TSTP Solution File: SWV369+1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SWV369+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 0.67s 0.89s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 115
% Syntax : Number of formulae : 1365 ( 893 unt; 52 typ; 0 def)
% Number of atoms : 7171 (2563 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 15927 (2144 ~;2074 |; 118 &;11499 @)
% ( 38 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 76 ( 76 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 52 usr; 9 con; 0-3 aty)
% Number of variables : 4131 ( 0 ^4125 !; 6 ?;4131 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_bad,type,
bad: $i ).
thf(tp_bottom,type,
bottom: $i ).
thf(tp_check_cpq,type,
check_cpq: $i > $o ).
thf(tp_contains_cpq,type,
contains_cpq: $i > $i > $o ).
thf(tp_contains_pq,type,
contains_pq: $i > $i > $o ).
thf(tp_contains_slb,type,
contains_slb: $i > $i > $o ).
thf(tp_create_pq,type,
create_pq: $i ).
thf(tp_create_slb,type,
create_slb: $i ).
thf(tp_findmin_cpq_eff,type,
findmin_cpq_eff: $i > $i ).
thf(tp_findmin_cpq_res,type,
findmin_cpq_res: $i > $i ).
thf(tp_findmin_pq_eff,type,
findmin_pq_eff: $i > $i > $i ).
thf(tp_findmin_pq_res,type,
findmin_pq_res: $i > $i > $i ).
thf(tp_findmin_pqp_res,type,
findmin_pqp_res: $i > $i ).
thf(tp_i,type,
i: $i > $i ).
thf(tp_insert_cpq,type,
insert_cpq: $i > $i > $i ).
thf(tp_insert_pq,type,
insert_pq: $i > $i > $i ).
thf(tp_insert_pqp,type,
insert_pqp: $i > $i > $i ).
thf(tp_insert_slb,type,
insert_slb: $i > $i > $i ).
thf(tp_isnonempty_pq,type,
isnonempty_pq: $i > $o ).
thf(tp_isnonempty_slb,type,
isnonempty_slb: $i > $o ).
thf(tp_issmallestelement_pq,type,
issmallestelement_pq: $i > $i > $o ).
thf(tp_less_than,type,
less_than: $i > $i > $o ).
thf(tp_lookup_slb,type,
lookup_slb: $i > $i > $i ).
thf(tp_ok,type,
ok: $i > $o ).
thf(tp_pair,type,
pair: $i > $i > $i ).
thf(tp_pair_in_list,type,
pair_in_list: $i > $i > $i > $o ).
thf(tp_phi,type,
phi: $i > $o ).
thf(tp_pi_find_min,type,
pi_find_min: $i > $o ).
thf(tp_pi_remove,type,
pi_remove: $i > $i > $o ).
thf(tp_pi_removemin,type,
pi_removemin: $i > $o ).
thf(tp_pi_sharp_find_min,type,
pi_sharp_find_min: $i > $i > $o ).
thf(tp_pi_sharp_remove,type,
pi_sharp_remove: $i > $i > $o ).
thf(tp_pi_sharp_removemin,type,
pi_sharp_removemin: $i > $i > $o ).
thf(tp_remove_cpq,type,
remove_cpq: $i > $i > $i ).
thf(tp_remove_pq,type,
remove_pq: $i > $i > $i ).
thf(tp_remove_pqp,type,
remove_pqp: $i > $i > $i ).
thf(tp_remove_slb,type,
remove_slb: $i > $i > $i ).
thf(tp_removemin_cpq_eff,type,
removemin_cpq_eff: $i > $i ).
thf(tp_removemin_cpq_res,type,
removemin_cpq_res: $i > $i ).
thf(tp_removemin_pq_eff,type,
removemin_pq_eff: $i > $i > $i ).
thf(tp_removemin_pq_res,type,
removemin_pq_res: $i > $i > $i ).
thf(tp_sK1_U,type,
sK1_U: $i ).
thf(tp_sK2_SY166,type,
sK2_SY166: $i ).
thf(tp_sK3_SY168,type,
sK3_SY168: $i ).
thf(tp_sK4_V,type,
sK4_V: $i > $i ).
thf(tp_sK5_V,type,
sK5_V: $i > $i ).
thf(tp_sK6_V,type,
sK6_V: $i > $i ).
thf(tp_sK7_W,type,
sK7_W: $i > $i > $i ).
thf(tp_strictly_less_than,type,
strictly_less_than: $i > $i > $o ).
thf(tp_succ_cpq,type,
succ_cpq: $i > $i > $o ).
thf(tp_triple,type,
triple: $i > $i > $i > $i ).
thf(tp_update_slb,type,
update_slb: $i > $i > $i ).
thf(1,axiom,
! [U: $i] :
( ( phi @ U )
<=> ? [V: $i] :
( ( succ_cpq @ U @ V )
& ( ok @ V )
& ( check_cpq @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax62) ).
thf(2,axiom,
! [U: $i] :
( ( pi_removemin @ U )
<=> ? [V: $i] : ( pi_sharp_find_min @ ( i @ U ) @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax61) ).
thf(3,axiom,
! [U: $i,V: $i] :
( ( pi_sharp_removemin @ U @ V )
<=> ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60) ).
thf(4,axiom,
! [U: $i] :
( ( pi_find_min @ U )
<=> ? [V: $i] : ( pi_sharp_find_min @ ( i @ U ) @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax59) ).
thf(5,axiom,
! [U: $i,V: $i] :
( ( pi_sharp_find_min @ U @ V )
<=> ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
thf(6,axiom,
! [U: $i,V: $i] :
( ( pi_remove @ U @ V )
<=> ( pi_sharp_remove @ ( i @ U ) @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
thf(7,axiom,
! [U: $i,V: $i] :
( ( pi_sharp_remove @ U @ V )
<=> ( contains_pq @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax56) ).
thf(8,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( i @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
= ( insert_pq @ ( i @ ( triple @ U @ V @ W ) ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
thf(9,axiom,
! [U: $i,V: $i] :
( ( i @ ( triple @ U @ create_slb @ V ) )
= create_pq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax54) ).
thf(10,axiom,
! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).
thf(11,axiom,
! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
thf(12,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( V != create_slb )
=> ( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
= ( findmin_pqp_res @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).
thf(13,axiom,
! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax50) ).
thf(14,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != create_slb )
& ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
& ( less_than @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) @ ( findmin_pqp_res @ U ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).
thf(15,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != create_slb )
& ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
& ( strictly_less_than @ ( findmin_pqp_res @ U ) @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax48) ).
thf(16,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != create_slb )
& ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax47) ).
thf(17,axiom,
! [U: $i,V: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ create_slb @ V ) )
= ( triple @ U @ create_slb @ bad ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).
thf(18,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( contains_slb @ V @ X )
& ( strictly_less_than @ X @ ( lookup_slb @ V @ X ) ) )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ bad ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).
thf(19,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( contains_slb @ V @ X )
& ( less_than @ ( lookup_slb @ V @ X ) @ X ) )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax44) ).
thf(20,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ U @ V @ bad ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax43) ).
thf(21,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( insert_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( insert_pqp @ U @ X ) @ ( insert_slb @ V @ ( pair @ X @ bottom ) ) @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).
thf(22,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ( W = bad ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax41) ).
thf(23,axiom,
! [U: $i,V: $i] :
( ( ok @ ( triple @ U @ V @ bad ) )
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax40) ).
thf(24,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
<=> ( contains_slb @ V @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
thf(25,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( strictly_less_than @ X @ Y )
=> ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
<=> $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
thf(26,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( less_than @ Y @ X )
=> ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
<=> ( check_cpq @ ( triple @ U @ V @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax37) ).
thf(27,axiom,
! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).
thf(28,axiom,
! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax35) ).
thf(29,axiom,
! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax34) ).
thf(30,axiom,
! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax33) ).
thf(31,axiom,
! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax32) ).
thf(32,axiom,
! [U: $i] : ( succ_cpq @ U @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).
thf(33,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( less_than @ W @ X )
=> ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax30) ).
thf(34,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( strictly_less_than @ X @ W )
=> ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax29) ).
thf(35,axiom,
! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
thf(36,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != W )
& ( contains_slb @ U @ W ) )
=> ( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( lookup_slb @ U @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax27) ).
thf(37,axiom,
! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
thf(38,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != W )
& ( contains_slb @ U @ W ) )
=> ( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( remove_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).
thf(39,axiom,
! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
thf(40,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
<=> ( ( pair_in_list @ U @ W @ Y )
| ( ( V = W )
& ( X = Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
thf(41,axiom,
! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
thf(42,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
<=> ( ( contains_slb @ U @ W )
| ( V = W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
thf(43,axiom,
! [U: $i] :
~ ( contains_slb @ create_slb @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
thf(44,axiom,
! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax19) ).
thf(45,axiom,
~ ( isnonempty_slb @ create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
thf(46,axiom,
! [U: $i,V: $i,W: $i] :
( ( insert_pq @ ( insert_pq @ U @ V ) @ W )
= ( insert_pq @ ( insert_pq @ U @ W ) @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
thf(47,axiom,
! [U: $i,V: $i] :
( ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) )
=> ( ( removemin_pq_res @ U @ V )
= V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
thf(48,axiom,
! [U: $i,V: $i] :
( ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) )
=> ( ( removemin_pq_eff @ U @ V )
= ( remove_pq @ U @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
thf(49,axiom,
! [U: $i,V: $i] :
( ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) )
=> ( ( findmin_pq_res @ U @ V )
= V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax14) ).
thf(50,axiom,
! [U: $i,V: $i] :
( ( ( contains_pq @ U @ V )
& ( issmallestelement_pq @ U @ V ) )
=> ( ( findmin_pq_eff @ U @ V )
= U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax13) ).
thf(51,axiom,
! [U: $i,V: $i,W: $i] :
( ( ( contains_pq @ U @ W )
& ( V != W ) )
=> ( ( remove_pq @ ( insert_pq @ U @ V ) @ W )
= ( insert_pq @ ( remove_pq @ U @ W ) @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax12) ).
thf(52,axiom,
! [U: $i,V: $i] :
( ( remove_pq @ ( insert_pq @ U @ V ) @ V )
= U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11) ).
thf(53,axiom,
! [U: $i,V: $i] :
( ( issmallestelement_pq @ U @ V )
<=> ! [W: $i] :
( ( contains_pq @ U @ W )
=> ( less_than @ V @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10) ).
thf(54,axiom,
! [U: $i,V: $i,W: $i] :
( ( contains_pq @ ( insert_pq @ U @ V ) @ W )
<=> ( ( contains_pq @ U @ W )
| ( V = W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax9) ).
thf(55,axiom,
! [U: $i] :
~ ( contains_pq @ create_pq @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8) ).
thf(56,axiom,
! [U: $i,V: $i] : ( isnonempty_pq @ ( insert_pq @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).
thf(57,axiom,
~ ( isnonempty_pq @ create_pq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
thf(58,axiom,
! [U: $i] : ( less_than @ bottom @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bottom_smallest) ).
thf(59,axiom,
! [U: $i,V: $i] :
( ( strictly_less_than @ U @ V )
<=> ( ( less_than @ U @ V )
& ~ ( less_than @ V @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).
thf(60,axiom,
! [U: $i] : ( less_than @ U @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(61,axiom,
! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
thf(62,axiom,
! [U: $i,V: $i,W: $i] :
( ( ( less_than @ U @ V )
& ( less_than @ V @ W ) )
=> ( less_than @ U @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(63,conjecture,
! [U: $i,V: $i,W: $i] :
( ( contains_cpq @ ( triple @ U @ create_slb @ V ) @ W )
<=> ( contains_pq @ ( i @ ( triple @ U @ create_slb @ V ) ) @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l5_co) ).
thf(64,negated_conjecture,
( ( ! [U: $i,V: $i,W: $i] :
( ( contains_cpq @ ( triple @ U @ create_slb @ V ) @ W )
<=> ( contains_pq @ ( i @ ( triple @ U @ create_slb @ V ) ) @ W ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[63]) ).
thf(65,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( contains_cpq @ ( triple @ U @ create_slb @ V ) @ W )
<=> ( contains_pq @ ( i @ ( triple @ U @ create_slb @ V ) ) @ W ) ) )
= $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,
( ( ! [SY166: $i,SY167: $i] :
( ( contains_cpq @ ( triple @ sK1_U @ create_slb @ SY166 ) @ SY167 )
<=> ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ SY166 ) ) @ SY167 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[65]) ).
thf(129,plain,
( ( ! [SY168: $i] :
( ( contains_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) @ SY168 )
<=> ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) ) @ SY168 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[128]) ).
thf(130,plain,
( ( ( contains_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) @ sK3_SY168 )
<=> ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) ) @ sK3_SY168 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[129]) ).
thf(131,plain,
( ( ( contains_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) @ sK3_SY168 )
=> ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) ) @ sK3_SY168 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[130]) ).
thf(132,plain,
( ( ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) ) @ sK3_SY168 )
=> ( contains_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) @ sK3_SY168 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[130]) ).
thf(133,plain,
( ( ~ ( ( contains_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) @ sK3_SY168 )
=> ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) ) @ sK3_SY168 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[131]) ).
thf(134,plain,
( ( ~ ( ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) ) @ sK3_SY168 )
=> ( contains_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) @ sK3_SY168 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[132]) ).
thf(135,plain,
( ( ( contains_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) @ sK3_SY168 )
& ~ ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) ) @ sK3_SY168 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[133]) ).
thf(136,plain,
( ( ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) ) @ sK3_SY168 )
& ~ ( contains_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) @ sK3_SY168 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[134]) ).
thf(137,plain,
( ( ! [U: $i] :
( ! [V: $i] :
( ~ ( ok @ V )
| ~ ( succ_cpq @ U @ V )
| ~ ( check_cpq @ V ) )
| ( phi @ U ) )
& ! [U: $i] :
( ~ ( phi @ U )
| ( ( ok @ ( sK4_V @ U ) )
& ( succ_cpq @ U @ ( sK4_V @ U ) )
& ( check_cpq @ ( sK4_V @ U ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(138,plain,
( ( ! [U: $i] :
( ! [V: $i] :
~ ( pi_sharp_find_min @ ( i @ U ) @ V )
| ( pi_removemin @ U ) )
& ! [U: $i] :
( ~ ( pi_removemin @ U )
| ( pi_sharp_find_min @ ( i @ U ) @ ( sK5_V @ U ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(139,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(140,plain,
( ( ! [U: $i] :
( ! [V: $i] :
~ ( pi_sharp_find_min @ ( i @ U ) @ V )
| ( pi_find_min @ U ) )
& ! [U: $i] :
( ~ ( pi_find_min @ U )
| ( pi_sharp_find_min @ ( i @ U ) @ ( sK6_V @ U ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(141,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(142,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(143,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(144,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(145,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(146,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(147,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(148,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(149,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
| ~ ( less_than @ ( lookup_slb @ V @ X ) @ X )
| ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[84]) ).
thf(150,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_slb @ V @ X )
| ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ U @ V @ bad ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[85]) ).
thf(151,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( triple @ U @ V @ W ) )
| ( W = bad ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(152,plain,
( ( ! [U: $i,V: $i] :
~ ( ok @ ( triple @ U @ V @ bad ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[88]) ).
thf(153,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(154,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(155,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(156,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[93]) ).
thf(157,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[94]) ).
thf(158,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(159,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(160,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(161,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(162,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(163,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(164,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(165,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(166,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(167,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(168,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(169,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(170,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(171,plain,
( ( ! [U: $i,V: $i] :
( ( ( contains_pq @ U @ ( sK7_W @ V @ U ) )
& ~ ( less_than @ V @ ( sK7_W @ V @ U ) ) )
| ( issmallestelement_pq @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( issmallestelement_pq @ U @ V )
| ! [W: $i] :
( ~ ( contains_pq @ U @ W )
| ( less_than @ V @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[118]) ).
thf(172,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(173,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(174,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(175,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( less_than @ U @ V )
| ~ ( less_than @ V @ W )
| ( less_than @ U @ W ) ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(176,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(177,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(178,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)],[173]) ).
thf(179,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(180,plain,
( ( ~ ( isnonempty_pq @ create_pq ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(181,plain,
( ( ! [U: $i,V: $i] : ( isnonempty_pq @ ( insert_pq @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(182,plain,
( ( ! [U: $i] :
~ ( contains_pq @ create_pq @ U ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(183,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)],[172]) ).
thf(184,plain,
( ( ! [U: $i,V: $i] :
( ( ( contains_pq @ U @ ( sK7_W @ V @ U ) )
& ~ ( less_than @ V @ ( sK7_W @ V @ U ) ) )
| ( issmallestelement_pq @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( issmallestelement_pq @ U @ V )
| ! [W: $i] :
( ~ ( contains_pq @ U @ W )
| ( less_than @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(185,plain,
( ( ! [U: $i,V: $i] :
( ( remove_pq @ ( insert_pq @ U @ V ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(186,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)],[170]) ).
thf(187,plain,
( ( ! [U: $i,V: $i] :
( ~ ( contains_pq @ U @ V )
| ~ ( issmallestelement_pq @ U @ V )
| ( ( findmin_pq_eff @ U @ V )
= U ) ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(188,plain,
( ( ! [U: $i,V: $i] :
( ~ ( contains_pq @ U @ V )
| ~ ( issmallestelement_pq @ U @ V )
| ( ( findmin_pq_res @ U @ V )
= V ) ) )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(189,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)],[167]) ).
thf(190,plain,
( ( ! [U: $i,V: $i] :
( ~ ( contains_pq @ U @ V )
| ~ ( issmallestelement_pq @ U @ V )
| ( ( removemin_pq_res @ U @ V )
= V ) ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(191,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(192,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(193,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(194,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(195,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)],[165]) ).
thf(196,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(197,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)],[164]) ).
thf(198,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(199,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)],[163]) ).
thf(200,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(201,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)],[162]) ).
thf(202,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(203,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)],[161]) ).
thf(204,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)],[160]) ).
thf(205,plain,
( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(206,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(207,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(208,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(209,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(210,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(211,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)],[155]) ).
thf(212,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)],[154]) ).
thf(213,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)],[153]) ).
thf(214,plain,
( ( ! [U: $i,V: $i] :
~ ( ok @ ( triple @ U @ V @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(215,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( triple @ U @ V @ W ) )
| ( W = bad ) ) )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(216,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(217,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)],[150]) ).
thf(218,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)],[149]) ).
thf(219,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)],[148]) ).
thf(220,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(221,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)],[147]) ).
thf(222,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)],[146]) ).
thf(223,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)],[145]) ).
thf(224,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(225,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)],[144]) ).
thf(226,plain,
( ( ! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(227,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(228,plain,
( ( ! [U: $i,V: $i] :
( ( i @ ( triple @ U @ create_slb @ V ) )
= create_pq ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(229,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(230,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)],[143]) ).
thf(231,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)],[142]) ).
thf(232,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)],[141]) ).
thf(233,plain,
( ( ! [U: $i] :
( ! [V: $i] :
~ ( pi_sharp_find_min @ ( i @ U ) @ V )
| ( pi_find_min @ U ) )
& ! [U: $i] :
( ~ ( pi_find_min @ U )
| ( pi_sharp_find_min @ ( i @ U ) @ ( sK6_V @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(234,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)],[139]) ).
thf(235,plain,
( ( ! [U: $i] :
( ! [V: $i] :
~ ( pi_sharp_find_min @ ( i @ U ) @ V )
| ( pi_removemin @ U ) )
& ! [U: $i] :
( ~ ( pi_removemin @ U )
| ( pi_sharp_find_min @ ( i @ U ) @ ( sK5_V @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(236,plain,
( ( ! [U: $i] :
( ! [V: $i] :
( ~ ( ok @ V )
| ~ ( succ_cpq @ U @ V )
| ~ ( check_cpq @ V ) )
| ( phi @ U ) )
& ! [U: $i] :
( ~ ( phi @ U )
| ( ( ok @ ( sK4_V @ U ) )
& ( succ_cpq @ U @ ( sK4_V @ U ) )
& ( check_cpq @ ( sK4_V @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(237,plain,
( ( ( contains_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) @ sK3_SY168 )
& ~ ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) ) @ sK3_SY168 ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(238,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)],[232]) ).
thf(239,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)],[230]) ).
thf(240,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)],[234]) ).
thf(241,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)],[178]) ).
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)],[197]) ).
thf(243,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( ok @ SX1 )
| ~ ( succ_cpq @ SX0 @ SX1 )
| ~ ( check_cpq @ SX1 ) )
| ( phi @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( phi @ SX0 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK4_V @ SX0 ) )
| ~ ( succ_cpq @ SX0 @ ( sK4_V @ SX0 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(244,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_find_min @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( pi_find_min @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK6_V @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(245,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( contains_pq @ SX0 @ ( sK7_W @ SX1 @ SX0 ) )
| ~ ~ ( less_than @ SX1 @ ( sK7_W @ SX1 @ SX0 ) ) )
| ( issmallestelement_pq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( issmallestelement_pq @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( contains_pq @ SX0 @ SX2 )
| ( less_than @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(246,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)],[183]) ).
thf(247,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)],[211]) ).
thf(248,plain,
( ( ~ ( ~ ( contains_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) @ sK3_SY168 )
| ~ ~ ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) ) @ sK3_SY168 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(249,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)],[213]) ).
thf(250,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)],[231]) ).
thf(251,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)],[195]) ).
thf(252,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_removemin @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( pi_removemin @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK5_V @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(253,plain,
! [SV1: $i] :
( ( ! [SY169: $i,SY170: $i] :
( ~ ( less_than @ SV1 @ SY169 )
| ~ ( less_than @ SY169 @ SY170 )
| ( less_than @ SV1 @ SY170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(254,plain,
! [SV2: $i] :
( ( ! [SY171: $i] :
( ( less_than @ SV2 @ SY171 )
| ( less_than @ SY171 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(255,plain,
! [SV3: $i] :
( ( less_than @ SV3 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(256,plain,
! [SV4: $i] :
( ( less_than @ bottom @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(257,plain,
( ( isnonempty_pq @ create_pq )
= $false ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(258,plain,
! [SV5: $i] :
( ( ! [SY172: $i] : ( isnonempty_pq @ ( insert_pq @ SV5 @ SY172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(259,plain,
! [SV6: $i] :
( ( ~ ( contains_pq @ create_pq @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(260,plain,
! [SV7: $i] :
( ( ! [SY173: $i] :
( ( remove_pq @ ( insert_pq @ SV7 @ SY173 ) @ SY173 )
= SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(261,plain,
! [SV8: $i] :
( ( ! [SY174: $i,SY175: $i] :
( ( SY174 = SY175 )
| ~ ( contains_pq @ SV8 @ SY175 )
| ( ( remove_pq @ ( insert_pq @ SV8 @ SY174 ) @ SY175 )
= ( insert_pq @ ( remove_pq @ SV8 @ SY175 ) @ SY174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(262,plain,
! [SV9: $i] :
( ( ! [SY176: $i] :
( ~ ( contains_pq @ SV9 @ SY176 )
| ~ ( issmallestelement_pq @ SV9 @ SY176 )
| ( ( findmin_pq_eff @ SV9 @ SY176 )
= SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(263,plain,
! [SV10: $i] :
( ( ! [SY177: $i] :
( ~ ( contains_pq @ SV10 @ SY177 )
| ~ ( issmallestelement_pq @ SV10 @ SY177 )
| ( ( findmin_pq_res @ SV10 @ SY177 )
= SY177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(264,plain,
! [SV11: $i] :
( ( ! [SY178: $i] :
( ~ ( contains_pq @ SV11 @ SY178 )
| ~ ( issmallestelement_pq @ SV11 @ SY178 )
| ( ( removemin_pq_eff @ SV11 @ SY178 )
= ( remove_pq @ SV11 @ SY178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(265,plain,
! [SV12: $i] :
( ( ! [SY179: $i] :
( ~ ( contains_pq @ SV12 @ SY179 )
| ~ ( issmallestelement_pq @ SV12 @ SY179 )
| ( ( removemin_pq_res @ SV12 @ SY179 )
= SY179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(266,plain,
! [SV13: $i] :
( ( ! [SY180: $i,SY181: $i] :
( ( insert_pq @ ( insert_pq @ SV13 @ SY180 ) @ SY181 )
= ( insert_pq @ ( insert_pq @ SV13 @ SY181 ) @ SY180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(267,plain,
( ( isnonempty_slb @ create_slb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(268,plain,
! [SV14: $i] :
( ( ! [SY182: $i,SY183: $i] : ( isnonempty_slb @ ( insert_slb @ SV14 @ ( pair @ SY182 @ SY183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(269,plain,
! [SV15: $i] :
( ( ~ ( contains_slb @ create_slb @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(270,plain,
! [SV16: $i] :
( ( ! [SY184: $i] :
~ ( pair_in_list @ create_slb @ SV16 @ SY184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(271,plain,
! [SV17: $i] :
( ( ! [SY185: $i,SY186: $i] :
( ( remove_slb @ ( insert_slb @ SV17 @ ( pair @ SY185 @ SY186 ) ) @ SY185 )
= SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(272,plain,
! [SV18: $i] :
( ( ! [SY187: $i,SY188: $i] :
( ( SY187 = SY188 )
| ~ ( contains_slb @ SV18 @ SY188 )
| ! [SY189: $i] :
( ( remove_slb @ ( insert_slb @ SV18 @ ( pair @ SY187 @ SY189 ) ) @ SY188 )
= ( insert_slb @ ( remove_slb @ SV18 @ SY188 ) @ ( pair @ SY187 @ SY189 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(273,plain,
! [SV19: $i] :
( ( ! [SY190: $i,SY191: $i] :
( ( lookup_slb @ ( insert_slb @ SV19 @ ( pair @ SY190 @ SY191 ) ) @ SY190 )
= SY191 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(274,plain,
! [SV20: $i] :
( ( ! [SY192: $i,SY193: $i] :
( ( SY192 = SY193 )
| ~ ( contains_slb @ SV20 @ SY193 )
| ! [SY194: $i] :
( ( lookup_slb @ ( insert_slb @ SV20 @ ( pair @ SY192 @ SY194 ) ) @ SY193 )
= ( lookup_slb @ SV20 @ SY193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(275,plain,
! [SV21: $i] :
( ( ( update_slb @ create_slb @ SV21 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(276,plain,
! [SV22: $i] :
( ( ! [SY195: $i,SY196: $i,SY197: $i] :
( ~ ( strictly_less_than @ SY197 @ SY196 )
| ( ( update_slb @ ( insert_slb @ SV22 @ ( pair @ SY195 @ SY197 ) ) @ SY196 )
= ( insert_slb @ ( update_slb @ SV22 @ SY196 ) @ ( pair @ SY195 @ SY196 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(277,plain,
! [SV23: $i] :
( ( ! [SY198: $i,SY199: $i,SY200: $i] :
( ~ ( less_than @ SY199 @ SY200 )
| ( ( update_slb @ ( insert_slb @ SV23 @ ( pair @ SY198 @ SY200 ) ) @ SY199 )
= ( insert_slb @ ( update_slb @ SV23 @ SY199 ) @ ( pair @ SY198 @ SY200 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(278,plain,
! [SV24: $i] :
( ( succ_cpq @ SV24 @ SV24 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(279,plain,
! [SV25: $i] :
( ( ! [SY201: $i] :
( ~ ( succ_cpq @ SV25 @ SY201 )
| ! [SY202: $i] : ( succ_cpq @ SV25 @ ( insert_cpq @ SY201 @ SY202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(280,plain,
! [SV26: $i] :
( ( ! [SY203: $i] :
( ~ ( succ_cpq @ SV26 @ SY203 )
| ! [SY204: $i] : ( succ_cpq @ SV26 @ ( remove_cpq @ SY203 @ SY204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(281,plain,
! [SV27: $i] :
( ( ! [SY205: $i] :
( ~ ( succ_cpq @ SV27 @ SY205 )
| ( succ_cpq @ SV27 @ ( findmin_cpq_eff @ SY205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(282,plain,
! [SV28: $i] :
( ( ! [SY206: $i] :
( ~ ( succ_cpq @ SV28 @ SY206 )
| ( succ_cpq @ SV28 @ ( removemin_cpq_eff @ SY206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(283,plain,
! [SV29: $i] :
( ( ! [SY207: $i] : ( check_cpq @ ( triple @ SV29 @ create_slb @ SY207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(284,plain,
! [SV30: $i] :
( ( ! [SY208: $i,SY209: $i,SY210: $i,SY211: $i] :
( ~ ( strictly_less_than @ SY210 @ SY211 )
| ~ ( check_cpq @ ( triple @ SV30 @ ( insert_slb @ SY208 @ ( pair @ SY210 @ SY211 ) ) @ SY209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(285,plain,
! [SV31: $i] :
( ( ! [SY212: $i] :
~ ( ok @ ( triple @ SV31 @ SY212 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(286,plain,
! [SV32: $i] :
( ( ! [SY213: $i,SY214: $i] :
( ( ok @ ( triple @ SV32 @ SY213 @ SY214 ) )
| ( SY214 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(287,plain,
! [SV33: $i] :
( ( ! [SY215: $i,SY216: $i,SY217: $i] :
( ( insert_cpq @ ( triple @ SV33 @ SY215 @ SY216 ) @ SY217 )
= ( triple @ ( insert_pqp @ SV33 @ SY217 ) @ ( insert_slb @ SY215 @ ( pair @ SY217 @ bottom ) ) @ SY216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(288,plain,
! [SV34: $i] :
( ( ! [SY218: $i,SY219: $i,SY220: $i] :
( ( contains_slb @ SY218 @ SY220 )
| ( ( remove_cpq @ ( triple @ SV34 @ SY218 @ SY219 ) @ SY220 )
= ( triple @ SV34 @ SY218 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(289,plain,
! [SV35: $i] :
( ( ! [SY221: $i,SY222: $i,SY223: $i] :
( ~ ( contains_slb @ SY221 @ SY223 )
| ~ ( less_than @ ( lookup_slb @ SY221 @ SY223 ) @ SY223 )
| ( ( remove_cpq @ ( triple @ SV35 @ SY221 @ SY222 ) @ SY223 )
= ( triple @ ( remove_pqp @ SV35 @ SY223 ) @ ( remove_slb @ SY221 @ SY223 ) @ SY222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(290,plain,
! [SV36: $i] :
( ( ! [SY224: $i,SY225: $i,SY226: $i] :
( ~ ( contains_slb @ SY224 @ SY226 )
| ~ ( strictly_less_than @ SY226 @ ( lookup_slb @ SY224 @ SY226 ) )
| ( ( remove_cpq @ ( triple @ SV36 @ SY224 @ SY225 ) @ SY226 )
= ( triple @ ( remove_pqp @ SV36 @ SY226 ) @ ( remove_slb @ SY224 @ SY226 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(291,plain,
! [SV37: $i] :
( ( ! [SY227: $i] :
( ( findmin_cpq_eff @ ( triple @ SV37 @ create_slb @ SY227 ) )
= ( triple @ SV37 @ create_slb @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(292,plain,
! [SV38: $i] :
( ( ! [SY228: $i] :
( ( SY228 = create_slb )
| ( contains_slb @ SY228 @ ( findmin_pqp_res @ SV38 ) )
| ! [SY229: $i] :
( ( findmin_cpq_eff @ ( triple @ SV38 @ SY228 @ SY229 ) )
= ( triple @ SV38 @ ( update_slb @ SY228 @ ( findmin_pqp_res @ SV38 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(293,plain,
! [SV39: $i] :
( ( ! [SY230: $i] :
( ( SY230 = create_slb )
| ~ ( contains_slb @ SY230 @ ( findmin_pqp_res @ SV39 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV39 ) @ ( lookup_slb @ SY230 @ ( findmin_pqp_res @ SV39 ) ) )
| ! [SY231: $i] :
( ( findmin_cpq_eff @ ( triple @ SV39 @ SY230 @ SY231 ) )
= ( triple @ SV39 @ ( update_slb @ SY230 @ ( findmin_pqp_res @ SV39 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(294,plain,
! [SV40: $i] :
( ( ! [SY232: $i] :
( ( SY232 = create_slb )
| ~ ( contains_slb @ SY232 @ ( findmin_pqp_res @ SV40 ) )
| ~ ( less_than @ ( lookup_slb @ SY232 @ ( findmin_pqp_res @ SV40 ) ) @ ( findmin_pqp_res @ SV40 ) )
| ! [SY233: $i] :
( ( findmin_cpq_eff @ ( triple @ SV40 @ SY232 @ SY233 ) )
= ( triple @ SV40 @ ( update_slb @ SY232 @ ( findmin_pqp_res @ SV40 ) ) @ SY233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(295,plain,
! [SV41: $i] :
( ( ! [SY234: $i] :
( ( findmin_cpq_res @ ( triple @ SV41 @ create_slb @ SY234 ) )
= bottom ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(296,plain,
! [SV42: $i] :
( ( ! [SY235: $i] :
( ( SY235 = create_slb )
| ! [SY236: $i] :
( ( findmin_cpq_res @ ( triple @ SV42 @ SY235 @ SY236 ) )
= ( findmin_pqp_res @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(297,plain,
! [SV43: $i] :
( ( ( removemin_cpq_eff @ SV43 )
= ( remove_cpq @ ( findmin_cpq_eff @ SV43 ) @ ( findmin_cpq_res @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(298,plain,
! [SV44: $i] :
( ( ( removemin_cpq_res @ SV44 )
= ( findmin_cpq_res @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(299,plain,
! [SV45: $i] :
( ( ! [SY237: $i] :
( ( i @ ( triple @ SV45 @ create_slb @ SY237 ) )
= create_pq ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(300,plain,
! [SV46: $i] :
( ( ! [SY238: $i,SY239: $i,SY240: $i,SY241: $i] :
( ( i @ ( triple @ SV46 @ ( insert_slb @ SY238 @ ( pair @ SY240 @ SY241 ) ) @ SY239 ) )
= ( insert_pq @ ( i @ ( triple @ SV46 @ SY238 @ SY239 ) ) @ SY240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(301,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)],[238]) ).
