i,SV30: $i,SV140: $i,SV116: $i] :
( ( ( strictly_less_than @ SV116 @ SV140 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV30 @ ( insert_slb @ SV76 @ ( pair @ SV116 @ SV140 ) ) @ SV105 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(606,plain,
! [SV109: $i,SV35: $i,SV119: $i,SV81: $i] :
( ( ( contains_slb @ SV81 @ SV119 )
= $false )
| ( ( ~ ( less_than @ ( lookup_slb @ SV81 @ SV119 ) @ SV119 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV35 @ SV81 @ SV109 ) @ SV119 )
= ( triple @ ( remove_pqp @ SV35 @ SV119 ) @ ( remove_slb @ SV81 @ SV119 ) @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(607,plain,
! [SV110: $i,SV36: $i,SV120: $i,SV82: $i] :
( ( ( contains_slb @ SV82 @ SV120 )
= $false )
| ( ( ~ ( strictly_less_than @ SV120 @ ( lookup_slb @ SV82 @ SV120 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV36 @ SV82 @ SV110 ) @ SV120 )
= ( triple @ ( remove_pqp @ SV36 @ SV120 ) @ ( remove_slb @ SV82 @ SV120 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(608,plain,
! [SV85: $i,SV39: $i] :
( ( ( strictly_less_than @ ( findmin_pqp_res @ SV39 ) @ ( lookup_slb @ SV85 @ ( findmin_pqp_res @ SV39 ) ) )
= $false )
| ( ( SV85 = create_slb )
= $true )
| ( ( contains_slb @ SV85 @ ( findmin_pqp_res @ SV39 ) )
= $false )
| ( ( ! [SY340: $i] :
( ( findmin_cpq_eff @ ( triple @ SV39 @ SV85 @ SY340 ) )
= ( triple @ SV39 @ ( update_slb @ SV85 @ ( findmin_pqp_res @ SV39 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(609,plain,
! [SV40: $i,SV86: $i] :
( ( ( less_than @ ( lookup_slb @ SV86 @ ( findmin_pqp_res @ SV40 ) ) @ ( findmin_pqp_res @ SV40 ) )
= $false )
| ( ( SV86 = create_slb )
= $true )
| ( ( contains_slb @ SV86 @ ( findmin_pqp_res @ SV40 ) )
= $false )
| ( ( ! [SY341: $i] :
( ( findmin_cpq_eff @ ( triple @ SV40 @ SV86 @ SY341 ) )
= ( triple @ SV40 @ ( update_slb @ SV86 @ ( findmin_pqp_res @ SV40 ) ) @ SY341 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(610,plain,
! [SV155: $i,SV143: $i,SV47: $i] :
( ( ( ~ ( contains_cpq @ ( triple @ SV47 @ sK1_U @ SV143 ) @ SV155 ) )
= $true )
| ( ( contains_pq @ ( i @ ( triple @ SV47 @ sK1_U @ SV143 ) ) @ SV155 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[568]) ).
thf(611,plain,
! [SV156: $i,SV144: $i,SV47: $i] :
( ( ( ~ ( contains_pq @ ( i @ ( triple @ SV47 @ sK1_U @ SV144 ) ) @ SV156 ) )
= $true )
| ( ( contains_cpq @ ( triple @ SV47 @ sK1_U @ SV144 ) @ SV156 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[569]) ).
thf(612,plain,
! [SV145: $i,SV123: $i] :
( ( ( pi_remove @ SV123 @ SV145 )
= $false )
| ( ( pi_sharp_remove @ ( i @ SV123 ) @ SV145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(613,plain,
! [SV146: $i,SV124: $i] :
( ( ( pi_sharp_remove @ ( i @ SV124 ) @ SV146 )
= $false )
| ( ( pi_remove @ SV124 @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(614,plain,
! [SV112: $i,SV91: $i,SV48: $i] :
( ( ~ ! [SY382: $i,SY383: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY382 ) ) @ SV112 @ SY383 )
| ( SV91 = SV112 )
| ( pair_in_list @ SV48 @ SV112 @ SY383 ) )
| ~ ! [SY384: $i,SY385: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY384 ) ) @ SV112 @ SY385 )
| ( SY384 = SY385 )
| ( pair_in_list @ SV48 @ SV112 @ SY385 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(615,plain,
! [SV48: $i,SV112: $i,SV91: $i] :
( ( ~ ! [SY386: $i,SY387: $i] :
( ( SV91 != SV112 )
| ( SY386 != SY387 )
| ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY386 ) ) @ SV112 @ SY387 ) )
| ~ ! [SY388: $i,SY389: $i] :
( ~ ( pair_in_list @ SV48 @ SV112 @ SY389 )
| ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY388 ) ) @ SV112 @ SY389 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(616,plain,
! [SV157: $i,SV125: $i] :
( ( ( pi_sharp_find_min @ ( i @ SV125 ) @ SV157 )
= $false )
| ( ( pi_find_min @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(617,plain,
! [SV158: $i,SV92: $i,SV49: $i] :
( ( ( ! [SY413: $i] :
~ ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY413 ) ) @ SV158 ) )
= $true )
| ( ( ( SV92 = SV158 )
| ( contains_slb @ SV49 @ SV158 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[576]) ).
thf(618,plain,
! [SV49: $i,SV92: $i] :
( ( ~ ! [SY357: $i] :
( ( SV92 != SY357 )
| ! [SY358: $i] : ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY358 ) ) @ SY357 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[577]) ).
thf(619,plain,
! [SV92: $i,SV49: $i] :
( ( ~ ! [SY359: $i] :
( ~ ( contains_slb @ SV49 @ SY359 )
| ! [SY360: $i] : ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY360 ) ) @ SY359 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[577]) ).
thf(620,plain,
! [SV166: $i,SV159: $i,SV93: $i,SV50: $i] :
( ( ~ ( contains_cpq @ ( triple @ SV50 @ SV93 @ SV159 ) @ SV166 )
| ( contains_slb @ SV93 @ SV166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(621,plain,
! [SV160: $i,SV50: $i,SV167: $i,SV93: $i] :
( ( ~ ( contains_slb @ SV93 @ SV167 )
| ( contains_cpq @ ( triple @ SV50 @ SV93 @ SV160 ) @ SV167 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(622,plain,
! [SV161: $i,SV127: $i] :
( ( ( pi_sharp_find_min @ ( i @ SV127 ) @ SV161 )
= $false )
| ( ( pi_removemin @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(623,plain,
! [SV147: $i,SV129: $i] :
( ( ( ~ ( contains_pq @ SV129 @ ( sK15_W @ SV147 @ SV129 ) )
| ~ ~ ( less_than @ SV147 @ ( sK15_W @ SV147 @ SV129 ) ) )
= $false )
| ( ( issmallestelement_pq @ SV129 @ SV147 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(624,plain,
! [SV148: $i,SV130: $i] :
( ( ( issmallestelement_pq @ SV130 @ SV148 )
= $false )
| ( ( ! [SY411: $i] :
( ~ ( contains_pq @ SV130 @ SY411 )
| ( less_than @ SV148 @ SY411 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(625,plain,
! [SV149: $i,SV131: $i] :
( ( ( ~ ( less_than @ SV131 @ SV149 ) )
= $true )
| ( ( less_than @ SV149 @ SV131 )
= $true )
| ( ( strictly_less_than @ SV131 @ SV149 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(626,plain,
! [SV168: $i] :
( ( ! [SY416: $i] :
( ~ ( strictly_less_than @ SV168 @ SY416 )
| ( less_than @ SV168 @ SY416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(627,plain,
! [SV169: $i] :
( ( ! [SY417: $i] :
( ~ ( strictly_less_than @ SV169 @ SY417 )
| ~ ( less_than @ SY417 @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(628,plain,
! [SV150: $i,SV132: $i] :
( ( ( ~ ( contains_pq @ SV132 @ SV150 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV132 @ SV150 ) )
= $true )
| ( ( pi_sharp_find_min @ SV132 @ SV150 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[587]) ).
thf(629,plain,
! [SV170: $i] :
( ( ! [SY418: $i] :
( ~ ( pi_sharp_find_min @ SV170 @ SY418 )
| ( contains_pq @ SV170 @ SY418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(630,plain,
! [SV171: $i] :
( ( ! [SY419: $i] :
( ~ ( pi_sharp_find_min @ SV171 @ SY419 )
| ( issmallestelement_pq @ SV171 @ SY419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(631,plain,
! [SV162: $i,SV151: $i,SV51: $i] :
( ( ( ~ ( contains_pq @ ( insert_pq @ SV51 @ SV151 ) @ SV162 ) )
= $true )
| ( ( ( SV151 = SV162 )
| ( contains_pq @ SV51 @ SV162 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[590]) ).
thf(632,plain,
! [SV51: $i] :
( ( ! [SY301: $i,SY302: $i] :
( ( SY301 != SY302 )
| ( contains_pq @ ( insert_pq @ SV51 @ SY301 ) @ SY302 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[591]) ).
thf(633,plain,
! [SV51: $i] :
( ( ! [SY303: $i,SY304: $i] :
( ~ ( contains_pq @ SV51 @ SY304 )
| ( contains_pq @ ( insert_pq @ SV51 @ SY303 ) @ SY304 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[592]) ).
thf(634,plain,
! [SV113: $i,SV94: $i,SV52: $i,SV172: $i] :
( ( ! [SY420: $i] :
( ~ ( less_than @ SY420 @ SV172 )
| ~ ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV94 @ ( pair @ SV172 @ SY420 ) ) @ SV113 ) )
| ( check_cpq @ ( triple @ SV52 @ SV94 @ SV113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(635,plain,
! [SV113: $i,SV94: $i,SV52: $i,SV173: $i] :
( ( ! [SY421: $i] :
( ~ ( less_than @ SY421 @ SV173 )
| ~ ( check_cpq @ ( triple @ SV52 @ SV94 @ SV113 ) )
| ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV94 @ ( pair @ SV173 @ SY421 ) ) @ SV113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(636,plain,
! [SV133: $i,SV163: $i] :
( ( ( ~ ( ok @ SV163 )
| ~ ( succ_cpq @ SV133 @ SV163 ) )
= $true )
| ( ( ~ ( check_cpq @ SV163 ) )
= $true )
| ( ( phi @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[595]) ).
thf(637,plain,
! [SV134: $i] :
( ( ( ~ ~ ( ~ ( ok @ ( sK12_V @ SV134 ) )
| ~ ( succ_cpq @ SV134 @ ( sK12_V @ SV134 ) ) )
| ~ ( check_cpq @ ( sK12_V @ SV134 ) ) )
= $false )
| ( ( phi @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(638,plain,
! [SV152: $i,SV135: $i] :
( ( ( contains_pq @ SV135 @ SV152 )
= $false )
| ( ( pi_sharp_remove @ SV135 @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(639,plain,
! [SV153: $i,SV136: $i] :
( ( ( pi_sharp_remove @ SV136 @ SV153 )
= $false )
| ( ( contains_pq @ SV136 @ SV153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[598]) ).
thf(640,plain,
! [SV154: $i,SV137: $i] :
( ( ( ~ ( contains_pq @ SV137 @ SV154 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV137 @ SV154 ) )
= $true )
| ( ( pi_sharp_removemin @ SV137 @ SV154 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[599]) ).
thf(641,plain,
! [SV174: $i] :
( ( ! [SY422: $i] :
( ~ ( pi_sharp_removemin @ SV174 @ SY422 )
| ( contains_pq @ SV174 @ SY422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(642,plain,
! [SV175: $i] :
( ( ! [SY423: $i] :
( ~ ( pi_sharp_removemin @ SV175 @ SY423 )
| ( issmallestelement_pq @ SV175 @ SY423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(643,plain,
! [SV105: $i,SV140: $i,SV116: $i,SV76: $i,SV30: $i] :
( ( ( check_cpq @ ( triple @ SV30 @ ( insert_slb @ SV76 @ ( pair @ SV116 @ SV140 ) ) @ SV105 ) )
= $false )
| ( ( strictly_less_than @ SV116 @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(644,plain,
! [SV109: $i,SV35: $i,SV119: $i,SV81: $i] :
( ( ( less_than @ ( lookup_slb @ SV81 @ SV119 ) @ SV119 )
= $false )
| ( ( contains_slb @ SV81 @ SV119 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV35 @ SV81 @ SV109 ) @ SV119 )
= ( triple @ ( remove_pqp @ SV35 @ SV119 ) @ ( remove_slb @ SV81 @ SV119 ) @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(645,plain,
! [SV110: $i,SV36: $i,SV82: $i,SV120: $i] :
( ( ( strictly_less_than @ SV120 @ ( lookup_slb @ SV82 @ SV120 ) )
= $false )
| ( ( contains_slb @ SV82 @ SV120 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV36 @ SV82 @ SV110 ) @ SV120 )
= ( triple @ ( remove_pqp @ SV36 @ SV120 ) @ ( remove_slb @ SV82 @ SV120 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(646,plain,
! [SV176: $i,SV85: $i,SV39: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV39 @ SV85 @ SV176 ) )
= ( triple @ SV39 @ ( update_slb @ SV85 @ ( findmin_pqp_res @ SV39 ) ) @ bad ) )
= $true )
| ( ( contains_slb @ SV85 @ ( findmin_pqp_res @ SV39 ) )
= $false )
| ( ( SV85 = create_slb )
= $true )
| ( ( strictly_less_than @ ( findmin_pqp_res @ SV39 ) @ ( lookup_slb @ SV85 @ ( findmin_pqp_res @ SV39 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(647,plain,
! [SV177: $i,SV86: $i,SV40: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV40 @ SV86 @ SV177 ) )
= ( triple @ SV40 @ ( update_slb @ SV86 @ ( findmin_pqp_res @ SV40 ) ) @ SV177 ) )
= $true )
| ( ( contains_slb @ SV86 @ ( findmin_pqp_res @ SV40 ) )
= $false )
| ( ( SV86 = create_slb )
= $true )
| ( ( less_than @ ( lookup_slb @ SV86 @ ( findmin_pqp_res @ SV40 ) ) @ ( findmin_pqp_res @ SV40 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(648,plain,
! [SV155: $i,SV143: $i,SV47: $i] :
( ( ( contains_cpq @ ( triple @ SV47 @ sK1_U @ SV143 ) @ SV155 )
= $false )
| ( ( contains_pq @ ( i @ ( triple @ SV47 @ sK1_U @ SV143 ) ) @ SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(649,plain,
! [SV156: $i,SV144: $i,SV47: $i] :
( ( ( contains_pq @ ( i @ ( triple @ SV47 @ sK1_U @ SV144 ) ) @ SV156 )
= $false )
| ( ( contains_cpq @ ( triple @ SV47 @ sK1_U @ SV144 ) @ SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(650,plain,
! [SV112: $i,SV91: $i,SV48: $i] :
( ( ~ ! [SY382: $i,SY383: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY382 ) ) @ SV112 @ SY383 )
| ( SV91 = SV112 )
| ( pair_in_list @ SV48 @ SV112 @ SY383 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[614]) ).
thf(651,plain,
! [SV112: $i,SV91: $i,SV48: $i] :
( ( ~ ! [SY384: $i,SY385: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY384 ) ) @ SV112 @ SY385 )
| ( SY384 = SY385 )
| ( pair_in_list @ SV48 @ SV112 @ SY385 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[614]) ).
thf(652,plain,
! [SV48: $i,SV112: $i,SV91: $i] :
( ( ~ ! [SY386: $i,SY387: $i] :
( ( SV91 != SV112 )
| ( SY386 != SY387 )
| ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY386 ) ) @ SV112 @ SY387 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[615]) ).
thf(653,plain,
! [SV91: $i,SV112: $i,SV48: $i] :
( ( ~ ! [SY388: $i,SY389: $i] :
( ~ ( pair_in_list @ SV48 @ SV112 @ SY389 )
| ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY388 ) ) @ SV112 @ SY389 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[615]) ).
thf(654,plain,
! [SV158: $i,SV178: $i,SV92: $i,SV49: $i] :
( ( ( ~ ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SV178 ) ) @ SV158 ) )
= $true )
| ( ( ( SV92 = SV158 )
| ( contains_slb @ SV49 @ SV158 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(655,plain,
! [SV49: $i,SV92: $i] :
( ( ! [SY357: $i] :
( ( SV92 != SY357 )
| ! [SY358: $i] : ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY358 ) ) @ SY357 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[618]) ).
thf(656,plain,
! [SV92: $i,SV49: $i] :
( ( ! [SY359: $i] :
( ~ ( contains_slb @ SV49 @ SY359 )
| ! [SY360: $i] : ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY360 ) ) @ SY359 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[619]) ).
thf(657,plain,
! [SV166: $i,SV159: $i,SV93: $i,SV50: $i] :
( ( ( ~ ( contains_cpq @ ( triple @ SV50 @ SV93 @ SV159 ) @ SV166 ) )
= $true )
| ( ( contains_slb @ SV93 @ SV166 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(658,plain,
! [SV160: $i,SV50: $i,SV167: $i,SV93: $i] :
( ( ( ~ ( contains_slb @ SV93 @ SV167 ) )
= $true )
| ( ( contains_cpq @ ( triple @ SV50 @ SV93 @ SV160 ) @ SV167 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[621]) ).
thf(659,plain,
! [SV147: $i,SV129: $i] :
( ( ( ~ ( contains_pq @ SV129 @ ( sK15_W @ SV147 @ SV129 ) ) )
= $false )
| ( ( issmallestelement_pq @ SV129 @ SV147 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[623]) ).
thf(660,plain,
! [SV129: $i,SV147: $i] :
( ( ( ~ ~ ( less_than @ SV147 @ ( sK15_W @ SV147 @ SV129 ) ) )
= $false )
| ( ( issmallestelement_pq @ SV129 @ SV147 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[623]) ).
thf(661,plain,
! [SV148: $i,SV179: $i,SV130: $i] :
( ( ( ~ ( contains_pq @ SV130 @ SV179 )
| ( less_than @ SV148 @ SV179 ) )
= $true )
| ( ( issmallestelement_pq @ SV130 @ SV148 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(662,plain,
! [SV149: $i,SV131: $i] :
( ( ( less_than @ SV131 @ SV149 )
= $false )
| ( ( less_than @ SV149 @ SV131 )
= $true )
| ( ( strictly_less_than @ SV131 @ SV149 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(663,plain,
! [SV180: $i,SV168: $i] :
( ( ~ ( strictly_less_than @ SV168 @ SV180 )
| ( less_than @ SV168 @ SV180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(664,plain,
! [SV181: $i,SV169: $i] :
( ( ~ ( strictly_less_than @ SV169 @ SV181 )
| ~ ( less_than @ SV181 @ SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(665,plain,
! [SV150: $i,SV132: $i] :
( ( ( contains_pq @ SV132 @ SV150 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV132 @ SV150 ) )
= $true )
| ( ( pi_sharp_find_min @ SV132 @ SV150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(666,plain,
! [SV182: $i,SV170: $i] :
( ( ~ ( pi_sharp_find_min @ SV170 @ SV182 )
| ( contains_pq @ SV170 @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(667,plain,
! [SV183: $i,SV171: $i] :
( ( ~ ( pi_sharp_find_min @ SV171 @ SV183 )
| ( issmallestelement_pq @ SV171 @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(668,plain,
! [SV162: $i,SV151: $i,SV51: $i] :
( ( ( contains_pq @ ( insert_pq @ SV51 @ SV151 ) @ SV162 )
= $false )
| ( ( ( SV151 = SV162 )
| ( contains_pq @ SV51 @ SV162 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(669,plain,
! [SV51: $i,SV184: $i] :
( ( ! [SY424: $i] :
( ( SV184 != SY424 )
| ( contains_pq @ ( insert_pq @ SV51 @ SV184 ) @ SY424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(670,plain,
! [SV185: $i,SV51: $i] :
( ( ! [SY425: $i] :
( ~ ( contains_pq @ SV51 @ SY425 )
| ( contains_pq @ ( insert_pq @ SV51 @ SV185 ) @ SY425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(671,plain,
! [SV113: $i,SV94: $i,SV52: $i,SV172: $i,SV186: $i] :
( ( ~ ( less_than @ SV186 @ SV172 )
| ~ ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV94 @ ( pair @ SV172 @ SV186 ) ) @ SV113 ) )
| ( check_cpq @ ( triple @ SV52 @ SV94 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(672,plain,
! [SV113: $i,SV94: $i,SV52: $i,SV173: $i,SV187: $i] :
( ( ~ ( less_than @ SV187 @ SV173 )
| ~ ( check_cpq @ ( triple @ SV52 @ SV94 @ SV113 ) )
| ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV94 @ ( pair @ SV173 @ SV187 ) ) @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(673,plain,
! [SV133: $i,SV163: $i] :
( ( ( ~ ( ok @ SV163 ) )
= $true )
| ( ( ~ ( succ_cpq @ SV133 @ SV163 ) )
= $true )
| ( ( ~ ( check_cpq @ SV163 ) )
= $true )
| ( ( phi @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[636]) ).
thf(674,plain,
! [SV134: $i] :
( ( ( ~ ~ ( ~ ( ok @ ( sK12_V @ SV134 ) )
| ~ ( succ_cpq @ SV134 @ ( sK12_V @ SV134 ) ) ) )
= $false )
| ( ( phi @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[637]) ).
thf(675,plain,
! [SV134: $i] :
( ( ( ~ ( check_cpq @ ( sK12_V @ SV134 ) ) )
= $false )
| ( ( phi @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[637]) ).
thf(676,plain,
! [SV154: $i,SV137: $i] :
( ( ( contains_pq @ SV137 @ SV154 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV137 @ SV154 ) )
= $true )
| ( ( pi_sharp_removemin @ SV137 @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(677,plain,
! [SV188: $i,SV174: $i] :
( ( ~ ( pi_sharp_removemin @ SV174 @ SV188 )
| ( contains_pq @ SV174 @ SV188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(678,plain,
! [SV189: $i,SV175: $i] :
( ( ~ ( pi_sharp_removemin @ SV175 @ SV189 )
| ( issmallestelement_pq @ SV175 @ SV189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(679,plain,
! [SV112: $i,SV91: $i,SV48: $i] :
( ( ! [SY382: $i,SY383: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY382 ) ) @ SV112 @ SY383 )
| ( SV91 = SV112 )
| ( pair_in_list @ SV48 @ SV112 @ SY383 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[650]) ).
thf(680,plain,
! [SV112: $i,SV91: $i,SV48: $i] :
( ( ! [SY384: $i,SY385: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY384 ) ) @ SV112 @ SY385 )
| ( SY384 = SY385 )
| ( pair_in_list @ SV48 @ SV112 @ SY385 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[651]) ).
thf(681,plain,
! [SV48: $i,SV112: $i,SV91: $i] :
( ( ! [SY386: $i,SY387: $i] :
( ( SV91 != SV112 )
| ( SY386 != SY387 )
| ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY386 ) ) @ SV112 @ SY387 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[652]) ).
thf(682,plain,
! [SV91: $i,SV112: $i,SV48: $i] :
( ( ! [SY388: $i,SY389: $i] :
( ~ ( pair_in_list @ SV48 @ SV112 @ SY389 )
| ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SY388 ) ) @ SV112 @ SY389 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[653]) ).
thf(683,plain,
! [SV158: $i,SV178: $i,SV92: $i,SV49: $i] :
( ( ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SV178 ) ) @ SV158 )
= $false )
| ( ( ( SV92 = SV158 )
| ( contains_slb @ SV49 @ SV158 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(684,plain,
! [SV49: $i,SV190: $i,SV92: $i] :
( ( ( SV92 != SV190 )
| ! [SY426: $i] : ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY426 ) ) @ SV190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(685,plain,
! [SV92: $i,SV191: $i,SV49: $i] :
( ( ~ ( contains_slb @ SV49 @ SV191 )
| ! [SY427: $i] : ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY427 ) ) @ SV191 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(686,plain,
! [SV166: $i,SV159: $i,SV93: $i,SV50: $i] :
( ( ( contains_cpq @ ( triple @ SV50 @ SV93 @ SV159 ) @ SV166 )
= $false )
| ( ( contains_slb @ SV93 @ SV166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(687,plain,
! [SV160: $i,SV50: $i,SV167: $i,SV93: $i] :
( ( ( contains_slb @ SV93 @ SV167 )
= $false )
| ( ( contains_cpq @ ( triple @ SV50 @ SV93 @ SV160 ) @ SV167 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(688,plain,
! [SV147: $i,SV129: $i] :
( ( ( contains_pq @ SV129 @ ( sK15_W @ SV147 @ SV129 ) )
= $true )
| ( ( issmallestelement_pq @ SV129 @ SV147 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[659]) ).