thf(302,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)],[239]) ).
thf(303,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)],[240]) ).
thf(304,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)],[241]) ).
thf(305,plain,
! [SV47: $i] :
( ( ! [SY242: $i,SY243: $i] :
~ ( ~ ~ ( ~ ! [SY244: $i,SY245: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SY242 @ SY244 ) ) @ SY243 @ SY245 )
| ( SY242 = SY243 )
| ( pair_in_list @ SV47 @ SY243 @ SY245 ) )
| ~ ! [SY246: $i,SY247: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SY242 @ SY246 ) ) @ SY243 @ SY247 )
| ( SY246 = SY247 )
| ( pair_in_list @ SV47 @ SY243 @ SY247 ) ) )
| ~ ~ ( ~ ! [SY248: $i,SY249: $i] :
( ( SY242 != SY243 )
| ( SY248 != SY249 )
| ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SY242 @ SY248 ) ) @ SY243 @ SY249 ) )
| ~ ! [SY250: $i,SY251: $i] :
( ~ ( pair_in_list @ SV47 @ SY243 @ SY251 )
| ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SY242 @ SY250 ) ) @ SY243 @ SY251 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(306,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( ok @ SX1 )
| ~ ( succ_cpq @ SX0 @ SX1 )
| ~ ( check_cpq @ SX1 ) )
| ( phi @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( phi @ SX0 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK4_V @ SX0 ) )
| ~ ( succ_cpq @ SX0 @ ( sK4_V @ SX0 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
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 ) @ ( sK6_V @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(308,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( contains_pq @ SX0 @ ( sK7_W @ SX1 @ SX0 ) )
| ~ ~ ( less_than @ SX1 @ ( sK7_W @ SX1 @ SX0 ) ) )
| ( issmallestelement_pq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( issmallestelement_pq @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( contains_pq @ SX0 @ SX2 )
| ( less_than @ SX1 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(309,plain,
! [SV48: $i] :
( ( ~ ( ~ ! [SY252: $i,SY253: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV48 @ SY252 ) @ SY253 )
| ( SY252 = SY253 )
| ( contains_pq @ SV48 @ SY253 ) )
| ~ ~ ( ~ ! [SY254: $i,SY255: $i] :
( ( SY254 != SY255 )
| ( contains_pq @ ( insert_pq @ SV48 @ SY254 ) @ SY255 ) )
| ~ ! [SY256: $i,SY257: $i] :
( ~ ( contains_pq @ SV48 @ SY257 )
| ( contains_pq @ ( insert_pq @ SV48 @ SY256 ) @ SY257 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(310,plain,
! [SV49: $i] :
( ( ! [SY258: $i,SY259: $i] :
~ ( ~ ! [SY260: $i,SY261: $i] :
( ~ ( less_than @ SY261 @ SY260 )
| ~ ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SY258 @ ( pair @ SY260 @ SY261 ) ) @ SY259 ) )
| ( check_cpq @ ( triple @ SV49 @ SY258 @ SY259 ) ) )
| ~ ! [SY262: $i,SY263: $i] :
( ~ ( less_than @ SY263 @ SY262 )
| ~ ( check_cpq @ ( triple @ SV49 @ SY258 @ SY259 ) )
| ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SY258 @ ( pair @ SY262 @ SY263 ) ) @ SY259 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(311,plain,
( ( ~ ( contains_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) @ sK3_SY168 )
| ~ ~ ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) ) @ sK3_SY168 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(312,plain,
! [SV50: $i] :
( ( ! [SY264: $i] :
~ ( ~ ! [SY265: $i,SY266: $i] :
( ~ ( contains_cpq @ ( triple @ SV50 @ SY264 @ SY265 ) @ SY266 )
| ( contains_slb @ SY264 @ SY266 ) )
| ~ ! [SY267: $i,SY268: $i] :
( ~ ( contains_slb @ SY264 @ SY268 )
| ( contains_cpq @ ( triple @ SV50 @ SY264 @ SY267 ) @ SY268 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(313,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_remove @ SX0 @ SX1 )
| ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 )
| ( pi_remove @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(314,plain,
! [SV51: $i] :
( ( ! [SY269: $i] :
~ ( ~ ! [SY270: $i] :
( ! [SY271: $i] :
~ ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SY269 @ SY271 ) ) @ SY270 )
| ( SY269 = SY270 )
| ( contains_slb @ SV51 @ SY270 ) )
| ~ ~ ( ~ ! [SY272: $i] :
( ( SY269 != SY272 )
| ! [SY273: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SY269 @ SY273 ) ) @ SY272 ) )
| ~ ! [SY274: $i] :
( ~ ( contains_slb @ SV51 @ SY274 )
| ! [SY275: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SY269 @ SY275 ) ) @ SY274 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(315,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_removemin @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( pi_removemin @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK5_V @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(316,plain,
! [SV52: $i,SV1: $i] :
( ( ! [SY276: $i] :
( ~ ( less_than @ SV1 @ SV52 )
| ~ ( less_than @ SV52 @ SY276 )
| ( less_than @ SV1 @ SY276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(317,plain,
! [SV53: $i,SV2: $i] :
( ( ( less_than @ SV2 @ SV53 )
| ( less_than @ SV53 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(318,plain,
! [SV54: $i,SV5: $i] :
( ( isnonempty_pq @ ( insert_pq @ SV5 @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(319,plain,
! [SV6: $i] :
( ( contains_pq @ create_pq @ SV6 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(320,plain,
! [SV55: $i,SV7: $i] :
( ( ( remove_pq @ ( insert_pq @ SV7 @ SV55 ) @ SV55 )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(321,plain,
! [SV8: $i,SV56: $i] :
( ( ! [SY277: $i] :
( ( SV56 = SY277 )
| ~ ( contains_pq @ SV8 @ SY277 )
| ( ( remove_pq @ ( insert_pq @ SV8 @ SV56 ) @ SY277 )
= ( insert_pq @ ( remove_pq @ SV8 @ SY277 ) @ SV56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(322,plain,
! [SV57: $i,SV9: $i] :
( ( ~ ( contains_pq @ SV9 @ SV57 )
| ~ ( issmallestelement_pq @ SV9 @ SV57 )
| ( ( findmin_pq_eff @ SV9 @ SV57 )
= SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(323,plain,
! [SV58: $i,SV10: $i] :
( ( ~ ( contains_pq @ SV10 @ SV58 )
| ~ ( issmallestelement_pq @ SV10 @ SV58 )
| ( ( findmin_pq_res @ SV10 @ SV58 )
= SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(324,plain,
! [SV59: $i,SV11: $i] :
( ( ~ ( contains_pq @ SV11 @ SV59 )
| ~ ( issmallestelement_pq @ SV11 @ SV59 )
| ( ( removemin_pq_eff @ SV11 @ SV59 )
= ( remove_pq @ SV11 @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(325,plain,
! [SV60: $i,SV12: $i] :
( ( ~ ( contains_pq @ SV12 @ SV60 )
| ~ ( issmallestelement_pq @ SV12 @ SV60 )
| ( ( removemin_pq_res @ SV12 @ SV60 )
= SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(326,plain,
! [SV61: $i,SV13: $i] :
( ( ! [SY278: $i] :
( ( insert_pq @ ( insert_pq @ SV13 @ SV61 ) @ SY278 )
= ( insert_pq @ ( insert_pq @ SV13 @ SY278 ) @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(327,plain,
! [SV62: $i,SV14: $i] :
( ( ! [SY279: $i] : ( isnonempty_slb @ ( insert_slb @ SV14 @ ( pair @ SV62 @ SY279 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(328,plain,
! [SV15: $i] :
( ( contains_slb @ create_slb @ SV15 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(329,plain,
! [SV63: $i,SV16: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV16 @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(330,plain,
! [SV64: $i,SV17: $i] :
( ( ! [SY280: $i] :
( ( remove_slb @ ( insert_slb @ SV17 @ ( pair @ SV64 @ SY280 ) ) @ SV64 )
= SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(331,plain,
! [SV18: $i,SV65: $i] :
( ( ! [SY281: $i] :
( ( SV65 = SY281 )
| ~ ( contains_slb @ SV18 @ SY281 )
| ! [SY282: $i] :
( ( remove_slb @ ( insert_slb @ SV18 @ ( pair @ SV65 @ SY282 ) ) @ SY281 )
= ( insert_slb @ ( remove_slb @ SV18 @ SY281 ) @ ( pair @ SV65 @ SY282 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(332,plain,
! [SV66: $i,SV19: $i] :
( ( ! [SY283: $i] :
( ( lookup_slb @ ( insert_slb @ SV19 @ ( pair @ SV66 @ SY283 ) ) @ SV66 )
= SY283 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(333,plain,
! [SV20: $i,SV67: $i] :
( ( ! [SY284: $i] :
( ( SV67 = SY284 )
| ~ ( contains_slb @ SV20 @ SY284 )
| ! [SY285: $i] :
( ( lookup_slb @ ( insert_slb @ SV20 @ ( pair @ SV67 @ SY285 ) ) @ SY284 )
= ( lookup_slb @ SV20 @ SY284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(334,plain,
! [SV68: $i,SV22: $i] :
( ( ! [SY286: $i,SY287: $i] :
( ~ ( strictly_less_than @ SY287 @ SY286 )
| ( ( update_slb @ ( insert_slb @ SV22 @ ( pair @ SV68 @ SY287 ) ) @ SY286 )
= ( insert_slb @ ( update_slb @ SV22 @ SY286 ) @ ( pair @ SV68 @ SY286 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(335,plain,
! [SV69: $i,SV23: $i] :
( ( ! [SY288: $i,SY289: $i] :
( ~ ( less_than @ SY288 @ SY289 )
| ( ( update_slb @ ( insert_slb @ SV23 @ ( pair @ SV69 @ SY289 ) ) @ SY288 )
= ( insert_slb @ ( update_slb @ SV23 @ SY288 ) @ ( pair @ SV69 @ SY289 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(336,plain,
! [SV70: $i,SV25: $i] :
( ( ~ ( succ_cpq @ SV25 @ SV70 )
| ! [SY290: $i] : ( succ_cpq @ SV25 @ ( insert_cpq @ SV70 @ SY290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(337,plain,
! [SV71: $i,SV26: $i] :
( ( ~ ( succ_cpq @ SV26 @ SV71 )
| ! [SY291: $i] : ( succ_cpq @ SV26 @ ( remove_cpq @ SV71 @ SY291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(338,plain,
! [SV72: $i,SV27: $i] :
( ( ~ ( succ_cpq @ SV27 @ SV72 )
| ( succ_cpq @ SV27 @ ( findmin_cpq_eff @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(339,plain,
! [SV73: $i,SV28: $i] :
( ( ~ ( succ_cpq @ SV28 @ SV73 )
| ( succ_cpq @ SV28 @ ( removemin_cpq_eff @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(340,plain,
! [SV74: $i,SV29: $i] :
( ( check_cpq @ ( triple @ SV29 @ create_slb @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(341,plain,
! [SV75: $i,SV30: $i] :
( ( ! [SY292: $i,SY293: $i,SY294: $i] :
( ~ ( strictly_less_than @ SY293 @ SY294 )
| ~ ( check_cpq @ ( triple @ SV30 @ ( insert_slb @ SV75 @ ( pair @ SY293 @ SY294 ) ) @ SY292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(342,plain,
! [SV76: $i,SV31: $i] :
( ( ~ ( ok @ ( triple @ SV31 @ SV76 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(343,plain,
! [SV77: $i,SV32: $i] :
( ( ! [SY295: $i] :
( ( ok @ ( triple @ SV32 @ SV77 @ SY295 ) )
| ( SY295 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(344,plain,
! [SV78: $i,SV33: $i] :
( ( ! [SY296: $i,SY297: $i] :
( ( insert_cpq @ ( triple @ SV33 @ SV78 @ SY296 ) @ SY297 )
= ( triple @ ( insert_pqp @ SV33 @ SY297 ) @ ( insert_slb @ SV78 @ ( pair @ SY297 @ bottom ) ) @ SY296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(345,plain,
! [SV34: $i,SV79: $i] :
( ( ! [SY298: $i,SY299: $i] :
( ( contains_slb @ SV79 @ SY299 )
| ( ( remove_cpq @ ( triple @ SV34 @ SV79 @ SY298 ) @ SY299 )
= ( triple @ SV34 @ SV79 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(346,plain,
! [SV35: $i,SV80: $i] :
( ( ! [SY300: $i,SY301: $i] :
( ~ ( contains_slb @ SV80 @ SY301 )
| ~ ( less_than @ ( lookup_slb @ SV80 @ SY301 ) @ SY301 )
| ( ( remove_cpq @ ( triple @ SV35 @ SV80 @ SY300 ) @ SY301 )
= ( triple @ ( remove_pqp @ SV35 @ SY301 ) @ ( remove_slb @ SV80 @ SY301 ) @ SY300 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(347,plain,
! [SV36: $i,SV81: $i] :
( ( ! [SY302: $i,SY303: $i] :
( ~ ( contains_slb @ SV81 @ SY303 )
| ~ ( strictly_less_than @ SY303 @ ( lookup_slb @ SV81 @ SY303 ) )
| ( ( remove_cpq @ ( triple @ SV36 @ SV81 @ SY302 ) @ SY303 )
= ( triple @ ( remove_pqp @ SV36 @ SY303 ) @ ( remove_slb @ SV81 @ SY303 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(348,plain,
! [SV82: $i,SV37: $i] :
( ( ( findmin_cpq_eff @ ( triple @ SV37 @ create_slb @ SV82 ) )
= ( triple @ SV37 @ create_slb @ bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(349,plain,
! [SV38: $i,SV83: $i] :
( ( ( SV83 = create_slb )
| ( contains_slb @ SV83 @ ( findmin_pqp_res @ SV38 ) )
| ! [SY304: $i] :
( ( findmin_cpq_eff @ ( triple @ SV38 @ SV83 @ SY304 ) )
= ( triple @ SV38 @ ( update_slb @ SV83 @ ( findmin_pqp_res @ SV38 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(350,plain,
! [SV39: $i,SV84: $i] :
( ( ( SV84 = create_slb )
| ~ ( contains_slb @ SV84 @ ( findmin_pqp_res @ SV39 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV39 ) @ ( lookup_slb @ SV84 @ ( findmin_pqp_res @ SV39 ) ) )
| ! [SY305: $i] :
( ( findmin_cpq_eff @ ( triple @ SV39 @ SV84 @ SY305 ) )
= ( triple @ SV39 @ ( update_slb @ SV84 @ ( findmin_pqp_res @ SV39 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(351,plain,
! [SV40: $i,SV85: $i] :
( ( ( SV85 = create_slb )
| ~ ( contains_slb @ SV85 @ ( findmin_pqp_res @ SV40 ) )
| ~ ( less_than @ ( lookup_slb @ SV85 @ ( findmin_pqp_res @ SV40 ) ) @ ( findmin_pqp_res @ SV40 ) )
| ! [SY306: $i] :
( ( findmin_cpq_eff @ ( triple @ SV40 @ SV85 @ SY306 ) )
= ( triple @ SV40 @ ( update_slb @ SV85 @ ( findmin_pqp_res @ SV40 ) ) @ SY306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(352,plain,
! [SV86: $i,SV41: $i] :
( ( ( findmin_cpq_res @ ( triple @ SV41 @ create_slb @ SV86 ) )
= bottom )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(353,plain,
! [SV42: $i,SV87: $i] :
( ( ( SV87 = create_slb )
| ! [SY307: $i] :
( ( findmin_cpq_res @ ( triple @ SV42 @ SV87 @ SY307 ) )
= ( findmin_pqp_res @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(354,plain,
! [SV88: $i,SV45: $i] :
( ( ( i @ ( triple @ SV45 @ create_slb @ SV88 ) )
= create_pq )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(355,plain,
! [SV89: $i,SV46: $i] :
( ( ! [SY308: $i,SY309: $i,SY310: $i] :
( ( i @ ( triple @ SV46 @ ( insert_slb @ SV89 @ ( pair @ SY309 @ SY310 ) ) @ SY308 ) )
= ( insert_pq @ ( i @ ( triple @ SV46 @ SV89 @ SY308 ) ) @ SY309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(356,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)],[301]) ).
thf(357,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)],[301]) ).
thf(358,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( contains_pq @ SX0 @ SX1 )
| ( pi_sharp_remove @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[302]) ).
thf(359,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[302]) ).
thf(360,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)],[303]) ).
thf(361,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)],[303]) ).
thf(362,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)],[304]) ).
thf(363,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)],[304]) ).
thf(364,plain,
! [SV90: $i,SV47: $i] :
( ( ! [SY311: $i] :
~ ( ~ ~ ( ~ ! [SY312: $i,SY313: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY312 ) ) @ SY311 @ SY313 )
| ( SV90 = SY311 )
| ( pair_in_list @ SV47 @ SY311 @ SY313 ) )
| ~ ! [SY314: $i,SY315: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY314 ) ) @ SY311 @ SY315 )
| ( SY314 = SY315 )
| ( pair_in_list @ SV47 @ SY311 @ SY315 ) ) )
| ~ ~ ( ~ ! [SY316: $i,SY317: $i] :
( ( SV90 != SY311 )
| ( SY316 != SY317 )
| ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY316 ) ) @ SY311 @ SY317 ) )
| ~ ! [SY318: $i,SY319: $i] :
( ~ ( pair_in_list @ SV47 @ SY311 @ SY319 )
| ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY318 ) ) @ SY311 @ SY319 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(365,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( ok @ SX1 )
| ~ ( succ_cpq @ SX0 @ SX1 )
| ~ ( check_cpq @ SX1 ) )
| ( phi @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[306]) ).
thf(366,plain,
( ( ~ ! [SX0: $i] :
( ~ ( phi @ SX0 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK4_V @ SX0 ) )
| ~ ( succ_cpq @ SX0 @ ( sK4_V @ SX0 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[306]) ).
thf(367,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(368,plain,
( ( ~ ! [SX0: $i] :
( ~ ( pi_find_min @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK6_V @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(369,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( contains_pq @ SX0 @ ( sK7_W @ SX1 @ SX0 ) )
| ~ ~ ( less_than @ SX1 @ ( sK7_W @ SX1 @ SX0 ) ) )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[308]) ).
thf(370,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)],[308]) ).
thf(371,plain,
! [SV48: $i] :
( ( ~ ! [SY252: $i,SY253: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV48 @ SY252 ) @ SY253 )
| ( SY252 = SY253 )
| ( contains_pq @ SV48 @ SY253 ) )
| ~ ~ ( ~ ! [SY254: $i,SY255: $i] :
( ( SY254 != SY255 )
| ( contains_pq @ ( insert_pq @ SV48 @ SY254 ) @ SY255 ) )
| ~ ! [SY256: $i,SY257: $i] :
( ~ ( contains_pq @ SV48 @ SY257 )
| ( contains_pq @ ( insert_pq @ SV48 @ SY256 ) @ SY257 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(372,plain,
! [SV91: $i,SV49: $i] :
( ( ! [SY320: $i] :
~ ( ~ ! [SY321: $i,SY322: $i] :
( ~ ( less_than @ SY322 @ SY321 )
| ~ ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SV91 @ ( pair @ SY321 @ SY322 ) ) @ SY320 ) )
| ( check_cpq @ ( triple @ SV49 @ SV91 @ SY320 ) ) )
| ~ ! [SY323: $i,SY324: $i] :
( ~ ( less_than @ SY324 @ SY323 )
| ~ ( check_cpq @ ( triple @ SV49 @ SV91 @ SY320 ) )
| ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SV91 @ ( pair @ SY323 @ SY324 ) ) @ SY320 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(373,plain,
( ( ~ ( contains_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) @ sK3_SY168 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(374,plain,
( ( ~ ~ ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) ) @ sK3_SY168 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(375,plain,
! [SV92: $i,SV50: $i] :
( ( ~ ( ~ ! [SY325: $i,SY326: $i] :
( ~ ( contains_cpq @ ( triple @ SV50 @ SV92 @ SY325 ) @ SY326 )
| ( contains_slb @ SV92 @ SY326 ) )
| ~ ! [SY327: $i,SY328: $i] :
( ~ ( contains_slb @ SV92 @ SY328 )
| ( contains_cpq @ ( triple @ SV50 @ SV92 @ SY327 ) @ SY328 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(376,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_remove @ SX0 @ SX1 )
| ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(377,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 )
| ( pi_remove @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(378,plain,
! [SV93: $i,SV51: $i] :
( ( ~ ( ~ ! [SY329: $i] :
( ! [SY330: $i] :
~ ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY330 ) ) @ SY329 )
| ( SV93 = SY329 )
| ( contains_slb @ SV51 @ SY329 ) )
| ~ ~ ( ~ ! [SY331: $i] :
( ( SV93 != SY331 )
| ! [SY332: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY332 ) ) @ SY331 ) )
| ~ ! [SY333: $i] :
( ~ ( contains_slb @ SV51 @ SY333 )
| ! [SY334: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY334 ) ) @ SY333 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(379,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_removemin @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[315]) ).
thf(380,plain,
( ( ~ ! [SX0: $i] :
( ~ ( pi_removemin @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK5_V @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[315]) ).