thf(689,plain,
! [SV129: $i,SV147: $i] :
( ( ( ~ ( less_than @ SV147 @ ( sK15_W @ SV147 @ SV129 ) ) )
= $true )
| ( ( issmallestelement_pq @ SV129 @ SV147 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[660]) ).
thf(690,plain,
! [SV148: $i,SV179: $i,SV130: $i] :
( ( ( ~ ( contains_pq @ SV130 @ SV179 ) )
= $true )
| ( ( less_than @ SV148 @ SV179 )
= $true )
| ( ( issmallestelement_pq @ SV130 @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[661]) ).
thf(691,plain,
! [SV180: $i,SV168: $i] :
( ( ( ~ ( strictly_less_than @ SV168 @ SV180 ) )
= $true )
| ( ( less_than @ SV168 @ SV180 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[663]) ).
thf(692,plain,
! [SV181: $i,SV169: $i] :
( ( ( ~ ( strictly_less_than @ SV169 @ SV181 ) )
= $true )
| ( ( ~ ( less_than @ SV181 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[664]) ).
thf(693,plain,
! [SV150: $i,SV132: $i] :
( ( ( issmallestelement_pq @ SV132 @ SV150 )
= $false )
| ( ( contains_pq @ SV132 @ SV150 )
= $false )
| ( ( pi_sharp_find_min @ SV132 @ SV150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(694,plain,
! [SV182: $i,SV170: $i] :
( ( ( ~ ( pi_sharp_find_min @ SV170 @ SV182 ) )
= $true )
| ( ( contains_pq @ SV170 @ SV182 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[666]) ).
thf(695,plain,
! [SV183: $i,SV171: $i] :
( ( ( ~ ( pi_sharp_find_min @ SV171 @ SV183 ) )
= $true )
| ( ( issmallestelement_pq @ SV171 @ SV183 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[667]) ).
thf(696,plain,
! [SV51: $i,SV162: $i,SV151: $i] :
( ( ( SV151 = SV162 )
= $true )
| ( ( contains_pq @ SV51 @ SV162 )
= $true )
| ( ( contains_pq @ ( insert_pq @ SV51 @ SV151 ) @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[668]) ).
thf(697,plain,
! [SV51: $i,SV192: $i,SV184: $i] :
( ( ( SV184 != SV192 )
| ( contains_pq @ ( insert_pq @ SV51 @ SV184 ) @ SV192 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(698,plain,
! [SV185: $i,SV193: $i,SV51: $i] :
( ( ~ ( contains_pq @ SV51 @ SV193 )
| ( contains_pq @ ( insert_pq @ SV51 @ SV185 ) @ SV193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(699,plain,
! [SV113: $i,SV94: $i,SV52: $i,SV172: $i,SV186: $i] :
( ( ( ~ ( less_than @ SV186 @ SV172 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV94 @ ( pair @ SV172 @ SV186 ) ) @ SV113 ) )
| ( check_cpq @ ( triple @ SV52 @ SV94 @ SV113 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[671]) ).
thf(700,plain,
! [SV113: $i,SV94: $i,SV52: $i,SV173: $i,SV187: $i] :
( ( ( ~ ( less_than @ SV187 @ SV173 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV52 @ SV94 @ SV113 ) )
| ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV94 @ ( pair @ SV173 @ SV187 ) ) @ SV113 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[672]) ).
thf(701,plain,
! [SV133: $i,SV163: $i] :
( ( ( ok @ SV163 )
= $false )
| ( ( ~ ( succ_cpq @ SV133 @ SV163 ) )
= $true )
| ( ( ~ ( check_cpq @ SV163 ) )
= $true )
| ( ( phi @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(702,plain,
! [SV134: $i] :
( ( ( ~ ( ~ ( ok @ ( sK12_V @ SV134 ) )
| ~ ( succ_cpq @ SV134 @ ( sK12_V @ SV134 ) ) ) )
= $true )
| ( ( phi @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[674]) ).
thf(703,plain,
! [SV134: $i] :
( ( ( check_cpq @ ( sK12_V @ SV134 ) )
= $true )
| ( ( phi @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[675]) ).
thf(704,plain,
! [SV154: $i,SV137: $i] :
( ( ( issmallestelement_pq @ SV137 @ SV154 )
= $false )
| ( ( contains_pq @ SV137 @ SV154 )
= $false )
| ( ( pi_sharp_removemin @ SV137 @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(705,plain,
! [SV188: $i,SV174: $i] :
( ( ( ~ ( pi_sharp_removemin @ SV174 @ SV188 ) )
= $true )
| ( ( contains_pq @ SV174 @ SV188 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[677]) ).
thf(706,plain,
! [SV189: $i,SV175: $i] :
( ( ( ~ ( pi_sharp_removemin @ SV175 @ SV189 ) )
= $true )
| ( ( issmallestelement_pq @ SV175 @ SV189 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[678]) ).
thf(707,plain,
! [SV112: $i,SV194: $i,SV91: $i,SV48: $i] :
( ( ! [SY428: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SV194 ) ) @ SV112 @ SY428 )
| ( SV91 = SV112 )
| ( pair_in_list @ SV48 @ SV112 @ SY428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(708,plain,
! [SV112: $i,SV195: $i,SV91: $i,SV48: $i] :
( ( ! [SY429: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SV195 ) ) @ SV112 @ SY429 )
| ( SV195 = SY429 )
| ( pair_in_list @ SV48 @ SV112 @ SY429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(709,plain,
! [SV48: $i,SV196: $i,SV112: $i,SV91: $i] :
( ( ! [SY430: $i] :
( ( SV91 != SV112 )
| ( SV196 != SY430 )
| ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SV196 ) ) @ SV112 @ SY430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(710,plain,
! [SV197: $i,SV91: $i,SV112: $i,SV48: $i] :
( ( ! [SY431: $i] :
( ~ ( pair_in_list @ SV48 @ SV112 @ SY431 )
| ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SV197 ) ) @ SV112 @ SY431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(711,plain,
! [SV178: $i,SV49: $i,SV158: $i,SV92: $i] :
( ( ( SV92 = SV158 )
= $true )
| ( ( contains_slb @ SV49 @ SV158 )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SV178 ) ) @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[683]) ).
thf(712,plain,
! [SV49: $i,SV190: $i,SV92: $i] :
( ( ( ( SV92 != SV190 ) )
= $true )
| ( ( ! [SY426: $i] : ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY426 ) ) @ SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[684]) ).
thf(713,plain,
! [SV92: $i,SV191: $i,SV49: $i] :
( ( ( ~ ( contains_slb @ SV49 @ SV191 ) )
= $true )
| ( ( ! [SY427: $i] : ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY427 ) ) @ SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[685]) ).
thf(714,plain,
! [SV129: $i,SV147: $i] :
( ( ( less_than @ SV147 @ ( sK15_W @ SV147 @ SV129 ) )
= $false )
| ( ( issmallestelement_pq @ SV129 @ SV147 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[689]) ).
thf(715,plain,
! [SV148: $i,SV179: $i,SV130: $i] :
( ( ( contains_pq @ SV130 @ SV179 )
= $false )
| ( ( less_than @ SV148 @ SV179 )
= $true )
| ( ( issmallestelement_pq @ SV130 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(716,plain,
! [SV180: $i,SV168: $i] :
( ( ( strictly_less_than @ SV168 @ SV180 )
= $false )
| ( ( less_than @ SV168 @ SV180 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[691]) ).
thf(717,plain,
! [SV181: $i,SV169: $i] :
( ( ( strictly_less_than @ SV169 @ SV181 )
= $false )
| ( ( ~ ( less_than @ SV181 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[692]) ).
thf(718,plain,
! [SV182: $i,SV170: $i] :
( ( ( pi_sharp_find_min @ SV170 @ SV182 )
= $false )
| ( ( contains_pq @ SV170 @ SV182 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[694]) ).
thf(719,plain,
! [SV183: $i,SV171: $i] :
( ( ( pi_sharp_find_min @ SV171 @ SV183 )
= $false )
| ( ( issmallestelement_pq @ SV171 @ SV183 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[695]) ).
thf(720,plain,
! [SV51: $i,SV192: $i,SV184: $i] :
( ( ( ( SV184 != SV192 ) )
= $true )
| ( ( contains_pq @ ( insert_pq @ SV51 @ SV184 ) @ SV192 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[697]) ).
thf(721,plain,
! [SV185: $i,SV193: $i,SV51: $i] :
( ( ( ~ ( contains_pq @ SV51 @ SV193 ) )
= $true )
| ( ( contains_pq @ ( insert_pq @ SV51 @ SV185 ) @ SV193 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[698]) ).
thf(722,plain,
! [SV113: $i,SV94: $i,SV52: $i,SV172: $i,SV186: $i] :
( ( ( less_than @ SV186 @ SV172 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV94 @ ( pair @ SV172 @ SV186 ) ) @ SV113 ) )
| ( check_cpq @ ( triple @ SV52 @ SV94 @ SV113 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(723,plain,
! [SV113: $i,SV94: $i,SV52: $i,SV173: $i,SV187: $i] :
( ( ( less_than @ SV187 @ SV173 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV52 @ SV94 @ SV113 ) )
| ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV94 @ ( pair @ SV173 @ SV187 ) ) @ SV113 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(724,plain,
! [SV163: $i,SV133: $i] :
( ( ( succ_cpq @ SV133 @ SV163 )
= $false )
| ( ( ok @ SV163 )
= $false )
| ( ( ~ ( check_cpq @ SV163 ) )
= $true )
| ( ( phi @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[701]) ).
thf(725,plain,
! [SV134: $i] :
( ( ( ~ ( ok @ ( sK12_V @ SV134 ) )
| ~ ( succ_cpq @ SV134 @ ( sK12_V @ SV134 ) ) )
= $false )
| ( ( phi @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(726,plain,
! [SV188: $i,SV174: $i] :
( ( ( pi_sharp_removemin @ SV174 @ SV188 )
= $false )
| ( ( contains_pq @ SV174 @ SV188 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(727,plain,
! [SV189: $i,SV175: $i] :
( ( ( pi_sharp_removemin @ SV175 @ SV189 )
= $false )
| ( ( issmallestelement_pq @ SV175 @ SV189 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(728,plain,
! [SV198: $i,SV112: $i,SV194: $i,SV91: $i,SV48: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SV194 ) ) @ SV112 @ SV198 )
| ( SV91 = SV112 )
| ( pair_in_list @ SV48 @ SV112 @ SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(729,plain,
! [SV199: $i,SV112: $i,SV195: $i,SV91: $i,SV48: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SV195 ) ) @ SV112 @ SV199 )
| ( SV195 = SV199 )
| ( pair_in_list @ SV48 @ SV112 @ SV199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(730,plain,
! [SV48: $i,SV200: $i,SV196: $i,SV112: $i,SV91: $i] :
( ( ( SV91 != SV112 )
| ( SV196 != SV200 )
| ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SV196 ) ) @ SV112 @ SV200 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(731,plain,
! [SV197: $i,SV91: $i,SV201: $i,SV112: $i,SV48: $i] :
( ( ~ ( pair_in_list @ SV48 @ SV112 @ SV201 )
| ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SV197 ) ) @ SV112 @ SV201 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(732,plain,
! [SV49: $i,SV190: $i,SV92: $i] :
( ( ( SV92 = SV190 )
= $false )
| ( ( ! [SY426: $i] : ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY426 ) ) @ SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(733,plain,
! [SV92: $i,SV191: $i,SV49: $i] :
( ( ( contains_slb @ SV49 @ SV191 )
= $false )
| ( ( ! [SY427: $i] : ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SY427 ) ) @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(734,plain,
! [SV169: $i,SV181: $i] :
( ( ( less_than @ SV181 @ SV169 )
= $false )
| ( ( strictly_less_than @ SV169 @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(735,plain,
! [SV51: $i,SV192: $i,SV184: $i] :
( ( ( SV184 = SV192 )
= $false )
| ( ( contains_pq @ ( insert_pq @ SV51 @ SV184 ) @ SV192 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(736,plain,
! [SV185: $i,SV193: $i,SV51: $i] :
( ( ( contains_pq @ SV51 @ SV193 )
= $false )
| ( ( contains_pq @ ( insert_pq @ SV51 @ SV185 ) @ SV193 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(737,plain,
! [SV113: $i,SV186: $i,SV172: $i,SV94: $i,SV52: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV94 @ ( pair @ SV172 @ SV186 ) ) @ SV113 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV52 @ SV94 @ SV113 ) )
= $true )
| ( ( less_than @ SV186 @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[722]) ).
thf(738,plain,
! [SV187: $i,SV173: $i,SV113: $i,SV94: $i,SV52: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV52 @ SV94 @ SV113 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV94 @ ( pair @ SV173 @ SV187 ) ) @ SV113 ) )
= $true )
| ( ( less_than @ SV187 @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[723]) ).
thf(739,plain,
! [SV133: $i,SV163: $i] :
( ( ( check_cpq @ SV163 )
= $false )
| ( ( ok @ SV163 )
= $false )
| ( ( succ_cpq @ SV133 @ SV163 )
= $false )
| ( ( phi @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(740,plain,
! [SV134: $i] :
( ( ( ~ ( ok @ ( sK12_V @ SV134 ) ) )
= $false )
| ( ( phi @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[725]) ).
thf(741,plain,
! [SV134: $i] :
( ( ( ~ ( succ_cpq @ SV134 @ ( sK12_V @ SV134 ) ) )
= $false )
| ( ( phi @ SV134 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[725]) ).
thf(742,plain,
! [SV198: $i,SV112: $i,SV194: $i,SV91: $i,SV48: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SV194 ) ) @ SV112 @ SV198 ) )
= $true )
| ( ( ( SV91 = SV112 )
| ( pair_in_list @ SV48 @ SV112 @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[728]) ).
thf(743,plain,
! [SV199: $i,SV112: $i,SV195: $i,SV91: $i,SV48: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SV195 ) ) @ SV112 @ SV199 ) )
= $true )
| ( ( ( SV195 = SV199 )
| ( pair_in_list @ SV48 @ SV112 @ SV199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[729]) ).
thf(744,plain,
! [SV48: $i,SV200: $i,SV196: $i,SV112: $i,SV91: $i] :
( ( ( ( SV91 != SV112 )
| ( SV196 != SV200 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SV196 ) ) @ SV112 @ SV200 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[730]) ).
thf(745,plain,
! [SV197: $i,SV91: $i,SV201: $i,SV112: $i,SV48: $i] :
( ( ( ~ ( pair_in_list @ SV48 @ SV112 @ SV201 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SV197 ) ) @ SV112 @ SV201 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[731]) ).
thf(746,plain,
! [SV190: $i,SV202: $i,SV92: $i,SV49: $i] :
( ( ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SV202 ) ) @ SV190 )
= $true )
| ( ( SV92 = SV190 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(747,plain,
! [SV191: $i,SV203: $i,SV92: $i,SV49: $i] :
( ( ( contains_slb @ ( insert_slb @ SV49 @ ( pair @ SV92 @ SV203 ) ) @ SV191 )
= $true )
| ( ( contains_slb @ SV49 @ SV191 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(748,plain,
! [SV113: $i,SV186: $i,SV172: $i,SV94: $i,SV52: $i] :
( ( ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV94 @ ( pair @ SV172 @ SV186 ) ) @ SV113 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV52 @ SV94 @ SV113 ) )
= $true )
| ( ( less_than @ SV186 @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[737]) ).
thf(749,plain,
! [SV187: $i,SV173: $i,SV113: $i,SV94: $i,SV52: $i] :
( ( ( check_cpq @ ( triple @ SV52 @ SV94 @ SV113 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV52 @ ( insert_slb @ SV94 @ ( pair @ SV173 @ SV187 ) ) @ SV113 ) )
= $true )
| ( ( less_than @ SV187 @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(750,plain,
! [SV134: $i] :
( ( ( ok @ ( sK12_V @ SV134 ) )
= $true )
| ( ( phi @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[740]) ).
thf(751,plain,
! [SV134: $i] :
( ( ( succ_cpq @ SV134 @ ( sK12_V @ SV134 ) )
= $true )
| ( ( phi @ SV134 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[741]) ).
thf(752,plain,
! [SV198: $i,SV112: $i,SV194: $i,SV91: $i,SV48: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SV194 ) ) @ SV112 @ SV198 )
= $false )
| ( ( ( SV91 = SV112 )
| ( pair_in_list @ SV48 @ SV112 @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[742]) ).
thf(753,plain,
! [SV199: $i,SV112: $i,SV195: $i,SV91: $i,SV48: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SV195 ) ) @ SV112 @ SV199 )
= $false )
| ( ( ( SV195 = SV199 )
| ( pair_in_list @ SV48 @ SV112 @ SV199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(754,plain,
! [SV48: $i,SV200: $i,SV196: $i,SV112: $i,SV91: $i] :
( ( ( ( SV91 != SV112 ) )
= $true )
| ( ( ( SV196 != SV200 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SV196 ) ) @ SV112 @ SV200 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[744]) ).
thf(755,plain,
! [SV197: $i,SV91: $i,SV201: $i,SV112: $i,SV48: $i] :
( ( ( pair_in_list @ SV48 @ SV112 @ SV201 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SV197 ) ) @ SV112 @ SV201 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[745]) ).
thf(756,plain,
! [SV194: $i,SV198: $i,SV48: $i,SV112: $i,SV91: $i] :
( ( ( SV91 = SV112 )
= $true )
| ( ( pair_in_list @ SV48 @ SV112 @ SV198 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SV194 ) ) @ SV112 @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[752]) ).
thf(757,plain,
! [SV91: $i,SV112: $i,SV48: $i,SV199: $i,SV195: $i] :
( ( ( SV195 = SV199 )
= $true )
| ( ( pair_in_list @ SV48 @ SV112 @ SV199 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SV195 ) ) @ SV112 @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(758,plain,
! [SV48: $i,SV200: $i,SV196: $i,SV112: $i,SV91: $i] :
( ( ( SV91 = SV112 )
= $false )
| ( ( ( SV196 != SV200 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SV196 ) ) @ SV112 @ SV200 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[754]) ).
thf(759,plain,
! [SV48: $i,SV112: $i,SV91: $i,SV200: $i,SV196: $i] :
( ( ( SV196 = SV200 )
= $false )
| ( ( SV91 = SV112 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV48 @ ( pair @ SV91 @ SV196 ) ) @ SV112 @ SV200 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(760,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[258,759,757,756,755,751,750,749,748,747,746,739,736,735,734,727,726,719,718,716,715,714,711,704,703,696,693,688,687,686,662,649,648,647,646,645,644,643,639,638,622,616,613,612,604,603,602,581,575,562,561,558,557,556,555,554,519,516,513,511,510,499,469,462,461,459,458,444,407,398,396,395,394,393,387,358,356,352,344,332,324,323,322,301,300,281,278,270,260,259]) ).
thf(761,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(762,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(763,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(764,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(765,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(766,plain,
( ( ~ ( isnonempty_pq @ create_pq ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(767,plain,
( ( ! [U: $i,V: $i] : ( isnonempty_pq @ ( insert_pq @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(768,plain,
( ( ! [U: $i] :
~ ( contains_pq @ create_pq @ U ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(769,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(770,plain,
( ( ! [U: $i,V: $i] :
( ( ( contains_pq @ U @ ( sK15_W @ V @ U ) )
& ~ ( less_than @ V @ ( sK15_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(771,plain,
( ( ! [U: $i,V: $i] :
( ( remove_pq @ ( insert_pq @ U @ V ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(772,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(773,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(774,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(775,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(776,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(777,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)],[111]) ).
thf(778,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(779,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(780,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(781,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(782,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(783,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(784,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(785,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(786,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(787,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(788,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(789,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(790,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(791,plain,
( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(792,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(793,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(794,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(795,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(796,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(797,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(798,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(799,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(800,plain,
( ( ! [U: $i,V: $i] :
~ ( ok @ ( triple @ U @ V @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(801,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( triple @ U @ V @ W ) )
| ( W = bad ) ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(802,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)],[86]) ).
thf(803,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(804,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(805,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(806,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ create_slb @ V ) )
= ( triple @ U @ create_slb @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(807,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(808,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(809,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(810,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(811,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(812,plain,
( ( ! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(813,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(814,plain,
( ( ! [U: $i,V: $i] :
( ( i @ ( triple @ U @ create_slb @ V ) )
= create_pq ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(815,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)],[73]) ).
thf(816,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(817,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(818,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(819,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 ) @ ( sK14_V @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(820,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(821,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 ) @ ( sK13_V @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(822,plain,
( ( ! [U: $i] :
( ! [V: $i] :
( ~ ( ok @ V )
| ~ ( succ_cpq @ U @ V )
| ~ ( check_cpq @ V ) )
| ( phi @ U ) )
& ! [U: $i] :
( ~ ( phi @ U )
| ( ( ok @ ( sK12_V @ U ) )
& ( succ_cpq @ U @ ( sK12_V @ U ) )
& ( check_cpq @ ( sK12_V @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(823,plain,
( ( ! [SY172: $i] :
( ! [SY173: $i,SY174: $i] :
( ~ ( contains_cpq @ ( triple @ SY172 @ sK1_U @ SY173 ) @ SY174 )
| ( contains_pq @ ( i @ ( triple @ SY172 @ sK1_U @ SY173 ) ) @ SY174 ) )
& ! [SY173: $i,SY174: $i] :
( ~ ( contains_pq @ ( i @ ( triple @ SY172 @ sK1_U @ SY173 ) ) @ SY174 )
| ( contains_cpq @ ( triple @ SY172 @ sK1_U @ SY173 ) @ SY174 ) ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(824,plain,
( ( ( contains_pq @ ( i @ ( triple @ sK7_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK9_SY194 @ sK10_SY197 ) ) @ sK8_SY190 ) ) @ sK11_SY199 )
& ~ ( contains_cpq @ ( triple @ sK7_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK9_SY194 @ sK10_SY197 ) ) @ sK8_SY190 ) @ sK11_SY199 ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(825,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( contains_pq @ SX0 @ ( sK15_W @ SX1 @ SX0 ) )
| ~ ~ ( less_than @ SX1 @ ( sK15_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)],[770]) ).
thf(826,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( ok @ SX1 )
| ~ ( succ_cpq @ SX0 @ SX1 )
| ~ ( check_cpq @ SX1 ) )
| ( phi @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( phi @ SX0 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK12_V @ SX0 ) )
| ~ ( succ_cpq @ SX0 @ ( sK12_V @ SX0 ) ) )
| ~ ( check_cpq @ ( sK12_V @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[822]) ).
thf(827,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)],[769]) ).
thf(828,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 ) @ ( sK14_V @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[819]) ).
thf(829,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)],[818]) ).
thf(830,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)],[783]) ).
thf(831,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)],[816]) ).
thf(832,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)],[764]) ).
thf(833,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)],[799]) ).
thf(834,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)],[820]) ).
thf(835,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)],[817]) ).
thf(836,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)],[797]) ).
thf(837,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( contains_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) @ SX2 )
| ( contains_pq @ ( i @ ( triple @ SX0 @ sK1_U @ SX1 ) ) @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( contains_pq @ ( i @ ( triple @ SX0 @ sK1_U @ SX1 ) ) @ SX2 )
| ( contains_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[823]) ).
thf(838,plain,
( ( ~ ( ~ ( contains_pq @ ( i @ ( triple @ sK7_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK9_SY194 @ sK10_SY197 ) ) @ sK8_SY190 ) ) @ sK11_SY199 )
| ~ ~ ( contains_cpq @ ( triple @ sK7_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK9_SY194 @ sK10_SY197 ) ) @ sK8_SY190 ) @ sK11_SY199 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[824]) ).
thf(839,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 ) @ ( sK13_V @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[821]) ).
thf(840,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)],[781]) ).
thf(841,plain,
! [SV204: $i] :
( ( ! [SY432: $i,SY433: $i] :
( ~ ( less_than @ SV204 @ SY432 )
| ~ ( less_than @ SY432 @ SY433 )
| ( less_than @ SV204 @ SY433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(842,plain,
! [SV205: $i] :
( ( ! [SY434: $i] :
( ( less_than @ SV205 @ SY434 )
| ( less_than @ SY434 @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(843,plain,
! [SV206: $i] :
( ( less_than @ SV206 @ SV206 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(844,plain,
! [SV207: $i] :
( ( less_than @ bottom @ SV207 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(845,plain,
( ( isnonempty_pq @ create_pq )
= $false ),
inference(extcnf_not_pos,[status(thm)],[766]) ).