thf(381,plain,
! [SV94: $i,SV52: $i,SV1: $i] :
( ( ~ ( less_than @ SV1 @ SV52 )
| ~ ( less_than @ SV52 @ SV94 )
| ( less_than @ SV1 @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(382,plain,
! [SV53: $i,SV2: $i] :
( ( ( less_than @ SV2 @ SV53 )
= $true )
| ( ( less_than @ SV53 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(383,plain,
! [SV8: $i,SV95: $i,SV56: $i] :
( ( ( SV56 = SV95 )
| ~ ( contains_pq @ SV8 @ SV95 )
| ( ( remove_pq @ ( insert_pq @ SV8 @ SV56 ) @ SV95 )
= ( insert_pq @ ( remove_pq @ SV8 @ SV95 ) @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(384,plain,
! [SV57: $i,SV9: $i] :
( ( ( ~ ( contains_pq @ SV9 @ SV57 )
| ~ ( issmallestelement_pq @ SV9 @ SV57 ) )
= $true )
| ( ( ( findmin_pq_eff @ SV9 @ SV57 )
= SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(385,plain,
! [SV58: $i,SV10: $i] :
( ( ( ~ ( contains_pq @ SV10 @ SV58 )
| ~ ( issmallestelement_pq @ SV10 @ SV58 ) )
= $true )
| ( ( ( findmin_pq_res @ SV10 @ SV58 )
= SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(386,plain,
! [SV59: $i,SV11: $i] :
( ( ( ~ ( contains_pq @ SV11 @ SV59 )
| ~ ( issmallestelement_pq @ SV11 @ SV59 ) )
= $true )
| ( ( ( removemin_pq_eff @ SV11 @ SV59 )
= ( remove_pq @ SV11 @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(387,plain,
! [SV60: $i,SV12: $i] :
( ( ( ~ ( contains_pq @ SV12 @ SV60 )
| ~ ( issmallestelement_pq @ SV12 @ SV60 ) )
= $true )
| ( ( ( removemin_pq_res @ SV12 @ SV60 )
= SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(388,plain,
! [SV96: $i,SV61: $i,SV13: $i] :
( ( ( insert_pq @ ( insert_pq @ SV13 @ SV61 ) @ SV96 )
= ( insert_pq @ ( insert_pq @ SV13 @ SV96 ) @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(389,plain,
! [SV97: $i,SV62: $i,SV14: $i] :
( ( isnonempty_slb @ ( insert_slb @ SV14 @ ( pair @ SV62 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(390,plain,
! [SV63: $i,SV16: $i] :
( ( pair_in_list @ create_slb @ SV16 @ SV63 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(391,plain,
! [SV98: $i,SV64: $i,SV17: $i] :
( ( ( remove_slb @ ( insert_slb @ SV17 @ ( pair @ SV64 @ SV98 ) ) @ SV64 )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(392,plain,
! [SV18: $i,SV99: $i,SV65: $i] :
( ( ( SV65 = SV99 )
| ~ ( contains_slb @ SV18 @ SV99 )
| ! [SY335: $i] :
( ( remove_slb @ ( insert_slb @ SV18 @ ( pair @ SV65 @ SY335 ) ) @ SV99 )
= ( insert_slb @ ( remove_slb @ SV18 @ SV99 ) @ ( pair @ SV65 @ SY335 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(393,plain,
! [SV100: $i,SV66: $i,SV19: $i] :
( ( ( lookup_slb @ ( insert_slb @ SV19 @ ( pair @ SV66 @ SV100 ) ) @ SV66 )
= SV100 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(394,plain,
! [SV20: $i,SV101: $i,SV67: $i] :
( ( ( SV67 = SV101 )
| ~ ( contains_slb @ SV20 @ SV101 )
| ! [SY336: $i] :
( ( lookup_slb @ ( insert_slb @ SV20 @ ( pair @ SV67 @ SY336 ) ) @ SV101 )
= ( lookup_slb @ SV20 @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(395,plain,
! [SV68: $i,SV22: $i,SV102: $i] :
( ( ! [SY337: $i] :
( ~ ( strictly_less_than @ SY337 @ SV102 )
| ( ( update_slb @ ( insert_slb @ SV22 @ ( pair @ SV68 @ SY337 ) ) @ SV102 )
= ( insert_slb @ ( update_slb @ SV22 @ SV102 ) @ ( pair @ SV68 @ SV102 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(396,plain,
! [SV69: $i,SV23: $i,SV103: $i] :
( ( ! [SY338: $i] :
( ~ ( less_than @ SV103 @ SY338 )
| ( ( update_slb @ ( insert_slb @ SV23 @ ( pair @ SV69 @ SY338 ) ) @ SV103 )
= ( insert_slb @ ( update_slb @ SV23 @ SV103 ) @ ( pair @ SV69 @ SY338 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(397,plain,
! [SV70: $i,SV25: $i] :
( ( ( ~ ( succ_cpq @ SV25 @ SV70 ) )
= $true )
| ( ( ! [SY290: $i] : ( succ_cpq @ SV25 @ ( insert_cpq @ SV70 @ SY290 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(398,plain,
! [SV71: $i,SV26: $i] :
( ( ( ~ ( succ_cpq @ SV26 @ SV71 ) )
= $true )
| ( ( ! [SY291: $i] : ( succ_cpq @ SV26 @ ( remove_cpq @ SV71 @ SY291 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(399,plain,
! [SV72: $i,SV27: $i] :
( ( ( ~ ( succ_cpq @ SV27 @ SV72 ) )
= $true )
| ( ( succ_cpq @ SV27 @ ( findmin_cpq_eff @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(400,plain,
! [SV73: $i,SV28: $i] :
( ( ( ~ ( succ_cpq @ SV28 @ SV73 ) )
= $true )
| ( ( succ_cpq @ SV28 @ ( removemin_cpq_eff @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(401,plain,
! [SV104: $i,SV75: $i,SV30: $i] :
( ( ! [SY339: $i,SY340: $i] :
( ~ ( strictly_less_than @ SY339 @ SY340 )
| ~ ( check_cpq @ ( triple @ SV30 @ ( insert_slb @ SV75 @ ( pair @ SY339 @ SY340 ) ) @ SV104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(402,plain,
! [SV76: $i,SV31: $i] :
( ( ok @ ( triple @ SV31 @ SV76 @ bad ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(403,plain,
! [SV105: $i,SV77: $i,SV32: $i] :
( ( ( ok @ ( triple @ SV32 @ SV77 @ SV105 ) )
| ( SV105 = bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(404,plain,
! [SV106: $i,SV78: $i,SV33: $i] :
( ( ! [SY341: $i] :
( ( insert_cpq @ ( triple @ SV33 @ SV78 @ SV106 ) @ SY341 )
= ( triple @ ( insert_pqp @ SV33 @ SY341 ) @ ( insert_slb @ SV78 @ ( pair @ SY341 @ bottom ) ) @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(405,plain,
! [SV107: $i,SV34: $i,SV79: $i] :
( ( ! [SY342: $i] :
( ( contains_slb @ SV79 @ SY342 )
| ( ( remove_cpq @ ( triple @ SV34 @ SV79 @ SV107 ) @ SY342 )
= ( triple @ SV34 @ SV79 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(406,plain,
! [SV108: $i,SV35: $i,SV80: $i] :
( ( ! [SY343: $i] :
( ~ ( contains_slb @ SV80 @ SY343 )
| ~ ( less_than @ ( lookup_slb @ SV80 @ SY343 ) @ SY343 )
| ( ( remove_cpq @ ( triple @ SV35 @ SV80 @ SV108 ) @ SY343 )
= ( triple @ ( remove_pqp @ SV35 @ SY343 ) @ ( remove_slb @ SV80 @ SY343 ) @ SV108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(407,plain,
! [SV109: $i,SV36: $i,SV81: $i] :
( ( ! [SY344: $i] :
( ~ ( contains_slb @ SV81 @ SY344 )
| ~ ( strictly_less_than @ SY344 @ ( lookup_slb @ SV81 @ SY344 ) )
| ( ( remove_cpq @ ( triple @ SV36 @ SV81 @ SV109 ) @ SY344 )
= ( triple @ ( remove_pqp @ SV36 @ SY344 ) @ ( remove_slb @ SV81 @ SY344 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(408,plain,
! [SV38: $i,SV83: $i] :
( ( ( ( SV83 = create_slb )
| ( contains_slb @ SV83 @ ( findmin_pqp_res @ SV38 ) ) )
= $true )
| ( ( ! [SY304: $i] :
( ( findmin_cpq_eff @ ( triple @ SV38 @ SV83 @ SY304 ) )
= ( triple @ SV38 @ ( update_slb @ SV83 @ ( findmin_pqp_res @ SV38 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(409,plain,
! [SV39: $i,SV84: $i] :
( ( ( ( SV84 = create_slb )
| ~ ( contains_slb @ SV84 @ ( findmin_pqp_res @ SV39 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV39 ) @ ( lookup_slb @ SV84 @ ( findmin_pqp_res @ SV39 ) ) ) )
= $true )
| ( ( ! [SY305: $i] :
( ( findmin_cpq_eff @ ( triple @ SV39 @ SV84 @ SY305 ) )
= ( triple @ SV39 @ ( update_slb @ SV84 @ ( findmin_pqp_res @ SV39 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(410,plain,
! [SV40: $i,SV85: $i] :
( ( ( ( SV85 = create_slb )
| ~ ( contains_slb @ SV85 @ ( findmin_pqp_res @ SV40 ) )
| ~ ( less_than @ ( lookup_slb @ SV85 @ ( findmin_pqp_res @ SV40 ) ) @ ( findmin_pqp_res @ SV40 ) ) )
= $true )
| ( ( ! [SY306: $i] :
( ( findmin_cpq_eff @ ( triple @ SV40 @ SV85 @ SY306 ) )
= ( triple @ SV40 @ ( update_slb @ SV85 @ ( findmin_pqp_res @ SV40 ) ) @ SY306 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(411,plain,
! [SV42: $i,SV87: $i] :
( ( ( SV87 = create_slb )
= $true )
| ( ( ! [SY307: $i] :
( ( findmin_cpq_res @ ( triple @ SV42 @ SV87 @ SY307 ) )
= ( findmin_pqp_res @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(412,plain,
! [SV110: $i,SV89: $i,SV46: $i] :
( ( ! [SY345: $i,SY346: $i] :
( ( i @ ( triple @ SV46 @ ( insert_slb @ SV89 @ ( pair @ SY345 @ SY346 ) ) @ SV110 ) )
= ( insert_pq @ ( i @ ( triple @ SV46 @ SV89 @ SV110 ) ) @ SY345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(413,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)],[356]) ).
thf(414,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)],[357]) ).
thf(415,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( contains_pq @ SX0 @ SX1 )
| ( pi_sharp_remove @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[358]) ).
thf(416,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(417,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)],[360]) ).
thf(418,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)],[361]) ).
thf(419,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)],[362]) ).
thf(420,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)],[363]) ).
thf(421,plain,
! [SV111: $i,SV90: $i,SV47: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY347: $i,SY348: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY347 ) ) @ SV111 @ SY348 )
| ( SV90 = SV111 )
| ( pair_in_list @ SV47 @ SV111 @ SY348 ) )
| ~ ! [SY349: $i,SY350: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY349 ) ) @ SV111 @ SY350 )
| ( SY349 = SY350 )
| ( pair_in_list @ SV47 @ SV111 @ SY350 ) ) )
| ~ ~ ( ~ ! [SY351: $i,SY352: $i] :
( ( SV90 != SV111 )
| ( SY351 != SY352 )
| ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY351 ) ) @ SV111 @ SY352 ) )
| ~ ! [SY353: $i,SY354: $i] :
( ~ ( pair_in_list @ SV47 @ SV111 @ SY354 )
| ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY353 ) ) @ SV111 @ SY354 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(422,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( ok @ SX1 )
| ~ ( succ_cpq @ SX0 @ SX1 )
| ~ ( check_cpq @ SX1 ) )
| ( phi @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[365]) ).
thf(423,plain,
( ( ! [SX0: $i] :
( ~ ( phi @ SX0 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK4_V @ SX0 ) )
| ~ ( succ_cpq @ SX0 @ ( sK4_V @ SX0 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(424,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_find_min @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(425,plain,
( ( ! [SX0: $i] :
( ~ ( pi_find_min @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK6_V @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(426,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( contains_pq @ SX0 @ ( sK7_W @ SX1 @ SX0 ) )
| ~ ~ ( less_than @ SX1 @ ( sK7_W @ SX1 @ SX0 ) ) )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(427,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)],[370]) ).
thf(428,plain,
! [SV48: $i] :
( ( ~ ! [SY252: $i,SY253: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV48 @ SY252 ) @ SY253 )
| ( SY252 = SY253 )
| ( contains_pq @ SV48 @ SY253 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(429,plain,
! [SV48: $i] :
( ( ~ ~ ( ~ ! [SY254: $i,SY255: $i] :
( ( SY254 != SY255 )
| ( contains_pq @ ( insert_pq @ SV48 @ SY254 ) @ SY255 ) )
| ~ ! [SY256: $i,SY257: $i] :
( ~ ( contains_pq @ SV48 @ SY257 )
| ( contains_pq @ ( insert_pq @ SV48 @ SY256 ) @ SY257 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(430,plain,
! [SV112: $i,SV91: $i,SV49: $i] :
( ( ~ ( ~ ! [SY355: $i,SY356: $i] :
( ~ ( less_than @ SY356 @ SY355 )
| ~ ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SV91 @ ( pair @ SY355 @ SY356 ) ) @ SV112 ) )
| ( check_cpq @ ( triple @ SV49 @ SV91 @ SV112 ) ) )
| ~ ! [SY357: $i,SY358: $i] :
( ~ ( less_than @ SY358 @ SY357 )
| ~ ( check_cpq @ ( triple @ SV49 @ SV91 @ SV112 ) )
| ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SV91 @ ( pair @ SY357 @ SY358 ) ) @ SV112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(431,plain,
( ( contains_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) @ sK3_SY168 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(432,plain,
( ( ~ ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) ) @ sK3_SY168 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[374]) ).
thf(433,plain,
! [SV92: $i,SV50: $i] :
( ( ~ ! [SY325: $i,SY326: $i] :
( ~ ( contains_cpq @ ( triple @ SV50 @ SV92 @ SY325 ) @ SY326 )
| ( contains_slb @ SV92 @ SY326 ) )
| ~ ! [SY327: $i,SY328: $i] :
( ~ ( contains_slb @ SV92 @ SY328 )
| ( contains_cpq @ ( triple @ SV50 @ SV92 @ SY327 ) @ SY328 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(434,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_remove @ SX0 @ SX1 )
| ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[376]) ).
thf(435,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 )
| ( pi_remove @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(436,plain,
! [SV93: $i,SV51: $i] :
( ( ~ ! [SY329: $i] :
( ! [SY330: $i] :
~ ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY330 ) ) @ SY329 )
| ( SV93 = SY329 )
| ( contains_slb @ SV51 @ SY329 ) )
| ~ ~ ( ~ ! [SY331: $i] :
( ( SV93 != SY331 )
| ! [SY332: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY332 ) ) @ SY331 ) )
| ~ ! [SY333: $i] :
( ~ ( contains_slb @ SV51 @ SY333 )
| ! [SY334: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY334 ) ) @ SY333 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(437,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_removemin @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[379]) ).
thf(438,plain,
( ( ! [SX0: $i] :
( ~ ( pi_removemin @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK5_V @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[380]) ).
thf(439,plain,
! [SV94: $i,SV52: $i,SV1: $i] :
( ( ( ~ ( less_than @ SV1 @ SV52 )
| ~ ( less_than @ SV52 @ SV94 ) )
= $true )
| ( ( less_than @ SV1 @ SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(440,plain,
! [SV8: $i,SV95: $i,SV56: $i] :
( ( ( ( SV56 = SV95 )
| ~ ( contains_pq @ SV8 @ SV95 ) )
= $true )
| ( ( ( remove_pq @ ( insert_pq @ SV8 @ SV56 ) @ SV95 )
= ( insert_pq @ ( remove_pq @ SV8 @ SV95 ) @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(441,plain,
! [SV57: $i,SV9: $i] :
( ( ( ~ ( contains_pq @ SV9 @ SV57 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV9 @ SV57 ) )
= $true )
| ( ( ( findmin_pq_eff @ SV9 @ SV57 )
= SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(442,plain,
! [SV58: $i,SV10: $i] :
( ( ( ~ ( contains_pq @ SV10 @ SV58 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV10 @ SV58 ) )
= $true )
| ( ( ( findmin_pq_res @ SV10 @ SV58 )
= SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(443,plain,
! [SV59: $i,SV11: $i] :
( ( ( ~ ( contains_pq @ SV11 @ SV59 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV11 @ SV59 ) )
= $true )
| ( ( ( removemin_pq_eff @ SV11 @ SV59 )
= ( remove_pq @ SV11 @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(444,plain,
! [SV60: $i,SV12: $i] :
( ( ( ~ ( contains_pq @ SV12 @ SV60 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV12 @ SV60 ) )
= $true )
| ( ( ( removemin_pq_res @ SV12 @ SV60 )
= SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(445,plain,
! [SV18: $i,SV99: $i,SV65: $i] :
( ( ( ( SV65 = SV99 )
| ~ ( contains_slb @ SV18 @ SV99 ) )
= $true )
| ( ( ! [SY335: $i] :
( ( remove_slb @ ( insert_slb @ SV18 @ ( pair @ SV65 @ SY335 ) ) @ SV99 )
= ( insert_slb @ ( remove_slb @ SV18 @ SV99 ) @ ( pair @ SV65 @ SY335 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(446,plain,
! [SV20: $i,SV101: $i,SV67: $i] :
( ( ( ( SV67 = SV101 )
| ~ ( contains_slb @ SV20 @ SV101 ) )
= $true )
| ( ( ! [SY336: $i] :
( ( lookup_slb @ ( insert_slb @ SV20 @ ( pair @ SV67 @ SY336 ) ) @ SV101 )
= ( lookup_slb @ SV20 @ SV101 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(447,plain,
! [SV68: $i,SV22: $i,SV102: $i,SV113: $i] :
( ( ~ ( strictly_less_than @ SV113 @ SV102 )
| ( ( update_slb @ ( insert_slb @ SV22 @ ( pair @ SV68 @ SV113 ) ) @ SV102 )
= ( insert_slb @ ( update_slb @ SV22 @ SV102 ) @ ( pair @ SV68 @ SV102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(448,plain,
! [SV69: $i,SV23: $i,SV114: $i,SV103: $i] :
( ( ~ ( less_than @ SV103 @ SV114 )
| ( ( update_slb @ ( insert_slb @ SV23 @ ( pair @ SV69 @ SV114 ) ) @ SV103 )
= ( insert_slb @ ( update_slb @ SV23 @ SV103 ) @ ( pair @ SV69 @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(449,plain,
! [SV70: $i,SV25: $i] :
( ( ( succ_cpq @ SV25 @ SV70 )
= $false )
| ( ( ! [SY290: $i] : ( succ_cpq @ SV25 @ ( insert_cpq @ SV70 @ SY290 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(450,plain,
! [SV71: $i,SV26: $i] :
( ( ( succ_cpq @ SV26 @ SV71 )
= $false )
| ( ( ! [SY291: $i] : ( succ_cpq @ SV26 @ ( remove_cpq @ SV71 @ SY291 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(451,plain,
! [SV72: $i,SV27: $i] :
( ( ( succ_cpq @ SV27 @ SV72 )
= $false )
| ( ( succ_cpq @ SV27 @ ( findmin_cpq_eff @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(452,plain,
! [SV73: $i,SV28: $i] :
( ( ( succ_cpq @ SV28 @ SV73 )
= $false )
| ( ( succ_cpq @ SV28 @ ( removemin_cpq_eff @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(453,plain,
! [SV104: $i,SV75: $i,SV30: $i,SV115: $i] :
( ( ! [SY359: $i] :
( ~ ( strictly_less_than @ SV115 @ SY359 )
| ~ ( check_cpq @ ( triple @ SV30 @ ( insert_slb @ SV75 @ ( pair @ SV115 @ SY359 ) ) @ SV104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(454,plain,
! [SV105: $i,SV77: $i,SV32: $i] :
( ( ( ok @ ( triple @ SV32 @ SV77 @ SV105 ) )
= $true )
| ( ( SV105 = bad )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(455,plain,
! [SV116: $i,SV106: $i,SV78: $i,SV33: $i] :
( ( ( insert_cpq @ ( triple @ SV33 @ SV78 @ SV106 ) @ SV116 )
= ( triple @ ( insert_pqp @ SV33 @ SV116 ) @ ( insert_slb @ SV78 @ ( pair @ SV116 @ bottom ) ) @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(456,plain,
! [SV107: $i,SV34: $i,SV117: $i,SV79: $i] :
( ( ( contains_slb @ SV79 @ SV117 )
| ( ( remove_cpq @ ( triple @ SV34 @ SV79 @ SV107 ) @ SV117 )
= ( triple @ SV34 @ SV79 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(457,plain,
! [SV108: $i,SV35: $i,SV118: $i,SV80: $i] :
( ( ~ ( contains_slb @ SV80 @ SV118 )
| ~ ( less_than @ ( lookup_slb @ SV80 @ SV118 ) @ SV118 )
| ( ( remove_cpq @ ( triple @ SV35 @ SV80 @ SV108 ) @ SV118 )
= ( triple @ ( remove_pqp @ SV35 @ SV118 ) @ ( remove_slb @ SV80 @ SV118 ) @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(458,plain,
! [SV109: $i,SV36: $i,SV119: $i,SV81: $i] :
( ( ~ ( contains_slb @ SV81 @ SV119 )
| ~ ( strictly_less_than @ SV119 @ ( lookup_slb @ SV81 @ SV119 ) )
| ( ( remove_cpq @ ( triple @ SV36 @ SV81 @ SV109 ) @ SV119 )
= ( triple @ ( remove_pqp @ SV36 @ SV119 ) @ ( remove_slb @ SV81 @ SV119 ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(459,plain,
! [SV38: $i,SV83: $i] :
( ( ( SV83 = create_slb )
= $true )
| ( ( contains_slb @ SV83 @ ( findmin_pqp_res @ SV38 ) )
= $true )
| ( ( ! [SY304: $i] :
( ( findmin_cpq_eff @ ( triple @ SV38 @ SV83 @ SY304 ) )
= ( triple @ SV38 @ ( update_slb @ SV83 @ ( findmin_pqp_res @ SV38 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(460,plain,
! [SV39: $i,SV84: $i] :
( ( ( ( SV84 = create_slb )
| ~ ( contains_slb @ SV84 @ ( findmin_pqp_res @ SV39 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV39 ) @ ( lookup_slb @ SV84 @ ( findmin_pqp_res @ SV39 ) ) ) )
= $true )
| ( ( ! [SY305: $i] :
( ( findmin_cpq_eff @ ( triple @ SV39 @ SV84 @ SY305 ) )
= ( triple @ SV39 @ ( update_slb @ SV84 @ ( findmin_pqp_res @ SV39 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(461,plain,
! [SV40: $i,SV85: $i] :
( ( ( ( SV85 = create_slb )
| ~ ( contains_slb @ SV85 @ ( findmin_pqp_res @ SV40 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV85 @ ( findmin_pqp_res @ SV40 ) ) @ ( findmin_pqp_res @ SV40 ) ) )
= $true )
| ( ( ! [SY306: $i] :
( ( findmin_cpq_eff @ ( triple @ SV40 @ SV85 @ SY306 ) )
= ( triple @ SV40 @ ( update_slb @ SV85 @ ( findmin_pqp_res @ SV40 ) ) @ SY306 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(462,plain,
! [SV120: $i,SV87: $i,SV42: $i] :
( ( ( ( findmin_cpq_res @ ( triple @ SV42 @ SV87 @ SV120 ) )
= ( findmin_pqp_res @ SV42 ) )
= $true )
| ( ( SV87 = create_slb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(463,plain,
! [SV110: $i,SV121: $i,SV89: $i,SV46: $i] :
( ( ! [SY360: $i] :
( ( i @ ( triple @ SV46 @ ( insert_slb @ SV89 @ ( pair @ SV121 @ SY360 ) ) @ SV110 ) )
= ( insert_pq @ ( i @ ( triple @ SV46 @ SV89 @ SV110 ) ) @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(464,plain,
! [SV122: $i] :
( ( ! [SY361: $i] :
( ~ ( contains_pq @ SV122 @ SY361 )
| ~ ( issmallestelement_pq @ SV122 @ SY361 )
| ( pi_sharp_find_min @ SV122 @ SY361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(465,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)],[414]) ).
thf(466,plain,
! [SV123: $i] :
( ( ! [SY362: $i] :
( ~ ( contains_pq @ SV123 @ SY362 )
| ( pi_sharp_remove @ SV123 @ SY362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(467,plain,
! [SV124: $i] :
( ( ! [SY363: $i] :
( ~ ( pi_sharp_remove @ SV124 @ SY363 )
| ( contains_pq @ SV124 @ SY363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(468,plain,
! [SV125: $i] :
( ( ! [SY364: $i] :
( ~ ( contains_pq @ SV125 @ SY364 )
| ~ ( issmallestelement_pq @ SV125 @ SY364 )
| ( pi_sharp_removemin @ SV125 @ SY364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(469,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)],[418]) ).
thf(470,plain,
! [SV126: $i] :
( ( ! [SY365: $i] :
( ~ ( less_than @ SV126 @ SY365 )
| ( less_than @ SY365 @ SV126 )
| ( strictly_less_than @ SV126 @ SY365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(471,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)],[420]) ).
thf(472,plain,
! [SV111: $i,SV90: $i,SV47: $i] :
( ( ~ ~ ( ~ ! [SY347: $i,SY348: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY347 ) ) @ SV111 @ SY348 )
| ( SV90 = SV111 )
| ( pair_in_list @ SV47 @ SV111 @ SY348 ) )
| ~ ! [SY349: $i,SY350: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY349 ) ) @ SV111 @ SY350 )
| ( SY349 = SY350 )
| ( pair_in_list @ SV47 @ SV111 @ SY350 ) ) )
| ~ ~ ( ~ ! [SY351: $i,SY352: $i] :
( ( SV90 != SV111 )
| ( SY351 != SY352 )
| ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY351 ) ) @ SV111 @ SY352 ) )
| ~ ! [SY353: $i,SY354: $i] :
( ~ ( pair_in_list @ SV47 @ SV111 @ SY354 )
| ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY353 ) ) @ SV111 @ SY354 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(473,plain,
! [SV127: $i] :
( ( ! [SY366: $i] :
( ~ ( ok @ SY366 )
| ~ ( succ_cpq @ SV127 @ SY366 )
| ~ ( check_cpq @ SY366 ) )
| ( phi @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(474,plain,
! [SV128: $i] :
( ( ~ ( phi @ SV128 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK4_V @ SV128 ) )
| ~ ( succ_cpq @ SV128 @ ( sK4_V @ SV128 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(475,plain,
! [SV129: $i] :
( ( ! [SY367: $i] :
~ ( pi_sharp_find_min @ ( i @ SV129 ) @ SY367 )
| ( pi_find_min @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(476,plain,
! [SV130: $i] :
( ( ~ ( pi_find_min @ SV130 )
| ( pi_sharp_find_min @ ( i @ SV130 ) @ ( sK6_V @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(477,plain,
! [SV131: $i] :
( ( ! [SY368: $i] :
( ~ ( ~ ( contains_pq @ SV131 @ ( sK7_W @ SY368 @ SV131 ) )
| ~ ~ ( less_than @ SY368 @ ( sK7_W @ SY368 @ SV131 ) ) )
| ( issmallestelement_pq @ SV131 @ SY368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(478,plain,
! [SV132: $i] :
( ( ! [SY369: $i] :
( ~ ( issmallestelement_pq @ SV132 @ SY369 )
| ! [SY370: $i] :
( ~ ( contains_pq @ SV132 @ SY370 )
| ( less_than @ SY369 @ SY370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(479,plain,
! [SV48: $i] :
( ( ! [SY252: $i,SY253: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV48 @ SY252 ) @ SY253 )
| ( SY252 = SY253 )
| ( contains_pq @ SV48 @ SY253 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(480,plain,
! [SV48: $i] :
( ( ~ ( ~ ! [SY254: $i,SY255: $i] :
( ( SY254 != SY255 )
| ( contains_pq @ ( insert_pq @ SV48 @ SY254 ) @ SY255 ) )
| ~ ! [SY256: $i,SY257: $i] :
( ~ ( contains_pq @ SV48 @ SY257 )
| ( contains_pq @ ( insert_pq @ SV48 @ SY256 ) @ SY257 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[429]) ).
thf(481,plain,
! [SV112: $i,SV91: $i,SV49: $i] :
( ( ~ ! [SY355: $i,SY356: $i] :
( ~ ( less_than @ SY356 @ SY355 )
| ~ ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SV91 @ ( pair @ SY355 @ SY356 ) ) @ SV112 ) )
| ( check_cpq @ ( triple @ SV49 @ SV91 @ SV112 ) ) )
| ~ ! [SY357: $i,SY358: $i] :
( ~ ( less_than @ SY358 @ SY357 )
| ~ ( check_cpq @ ( triple @ SV49 @ SV91 @ SV112 ) )
| ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SV91 @ ( pair @ SY357 @ SY358 ) ) @ SV112 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(482,plain,
( ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) ) @ sK3_SY168 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(483,plain,
! [SV92: $i,SV50: $i] :
( ( ~ ! [SY325: $i,SY326: $i] :
( ~ ( contains_cpq @ ( triple @ SV50 @ SV92 @ SY325 ) @ SY326 )
| ( contains_slb @ SV92 @ SY326 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(484,plain,
! [SV50: $i,SV92: $i] :
( ( ~ ! [SY327: $i,SY328: $i] :
( ~ ( contains_slb @ SV92 @ SY328 )
| ( contains_cpq @ ( triple @ SV50 @ SV92 @ SY327 ) @ SY328 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(485,plain,
! [SV133: $i] :
( ( ! [SY371: $i] :
( ~ ( pi_remove @ SV133 @ SY371 )
| ( pi_sharp_remove @ ( i @ SV133 ) @ SY371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(486,plain,
! [SV134: $i] :
( ( ! [SY372: $i] :
( ~ ( pi_sharp_remove @ ( i @ SV134 ) @ SY372 )
| ( pi_remove @ SV134 @ SY372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(487,plain,
! [SV93: $i,SV51: $i] :
( ( ~ ! [SY329: $i] :
( ! [SY330: $i] :
~ ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY330 ) ) @ SY329 )
| ( SV93 = SY329 )
| ( contains_slb @ SV51 @ SY329 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[436]) ).
thf(488,plain,
! [SV51: $i,SV93: $i] :
( ( ~ ~ ( ~ ! [SY331: $i] :
( ( SV93 != SY331 )
| ! [SY332: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY332 ) ) @ SY331 ) )
| ~ ! [SY333: $i] :
( ~ ( contains_slb @ SV51 @ SY333 )
| ! [SY334: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY334 ) ) @ SY333 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[436]) ).
thf(489,plain,
! [SV135: $i] :
( ( ! [SY373: $i] :
~ ( pi_sharp_find_min @ ( i @ SV135 ) @ SY373 )
| ( pi_removemin @ SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(490,plain,
! [SV136: $i] :
( ( ~ ( pi_removemin @ SV136 )
| ( pi_sharp_find_min @ ( i @ SV136 ) @ ( sK5_V @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(491,plain,
! [SV94: $i,SV52: $i,SV1: $i] :
( ( ( ~ ( less_than @ SV1 @ SV52 ) )
= $true )
| ( ( ~ ( less_than @ SV52 @ SV94 ) )
= $true )
| ( ( less_than @ SV1 @ SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(492,plain,
! [SV8: $i,SV95: $i,SV56: $i] :
( ( ( SV56 = SV95 )
= $true )
| ( ( ~ ( contains_pq @ SV8 @ SV95 ) )
= $true )
| ( ( ( remove_pq @ ( insert_pq @ SV8 @ SV56 ) @ SV95 )
= ( insert_pq @ ( remove_pq @ SV8 @ SV95 ) @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(493,plain,
! [SV57: $i,SV9: $i] :
( ( ( contains_pq @ SV9 @ SV57 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV9 @ SV57 ) )
= $true )
| ( ( ( findmin_pq_eff @ SV9 @ SV57 )
= SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(494,plain,
! [SV58: $i,SV10: $i] :
( ( ( contains_pq @ SV10 @ SV58 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV10 @ SV58 ) )
= $true )
| ( ( ( findmin_pq_res @ SV10 @ SV58 )
= SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(495,plain,
! [SV59: $i,SV11: $i] :
( ( ( contains_pq @ SV11 @ SV59 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV11 @ SV59 ) )
= $true )
| ( ( ( removemin_pq_eff @ SV11 @ SV59 )
= ( remove_pq @ SV11 @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(496,plain,
! [SV60: $i,SV12: $i] :
( ( ( contains_pq @ SV12 @ SV60 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV12 @ SV60 ) )
= $true )
| ( ( ( removemin_pq_res @ SV12 @ SV60 )
= SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(497,plain,
! [SV18: $i,SV99: $i,SV65: $i] :
( ( ( SV65 = SV99 )
= $true )
| ( ( ~ ( contains_slb @ SV18 @ SV99 ) )
= $true )
| ( ( ! [SY335: $i] :
( ( remove_slb @ ( insert_slb @ SV18 @ ( pair @ SV65 @ SY335 ) ) @ SV99 )
= ( insert_slb @ ( remove_slb @ SV18 @ SV99 ) @ ( pair @ SV65 @ SY335 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(498,plain,
! [SV20: $i,SV101: $i,SV67: $i] :
( ( ( SV67 = SV101 )
= $true )
| ( ( ~ ( contains_slb @ SV20 @ SV101 ) )
= $true )
| ( ( ! [SY336: $i] :
( ( lookup_slb @ ( insert_slb @ SV20 @ ( pair @ SV67 @ SY336 ) ) @ SV101 )
= ( lookup_slb @ SV20 @ SV101 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[446]) ).
thf(499,plain,
! [SV68: $i,SV22: $i,SV102: $i,SV113: $i] :
( ( ( ~ ( strictly_less_than @ SV113 @ SV102 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV22 @ ( pair @ SV68 @ SV113 ) ) @ SV102 )
= ( insert_slb @ ( update_slb @ SV22 @ SV102 ) @ ( pair @ SV68 @ SV102 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[447]) ).
thf(500,plain,
! [SV69: $i,SV23: $i,SV114: $i,SV103: $i] :
( ( ( ~ ( less_than @ SV103 @ SV114 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV23 @ ( pair @ SV69 @ SV114 ) ) @ SV103 )
= ( insert_slb @ ( update_slb @ SV23 @ SV103 ) @ ( pair @ SV69 @ SV114 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[448]) ).
thf(501,plain,
! [SV137: $i,SV70: $i,SV25: $i] :
( ( ( succ_cpq @ SV25 @ ( insert_cpq @ SV70 @ SV137 ) )
= $true )
| ( ( succ_cpq @ SV25 @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(502,plain,
! [SV138: $i,SV71: $i,SV26: $i] :
( ( ( succ_cpq @ SV26 @ ( remove_cpq @ SV71 @ SV138 ) )
= $true )
| ( ( succ_cpq @ SV26 @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(503,plain,
! [SV104: $i,SV75: $i,SV30: $i,SV139: $i,SV115: $i] :
( ( ~ ( strictly_less_than @ SV115 @ SV139 )
| ~ ( check_cpq @ ( triple @ SV30 @ ( insert_slb @ SV75 @ ( pair @ SV115 @ SV139 ) ) @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(504,plain,
! [SV107: $i,SV34: $i,SV117: $i,SV79: $i] :
( ( ( contains_slb @ SV79 @ SV117 )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV34 @ SV79 @ SV107 ) @ SV117 )
= ( triple @ SV34 @ SV79 @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[456]) ).
thf(505,plain,
! [SV108: $i,SV35: $i,SV118: $i,SV80: $i] :
( ( ( ~ ( contains_slb @ SV80 @ SV118 )
| ~ ( less_than @ ( lookup_slb @ SV80 @ SV118 ) @ SV118 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV35 @ SV80 @ SV108 ) @ SV118 )
= ( triple @ ( remove_pqp @ SV35 @ SV118 ) @ ( remove_slb @ SV80 @ SV118 ) @ SV108 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(506,plain,
! [SV109: $i,SV36: $i,SV119: $i,SV81: $i] :
( ( ( ~ ( contains_slb @ SV81 @ SV119 )
| ~ ( strictly_less_than @ SV119 @ ( lookup_slb @ SV81 @ SV119 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV36 @ SV81 @ SV109 ) @ SV119 )
= ( triple @ ( remove_pqp @ SV36 @ SV119 ) @ ( remove_slb @ SV81 @ SV119 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[458]) ).
thf(507,plain,
! [SV140: $i,SV83: $i,SV38: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV38 @ SV83 @ SV140 ) )
= ( triple @ SV38 @ ( update_slb @ SV83 @ ( findmin_pqp_res @ SV38 ) ) @ bad ) )
= $true )
| ( ( contains_slb @ SV83 @ ( findmin_pqp_res @ SV38 ) )
= $true )
| ( ( SV83 = create_slb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(508,plain,
! [SV39: $i,SV84: $i] :
( ( ( SV84 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV84 @ ( findmin_pqp_res @ SV39 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV39 ) @ ( lookup_slb @ SV84 @ ( findmin_pqp_res @ SV39 ) ) ) )
= $true )
| ( ( ! [SY305: $i] :
( ( findmin_cpq_eff @ ( triple @ SV39 @ SV84 @ SY305 ) )
= ( triple @ SV39 @ ( update_slb @ SV84 @ ( findmin_pqp_res @ SV39 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[460]) ).
thf(509,plain,
! [SV40: $i,SV85: $i] :
( ( ( SV85 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV85 @ ( findmin_pqp_res @ SV40 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV85 @ ( findmin_pqp_res @ SV40 ) ) @ ( findmin_pqp_res @ SV40 ) ) )
= $true )
| ( ( ! [SY306: $i] :
( ( findmin_cpq_eff @ ( triple @ SV40 @ SV85 @ SY306 ) )
= ( triple @ SV40 @ ( update_slb @ SV85 @ ( findmin_pqp_res @ SV40 ) ) @ SY306 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(510,plain,
! [SV110: $i,SV141: $i,SV121: $i,SV89: $i,SV46: $i] :
( ( ( i @ ( triple @ SV46 @ ( insert_slb @ SV89 @ ( pair @ SV121 @ SV141 ) ) @ SV110 ) )
= ( insert_pq @ ( i @ ( triple @ SV46 @ SV89 @ SV110 ) ) @ SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(511,plain,
! [SV142: $i,SV122: $i] :
( ( ~ ( contains_pq @ SV122 @ SV142 )
| ~ ( issmallestelement_pq @ SV122 @ SV142 )
| ( pi_sharp_find_min @ SV122 @ SV142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(512,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(513,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(514,plain,
! [SV143: $i,SV123: $i] :
( ( ~ ( contains_pq @ SV123 @ SV143 )
| ( pi_sharp_remove @ SV123 @ SV143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(515,plain,
! [SV144: $i,SV124: $i] :
( ( ~ ( pi_sharp_remove @ SV124 @ SV144 )
| ( contains_pq @ SV124 @ SV144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(516,plain,
! [SV145: $i,SV125: $i] :
( ( ~ ( contains_pq @ SV125 @ SV145 )
| ~ ( issmallestelement_pq @ SV125 @ SV145 )
| ( pi_sharp_removemin @ SV125 @ SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(517,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[469]) ).
thf(518,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[469]) ).
thf(519,plain,
! [SV146: $i,SV126: $i] :
( ( ~ ( less_than @ SV126 @ SV146 )
| ( less_than @ SV146 @ SV126 )
| ( strictly_less_than @ SV126 @ SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(520,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[471]) ).
thf(521,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[471]) ).
thf(522,plain,
! [SV111: $i,SV90: $i,SV47: $i] :
( ( ~ ~ ( ~ ! [SY347: $i,SY348: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY347 ) ) @ SV111 @ SY348 )
| ( SV90 = SV111 )
| ( pair_in_list @ SV47 @ SV111 @ SY348 ) )
| ~ ! [SY349: $i,SY350: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY349 ) ) @ SV111 @ SY350 )
| ( SY349 = SY350 )
| ( pair_in_list @ SV47 @ SV111 @ SY350 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[472]) ).
thf(523,plain,
! [SV47: $i,SV111: $i,SV90: $i] :
( ( ~ ~ ( ~ ! [SY351: $i,SY352: $i] :
( ( SV90 != SV111 )
| ( SY351 != SY352 )
| ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY351 ) ) @ SV111 @ SY352 ) )
| ~ ! [SY353: $i,SY354: $i] :
( ~ ( pair_in_list @ SV47 @ SV111 @ SY354 )
| ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY353 ) ) @ SV111 @ SY354 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[472]) ).
thf(524,plain,
! [SV127: $i] :
( ( ( ! [SY366: $i] :
( ~ ( ok @ SY366 )
| ~ ( succ_cpq @ SV127 @ SY366 )
| ~ ( check_cpq @ SY366 ) ) )
= $true )
| ( ( phi @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(525,plain,
! [SV128: $i] :
( ( ( ~ ( phi @ SV128 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ok @ ( sK4_V @ SV128 ) )
| ~ ( succ_cpq @ SV128 @ ( sK4_V @ SV128 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SV128 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(526,plain,
! [SV129: $i] :
( ( ( ! [SY367: $i] :
~ ( pi_sharp_find_min @ ( i @ SV129 ) @ SY367 ) )
= $true )
| ( ( pi_find_min @ SV129 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(527,plain,
! [SV130: $i] :
( ( ( ~ ( pi_find_min @ SV130 ) )
= $true )
| ( ( pi_sharp_find_min @ ( i @ SV130 ) @ ( sK6_V @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(528,plain,
! [SV147: $i,SV131: $i] :
( ( ~ ( ~ ( contains_pq @ SV131 @ ( sK7_W @ SV147 @ SV131 ) )
| ~ ~ ( less_than @ SV147 @ ( sK7_W @ SV147 @ SV131 ) ) )
| ( issmallestelement_pq @ SV131 @ SV147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(529,plain,
! [SV148: $i,SV132: $i] :
( ( ~ ( issmallestelement_pq @ SV132 @ SV148 )
| ! [SY374: $i] :
( ~ ( contains_pq @ SV132 @ SY374 )
| ( less_than @ SV148 @ SY374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(530,plain,
! [SV149: $i,SV48: $i] :
( ( ! [SY375: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV48 @ SV149 ) @ SY375 )
| ( SV149 = SY375 )
| ( contains_pq @ SV48 @ SY375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(531,plain,
! [SV48: $i] :
( ( ~ ! [SY254: $i,SY255: $i] :
( ( SY254 != SY255 )
| ( contains_pq @ ( insert_pq @ SV48 @ SY254 ) @ SY255 ) )
| ~ ! [SY256: $i,SY257: $i] :
( ~ ( contains_pq @ SV48 @ SY257 )
| ( contains_pq @ ( insert_pq @ SV48 @ SY256 ) @ SY257 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(532,plain,
! [SV112: $i,SV91: $i,SV49: $i] :
( ( ~ ! [SY355: $i,SY356: $i] :
( ~ ( less_than @ SY356 @ SY355 )
| ~ ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SV91 @ ( pair @ SY355 @ SY356 ) ) @ SV112 ) )
| ( check_cpq @ ( triple @ SV49 @ SV91 @ SV112 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[481]) ).
thf(533,plain,
! [SV112: $i,SV91: $i,SV49: $i] :
( ( ~ ! [SY357: $i,SY358: $i] :
( ~ ( less_than @ SY358 @ SY357 )
| ~ ( check_cpq @ ( triple @ SV49 @ SV91 @ SV112 ) )
| ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SV91 @ ( pair @ SY357 @ SY358 ) ) @ SV112 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[481]) ).
thf(534,plain,
! [SV92: $i,SV50: $i] :
( ( ! [SY325: $i,SY326: $i] :
( ~ ( contains_cpq @ ( triple @ SV50 @ SV92 @ SY325 ) @ SY326 )
| ( contains_slb @ SV92 @ SY326 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(535,plain,
! [SV50: $i,SV92: $i] :
( ( ! [SY327: $i,SY328: $i] :
( ~ ( contains_slb @ SV92 @ SY328 )
| ( contains_cpq @ ( triple @ SV50 @ SV92 @ SY327 ) @ SY328 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[484]) ).
thf(536,plain,
! [SV150: $i,SV133: $i] :
( ( ~ ( pi_remove @ SV133 @ SV150 )
| ( pi_sharp_remove @ ( i @ SV133 ) @ SV150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(537,plain,
! [SV151: $i,SV134: $i] :
( ( ~ ( pi_sharp_remove @ ( i @ SV134 ) @ SV151 )
| ( pi_remove @ SV134 @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(538,plain,
! [SV93: $i,SV51: $i] :
( ( ! [SY329: $i] :
( ! [SY330: $i] :
~ ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY330 ) ) @ SY329 )
| ( SV93 = SY329 )
| ( contains_slb @ SV51 @ SY329 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(539,plain,
! [SV51: $i,SV93: $i] :
( ( ~ ( ~ ! [SY331: $i] :
( ( SV93 != SY331 )
| ! [SY332: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY332 ) ) @ SY331 ) )
| ~ ! [SY333: $i] :
( ~ ( contains_slb @ SV51 @ SY333 )
| ! [SY334: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY334 ) ) @ SY333 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[488]) ).
thf(540,plain,
! [SV135: $i] :
( ( ( ! [SY373: $i] :
~ ( pi_sharp_find_min @ ( i @ SV135 ) @ SY373 ) )
= $true )
| ( ( pi_removemin @ SV135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(541,plain,
! [SV136: $i] :
( ( ( ~ ( pi_removemin @ SV136 ) )
= $true )
| ( ( pi_sharp_find_min @ ( i @ SV136 ) @ ( sK5_V @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(542,plain,
! [SV94: $i,SV52: $i,SV1: $i] :
( ( ( less_than @ SV1 @ SV52 )
= $false )
| ( ( ~ ( less_than @ SV52 @ SV94 ) )
= $true )
| ( ( less_than @ SV1 @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(543,plain,
! [SV56: $i,SV95: $i,SV8: $i] :
( ( ( contains_pq @ SV8 @ SV95 )
= $false )
| ( ( SV56 = SV95 )
= $true )
| ( ( ( remove_pq @ ( insert_pq @ SV8 @ SV56 ) @ SV95 )
= ( insert_pq @ ( remove_pq @ SV8 @ SV95 ) @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(544,plain,
! [SV57: $i,SV9: $i] :
( ( ( issmallestelement_pq @ SV9 @ SV57 )
= $false )
| ( ( contains_pq @ SV9 @ SV57 )
= $false )
| ( ( ( findmin_pq_eff @ SV9 @ SV57 )
= SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(545,plain,
! [SV58: $i,SV10: $i] :
( ( ( issmallestelement_pq @ SV10 @ SV58 )
= $false )
| ( ( contains_pq @ SV10 @ SV58 )
= $false )
| ( ( ( findmin_pq_res @ SV10 @ SV58 )
= SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(546,plain,
! [SV59: $i,SV11: $i] :
( ( ( issmallestelement_pq @ SV11 @ SV59 )
= $false )
| ( ( contains_pq @ SV11 @ SV59 )
= $false )
| ( ( ( removemin_pq_eff @ SV11 @ SV59 )
= ( remove_pq @ SV11 @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(547,plain,
! [SV60: $i,SV12: $i] :
( ( ( issmallestelement_pq @ SV12 @ SV60 )
= $false )
| ( ( contains_pq @ SV12 @ SV60 )
= $false )
| ( ( ( removemin_pq_res @ SV12 @ SV60 )
= SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(548,plain,
! [SV65: $i,SV99: $i,SV18: $i] :
( ( ( contains_slb @ SV18 @ SV99 )
= $false )
| ( ( SV65 = SV99 )
= $true )
| ( ( ! [SY335: $i] :
( ( remove_slb @ ( insert_slb @ SV18 @ ( pair @ SV65 @ SY335 ) ) @ SV99 )
= ( insert_slb @ ( remove_slb @ SV18 @ SV99 ) @ ( pair @ SV65 @ SY335 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(549,plain,
! [SV67: $i,SV101: $i,SV20: $i] :
( ( ( contains_slb @ SV20 @ SV101 )
= $false )
| ( ( SV67 = SV101 )
= $true )
| ( ( ! [SY336: $i] :
( ( lookup_slb @ ( insert_slb @ SV20 @ ( pair @ SV67 @ SY336 ) ) @ SV101 )
= ( lookup_slb @ SV20 @ SV101 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(550,plain,
! [SV68: $i,SV22: $i,SV102: $i,SV113: $i] :
( ( ( strictly_less_than @ SV113 @ SV102 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV22 @ ( pair @ SV68 @ SV113 ) ) @ SV102 )
= ( insert_slb @ ( update_slb @ SV22 @ SV102 ) @ ( pair @ SV68 @ SV102 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(551,plain,
! [SV69: $i,SV23: $i,SV114: $i,SV103: $i] :
( ( ( less_than @ SV103 @ SV114 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV23 @ ( pair @ SV69 @ SV114 ) ) @ SV103 )
= ( insert_slb @ ( update_slb @ SV23 @ SV103 ) @ ( pair @ SV69 @ SV114 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(552,plain,
! [SV104: $i,SV75: $i,SV30: $i,SV139: $i,SV115: $i] :
( ( ( ~ ( strictly_less_than @ SV115 @ SV139 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV30 @ ( insert_slb @ SV75 @ ( pair @ SV115 @ SV139 ) ) @ SV104 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(553,plain,
! [SV108: $i,SV35: $i,SV118: $i,SV80: $i] :
( ( ( ~ ( contains_slb @ SV80 @ SV118 ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV80 @ SV118 ) @ SV118 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV35 @ SV80 @ SV108 ) @ SV118 )
= ( triple @ ( remove_pqp @ SV35 @ SV118 ) @ ( remove_slb @ SV80 @ SV118 ) @ SV108 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(554,plain,
! [SV109: $i,SV36: $i,SV119: $i,SV81: $i] :
( ( ( ~ ( contains_slb @ SV81 @ SV119 ) )
= $true )
| ( ( ~ ( strictly_less_than @ SV119 @ ( lookup_slb @ SV81 @ SV119 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV36 @ SV81 @ SV109 ) @ SV119 )
= ( triple @ ( remove_pqp @ SV36 @ SV119 ) @ ( remove_slb @ SV81 @ SV119 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[506]) ).
thf(555,plain,
! [SV39: $i,SV84: $i] :
( ( ( contains_slb @ SV84 @ ( findmin_pqp_res @ SV39 ) )
= $false )
| ( ( SV84 = create_slb )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV39 ) @ ( lookup_slb @ SV84 @ ( findmin_pqp_res @ SV39 ) ) ) )
= $true )
| ( ( ! [SY305: $i] :
( ( findmin_cpq_eff @ ( triple @ SV39 @ SV84 @ SY305 ) )
= ( triple @ SV39 @ ( update_slb @ SV84 @ ( findmin_pqp_res @ SV39 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(556,plain,
! [SV40: $i,SV85: $i] :
( ( ( contains_slb @ SV85 @ ( findmin_pqp_res @ SV40 ) )
= $false )
| ( ( SV85 = create_slb )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV85 @ ( findmin_pqp_res @ SV40 ) ) @ ( findmin_pqp_res @ SV40 ) ) )
= $true )
| ( ( ! [SY306: $i] :
( ( findmin_cpq_eff @ ( triple @ SV40 @ SV85 @ SY306 ) )
= ( triple @ SV40 @ ( update_slb @ SV85 @ ( findmin_pqp_res @ SV40 ) ) @ SY306 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[509]) ).
thf(557,plain,
! [SV142: $i,SV122: $i] :
( ( ( ~ ( contains_pq @ SV122 @ SV142 )
| ~ ( issmallestelement_pq @ SV122 @ SV142 ) )
= $true )
| ( ( pi_sharp_find_min @ SV122 @ SV142 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[511]) ).
thf(558,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[512]) ).
thf(559,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[513]) ).
thf(560,plain,
! [SV143: $i,SV123: $i] :
( ( ( ~ ( contains_pq @ SV123 @ SV143 ) )
= $true )
| ( ( pi_sharp_remove @ SV123 @ SV143 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(561,plain,
! [SV144: $i,SV124: $i] :
( ( ( ~ ( pi_sharp_remove @ SV124 @ SV144 ) )
= $true )
| ( ( contains_pq @ SV124 @ SV144 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(562,plain,
! [SV145: $i,SV125: $i] :
( ( ( ~ ( contains_pq @ SV125 @ SV145 )
| ~ ( issmallestelement_pq @ SV125 @ SV145 ) )
= $true )
| ( ( pi_sharp_removemin @ SV125 @ SV145 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(563,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[517]) ).
thf(564,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[518]) ).
thf(565,plain,
! [SV146: $i,SV126: $i] :
( ( ( ~ ( less_than @ SV126 @ SV146 )
| ( less_than @ SV146 @ SV126 ) )
= $true )
| ( ( strictly_less_than @ SV126 @ SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(566,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(567,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(568,plain,
! [SV111: $i,SV90: $i,SV47: $i] :
( ( ~ ( ~ ! [SY347: $i,SY348: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY347 ) ) @ SV111 @ SY348 )
| ( SV90 = SV111 )
| ( pair_in_list @ SV47 @ SV111 @ SY348 ) )
| ~ ! [SY349: $i,SY350: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY349 ) ) @ SV111 @ SY350 )
| ( SY349 = SY350 )
| ( pair_in_list @ SV47 @ SV111 @ SY350 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(569,plain,
! [SV47: $i,SV111: $i,SV90: $i] :
( ( ~ ( ~ ! [SY351: $i,SY352: $i] :
( ( SV90 != SV111 )
| ( SY351 != SY352 )
| ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY351 ) ) @ SV111 @ SY352 ) )
| ~ ! [SY353: $i,SY354: $i] :
( ~ ( pair_in_list @ SV47 @ SV111 @ SY354 )
| ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY353 ) ) @ SV111 @ SY354 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[523]) ).
thf(570,plain,
! [SV127: $i,SV152: $i] :
( ( ( ~ ( ok @ SV152 )
| ~ ( succ_cpq @ SV127 @ SV152 )
| ~ ( check_cpq @ SV152 ) )
= $true )
| ( ( phi @ SV127 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(571,plain,
! [SV128: $i] :
( ( ( phi @ SV128 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( ok @ ( sK4_V @ SV128 ) )
| ~ ( succ_cpq @ SV128 @ ( sK4_V @ SV128 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SV128 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(572,plain,
! [SV153: $i,SV129: $i] :
( ( ( ~ ( pi_sharp_find_min @ ( i @ SV129 ) @ SV153 ) )
= $true )
| ( ( pi_find_min @ SV129 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(573,plain,
! [SV130: $i] :
( ( ( pi_find_min @ SV130 )
= $false )
| ( ( pi_sharp_find_min @ ( i @ SV130 ) @ ( sK6_V @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(574,plain,
! [SV147: $i,SV131: $i] :
( ( ( ~ ( ~ ( contains_pq @ SV131 @ ( sK7_W @ SV147 @ SV131 ) )
| ~ ~ ( less_than @ SV147 @ ( sK7_W @ SV147 @ SV131 ) ) ) )
= $true )
| ( ( issmallestelement_pq @ SV131 @ SV147 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[528]) ).