thf(846,plain,
! [SV208: $i] :
( ( ! [SY435: $i] : ( isnonempty_pq @ ( insert_pq @ SV208 @ SY435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(847,plain,
! [SV209: $i] :
( ( ~ ( contains_pq @ create_pq @ SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(848,plain,
! [SV210: $i] :
( ( ! [SY436: $i] :
( ( remove_pq @ ( insert_pq @ SV210 @ SY436 ) @ SY436 )
= SV210 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(849,plain,
! [SV211: $i] :
( ( ! [SY437: $i,SY438: $i] :
( ( SY437 = SY438 )
| ~ ( contains_pq @ SV211 @ SY438 )
| ( ( remove_pq @ ( insert_pq @ SV211 @ SY437 ) @ SY438 )
= ( insert_pq @ ( remove_pq @ SV211 @ SY438 ) @ SY437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(850,plain,
! [SV212: $i] :
( ( ! [SY439: $i] :
( ~ ( contains_pq @ SV212 @ SY439 )
| ~ ( issmallestelement_pq @ SV212 @ SY439 )
| ( ( findmin_pq_eff @ SV212 @ SY439 )
= SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(851,plain,
! [SV213: $i] :
( ( ! [SY440: $i] :
( ~ ( contains_pq @ SV213 @ SY440 )
| ~ ( issmallestelement_pq @ SV213 @ SY440 )
| ( ( findmin_pq_res @ SV213 @ SY440 )
= SY440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(852,plain,
! [SV214: $i] :
( ( ! [SY441: $i] :
( ~ ( contains_pq @ SV214 @ SY441 )
| ~ ( issmallestelement_pq @ SV214 @ SY441 )
| ( ( removemin_pq_eff @ SV214 @ SY441 )
= ( remove_pq @ SV214 @ SY441 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(853,plain,
! [SV215: $i] :
( ( ! [SY442: $i] :
( ~ ( contains_pq @ SV215 @ SY442 )
| ~ ( issmallestelement_pq @ SV215 @ SY442 )
| ( ( removemin_pq_res @ SV215 @ SY442 )
= SY442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(854,plain,
! [SV216: $i] :
( ( ! [SY443: $i,SY444: $i] :
( ( insert_pq @ ( insert_pq @ SV216 @ SY443 ) @ SY444 )
= ( insert_pq @ ( insert_pq @ SV216 @ SY444 ) @ SY443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(855,plain,
( ( isnonempty_slb @ create_slb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[778]) ).
thf(856,plain,
! [SV217: $i] :
( ( ! [SY445: $i,SY446: $i] : ( isnonempty_slb @ ( insert_slb @ SV217 @ ( pair @ SY445 @ SY446 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(857,plain,
! [SV218: $i] :
( ( ~ ( contains_slb @ create_slb @ SV218 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(858,plain,
! [SV219: $i] :
( ( ! [SY447: $i] :
~ ( pair_in_list @ create_slb @ SV219 @ SY447 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(859,plain,
! [SV220: $i] :
( ( ! [SY448: $i,SY449: $i] :
( ( remove_slb @ ( insert_slb @ SV220 @ ( pair @ SY448 @ SY449 ) ) @ SY448 )
= SV220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(860,plain,
! [SV221: $i] :
( ( ! [SY450: $i,SY451: $i] :
( ( SY450 = SY451 )
| ~ ( contains_slb @ SV221 @ SY451 )
| ! [SY452: $i] :
( ( remove_slb @ ( insert_slb @ SV221 @ ( pair @ SY450 @ SY452 ) ) @ SY451 )
= ( insert_slb @ ( remove_slb @ SV221 @ SY451 ) @ ( pair @ SY450 @ SY452 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(861,plain,
! [SV222: $i] :
( ( ! [SY453: $i,SY454: $i] :
( ( lookup_slb @ ( insert_slb @ SV222 @ ( pair @ SY453 @ SY454 ) ) @ SY453 )
= SY454 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(862,plain,
! [SV223: $i] :
( ( ! [SY455: $i,SY456: $i] :
( ( SY455 = SY456 )
| ~ ( contains_slb @ SV223 @ SY456 )
| ! [SY457: $i] :
( ( lookup_slb @ ( insert_slb @ SV223 @ ( pair @ SY455 @ SY457 ) ) @ SY456 )
= ( lookup_slb @ SV223 @ SY456 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(863,plain,
! [SV224: $i] :
( ( ( update_slb @ create_slb @ SV224 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(864,plain,
! [SV225: $i] :
( ( ! [SY458: $i,SY459: $i,SY460: $i] :
( ~ ( strictly_less_than @ SY460 @ SY459 )
| ( ( update_slb @ ( insert_slb @ SV225 @ ( pair @ SY458 @ SY460 ) ) @ SY459 )
= ( insert_slb @ ( update_slb @ SV225 @ SY459 ) @ ( pair @ SY458 @ SY459 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(865,plain,
! [SV226: $i] :
( ( ! [SY461: $i,SY462: $i,SY463: $i] :
( ~ ( less_than @ SY462 @ SY463 )
| ( ( update_slb @ ( insert_slb @ SV226 @ ( pair @ SY461 @ SY463 ) ) @ SY462 )
= ( insert_slb @ ( update_slb @ SV226 @ SY462 ) @ ( pair @ SY461 @ SY463 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(866,plain,
! [SV227: $i] :
( ( succ_cpq @ SV227 @ SV227 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(867,plain,
! [SV228: $i] :
( ( ! [SY464: $i] :
( ~ ( succ_cpq @ SV228 @ SY464 )
| ! [SY465: $i] : ( succ_cpq @ SV228 @ ( insert_cpq @ SY464 @ SY465 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(868,plain,
! [SV229: $i] :
( ( ! [SY466: $i] :
( ~ ( succ_cpq @ SV229 @ SY466 )
| ! [SY467: $i] : ( succ_cpq @ SV229 @ ( remove_cpq @ SY466 @ SY467 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(869,plain,
! [SV230: $i] :
( ( ! [SY468: $i] :
( ~ ( succ_cpq @ SV230 @ SY468 )
| ( succ_cpq @ SV230 @ ( findmin_cpq_eff @ SY468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(870,plain,
! [SV231: $i] :
( ( ! [SY469: $i] :
( ~ ( succ_cpq @ SV231 @ SY469 )
| ( succ_cpq @ SV231 @ ( removemin_cpq_eff @ SY469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(871,plain,
! [SV232: $i] :
( ( ! [SY470: $i] : ( check_cpq @ ( triple @ SV232 @ create_slb @ SY470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(872,plain,
! [SV233: $i] :
( ( ! [SY471: $i,SY472: $i,SY473: $i,SY474: $i] :
( ~ ( strictly_less_than @ SY473 @ SY474 )
| ~ ( check_cpq @ ( triple @ SV233 @ ( insert_slb @ SY471 @ ( pair @ SY473 @ SY474 ) ) @ SY472 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(873,plain,
! [SV234: $i] :
( ( ! [SY475: $i] :
~ ( ok @ ( triple @ SV234 @ SY475 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(874,plain,
! [SV235: $i] :
( ( ! [SY476: $i,SY477: $i] :
( ( ok @ ( triple @ SV235 @ SY476 @ SY477 ) )
| ( SY477 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(875,plain,
! [SV236: $i] :
( ( ! [SY478: $i,SY479: $i,SY480: $i] :
( ( insert_cpq @ ( triple @ SV236 @ SY478 @ SY479 ) @ SY480 )
= ( triple @ ( insert_pqp @ SV236 @ SY480 ) @ ( insert_slb @ SY478 @ ( pair @ SY480 @ bottom ) ) @ SY479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(876,plain,
! [SV237: $i] :
( ( ! [SY481: $i,SY482: $i,SY483: $i] :
( ( contains_slb @ SY481 @ SY483 )
| ( ( remove_cpq @ ( triple @ SV237 @ SY481 @ SY482 ) @ SY483 )
= ( triple @ SV237 @ SY481 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(877,plain,
! [SV238: $i] :
( ( ! [SY484: $i,SY485: $i,SY486: $i] :
( ~ ( contains_slb @ SY484 @ SY486 )
| ~ ( less_than @ ( lookup_slb @ SY484 @ SY486 ) @ SY486 )
| ( ( remove_cpq @ ( triple @ SV238 @ SY484 @ SY485 ) @ SY486 )
= ( triple @ ( remove_pqp @ SV238 @ SY486 ) @ ( remove_slb @ SY484 @ SY486 ) @ SY485 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(878,plain,
! [SV239: $i] :
( ( ! [SY487: $i,SY488: $i,SY489: $i] :
( ~ ( contains_slb @ SY487 @ SY489 )
| ~ ( strictly_less_than @ SY489 @ ( lookup_slb @ SY487 @ SY489 ) )
| ( ( remove_cpq @ ( triple @ SV239 @ SY487 @ SY488 ) @ SY489 )
= ( triple @ ( remove_pqp @ SV239 @ SY489 ) @ ( remove_slb @ SY487 @ SY489 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(879,plain,
! [SV240: $i] :
( ( ! [SY490: $i] :
( ( findmin_cpq_eff @ ( triple @ SV240 @ create_slb @ SY490 ) )
= ( triple @ SV240 @ create_slb @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(880,plain,
! [SV241: $i] :
( ( ! [SY491: $i] :
( ( SY491 = create_slb )
| ( contains_slb @ SY491 @ ( findmin_pqp_res @ SV241 ) )
| ! [SY492: $i] :
( ( findmin_cpq_eff @ ( triple @ SV241 @ SY491 @ SY492 ) )
= ( triple @ SV241 @ ( update_slb @ SY491 @ ( findmin_pqp_res @ SV241 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(881,plain,
! [SV242: $i] :
( ( ! [SY493: $i] :
( ( SY493 = create_slb )
| ~ ( contains_slb @ SY493 @ ( findmin_pqp_res @ SV242 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV242 ) @ ( lookup_slb @ SY493 @ ( findmin_pqp_res @ SV242 ) ) )
| ! [SY494: $i] :
( ( findmin_cpq_eff @ ( triple @ SV242 @ SY493 @ SY494 ) )
= ( triple @ SV242 @ ( update_slb @ SY493 @ ( findmin_pqp_res @ SV242 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(882,plain,
! [SV243: $i] :
( ( ! [SY495: $i] :
( ( SY495 = create_slb )
| ~ ( contains_slb @ SY495 @ ( findmin_pqp_res @ SV243 ) )
| ~ ( less_than @ ( lookup_slb @ SY495 @ ( findmin_pqp_res @ SV243 ) ) @ ( findmin_pqp_res @ SV243 ) )
| ! [SY496: $i] :
( ( findmin_cpq_eff @ ( triple @ SV243 @ SY495 @ SY496 ) )
= ( triple @ SV243 @ ( update_slb @ SY495 @ ( findmin_pqp_res @ SV243 ) ) @ SY496 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(883,plain,
! [SV244: $i] :
( ( ! [SY497: $i] :
( ( findmin_cpq_res @ ( triple @ SV244 @ create_slb @ SY497 ) )
= bottom ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(884,plain,
! [SV245: $i] :
( ( ! [SY498: $i] :
( ( SY498 = create_slb )
| ! [SY499: $i] :
( ( findmin_cpq_res @ ( triple @ SV245 @ SY498 @ SY499 ) )
= ( findmin_pqp_res @ SV245 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(885,plain,
! [SV246: $i] :
( ( ( removemin_cpq_eff @ SV246 )
= ( remove_cpq @ ( findmin_cpq_eff @ SV246 ) @ ( findmin_cpq_res @ SV246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(886,plain,
! [SV247: $i] :
( ( ( removemin_cpq_res @ SV247 )
= ( findmin_cpq_res @ SV247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(887,plain,
! [SV248: $i] :
( ( ! [SY500: $i] :
( ( i @ ( triple @ SV248 @ create_slb @ SY500 ) )
= create_pq ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(888,plain,
! [SV249: $i] :
( ( ! [SY501: $i,SY502: $i,SY503: $i,SY504: $i] :
( ( i @ ( triple @ SV249 @ ( insert_slb @ SY501 @ ( pair @ SY503 @ SY504 ) ) @ SY502 ) )
= ( insert_pq @ ( i @ ( triple @ SV249 @ SY501 @ SY502 ) ) @ SY503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(889,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( contains_pq @ SX0 @ ( sK15_W @ SX1 @ SX0 ) )
| ~ ~ ( less_than @ SX1 @ ( sK15_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)],[825]) ).
thf(890,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( ok @ SX1 )
| ~ ( succ_cpq @ SX0 @ SX1 )
| ~ ( check_cpq @ SX1 ) )
| ( phi @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( phi @ SX0 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK12_V @ SX0 ) )
| ~ ( succ_cpq @ SX0 @ ( sK12_V @ SX0 ) ) )
| ~ ( check_cpq @ ( sK12_V @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[826]) ).
thf(891,plain,
! [SV250: $i] :
( ( ~ ( ~ ! [SY505: $i,SY506: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV250 @ SY505 ) @ SY506 )
| ( SY505 = SY506 )
| ( contains_pq @ SV250 @ SY506 ) )
| ~ ~ ( ~ ! [SY507: $i,SY508: $i] :
( ( SY507 != SY508 )
| ( contains_pq @ ( insert_pq @ SV250 @ SY507 ) @ SY508 ) )
| ~ ! [SY509: $i,SY510: $i] :
( ~ ( contains_pq @ SV250 @ SY510 )
| ( contains_pq @ ( insert_pq @ SV250 @ SY509 ) @ SY510 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(892,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 ) @ ( sK14_V @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[828]) ).
thf(893,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)],[829]) ).
thf(894,plain,
! [SV251: $i] :
( ( ! [SY511: $i,SY512: $i] :
~ ( ~ ~ ( ~ ! [SY513: $i,SY514: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SY511 @ SY513 ) ) @ SY512 @ SY514 )
| ( SY511 = SY512 )
| ( pair_in_list @ SV251 @ SY512 @ SY514 ) )
| ~ ! [SY515: $i,SY516: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SY511 @ SY515 ) ) @ SY512 @ SY516 )
| ( SY515 = SY516 )
| ( pair_in_list @ SV251 @ SY512 @ SY516 ) ) )
| ~ ~ ( ~ ! [SY517: $i,SY518: $i] :
( ( SY511 != SY512 )
| ( SY517 != SY518 )
| ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SY511 @ SY517 ) ) @ SY512 @ SY518 ) )
| ~ ! [SY519: $i,SY520: $i] :
( ~ ( pair_in_list @ SV251 @ SY512 @ SY520 )
| ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SY511 @ SY519 ) ) @ SY512 @ SY520 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(895,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)],[831]) ).
thf(896,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)],[832]) ).
thf(897,plain,
! [SV252: $i] :
( ( ! [SY521: $i] :
~ ( ~ ! [SY522: $i,SY523: $i] :
( ~ ( contains_cpq @ ( triple @ SV252 @ SY521 @ SY522 ) @ SY523 )
| ( contains_slb @ SY521 @ SY523 ) )
| ~ ! [SY524: $i,SY525: $i] :
( ~ ( contains_slb @ SY521 @ SY525 )
| ( contains_cpq @ ( triple @ SV252 @ SY521 @ SY524 ) @ SY525 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(898,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)],[834]) ).
thf(899,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)],[835]) ).
thf(900,plain,
! [SV253: $i] :
( ( ! [SY526: $i,SY527: $i] :
~ ( ~ ! [SY528: $i,SY529: $i] :
( ~ ( less_than @ SY529 @ SY528 )
| ~ ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SY526 @ ( pair @ SY528 @ SY529 ) ) @ SY527 ) )
| ( check_cpq @ ( triple @ SV253 @ SY526 @ SY527 ) ) )
| ~ ! [SY530: $i,SY531: $i] :
( ~ ( less_than @ SY531 @ SY530 )
| ~ ( check_cpq @ ( triple @ SV253 @ SY526 @ SY527 ) )
| ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SY526 @ ( pair @ SY530 @ SY531 ) ) @ SY527 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(901,plain,
! [SV254: $i] :
( ( ~ ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( contains_cpq @ ( triple @ SV254 @ sK1_U @ SY532 ) @ SY533 )
| ( contains_pq @ ( i @ ( triple @ SV254 @ sK1_U @ SY532 ) ) @ SY533 ) )
| ~ ! [SY534: $i,SY535: $i] :
( ~ ( contains_pq @ ( i @ ( triple @ SV254 @ sK1_U @ SY534 ) ) @ SY535 )
| ( contains_cpq @ ( triple @ SV254 @ sK1_U @ SY534 ) @ SY535 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(902,plain,
( ( ~ ( contains_pq @ ( i @ ( triple @ sK7_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK9_SY194 @ sK10_SY197 ) ) @ sK8_SY190 ) ) @ sK11_SY199 )
| ~ ~ ( contains_cpq @ ( triple @ sK7_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK9_SY194 @ sK10_SY197 ) ) @ sK8_SY190 ) @ sK11_SY199 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[838]) ).
thf(903,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 ) @ ( sK13_V @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[839]) ).
thf(904,plain,
! [SV255: $i] :
( ( ! [SY536: $i] :
~ ( ~ ! [SY537: $i] :
( ! [SY538: $i] :
~ ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SY536 @ SY538 ) ) @ SY537 )
| ( SY536 = SY537 )
| ( contains_slb @ SV255 @ SY537 ) )
| ~ ~ ( ~ ! [SY539: $i] :
( ( SY536 != SY539 )
| ! [SY540: $i] : ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SY536 @ SY540 ) ) @ SY539 ) )
| ~ ! [SY541: $i] :
( ~ ( contains_slb @ SV255 @ SY541 )
| ! [SY542: $i] : ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SY536 @ SY542 ) ) @ SY541 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(905,plain,
! [SV256: $i,SV204: $i] :
( ( ! [SY543: $i] :
( ~ ( less_than @ SV204 @ SV256 )
| ~ ( less_than @ SV256 @ SY543 )
| ( less_than @ SV204 @ SY543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(906,plain,
! [SV257: $i,SV205: $i] :
( ( ( less_than @ SV205 @ SV257 )
| ( less_than @ SV257 @ SV205 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(907,plain,
! [SV258: $i,SV208: $i] :
( ( isnonempty_pq @ ( insert_pq @ SV208 @ SV258 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(908,plain,
! [SV209: $i] :
( ( contains_pq @ create_pq @ SV209 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[847]) ).
thf(909,plain,
! [SV259: $i,SV210: $i] :
( ( ( remove_pq @ ( insert_pq @ SV210 @ SV259 ) @ SV259 )
= SV210 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(910,plain,
! [SV211: $i,SV260: $i] :
( ( ! [SY544: $i] :
( ( SV260 = SY544 )
| ~ ( contains_pq @ SV211 @ SY544 )
| ( ( remove_pq @ ( insert_pq @ SV211 @ SV260 ) @ SY544 )
= ( insert_pq @ ( remove_pq @ SV211 @ SY544 ) @ SV260 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(911,plain,
! [SV261: $i,SV212: $i] :
( ( ~ ( contains_pq @ SV212 @ SV261 )
| ~ ( issmallestelement_pq @ SV212 @ SV261 )
| ( ( findmin_pq_eff @ SV212 @ SV261 )
= SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(912,plain,
! [SV262: $i,SV213: $i] :
( ( ~ ( contains_pq @ SV213 @ SV262 )
| ~ ( issmallestelement_pq @ SV213 @ SV262 )
| ( ( findmin_pq_res @ SV213 @ SV262 )
= SV262 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(913,plain,
! [SV263: $i,SV214: $i] :
( ( ~ ( contains_pq @ SV214 @ SV263 )
| ~ ( issmallestelement_pq @ SV214 @ SV263 )
| ( ( removemin_pq_eff @ SV214 @ SV263 )
= ( remove_pq @ SV214 @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(914,plain,
! [SV264: $i,SV215: $i] :
( ( ~ ( contains_pq @ SV215 @ SV264 )
| ~ ( issmallestelement_pq @ SV215 @ SV264 )
| ( ( removemin_pq_res @ SV215 @ SV264 )
= SV264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(915,plain,
! [SV265: $i,SV216: $i] :
( ( ! [SY545: $i] :
( ( insert_pq @ ( insert_pq @ SV216 @ SV265 ) @ SY545 )
= ( insert_pq @ ( insert_pq @ SV216 @ SY545 ) @ SV265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(916,plain,
! [SV266: $i,SV217: $i] :
( ( ! [SY546: $i] : ( isnonempty_slb @ ( insert_slb @ SV217 @ ( pair @ SV266 @ SY546 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(917,plain,
! [SV218: $i] :
( ( contains_slb @ create_slb @ SV218 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[857]) ).
thf(918,plain,
! [SV267: $i,SV219: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV219 @ SV267 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(919,plain,
! [SV268: $i,SV220: $i] :
( ( ! [SY547: $i] :
( ( remove_slb @ ( insert_slb @ SV220 @ ( pair @ SV268 @ SY547 ) ) @ SV268 )
= SV220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(920,plain,
! [SV221: $i,SV269: $i] :
( ( ! [SY548: $i] :
( ( SV269 = SY548 )
| ~ ( contains_slb @ SV221 @ SY548 )
| ! [SY549: $i] :
( ( remove_slb @ ( insert_slb @ SV221 @ ( pair @ SV269 @ SY549 ) ) @ SY548 )
= ( insert_slb @ ( remove_slb @ SV221 @ SY548 ) @ ( pair @ SV269 @ SY549 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(921,plain,
! [SV270: $i,SV222: $i] :
( ( ! [SY550: $i] :
( ( lookup_slb @ ( insert_slb @ SV222 @ ( pair @ SV270 @ SY550 ) ) @ SV270 )
= SY550 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(922,plain,
! [SV223: $i,SV271: $i] :
( ( ! [SY551: $i] :
( ( SV271 = SY551 )
| ~ ( contains_slb @ SV223 @ SY551 )
| ! [SY552: $i] :
( ( lookup_slb @ ( insert_slb @ SV223 @ ( pair @ SV271 @ SY552 ) ) @ SY551 )
= ( lookup_slb @ SV223 @ SY551 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(923,plain,
! [SV272: $i,SV225: $i] :
( ( ! [SY553: $i,SY554: $i] :
( ~ ( strictly_less_than @ SY554 @ SY553 )
| ( ( update_slb @ ( insert_slb @ SV225 @ ( pair @ SV272 @ SY554 ) ) @ SY553 )
= ( insert_slb @ ( update_slb @ SV225 @ SY553 ) @ ( pair @ SV272 @ SY553 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(924,plain,
! [SV273: $i,SV226: $i] :
( ( ! [SY555: $i,SY556: $i] :
( ~ ( less_than @ SY555 @ SY556 )
| ( ( update_slb @ ( insert_slb @ SV226 @ ( pair @ SV273 @ SY556 ) ) @ SY555 )
= ( insert_slb @ ( update_slb @ SV226 @ SY555 ) @ ( pair @ SV273 @ SY556 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(925,plain,
! [SV274: $i,SV228: $i] :
( ( ~ ( succ_cpq @ SV228 @ SV274 )
| ! [SY557: $i] : ( succ_cpq @ SV228 @ ( insert_cpq @ SV274 @ SY557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(926,plain,
! [SV275: $i,SV229: $i] :
( ( ~ ( succ_cpq @ SV229 @ SV275 )
| ! [SY558: $i] : ( succ_cpq @ SV229 @ ( remove_cpq @ SV275 @ SY558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(927,plain,
! [SV276: $i,SV230: $i] :
( ( ~ ( succ_cpq @ SV230 @ SV276 )
| ( succ_cpq @ SV230 @ ( findmin_cpq_eff @ SV276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(928,plain,
! [SV277: $i,SV231: $i] :
( ( ~ ( succ_cpq @ SV231 @ SV277 )
| ( succ_cpq @ SV231 @ ( removemin_cpq_eff @ SV277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(929,plain,
! [SV278: $i,SV232: $i] :
( ( check_cpq @ ( triple @ SV232 @ create_slb @ SV278 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(930,plain,
! [SV279: $i,SV233: $i] :
( ( ! [SY559: $i,SY560: $i,SY561: $i] :
( ~ ( strictly_less_than @ SY560 @ SY561 )
| ~ ( check_cpq @ ( triple @ SV233 @ ( insert_slb @ SV279 @ ( pair @ SY560 @ SY561 ) ) @ SY559 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(931,plain,
! [SV280: $i,SV234: $i] :
( ( ~ ( ok @ ( triple @ SV234 @ SV280 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(932,plain,
! [SV281: $i,SV235: $i] :
( ( ! [SY562: $i] :
( ( ok @ ( triple @ SV235 @ SV281 @ SY562 ) )
| ( SY562 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(933,plain,
! [SV282: $i,SV236: $i] :
( ( ! [SY563: $i,SY564: $i] :
( ( insert_cpq @ ( triple @ SV236 @ SV282 @ SY563 ) @ SY564 )
= ( triple @ ( insert_pqp @ SV236 @ SY564 ) @ ( insert_slb @ SV282 @ ( pair @ SY564 @ bottom ) ) @ SY563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(934,plain,
! [SV237: $i,SV283: $i] :
( ( ! [SY565: $i,SY566: $i] :
( ( contains_slb @ SV283 @ SY566 )
| ( ( remove_cpq @ ( triple @ SV237 @ SV283 @ SY565 ) @ SY566 )
= ( triple @ SV237 @ SV283 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(935,plain,
! [SV238: $i,SV284: $i] :
( ( ! [SY567: $i,SY568: $i] :
( ~ ( contains_slb @ SV284 @ SY568 )
| ~ ( less_than @ ( lookup_slb @ SV284 @ SY568 ) @ SY568 )
| ( ( remove_cpq @ ( triple @ SV238 @ SV284 @ SY567 ) @ SY568 )
= ( triple @ ( remove_pqp @ SV238 @ SY568 ) @ ( remove_slb @ SV284 @ SY568 ) @ SY567 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(936,plain,
! [SV239: $i,SV285: $i] :
( ( ! [SY569: $i,SY570: $i] :
( ~ ( contains_slb @ SV285 @ SY570 )
| ~ ( strictly_less_than @ SY570 @ ( lookup_slb @ SV285 @ SY570 ) )
| ( ( remove_cpq @ ( triple @ SV239 @ SV285 @ SY569 ) @ SY570 )
= ( triple @ ( remove_pqp @ SV239 @ SY570 ) @ ( remove_slb @ SV285 @ SY570 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(937,plain,
! [SV286: $i,SV240: $i] :
( ( ( findmin_cpq_eff @ ( triple @ SV240 @ create_slb @ SV286 ) )
= ( triple @ SV240 @ create_slb @ bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(938,plain,
! [SV241: $i,SV287: $i] :
( ( ( SV287 = create_slb )
| ( contains_slb @ SV287 @ ( findmin_pqp_res @ SV241 ) )
| ! [SY571: $i] :
( ( findmin_cpq_eff @ ( triple @ SV241 @ SV287 @ SY571 ) )
= ( triple @ SV241 @ ( update_slb @ SV287 @ ( findmin_pqp_res @ SV241 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(939,plain,
! [SV242: $i,SV288: $i] :
( ( ( SV288 = create_slb )
| ~ ( contains_slb @ SV288 @ ( findmin_pqp_res @ SV242 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV242 ) @ ( lookup_slb @ SV288 @ ( findmin_pqp_res @ SV242 ) ) )
| ! [SY572: $i] :
( ( findmin_cpq_eff @ ( triple @ SV242 @ SV288 @ SY572 ) )
= ( triple @ SV242 @ ( update_slb @ SV288 @ ( findmin_pqp_res @ SV242 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(940,plain,
! [SV243: $i,SV289: $i] :
( ( ( SV289 = create_slb )
| ~ ( contains_slb @ SV289 @ ( findmin_pqp_res @ SV243 ) )
| ~ ( less_than @ ( lookup_slb @ SV289 @ ( findmin_pqp_res @ SV243 ) ) @ ( findmin_pqp_res @ SV243 ) )
| ! [SY573: $i] :
( ( findmin_cpq_eff @ ( triple @ SV243 @ SV289 @ SY573 ) )
= ( triple @ SV243 @ ( update_slb @ SV289 @ ( findmin_pqp_res @ SV243 ) ) @ SY573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(941,plain,
! [SV290: $i,SV244: $i] :
( ( ( findmin_cpq_res @ ( triple @ SV244 @ create_slb @ SV290 ) )
= bottom )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(942,plain,
! [SV245: $i,SV291: $i] :
( ( ( SV291 = create_slb )
| ! [SY574: $i] :
( ( findmin_cpq_res @ ( triple @ SV245 @ SV291 @ SY574 ) )
= ( findmin_pqp_res @ SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(943,plain,
! [SV292: $i,SV248: $i] :
( ( ( i @ ( triple @ SV248 @ create_slb @ SV292 ) )
= create_pq )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(944,plain,
! [SV293: $i,SV249: $i] :
( ( ! [SY575: $i,SY576: $i,SY577: $i] :
( ( i @ ( triple @ SV249 @ ( insert_slb @ SV293 @ ( pair @ SY576 @ SY577 ) ) @ SY575 ) )
= ( insert_pq @ ( i @ ( triple @ SV249 @ SV293 @ SY575 ) ) @ SY576 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(945,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( contains_pq @ SX0 @ ( sK15_W @ SX1 @ SX0 ) )
| ~ ~ ( less_than @ SX1 @ ( sK15_W @ SX1 @ SX0 ) ) )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[889]) ).
thf(946,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)],[889]) ).
thf(947,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( ok @ SX1 )
| ~ ( succ_cpq @ SX0 @ SX1 )
| ~ ( check_cpq @ SX1 ) )
| ( phi @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[890]) ).
thf(948,plain,
( ( ~ ! [SX0: $i] :
( ~ ( phi @ SX0 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK12_V @ SX0 ) )
| ~ ( succ_cpq @ SX0 @ ( sK12_V @ SX0 ) ) )
| ~ ( check_cpq @ ( sK12_V @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[890]) ).
thf(949,plain,
! [SV250: $i] :
( ( ~ ! [SY505: $i,SY506: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV250 @ SY505 ) @ SY506 )
| ( SY505 = SY506 )
| ( contains_pq @ SV250 @ SY506 ) )
| ~ ~ ( ~ ! [SY507: $i,SY508: $i] :
( ( SY507 != SY508 )
| ( contains_pq @ ( insert_pq @ SV250 @ SY507 ) @ SY508 ) )
| ~ ! [SY509: $i,SY510: $i] :
( ~ ( contains_pq @ SV250 @ SY510 )
| ( contains_pq @ ( insert_pq @ SV250 @ SY509 ) @ SY510 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[891]) ).
thf(950,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_find_min @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[892]) ).
thf(951,plain,
( ( ~ ! [SX0: $i] :
( ~ ( pi_find_min @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK14_V @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[892]) ).
thf(952,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)],[893]) ).
thf(953,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)],[893]) ).
thf(954,plain,
! [SV294: $i,SV251: $i] :
( ( ! [SY578: $i] :
~ ( ~ ~ ( ~ ! [SY579: $i,SY580: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY579 ) ) @ SY578 @ SY580 )
| ( SV294 = SY578 )
| ( pair_in_list @ SV251 @ SY578 @ SY580 ) )
| ~ ! [SY581: $i,SY582: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY581 ) ) @ SY578 @ SY582 )
| ( SY581 = SY582 )
| ( pair_in_list @ SV251 @ SY578 @ SY582 ) ) )
| ~ ~ ( ~ ! [SY583: $i,SY584: $i] :
( ( SV294 != SY578 )
| ( SY583 != SY584 )
| ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY583 ) ) @ SY578 @ SY584 ) )
| ~ ! [SY585: $i,SY586: $i] :
( ~ ( pair_in_list @ SV251 @ SY578 @ SY586 )
| ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY585 ) ) @ SY578 @ SY586 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(955,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( contains_pq @ SX0 @ SX1 )
| ( pi_sharp_remove @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(956,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[895]) ).
thf(957,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)],[896]) ).
thf(958,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)],[896]) ).
thf(959,plain,
! [SV295: $i,SV252: $i] :
( ( ~ ( ~ ! [SY587: $i,SY588: $i] :
( ~ ( contains_cpq @ ( triple @ SV252 @ SV295 @ SY587 ) @ SY588 )
| ( contains_slb @ SV295 @ SY588 ) )
| ~ ! [SY589: $i,SY590: $i] :
( ~ ( contains_slb @ SV295 @ SY590 )
| ( contains_cpq @ ( triple @ SV252 @ SV295 @ SY589 ) @ SY590 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(960,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)],[898]) ).
thf(961,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)],[898]) ).
thf(962,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_remove @ SX0 @ SX1 )
| ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[899]) ).
thf(963,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 )
| ( pi_remove @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[899]) ).
thf(964,plain,
! [SV296: $i,SV253: $i] :
( ( ! [SY591: $i] :
~ ( ~ ! [SY592: $i,SY593: $i] :
( ~ ( less_than @ SY593 @ SY592 )
| ~ ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SV296 @ ( pair @ SY592 @ SY593 ) ) @ SY591 ) )
| ( check_cpq @ ( triple @ SV253 @ SV296 @ SY591 ) ) )
| ~ ! [SY594: $i,SY595: $i] :
( ~ ( less_than @ SY595 @ SY594 )
| ~ ( check_cpq @ ( triple @ SV253 @ SV296 @ SY591 ) )
| ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SV296 @ ( pair @ SY594 @ SY595 ) ) @ SY591 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(965,plain,
! [SV254: $i] :
( ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( contains_cpq @ ( triple @ SV254 @ sK1_U @ SY532 ) @ SY533 )
| ( contains_pq @ ( i @ ( triple @ SV254 @ sK1_U @ SY532 ) ) @ SY533 ) )
| ~ ! [SY534: $i,SY535: $i] :
( ~ ( contains_pq @ ( i @ ( triple @ SV254 @ sK1_U @ SY534 ) ) @ SY535 )
| ( contains_cpq @ ( triple @ SV254 @ sK1_U @ SY534 ) @ SY535 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(966,plain,
( ( ~ ( contains_pq @ ( i @ ( triple @ sK7_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK9_SY194 @ sK10_SY197 ) ) @ sK8_SY190 ) ) @ sK11_SY199 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[902]) ).
thf(967,plain,
( ( ~ ~ ( contains_cpq @ ( triple @ sK7_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK9_SY194 @ sK10_SY197 ) ) @ sK8_SY190 ) @ sK11_SY199 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[902]) ).
thf(968,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_removemin @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[903]) ).
thf(969,plain,
( ( ~ ! [SX0: $i] :
( ~ ( pi_removemin @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK13_V @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[903]) ).
thf(970,plain,
! [SV297: $i,SV255: $i] :
( ( ~ ( ~ ! [SY596: $i] :
( ! [SY597: $i] :
~ ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY597 ) ) @ SY596 )
| ( SV297 = SY596 )
| ( contains_slb @ SV255 @ SY596 ) )
| ~ ~ ( ~ ! [SY598: $i] :
( ( SV297 != SY598 )
| ! [SY599: $i] : ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY599 ) ) @ SY598 ) )
| ~ ! [SY600: $i] :
( ~ ( contains_slb @ SV255 @ SY600 )
| ! [SY601: $i] : ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY601 ) ) @ SY600 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(971,plain,
! [SV298: $i,SV256: $i,SV204: $i] :
( ( ~ ( less_than @ SV204 @ SV256 )
| ~ ( less_than @ SV256 @ SV298 )
| ( less_than @ SV204 @ SV298 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(972,plain,
! [SV257: $i,SV205: $i] :
( ( ( less_than @ SV205 @ SV257 )
= $true )
| ( ( less_than @ SV257 @ SV205 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[906]) ).
thf(973,plain,
! [SV211: $i,SV299: $i,SV260: $i] :
( ( ( SV260 = SV299 )
| ~ ( contains_pq @ SV211 @ SV299 )
| ( ( remove_pq @ ( insert_pq @ SV211 @ SV260 ) @ SV299 )
= ( insert_pq @ ( remove_pq @ SV211 @ SV299 ) @ SV260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(974,plain,
! [SV261: $i,SV212: $i] :
( ( ( ~ ( contains_pq @ SV212 @ SV261 )
| ~ ( issmallestelement_pq @ SV212 @ SV261 ) )
= $true )
| ( ( ( findmin_pq_eff @ SV212 @ SV261 )
= SV212 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[911]) ).
thf(975,plain,
! [SV262: $i,SV213: $i] :
( ( ( ~ ( contains_pq @ SV213 @ SV262 )
| ~ ( issmallestelement_pq @ SV213 @ SV262 ) )
= $true )
| ( ( ( findmin_pq_res @ SV213 @ SV262 )
= SV262 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(976,plain,
! [SV263: $i,SV214: $i] :
( ( ( ~ ( contains_pq @ SV214 @ SV263 )
| ~ ( issmallestelement_pq @ SV214 @ SV263 ) )
= $true )
| ( ( ( removemin_pq_eff @ SV214 @ SV263 )
= ( remove_pq @ SV214 @ SV263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[913]) ).
thf(977,plain,
! [SV264: $i,SV215: $i] :
( ( ( ~ ( contains_pq @ SV215 @ SV264 )
| ~ ( issmallestelement_pq @ SV215 @ SV264 ) )
= $true )
| ( ( ( removemin_pq_res @ SV215 @ SV264 )
= SV264 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[914]) ).
thf(978,plain,
! [SV300: $i,SV265: $i,SV216: $i] :
( ( ( insert_pq @ ( insert_pq @ SV216 @ SV265 ) @ SV300 )
= ( insert_pq @ ( insert_pq @ SV216 @ SV300 ) @ SV265 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(979,plain,
! [SV301: $i,SV266: $i,SV217: $i] :
( ( isnonempty_slb @ ( insert_slb @ SV217 @ ( pair @ SV266 @ SV301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(980,plain,
! [SV267: $i,SV219: $i] :
( ( pair_in_list @ create_slb @ SV219 @ SV267 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(981,plain,
! [SV302: $i,SV268: $i,SV220: $i] :
( ( ( remove_slb @ ( insert_slb @ SV220 @ ( pair @ SV268 @ SV302 ) ) @ SV268 )
= SV220 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(982,plain,
! [SV221: $i,SV303: $i,SV269: $i] :
( ( ( SV269 = SV303 )
| ~ ( contains_slb @ SV221 @ SV303 )
| ! [SY602: $i] :
( ( remove_slb @ ( insert_slb @ SV221 @ ( pair @ SV269 @ SY602 ) ) @ SV303 )
= ( insert_slb @ ( remove_slb @ SV221 @ SV303 ) @ ( pair @ SV269 @ SY602 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(983,plain,
! [SV304: $i,SV270: $i,SV222: $i] :
( ( ( lookup_slb @ ( insert_slb @ SV222 @ ( pair @ SV270 @ SV304 ) ) @ SV270 )
= SV304 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(984,plain,
! [SV223: $i,SV305: $i,SV271: $i] :
( ( ( SV271 = SV305 )
| ~ ( contains_slb @ SV223 @ SV305 )
| ! [SY603: $i] :
( ( lookup_slb @ ( insert_slb @ SV223 @ ( pair @ SV271 @ SY603 ) ) @ SV305 )
= ( lookup_slb @ SV223 @ SV305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(985,plain,
! [SV272: $i,SV225: $i,SV306: $i] :
( ( ! [SY604: $i] :
( ~ ( strictly_less_than @ SY604 @ SV306 )
| ( ( update_slb @ ( insert_slb @ SV225 @ ( pair @ SV272 @ SY604 ) ) @ SV306 )
= ( insert_slb @ ( update_slb @ SV225 @ SV306 ) @ ( pair @ SV272 @ SV306 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(986,plain,
! [SV273: $i,SV226: $i,SV307: $i] :
( ( ! [SY605: $i] :
( ~ ( less_than @ SV307 @ SY605 )
| ( ( update_slb @ ( insert_slb @ SV226 @ ( pair @ SV273 @ SY605 ) ) @ SV307 )
= ( insert_slb @ ( update_slb @ SV226 @ SV307 ) @ ( pair @ SV273 @ SY605 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(987,plain,
! [SV274: $i,SV228: $i] :
( ( ( ~ ( succ_cpq @ SV228 @ SV274 ) )
= $true )
| ( ( ! [SY557: $i] : ( succ_cpq @ SV228 @ ( insert_cpq @ SV274 @ SY557 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[925]) ).
thf(988,plain,
! [SV275: $i,SV229: $i] :
( ( ( ~ ( succ_cpq @ SV229 @ SV275 ) )
= $true )
| ( ( ! [SY558: $i] : ( succ_cpq @ SV229 @ ( remove_cpq @ SV275 @ SY558 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[926]) ).
thf(989,plain,
! [SV276: $i,SV230: $i] :
( ( ( ~ ( succ_cpq @ SV230 @ SV276 ) )
= $true )
| ( ( succ_cpq @ SV230 @ ( findmin_cpq_eff @ SV276 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[927]) ).
thf(990,plain,
! [SV277: $i,SV231: $i] :
( ( ( ~ ( succ_cpq @ SV231 @ SV277 ) )
= $true )
| ( ( succ_cpq @ SV231 @ ( removemin_cpq_eff @ SV277 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[928]) ).
thf(991,plain,
! [SV308: $i,SV279: $i,SV233: $i] :
( ( ! [SY606: $i,SY607: $i] :
( ~ ( strictly_less_than @ SY606 @ SY607 )
| ~ ( check_cpq @ ( triple @ SV233 @ ( insert_slb @ SV279 @ ( pair @ SY606 @ SY607 ) ) @ SV308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(992,plain,
! [SV280: $i,SV234: $i] :
( ( ok @ ( triple @ SV234 @ SV280 @ bad ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[931]) ).
thf(993,plain,
! [SV309: $i,SV281: $i,SV235: $i] :
( ( ( ok @ ( triple @ SV235 @ SV281 @ SV309 ) )
| ( SV309 = bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(994,plain,
! [SV310: $i,SV282: $i,SV236: $i] :
( ( ! [SY608: $i] :
( ( insert_cpq @ ( triple @ SV236 @ SV282 @ SV310 ) @ SY608 )
= ( triple @ ( insert_pqp @ SV236 @ SY608 ) @ ( insert_slb @ SV282 @ ( pair @ SY608 @ bottom ) ) @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(995,plain,
! [SV311: $i,SV237: $i,SV283: $i] :
( ( ! [SY609: $i] :
( ( contains_slb @ SV283 @ SY609 )
| ( ( remove_cpq @ ( triple @ SV237 @ SV283 @ SV311 ) @ SY609 )
= ( triple @ SV237 @ SV283 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(996,plain,
! [SV312: $i,SV238: $i,SV284: $i] :
( ( ! [SY610: $i] :
( ~ ( contains_slb @ SV284 @ SY610 )
| ~ ( less_than @ ( lookup_slb @ SV284 @ SY610 ) @ SY610 )
| ( ( remove_cpq @ ( triple @ SV238 @ SV284 @ SV312 ) @ SY610 )
= ( triple @ ( remove_pqp @ SV238 @ SY610 ) @ ( remove_slb @ SV284 @ SY610 ) @ SV312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(997,plain,
! [SV313: $i,SV239: $i,SV285: $i] :
( ( ! [SY611: $i] :
( ~ ( contains_slb @ SV285 @ SY611 )
| ~ ( strictly_less_than @ SY611 @ ( lookup_slb @ SV285 @ SY611 ) )
| ( ( remove_cpq @ ( triple @ SV239 @ SV285 @ SV313 ) @ SY611 )
= ( triple @ ( remove_pqp @ SV239 @ SY611 ) @ ( remove_slb @ SV285 @ SY611 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(998,plain,
! [SV241: $i,SV287: $i] :
( ( ( ( SV287 = create_slb )
| ( contains_slb @ SV287 @ ( findmin_pqp_res @ SV241 ) ) )
= $true )
| ( ( ! [SY571: $i] :
( ( findmin_cpq_eff @ ( triple @ SV241 @ SV287 @ SY571 ) )
= ( triple @ SV241 @ ( update_slb @ SV287 @ ( findmin_pqp_res @ SV241 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[938]) ).
thf(999,plain,
! [SV242: $i,SV288: $i] :
( ( ( ( SV288 = create_slb )
| ~ ( contains_slb @ SV288 @ ( findmin_pqp_res @ SV242 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV242 ) @ ( lookup_slb @ SV288 @ ( findmin_pqp_res @ SV242 ) ) ) )
= $true )
| ( ( ! [SY572: $i] :
( ( findmin_cpq_eff @ ( triple @ SV242 @ SV288 @ SY572 ) )
= ( triple @ SV242 @ ( update_slb @ SV288 @ ( findmin_pqp_res @ SV242 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[939]) ).
thf(1000,plain,
! [SV243: $i,SV289: $i] :
( ( ( ( SV289 = create_slb )
| ~ ( contains_slb @ SV289 @ ( findmin_pqp_res @ SV243 ) )
| ~ ( less_than @ ( lookup_slb @ SV289 @ ( findmin_pqp_res @ SV243 ) ) @ ( findmin_pqp_res @ SV243 ) ) )
= $true )
| ( ( ! [SY573: $i] :
( ( findmin_cpq_eff @ ( triple @ SV243 @ SV289 @ SY573 ) )
= ( triple @ SV243 @ ( update_slb @ SV289 @ ( findmin_pqp_res @ SV243 ) ) @ SY573 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[940]) ).
thf(1001,plain,
! [SV245: $i,SV291: $i] :
( ( ( SV291 = create_slb )
= $true )
| ( ( ! [SY574: $i] :
( ( findmin_cpq_res @ ( triple @ SV245 @ SV291 @ SY574 ) )
= ( findmin_pqp_res @ SV245 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[942]) ).
thf(1002,plain,
! [SV314: $i,SV293: $i,SV249: $i] :
( ( ! [SY612: $i,SY613: $i] :
( ( i @ ( triple @ SV249 @ ( insert_slb @ SV293 @ ( pair @ SY612 @ SY613 ) ) @ SV314 ) )
= ( insert_pq @ ( i @ ( triple @ SV249 @ SV293 @ SV314 ) ) @ SY612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1003,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( contains_pq @ SX0 @ ( sK15_W @ SX1 @ SX0 ) )
| ~ ~ ( less_than @ SX1 @ ( sK15_W @ SX1 @ SX0 ) ) )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[945]) ).
thf(1004,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)],[946]) ).
thf(1005,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( ok @ SX1 )
| ~ ( succ_cpq @ SX0 @ SX1 )
| ~ ( check_cpq @ SX1 ) )
| ( phi @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[947]) ).
thf(1006,plain,
( ( ! [SX0: $i] :
( ~ ( phi @ SX0 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK12_V @ SX0 ) )
| ~ ( succ_cpq @ SX0 @ ( sK12_V @ SX0 ) ) )
| ~ ( check_cpq @ ( sK12_V @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[948]) ).
thf(1007,plain,
! [SV250: $i] :
( ( ~ ! [SY505: $i,SY506: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV250 @ SY505 ) @ SY506 )
| ( SY505 = SY506 )
| ( contains_pq @ SV250 @ SY506 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[949]) ).
thf(1008,plain,
! [SV250: $i] :
( ( ~ ~ ( ~ ! [SY507: $i,SY508: $i] :
( ( SY507 != SY508 )
| ( contains_pq @ ( insert_pq @ SV250 @ SY507 ) @ SY508 ) )
| ~ ! [SY509: $i,SY510: $i] :
( ~ ( contains_pq @ SV250 @ SY510 )
| ( contains_pq @ ( insert_pq @ SV250 @ SY509 ) @ SY510 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[949]) ).
thf(1009,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_find_min @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[950]) ).
thf(1010,plain,
( ( ! [SX0: $i] :
( ~ ( pi_find_min @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK14_V @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[951]) ).
thf(1011,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)],[952]) ).
thf(1012,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)],[953]) ).
thf(1013,plain,
! [SV315: $i,SV294: $i,SV251: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY614: $i,SY615: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY614 ) ) @ SV315 @ SY615 )
| ( SV294 = SV315 )
| ( pair_in_list @ SV251 @ SV315 @ SY615 ) )
| ~ ! [SY616: $i,SY617: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY616 ) ) @ SV315 @ SY617 )
| ( SY616 = SY617 )
| ( pair_in_list @ SV251 @ SV315 @ SY617 ) ) )
| ~ ~ ( ~ ! [SY618: $i,SY619: $i] :
( ( SV294 != SV315 )
| ( SY618 != SY619 )
| ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY618 ) ) @ SV315 @ SY619 ) )
| ~ ! [SY620: $i,SY621: $i] :
( ~ ( pair_in_list @ SV251 @ SV315 @ SY621 )
| ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY620 ) ) @ SV315 @ SY621 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1014,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( contains_pq @ SX0 @ SX1 )
| ( pi_sharp_remove @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[955]) ).
thf(1015,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[956]) ).
thf(1016,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)],[957]) ).
thf(1017,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)],[958]) ).
thf(1018,plain,
! [SV295: $i,SV252: $i] :
( ( ~ ! [SY587: $i,SY588: $i] :
( ~ ( contains_cpq @ ( triple @ SV252 @ SV295 @ SY587 ) @ SY588 )
| ( contains_slb @ SV295 @ SY588 ) )
| ~ ! [SY589: $i,SY590: $i] :
( ~ ( contains_slb @ SV295 @ SY590 )
| ( contains_cpq @ ( triple @ SV252 @ SV295 @ SY589 ) @ SY590 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(1019,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)],[960]) ).