thf(575,plain,
! [SV148: $i,SV132: $i] :
( ( ( ~ ( issmallestelement_pq @ SV132 @ SV148 ) )
= $true )
| ( ( ! [SY374: $i] :
( ~ ( contains_pq @ SV132 @ SY374 )
| ( less_than @ SV148 @ SY374 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[529]) ).
thf(576,plain,
! [SV154: $i,SV149: $i,SV48: $i] :
( ( ~ ( contains_pq @ ( insert_pq @ SV48 @ SV149 ) @ SV154 )
| ( SV149 = SV154 )
| ( contains_pq @ SV48 @ SV154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(577,plain,
! [SV48: $i] :
( ( ~ ! [SY254: $i,SY255: $i] :
( ( SY254 != SY255 )
| ( contains_pq @ ( insert_pq @ SV48 @ SY254 ) @ SY255 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[531]) ).
thf(578,plain,
! [SV48: $i] :
( ( ~ ! [SY256: $i,SY257: $i] :
( ~ ( contains_pq @ SV48 @ SY257 )
| ( contains_pq @ ( insert_pq @ SV48 @ SY256 ) @ SY257 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[531]) ).
thf(579,plain,
! [SV112: $i,SV91: $i,SV49: $i] :
( ( ! [SY355: $i,SY356: $i] :
( ~ ( less_than @ SY356 @ SY355 )
| ~ ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SV91 @ ( pair @ SY355 @ SY356 ) ) @ SV112 ) )
| ( check_cpq @ ( triple @ SV49 @ SV91 @ SV112 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[532]) ).
thf(580,plain,
! [SV112: $i,SV91: $i,SV49: $i] :
( ( ! [SY357: $i,SY358: $i] :
( ~ ( less_than @ SY358 @ SY357 )
| ~ ( check_cpq @ ( triple @ SV49 @ SV91 @ SV112 ) )
| ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SV91 @ ( pair @ SY357 @ SY358 ) ) @ SV112 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[533]) ).
thf(581,plain,
! [SV155: $i,SV92: $i,SV50: $i] :
( ( ! [SY376: $i] :
( ~ ( contains_cpq @ ( triple @ SV50 @ SV92 @ SV155 ) @ SY376 )
| ( contains_slb @ SV92 @ SY376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(582,plain,
! [SV156: $i,SV50: $i,SV92: $i] :
( ( ! [SY377: $i] :
( ~ ( contains_slb @ SV92 @ SY377 )
| ( contains_cpq @ ( triple @ SV50 @ SV92 @ SV156 ) @ SY377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(583,plain,
! [SV150: $i,SV133: $i] :
( ( ( ~ ( pi_remove @ SV133 @ SV150 ) )
= $true )
| ( ( pi_sharp_remove @ ( i @ SV133 ) @ SV150 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[536]) ).
thf(584,plain,
! [SV151: $i,SV134: $i] :
( ( ( ~ ( pi_sharp_remove @ ( i @ SV134 ) @ SV151 ) )
= $true )
| ( ( pi_remove @ SV134 @ SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[537]) ).
thf(585,plain,
! [SV157: $i,SV93: $i,SV51: $i] :
( ( ! [SY378: $i] :
~ ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY378 ) ) @ SV157 )
| ( SV93 = SV157 )
| ( contains_slb @ SV51 @ SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(586,plain,
! [SV51: $i,SV93: $i] :
( ( ~ ! [SY331: $i] :
( ( SV93 != SY331 )
| ! [SY332: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY332 ) ) @ SY331 ) )
| ~ ! [SY333: $i] :
( ~ ( contains_slb @ SV51 @ SY333 )
| ! [SY334: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY334 ) ) @ SY333 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(587,plain,
! [SV158: $i,SV135: $i] :
( ( ( ~ ( pi_sharp_find_min @ ( i @ SV135 ) @ SV158 ) )
= $true )
| ( ( pi_removemin @ SV135 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(588,plain,
! [SV136: $i] :
( ( ( pi_removemin @ SV136 )
= $false )
| ( ( pi_sharp_find_min @ ( i @ SV136 ) @ ( sK5_V @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(589,plain,
! [SV1: $i,SV94: $i,SV52: $i] :
( ( ( less_than @ SV52 @ SV94 )
= $false )
| ( ( less_than @ SV1 @ SV52 )
= $false )
| ( ( less_than @ SV1 @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(590,plain,
! [SV99: $i,SV159: $i,SV65: $i,SV18: $i] :
( ( ( ( remove_slb @ ( insert_slb @ SV18 @ ( pair @ SV65 @ SV159 ) ) @ SV99 )
= ( insert_slb @ ( remove_slb @ SV18 @ SV99 ) @ ( pair @ SV65 @ SV159 ) ) )
= $true )
| ( ( SV65 = SV99 )
= $true )
| ( ( contains_slb @ SV18 @ SV99 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(591,plain,
! [SV101: $i,SV160: $i,SV67: $i,SV20: $i] :
( ( ( ( lookup_slb @ ( insert_slb @ SV20 @ ( pair @ SV67 @ SV160 ) ) @ SV101 )
= ( lookup_slb @ SV20 @ SV101 ) )
= $true )
| ( ( SV67 = SV101 )
= $true )
| ( ( contains_slb @ SV20 @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(592,plain,
! [SV104: $i,SV75: $i,SV30: $i,SV139: $i,SV115: $i] :
( ( ( strictly_less_than @ SV115 @ SV139 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV30 @ ( insert_slb @ SV75 @ ( pair @ SV115 @ SV139 ) ) @ SV104 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(593,plain,
! [SV108: $i,SV35: $i,SV118: $i,SV80: $i] :
( ( ( contains_slb @ SV80 @ SV118 )
= $false )
| ( ( ~ ( less_than @ ( lookup_slb @ SV80 @ SV118 ) @ SV118 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV35 @ SV80 @ SV108 ) @ SV118 )
= ( triple @ ( remove_pqp @ SV35 @ SV118 ) @ ( remove_slb @ SV80 @ SV118 ) @ SV108 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(594,plain,
! [SV109: $i,SV36: $i,SV119: $i,SV81: $i] :
( ( ( contains_slb @ SV81 @ SV119 )
= $false )
| ( ( ~ ( strictly_less_than @ SV119 @ ( lookup_slb @ SV81 @ SV119 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV36 @ SV81 @ SV109 ) @ SV119 )
= ( triple @ ( remove_pqp @ SV36 @ SV119 ) @ ( remove_slb @ SV81 @ SV119 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(595,plain,
! [SV84: $i,SV39: $i] :
( ( ( strictly_less_than @ ( findmin_pqp_res @ SV39 ) @ ( lookup_slb @ SV84 @ ( findmin_pqp_res @ SV39 ) ) )
= $false )
| ( ( SV84 = create_slb )
= $true )
| ( ( contains_slb @ SV84 @ ( findmin_pqp_res @ SV39 ) )
= $false )
| ( ( ! [SY305: $i] :
( ( findmin_cpq_eff @ ( triple @ SV39 @ SV84 @ SY305 ) )
= ( triple @ SV39 @ ( update_slb @ SV84 @ ( findmin_pqp_res @ SV39 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(596,plain,
! [SV40: $i,SV85: $i] :
( ( ( less_than @ ( lookup_slb @ SV85 @ ( findmin_pqp_res @ SV40 ) ) @ ( findmin_pqp_res @ SV40 ) )
= $false )
| ( ( SV85 = create_slb )
= $true )
| ( ( contains_slb @ SV85 @ ( findmin_pqp_res @ SV40 ) )
= $false )
| ( ( ! [SY306: $i] :
( ( findmin_cpq_eff @ ( triple @ SV40 @ SV85 @ SY306 ) )
= ( triple @ SV40 @ ( update_slb @ SV85 @ ( findmin_pqp_res @ SV40 ) ) @ SY306 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(597,plain,
! [SV142: $i,SV122: $i] :
( ( ( ~ ( contains_pq @ SV122 @ SV142 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV122 @ SV142 ) )
= $true )
| ( ( pi_sharp_find_min @ SV122 @ SV142 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(598,plain,
! [SV161: $i] :
( ( ! [SY379: $i] :
( ~ ( pi_sharp_find_min @ SV161 @ SY379 )
| ( contains_pq @ SV161 @ SY379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(599,plain,
! [SV162: $i] :
( ( ! [SY380: $i] :
( ~ ( pi_sharp_find_min @ SV162 @ SY380 )
| ( issmallestelement_pq @ SV162 @ SY380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(600,plain,
! [SV143: $i,SV123: $i] :
( ( ( contains_pq @ SV123 @ SV143 )
= $false )
| ( ( pi_sharp_remove @ SV123 @ SV143 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(601,plain,
! [SV144: $i,SV124: $i] :
( ( ( pi_sharp_remove @ SV124 @ SV144 )
= $false )
| ( ( contains_pq @ SV124 @ SV144 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(602,plain,
! [SV145: $i,SV125: $i] :
( ( ( ~ ( contains_pq @ SV125 @ SV145 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV125 @ SV145 ) )
= $true )
| ( ( pi_sharp_removemin @ SV125 @ SV145 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(603,plain,
! [SV163: $i] :
( ( ! [SY381: $i] :
( ~ ( pi_sharp_removemin @ SV163 @ SY381 )
| ( contains_pq @ SV163 @ SY381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(604,plain,
! [SV164: $i] :
( ( ! [SY382: $i] :
( ~ ( pi_sharp_removemin @ SV164 @ SY382 )
| ( issmallestelement_pq @ SV164 @ SY382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(605,plain,
! [SV146: $i,SV126: $i] :
( ( ( ~ ( less_than @ SV126 @ SV146 ) )
= $true )
| ( ( less_than @ SV146 @ SV126 )
= $true )
| ( ( strictly_less_than @ SV126 @ SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(606,plain,
! [SV165: $i] :
( ( ! [SY383: $i] :
( ~ ( strictly_less_than @ SV165 @ SY383 )
| ( less_than @ SV165 @ SY383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(607,plain,
! [SV166: $i] :
( ( ! [SY384: $i] :
( ~ ( strictly_less_than @ SV166 @ SY384 )
| ~ ( less_than @ SY384 @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(608,plain,
! [SV111: $i,SV90: $i,SV47: $i] :
( ( ~ ! [SY347: $i,SY348: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY347 ) ) @ SV111 @ SY348 )
| ( SV90 = SV111 )
| ( pair_in_list @ SV47 @ SV111 @ SY348 ) )
| ~ ! [SY349: $i,SY350: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY349 ) ) @ SV111 @ SY350 )
| ( SY349 = SY350 )
| ( pair_in_list @ SV47 @ SV111 @ SY350 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(609,plain,
! [SV47: $i,SV111: $i,SV90: $i] :
( ( ~ ! [SY351: $i,SY352: $i] :
( ( SV90 != SV111 )
| ( SY351 != SY352 )
| ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY351 ) ) @ SV111 @ SY352 ) )
| ~ ! [SY353: $i,SY354: $i] :
( ~ ( pair_in_list @ SV47 @ SV111 @ SY354 )
| ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY353 ) ) @ SV111 @ SY354 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(610,plain,
! [SV127: $i,SV152: $i] :
( ( ( ~ ( ok @ SV152 )
| ~ ( succ_cpq @ SV127 @ SV152 ) )
= $true )
| ( ( ~ ( check_cpq @ SV152 ) )
= $true )
| ( ( phi @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[570]) ).
thf(611,plain,
! [SV128: $i] :
( ( ( ~ ~ ( ~ ( ok @ ( sK4_V @ SV128 ) )
| ~ ( succ_cpq @ SV128 @ ( sK4_V @ SV128 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SV128 ) ) )
= $false )
| ( ( phi @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(612,plain,
! [SV153: $i,SV129: $i] :
( ( ( pi_sharp_find_min @ ( i @ SV129 ) @ SV153 )
= $false )
| ( ( pi_find_min @ SV129 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(613,plain,
! [SV147: $i,SV131: $i] :
( ( ( ~ ( contains_pq @ SV131 @ ( sK7_W @ SV147 @ SV131 ) )
| ~ ~ ( less_than @ SV147 @ ( sK7_W @ SV147 @ SV131 ) ) )
= $false )
| ( ( issmallestelement_pq @ SV131 @ SV147 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(614,plain,
! [SV148: $i,SV132: $i] :
( ( ( issmallestelement_pq @ SV132 @ SV148 )
= $false )
| ( ( ! [SY374: $i] :
( ~ ( contains_pq @ SV132 @ SY374 )
| ( less_than @ SV148 @ SY374 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(615,plain,
! [SV154: $i,SV149: $i,SV48: $i] :
( ( ( ~ ( contains_pq @ ( insert_pq @ SV48 @ SV149 ) @ SV154 ) )
= $true )
| ( ( ( SV149 = SV154 )
| ( contains_pq @ SV48 @ SV154 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[576]) ).
thf(616,plain,
! [SV48: $i] :
( ( ! [SY254: $i,SY255: $i] :
( ( SY254 != SY255 )
| ( contains_pq @ ( insert_pq @ SV48 @ SY254 ) @ SY255 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[577]) ).
thf(617,plain,
! [SV48: $i] :
( ( ! [SY256: $i,SY257: $i] :
( ~ ( contains_pq @ SV48 @ SY257 )
| ( contains_pq @ ( insert_pq @ SV48 @ SY256 ) @ SY257 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[578]) ).
thf(618,plain,
! [SV112: $i,SV91: $i,SV49: $i,SV167: $i] :
( ( ! [SY385: $i] :
( ~ ( less_than @ SY385 @ SV167 )
| ~ ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SV91 @ ( pair @ SV167 @ SY385 ) ) @ SV112 ) )
| ( check_cpq @ ( triple @ SV49 @ SV91 @ SV112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(619,plain,
! [SV112: $i,SV91: $i,SV49: $i,SV168: $i] :
( ( ! [SY386: $i] :
( ~ ( less_than @ SY386 @ SV168 )
| ~ ( check_cpq @ ( triple @ SV49 @ SV91 @ SV112 ) )
| ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SV91 @ ( pair @ SV168 @ SY386 ) ) @ SV112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(620,plain,
! [SV169: $i,SV155: $i,SV92: $i,SV50: $i] :
( ( ~ ( contains_cpq @ ( triple @ SV50 @ SV92 @ SV155 ) @ SV169 )
| ( contains_slb @ SV92 @ SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(621,plain,
! [SV156: $i,SV50: $i,SV170: $i,SV92: $i] :
( ( ~ ( contains_slb @ SV92 @ SV170 )
| ( contains_cpq @ ( triple @ SV50 @ SV92 @ SV156 ) @ SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(622,plain,
! [SV150: $i,SV133: $i] :
( ( ( pi_remove @ SV133 @ SV150 )
= $false )
| ( ( pi_sharp_remove @ ( i @ SV133 ) @ SV150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(623,plain,
! [SV151: $i,SV134: $i] :
( ( ( pi_sharp_remove @ ( i @ SV134 ) @ SV151 )
= $false )
| ( ( pi_remove @ SV134 @ SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(624,plain,
! [SV157: $i,SV93: $i,SV51: $i] :
( ( ( ! [SY378: $i] :
~ ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY378 ) ) @ SV157 ) )
= $true )
| ( ( ( SV93 = SV157 )
| ( contains_slb @ SV51 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[585]) ).
thf(625,plain,
! [SV51: $i,SV93: $i] :
( ( ~ ! [SY331: $i] :
( ( SV93 != SY331 )
| ! [SY332: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY332 ) ) @ SY331 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[586]) ).
thf(626,plain,
! [SV93: $i,SV51: $i] :
( ( ~ ! [SY333: $i] :
( ~ ( contains_slb @ SV51 @ SY333 )
| ! [SY334: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY334 ) ) @ SY333 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[586]) ).
thf(627,plain,
! [SV158: $i,SV135: $i] :
( ( ( pi_sharp_find_min @ ( i @ SV135 ) @ SV158 )
= $false )
| ( ( pi_removemin @ SV135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(628,plain,
! [SV104: $i,SV139: $i,SV115: $i,SV75: $i,SV30: $i] :
( ( ( check_cpq @ ( triple @ SV30 @ ( insert_slb @ SV75 @ ( pair @ SV115 @ SV139 ) ) @ SV104 ) )
= $false )
| ( ( strictly_less_than @ SV115 @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(629,plain,
! [SV108: $i,SV35: $i,SV118: $i,SV80: $i] :
( ( ( less_than @ ( lookup_slb @ SV80 @ SV118 ) @ SV118 )
= $false )
| ( ( contains_slb @ SV80 @ SV118 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV35 @ SV80 @ SV108 ) @ SV118 )
= ( triple @ ( remove_pqp @ SV35 @ SV118 ) @ ( remove_slb @ SV80 @ SV118 ) @ SV108 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(630,plain,
! [SV109: $i,SV36: $i,SV81: $i,SV119: $i] :
( ( ( strictly_less_than @ SV119 @ ( lookup_slb @ SV81 @ SV119 ) )
= $false )
| ( ( contains_slb @ SV81 @ SV119 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV36 @ SV81 @ SV109 ) @ SV119 )
= ( triple @ ( remove_pqp @ SV36 @ SV119 ) @ ( remove_slb @ SV81 @ SV119 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(631,plain,
! [SV171: $i,SV84: $i,SV39: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV39 @ SV84 @ SV171 ) )
= ( triple @ SV39 @ ( update_slb @ SV84 @ ( findmin_pqp_res @ SV39 ) ) @ bad ) )
= $true )
| ( ( contains_slb @ SV84 @ ( findmin_pqp_res @ SV39 ) )
= $false )
| ( ( SV84 = create_slb )
= $true )
| ( ( strictly_less_than @ ( findmin_pqp_res @ SV39 ) @ ( lookup_slb @ SV84 @ ( findmin_pqp_res @ SV39 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(632,plain,
! [SV172: $i,SV85: $i,SV40: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV40 @ SV85 @ SV172 ) )
= ( triple @ SV40 @ ( update_slb @ SV85 @ ( findmin_pqp_res @ SV40 ) ) @ SV172 ) )
= $true )
| ( ( contains_slb @ SV85 @ ( findmin_pqp_res @ SV40 ) )
= $false )
| ( ( SV85 = create_slb )
= $true )
| ( ( less_than @ ( lookup_slb @ SV85 @ ( findmin_pqp_res @ SV40 ) ) @ ( findmin_pqp_res @ SV40 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(633,plain,
! [SV142: $i,SV122: $i] :
( ( ( contains_pq @ SV122 @ SV142 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV122 @ SV142 ) )
= $true )
| ( ( pi_sharp_find_min @ SV122 @ SV142 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(634,plain,
! [SV173: $i,SV161: $i] :
( ( ~ ( pi_sharp_find_min @ SV161 @ SV173 )
| ( contains_pq @ SV161 @ SV173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(635,plain,
! [SV174: $i,SV162: $i] :
( ( ~ ( pi_sharp_find_min @ SV162 @ SV174 )
| ( issmallestelement_pq @ SV162 @ SV174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(636,plain,
! [SV145: $i,SV125: $i] :
( ( ( contains_pq @ SV125 @ SV145 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV125 @ SV145 ) )
= $true )
| ( ( pi_sharp_removemin @ SV125 @ SV145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(637,plain,
! [SV175: $i,SV163: $i] :
( ( ~ ( pi_sharp_removemin @ SV163 @ SV175 )
| ( contains_pq @ SV163 @ SV175 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(638,plain,
! [SV176: $i,SV164: $i] :
( ( ~ ( pi_sharp_removemin @ SV164 @ SV176 )
| ( issmallestelement_pq @ SV164 @ SV176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(639,plain,
! [SV146: $i,SV126: $i] :
( ( ( less_than @ SV126 @ SV146 )
= $false )
| ( ( less_than @ SV146 @ SV126 )
= $true )
| ( ( strictly_less_than @ SV126 @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(640,plain,
! [SV177: $i,SV165: $i] :
( ( ~ ( strictly_less_than @ SV165 @ SV177 )
| ( less_than @ SV165 @ SV177 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(641,plain,
! [SV178: $i,SV166: $i] :
( ( ~ ( strictly_less_than @ SV166 @ SV178 )
| ~ ( less_than @ SV178 @ SV166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(642,plain,
! [SV111: $i,SV90: $i,SV47: $i] :
( ( ~ ! [SY347: $i,SY348: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY347 ) ) @ SV111 @ SY348 )
| ( SV90 = SV111 )
| ( pair_in_list @ SV47 @ SV111 @ SY348 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[608]) ).
thf(643,plain,
! [SV111: $i,SV90: $i,SV47: $i] :
( ( ~ ! [SY349: $i,SY350: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY349 ) ) @ SV111 @ SY350 )
| ( SY349 = SY350 )
| ( pair_in_list @ SV47 @ SV111 @ SY350 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[608]) ).
thf(644,plain,
! [SV47: $i,SV111: $i,SV90: $i] :
( ( ~ ! [SY351: $i,SY352: $i] :
( ( SV90 != SV111 )
| ( SY351 != SY352 )
| ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY351 ) ) @ SV111 @ SY352 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[609]) ).
thf(645,plain,
! [SV90: $i,SV111: $i,SV47: $i] :
( ( ~ ! [SY353: $i,SY354: $i] :
( ~ ( pair_in_list @ SV47 @ SV111 @ SY354 )
| ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY353 ) ) @ SV111 @ SY354 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[609]) ).
thf(646,plain,
! [SV127: $i,SV152: $i] :
( ( ( ~ ( ok @ SV152 ) )
= $true )
| ( ( ~ ( succ_cpq @ SV127 @ SV152 ) )
= $true )
| ( ( ~ ( check_cpq @ SV152 ) )
= $true )
| ( ( phi @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[610]) ).
thf(647,plain,
! [SV128: $i] :
( ( ( ~ ~ ( ~ ( ok @ ( sK4_V @ SV128 ) )
| ~ ( succ_cpq @ SV128 @ ( sK4_V @ SV128 ) ) ) )
= $false )
| ( ( phi @ SV128 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[611]) ).
thf(648,plain,
! [SV128: $i] :
( ( ( ~ ( check_cpq @ ( sK4_V @ SV128 ) ) )
= $false )
| ( ( phi @ SV128 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[611]) ).
thf(649,plain,
! [SV147: $i,SV131: $i] :
( ( ( ~ ( contains_pq @ SV131 @ ( sK7_W @ SV147 @ SV131 ) ) )
= $false )
| ( ( issmallestelement_pq @ SV131 @ SV147 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[613]) ).
thf(650,plain,
! [SV131: $i,SV147: $i] :
( ( ( ~ ~ ( less_than @ SV147 @ ( sK7_W @ SV147 @ SV131 ) ) )
= $false )
| ( ( issmallestelement_pq @ SV131 @ SV147 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[613]) ).
thf(651,plain,
! [SV148: $i,SV179: $i,SV132: $i] :
( ( ( ~ ( contains_pq @ SV132 @ SV179 )
| ( less_than @ SV148 @ SV179 ) )
= $true )
| ( ( issmallestelement_pq @ SV132 @ SV148 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(652,plain,
! [SV154: $i,SV149: $i,SV48: $i] :
( ( ( contains_pq @ ( insert_pq @ SV48 @ SV149 ) @ SV154 )
= $false )
| ( ( ( SV149 = SV154 )
| ( contains_pq @ SV48 @ SV154 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(653,plain,
! [SV48: $i,SV180: $i] :
( ( ! [SY387: $i] :
( ( SV180 != SY387 )
| ( contains_pq @ ( insert_pq @ SV48 @ SV180 ) @ SY387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(654,plain,
! [SV181: $i,SV48: $i] :
( ( ! [SY388: $i] :
( ~ ( contains_pq @ SV48 @ SY388 )
| ( contains_pq @ ( insert_pq @ SV48 @ SV181 ) @ SY388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(655,plain,
! [SV112: $i,SV91: $i,SV49: $i,SV167: $i,SV182: $i] :
( ( ~ ( less_than @ SV182 @ SV167 )
| ~ ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SV91 @ ( pair @ SV167 @ SV182 ) ) @ SV112 ) )
| ( check_cpq @ ( triple @ SV49 @ SV91 @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(656,plain,
! [SV112: $i,SV91: $i,SV49: $i,SV168: $i,SV183: $i] :
( ( ~ ( less_than @ SV183 @ SV168 )
| ~ ( check_cpq @ ( triple @ SV49 @ SV91 @ SV112 ) )
| ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SV91 @ ( pair @ SV168 @ SV183 ) ) @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(657,plain,
! [SV169: $i,SV155: $i,SV92: $i,SV50: $i] :
( ( ( ~ ( contains_cpq @ ( triple @ SV50 @ SV92 @ SV155 ) @ SV169 ) )
= $true )
| ( ( contains_slb @ SV92 @ SV169 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(658,plain,
! [SV156: $i,SV50: $i,SV170: $i,SV92: $i] :
( ( ( ~ ( contains_slb @ SV92 @ SV170 ) )
= $true )
| ( ( contains_cpq @ ( triple @ SV50 @ SV92 @ SV156 ) @ SV170 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[621]) ).
thf(659,plain,
! [SV157: $i,SV184: $i,SV93: $i,SV51: $i] :
( ( ( ~ ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SV184 ) ) @ SV157 ) )
= $true )
| ( ( ( SV93 = SV157 )
| ( contains_slb @ SV51 @ SV157 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(660,plain,
! [SV51: $i,SV93: $i] :
( ( ! [SY331: $i] :
( ( SV93 != SY331 )
| ! [SY332: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY332 ) ) @ SY331 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[625]) ).
thf(661,plain,
! [SV93: $i,SV51: $i] :
( ( ! [SY333: $i] :
( ~ ( contains_slb @ SV51 @ SY333 )
| ! [SY334: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY334 ) ) @ SY333 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[626]) ).
thf(662,plain,
! [SV142: $i,SV122: $i] :
( ( ( issmallestelement_pq @ SV122 @ SV142 )
= $false )
| ( ( contains_pq @ SV122 @ SV142 )
= $false )
| ( ( pi_sharp_find_min @ SV122 @ SV142 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(663,plain,
! [SV173: $i,SV161: $i] :
( ( ( ~ ( pi_sharp_find_min @ SV161 @ SV173 ) )
= $true )
| ( ( contains_pq @ SV161 @ SV173 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[634]) ).
thf(664,plain,
! [SV174: $i,SV162: $i] :
( ( ( ~ ( pi_sharp_find_min @ SV162 @ SV174 ) )
= $true )
| ( ( issmallestelement_pq @ SV162 @ SV174 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[635]) ).
thf(665,plain,
! [SV145: $i,SV125: $i] :
( ( ( issmallestelement_pq @ SV125 @ SV145 )
= $false )
| ( ( contains_pq @ SV125 @ SV145 )
= $false )
| ( ( pi_sharp_removemin @ SV125 @ SV145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(666,plain,
! [SV175: $i,SV163: $i] :
( ( ( ~ ( pi_sharp_removemin @ SV163 @ SV175 ) )
= $true )
| ( ( contains_pq @ SV163 @ SV175 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[637]) ).
thf(667,plain,
! [SV176: $i,SV164: $i] :
( ( ( ~ ( pi_sharp_removemin @ SV164 @ SV176 ) )
= $true )
| ( ( issmallestelement_pq @ SV164 @ SV176 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[638]) ).
thf(668,plain,
! [SV177: $i,SV165: $i] :
( ( ( ~ ( strictly_less_than @ SV165 @ SV177 ) )
= $true )
| ( ( less_than @ SV165 @ SV177 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(669,plain,
! [SV178: $i,SV166: $i] :
( ( ( ~ ( strictly_less_than @ SV166 @ SV178 ) )
= $true )
| ( ( ~ ( less_than @ SV178 @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[641]) ).
thf(670,plain,
! [SV111: $i,SV90: $i,SV47: $i] :
( ( ! [SY347: $i,SY348: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY347 ) ) @ SV111 @ SY348 )
| ( SV90 = SV111 )
| ( pair_in_list @ SV47 @ SV111 @ SY348 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[642]) ).
thf(671,plain,
! [SV111: $i,SV90: $i,SV47: $i] :
( ( ! [SY349: $i,SY350: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY349 ) ) @ SV111 @ SY350 )
| ( SY349 = SY350 )
| ( pair_in_list @ SV47 @ SV111 @ SY350 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[643]) ).
thf(672,plain,
! [SV47: $i,SV111: $i,SV90: $i] :
( ( ! [SY351: $i,SY352: $i] :
( ( SV90 != SV111 )
| ( SY351 != SY352 )
| ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY351 ) ) @ SV111 @ SY352 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[644]) ).
thf(673,plain,
! [SV90: $i,SV111: $i,SV47: $i] :
( ( ! [SY353: $i,SY354: $i] :
( ~ ( pair_in_list @ SV47 @ SV111 @ SY354 )
| ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SY353 ) ) @ SV111 @ SY354 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[645]) ).
thf(674,plain,
! [SV127: $i,SV152: $i] :
( ( ( ok @ SV152 )
= $false )
| ( ( ~ ( succ_cpq @ SV127 @ SV152 ) )
= $true )
| ( ( ~ ( check_cpq @ SV152 ) )
= $true )
| ( ( phi @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(675,plain,
! [SV128: $i] :
( ( ( ~ ( ~ ( ok @ ( sK4_V @ SV128 ) )
| ~ ( succ_cpq @ SV128 @ ( sK4_V @ SV128 ) ) ) )
= $true )
| ( ( phi @ SV128 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[647]) ).
thf(676,plain,
! [SV128: $i] :
( ( ( check_cpq @ ( sK4_V @ SV128 ) )
= $true )
| ( ( phi @ SV128 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[648]) ).
thf(677,plain,
! [SV147: $i,SV131: $i] :
( ( ( contains_pq @ SV131 @ ( sK7_W @ SV147 @ SV131 ) )
= $true )
| ( ( issmallestelement_pq @ SV131 @ SV147 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[649]) ).
thf(678,plain,
! [SV131: $i,SV147: $i] :
( ( ( ~ ( less_than @ SV147 @ ( sK7_W @ SV147 @ SV131 ) ) )
= $true )
| ( ( issmallestelement_pq @ SV131 @ SV147 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[650]) ).
thf(679,plain,
! [SV148: $i,SV179: $i,SV132: $i] :
( ( ( ~ ( contains_pq @ SV132 @ SV179 ) )
= $true )
| ( ( less_than @ SV148 @ SV179 )
= $true )
| ( ( issmallestelement_pq @ SV132 @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[651]) ).
thf(680,plain,
! [SV48: $i,SV154: $i,SV149: $i] :
( ( ( SV149 = SV154 )
= $true )
| ( ( contains_pq @ SV48 @ SV154 )
= $true )
| ( ( contains_pq @ ( insert_pq @ SV48 @ SV149 ) @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[652]) ).
thf(681,plain,
! [SV48: $i,SV185: $i,SV180: $i] :
( ( ( SV180 != SV185 )
| ( contains_pq @ ( insert_pq @ SV48 @ SV180 ) @ SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(682,plain,
! [SV181: $i,SV186: $i,SV48: $i] :
( ( ~ ( contains_pq @ SV48 @ SV186 )
| ( contains_pq @ ( insert_pq @ SV48 @ SV181 ) @ SV186 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(683,plain,
! [SV112: $i,SV91: $i,SV49: $i,SV167: $i,SV182: $i] :
( ( ( ~ ( less_than @ SV182 @ SV167 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SV91 @ ( pair @ SV167 @ SV182 ) ) @ SV112 ) )
| ( check_cpq @ ( triple @ SV49 @ SV91 @ SV112 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[655]) ).
thf(684,plain,
! [SV112: $i,SV91: $i,SV49: $i,SV168: $i,SV183: $i] :
( ( ( ~ ( less_than @ SV183 @ SV168 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV49 @ SV91 @ SV112 ) )
| ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SV91 @ ( pair @ SV168 @ SV183 ) ) @ SV112 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[656]) ).
thf(685,plain,
! [SV169: $i,SV155: $i,SV92: $i,SV50: $i] :
( ( ( contains_cpq @ ( triple @ SV50 @ SV92 @ SV155 ) @ SV169 )
= $false )
| ( ( contains_slb @ SV92 @ SV169 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(686,plain,
! [SV156: $i,SV50: $i,SV170: $i,SV92: $i] :
( ( ( contains_slb @ SV92 @ SV170 )
= $false )
| ( ( contains_cpq @ ( triple @ SV50 @ SV92 @ SV156 ) @ SV170 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(687,plain,
! [SV157: $i,SV184: $i,SV93: $i,SV51: $i] :
( ( ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SV184 ) ) @ SV157 )
= $false )
| ( ( ( SV93 = SV157 )
| ( contains_slb @ SV51 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(688,plain,
! [SV51: $i,SV187: $i,SV93: $i] :
( ( ( SV93 != SV187 )
| ! [SY389: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY389 ) ) @ SV187 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(689,plain,
! [SV93: $i,SV188: $i,SV51: $i] :
( ( ~ ( contains_slb @ SV51 @ SV188 )
| ! [SY390: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY390 ) ) @ SV188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(690,plain,
! [SV173: $i,SV161: $i] :
( ( ( pi_sharp_find_min @ SV161 @ SV173 )
= $false )
| ( ( contains_pq @ SV161 @ SV173 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[663]) ).
thf(691,plain,
! [SV174: $i,SV162: $i] :
( ( ( pi_sharp_find_min @ SV162 @ SV174 )
= $false )
| ( ( issmallestelement_pq @ SV162 @ SV174 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(692,plain,
! [SV175: $i,SV163: $i] :
( ( ( pi_sharp_removemin @ SV163 @ SV175 )
= $false )
| ( ( contains_pq @ SV163 @ SV175 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[666]) ).
thf(693,plain,
! [SV176: $i,SV164: $i] :
( ( ( pi_sharp_removemin @ SV164 @ SV176 )
= $false )
| ( ( issmallestelement_pq @ SV164 @ SV176 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(694,plain,
! [SV177: $i,SV165: $i] :
( ( ( strictly_less_than @ SV165 @ SV177 )
= $false )
| ( ( less_than @ SV165 @ SV177 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[668]) ).
thf(695,plain,
! [SV178: $i,SV166: $i] :
( ( ( strictly_less_than @ SV166 @ SV178 )
= $false )
| ( ( ~ ( less_than @ SV178 @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(696,plain,
! [SV111: $i,SV189: $i,SV90: $i,SV47: $i] :
( ( ! [SY391: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SV189 ) ) @ SV111 @ SY391 )
| ( SV90 = SV111 )
| ( pair_in_list @ SV47 @ SV111 @ SY391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(697,plain,
! [SV111: $i,SV190: $i,SV90: $i,SV47: $i] :
( ( ! [SY392: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SV190 ) ) @ SV111 @ SY392 )
| ( SV190 = SY392 )
| ( pair_in_list @ SV47 @ SV111 @ SY392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(698,plain,
! [SV47: $i,SV191: $i,SV111: $i,SV90: $i] :
( ( ! [SY393: $i] :
( ( SV90 != SV111 )
| ( SV191 != SY393 )
| ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SV191 ) ) @ SV111 @ SY393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(699,plain,
! [SV192: $i,SV90: $i,SV111: $i,SV47: $i] :
( ( ! [SY394: $i] :
( ~ ( pair_in_list @ SV47 @ SV111 @ SY394 )
| ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SV192 ) ) @ SV111 @ SY394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(700,plain,
! [SV152: $i,SV127: $i] :
( ( ( succ_cpq @ SV127 @ SV152 )
= $false )
| ( ( ok @ SV152 )
= $false )
| ( ( ~ ( check_cpq @ SV152 ) )
= $true )
| ( ( phi @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(701,plain,
! [SV128: $i] :
( ( ( ~ ( ok @ ( sK4_V @ SV128 ) )
| ~ ( succ_cpq @ SV128 @ ( sK4_V @ SV128 ) ) )
= $false )
| ( ( phi @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(702,plain,
! [SV131: $i,SV147: $i] :
( ( ( less_than @ SV147 @ ( sK7_W @ SV147 @ SV131 ) )
= $false )
| ( ( issmallestelement_pq @ SV131 @ SV147 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(703,plain,
! [SV148: $i,SV179: $i,SV132: $i] :
( ( ( contains_pq @ SV132 @ SV179 )
= $false )
| ( ( less_than @ SV148 @ SV179 )
= $true )
| ( ( issmallestelement_pq @ SV132 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(704,plain,
! [SV48: $i,SV185: $i,SV180: $i] :
( ( ( ( SV180 != SV185 ) )
= $true )
| ( ( contains_pq @ ( insert_pq @ SV48 @ SV180 ) @ SV185 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[681]) ).
thf(705,plain,
! [SV181: $i,SV186: $i,SV48: $i] :
( ( ( ~ ( contains_pq @ SV48 @ SV186 ) )
= $true )
| ( ( contains_pq @ ( insert_pq @ SV48 @ SV181 ) @ SV186 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[682]) ).
thf(706,plain,
! [SV112: $i,SV91: $i,SV49: $i,SV167: $i,SV182: $i] :
( ( ( less_than @ SV182 @ SV167 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SV91 @ ( pair @ SV167 @ SV182 ) ) @ SV112 ) )
| ( check_cpq @ ( triple @ SV49 @ SV91 @ SV112 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(707,plain,
! [SV112: $i,SV91: $i,SV49: $i,SV168: $i,SV183: $i] :
( ( ( less_than @ SV183 @ SV168 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV49 @ SV91 @ SV112 ) )
| ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SV91 @ ( pair @ SV168 @ SV183 ) ) @ SV112 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(708,plain,
! [SV184: $i,SV51: $i,SV157: $i,SV93: $i] :
( ( ( SV93 = SV157 )
= $true )
| ( ( contains_slb @ SV51 @ SV157 )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SV184 ) ) @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[687]) ).
thf(709,plain,
! [SV51: $i,SV187: $i,SV93: $i] :
( ( ( ( SV93 != SV187 ) )
= $true )
| ( ( ! [SY389: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY389 ) ) @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[688]) ).
thf(710,plain,
! [SV93: $i,SV188: $i,SV51: $i] :
( ( ( ~ ( contains_slb @ SV51 @ SV188 ) )
= $true )
| ( ( ! [SY390: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY390 ) ) @ SV188 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[689]) ).
thf(711,plain,
! [SV166: $i,SV178: $i] :
( ( ( less_than @ SV178 @ SV166 )
= $false )
| ( ( strictly_less_than @ SV166 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[695]) ).
thf(712,plain,
! [SV193: $i,SV111: $i,SV189: $i,SV90: $i,SV47: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SV189 ) ) @ SV111 @ SV193 )
| ( SV90 = SV111 )
| ( pair_in_list @ SV47 @ SV111 @ SV193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(713,plain,
! [SV194: $i,SV111: $i,SV190: $i,SV90: $i,SV47: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SV190 ) ) @ SV111 @ SV194 )
| ( SV190 = SV194 )
| ( pair_in_list @ SV47 @ SV111 @ SV194 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(714,plain,
! [SV47: $i,SV195: $i,SV191: $i,SV111: $i,SV90: $i] :
( ( ( SV90 != SV111 )
| ( SV191 != SV195 )
| ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SV191 ) ) @ SV111 @ SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(715,plain,
! [SV192: $i,SV90: $i,SV196: $i,SV111: $i,SV47: $i] :
( ( ~ ( pair_in_list @ SV47 @ SV111 @ SV196 )
| ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SV192 ) ) @ SV111 @ SV196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(716,plain,
! [SV127: $i,SV152: $i] :
( ( ( check_cpq @ SV152 )
= $false )
| ( ( ok @ SV152 )
= $false )
| ( ( succ_cpq @ SV127 @ SV152 )
= $false )
| ( ( phi @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(717,plain,
! [SV128: $i] :
( ( ( ~ ( ok @ ( sK4_V @ SV128 ) ) )
= $false )
| ( ( phi @ SV128 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[701]) ).
thf(718,plain,
! [SV128: $i] :
( ( ( ~ ( succ_cpq @ SV128 @ ( sK4_V @ SV128 ) ) )
= $false )
| ( ( phi @ SV128 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[701]) ).
thf(719,plain,
! [SV48: $i,SV185: $i,SV180: $i] :
( ( ( SV180 = SV185 )
= $false )
| ( ( contains_pq @ ( insert_pq @ SV48 @ SV180 ) @ SV185 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(720,plain,
! [SV181: $i,SV186: $i,SV48: $i] :
( ( ( contains_pq @ SV48 @ SV186 )
= $false )
| ( ( contains_pq @ ( insert_pq @ SV48 @ SV181 ) @ SV186 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(721,plain,
! [SV112: $i,SV182: $i,SV167: $i,SV91: $i,SV49: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SV91 @ ( pair @ SV167 @ SV182 ) ) @ SV112 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV49 @ SV91 @ SV112 ) )
= $true )
| ( ( less_than @ SV182 @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[706]) ).
thf(722,plain,
! [SV183: $i,SV168: $i,SV112: $i,SV91: $i,SV49: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV49 @ SV91 @ SV112 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SV91 @ ( pair @ SV168 @ SV183 ) ) @ SV112 ) )
= $true )
| ( ( less_than @ SV183 @ SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[707]) ).
thf(723,plain,
! [SV51: $i,SV187: $i,SV93: $i] :
( ( ( SV93 = SV187 )
= $false )
| ( ( ! [SY389: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY389 ) ) @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[709]) ).
thf(724,plain,
! [SV93: $i,SV188: $i,SV51: $i] :
( ( ( contains_slb @ SV51 @ SV188 )
= $false )
| ( ( ! [SY390: $i] : ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SY390 ) ) @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(725,plain,
! [SV193: $i,SV111: $i,SV189: $i,SV90: $i,SV47: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SV189 ) ) @ SV111 @ SV193 ) )
= $true )
| ( ( ( SV90 = SV111 )
| ( pair_in_list @ SV47 @ SV111 @ SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[712]) ).
thf(726,plain,
! [SV194: $i,SV111: $i,SV190: $i,SV90: $i,SV47: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SV190 ) ) @ SV111 @ SV194 ) )
= $true )
| ( ( ( SV190 = SV194 )
| ( pair_in_list @ SV47 @ SV111 @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[713]) ).
thf(727,plain,
! [SV47: $i,SV195: $i,SV191: $i,SV111: $i,SV90: $i] :
( ( ( ( SV90 != SV111 )
| ( SV191 != SV195 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SV191 ) ) @ SV111 @ SV195 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[714]) ).
thf(728,plain,
! [SV192: $i,SV90: $i,SV196: $i,SV111: $i,SV47: $i] :
( ( ( ~ ( pair_in_list @ SV47 @ SV111 @ SV196 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SV192 ) ) @ SV111 @ SV196 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[715]) ).
thf(729,plain,
! [SV128: $i] :
( ( ( ok @ ( sK4_V @ SV128 ) )
= $true )
| ( ( phi @ SV128 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[717]) ).
thf(730,plain,
! [SV128: $i] :
( ( ( succ_cpq @ SV128 @ ( sK4_V @ SV128 ) )
= $true )
| ( ( phi @ SV128 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[718]) ).
thf(731,plain,
! [SV112: $i,SV182: $i,SV167: $i,SV91: $i,SV49: $i] :
( ( ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SV91 @ ( pair @ SV167 @ SV182 ) ) @ SV112 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV49 @ SV91 @ SV112 ) )
= $true )
| ( ( less_than @ SV182 @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(732,plain,
! [SV183: $i,SV168: $i,SV112: $i,SV91: $i,SV49: $i] :
( ( ( check_cpq @ ( triple @ SV49 @ SV91 @ SV112 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV49 @ ( insert_slb @ SV91 @ ( pair @ SV168 @ SV183 ) ) @ SV112 ) )
= $true )
| ( ( less_than @ SV183 @ SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[722]) ).
thf(733,plain,
! [SV187: $i,SV197: $i,SV93: $i,SV51: $i] :
( ( ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SV197 ) ) @ SV187 )
= $true )
| ( ( SV93 = SV187 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(734,plain,
! [SV188: $i,SV198: $i,SV93: $i,SV51: $i] :
( ( ( contains_slb @ ( insert_slb @ SV51 @ ( pair @ SV93 @ SV198 ) ) @ SV188 )
= $true )
| ( ( contains_slb @ SV51 @ SV188 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(735,plain,
! [SV193: $i,SV111: $i,SV189: $i,SV90: $i,SV47: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SV189 ) ) @ SV111 @ SV193 )
= $false )
| ( ( ( SV90 = SV111 )
| ( pair_in_list @ SV47 @ SV111 @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(736,plain,
! [SV194: $i,SV111: $i,SV190: $i,SV90: $i,SV47: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SV190 ) ) @ SV111 @ SV194 )
= $false )
| ( ( ( SV190 = SV194 )
| ( pair_in_list @ SV47 @ SV111 @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[726]) ).
thf(737,plain,
! [SV47: $i,SV195: $i,SV191: $i,SV111: $i,SV90: $i] :
( ( ( ( SV90 != SV111 ) )
= $true )
| ( ( ( SV191 != SV195 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SV191 ) ) @ SV111 @ SV195 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(738,plain,
! [SV192: $i,SV90: $i,SV196: $i,SV111: $i,SV47: $i] :
( ( ( pair_in_list @ SV47 @ SV111 @ SV196 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SV192 ) ) @ SV111 @ SV196 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(739,plain,
! [SV189: $i,SV193: $i,SV47: $i,SV111: $i,SV90: $i] :
( ( ( SV90 = SV111 )
= $true )
| ( ( pair_in_list @ SV47 @ SV111 @ SV193 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SV189 ) ) @ SV111 @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[735]) ).
thf(740,plain,
! [SV90: $i,SV111: $i,SV47: $i,SV194: $i,SV190: $i] :
( ( ( SV190 = SV194 )
= $true )
| ( ( pair_in_list @ SV47 @ SV111 @ SV194 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SV190 ) ) @ SV111 @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(741,plain,
! [SV47: $i,SV195: $i,SV191: $i,SV111: $i,SV90: $i] :
( ( ( SV90 = SV111 )
= $false )
| ( ( ( SV191 != SV195 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SV191 ) ) @ SV111 @ SV195 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[737]) ).
thf(742,plain,
! [SV47: $i,SV111: $i,SV90: $i,SV195: $i,SV191: $i] :
( ( ( SV191 = SV195 )
= $false )
| ( ( SV90 = SV111 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV47 @ ( pair @ SV90 @ SV191 ) ) @ SV111 @ SV195 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[741]) ).
thf(743,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[255,742,740,739,738,734,733,732,731,730,729,720,719,716,711,708,703,702,694,693,692,691,690,686,685,680,677,676,665,662,639,632,631,630,629,628,627,623,622,612,601,600,591,590,589,588,573,551,550,547,546,545,544,543,510,507,504,502,501,482,462,455,454,452,451,431,402,393,391,390,389,388,382,354,352,348,340,328,320,319,318,298,297,278,275,267,257,256]) ).
thf(744,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( less_than @ U @ V )
| ~ ( less_than @ V @ W )
| ( less_than @ U @ W ) ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(745,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(746,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(747,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)],[173]) ).
thf(748,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(749,plain,
( ( ~ ( isnonempty_pq @ create_pq ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(750,plain,
( ( ! [U: $i,V: $i] : ( isnonempty_pq @ ( insert_pq @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(751,plain,
( ( ! [U: $i] :
~ ( contains_pq @ create_pq @ U ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(752,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)],[172]) ).
thf(753,plain,
( ( ! [U: $i,V: $i] :
( ( ( contains_pq @ U @ ( sK7_W @ V @ U ) )
& ~ ( less_than @ V @ ( sK7_W @ V @ U ) ) )
| ( issmallestelement_pq @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( issmallestelement_pq @ U @ V )
| ! [W: $i] :
( ~ ( contains_pq @ U @ W )
| ( less_than @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(754,plain,
( ( ! [U: $i,V: $i] :
( ( remove_pq @ ( insert_pq @ U @ V ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(755,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)],[170]) ).
thf(756,plain,
( ( ! [U: $i,V: $i] :
( ~ ( contains_pq @ U @ V )
| ~ ( issmallestelement_pq @ U @ V )
| ( ( findmin_pq_eff @ U @ V )
= U ) ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(757,plain,
( ( ! [U: $i,V: $i] :
( ~ ( contains_pq @ U @ V )
| ~ ( issmallestelement_pq @ U @ V )
| ( ( findmin_pq_res @ U @ V )
= V ) ) )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(758,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)],[167]) ).
thf(759,plain,
( ( ! [U: $i,V: $i] :
( ~ ( contains_pq @ U @ V )
| ~ ( issmallestelement_pq @ U @ V )
| ( ( removemin_pq_res @ U @ V )
= V ) ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(760,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(761,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(762,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(763,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(764,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)],[165]) ).
thf(765,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(766,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)],[164]) ).
thf(767,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(768,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)],[163]) ).
thf(769,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(770,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)],[162]) ).
thf(771,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(772,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)],[161]) ).
thf(773,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)],[160]) ).
thf(774,plain,
( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(775,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(776,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(777,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(778,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(779,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(780,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)],[155]) ).
thf(781,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)],[154]) ).
thf(782,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)],[153]) ).
thf(783,plain,
( ( ! [U: $i,V: $i] :
~ ( ok @ ( triple @ U @ V @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(784,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( triple @ U @ V @ W ) )
| ( W = bad ) ) )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(785,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(786,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)],[150]) ).
thf(787,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)],[149]) ).
thf(788,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)],[148]) ).
thf(789,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(790,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)],[147]) ).
thf(791,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)],[146]) ).
thf(792,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)],[145]) ).
thf(793,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(794,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)],[144]) ).
thf(795,plain,
( ( ! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(796,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(797,plain,
( ( ! [U: $i,V: $i] :
( ( i @ ( triple @ U @ create_slb @ V ) )
= create_pq ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(798,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(799,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)],[143]) ).
thf(800,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)],[142]) ).
thf(801,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)],[141]) ).
thf(802,plain,
( ( ! [U: $i] :
( ! [V: $i] :
~ ( pi_sharp_find_min @ ( i @ U ) @ V )
| ( pi_find_min @ U ) )
& ! [U: $i] :
( ~ ( pi_find_min @ U )
| ( pi_sharp_find_min @ ( i @ U ) @ ( sK6_V @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(803,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)],[139]) ).
thf(804,plain,
( ( ! [U: $i] :
( ! [V: $i] :
~ ( pi_sharp_find_min @ ( i @ U ) @ V )
| ( pi_removemin @ U ) )
& ! [U: $i] :
( ~ ( pi_removemin @ U )
| ( pi_sharp_find_min @ ( i @ U ) @ ( sK5_V @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(805,plain,
( ( ! [U: $i] :
( ! [V: $i] :
( ~ ( ok @ V )
| ~ ( succ_cpq @ U @ V )
| ~ ( check_cpq @ V ) )
| ( phi @ U ) )
& ! [U: $i] :
( ~ ( phi @ U )
| ( ( ok @ ( sK4_V @ U ) )
& ( succ_cpq @ U @ ( sK4_V @ U ) )
& ( check_cpq @ ( sK4_V @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(806,plain,
( ( ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) ) @ sK3_SY168 )
& ~ ( contains_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) @ sK3_SY168 ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(807,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( ok @ SX1 )
| ~ ( succ_cpq @ SX0 @ SX1 )
| ~ ( check_cpq @ SX1 ) )
| ( phi @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( phi @ SX0 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK4_V @ SX0 ) )
| ~ ( succ_cpq @ SX0 @ ( sK4_V @ SX0 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[805]) ).
thf(808,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)],[782]) ).
thf(809,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_find_min @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( pi_find_min @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK6_V @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[802]) ).
thf(810,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)],[801]) ).
thf(811,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)],[764]) ).
thf(812,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)],[799]) ).
thf(813,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)],[747]) ).
thf(814,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( contains_pq @ SX0 @ ( sK7_W @ SX1 @ SX0 ) )
| ~ ~ ( less_than @ SX1 @ ( sK7_W @ SX1 @ SX0 ) ) )
| ( issmallestelement_pq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( issmallestelement_pq @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( contains_pq @ SX0 @ SX2 )
| ( less_than @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[753]) ).
thf(815,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)],[803]) ).
thf(816,plain,
( ( ~ ( ~ ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) ) @ sK3_SY168 )
| ~ ~ ( contains_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) @ sK3_SY168 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[806]) ).
thf(817,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)],[766]) ).
thf(818,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)],[752]) ).
thf(819,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)],[800]) ).
thf(820,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_removemin @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( pi_removemin @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK5_V @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[804]) ).
thf(821,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)],[780]) ).
thf(822,plain,
! [SV199: $i] :
( ( ! [SY395: $i,SY396: $i] :
( ~ ( less_than @ SV199 @ SY395 )
| ~ ( less_than @ SY395 @ SY396 )
| ( less_than @ SV199 @ SY396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(823,plain,
! [SV200: $i] :
( ( ! [SY397: $i] :
( ( less_than @ SV200 @ SY397 )
| ( less_than @ SY397 @ SV200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(824,plain,
! [SV201: $i] :
( ( less_than @ SV201 @ SV201 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(825,plain,
! [SV202: $i] :
( ( less_than @ bottom @ SV202 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(826,plain,
( ( isnonempty_pq @ create_pq )
= $false ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(827,plain,
! [SV203: $i] :
( ( ! [SY398: $i] : ( isnonempty_pq @ ( insert_pq @ SV203 @ SY398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(828,plain,
! [SV204: $i] :
( ( ~ ( contains_pq @ create_pq @ SV204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(829,plain,
! [SV205: $i] :
( ( ! [SY399: $i] :
( ( remove_pq @ ( insert_pq @ SV205 @ SY399 ) @ SY399 )
= SV205 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(830,plain,
! [SV206: $i] :
( ( ! [SY400: $i,SY401: $i] :
( ( SY400 = SY401 )
| ~ ( contains_pq @ SV206 @ SY401 )
| ( ( remove_pq @ ( insert_pq @ SV206 @ SY400 ) @ SY401 )
= ( insert_pq @ ( remove_pq @ SV206 @ SY401 ) @ SY400 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(831,plain,
! [SV207: $i] :
( ( ! [SY402: $i] :
( ~ ( contains_pq @ SV207 @ SY402 )
| ~ ( issmallestelement_pq @ SV207 @ SY402 )
| ( ( findmin_pq_eff @ SV207 @ SY402 )
= SV207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(832,plain,
! [SV208: $i] :
( ( ! [SY403: $i] :
( ~ ( contains_pq @ SV208 @ SY403 )
| ~ ( issmallestelement_pq @ SV208 @ SY403 )
| ( ( findmin_pq_res @ SV208 @ SY403 )
= SY403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(833,plain,
! [SV209: $i] :
( ( ! [SY404: $i] :
( ~ ( contains_pq @ SV209 @ SY404 )
| ~ ( issmallestelement_pq @ SV209 @ SY404 )
| ( ( removemin_pq_eff @ SV209 @ SY404 )
= ( remove_pq @ SV209 @ SY404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(834,plain,
! [SV210: $i] :
( ( ! [SY405: $i] :
( ~ ( contains_pq @ SV210 @ SY405 )
| ~ ( issmallestelement_pq @ SV210 @ SY405 )
| ( ( removemin_pq_res @ SV210 @ SY405 )
= SY405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(835,plain,
! [SV211: $i] :
( ( ! [SY406: $i,SY407: $i] :
( ( insert_pq @ ( insert_pq @ SV211 @ SY406 ) @ SY407 )
= ( insert_pq @ ( insert_pq @ SV211 @ SY407 ) @ SY406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(836,plain,
( ( isnonempty_slb @ create_slb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[761]) ).