thf(1020,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)],[961]) ).
thf(1021,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_remove @ SX0 @ SX1 )
| ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[962]) ).
thf(1022,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 )
| ( pi_remove @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[963]) ).
thf(1023,plain,
! [SV316: $i,SV296: $i,SV253: $i] :
( ( ~ ( ~ ! [SY622: $i,SY623: $i] :
( ~ ( less_than @ SY623 @ SY622 )
| ~ ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SV296 @ ( pair @ SY622 @ SY623 ) ) @ SV316 ) )
| ( check_cpq @ ( triple @ SV253 @ SV296 @ SV316 ) ) )
| ~ ! [SY624: $i,SY625: $i] :
( ~ ( less_than @ SY625 @ SY624 )
| ~ ( check_cpq @ ( triple @ SV253 @ SV296 @ SV316 ) )
| ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SV296 @ ( pair @ SY624 @ SY625 ) ) @ SV316 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1024,plain,
! [SV254: $i] :
( ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( contains_cpq @ ( triple @ SV254 @ sK1_U @ SY532 ) @ SY533 )
| ( contains_pq @ ( i @ ( triple @ SV254 @ sK1_U @ SY532 ) ) @ SY533 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[965]) ).
thf(1025,plain,
! [SV254: $i] :
( ( ~ ! [SY534: $i,SY535: $i] :
( ~ ( contains_pq @ ( i @ ( triple @ SV254 @ sK1_U @ SY534 ) ) @ SY535 )
| ( contains_cpq @ ( triple @ SV254 @ sK1_U @ SY534 ) @ SY535 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[965]) ).
thf(1026,plain,
( ( contains_pq @ ( i @ ( triple @ sK7_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK9_SY194 @ sK10_SY197 ) ) @ sK8_SY190 ) ) @ sK11_SY199 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[966]) ).
thf(1027,plain,
( ( ~ ( contains_cpq @ ( triple @ sK7_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK9_SY194 @ sK10_SY197 ) ) @ sK8_SY190 ) @ sK11_SY199 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[967]) ).
thf(1028,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_removemin @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[968]) ).
thf(1029,plain,
( ( ! [SX0: $i] :
( ~ ( pi_removemin @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK13_V @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[969]) ).
thf(1030,plain,
! [SV297: $i,SV255: $i] :
( ( ~ ! [SY596: $i] :
( ! [SY597: $i] :
~ ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY597 ) ) @ SY596 )
| ( SV297 = SY596 )
| ( contains_slb @ SV255 @ SY596 ) )
| ~ ~ ( ~ ! [SY598: $i] :
( ( SV297 != SY598 )
| ! [SY599: $i] : ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY599 ) ) @ SY598 ) )
| ~ ! [SY600: $i] :
( ~ ( contains_slb @ SV255 @ SY600 )
| ! [SY601: $i] : ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY601 ) ) @ SY600 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[970]) ).
thf(1031,plain,
! [SV298: $i,SV256: $i,SV204: $i] :
( ( ( ~ ( less_than @ SV204 @ SV256 )
| ~ ( less_than @ SV256 @ SV298 ) )
= $true )
| ( ( less_than @ SV204 @ SV298 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[971]) ).
thf(1032,plain,
! [SV211: $i,SV299: $i,SV260: $i] :
( ( ( ( SV260 = SV299 )
| ~ ( contains_pq @ SV211 @ SV299 ) )
= $true )
| ( ( ( remove_pq @ ( insert_pq @ SV211 @ SV260 ) @ SV299 )
= ( insert_pq @ ( remove_pq @ SV211 @ SV299 ) @ SV260 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[973]) ).
thf(1033,plain,
! [SV261: $i,SV212: $i] :
( ( ( ~ ( contains_pq @ SV212 @ SV261 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV212 @ SV261 ) )
= $true )
| ( ( ( findmin_pq_eff @ SV212 @ SV261 )
= SV212 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[974]) ).
thf(1034,plain,
! [SV262: $i,SV213: $i] :
( ( ( ~ ( contains_pq @ SV213 @ SV262 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV213 @ SV262 ) )
= $true )
| ( ( ( findmin_pq_res @ SV213 @ SV262 )
= SV262 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[975]) ).
thf(1035,plain,
! [SV263: $i,SV214: $i] :
( ( ( ~ ( contains_pq @ SV214 @ SV263 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV214 @ SV263 ) )
= $true )
| ( ( ( removemin_pq_eff @ SV214 @ SV263 )
= ( remove_pq @ SV214 @ SV263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[976]) ).
thf(1036,plain,
! [SV264: $i,SV215: $i] :
( ( ( ~ ( contains_pq @ SV215 @ SV264 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV215 @ SV264 ) )
= $true )
| ( ( ( removemin_pq_res @ SV215 @ SV264 )
= SV264 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[977]) ).
thf(1037,plain,
! [SV221: $i,SV303: $i,SV269: $i] :
( ( ( ( SV269 = SV303 )
| ~ ( contains_slb @ SV221 @ SV303 ) )
= $true )
| ( ( ! [SY602: $i] :
( ( remove_slb @ ( insert_slb @ SV221 @ ( pair @ SV269 @ SY602 ) ) @ SV303 )
= ( insert_slb @ ( remove_slb @ SV221 @ SV303 ) @ ( pair @ SV269 @ SY602 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[982]) ).
thf(1038,plain,
! [SV223: $i,SV305: $i,SV271: $i] :
( ( ( ( SV271 = SV305 )
| ~ ( contains_slb @ SV223 @ SV305 ) )
= $true )
| ( ( ! [SY603: $i] :
( ( lookup_slb @ ( insert_slb @ SV223 @ ( pair @ SV271 @ SY603 ) ) @ SV305 )
= ( lookup_slb @ SV223 @ SV305 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[984]) ).
thf(1039,plain,
! [SV272: $i,SV225: $i,SV306: $i,SV317: $i] :
( ( ~ ( strictly_less_than @ SV317 @ SV306 )
| ( ( update_slb @ ( insert_slb @ SV225 @ ( pair @ SV272 @ SV317 ) ) @ SV306 )
= ( insert_slb @ ( update_slb @ SV225 @ SV306 ) @ ( pair @ SV272 @ SV306 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1040,plain,
! [SV273: $i,SV226: $i,SV318: $i,SV307: $i] :
( ( ~ ( less_than @ SV307 @ SV318 )
| ( ( update_slb @ ( insert_slb @ SV226 @ ( pair @ SV273 @ SV318 ) ) @ SV307 )
= ( insert_slb @ ( update_slb @ SV226 @ SV307 ) @ ( pair @ SV273 @ SV318 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1041,plain,
! [SV274: $i,SV228: $i] :
( ( ( succ_cpq @ SV228 @ SV274 )
= $false )
| ( ( ! [SY557: $i] : ( succ_cpq @ SV228 @ ( insert_cpq @ SV274 @ SY557 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1042,plain,
! [SV275: $i,SV229: $i] :
( ( ( succ_cpq @ SV229 @ SV275 )
= $false )
| ( ( ! [SY558: $i] : ( succ_cpq @ SV229 @ ( remove_cpq @ SV275 @ SY558 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1043,plain,
! [SV276: $i,SV230: $i] :
( ( ( succ_cpq @ SV230 @ SV276 )
= $false )
| ( ( succ_cpq @ SV230 @ ( findmin_cpq_eff @ SV276 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1044,plain,
! [SV277: $i,SV231: $i] :
( ( ( succ_cpq @ SV231 @ SV277 )
= $false )
| ( ( succ_cpq @ SV231 @ ( removemin_cpq_eff @ SV277 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1045,plain,
! [SV308: $i,SV279: $i,SV233: $i,SV319: $i] :
( ( ! [SY626: $i] :
( ~ ( strictly_less_than @ SV319 @ SY626 )
| ~ ( check_cpq @ ( triple @ SV233 @ ( insert_slb @ SV279 @ ( pair @ SV319 @ SY626 ) ) @ SV308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1046,plain,
! [SV309: $i,SV281: $i,SV235: $i] :
( ( ( ok @ ( triple @ SV235 @ SV281 @ SV309 ) )
= $true )
| ( ( SV309 = bad )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[993]) ).
thf(1047,plain,
! [SV320: $i,SV310: $i,SV282: $i,SV236: $i] :
( ( ( insert_cpq @ ( triple @ SV236 @ SV282 @ SV310 ) @ SV320 )
= ( triple @ ( insert_pqp @ SV236 @ SV320 ) @ ( insert_slb @ SV282 @ ( pair @ SV320 @ bottom ) ) @ SV310 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1048,plain,
! [SV311: $i,SV237: $i,SV321: $i,SV283: $i] :
( ( ( contains_slb @ SV283 @ SV321 )
| ( ( remove_cpq @ ( triple @ SV237 @ SV283 @ SV311 ) @ SV321 )
= ( triple @ SV237 @ SV283 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1049,plain,
! [SV312: $i,SV238: $i,SV322: $i,SV284: $i] :
( ( ~ ( contains_slb @ SV284 @ SV322 )
| ~ ( less_than @ ( lookup_slb @ SV284 @ SV322 ) @ SV322 )
| ( ( remove_cpq @ ( triple @ SV238 @ SV284 @ SV312 ) @ SV322 )
= ( triple @ ( remove_pqp @ SV238 @ SV322 ) @ ( remove_slb @ SV284 @ SV322 ) @ SV312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1050,plain,
! [SV313: $i,SV239: $i,SV323: $i,SV285: $i] :
( ( ~ ( contains_slb @ SV285 @ SV323 )
| ~ ( strictly_less_than @ SV323 @ ( lookup_slb @ SV285 @ SV323 ) )
| ( ( remove_cpq @ ( triple @ SV239 @ SV285 @ SV313 ) @ SV323 )
= ( triple @ ( remove_pqp @ SV239 @ SV323 ) @ ( remove_slb @ SV285 @ SV323 ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1051,plain,
! [SV241: $i,SV287: $i] :
( ( ( SV287 = create_slb )
= $true )
| ( ( contains_slb @ SV287 @ ( findmin_pqp_res @ SV241 ) )
= $true )
| ( ( ! [SY571: $i] :
( ( findmin_cpq_eff @ ( triple @ SV241 @ SV287 @ SY571 ) )
= ( triple @ SV241 @ ( update_slb @ SV287 @ ( findmin_pqp_res @ SV241 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[998]) ).
thf(1052,plain,
! [SV242: $i,SV288: $i] :
( ( ( ( SV288 = create_slb )
| ~ ( contains_slb @ SV288 @ ( findmin_pqp_res @ SV242 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV242 ) @ ( lookup_slb @ SV288 @ ( findmin_pqp_res @ SV242 ) ) ) )
= $true )
| ( ( ! [SY572: $i] :
( ( findmin_cpq_eff @ ( triple @ SV242 @ SV288 @ SY572 ) )
= ( triple @ SV242 @ ( update_slb @ SV288 @ ( findmin_pqp_res @ SV242 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[999]) ).
thf(1053,plain,
! [SV243: $i,SV289: $i] :
( ( ( ( SV289 = create_slb )
| ~ ( contains_slb @ SV289 @ ( findmin_pqp_res @ SV243 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV289 @ ( findmin_pqp_res @ SV243 ) ) @ ( findmin_pqp_res @ SV243 ) ) )
= $true )
| ( ( ! [SY573: $i] :
( ( findmin_cpq_eff @ ( triple @ SV243 @ SV289 @ SY573 ) )
= ( triple @ SV243 @ ( update_slb @ SV289 @ ( findmin_pqp_res @ SV243 ) ) @ SY573 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1000]) ).
thf(1054,plain,
! [SV324: $i,SV291: $i,SV245: $i] :
( ( ( ( findmin_cpq_res @ ( triple @ SV245 @ SV291 @ SV324 ) )
= ( findmin_pqp_res @ SV245 ) )
= $true )
| ( ( SV291 = create_slb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1055,plain,
! [SV314: $i,SV325: $i,SV293: $i,SV249: $i] :
( ( ! [SY627: $i] :
( ( i @ ( triple @ SV249 @ ( insert_slb @ SV293 @ ( pair @ SV325 @ SY627 ) ) @ SV314 ) )
= ( insert_pq @ ( i @ ( triple @ SV249 @ SV293 @ SV314 ) ) @ SV325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1056,plain,
! [SV326: $i] :
( ( ! [SY628: $i] :
( ~ ( ~ ( contains_pq @ SV326 @ ( sK15_W @ SY628 @ SV326 ) )
| ~ ~ ( less_than @ SY628 @ ( sK15_W @ SY628 @ SV326 ) ) )
| ( issmallestelement_pq @ SV326 @ SY628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1057,plain,
! [SV327: $i] :
( ( ! [SY629: $i] :
( ~ ( issmallestelement_pq @ SV327 @ SY629 )
| ! [SY630: $i] :
( ~ ( contains_pq @ SV327 @ SY630 )
| ( less_than @ SY629 @ SY630 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1058,plain,
! [SV328: $i] :
( ( ! [SY631: $i] :
( ~ ( ok @ SY631 )
| ~ ( succ_cpq @ SV328 @ SY631 )
| ~ ( check_cpq @ SY631 ) )
| ( phi @ SV328 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1059,plain,
! [SV329: $i] :
( ( ~ ( phi @ SV329 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK12_V @ SV329 ) )
| ~ ( succ_cpq @ SV329 @ ( sK12_V @ SV329 ) ) )
| ~ ( check_cpq @ ( sK12_V @ SV329 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1060,plain,
! [SV250: $i] :
( ( ! [SY505: $i,SY506: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV250 @ SY505 ) @ SY506 )
| ( SY505 = SY506 )
| ( contains_pq @ SV250 @ SY506 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1007]) ).
thf(1061,plain,
! [SV250: $i] :
( ( ~ ( ~ ! [SY507: $i,SY508: $i] :
( ( SY507 != SY508 )
| ( contains_pq @ ( insert_pq @ SV250 @ SY507 ) @ SY508 ) )
| ~ ! [SY509: $i,SY510: $i] :
( ~ ( contains_pq @ SV250 @ SY510 )
| ( contains_pq @ ( insert_pq @ SV250 @ SY509 ) @ SY510 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1008]) ).
thf(1062,plain,
! [SV330: $i] :
( ( ! [SY632: $i] :
~ ( pi_sharp_find_min @ ( i @ SV330 ) @ SY632 )
| ( pi_find_min @ SV330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1063,plain,
! [SV331: $i] :
( ( ~ ( pi_find_min @ SV331 )
| ( pi_sharp_find_min @ ( i @ SV331 ) @ ( sK14_V @ SV331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1064,plain,
! [SV332: $i] :
( ( ! [SY633: $i] :
( ~ ( contains_pq @ SV332 @ SY633 )
| ~ ( issmallestelement_pq @ SV332 @ SY633 )
| ( pi_sharp_find_min @ SV332 @ SY633 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1065,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)],[1012]) ).
thf(1066,plain,
! [SV315: $i,SV294: $i,SV251: $i] :
( ( ~ ~ ( ~ ! [SY614: $i,SY615: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY614 ) ) @ SV315 @ SY615 )
| ( SV294 = SV315 )
| ( pair_in_list @ SV251 @ SV315 @ SY615 ) )
| ~ ! [SY616: $i,SY617: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY616 ) ) @ SV315 @ SY617 )
| ( SY616 = SY617 )
| ( pair_in_list @ SV251 @ SV315 @ SY617 ) ) )
| ~ ~ ( ~ ! [SY618: $i,SY619: $i] :
( ( SV294 != SV315 )
| ( SY618 != SY619 )
| ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY618 ) ) @ SV315 @ SY619 ) )
| ~ ! [SY620: $i,SY621: $i] :
( ~ ( pair_in_list @ SV251 @ SV315 @ SY621 )
| ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY620 ) ) @ SV315 @ SY621 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1067,plain,
! [SV333: $i] :
( ( ! [SY634: $i] :
( ~ ( contains_pq @ SV333 @ SY634 )
| ( pi_sharp_remove @ SV333 @ SY634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1068,plain,
! [SV334: $i] :
( ( ! [SY635: $i] :
( ~ ( pi_sharp_remove @ SV334 @ SY635 )
| ( contains_pq @ SV334 @ SY635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1069,plain,
! [SV335: $i] :
( ( ! [SY636: $i] :
( ~ ( less_than @ SV335 @ SY636 )
| ( less_than @ SY636 @ SV335 )
| ( strictly_less_than @ SV335 @ SY636 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1070,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)],[1017]) ).
thf(1071,plain,
! [SV295: $i,SV252: $i] :
( ( ~ ! [SY587: $i,SY588: $i] :
( ~ ( contains_cpq @ ( triple @ SV252 @ SV295 @ SY587 ) @ SY588 )
| ( contains_slb @ SV295 @ SY588 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1018]) ).
thf(1072,plain,
! [SV252: $i,SV295: $i] :
( ( ~ ! [SY589: $i,SY590: $i] :
( ~ ( contains_slb @ SV295 @ SY590 )
| ( contains_cpq @ ( triple @ SV252 @ SV295 @ SY589 ) @ SY590 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1018]) ).
thf(1073,plain,
! [SV336: $i] :
( ( ! [SY637: $i] :
( ~ ( contains_pq @ SV336 @ SY637 )
| ~ ( issmallestelement_pq @ SV336 @ SY637 )
| ( pi_sharp_removemin @ SV336 @ SY637 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1074,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)],[1020]) ).
thf(1075,plain,
! [SV337: $i] :
( ( ! [SY638: $i] :
( ~ ( pi_remove @ SV337 @ SY638 )
| ( pi_sharp_remove @ ( i @ SV337 ) @ SY638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1076,plain,
! [SV338: $i] :
( ( ! [SY639: $i] :
( ~ ( pi_sharp_remove @ ( i @ SV338 ) @ SY639 )
| ( pi_remove @ SV338 @ SY639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1077,plain,
! [SV316: $i,SV296: $i,SV253: $i] :
( ( ~ ! [SY622: $i,SY623: $i] :
( ~ ( less_than @ SY623 @ SY622 )
| ~ ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SV296 @ ( pair @ SY622 @ SY623 ) ) @ SV316 ) )
| ( check_cpq @ ( triple @ SV253 @ SV296 @ SV316 ) ) )
| ~ ! [SY624: $i,SY625: $i] :
( ~ ( less_than @ SY625 @ SY624 )
| ~ ( check_cpq @ ( triple @ SV253 @ SV296 @ SV316 ) )
| ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SV296 @ ( pair @ SY624 @ SY625 ) ) @ SV316 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1078,plain,
! [SV254: $i] :
( ( ! [SY532: $i,SY533: $i] :
( ~ ( contains_cpq @ ( triple @ SV254 @ sK1_U @ SY532 ) @ SY533 )
| ( contains_pq @ ( i @ ( triple @ SV254 @ sK1_U @ SY532 ) ) @ SY533 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1024]) ).
thf(1079,plain,
! [SV254: $i] :
( ( ! [SY534: $i,SY535: $i] :
( ~ ( contains_pq @ ( i @ ( triple @ SV254 @ sK1_U @ SY534 ) ) @ SY535 )
| ( contains_cpq @ ( triple @ SV254 @ sK1_U @ SY534 ) @ SY535 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1025]) ).
thf(1080,plain,
( ( contains_cpq @ ( triple @ sK7_SY175 @ ( insert_slb @ sK1_U @ ( pair @ sK9_SY194 @ sK10_SY197 ) ) @ sK8_SY190 ) @ sK11_SY199 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1027]) ).
thf(1081,plain,
! [SV339: $i] :
( ( ! [SY640: $i] :
~ ( pi_sharp_find_min @ ( i @ SV339 ) @ SY640 )
| ( pi_removemin @ SV339 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1082,plain,
! [SV340: $i] :
( ( ~ ( pi_removemin @ SV340 )
| ( pi_sharp_find_min @ ( i @ SV340 ) @ ( sK13_V @ SV340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1083,plain,
! [SV297: $i,SV255: $i] :
( ( ~ ! [SY596: $i] :
( ! [SY597: $i] :
~ ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY597 ) ) @ SY596 )
| ( SV297 = SY596 )
| ( contains_slb @ SV255 @ SY596 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1030]) ).
thf(1084,plain,
! [SV255: $i,SV297: $i] :
( ( ~ ~ ( ~ ! [SY598: $i] :
( ( SV297 != SY598 )
| ! [SY599: $i] : ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY599 ) ) @ SY598 ) )
| ~ ! [SY600: $i] :
( ~ ( contains_slb @ SV255 @ SY600 )
| ! [SY601: $i] : ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY601 ) ) @ SY600 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1030]) ).
thf(1085,plain,
! [SV298: $i,SV256: $i,SV204: $i] :
( ( ( ~ ( less_than @ SV204 @ SV256 ) )
= $true )
| ( ( ~ ( less_than @ SV256 @ SV298 ) )
= $true )
| ( ( less_than @ SV204 @ SV298 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1031]) ).
thf(1086,plain,
! [SV211: $i,SV299: $i,SV260: $i] :
( ( ( SV260 = SV299 )
= $true )
| ( ( ~ ( contains_pq @ SV211 @ SV299 ) )
= $true )
| ( ( ( remove_pq @ ( insert_pq @ SV211 @ SV260 ) @ SV299 )
= ( insert_pq @ ( remove_pq @ SV211 @ SV299 ) @ SV260 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1087,plain,
! [SV261: $i,SV212: $i] :
( ( ( contains_pq @ SV212 @ SV261 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV212 @ SV261 ) )
= $true )
| ( ( ( findmin_pq_eff @ SV212 @ SV261 )
= SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1033]) ).
thf(1088,plain,
! [SV262: $i,SV213: $i] :
( ( ( contains_pq @ SV213 @ SV262 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV213 @ SV262 ) )
= $true )
| ( ( ( findmin_pq_res @ SV213 @ SV262 )
= SV262 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1089,plain,
! [SV263: $i,SV214: $i] :
( ( ( contains_pq @ SV214 @ SV263 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV214 @ SV263 ) )
= $true )
| ( ( ( removemin_pq_eff @ SV214 @ SV263 )
= ( remove_pq @ SV214 @ SV263 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1090,plain,
! [SV264: $i,SV215: $i] :
( ( ( contains_pq @ SV215 @ SV264 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV215 @ SV264 ) )
= $true )
| ( ( ( removemin_pq_res @ SV215 @ SV264 )
= SV264 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1091,plain,
! [SV221: $i,SV303: $i,SV269: $i] :
( ( ( SV269 = SV303 )
= $true )
| ( ( ~ ( contains_slb @ SV221 @ SV303 ) )
= $true )
| ( ( ! [SY602: $i] :
( ( remove_slb @ ( insert_slb @ SV221 @ ( pair @ SV269 @ SY602 ) ) @ SV303 )
= ( insert_slb @ ( remove_slb @ SV221 @ SV303 ) @ ( pair @ SV269 @ SY602 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1037]) ).
thf(1092,plain,
! [SV223: $i,SV305: $i,SV271: $i] :
( ( ( SV271 = SV305 )
= $true )
| ( ( ~ ( contains_slb @ SV223 @ SV305 ) )
= $true )
| ( ( ! [SY603: $i] :
( ( lookup_slb @ ( insert_slb @ SV223 @ ( pair @ SV271 @ SY603 ) ) @ SV305 )
= ( lookup_slb @ SV223 @ SV305 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1038]) ).
thf(1093,plain,
! [SV272: $i,SV225: $i,SV306: $i,SV317: $i] :
( ( ( ~ ( strictly_less_than @ SV317 @ SV306 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV225 @ ( pair @ SV272 @ SV317 ) ) @ SV306 )
= ( insert_slb @ ( update_slb @ SV225 @ SV306 ) @ ( pair @ SV272 @ SV306 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1039]) ).
thf(1094,plain,
! [SV273: $i,SV226: $i,SV318: $i,SV307: $i] :
( ( ( ~ ( less_than @ SV307 @ SV318 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV226 @ ( pair @ SV273 @ SV318 ) ) @ SV307 )
= ( insert_slb @ ( update_slb @ SV226 @ SV307 ) @ ( pair @ SV273 @ SV318 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1040]) ).
thf(1095,plain,
! [SV341: $i,SV274: $i,SV228: $i] :
( ( ( succ_cpq @ SV228 @ ( insert_cpq @ SV274 @ SV341 ) )
= $true )
| ( ( succ_cpq @ SV228 @ SV274 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1096,plain,
! [SV342: $i,SV275: $i,SV229: $i] :
( ( ( succ_cpq @ SV229 @ ( remove_cpq @ SV275 @ SV342 ) )
= $true )
| ( ( succ_cpq @ SV229 @ SV275 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1097,plain,
! [SV308: $i,SV279: $i,SV233: $i,SV343: $i,SV319: $i] :
( ( ~ ( strictly_less_than @ SV319 @ SV343 )
| ~ ( check_cpq @ ( triple @ SV233 @ ( insert_slb @ SV279 @ ( pair @ SV319 @ SV343 ) ) @ SV308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1098,plain,
! [SV311: $i,SV237: $i,SV321: $i,SV283: $i] :
( ( ( contains_slb @ SV283 @ SV321 )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV237 @ SV283 @ SV311 ) @ SV321 )
= ( triple @ SV237 @ SV283 @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1099,plain,
! [SV312: $i,SV238: $i,SV322: $i,SV284: $i] :
( ( ( ~ ( contains_slb @ SV284 @ SV322 )
| ~ ( less_than @ ( lookup_slb @ SV284 @ SV322 ) @ SV322 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV238 @ SV284 @ SV312 ) @ SV322 )
= ( triple @ ( remove_pqp @ SV238 @ SV322 ) @ ( remove_slb @ SV284 @ SV322 ) @ SV312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1049]) ).
thf(1100,plain,
! [SV313: $i,SV239: $i,SV323: $i,SV285: $i] :
( ( ( ~ ( contains_slb @ SV285 @ SV323 )
| ~ ( strictly_less_than @ SV323 @ ( lookup_slb @ SV285 @ SV323 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV239 @ SV285 @ SV313 ) @ SV323 )
= ( triple @ ( remove_pqp @ SV239 @ SV323 ) @ ( remove_slb @ SV285 @ SV323 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1050]) ).
thf(1101,plain,
! [SV344: $i,SV287: $i,SV241: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV241 @ SV287 @ SV344 ) )
= ( triple @ SV241 @ ( update_slb @ SV287 @ ( findmin_pqp_res @ SV241 ) ) @ bad ) )
= $true )
| ( ( contains_slb @ SV287 @ ( findmin_pqp_res @ SV241 ) )
= $true )
| ( ( SV287 = create_slb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1102,plain,
! [SV242: $i,SV288: $i] :
( ( ( SV288 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV288 @ ( findmin_pqp_res @ SV242 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV242 ) @ ( lookup_slb @ SV288 @ ( findmin_pqp_res @ SV242 ) ) ) )
= $true )
| ( ( ! [SY572: $i] :
( ( findmin_cpq_eff @ ( triple @ SV242 @ SV288 @ SY572 ) )
= ( triple @ SV242 @ ( update_slb @ SV288 @ ( findmin_pqp_res @ SV242 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1052]) ).
thf(1103,plain,
! [SV243: $i,SV289: $i] :
( ( ( SV289 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV289 @ ( findmin_pqp_res @ SV243 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV289 @ ( findmin_pqp_res @ SV243 ) ) @ ( findmin_pqp_res @ SV243 ) ) )
= $true )
| ( ( ! [SY573: $i] :
( ( findmin_cpq_eff @ ( triple @ SV243 @ SV289 @ SY573 ) )
= ( triple @ SV243 @ ( update_slb @ SV289 @ ( findmin_pqp_res @ SV243 ) ) @ SY573 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1053]) ).
thf(1104,plain,
! [SV314: $i,SV345: $i,SV325: $i,SV293: $i,SV249: $i] :
( ( ( i @ ( triple @ SV249 @ ( insert_slb @ SV293 @ ( pair @ SV325 @ SV345 ) ) @ SV314 ) )
= ( insert_pq @ ( i @ ( triple @ SV249 @ SV293 @ SV314 ) ) @ SV325 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1105,plain,
! [SV346: $i,SV326: $i] :
( ( ~ ( ~ ( contains_pq @ SV326 @ ( sK15_W @ SV346 @ SV326 ) )
| ~ ~ ( less_than @ SV346 @ ( sK15_W @ SV346 @ SV326 ) ) )
| ( issmallestelement_pq @ SV326 @ SV346 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1106,plain,
! [SV347: $i,SV327: $i] :
( ( ~ ( issmallestelement_pq @ SV327 @ SV347 )
| ! [SY641: $i] :
( ~ ( contains_pq @ SV327 @ SY641 )
| ( less_than @ SV347 @ SY641 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1107,plain,
! [SV328: $i] :
( ( ( ! [SY631: $i] :
( ~ ( ok @ SY631 )
| ~ ( succ_cpq @ SV328 @ SY631 )
| ~ ( check_cpq @ SY631 ) ) )
= $true )
| ( ( phi @ SV328 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1058]) ).
thf(1108,plain,
! [SV329: $i] :
( ( ( ~ ( phi @ SV329 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ok @ ( sK12_V @ SV329 ) )
| ~ ( succ_cpq @ SV329 @ ( sK12_V @ SV329 ) ) )
| ~ ( check_cpq @ ( sK12_V @ SV329 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1059]) ).
thf(1109,plain,
! [SV348: $i,SV250: $i] :
( ( ! [SY642: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV250 @ SV348 ) @ SY642 )
| ( SV348 = SY642 )
| ( contains_pq @ SV250 @ SY642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1110,plain,
! [SV250: $i] :
( ( ~ ! [SY507: $i,SY508: $i] :
( ( SY507 != SY508 )
| ( contains_pq @ ( insert_pq @ SV250 @ SY507 ) @ SY508 ) )
| ~ ! [SY509: $i,SY510: $i] :
( ~ ( contains_pq @ SV250 @ SY510 )
| ( contains_pq @ ( insert_pq @ SV250 @ SY509 ) @ SY510 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1061]) ).
thf(1111,plain,
! [SV330: $i] :
( ( ( ! [SY632: $i] :
~ ( pi_sharp_find_min @ ( i @ SV330 ) @ SY632 ) )
= $true )
| ( ( pi_find_min @ SV330 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1062]) ).
thf(1112,plain,
! [SV331: $i] :
( ( ( ~ ( pi_find_min @ SV331 ) )
= $true )
| ( ( pi_sharp_find_min @ ( i @ SV331 ) @ ( sK14_V @ SV331 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1063]) ).
thf(1113,plain,
! [SV349: $i,SV332: $i] :
( ( ~ ( contains_pq @ SV332 @ SV349 )
| ~ ( issmallestelement_pq @ SV332 @ SV349 )
| ( pi_sharp_find_min @ SV332 @ SV349 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1114,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1065]) ).
thf(1115,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1065]) ).
thf(1116,plain,
! [SV315: $i,SV294: $i,SV251: $i] :
( ( ~ ~ ( ~ ! [SY614: $i,SY615: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY614 ) ) @ SV315 @ SY615 )
| ( SV294 = SV315 )
| ( pair_in_list @ SV251 @ SV315 @ SY615 ) )
| ~ ! [SY616: $i,SY617: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY616 ) ) @ SV315 @ SY617 )
| ( SY616 = SY617 )
| ( pair_in_list @ SV251 @ SV315 @ SY617 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1066]) ).
thf(1117,plain,
! [SV251: $i,SV315: $i,SV294: $i] :
( ( ~ ~ ( ~ ! [SY618: $i,SY619: $i] :
( ( SV294 != SV315 )
| ( SY618 != SY619 )
| ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY618 ) ) @ SV315 @ SY619 ) )
| ~ ! [SY620: $i,SY621: $i] :
( ~ ( pair_in_list @ SV251 @ SV315 @ SY621 )
| ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY620 ) ) @ SV315 @ SY621 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1066]) ).
thf(1118,plain,
! [SV350: $i,SV333: $i] :
( ( ~ ( contains_pq @ SV333 @ SV350 )
| ( pi_sharp_remove @ SV333 @ SV350 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1119,plain,
! [SV351: $i,SV334: $i] :
( ( ~ ( pi_sharp_remove @ SV334 @ SV351 )
| ( contains_pq @ SV334 @ SV351 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1120,plain,
! [SV352: $i,SV335: $i] :
( ( ~ ( less_than @ SV335 @ SV352 )
| ( less_than @ SV352 @ SV335 )
| ( strictly_less_than @ SV335 @ SV352 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1121,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1070]) ).
thf(1122,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1070]) ).
thf(1123,plain,
! [SV295: $i,SV252: $i] :
( ( ! [SY587: $i,SY588: $i] :
( ~ ( contains_cpq @ ( triple @ SV252 @ SV295 @ SY587 ) @ SY588 )
| ( contains_slb @ SV295 @ SY588 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1071]) ).
thf(1124,plain,
! [SV252: $i,SV295: $i] :
( ( ! [SY589: $i,SY590: $i] :
( ~ ( contains_slb @ SV295 @ SY590 )
| ( contains_cpq @ ( triple @ SV252 @ SV295 @ SY589 ) @ SY590 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1072]) ).
thf(1125,plain,
! [SV353: $i,SV336: $i] :
( ( ~ ( contains_pq @ SV336 @ SV353 )
| ~ ( issmallestelement_pq @ SV336 @ SV353 )
| ( pi_sharp_removemin @ SV336 @ SV353 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1126,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1074]) ).
thf(1127,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1074]) ).
thf(1128,plain,
! [SV354: $i,SV337: $i] :
( ( ~ ( pi_remove @ SV337 @ SV354 )
| ( pi_sharp_remove @ ( i @ SV337 ) @ SV354 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1129,plain,
! [SV355: $i,SV338: $i] :
( ( ~ ( pi_sharp_remove @ ( i @ SV338 ) @ SV355 )
| ( pi_remove @ SV338 @ SV355 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1130,plain,
! [SV316: $i,SV296: $i,SV253: $i] :
( ( ~ ! [SY622: $i,SY623: $i] :
( ~ ( less_than @ SY623 @ SY622 )
| ~ ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SV296 @ ( pair @ SY622 @ SY623 ) ) @ SV316 ) )
| ( check_cpq @ ( triple @ SV253 @ SV296 @ SV316 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1077]) ).
thf(1131,plain,
! [SV316: $i,SV296: $i,SV253: $i] :
( ( ~ ! [SY624: $i,SY625: $i] :
( ~ ( less_than @ SY625 @ SY624 )
| ~ ( check_cpq @ ( triple @ SV253 @ SV296 @ SV316 ) )
| ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SV296 @ ( pair @ SY624 @ SY625 ) ) @ SV316 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1077]) ).
thf(1132,plain,
! [SV356: $i,SV254: $i] :
( ( ! [SY643: $i] :
( ~ ( contains_cpq @ ( triple @ SV254 @ sK1_U @ SV356 ) @ SY643 )
| ( contains_pq @ ( i @ ( triple @ SV254 @ sK1_U @ SV356 ) ) @ SY643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1133,plain,
! [SV357: $i,SV254: $i] :
( ( ! [SY644: $i] :
( ~ ( contains_pq @ ( i @ ( triple @ SV254 @ sK1_U @ SV357 ) ) @ SY644 )
| ( contains_cpq @ ( triple @ SV254 @ sK1_U @ SV357 ) @ SY644 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1134,plain,
! [SV339: $i] :
( ( ( ! [SY640: $i] :
~ ( pi_sharp_find_min @ ( i @ SV339 ) @ SY640 ) )
= $true )
| ( ( pi_removemin @ SV339 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1081]) ).
thf(1135,plain,
! [SV340: $i] :
( ( ( ~ ( pi_removemin @ SV340 ) )
= $true )
| ( ( pi_sharp_find_min @ ( i @ SV340 ) @ ( sK13_V @ SV340 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1082]) ).
thf(1136,plain,
! [SV297: $i,SV255: $i] :
( ( ! [SY596: $i] :
( ! [SY597: $i] :
~ ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY597 ) ) @ SY596 )
| ( SV297 = SY596 )
| ( contains_slb @ SV255 @ SY596 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1083]) ).
thf(1137,plain,
! [SV255: $i,SV297: $i] :
( ( ~ ( ~ ! [SY598: $i] :
( ( SV297 != SY598 )
| ! [SY599: $i] : ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY599 ) ) @ SY598 ) )
| ~ ! [SY600: $i] :
( ~ ( contains_slb @ SV255 @ SY600 )
| ! [SY601: $i] : ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY601 ) ) @ SY600 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1084]) ).
thf(1138,plain,
! [SV298: $i,SV256: $i,SV204: $i] :
( ( ( less_than @ SV204 @ SV256 )
= $false )
| ( ( ~ ( less_than @ SV256 @ SV298 ) )
= $true )
| ( ( less_than @ SV204 @ SV298 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1139,plain,
! [SV260: $i,SV299: $i,SV211: $i] :
( ( ( contains_pq @ SV211 @ SV299 )
= $false )
| ( ( SV260 = SV299 )
= $true )
| ( ( ( remove_pq @ ( insert_pq @ SV211 @ SV260 ) @ SV299 )
= ( insert_pq @ ( remove_pq @ SV211 @ SV299 ) @ SV260 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1140,plain,
! [SV261: $i,SV212: $i] :
( ( ( issmallestelement_pq @ SV212 @ SV261 )
= $false )
| ( ( contains_pq @ SV212 @ SV261 )
= $false )
| ( ( ( findmin_pq_eff @ SV212 @ SV261 )
= SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1087]) ).
thf(1141,plain,
! [SV262: $i,SV213: $i] :
( ( ( issmallestelement_pq @ SV213 @ SV262 )
= $false )
| ( ( contains_pq @ SV213 @ SV262 )
= $false )
| ( ( ( findmin_pq_res @ SV213 @ SV262 )
= SV262 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1142,plain,
! [SV263: $i,SV214: $i] :
( ( ( issmallestelement_pq @ SV214 @ SV263 )
= $false )
| ( ( contains_pq @ SV214 @ SV263 )
= $false )
| ( ( ( removemin_pq_eff @ SV214 @ SV263 )
= ( remove_pq @ SV214 @ SV263 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1143,plain,
! [SV264: $i,SV215: $i] :
( ( ( issmallestelement_pq @ SV215 @ SV264 )
= $false )
| ( ( contains_pq @ SV215 @ SV264 )
= $false )
| ( ( ( removemin_pq_res @ SV215 @ SV264 )
= SV264 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1090]) ).
thf(1144,plain,
! [SV269: $i,SV303: $i,SV221: $i] :
( ( ( contains_slb @ SV221 @ SV303 )
= $false )
| ( ( SV269 = SV303 )
= $true )
| ( ( ! [SY602: $i] :
( ( remove_slb @ ( insert_slb @ SV221 @ ( pair @ SV269 @ SY602 ) ) @ SV303 )
= ( insert_slb @ ( remove_slb @ SV221 @ SV303 ) @ ( pair @ SV269 @ SY602 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1145,plain,
! [SV271: $i,SV305: $i,SV223: $i] :
( ( ( contains_slb @ SV223 @ SV305 )
= $false )
| ( ( SV271 = SV305 )
= $true )
| ( ( ! [SY603: $i] :
( ( lookup_slb @ ( insert_slb @ SV223 @ ( pair @ SV271 @ SY603 ) ) @ SV305 )
= ( lookup_slb @ SV223 @ SV305 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1146,plain,
! [SV272: $i,SV225: $i,SV306: $i,SV317: $i] :
( ( ( strictly_less_than @ SV317 @ SV306 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV225 @ ( pair @ SV272 @ SV317 ) ) @ SV306 )
= ( insert_slb @ ( update_slb @ SV225 @ SV306 ) @ ( pair @ SV272 @ SV306 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1147,plain,
! [SV273: $i,SV226: $i,SV318: $i,SV307: $i] :
( ( ( less_than @ SV307 @ SV318 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV226 @ ( pair @ SV273 @ SV318 ) ) @ SV307 )
= ( insert_slb @ ( update_slb @ SV226 @ SV307 ) @ ( pair @ SV273 @ SV318 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1094]) ).
thf(1148,plain,
! [SV308: $i,SV279: $i,SV233: $i,SV343: $i,SV319: $i] :
( ( ( ~ ( strictly_less_than @ SV319 @ SV343 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV233 @ ( insert_slb @ SV279 @ ( pair @ SV319 @ SV343 ) ) @ SV308 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1097]) ).
thf(1149,plain,
! [SV312: $i,SV238: $i,SV322: $i,SV284: $i] :
( ( ( ~ ( contains_slb @ SV284 @ SV322 ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV284 @ SV322 ) @ SV322 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV238 @ SV284 @ SV312 ) @ SV322 )
= ( triple @ ( remove_pqp @ SV238 @ SV322 ) @ ( remove_slb @ SV284 @ SV322 ) @ SV312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1099]) ).
thf(1150,plain,
! [SV313: $i,SV239: $i,SV323: $i,SV285: $i] :
( ( ( ~ ( contains_slb @ SV285 @ SV323 ) )
= $true )
| ( ( ~ ( strictly_less_than @ SV323 @ ( lookup_slb @ SV285 @ SV323 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV239 @ SV285 @ SV313 ) @ SV323 )
= ( triple @ ( remove_pqp @ SV239 @ SV323 ) @ ( remove_slb @ SV285 @ SV323 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1100]) ).
thf(1151,plain,
! [SV242: $i,SV288: $i] :
( ( ( contains_slb @ SV288 @ ( findmin_pqp_res @ SV242 ) )
= $false )
| ( ( SV288 = create_slb )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV242 ) @ ( lookup_slb @ SV288 @ ( findmin_pqp_res @ SV242 ) ) ) )
= $true )
| ( ( ! [SY572: $i] :
( ( findmin_cpq_eff @ ( triple @ SV242 @ SV288 @ SY572 ) )
= ( triple @ SV242 @ ( update_slb @ SV288 @ ( findmin_pqp_res @ SV242 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1152,plain,
! [SV243: $i,SV289: $i] :
( ( ( contains_slb @ SV289 @ ( findmin_pqp_res @ SV243 ) )
= $false )
| ( ( SV289 = create_slb )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV289 @ ( findmin_pqp_res @ SV243 ) ) @ ( findmin_pqp_res @ SV243 ) ) )
= $true )
| ( ( ! [SY573: $i] :
( ( findmin_cpq_eff @ ( triple @ SV243 @ SV289 @ SY573 ) )
= ( triple @ SV243 @ ( update_slb @ SV289 @ ( findmin_pqp_res @ SV243 ) ) @ SY573 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1103]) ).
thf(1153,plain,
! [SV346: $i,SV326: $i] :
( ( ( ~ ( ~ ( contains_pq @ SV326 @ ( sK15_W @ SV346 @ SV326 ) )
| ~ ~ ( less_than @ SV346 @ ( sK15_W @ SV346 @ SV326 ) ) ) )
= $true )
| ( ( issmallestelement_pq @ SV326 @ SV346 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1105]) ).
thf(1154,plain,
! [SV347: $i,SV327: $i] :
( ( ( ~ ( issmallestelement_pq @ SV327 @ SV347 ) )
= $true )
| ( ( ! [SY641: $i] :
( ~ ( contains_pq @ SV327 @ SY641 )
| ( less_than @ SV347 @ SY641 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1106]) ).
thf(1155,plain,
! [SV328: $i,SV358: $i] :
( ( ( ~ ( ok @ SV358 )
| ~ ( succ_cpq @ SV328 @ SV358 )
| ~ ( check_cpq @ SV358 ) )
= $true )
| ( ( phi @ SV328 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1156,plain,
! [SV329: $i] :
( ( ( phi @ SV329 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( ok @ ( sK12_V @ SV329 ) )
| ~ ( succ_cpq @ SV329 @ ( sK12_V @ SV329 ) ) )
| ~ ( check_cpq @ ( sK12_V @ SV329 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1108]) ).
thf(1157,plain,
! [SV359: $i,SV348: $i,SV250: $i] :
( ( ~ ( contains_pq @ ( insert_pq @ SV250 @ SV348 ) @ SV359 )
| ( SV348 = SV359 )
| ( contains_pq @ SV250 @ SV359 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1158,plain,
! [SV250: $i] :
( ( ~ ! [SY507: $i,SY508: $i] :
( ( SY507 != SY508 )
| ( contains_pq @ ( insert_pq @ SV250 @ SY507 ) @ SY508 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1110]) ).
thf(1159,plain,
! [SV250: $i] :
( ( ~ ! [SY509: $i,SY510: $i] :
( ~ ( contains_pq @ SV250 @ SY510 )
| ( contains_pq @ ( insert_pq @ SV250 @ SY509 ) @ SY510 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1110]) ).
thf(1160,plain,
! [SV360: $i,SV330: $i] :
( ( ( ~ ( pi_sharp_find_min @ ( i @ SV330 ) @ SV360 ) )
= $true )
| ( ( pi_find_min @ SV330 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1161,plain,
! [SV331: $i] :
( ( ( pi_find_min @ SV331 )
= $false )
| ( ( pi_sharp_find_min @ ( i @ SV331 ) @ ( sK14_V @ SV331 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1162,plain,
! [SV349: $i,SV332: $i] :
( ( ( ~ ( contains_pq @ SV332 @ SV349 )
| ~ ( issmallestelement_pq @ SV332 @ SV349 ) )
= $true )
| ( ( pi_sharp_find_min @ SV332 @ SV349 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1113]) ).
thf(1163,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1114]) ).
thf(1164,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1115]) ).
thf(1165,plain,
! [SV315: $i,SV294: $i,SV251: $i] :
( ( ~ ( ~ ! [SY614: $i,SY615: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY614 ) ) @ SV315 @ SY615 )
| ( SV294 = SV315 )
| ( pair_in_list @ SV251 @ SV315 @ SY615 ) )
| ~ ! [SY616: $i,SY617: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY616 ) ) @ SV315 @ SY617 )
| ( SY616 = SY617 )
| ( pair_in_list @ SV251 @ SV315 @ SY617 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1116]) ).
thf(1166,plain,
! [SV251: $i,SV315: $i,SV294: $i] :
( ( ~ ( ~ ! [SY618: $i,SY619: $i] :
( ( SV294 != SV315 )
| ( SY618 != SY619 )
| ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY618 ) ) @ SV315 @ SY619 ) )
| ~ ! [SY620: $i,SY621: $i] :
( ~ ( pair_in_list @ SV251 @ SV315 @ SY621 )
| ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY620 ) ) @ SV315 @ SY621 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1117]) ).
thf(1167,plain,
! [SV350: $i,SV333: $i] :
( ( ( ~ ( contains_pq @ SV333 @ SV350 ) )
= $true )
| ( ( pi_sharp_remove @ SV333 @ SV350 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1118]) ).
thf(1168,plain,
! [SV351: $i,SV334: $i] :
( ( ( ~ ( pi_sharp_remove @ SV334 @ SV351 ) )
= $true )
| ( ( contains_pq @ SV334 @ SV351 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1119]) ).
thf(1169,plain,
! [SV352: $i,SV335: $i] :
( ( ( ~ ( less_than @ SV335 @ SV352 )
| ( less_than @ SV352 @ SV335 ) )
= $true )
| ( ( strictly_less_than @ SV335 @ SV352 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1120]) ).
thf(1170,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1121]) ).
thf(1171,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1122]) ).
thf(1172,plain,
! [SV361: $i,SV295: $i,SV252: $i] :
( ( ! [SY645: $i] :
( ~ ( contains_cpq @ ( triple @ SV252 @ SV295 @ SV361 ) @ SY645 )
| ( contains_slb @ SV295 @ SY645 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1173,plain,
! [SV362: $i,SV252: $i,SV295: $i] :
( ( ! [SY646: $i] :
( ~ ( contains_slb @ SV295 @ SY646 )
| ( contains_cpq @ ( triple @ SV252 @ SV295 @ SV362 ) @ SY646 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1174,plain,
! [SV353: $i,SV336: $i] :
( ( ( ~ ( contains_pq @ SV336 @ SV353 )
| ~ ( issmallestelement_pq @ SV336 @ SV353 ) )
= $true )
| ( ( pi_sharp_removemin @ SV336 @ SV353 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1125]) ).
thf(1175,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1126]) ).
thf(1176,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1127]) ).
thf(1177,plain,
! [SV354: $i,SV337: $i] :
( ( ( ~ ( pi_remove @ SV337 @ SV354 ) )
= $true )
| ( ( pi_sharp_remove @ ( i @ SV337 ) @ SV354 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1128]) ).
thf(1178,plain,
! [SV355: $i,SV338: $i] :
( ( ( ~ ( pi_sharp_remove @ ( i @ SV338 ) @ SV355 ) )
= $true )
| ( ( pi_remove @ SV338 @ SV355 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1129]) ).
thf(1179,plain,
! [SV316: $i,SV296: $i,SV253: $i] :
( ( ! [SY622: $i,SY623: $i] :
( ~ ( less_than @ SY623 @ SY622 )
| ~ ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SV296 @ ( pair @ SY622 @ SY623 ) ) @ SV316 ) )
| ( check_cpq @ ( triple @ SV253 @ SV296 @ SV316 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1130]) ).