thf(837,plain,
! [SV212: $i] :
( ( ! [SY408: $i,SY409: $i] : ( isnonempty_slb @ ( insert_slb @ SV212 @ ( pair @ SY408 @ SY409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(838,plain,
! [SV213: $i] :
( ( ~ ( contains_slb @ create_slb @ SV213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(839,plain,
! [SV214: $i] :
( ( ! [SY410: $i] :
~ ( pair_in_list @ create_slb @ SV214 @ SY410 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(840,plain,
! [SV215: $i] :
( ( ! [SY411: $i,SY412: $i] :
( ( remove_slb @ ( insert_slb @ SV215 @ ( pair @ SY411 @ SY412 ) ) @ SY411 )
= SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(841,plain,
! [SV216: $i] :
( ( ! [SY413: $i,SY414: $i] :
( ( SY413 = SY414 )
| ~ ( contains_slb @ SV216 @ SY414 )
| ! [SY415: $i] :
( ( remove_slb @ ( insert_slb @ SV216 @ ( pair @ SY413 @ SY415 ) ) @ SY414 )
= ( insert_slb @ ( remove_slb @ SV216 @ SY414 ) @ ( pair @ SY413 @ SY415 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(842,plain,
! [SV217: $i] :
( ( ! [SY416: $i,SY417: $i] :
( ( lookup_slb @ ( insert_slb @ SV217 @ ( pair @ SY416 @ SY417 ) ) @ SY416 )
= SY417 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(843,plain,
! [SV218: $i] :
( ( ! [SY418: $i,SY419: $i] :
( ( SY418 = SY419 )
| ~ ( contains_slb @ SV218 @ SY419 )
| ! [SY420: $i] :
( ( lookup_slb @ ( insert_slb @ SV218 @ ( pair @ SY418 @ SY420 ) ) @ SY419 )
= ( lookup_slb @ SV218 @ SY419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(844,plain,
! [SV219: $i] :
( ( ( update_slb @ create_slb @ SV219 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(845,plain,
! [SV220: $i] :
( ( ! [SY421: $i,SY422: $i,SY423: $i] :
( ~ ( strictly_less_than @ SY423 @ SY422 )
| ( ( update_slb @ ( insert_slb @ SV220 @ ( pair @ SY421 @ SY423 ) ) @ SY422 )
= ( insert_slb @ ( update_slb @ SV220 @ SY422 ) @ ( pair @ SY421 @ SY422 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(846,plain,
! [SV221: $i] :
( ( ! [SY424: $i,SY425: $i,SY426: $i] :
( ~ ( less_than @ SY425 @ SY426 )
| ( ( update_slb @ ( insert_slb @ SV221 @ ( pair @ SY424 @ SY426 ) ) @ SY425 )
= ( insert_slb @ ( update_slb @ SV221 @ SY425 ) @ ( pair @ SY424 @ SY426 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(847,plain,
! [SV222: $i] :
( ( succ_cpq @ SV222 @ SV222 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(848,plain,
! [SV223: $i] :
( ( ! [SY427: $i] :
( ~ ( succ_cpq @ SV223 @ SY427 )
| ! [SY428: $i] : ( succ_cpq @ SV223 @ ( insert_cpq @ SY427 @ SY428 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(849,plain,
! [SV224: $i] :
( ( ! [SY429: $i] :
( ~ ( succ_cpq @ SV224 @ SY429 )
| ! [SY430: $i] : ( succ_cpq @ SV224 @ ( remove_cpq @ SY429 @ SY430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(850,plain,
! [SV225: $i] :
( ( ! [SY431: $i] :
( ~ ( succ_cpq @ SV225 @ SY431 )
| ( succ_cpq @ SV225 @ ( findmin_cpq_eff @ SY431 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(851,plain,
! [SV226: $i] :
( ( ! [SY432: $i] :
( ~ ( succ_cpq @ SV226 @ SY432 )
| ( succ_cpq @ SV226 @ ( removemin_cpq_eff @ SY432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(852,plain,
! [SV227: $i] :
( ( ! [SY433: $i] : ( check_cpq @ ( triple @ SV227 @ create_slb @ SY433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(853,plain,
! [SV228: $i] :
( ( ! [SY434: $i,SY435: $i,SY436: $i,SY437: $i] :
( ~ ( strictly_less_than @ SY436 @ SY437 )
| ~ ( check_cpq @ ( triple @ SV228 @ ( insert_slb @ SY434 @ ( pair @ SY436 @ SY437 ) ) @ SY435 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(854,plain,
! [SV229: $i] :
( ( ! [SY438: $i] :
~ ( ok @ ( triple @ SV229 @ SY438 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(855,plain,
! [SV230: $i] :
( ( ! [SY439: $i,SY440: $i] :
( ( ok @ ( triple @ SV230 @ SY439 @ SY440 ) )
| ( SY440 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(856,plain,
! [SV231: $i] :
( ( ! [SY441: $i,SY442: $i,SY443: $i] :
( ( insert_cpq @ ( triple @ SV231 @ SY441 @ SY442 ) @ SY443 )
= ( triple @ ( insert_pqp @ SV231 @ SY443 ) @ ( insert_slb @ SY441 @ ( pair @ SY443 @ bottom ) ) @ SY442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(857,plain,
! [SV232: $i] :
( ( ! [SY444: $i,SY445: $i,SY446: $i] :
( ( contains_slb @ SY444 @ SY446 )
| ( ( remove_cpq @ ( triple @ SV232 @ SY444 @ SY445 ) @ SY446 )
= ( triple @ SV232 @ SY444 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(858,plain,
! [SV233: $i] :
( ( ! [SY447: $i,SY448: $i,SY449: $i] :
( ~ ( contains_slb @ SY447 @ SY449 )
| ~ ( less_than @ ( lookup_slb @ SY447 @ SY449 ) @ SY449 )
| ( ( remove_cpq @ ( triple @ SV233 @ SY447 @ SY448 ) @ SY449 )
= ( triple @ ( remove_pqp @ SV233 @ SY449 ) @ ( remove_slb @ SY447 @ SY449 ) @ SY448 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(859,plain,
! [SV234: $i] :
( ( ! [SY450: $i,SY451: $i,SY452: $i] :
( ~ ( contains_slb @ SY450 @ SY452 )
| ~ ( strictly_less_than @ SY452 @ ( lookup_slb @ SY450 @ SY452 ) )
| ( ( remove_cpq @ ( triple @ SV234 @ SY450 @ SY451 ) @ SY452 )
= ( triple @ ( remove_pqp @ SV234 @ SY452 ) @ ( remove_slb @ SY450 @ SY452 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(860,plain,
! [SV235: $i] :
( ( ! [SY453: $i] :
( ( findmin_cpq_eff @ ( triple @ SV235 @ create_slb @ SY453 ) )
= ( triple @ SV235 @ create_slb @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(861,plain,
! [SV236: $i] :
( ( ! [SY454: $i] :
( ( SY454 = create_slb )
| ( contains_slb @ SY454 @ ( findmin_pqp_res @ SV236 ) )
| ! [SY455: $i] :
( ( findmin_cpq_eff @ ( triple @ SV236 @ SY454 @ SY455 ) )
= ( triple @ SV236 @ ( update_slb @ SY454 @ ( findmin_pqp_res @ SV236 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(862,plain,
! [SV237: $i] :
( ( ! [SY456: $i] :
( ( SY456 = create_slb )
| ~ ( contains_slb @ SY456 @ ( findmin_pqp_res @ SV237 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV237 ) @ ( lookup_slb @ SY456 @ ( findmin_pqp_res @ SV237 ) ) )
| ! [SY457: $i] :
( ( findmin_cpq_eff @ ( triple @ SV237 @ SY456 @ SY457 ) )
= ( triple @ SV237 @ ( update_slb @ SY456 @ ( findmin_pqp_res @ SV237 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(863,plain,
! [SV238: $i] :
( ( ! [SY458: $i] :
( ( SY458 = create_slb )
| ~ ( contains_slb @ SY458 @ ( findmin_pqp_res @ SV238 ) )
| ~ ( less_than @ ( lookup_slb @ SY458 @ ( findmin_pqp_res @ SV238 ) ) @ ( findmin_pqp_res @ SV238 ) )
| ! [SY459: $i] :
( ( findmin_cpq_eff @ ( triple @ SV238 @ SY458 @ SY459 ) )
= ( triple @ SV238 @ ( update_slb @ SY458 @ ( findmin_pqp_res @ SV238 ) ) @ SY459 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(864,plain,
! [SV239: $i] :
( ( ! [SY460: $i] :
( ( findmin_cpq_res @ ( triple @ SV239 @ create_slb @ SY460 ) )
= bottom ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(865,plain,
! [SV240: $i] :
( ( ! [SY461: $i] :
( ( SY461 = create_slb )
| ! [SY462: $i] :
( ( findmin_cpq_res @ ( triple @ SV240 @ SY461 @ SY462 ) )
= ( findmin_pqp_res @ SV240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(866,plain,
! [SV241: $i] :
( ( ( removemin_cpq_eff @ SV241 )
= ( remove_cpq @ ( findmin_cpq_eff @ SV241 ) @ ( findmin_cpq_res @ SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(867,plain,
! [SV242: $i] :
( ( ( removemin_cpq_res @ SV242 )
= ( findmin_cpq_res @ SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(868,plain,
! [SV243: $i] :
( ( ! [SY463: $i] :
( ( i @ ( triple @ SV243 @ create_slb @ SY463 ) )
= create_pq ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(869,plain,
! [SV244: $i] :
( ( ! [SY464: $i,SY465: $i,SY466: $i,SY467: $i] :
( ( i @ ( triple @ SV244 @ ( insert_slb @ SY464 @ ( pair @ SY466 @ SY467 ) ) @ SY465 ) )
= ( insert_pq @ ( i @ ( triple @ SV244 @ SY464 @ SY465 ) ) @ SY466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(870,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( ok @ SX1 )
| ~ ( succ_cpq @ SX0 @ SX1 )
| ~ ( check_cpq @ SX1 ) )
| ( phi @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( phi @ SX0 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK4_V @ SX0 ) )
| ~ ( succ_cpq @ SX0 @ ( sK4_V @ SX0 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(871,plain,
! [SV245: $i] :
( ( ! [SY468: $i] :
~ ( ~ ! [SY469: $i,SY470: $i] :
( ~ ( contains_cpq @ ( triple @ SV245 @ SY468 @ SY469 ) @ SY470 )
| ( contains_slb @ SY468 @ SY470 ) )
| ~ ! [SY471: $i,SY472: $i] :
( ~ ( contains_slb @ SY468 @ SY472 )
| ( contains_cpq @ ( triple @ SV245 @ SY468 @ SY471 ) @ SY472 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(872,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_find_min @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( pi_find_min @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK6_V @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(873,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)],[810]) ).
thf(874,plain,
! [SV246: $i] :
( ( ! [SY473: $i] :
~ ( ~ ! [SY474: $i] :
( ! [SY475: $i] :
~ ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SY473 @ SY475 ) ) @ SY474 )
| ( SY473 = SY474 )
| ( contains_slb @ SV246 @ SY474 ) )
| ~ ~ ( ~ ! [SY476: $i] :
( ( SY473 != SY476 )
| ! [SY477: $i] : ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SY473 @ SY477 ) ) @ SY476 ) )
| ~ ! [SY478: $i] :
( ~ ( contains_slb @ SV246 @ SY478 )
| ! [SY479: $i] : ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SY473 @ SY479 ) ) @ SY478 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(875,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)],[812]) ).
thf(876,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)],[813]) ).
thf(877,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( contains_pq @ SX0 @ ( sK7_W @ SX1 @ SX0 ) )
| ~ ~ ( less_than @ SX1 @ ( sK7_W @ SX1 @ SX0 ) ) )
| ( issmallestelement_pq @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( issmallestelement_pq @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( contains_pq @ SX0 @ SX2 )
| ( less_than @ SX1 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[814]) ).
thf(878,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)],[815]) ).
thf(879,plain,
( ( ~ ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) ) @ sK3_SY168 )
| ~ ~ ( contains_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) @ sK3_SY168 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(880,plain,
! [SV247: $i] :
( ( ! [SY480: $i,SY481: $i] :
~ ( ~ ~ ( ~ ! [SY482: $i,SY483: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SY480 @ SY482 ) ) @ SY481 @ SY483 )
| ( SY480 = SY481 )
| ( pair_in_list @ SV247 @ SY481 @ SY483 ) )
| ~ ! [SY484: $i,SY485: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SY480 @ SY484 ) ) @ SY481 @ SY485 )
| ( SY484 = SY485 )
| ( pair_in_list @ SV247 @ SY481 @ SY485 ) ) )
| ~ ~ ( ~ ! [SY486: $i,SY487: $i] :
( ( SY480 != SY481 )
| ( SY486 != SY487 )
| ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SY480 @ SY486 ) ) @ SY481 @ SY487 ) )
| ~ ! [SY488: $i,SY489: $i] :
( ~ ( pair_in_list @ SV247 @ SY481 @ SY489 )
| ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SY480 @ SY488 ) ) @ SY481 @ SY489 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(881,plain,
! [SV248: $i] :
( ( ~ ( ~ ! [SY490: $i,SY491: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV248 @ SY490 ) @ SY491 )
| ( SY490 = SY491 )
| ( contains_pq @ SV248 @ SY491 ) )
| ~ ~ ( ~ ! [SY492: $i,SY493: $i] :
( ( SY492 != SY493 )
| ( contains_pq @ ( insert_pq @ SV248 @ SY492 ) @ SY493 ) )
| ~ ! [SY494: $i,SY495: $i] :
( ~ ( contains_pq @ SV248 @ SY495 )
| ( contains_pq @ ( insert_pq @ SV248 @ SY494 ) @ SY495 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(882,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)],[819]) ).
thf(883,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_removemin @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( pi_removemin @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK5_V @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[820]) ).
thf(884,plain,
! [SV249: $i] :
( ( ! [SY496: $i,SY497: $i] :
~ ( ~ ! [SY498: $i,SY499: $i] :
( ~ ( less_than @ SY499 @ SY498 )
| ~ ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SY496 @ ( pair @ SY498 @ SY499 ) ) @ SY497 ) )
| ( check_cpq @ ( triple @ SV249 @ SY496 @ SY497 ) ) )
| ~ ! [SY500: $i,SY501: $i] :
( ~ ( less_than @ SY501 @ SY500 )
| ~ ( check_cpq @ ( triple @ SV249 @ SY496 @ SY497 ) )
| ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SY496 @ ( pair @ SY500 @ SY501 ) ) @ SY497 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(885,plain,
! [SV250: $i,SV199: $i] :
( ( ! [SY502: $i] :
( ~ ( less_than @ SV199 @ SV250 )
| ~ ( less_than @ SV250 @ SY502 )
| ( less_than @ SV199 @ SY502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(886,plain,
! [SV251: $i,SV200: $i] :
( ( ( less_than @ SV200 @ SV251 )
| ( less_than @ SV251 @ SV200 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(887,plain,
! [SV252: $i,SV203: $i] :
( ( isnonempty_pq @ ( insert_pq @ SV203 @ SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(888,plain,
! [SV204: $i] :
( ( contains_pq @ create_pq @ SV204 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[828]) ).
thf(889,plain,
! [SV253: $i,SV205: $i] :
( ( ( remove_pq @ ( insert_pq @ SV205 @ SV253 ) @ SV253 )
= SV205 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(890,plain,
! [SV206: $i,SV254: $i] :
( ( ! [SY503: $i] :
( ( SV254 = SY503 )
| ~ ( contains_pq @ SV206 @ SY503 )
| ( ( remove_pq @ ( insert_pq @ SV206 @ SV254 ) @ SY503 )
= ( insert_pq @ ( remove_pq @ SV206 @ SY503 ) @ SV254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(891,plain,
! [SV255: $i,SV207: $i] :
( ( ~ ( contains_pq @ SV207 @ SV255 )
| ~ ( issmallestelement_pq @ SV207 @ SV255 )
| ( ( findmin_pq_eff @ SV207 @ SV255 )
= SV207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(892,plain,
! [SV256: $i,SV208: $i] :
( ( ~ ( contains_pq @ SV208 @ SV256 )
| ~ ( issmallestelement_pq @ SV208 @ SV256 )
| ( ( findmin_pq_res @ SV208 @ SV256 )
= SV256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(893,plain,
! [SV257: $i,SV209: $i] :
( ( ~ ( contains_pq @ SV209 @ SV257 )
| ~ ( issmallestelement_pq @ SV209 @ SV257 )
| ( ( removemin_pq_eff @ SV209 @ SV257 )
= ( remove_pq @ SV209 @ SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(894,plain,
! [SV258: $i,SV210: $i] :
( ( ~ ( contains_pq @ SV210 @ SV258 )
| ~ ( issmallestelement_pq @ SV210 @ SV258 )
| ( ( removemin_pq_res @ SV210 @ SV258 )
= SV258 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(895,plain,
! [SV259: $i,SV211: $i] :
( ( ! [SY504: $i] :
( ( insert_pq @ ( insert_pq @ SV211 @ SV259 ) @ SY504 )
= ( insert_pq @ ( insert_pq @ SV211 @ SY504 ) @ SV259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(896,plain,
! [SV260: $i,SV212: $i] :
( ( ! [SY505: $i] : ( isnonempty_slb @ ( insert_slb @ SV212 @ ( pair @ SV260 @ SY505 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(897,plain,
! [SV213: $i] :
( ( contains_slb @ create_slb @ SV213 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[838]) ).
thf(898,plain,
! [SV261: $i,SV214: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV214 @ SV261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(899,plain,
! [SV262: $i,SV215: $i] :
( ( ! [SY506: $i] :
( ( remove_slb @ ( insert_slb @ SV215 @ ( pair @ SV262 @ SY506 ) ) @ SV262 )
= SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(900,plain,
! [SV216: $i,SV263: $i] :
( ( ! [SY507: $i] :
( ( SV263 = SY507 )
| ~ ( contains_slb @ SV216 @ SY507 )
| ! [SY508: $i] :
( ( remove_slb @ ( insert_slb @ SV216 @ ( pair @ SV263 @ SY508 ) ) @ SY507 )
= ( insert_slb @ ( remove_slb @ SV216 @ SY507 ) @ ( pair @ SV263 @ SY508 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(901,plain,
! [SV264: $i,SV217: $i] :
( ( ! [SY509: $i] :
( ( lookup_slb @ ( insert_slb @ SV217 @ ( pair @ SV264 @ SY509 ) ) @ SV264 )
= SY509 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(902,plain,
! [SV218: $i,SV265: $i] :
( ( ! [SY510: $i] :
( ( SV265 = SY510 )
| ~ ( contains_slb @ SV218 @ SY510 )
| ! [SY511: $i] :
( ( lookup_slb @ ( insert_slb @ SV218 @ ( pair @ SV265 @ SY511 ) ) @ SY510 )
= ( lookup_slb @ SV218 @ SY510 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(903,plain,
! [SV266: $i,SV220: $i] :
( ( ! [SY512: $i,SY513: $i] :
( ~ ( strictly_less_than @ SY513 @ SY512 )
| ( ( update_slb @ ( insert_slb @ SV220 @ ( pair @ SV266 @ SY513 ) ) @ SY512 )
= ( insert_slb @ ( update_slb @ SV220 @ SY512 ) @ ( pair @ SV266 @ SY512 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(904,plain,
! [SV267: $i,SV221: $i] :
( ( ! [SY514: $i,SY515: $i] :
( ~ ( less_than @ SY514 @ SY515 )
| ( ( update_slb @ ( insert_slb @ SV221 @ ( pair @ SV267 @ SY515 ) ) @ SY514 )
= ( insert_slb @ ( update_slb @ SV221 @ SY514 ) @ ( pair @ SV267 @ SY515 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(905,plain,
! [SV268: $i,SV223: $i] :
( ( ~ ( succ_cpq @ SV223 @ SV268 )
| ! [SY516: $i] : ( succ_cpq @ SV223 @ ( insert_cpq @ SV268 @ SY516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(906,plain,
! [SV269: $i,SV224: $i] :
( ( ~ ( succ_cpq @ SV224 @ SV269 )
| ! [SY517: $i] : ( succ_cpq @ SV224 @ ( remove_cpq @ SV269 @ SY517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(907,plain,
! [SV270: $i,SV225: $i] :
( ( ~ ( succ_cpq @ SV225 @ SV270 )
| ( succ_cpq @ SV225 @ ( findmin_cpq_eff @ SV270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(908,plain,
! [SV271: $i,SV226: $i] :
( ( ~ ( succ_cpq @ SV226 @ SV271 )
| ( succ_cpq @ SV226 @ ( removemin_cpq_eff @ SV271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(909,plain,
! [SV272: $i,SV227: $i] :
( ( check_cpq @ ( triple @ SV227 @ create_slb @ SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(910,plain,
! [SV273: $i,SV228: $i] :
( ( ! [SY518: $i,SY519: $i,SY520: $i] :
( ~ ( strictly_less_than @ SY519 @ SY520 )
| ~ ( check_cpq @ ( triple @ SV228 @ ( insert_slb @ SV273 @ ( pair @ SY519 @ SY520 ) ) @ SY518 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(911,plain,
! [SV274: $i,SV229: $i] :
( ( ~ ( ok @ ( triple @ SV229 @ SV274 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(912,plain,
! [SV275: $i,SV230: $i] :
( ( ! [SY521: $i] :
( ( ok @ ( triple @ SV230 @ SV275 @ SY521 ) )
| ( SY521 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(913,plain,
! [SV276: $i,SV231: $i] :
( ( ! [SY522: $i,SY523: $i] :
( ( insert_cpq @ ( triple @ SV231 @ SV276 @ SY522 ) @ SY523 )
= ( triple @ ( insert_pqp @ SV231 @ SY523 ) @ ( insert_slb @ SV276 @ ( pair @ SY523 @ bottom ) ) @ SY522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(914,plain,
! [SV232: $i,SV277: $i] :
( ( ! [SY524: $i,SY525: $i] :
( ( contains_slb @ SV277 @ SY525 )
| ( ( remove_cpq @ ( triple @ SV232 @ SV277 @ SY524 ) @ SY525 )
= ( triple @ SV232 @ SV277 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(915,plain,
! [SV233: $i,SV278: $i] :
( ( ! [SY526: $i,SY527: $i] :
( ~ ( contains_slb @ SV278 @ SY527 )
| ~ ( less_than @ ( lookup_slb @ SV278 @ SY527 ) @ SY527 )
| ( ( remove_cpq @ ( triple @ SV233 @ SV278 @ SY526 ) @ SY527 )
= ( triple @ ( remove_pqp @ SV233 @ SY527 ) @ ( remove_slb @ SV278 @ SY527 ) @ SY526 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(916,plain,
! [SV234: $i,SV279: $i] :
( ( ! [SY528: $i,SY529: $i] :
( ~ ( contains_slb @ SV279 @ SY529 )
| ~ ( strictly_less_than @ SY529 @ ( lookup_slb @ SV279 @ SY529 ) )
| ( ( remove_cpq @ ( triple @ SV234 @ SV279 @ SY528 ) @ SY529 )
= ( triple @ ( remove_pqp @ SV234 @ SY529 ) @ ( remove_slb @ SV279 @ SY529 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(917,plain,
! [SV280: $i,SV235: $i] :
( ( ( findmin_cpq_eff @ ( triple @ SV235 @ create_slb @ SV280 ) )
= ( triple @ SV235 @ create_slb @ bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(918,plain,
! [SV236: $i,SV281: $i] :
( ( ( SV281 = create_slb )
| ( contains_slb @ SV281 @ ( findmin_pqp_res @ SV236 ) )
| ! [SY530: $i] :
( ( findmin_cpq_eff @ ( triple @ SV236 @ SV281 @ SY530 ) )
= ( triple @ SV236 @ ( update_slb @ SV281 @ ( findmin_pqp_res @ SV236 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(919,plain,
! [SV237: $i,SV282: $i] :
( ( ( SV282 = create_slb )
| ~ ( contains_slb @ SV282 @ ( findmin_pqp_res @ SV237 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV237 ) @ ( lookup_slb @ SV282 @ ( findmin_pqp_res @ SV237 ) ) )
| ! [SY531: $i] :
( ( findmin_cpq_eff @ ( triple @ SV237 @ SV282 @ SY531 ) )
= ( triple @ SV237 @ ( update_slb @ SV282 @ ( findmin_pqp_res @ SV237 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(920,plain,
! [SV238: $i,SV283: $i] :
( ( ( SV283 = create_slb )
| ~ ( contains_slb @ SV283 @ ( findmin_pqp_res @ SV238 ) )
| ~ ( less_than @ ( lookup_slb @ SV283 @ ( findmin_pqp_res @ SV238 ) ) @ ( findmin_pqp_res @ SV238 ) )
| ! [SY532: $i] :
( ( findmin_cpq_eff @ ( triple @ SV238 @ SV283 @ SY532 ) )
= ( triple @ SV238 @ ( update_slb @ SV283 @ ( findmin_pqp_res @ SV238 ) ) @ SY532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(921,plain,
! [SV284: $i,SV239: $i] :
( ( ( findmin_cpq_res @ ( triple @ SV239 @ create_slb @ SV284 ) )
= bottom )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(922,plain,
! [SV240: $i,SV285: $i] :
( ( ( SV285 = create_slb )
| ! [SY533: $i] :
( ( findmin_cpq_res @ ( triple @ SV240 @ SV285 @ SY533 ) )
= ( findmin_pqp_res @ SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(923,plain,
! [SV286: $i,SV243: $i] :
( ( ( i @ ( triple @ SV243 @ create_slb @ SV286 ) )
= create_pq )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(924,plain,
! [SV287: $i,SV244: $i] :
( ( ! [SY534: $i,SY535: $i,SY536: $i] :
( ( i @ ( triple @ SV244 @ ( insert_slb @ SV287 @ ( pair @ SY535 @ SY536 ) ) @ SY534 ) )
= ( insert_pq @ ( i @ ( triple @ SV244 @ SV287 @ SY534 ) ) @ SY535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(925,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( ok @ SX1 )
| ~ ( succ_cpq @ SX0 @ SX1 )
| ~ ( check_cpq @ SX1 ) )
| ( phi @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[870]) ).
thf(926,plain,
( ( ~ ! [SX0: $i] :
( ~ ( phi @ SX0 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK4_V @ SX0 ) )
| ~ ( succ_cpq @ SX0 @ ( sK4_V @ SX0 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[870]) ).
thf(927,plain,
! [SV288: $i,SV245: $i] :
( ( ~ ( ~ ! [SY537: $i,SY538: $i] :
( ~ ( contains_cpq @ ( triple @ SV245 @ SV288 @ SY537 ) @ SY538 )
| ( contains_slb @ SV288 @ SY538 ) )
| ~ ! [SY539: $i,SY540: $i] :
( ~ ( contains_slb @ SV288 @ SY540 )
| ( contains_cpq @ ( triple @ SV245 @ SV288 @ SY539 ) @ SY540 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(928,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_find_min @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[872]) ).
thf(929,plain,
( ( ~ ! [SX0: $i] :
( ~ ( pi_find_min @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK6_V @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[872]) ).
thf(930,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)],[873]) ).
thf(931,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)],[873]) ).