thf(1180,plain,
! [SV316: $i,SV296: $i,SV253: $i] :
( ( ! [SY624: $i,SY625: $i] :
( ~ ( less_than @ SY625 @ SY624 )
| ~ ( check_cpq @ ( triple @ SV253 @ SV296 @ SV316 ) )
| ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SV296 @ ( pair @ SY624 @ SY625 ) ) @ SV316 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1131]) ).
thf(1181,plain,
! [SV363: $i,SV356: $i,SV254: $i] :
( ( ~ ( contains_cpq @ ( triple @ SV254 @ sK1_U @ SV356 ) @ SV363 )
| ( contains_pq @ ( i @ ( triple @ SV254 @ sK1_U @ SV356 ) ) @ SV363 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1182,plain,
! [SV364: $i,SV357: $i,SV254: $i] :
( ( ~ ( contains_pq @ ( i @ ( triple @ SV254 @ sK1_U @ SV357 ) ) @ SV364 )
| ( contains_cpq @ ( triple @ SV254 @ sK1_U @ SV357 ) @ SV364 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1183,plain,
! [SV365: $i,SV339: $i] :
( ( ( ~ ( pi_sharp_find_min @ ( i @ SV339 ) @ SV365 ) )
= $true )
| ( ( pi_removemin @ SV339 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1184,plain,
! [SV340: $i] :
( ( ( pi_removemin @ SV340 )
= $false )
| ( ( pi_sharp_find_min @ ( i @ SV340 ) @ ( sK13_V @ SV340 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1135]) ).
thf(1185,plain,
! [SV366: $i,SV297: $i,SV255: $i] :
( ( ! [SY647: $i] :
~ ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY647 ) ) @ SV366 )
| ( SV297 = SV366 )
| ( contains_slb @ SV255 @ SV366 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1186,plain,
! [SV255: $i,SV297: $i] :
( ( ~ ! [SY598: $i] :
( ( SV297 != SY598 )
| ! [SY599: $i] : ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY599 ) ) @ SY598 ) )
| ~ ! [SY600: $i] :
( ~ ( contains_slb @ SV255 @ SY600 )
| ! [SY601: $i] : ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY601 ) ) @ SY600 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1187,plain,
! [SV204: $i,SV298: $i,SV256: $i] :
( ( ( less_than @ SV256 @ SV298 )
= $false )
| ( ( less_than @ SV204 @ SV256 )
= $false )
| ( ( less_than @ SV204 @ SV298 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1188,plain,
! [SV303: $i,SV367: $i,SV269: $i,SV221: $i] :
( ( ( ( remove_slb @ ( insert_slb @ SV221 @ ( pair @ SV269 @ SV367 ) ) @ SV303 )
= ( insert_slb @ ( remove_slb @ SV221 @ SV303 ) @ ( pair @ SV269 @ SV367 ) ) )
= $true )
| ( ( SV269 = SV303 )
= $true )
| ( ( contains_slb @ SV221 @ SV303 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1189,plain,
! [SV305: $i,SV368: $i,SV271: $i,SV223: $i] :
( ( ( ( lookup_slb @ ( insert_slb @ SV223 @ ( pair @ SV271 @ SV368 ) ) @ SV305 )
= ( lookup_slb @ SV223 @ SV305 ) )
= $true )
| ( ( SV271 = SV305 )
= $true )
| ( ( contains_slb @ SV223 @ SV305 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1190,plain,
! [SV308: $i,SV279: $i,SV233: $i,SV343: $i,SV319: $i] :
( ( ( strictly_less_than @ SV319 @ SV343 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV233 @ ( insert_slb @ SV279 @ ( pair @ SV319 @ SV343 ) ) @ SV308 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1191,plain,
! [SV312: $i,SV238: $i,SV322: $i,SV284: $i] :
( ( ( contains_slb @ SV284 @ SV322 )
= $false )
| ( ( ~ ( less_than @ ( lookup_slb @ SV284 @ SV322 ) @ SV322 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV238 @ SV284 @ SV312 ) @ SV322 )
= ( triple @ ( remove_pqp @ SV238 @ SV322 ) @ ( remove_slb @ SV284 @ SV322 ) @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1192,plain,
! [SV313: $i,SV239: $i,SV323: $i,SV285: $i] :
( ( ( contains_slb @ SV285 @ SV323 )
= $false )
| ( ( ~ ( strictly_less_than @ SV323 @ ( lookup_slb @ SV285 @ SV323 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV239 @ SV285 @ SV313 ) @ SV323 )
= ( triple @ ( remove_pqp @ SV239 @ SV323 ) @ ( remove_slb @ SV285 @ SV323 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1193,plain,
! [SV288: $i,SV242: $i] :
( ( ( strictly_less_than @ ( findmin_pqp_res @ SV242 ) @ ( lookup_slb @ SV288 @ ( findmin_pqp_res @ SV242 ) ) )
= $false )
| ( ( SV288 = create_slb )
= $true )
| ( ( contains_slb @ SV288 @ ( findmin_pqp_res @ SV242 ) )
= $false )
| ( ( ! [SY572: $i] :
( ( findmin_cpq_eff @ ( triple @ SV242 @ SV288 @ SY572 ) )
= ( triple @ SV242 @ ( update_slb @ SV288 @ ( findmin_pqp_res @ SV242 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1194,plain,
! [SV243: $i,SV289: $i] :
( ( ( less_than @ ( lookup_slb @ SV289 @ ( findmin_pqp_res @ SV243 ) ) @ ( findmin_pqp_res @ SV243 ) )
= $false )
| ( ( SV289 = create_slb )
= $true )
| ( ( contains_slb @ SV289 @ ( findmin_pqp_res @ SV243 ) )
= $false )
| ( ( ! [SY573: $i] :
( ( findmin_cpq_eff @ ( triple @ SV243 @ SV289 @ SY573 ) )
= ( triple @ SV243 @ ( update_slb @ SV289 @ ( findmin_pqp_res @ SV243 ) ) @ SY573 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1152]) ).
thf(1195,plain,
! [SV346: $i,SV326: $i] :
( ( ( ~ ( contains_pq @ SV326 @ ( sK15_W @ SV346 @ SV326 ) )
| ~ ~ ( less_than @ SV346 @ ( sK15_W @ SV346 @ SV326 ) ) )
= $false )
| ( ( issmallestelement_pq @ SV326 @ SV346 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1196,plain,
! [SV347: $i,SV327: $i] :
( ( ( issmallestelement_pq @ SV327 @ SV347 )
= $false )
| ( ( ! [SY641: $i] :
( ~ ( contains_pq @ SV327 @ SY641 )
| ( less_than @ SV347 @ SY641 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1154]) ).
thf(1197,plain,
! [SV328: $i,SV358: $i] :
( ( ( ~ ( ok @ SV358 )
| ~ ( succ_cpq @ SV328 @ SV358 ) )
= $true )
| ( ( ~ ( check_cpq @ SV358 ) )
= $true )
| ( ( phi @ SV328 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1198,plain,
! [SV329: $i] :
( ( ( ~ ~ ( ~ ( ok @ ( sK12_V @ SV329 ) )
| ~ ( succ_cpq @ SV329 @ ( sK12_V @ SV329 ) ) )
| ~ ( check_cpq @ ( sK12_V @ SV329 ) ) )
= $false )
| ( ( phi @ SV329 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1199,plain,
! [SV359: $i,SV348: $i,SV250: $i] :
( ( ( ~ ( contains_pq @ ( insert_pq @ SV250 @ SV348 ) @ SV359 ) )
= $true )
| ( ( ( SV348 = SV359 )
| ( contains_pq @ SV250 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1157]) ).
thf(1200,plain,
! [SV250: $i] :
( ( ! [SY507: $i,SY508: $i] :
( ( SY507 != SY508 )
| ( contains_pq @ ( insert_pq @ SV250 @ SY507 ) @ SY508 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1158]) ).
thf(1201,plain,
! [SV250: $i] :
( ( ! [SY509: $i,SY510: $i] :
( ~ ( contains_pq @ SV250 @ SY510 )
| ( contains_pq @ ( insert_pq @ SV250 @ SY509 ) @ SY510 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1159]) ).
thf(1202,plain,
! [SV360: $i,SV330: $i] :
( ( ( pi_sharp_find_min @ ( i @ SV330 ) @ SV360 )
= $false )
| ( ( pi_find_min @ SV330 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1160]) ).
thf(1203,plain,
! [SV349: $i,SV332: $i] :
( ( ( ~ ( contains_pq @ SV332 @ SV349 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV332 @ SV349 ) )
= $true )
| ( ( pi_sharp_find_min @ SV332 @ SV349 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1162]) ).
thf(1204,plain,
! [SV369: $i] :
( ( ! [SY648: $i] :
( ~ ( pi_sharp_find_min @ SV369 @ SY648 )
| ( contains_pq @ SV369 @ SY648 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1205,plain,
! [SV370: $i] :
( ( ! [SY649: $i] :
( ~ ( pi_sharp_find_min @ SV370 @ SY649 )
| ( issmallestelement_pq @ SV370 @ SY649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1206,plain,
! [SV315: $i,SV294: $i,SV251: $i] :
( ( ~ ! [SY614: $i,SY615: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY614 ) ) @ SV315 @ SY615 )
| ( SV294 = SV315 )
| ( pair_in_list @ SV251 @ SV315 @ SY615 ) )
| ~ ! [SY616: $i,SY617: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY616 ) ) @ SV315 @ SY617 )
| ( SY616 = SY617 )
| ( pair_in_list @ SV251 @ SV315 @ SY617 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1165]) ).
thf(1207,plain,
! [SV251: $i,SV315: $i,SV294: $i] :
( ( ~ ! [SY618: $i,SY619: $i] :
( ( SV294 != SV315 )
| ( SY618 != SY619 )
| ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY618 ) ) @ SV315 @ SY619 ) )
| ~ ! [SY620: $i,SY621: $i] :
( ~ ( pair_in_list @ SV251 @ SV315 @ SY621 )
| ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY620 ) ) @ SV315 @ SY621 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1166]) ).
thf(1208,plain,
! [SV350: $i,SV333: $i] :
( ( ( contains_pq @ SV333 @ SV350 )
= $false )
| ( ( pi_sharp_remove @ SV333 @ SV350 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1209,plain,
! [SV351: $i,SV334: $i] :
( ( ( pi_sharp_remove @ SV334 @ SV351 )
= $false )
| ( ( contains_pq @ SV334 @ SV351 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1210,plain,
! [SV352: $i,SV335: $i] :
( ( ( ~ ( less_than @ SV335 @ SV352 ) )
= $true )
| ( ( less_than @ SV352 @ SV335 )
= $true )
| ( ( strictly_less_than @ SV335 @ SV352 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1169]) ).
thf(1211,plain,
! [SV371: $i] :
( ( ! [SY650: $i] :
( ~ ( strictly_less_than @ SV371 @ SY650 )
| ( less_than @ SV371 @ SY650 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1212,plain,
! [SV372: $i] :
( ( ! [SY651: $i] :
( ~ ( strictly_less_than @ SV372 @ SY651 )
| ~ ( less_than @ SY651 @ SV372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1213,plain,
! [SV373: $i,SV361: $i,SV295: $i,SV252: $i] :
( ( ~ ( contains_cpq @ ( triple @ SV252 @ SV295 @ SV361 ) @ SV373 )
| ( contains_slb @ SV295 @ SV373 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1214,plain,
! [SV362: $i,SV252: $i,SV374: $i,SV295: $i] :
( ( ~ ( contains_slb @ SV295 @ SV374 )
| ( contains_cpq @ ( triple @ SV252 @ SV295 @ SV362 ) @ SV374 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1215,plain,
! [SV353: $i,SV336: $i] :
( ( ( ~ ( contains_pq @ SV336 @ SV353 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV336 @ SV353 ) )
= $true )
| ( ( pi_sharp_removemin @ SV336 @ SV353 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1174]) ).
thf(1216,plain,
! [SV375: $i] :
( ( ! [SY652: $i] :
( ~ ( pi_sharp_removemin @ SV375 @ SY652 )
| ( contains_pq @ SV375 @ SY652 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1217,plain,
! [SV376: $i] :
( ( ! [SY653: $i] :
( ~ ( pi_sharp_removemin @ SV376 @ SY653 )
| ( issmallestelement_pq @ SV376 @ SY653 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1218,plain,
! [SV354: $i,SV337: $i] :
( ( ( pi_remove @ SV337 @ SV354 )
= $false )
| ( ( pi_sharp_remove @ ( i @ SV337 ) @ SV354 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1177]) ).
thf(1219,plain,
! [SV355: $i,SV338: $i] :
( ( ( pi_sharp_remove @ ( i @ SV338 ) @ SV355 )
= $false )
| ( ( pi_remove @ SV338 @ SV355 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1178]) ).
thf(1220,plain,
! [SV316: $i,SV296: $i,SV253: $i,SV377: $i] :
( ( ! [SY654: $i] :
( ~ ( less_than @ SY654 @ SV377 )
| ~ ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SV296 @ ( pair @ SV377 @ SY654 ) ) @ SV316 ) )
| ( check_cpq @ ( triple @ SV253 @ SV296 @ SV316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1221,plain,
! [SV316: $i,SV296: $i,SV253: $i,SV378: $i] :
( ( ! [SY655: $i] :
( ~ ( less_than @ SY655 @ SV378 )
| ~ ( check_cpq @ ( triple @ SV253 @ SV296 @ SV316 ) )
| ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SV296 @ ( pair @ SV378 @ SY655 ) ) @ SV316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1222,plain,
! [SV363: $i,SV356: $i,SV254: $i] :
( ( ( ~ ( contains_cpq @ ( triple @ SV254 @ sK1_U @ SV356 ) @ SV363 ) )
= $true )
| ( ( contains_pq @ ( i @ ( triple @ SV254 @ sK1_U @ SV356 ) ) @ SV363 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1181]) ).
thf(1223,plain,
! [SV364: $i,SV357: $i,SV254: $i] :
( ( ( ~ ( contains_pq @ ( i @ ( triple @ SV254 @ sK1_U @ SV357 ) ) @ SV364 ) )
= $true )
| ( ( contains_cpq @ ( triple @ SV254 @ sK1_U @ SV357 ) @ SV364 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1182]) ).
thf(1224,plain,
! [SV365: $i,SV339: $i] :
( ( ( pi_sharp_find_min @ ( i @ SV339 ) @ SV365 )
= $false )
| ( ( pi_removemin @ SV339 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1225,plain,
! [SV366: $i,SV297: $i,SV255: $i] :
( ( ( ! [SY647: $i] :
~ ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY647 ) ) @ SV366 ) )
= $true )
| ( ( ( SV297 = SV366 )
| ( contains_slb @ SV255 @ SV366 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1185]) ).
thf(1226,plain,
! [SV255: $i,SV297: $i] :
( ( ~ ! [SY598: $i] :
( ( SV297 != SY598 )
| ! [SY599: $i] : ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY599 ) ) @ SY598 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1186]) ).
thf(1227,plain,
! [SV297: $i,SV255: $i] :
( ( ~ ! [SY600: $i] :
( ~ ( contains_slb @ SV255 @ SY600 )
| ! [SY601: $i] : ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY601 ) ) @ SY600 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1186]) ).
thf(1228,plain,
! [SV308: $i,SV343: $i,SV319: $i,SV279: $i,SV233: $i] :
( ( ( check_cpq @ ( triple @ SV233 @ ( insert_slb @ SV279 @ ( pair @ SV319 @ SV343 ) ) @ SV308 ) )
= $false )
| ( ( strictly_less_than @ SV319 @ SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1190]) ).
thf(1229,plain,
! [SV312: $i,SV238: $i,SV322: $i,SV284: $i] :
( ( ( less_than @ ( lookup_slb @ SV284 @ SV322 ) @ SV322 )
= $false )
| ( ( contains_slb @ SV284 @ SV322 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV238 @ SV284 @ SV312 ) @ SV322 )
= ( triple @ ( remove_pqp @ SV238 @ SV322 ) @ ( remove_slb @ SV284 @ SV322 ) @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1230,plain,
! [SV313: $i,SV239: $i,SV285: $i,SV323: $i] :
( ( ( strictly_less_than @ SV323 @ ( lookup_slb @ SV285 @ SV323 ) )
= $false )
| ( ( contains_slb @ SV285 @ SV323 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV239 @ SV285 @ SV313 ) @ SV323 )
= ( triple @ ( remove_pqp @ SV239 @ SV323 ) @ ( remove_slb @ SV285 @ SV323 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1231,plain,
! [SV379: $i,SV288: $i,SV242: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV242 @ SV288 @ SV379 ) )
= ( triple @ SV242 @ ( update_slb @ SV288 @ ( findmin_pqp_res @ SV242 ) ) @ bad ) )
= $true )
| ( ( contains_slb @ SV288 @ ( findmin_pqp_res @ SV242 ) )
= $false )
| ( ( SV288 = create_slb )
= $true )
| ( ( strictly_less_than @ ( findmin_pqp_res @ SV242 ) @ ( lookup_slb @ SV288 @ ( findmin_pqp_res @ SV242 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1232,plain,
! [SV380: $i,SV289: $i,SV243: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV243 @ SV289 @ SV380 ) )
= ( triple @ SV243 @ ( update_slb @ SV289 @ ( findmin_pqp_res @ SV243 ) ) @ SV380 ) )
= $true )
| ( ( contains_slb @ SV289 @ ( findmin_pqp_res @ SV243 ) )
= $false )
| ( ( SV289 = create_slb )
= $true )
| ( ( less_than @ ( lookup_slb @ SV289 @ ( findmin_pqp_res @ SV243 ) ) @ ( findmin_pqp_res @ SV243 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1233,plain,
! [SV346: $i,SV326: $i] :
( ( ( ~ ( contains_pq @ SV326 @ ( sK15_W @ SV346 @ SV326 ) ) )
= $false )
| ( ( issmallestelement_pq @ SV326 @ SV346 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1195]) ).
thf(1234,plain,
! [SV326: $i,SV346: $i] :
( ( ( ~ ~ ( less_than @ SV346 @ ( sK15_W @ SV346 @ SV326 ) ) )
= $false )
| ( ( issmallestelement_pq @ SV326 @ SV346 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1195]) ).
thf(1235,plain,
! [SV347: $i,SV381: $i,SV327: $i] :
( ( ( ~ ( contains_pq @ SV327 @ SV381 )
| ( less_than @ SV347 @ SV381 ) )
= $true )
| ( ( issmallestelement_pq @ SV327 @ SV347 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1236,plain,
! [SV328: $i,SV358: $i] :
( ( ( ~ ( ok @ SV358 ) )
= $true )
| ( ( ~ ( succ_cpq @ SV328 @ SV358 ) )
= $true )
| ( ( ~ ( check_cpq @ SV358 ) )
= $true )
| ( ( phi @ SV328 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1197]) ).
thf(1237,plain,
! [SV329: $i] :
( ( ( ~ ~ ( ~ ( ok @ ( sK12_V @ SV329 ) )
| ~ ( succ_cpq @ SV329 @ ( sK12_V @ SV329 ) ) ) )
= $false )
| ( ( phi @ SV329 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1198]) ).
thf(1238,plain,
! [SV329: $i] :
( ( ( ~ ( check_cpq @ ( sK12_V @ SV329 ) ) )
= $false )
| ( ( phi @ SV329 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1198]) ).
thf(1239,plain,
! [SV359: $i,SV348: $i,SV250: $i] :
( ( ( contains_pq @ ( insert_pq @ SV250 @ SV348 ) @ SV359 )
= $false )
| ( ( ( SV348 = SV359 )
| ( contains_pq @ SV250 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1240,plain,
! [SV250: $i,SV382: $i] :
( ( ! [SY656: $i] :
( ( SV382 != SY656 )
| ( contains_pq @ ( insert_pq @ SV250 @ SV382 ) @ SY656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1241,plain,
! [SV383: $i,SV250: $i] :
( ( ! [SY657: $i] :
( ~ ( contains_pq @ SV250 @ SY657 )
| ( contains_pq @ ( insert_pq @ SV250 @ SV383 ) @ SY657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1242,plain,
! [SV349: $i,SV332: $i] :
( ( ( contains_pq @ SV332 @ SV349 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV332 @ SV349 ) )
= $true )
| ( ( pi_sharp_find_min @ SV332 @ SV349 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1243,plain,
! [SV384: $i,SV369: $i] :
( ( ~ ( pi_sharp_find_min @ SV369 @ SV384 )
| ( contains_pq @ SV369 @ SV384 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1244,plain,
! [SV385: $i,SV370: $i] :
( ( ~ ( pi_sharp_find_min @ SV370 @ SV385 )
| ( issmallestelement_pq @ SV370 @ SV385 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1245,plain,
! [SV315: $i,SV294: $i,SV251: $i] :
( ( ~ ! [SY614: $i,SY615: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY614 ) ) @ SV315 @ SY615 )
| ( SV294 = SV315 )
| ( pair_in_list @ SV251 @ SV315 @ SY615 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1206]) ).
thf(1246,plain,
! [SV315: $i,SV294: $i,SV251: $i] :
( ( ~ ! [SY616: $i,SY617: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY616 ) ) @ SV315 @ SY617 )
| ( SY616 = SY617 )
| ( pair_in_list @ SV251 @ SV315 @ SY617 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1206]) ).
thf(1247,plain,
! [SV251: $i,SV315: $i,SV294: $i] :
( ( ~ ! [SY618: $i,SY619: $i] :
( ( SV294 != SV315 )
| ( SY618 != SY619 )
| ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY618 ) ) @ SV315 @ SY619 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1207]) ).
thf(1248,plain,
! [SV294: $i,SV315: $i,SV251: $i] :
( ( ~ ! [SY620: $i,SY621: $i] :
( ~ ( pair_in_list @ SV251 @ SV315 @ SY621 )
| ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY620 ) ) @ SV315 @ SY621 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1207]) ).
thf(1249,plain,
! [SV352: $i,SV335: $i] :
( ( ( less_than @ SV335 @ SV352 )
= $false )
| ( ( less_than @ SV352 @ SV335 )
= $true )
| ( ( strictly_less_than @ SV335 @ SV352 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1210]) ).
thf(1250,plain,
! [SV386: $i,SV371: $i] :
( ( ~ ( strictly_less_than @ SV371 @ SV386 )
| ( less_than @ SV371 @ SV386 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1251,plain,
! [SV387: $i,SV372: $i] :
( ( ~ ( strictly_less_than @ SV372 @ SV387 )
| ~ ( less_than @ SV387 @ SV372 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1252,plain,
! [SV373: $i,SV361: $i,SV295: $i,SV252: $i] :
( ( ( ~ ( contains_cpq @ ( triple @ SV252 @ SV295 @ SV361 ) @ SV373 ) )
= $true )
| ( ( contains_slb @ SV295 @ SV373 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1213]) ).
thf(1253,plain,
! [SV362: $i,SV252: $i,SV374: $i,SV295: $i] :
( ( ( ~ ( contains_slb @ SV295 @ SV374 ) )
= $true )
| ( ( contains_cpq @ ( triple @ SV252 @ SV295 @ SV362 ) @ SV374 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1214]) ).
thf(1254,plain,
! [SV353: $i,SV336: $i] :
( ( ( contains_pq @ SV336 @ SV353 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV336 @ SV353 ) )
= $true )
| ( ( pi_sharp_removemin @ SV336 @ SV353 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1255,plain,
! [SV388: $i,SV375: $i] :
( ( ~ ( pi_sharp_removemin @ SV375 @ SV388 )
| ( contains_pq @ SV375 @ SV388 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1256,plain,
! [SV389: $i,SV376: $i] :
( ( ~ ( pi_sharp_removemin @ SV376 @ SV389 )
| ( issmallestelement_pq @ SV376 @ SV389 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1257,plain,
! [SV316: $i,SV296: $i,SV253: $i,SV377: $i,SV390: $i] :
( ( ~ ( less_than @ SV390 @ SV377 )
| ~ ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SV296 @ ( pair @ SV377 @ SV390 ) ) @ SV316 ) )
| ( check_cpq @ ( triple @ SV253 @ SV296 @ SV316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1258,plain,
! [SV316: $i,SV296: $i,SV253: $i,SV378: $i,SV391: $i] :
( ( ~ ( less_than @ SV391 @ SV378 )
| ~ ( check_cpq @ ( triple @ SV253 @ SV296 @ SV316 ) )
| ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SV296 @ ( pair @ SV378 @ SV391 ) ) @ SV316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1259,plain,
! [SV363: $i,SV356: $i,SV254: $i] :
( ( ( contains_cpq @ ( triple @ SV254 @ sK1_U @ SV356 ) @ SV363 )
= $false )
| ( ( contains_pq @ ( i @ ( triple @ SV254 @ sK1_U @ SV356 ) ) @ SV363 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1260,plain,
! [SV364: $i,SV357: $i,SV254: $i] :
( ( ( contains_pq @ ( i @ ( triple @ SV254 @ sK1_U @ SV357 ) ) @ SV364 )
= $false )
| ( ( contains_cpq @ ( triple @ SV254 @ sK1_U @ SV357 ) @ SV364 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1261,plain,
! [SV366: $i,SV392: $i,SV297: $i,SV255: $i] :
( ( ( ~ ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SV392 ) ) @ SV366 ) )
= $true )
| ( ( ( SV297 = SV366 )
| ( contains_slb @ SV255 @ SV366 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1262,plain,
! [SV255: $i,SV297: $i] :
( ( ! [SY598: $i] :
( ( SV297 != SY598 )
| ! [SY599: $i] : ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY599 ) ) @ SY598 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1226]) ).
thf(1263,plain,
! [SV297: $i,SV255: $i] :
( ( ! [SY600: $i] :
( ~ ( contains_slb @ SV255 @ SY600 )
| ! [SY601: $i] : ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY601 ) ) @ SY600 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1227]) ).
thf(1264,plain,
! [SV346: $i,SV326: $i] :
( ( ( contains_pq @ SV326 @ ( sK15_W @ SV346 @ SV326 ) )
= $true )
| ( ( issmallestelement_pq @ SV326 @ SV346 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1233]) ).
thf(1265,plain,
! [SV326: $i,SV346: $i] :
( ( ( ~ ( less_than @ SV346 @ ( sK15_W @ SV346 @ SV326 ) ) )
= $true )
| ( ( issmallestelement_pq @ SV326 @ SV346 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1234]) ).
thf(1266,plain,
! [SV347: $i,SV381: $i,SV327: $i] :
( ( ( ~ ( contains_pq @ SV327 @ SV381 ) )
= $true )
| ( ( less_than @ SV347 @ SV381 )
= $true )
| ( ( issmallestelement_pq @ SV327 @ SV347 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1235]) ).
thf(1267,plain,
! [SV328: $i,SV358: $i] :
( ( ( ok @ SV358 )
= $false )
| ( ( ~ ( succ_cpq @ SV328 @ SV358 ) )
= $true )
| ( ( ~ ( check_cpq @ SV358 ) )
= $true )
| ( ( phi @ SV328 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1268,plain,
! [SV329: $i] :
( ( ( ~ ( ~ ( ok @ ( sK12_V @ SV329 ) )
| ~ ( succ_cpq @ SV329 @ ( sK12_V @ SV329 ) ) ) )
= $true )
| ( ( phi @ SV329 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1237]) ).
thf(1269,plain,
! [SV329: $i] :
( ( ( check_cpq @ ( sK12_V @ SV329 ) )
= $true )
| ( ( phi @ SV329 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1238]) ).
thf(1270,plain,
! [SV250: $i,SV359: $i,SV348: $i] :
( ( ( SV348 = SV359 )
= $true )
| ( ( contains_pq @ SV250 @ SV359 )
= $true )
| ( ( contains_pq @ ( insert_pq @ SV250 @ SV348 ) @ SV359 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1271,plain,
! [SV250: $i,SV393: $i,SV382: $i] :
( ( ( SV382 != SV393 )
| ( contains_pq @ ( insert_pq @ SV250 @ SV382 ) @ SV393 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1272,plain,
! [SV383: $i,SV394: $i,SV250: $i] :
( ( ~ ( contains_pq @ SV250 @ SV394 )
| ( contains_pq @ ( insert_pq @ SV250 @ SV383 ) @ SV394 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1273,plain,
! [SV349: $i,SV332: $i] :
( ( ( issmallestelement_pq @ SV332 @ SV349 )
= $false )
| ( ( contains_pq @ SV332 @ SV349 )
= $false )
| ( ( pi_sharp_find_min @ SV332 @ SV349 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1274,plain,
! [SV384: $i,SV369: $i] :
( ( ( ~ ( pi_sharp_find_min @ SV369 @ SV384 ) )
= $true )
| ( ( contains_pq @ SV369 @ SV384 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1243]) ).
thf(1275,plain,
! [SV385: $i,SV370: $i] :
( ( ( ~ ( pi_sharp_find_min @ SV370 @ SV385 ) )
= $true )
| ( ( issmallestelement_pq @ SV370 @ SV385 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1244]) ).
thf(1276,plain,
! [SV315: $i,SV294: $i,SV251: $i] :
( ( ! [SY614: $i,SY615: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY614 ) ) @ SV315 @ SY615 )
| ( SV294 = SV315 )
| ( pair_in_list @ SV251 @ SV315 @ SY615 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1245]) ).
thf(1277,plain,
! [SV315: $i,SV294: $i,SV251: $i] :
( ( ! [SY616: $i,SY617: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY616 ) ) @ SV315 @ SY617 )
| ( SY616 = SY617 )
| ( pair_in_list @ SV251 @ SV315 @ SY617 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1246]) ).
thf(1278,plain,
! [SV251: $i,SV315: $i,SV294: $i] :
( ( ! [SY618: $i,SY619: $i] :
( ( SV294 != SV315 )
| ( SY618 != SY619 )
| ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY618 ) ) @ SV315 @ SY619 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1247]) ).
thf(1279,plain,
! [SV294: $i,SV315: $i,SV251: $i] :
( ( ! [SY620: $i,SY621: $i] :
( ~ ( pair_in_list @ SV251 @ SV315 @ SY621 )
| ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SY620 ) ) @ SV315 @ SY621 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1248]) ).
thf(1280,plain,
! [SV386: $i,SV371: $i] :
( ( ( ~ ( strictly_less_than @ SV371 @ SV386 ) )
= $true )
| ( ( less_than @ SV371 @ SV386 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1250]) ).
thf(1281,plain,
! [SV387: $i,SV372: $i] :
( ( ( ~ ( strictly_less_than @ SV372 @ SV387 ) )
= $true )
| ( ( ~ ( less_than @ SV387 @ SV372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1251]) ).
thf(1282,plain,
! [SV373: $i,SV361: $i,SV295: $i,SV252: $i] :
( ( ( contains_cpq @ ( triple @ SV252 @ SV295 @ SV361 ) @ SV373 )
= $false )
| ( ( contains_slb @ SV295 @ SV373 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1252]) ).
thf(1283,plain,
! [SV362: $i,SV252: $i,SV374: $i,SV295: $i] :
( ( ( contains_slb @ SV295 @ SV374 )
= $false )
| ( ( contains_cpq @ ( triple @ SV252 @ SV295 @ SV362 ) @ SV374 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1253]) ).
thf(1284,plain,
! [SV353: $i,SV336: $i] :
( ( ( issmallestelement_pq @ SV336 @ SV353 )
= $false )
| ( ( contains_pq @ SV336 @ SV353 )
= $false )
| ( ( pi_sharp_removemin @ SV336 @ SV353 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1285,plain,
! [SV388: $i,SV375: $i] :
( ( ( ~ ( pi_sharp_removemin @ SV375 @ SV388 ) )
= $true )
| ( ( contains_pq @ SV375 @ SV388 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1255]) ).
thf(1286,plain,
! [SV389: $i,SV376: $i] :
( ( ( ~ ( pi_sharp_removemin @ SV376 @ SV389 ) )
= $true )
| ( ( issmallestelement_pq @ SV376 @ SV389 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1256]) ).
thf(1287,plain,
! [SV316: $i,SV296: $i,SV253: $i,SV377: $i,SV390: $i] :
( ( ( ~ ( less_than @ SV390 @ SV377 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SV296 @ ( pair @ SV377 @ SV390 ) ) @ SV316 ) )
| ( check_cpq @ ( triple @ SV253 @ SV296 @ SV316 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1257]) ).
thf(1288,plain,
! [SV316: $i,SV296: $i,SV253: $i,SV378: $i,SV391: $i] :
( ( ( ~ ( less_than @ SV391 @ SV378 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV253 @ SV296 @ SV316 ) )
| ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SV296 @ ( pair @ SV378 @ SV391 ) ) @ SV316 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1258]) ).
thf(1289,plain,
! [SV366: $i,SV392: $i,SV297: $i,SV255: $i] :
( ( ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SV392 ) ) @ SV366 )
= $false )
| ( ( ( SV297 = SV366 )
| ( contains_slb @ SV255 @ SV366 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1261]) ).
thf(1290,plain,
! [SV255: $i,SV395: $i,SV297: $i] :
( ( ( SV297 != SV395 )
| ! [SY658: $i] : ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY658 ) ) @ SV395 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1291,plain,
! [SV297: $i,SV396: $i,SV255: $i] :
( ( ~ ( contains_slb @ SV255 @ SV396 )
| ! [SY659: $i] : ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY659 ) ) @ SV396 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1292,plain,
! [SV326: $i,SV346: $i] :
( ( ( less_than @ SV346 @ ( sK15_W @ SV346 @ SV326 ) )
= $false )
| ( ( issmallestelement_pq @ SV326 @ SV346 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1293,plain,
! [SV347: $i,SV381: $i,SV327: $i] :
( ( ( contains_pq @ SV327 @ SV381 )
= $false )
| ( ( less_than @ SV347 @ SV381 )
= $true )
| ( ( issmallestelement_pq @ SV327 @ SV347 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1266]) ).
thf(1294,plain,
! [SV358: $i,SV328: $i] :
( ( ( succ_cpq @ SV328 @ SV358 )
= $false )
| ( ( ok @ SV358 )
= $false )
| ( ( ~ ( check_cpq @ SV358 ) )
= $true )
| ( ( phi @ SV328 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1267]) ).
thf(1295,plain,
! [SV329: $i] :
( ( ( ~ ( ok @ ( sK12_V @ SV329 ) )
| ~ ( succ_cpq @ SV329 @ ( sK12_V @ SV329 ) ) )
= $false )
| ( ( phi @ SV329 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1296,plain,
! [SV250: $i,SV393: $i,SV382: $i] :
( ( ( ( SV382 != SV393 ) )
= $true )
| ( ( contains_pq @ ( insert_pq @ SV250 @ SV382 ) @ SV393 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1271]) ).
thf(1297,plain,
! [SV383: $i,SV394: $i,SV250: $i] :
( ( ( ~ ( contains_pq @ SV250 @ SV394 ) )
= $true )
| ( ( contains_pq @ ( insert_pq @ SV250 @ SV383 ) @ SV394 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1272]) ).
thf(1298,plain,
! [SV384: $i,SV369: $i] :
( ( ( pi_sharp_find_min @ SV369 @ SV384 )
= $false )
| ( ( contains_pq @ SV369 @ SV384 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1299,plain,
! [SV385: $i,SV370: $i] :
( ( ( pi_sharp_find_min @ SV370 @ SV385 )
= $false )
| ( ( issmallestelement_pq @ SV370 @ SV385 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1275]) ).
thf(1300,plain,
! [SV315: $i,SV397: $i,SV294: $i,SV251: $i] :
( ( ! [SY660: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SV397 ) ) @ SV315 @ SY660 )
| ( SV294 = SV315 )
| ( pair_in_list @ SV251 @ SV315 @ SY660 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1301,plain,
! [SV315: $i,SV398: $i,SV294: $i,SV251: $i] :
( ( ! [SY661: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SV398 ) ) @ SV315 @ SY661 )
| ( SV398 = SY661 )
| ( pair_in_list @ SV251 @ SV315 @ SY661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1302,plain,
! [SV251: $i,SV399: $i,SV315: $i,SV294: $i] :
( ( ! [SY662: $i] :
( ( SV294 != SV315 )
| ( SV399 != SY662 )
| ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SV399 ) ) @ SV315 @ SY662 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1303,plain,
! [SV400: $i,SV294: $i,SV315: $i,SV251: $i] :
( ( ! [SY663: $i] :
( ~ ( pair_in_list @ SV251 @ SV315 @ SY663 )
| ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SV400 ) ) @ SV315 @ SY663 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1304,plain,
! [SV386: $i,SV371: $i] :
( ( ( strictly_less_than @ SV371 @ SV386 )
= $false )
| ( ( less_than @ SV371 @ SV386 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1305,plain,
! [SV387: $i,SV372: $i] :
( ( ( strictly_less_than @ SV372 @ SV387 )
= $false )
| ( ( ~ ( less_than @ SV387 @ SV372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1306,plain,
! [SV388: $i,SV375: $i] :
( ( ( pi_sharp_removemin @ SV375 @ SV388 )
= $false )
| ( ( contains_pq @ SV375 @ SV388 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1285]) ).
thf(1307,plain,
! [SV389: $i,SV376: $i] :
( ( ( pi_sharp_removemin @ SV376 @ SV389 )
= $false )
| ( ( issmallestelement_pq @ SV376 @ SV389 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1286]) ).
thf(1308,plain,
! [SV316: $i,SV296: $i,SV253: $i,SV377: $i,SV390: $i] :
( ( ( less_than @ SV390 @ SV377 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SV296 @ ( pair @ SV377 @ SV390 ) ) @ SV316 ) )
| ( check_cpq @ ( triple @ SV253 @ SV296 @ SV316 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1309,plain,
! [SV316: $i,SV296: $i,SV253: $i,SV378: $i,SV391: $i] :
( ( ( less_than @ SV391 @ SV378 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV253 @ SV296 @ SV316 ) )
| ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SV296 @ ( pair @ SV378 @ SV391 ) ) @ SV316 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1288]) ).
thf(1310,plain,
! [SV392: $i,SV255: $i,SV366: $i,SV297: $i] :
( ( ( SV297 = SV366 )
= $true )
| ( ( contains_slb @ SV255 @ SV366 )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SV392 ) ) @ SV366 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1289]) ).
thf(1311,plain,
! [SV255: $i,SV395: $i,SV297: $i] :
( ( ( ( SV297 != SV395 ) )
= $true )
| ( ( ! [SY658: $i] : ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY658 ) ) @ SV395 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1290]) ).
thf(1312,plain,
! [SV297: $i,SV396: $i,SV255: $i] :
( ( ( ~ ( contains_slb @ SV255 @ SV396 ) )
= $true )
| ( ( ! [SY659: $i] : ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY659 ) ) @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1291]) ).
thf(1313,plain,
! [SV328: $i,SV358: $i] :
( ( ( check_cpq @ SV358 )
= $false )
| ( ( ok @ SV358 )
= $false )
| ( ( succ_cpq @ SV328 @ SV358 )
= $false )
| ( ( phi @ SV328 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1314,plain,
! [SV329: $i] :
( ( ( ~ ( ok @ ( sK12_V @ SV329 ) ) )
= $false )
| ( ( phi @ SV329 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1295]) ).
thf(1315,plain,
! [SV329: $i] :
( ( ( ~ ( succ_cpq @ SV329 @ ( sK12_V @ SV329 ) ) )
= $false )
| ( ( phi @ SV329 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1295]) ).
thf(1316,plain,
! [SV250: $i,SV393: $i,SV382: $i] :
( ( ( SV382 = SV393 )
= $false )
| ( ( contains_pq @ ( insert_pq @ SV250 @ SV382 ) @ SV393 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1296]) ).
thf(1317,plain,
! [SV383: $i,SV394: $i,SV250: $i] :
( ( ( contains_pq @ SV250 @ SV394 )
= $false )
| ( ( contains_pq @ ( insert_pq @ SV250 @ SV383 ) @ SV394 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1297]) ).
thf(1318,plain,
! [SV401: $i,SV315: $i,SV397: $i,SV294: $i,SV251: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SV397 ) ) @ SV315 @ SV401 )
| ( SV294 = SV315 )
| ( pair_in_list @ SV251 @ SV315 @ SV401 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1319,plain,
! [SV402: $i,SV315: $i,SV398: $i,SV294: $i,SV251: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SV398 ) ) @ SV315 @ SV402 )
| ( SV398 = SV402 )
| ( pair_in_list @ SV251 @ SV315 @ SV402 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1320,plain,
! [SV251: $i,SV403: $i,SV399: $i,SV315: $i,SV294: $i] :
( ( ( SV294 != SV315 )
| ( SV399 != SV403 )
| ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SV399 ) ) @ SV315 @ SV403 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1321,plain,
! [SV400: $i,SV294: $i,SV404: $i,SV315: $i,SV251: $i] :
( ( ~ ( pair_in_list @ SV251 @ SV315 @ SV404 )
| ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SV400 ) ) @ SV315 @ SV404 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1322,plain,
! [SV372: $i,SV387: $i] :
( ( ( less_than @ SV387 @ SV372 )
= $false )
| ( ( strictly_less_than @ SV372 @ SV387 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1305]) ).
thf(1323,plain,
! [SV316: $i,SV390: $i,SV377: $i,SV296: $i,SV253: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SV296 @ ( pair @ SV377 @ SV390 ) ) @ SV316 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV253 @ SV296 @ SV316 ) )
= $true )
| ( ( less_than @ SV390 @ SV377 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1308]) ).
thf(1324,plain,
! [SV391: $i,SV378: $i,SV316: $i,SV296: $i,SV253: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV253 @ SV296 @ SV316 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SV296 @ ( pair @ SV378 @ SV391 ) ) @ SV316 ) )
= $true )
| ( ( less_than @ SV391 @ SV378 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1309]) ).
thf(1325,plain,
! [SV255: $i,SV395: $i,SV297: $i] :
( ( ( SV297 = SV395 )
= $false )
| ( ( ! [SY658: $i] : ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY658 ) ) @ SV395 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1311]) ).
thf(1326,plain,
! [SV297: $i,SV396: $i,SV255: $i] :
( ( ( contains_slb @ SV255 @ SV396 )
= $false )
| ( ( ! [SY659: $i] : ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SY659 ) ) @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1312]) ).
thf(1327,plain,
! [SV329: $i] :
( ( ( ok @ ( sK12_V @ SV329 ) )
= $true )
| ( ( phi @ SV329 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1314]) ).
thf(1328,plain,
! [SV329: $i] :
( ( ( succ_cpq @ SV329 @ ( sK12_V @ SV329 ) )
= $true )
| ( ( phi @ SV329 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1315]) ).
thf(1329,plain,
! [SV401: $i,SV315: $i,SV397: $i,SV294: $i,SV251: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SV397 ) ) @ SV315 @ SV401 ) )
= $true )
| ( ( ( SV294 = SV315 )
| ( pair_in_list @ SV251 @ SV315 @ SV401 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1318]) ).
thf(1330,plain,
! [SV402: $i,SV315: $i,SV398: $i,SV294: $i,SV251: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SV398 ) ) @ SV315 @ SV402 ) )
= $true )
| ( ( ( SV398 = SV402 )
| ( pair_in_list @ SV251 @ SV315 @ SV402 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1319]) ).
thf(1331,plain,
! [SV251: $i,SV403: $i,SV399: $i,SV315: $i,SV294: $i] :
( ( ( ( SV294 != SV315 )
| ( SV399 != SV403 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SV399 ) ) @ SV315 @ SV403 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1320]) ).
thf(1332,plain,
! [SV400: $i,SV294: $i,SV404: $i,SV315: $i,SV251: $i] :
( ( ( ~ ( pair_in_list @ SV251 @ SV315 @ SV404 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SV400 ) ) @ SV315 @ SV404 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1321]) ).
thf(1333,plain,
! [SV316: $i,SV390: $i,SV377: $i,SV296: $i,SV253: $i] :
( ( ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SV296 @ ( pair @ SV377 @ SV390 ) ) @ SV316 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV253 @ SV296 @ SV316 ) )
= $true )
| ( ( less_than @ SV390 @ SV377 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1323]) ).
thf(1334,plain,
! [SV391: $i,SV378: $i,SV316: $i,SV296: $i,SV253: $i] :
( ( ( check_cpq @ ( triple @ SV253 @ SV296 @ SV316 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV253 @ ( insert_slb @ SV296 @ ( pair @ SV378 @ SV391 ) ) @ SV316 ) )
= $true )
| ( ( less_than @ SV391 @ SV378 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1324]) ).
thf(1335,plain,
! [SV395: $i,SV405: $i,SV297: $i,SV255: $i] :
( ( ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SV405 ) ) @ SV395 )
= $true )
| ( ( SV297 = SV395 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1336,plain,
! [SV396: $i,SV406: $i,SV297: $i,SV255: $i] :
( ( ( contains_slb @ ( insert_slb @ SV255 @ ( pair @ SV297 @ SV406 ) ) @ SV396 )
= $true )
| ( ( contains_slb @ SV255 @ SV396 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1337,plain,
! [SV401: $i,SV315: $i,SV397: $i,SV294: $i,SV251: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SV397 ) ) @ SV315 @ SV401 )
= $false )
| ( ( ( SV294 = SV315 )
| ( pair_in_list @ SV251 @ SV315 @ SV401 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1329]) ).
thf(1338,plain,
! [SV402: $i,SV315: $i,SV398: $i,SV294: $i,SV251: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SV398 ) ) @ SV315 @ SV402 )
= $false )
| ( ( ( SV398 = SV402 )
| ( pair_in_list @ SV251 @ SV315 @ SV402 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1330]) ).
thf(1339,plain,
! [SV251: $i,SV403: $i,SV399: $i,SV315: $i,SV294: $i] :
( ( ( ( SV294 != SV315 ) )
= $true )
| ( ( ( SV399 != SV403 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SV399 ) ) @ SV315 @ SV403 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1331]) ).
thf(1340,plain,
! [SV400: $i,SV294: $i,SV404: $i,SV315: $i,SV251: $i] :
( ( ( pair_in_list @ SV251 @ SV315 @ SV404 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SV400 ) ) @ SV315 @ SV404 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1332]) ).
thf(1341,plain,
! [SV397: $i,SV401: $i,SV251: $i,SV315: $i,SV294: $i] :
( ( ( SV294 = SV315 )
= $true )
| ( ( pair_in_list @ SV251 @ SV315 @ SV401 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SV397 ) ) @ SV315 @ SV401 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1337]) ).
thf(1342,plain,
! [SV294: $i,SV315: $i,SV251: $i,SV402: $i,SV398: $i] :
( ( ( SV398 = SV402 )
= $true )
| ( ( pair_in_list @ SV251 @ SV315 @ SV402 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SV398 ) ) @ SV315 @ SV402 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1338]) ).
thf(1343,plain,
! [SV251: $i,SV403: $i,SV399: $i,SV315: $i,SV294: $i] :
( ( ( SV294 = SV315 )
= $false )
| ( ( ( SV399 != SV403 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SV399 ) ) @ SV315 @ SV403 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1344,plain,
! [SV251: $i,SV315: $i,SV294: $i,SV403: $i,SV399: $i] :
( ( ( SV399 = SV403 )
= $false )
| ( ( SV294 = SV315 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV251 @ ( pair @ SV294 @ SV399 ) ) @ SV315 @ SV403 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1343]) ).
thf(1345,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[843,1344,1342,1341,1340,1336,1335,1334,1333,1328,1327,1322,1317,1316,1313,1310,1307,1306,1304,1299,1298,1293,1292,1284,1283,1282,1273,1270,1269,1264,1260,1259,1249,1232,1231,1230,1229,1228,1224,1219,1218,1209,1208,1202,1189,1188,1187,1184,1161,1147,1146,1143,1142,1141,1140,1139,1104,1101,1098,1096,1095,1080,1054,1047,1046,1044,1043,1026,992,983,981,980,979,978,972,943,941,937,929,917,909,908,907,886,885,866,863,855,845,844]) ).
thf(1346,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1345,760]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SWV370+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.10 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Wed Jun 15 00:50:13 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.13/0.32 .
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 62
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 0
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.13/0.36 ..
% 0.13/0.38 (rf:0,axioms:62,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:64,loop_count:0,foatp_calls:0,translation:fof_full)...................................................................................
% 2.35/2.56
% 2.35/2.56 ********************************
% 2.35/2.56 * All subproblems solved! *
% 2.35/2.56 ********************************
% 2.35/2.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:63,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:73,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:1345,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.97/3.19
% 2.97/3.19 %**** Beginning of derivation protocol ****
% 2.97/3.19 % SZS output start CNFRefutation
% See solution above
% 3.01/3.19
% 3.01/3.19 %**** End of derivation protocol ****
% 3.01/3.19 %**** no. of clauses in derivation: 1346 ****
% 3.01/3.19 %**** clause counter: 1345 ****
% 3.01/3.19
% 3.01/3.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:63,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:73,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:1345,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------