thf(932,plain,
! [SV289: $i,SV246: $i] :
( ( ~ ( ~ ! [SY541: $i] :
( ! [SY542: $i] :
~ ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY542 ) ) @ SY541 )
| ( SV289 = SY541 )
| ( contains_slb @ SV246 @ SY541 ) )
| ~ ~ ( ~ ! [SY543: $i] :
( ( SV289 != SY543 )
| ! [SY544: $i] : ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY544 ) ) @ SY543 ) )
| ~ ! [SY545: $i] :
( ~ ( contains_slb @ SV246 @ SY545 )
| ! [SY546: $i] : ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY546 ) ) @ SY545 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(933,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( contains_pq @ SX0 @ SX1 )
| ( pi_sharp_remove @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[875]) ).
thf(934,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[875]) ).
thf(935,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)],[876]) ).
thf(936,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)],[876]) ).
thf(937,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( contains_pq @ SX0 @ ( sK7_W @ SX1 @ SX0 ) )
| ~ ~ ( less_than @ SX1 @ ( sK7_W @ SX1 @ SX0 ) ) )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[877]) ).
thf(938,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)],[877]) ).
thf(939,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)],[878]) ).
thf(940,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)],[878]) ).
thf(941,plain,
( ( ~ ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) ) @ sK3_SY168 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[879]) ).
thf(942,plain,
( ( ~ ~ ( contains_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) @ sK3_SY168 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[879]) ).
thf(943,plain,
! [SV290: $i,SV247: $i] :
( ( ! [SY547: $i] :
~ ( ~ ~ ( ~ ! [SY548: $i,SY549: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY548 ) ) @ SY547 @ SY549 )
| ( SV290 = SY547 )
| ( pair_in_list @ SV247 @ SY547 @ SY549 ) )
| ~ ! [SY550: $i,SY551: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY550 ) ) @ SY547 @ SY551 )
| ( SY550 = SY551 )
| ( pair_in_list @ SV247 @ SY547 @ SY551 ) ) )
| ~ ~ ( ~ ! [SY552: $i,SY553: $i] :
( ( SV290 != SY547 )
| ( SY552 != SY553 )
| ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY552 ) ) @ SY547 @ SY553 ) )
| ~ ! [SY554: $i,SY555: $i] :
( ~ ( pair_in_list @ SV247 @ SY547 @ SY555 )
| ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY554 ) ) @ SY547 @ SY555 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(944,plain,
! [SV248: $i] :
( ( ~ ! [SY490: $i,SY491: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV248 @ SY490 ) @ SY491 )
| ( SY490 = SY491 )
| ( contains_pq @ SV248 @ SY491 ) )
| ~ ~ ( ~ ! [SY492: $i,SY493: $i] :
( ( SY492 != SY493 )
| ( contains_pq @ ( insert_pq @ SV248 @ SY492 ) @ SY493 ) )
| ~ ! [SY494: $i,SY495: $i] :
( ~ ( contains_pq @ SV248 @ SY495 )
| ( contains_pq @ ( insert_pq @ SV248 @ SY494 ) @ SY495 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(945,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_remove @ SX0 @ SX1 )
| ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[882]) ).
thf(946,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 )
| ( pi_remove @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[882]) ).
thf(947,plain,
( ( ~ ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_removemin @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[883]) ).
thf(948,plain,
( ( ~ ! [SX0: $i] :
( ~ ( pi_removemin @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK5_V @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[883]) ).
thf(949,plain,
! [SV291: $i,SV249: $i] :
( ( ! [SY556: $i] :
~ ( ~ ! [SY557: $i,SY558: $i] :
( ~ ( less_than @ SY558 @ SY557 )
| ~ ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SV291 @ ( pair @ SY557 @ SY558 ) ) @ SY556 ) )
| ( check_cpq @ ( triple @ SV249 @ SV291 @ SY556 ) ) )
| ~ ! [SY559: $i,SY560: $i] :
( ~ ( less_than @ SY560 @ SY559 )
| ~ ( check_cpq @ ( triple @ SV249 @ SV291 @ SY556 ) )
| ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SV291 @ ( pair @ SY559 @ SY560 ) ) @ SY556 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(950,plain,
! [SV292: $i,SV250: $i,SV199: $i] :
( ( ~ ( less_than @ SV199 @ SV250 )
| ~ ( less_than @ SV250 @ SV292 )
| ( less_than @ SV199 @ SV292 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(951,plain,
! [SV251: $i,SV200: $i] :
( ( ( less_than @ SV200 @ SV251 )
= $true )
| ( ( less_than @ SV251 @ SV200 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[886]) ).
thf(952,plain,
! [SV206: $i,SV293: $i,SV254: $i] :
( ( ( SV254 = SV293 )
| ~ ( contains_pq @ SV206 @ SV293 )
| ( ( remove_pq @ ( insert_pq @ SV206 @ SV254 ) @ SV293 )
= ( insert_pq @ ( remove_pq @ SV206 @ SV293 ) @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(953,plain,
! [SV255: $i,SV207: $i] :
( ( ( ~ ( contains_pq @ SV207 @ SV255 )
| ~ ( issmallestelement_pq @ SV207 @ SV255 ) )
= $true )
| ( ( ( findmin_pq_eff @ SV207 @ SV255 )
= SV207 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(954,plain,
! [SV256: $i,SV208: $i] :
( ( ( ~ ( contains_pq @ SV208 @ SV256 )
| ~ ( issmallestelement_pq @ SV208 @ SV256 ) )
= $true )
| ( ( ( findmin_pq_res @ SV208 @ SV256 )
= SV256 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[892]) ).
thf(955,plain,
! [SV257: $i,SV209: $i] :
( ( ( ~ ( contains_pq @ SV209 @ SV257 )
| ~ ( issmallestelement_pq @ SV209 @ SV257 ) )
= $true )
| ( ( ( removemin_pq_eff @ SV209 @ SV257 )
= ( remove_pq @ SV209 @ SV257 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[893]) ).
thf(956,plain,
! [SV258: $i,SV210: $i] :
( ( ( ~ ( contains_pq @ SV210 @ SV258 )
| ~ ( issmallestelement_pq @ SV210 @ SV258 ) )
= $true )
| ( ( ( removemin_pq_res @ SV210 @ SV258 )
= SV258 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[894]) ).
thf(957,plain,
! [SV294: $i,SV259: $i,SV211: $i] :
( ( ( insert_pq @ ( insert_pq @ SV211 @ SV259 ) @ SV294 )
= ( insert_pq @ ( insert_pq @ SV211 @ SV294 ) @ SV259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(958,plain,
! [SV295: $i,SV260: $i,SV212: $i] :
( ( isnonempty_slb @ ( insert_slb @ SV212 @ ( pair @ SV260 @ SV295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(959,plain,
! [SV261: $i,SV214: $i] :
( ( pair_in_list @ create_slb @ SV214 @ SV261 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(960,plain,
! [SV296: $i,SV262: $i,SV215: $i] :
( ( ( remove_slb @ ( insert_slb @ SV215 @ ( pair @ SV262 @ SV296 ) ) @ SV262 )
= SV215 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(961,plain,
! [SV216: $i,SV297: $i,SV263: $i] :
( ( ( SV263 = SV297 )
| ~ ( contains_slb @ SV216 @ SV297 )
| ! [SY561: $i] :
( ( remove_slb @ ( insert_slb @ SV216 @ ( pair @ SV263 @ SY561 ) ) @ SV297 )
= ( insert_slb @ ( remove_slb @ SV216 @ SV297 ) @ ( pair @ SV263 @ SY561 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(962,plain,
! [SV298: $i,SV264: $i,SV217: $i] :
( ( ( lookup_slb @ ( insert_slb @ SV217 @ ( pair @ SV264 @ SV298 ) ) @ SV264 )
= SV298 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(963,plain,
! [SV218: $i,SV299: $i,SV265: $i] :
( ( ( SV265 = SV299 )
| ~ ( contains_slb @ SV218 @ SV299 )
| ! [SY562: $i] :
( ( lookup_slb @ ( insert_slb @ SV218 @ ( pair @ SV265 @ SY562 ) ) @ SV299 )
= ( lookup_slb @ SV218 @ SV299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(964,plain,
! [SV266: $i,SV220: $i,SV300: $i] :
( ( ! [SY563: $i] :
( ~ ( strictly_less_than @ SY563 @ SV300 )
| ( ( update_slb @ ( insert_slb @ SV220 @ ( pair @ SV266 @ SY563 ) ) @ SV300 )
= ( insert_slb @ ( update_slb @ SV220 @ SV300 ) @ ( pair @ SV266 @ SV300 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(965,plain,
! [SV267: $i,SV221: $i,SV301: $i] :
( ( ! [SY564: $i] :
( ~ ( less_than @ SV301 @ SY564 )
| ( ( update_slb @ ( insert_slb @ SV221 @ ( pair @ SV267 @ SY564 ) ) @ SV301 )
= ( insert_slb @ ( update_slb @ SV221 @ SV301 ) @ ( pair @ SV267 @ SY564 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(966,plain,
! [SV268: $i,SV223: $i] :
( ( ( ~ ( succ_cpq @ SV223 @ SV268 ) )
= $true )
| ( ( ! [SY516: $i] : ( succ_cpq @ SV223 @ ( insert_cpq @ SV268 @ SY516 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[905]) ).
thf(967,plain,
! [SV269: $i,SV224: $i] :
( ( ( ~ ( succ_cpq @ SV224 @ SV269 ) )
= $true )
| ( ( ! [SY517: $i] : ( succ_cpq @ SV224 @ ( remove_cpq @ SV269 @ SY517 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[906]) ).
thf(968,plain,
! [SV270: $i,SV225: $i] :
( ( ( ~ ( succ_cpq @ SV225 @ SV270 ) )
= $true )
| ( ( succ_cpq @ SV225 @ ( findmin_cpq_eff @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[907]) ).
thf(969,plain,
! [SV271: $i,SV226: $i] :
( ( ( ~ ( succ_cpq @ SV226 @ SV271 ) )
= $true )
| ( ( succ_cpq @ SV226 @ ( removemin_cpq_eff @ SV271 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(970,plain,
! [SV302: $i,SV273: $i,SV228: $i] :
( ( ! [SY565: $i,SY566: $i] :
( ~ ( strictly_less_than @ SY565 @ SY566 )
| ~ ( check_cpq @ ( triple @ SV228 @ ( insert_slb @ SV273 @ ( pair @ SY565 @ SY566 ) ) @ SV302 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(971,plain,
! [SV274: $i,SV229: $i] :
( ( ok @ ( triple @ SV229 @ SV274 @ bad ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(972,plain,
! [SV303: $i,SV275: $i,SV230: $i] :
( ( ( ok @ ( triple @ SV230 @ SV275 @ SV303 ) )
| ( SV303 = bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(973,plain,
! [SV304: $i,SV276: $i,SV231: $i] :
( ( ! [SY567: $i] :
( ( insert_cpq @ ( triple @ SV231 @ SV276 @ SV304 ) @ SY567 )
= ( triple @ ( insert_pqp @ SV231 @ SY567 ) @ ( insert_slb @ SV276 @ ( pair @ SY567 @ bottom ) ) @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(974,plain,
! [SV305: $i,SV232: $i,SV277: $i] :
( ( ! [SY568: $i] :
( ( contains_slb @ SV277 @ SY568 )
| ( ( remove_cpq @ ( triple @ SV232 @ SV277 @ SV305 ) @ SY568 )
= ( triple @ SV232 @ SV277 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(975,plain,
! [SV306: $i,SV233: $i,SV278: $i] :
( ( ! [SY569: $i] :
( ~ ( contains_slb @ SV278 @ SY569 )
| ~ ( less_than @ ( lookup_slb @ SV278 @ SY569 ) @ SY569 )
| ( ( remove_cpq @ ( triple @ SV233 @ SV278 @ SV306 ) @ SY569 )
= ( triple @ ( remove_pqp @ SV233 @ SY569 ) @ ( remove_slb @ SV278 @ SY569 ) @ SV306 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(976,plain,
! [SV307: $i,SV234: $i,SV279: $i] :
( ( ! [SY570: $i] :
( ~ ( contains_slb @ SV279 @ SY570 )
| ~ ( strictly_less_than @ SY570 @ ( lookup_slb @ SV279 @ SY570 ) )
| ( ( remove_cpq @ ( triple @ SV234 @ SV279 @ SV307 ) @ SY570 )
= ( triple @ ( remove_pqp @ SV234 @ SY570 ) @ ( remove_slb @ SV279 @ SY570 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(977,plain,
! [SV236: $i,SV281: $i] :
( ( ( ( SV281 = create_slb )
| ( contains_slb @ SV281 @ ( findmin_pqp_res @ SV236 ) ) )
= $true )
| ( ( ! [SY530: $i] :
( ( findmin_cpq_eff @ ( triple @ SV236 @ SV281 @ SY530 ) )
= ( triple @ SV236 @ ( update_slb @ SV281 @ ( findmin_pqp_res @ SV236 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(978,plain,
! [SV237: $i,SV282: $i] :
( ( ( ( SV282 = create_slb )
| ~ ( contains_slb @ SV282 @ ( findmin_pqp_res @ SV237 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV237 ) @ ( lookup_slb @ SV282 @ ( findmin_pqp_res @ SV237 ) ) ) )
= $true )
| ( ( ! [SY531: $i] :
( ( findmin_cpq_eff @ ( triple @ SV237 @ SV282 @ SY531 ) )
= ( triple @ SV237 @ ( update_slb @ SV282 @ ( findmin_pqp_res @ SV237 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[919]) ).
thf(979,plain,
! [SV238: $i,SV283: $i] :
( ( ( ( SV283 = create_slb )
| ~ ( contains_slb @ SV283 @ ( findmin_pqp_res @ SV238 ) )
| ~ ( less_than @ ( lookup_slb @ SV283 @ ( findmin_pqp_res @ SV238 ) ) @ ( findmin_pqp_res @ SV238 ) ) )
= $true )
| ( ( ! [SY532: $i] :
( ( findmin_cpq_eff @ ( triple @ SV238 @ SV283 @ SY532 ) )
= ( triple @ SV238 @ ( update_slb @ SV283 @ ( findmin_pqp_res @ SV238 ) ) @ SY532 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[920]) ).
thf(980,plain,
! [SV240: $i,SV285: $i] :
( ( ( SV285 = create_slb )
= $true )
| ( ( ! [SY533: $i] :
( ( findmin_cpq_res @ ( triple @ SV240 @ SV285 @ SY533 ) )
= ( findmin_pqp_res @ SV240 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[922]) ).
thf(981,plain,
! [SV308: $i,SV287: $i,SV244: $i] :
( ( ! [SY571: $i,SY572: $i] :
( ( i @ ( triple @ SV244 @ ( insert_slb @ SV287 @ ( pair @ SY571 @ SY572 ) ) @ SV308 ) )
= ( insert_pq @ ( i @ ( triple @ SV244 @ SV287 @ SV308 ) ) @ SY571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(982,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ~ ( ok @ SX1 )
| ~ ( succ_cpq @ SX0 @ SX1 )
| ~ ( check_cpq @ SX1 ) )
| ( phi @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[925]) ).
thf(983,plain,
( ( ! [SX0: $i] :
( ~ ( phi @ SX0 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK4_V @ SX0 ) )
| ~ ( succ_cpq @ SX0 @ ( sK4_V @ SX0 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[926]) ).
thf(984,plain,
! [SV288: $i,SV245: $i] :
( ( ~ ! [SY537: $i,SY538: $i] :
( ~ ( contains_cpq @ ( triple @ SV245 @ SV288 @ SY537 ) @ SY538 )
| ( contains_slb @ SV288 @ SY538 ) )
| ~ ! [SY539: $i,SY540: $i] :
( ~ ( contains_slb @ SV288 @ SY540 )
| ( contains_cpq @ ( triple @ SV245 @ SV288 @ SY539 ) @ SY540 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(985,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_find_min @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[928]) ).
thf(986,plain,
( ( ! [SX0: $i] :
( ~ ( pi_find_min @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK6_V @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[929]) ).
thf(987,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)],[930]) ).
thf(988,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)],[931]) ).
thf(989,plain,
! [SV289: $i,SV246: $i] :
( ( ~ ! [SY541: $i] :
( ! [SY542: $i] :
~ ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY542 ) ) @ SY541 )
| ( SV289 = SY541 )
| ( contains_slb @ SV246 @ SY541 ) )
| ~ ~ ( ~ ! [SY543: $i] :
( ( SV289 != SY543 )
| ! [SY544: $i] : ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY544 ) ) @ SY543 ) )
| ~ ! [SY545: $i] :
( ~ ( contains_slb @ SV246 @ SY545 )
| ! [SY546: $i] : ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY546 ) ) @ SY545 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[932]) ).
thf(990,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( contains_pq @ SX0 @ SX1 )
| ( pi_sharp_remove @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[933]) ).
thf(991,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[934]) ).
thf(992,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)],[935]) ).
thf(993,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)],[936]) ).
thf(994,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( contains_pq @ SX0 @ ( sK7_W @ SX1 @ SX0 ) )
| ~ ~ ( less_than @ SX1 @ ( sK7_W @ SX1 @ SX0 ) ) )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[937]) ).
thf(995,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)],[938]) ).
thf(996,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)],[939]) ).
thf(997,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)],[940]) ).
thf(998,plain,
( ( contains_pq @ ( i @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) ) @ sK3_SY168 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[941]) ).
thf(999,plain,
( ( ~ ( contains_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) @ sK3_SY168 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[942]) ).
thf(1000,plain,
! [SV309: $i,SV290: $i,SV247: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY573: $i,SY574: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY573 ) ) @ SV309 @ SY574 )
| ( SV290 = SV309 )
| ( pair_in_list @ SV247 @ SV309 @ SY574 ) )
| ~ ! [SY575: $i,SY576: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY575 ) ) @ SV309 @ SY576 )
| ( SY575 = SY576 )
| ( pair_in_list @ SV247 @ SV309 @ SY576 ) ) )
| ~ ~ ( ~ ! [SY577: $i,SY578: $i] :
( ( SV290 != SV309 )
| ( SY577 != SY578 )
| ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY577 ) ) @ SV309 @ SY578 ) )
| ~ ! [SY579: $i,SY580: $i] :
( ~ ( pair_in_list @ SV247 @ SV309 @ SY580 )
| ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY579 ) ) @ SV309 @ SY580 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1001,plain,
! [SV248: $i] :
( ( ~ ! [SY490: $i,SY491: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV248 @ SY490 ) @ SY491 )
| ( SY490 = SY491 )
| ( contains_pq @ SV248 @ SY491 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[944]) ).
thf(1002,plain,
! [SV248: $i] :
( ( ~ ~ ( ~ ! [SY492: $i,SY493: $i] :
( ( SY492 != SY493 )
| ( contains_pq @ ( insert_pq @ SV248 @ SY492 ) @ SY493 ) )
| ~ ! [SY494: $i,SY495: $i] :
( ~ ( contains_pq @ SV248 @ SY495 )
| ( contains_pq @ ( insert_pq @ SV248 @ SY494 ) @ SY495 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[944]) ).
thf(1003,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_remove @ SX0 @ SX1 )
| ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[945]) ).
thf(1004,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_remove @ ( i @ SX0 ) @ SX1 )
| ( pi_remove @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[946]) ).
thf(1005,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( pi_sharp_find_min @ ( i @ SX0 ) @ SX1 )
| ( pi_removemin @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[947]) ).
thf(1006,plain,
( ( ! [SX0: $i] :
( ~ ( pi_removemin @ SX0 )
| ( pi_sharp_find_min @ ( i @ SX0 ) @ ( sK5_V @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[948]) ).
thf(1007,plain,
! [SV310: $i,SV291: $i,SV249: $i] :
( ( ~ ( ~ ! [SY581: $i,SY582: $i] :
( ~ ( less_than @ SY582 @ SY581 )
| ~ ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SV291 @ ( pair @ SY581 @ SY582 ) ) @ SV310 ) )
| ( check_cpq @ ( triple @ SV249 @ SV291 @ SV310 ) ) )
| ~ ! [SY583: $i,SY584: $i] :
( ~ ( less_than @ SY584 @ SY583 )
| ~ ( check_cpq @ ( triple @ SV249 @ SV291 @ SV310 ) )
| ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SV291 @ ( pair @ SY583 @ SY584 ) ) @ SV310 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1008,plain,
! [SV292: $i,SV250: $i,SV199: $i] :
( ( ( ~ ( less_than @ SV199 @ SV250 )
| ~ ( less_than @ SV250 @ SV292 ) )
= $true )
| ( ( less_than @ SV199 @ SV292 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[950]) ).
thf(1009,plain,
! [SV206: $i,SV293: $i,SV254: $i] :
( ( ( ( SV254 = SV293 )
| ~ ( contains_pq @ SV206 @ SV293 ) )
= $true )
| ( ( ( remove_pq @ ( insert_pq @ SV206 @ SV254 ) @ SV293 )
= ( insert_pq @ ( remove_pq @ SV206 @ SV293 ) @ SV254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[952]) ).
thf(1010,plain,
! [SV255: $i,SV207: $i] :
( ( ( ~ ( contains_pq @ SV207 @ SV255 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV207 @ SV255 ) )
= $true )
| ( ( ( findmin_pq_eff @ SV207 @ SV255 )
= SV207 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[953]) ).
thf(1011,plain,
! [SV256: $i,SV208: $i] :
( ( ( ~ ( contains_pq @ SV208 @ SV256 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV208 @ SV256 ) )
= $true )
| ( ( ( findmin_pq_res @ SV208 @ SV256 )
= SV256 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[954]) ).
thf(1012,plain,
! [SV257: $i,SV209: $i] :
( ( ( ~ ( contains_pq @ SV209 @ SV257 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV209 @ SV257 ) )
= $true )
| ( ( ( removemin_pq_eff @ SV209 @ SV257 )
= ( remove_pq @ SV209 @ SV257 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[955]) ).
thf(1013,plain,
! [SV258: $i,SV210: $i] :
( ( ( ~ ( contains_pq @ SV210 @ SV258 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV210 @ SV258 ) )
= $true )
| ( ( ( removemin_pq_res @ SV210 @ SV258 )
= SV258 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[956]) ).
thf(1014,plain,
! [SV216: $i,SV297: $i,SV263: $i] :
( ( ( ( SV263 = SV297 )
| ~ ( contains_slb @ SV216 @ SV297 ) )
= $true )
| ( ( ! [SY561: $i] :
( ( remove_slb @ ( insert_slb @ SV216 @ ( pair @ SV263 @ SY561 ) ) @ SV297 )
= ( insert_slb @ ( remove_slb @ SV216 @ SV297 ) @ ( pair @ SV263 @ SY561 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[961]) ).
thf(1015,plain,
! [SV218: $i,SV299: $i,SV265: $i] :
( ( ( ( SV265 = SV299 )
| ~ ( contains_slb @ SV218 @ SV299 ) )
= $true )
| ( ( ! [SY562: $i] :
( ( lookup_slb @ ( insert_slb @ SV218 @ ( pair @ SV265 @ SY562 ) ) @ SV299 )
= ( lookup_slb @ SV218 @ SV299 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[963]) ).
thf(1016,plain,
! [SV266: $i,SV220: $i,SV300: $i,SV311: $i] :
( ( ~ ( strictly_less_than @ SV311 @ SV300 )
| ( ( update_slb @ ( insert_slb @ SV220 @ ( pair @ SV266 @ SV311 ) ) @ SV300 )
= ( insert_slb @ ( update_slb @ SV220 @ SV300 ) @ ( pair @ SV266 @ SV300 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1017,plain,
! [SV267: $i,SV221: $i,SV312: $i,SV301: $i] :
( ( ~ ( less_than @ SV301 @ SV312 )
| ( ( update_slb @ ( insert_slb @ SV221 @ ( pair @ SV267 @ SV312 ) ) @ SV301 )
= ( insert_slb @ ( update_slb @ SV221 @ SV301 ) @ ( pair @ SV267 @ SV312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1018,plain,
! [SV268: $i,SV223: $i] :
( ( ( succ_cpq @ SV223 @ SV268 )
= $false )
| ( ( ! [SY516: $i] : ( succ_cpq @ SV223 @ ( insert_cpq @ SV268 @ SY516 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1019,plain,
! [SV269: $i,SV224: $i] :
( ( ( succ_cpq @ SV224 @ SV269 )
= $false )
| ( ( ! [SY517: $i] : ( succ_cpq @ SV224 @ ( remove_cpq @ SV269 @ SY517 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[967]) ).
thf(1020,plain,
! [SV270: $i,SV225: $i] :
( ( ( succ_cpq @ SV225 @ SV270 )
= $false )
| ( ( succ_cpq @ SV225 @ ( findmin_cpq_eff @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[968]) ).
thf(1021,plain,
! [SV271: $i,SV226: $i] :
( ( ( succ_cpq @ SV226 @ SV271 )
= $false )
| ( ( succ_cpq @ SV226 @ ( removemin_cpq_eff @ SV271 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[969]) ).
thf(1022,plain,
! [SV302: $i,SV273: $i,SV228: $i,SV313: $i] :
( ( ! [SY585: $i] :
( ~ ( strictly_less_than @ SV313 @ SY585 )
| ~ ( check_cpq @ ( triple @ SV228 @ ( insert_slb @ SV273 @ ( pair @ SV313 @ SY585 ) ) @ SV302 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1023,plain,
! [SV303: $i,SV275: $i,SV230: $i] :
( ( ( ok @ ( triple @ SV230 @ SV275 @ SV303 ) )
= $true )
| ( ( SV303 = bad )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[972]) ).
thf(1024,plain,
! [SV314: $i,SV304: $i,SV276: $i,SV231: $i] :
( ( ( insert_cpq @ ( triple @ SV231 @ SV276 @ SV304 ) @ SV314 )
= ( triple @ ( insert_pqp @ SV231 @ SV314 ) @ ( insert_slb @ SV276 @ ( pair @ SV314 @ bottom ) ) @ SV304 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1025,plain,
! [SV305: $i,SV232: $i,SV315: $i,SV277: $i] :
( ( ( contains_slb @ SV277 @ SV315 )
| ( ( remove_cpq @ ( triple @ SV232 @ SV277 @ SV305 ) @ SV315 )
= ( triple @ SV232 @ SV277 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1026,plain,
! [SV306: $i,SV233: $i,SV316: $i,SV278: $i] :
( ( ~ ( contains_slb @ SV278 @ SV316 )
| ~ ( less_than @ ( lookup_slb @ SV278 @ SV316 ) @ SV316 )
| ( ( remove_cpq @ ( triple @ SV233 @ SV278 @ SV306 ) @ SV316 )
= ( triple @ ( remove_pqp @ SV233 @ SV316 ) @ ( remove_slb @ SV278 @ SV316 ) @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1027,plain,
! [SV307: $i,SV234: $i,SV317: $i,SV279: $i] :
( ( ~ ( contains_slb @ SV279 @ SV317 )
| ~ ( strictly_less_than @ SV317 @ ( lookup_slb @ SV279 @ SV317 ) )
| ( ( remove_cpq @ ( triple @ SV234 @ SV279 @ SV307 ) @ SV317 )
= ( triple @ ( remove_pqp @ SV234 @ SV317 ) @ ( remove_slb @ SV279 @ SV317 ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1028,plain,
! [SV236: $i,SV281: $i] :
( ( ( SV281 = create_slb )
= $true )
| ( ( contains_slb @ SV281 @ ( findmin_pqp_res @ SV236 ) )
= $true )
| ( ( ! [SY530: $i] :
( ( findmin_cpq_eff @ ( triple @ SV236 @ SV281 @ SY530 ) )
= ( triple @ SV236 @ ( update_slb @ SV281 @ ( findmin_pqp_res @ SV236 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[977]) ).
thf(1029,plain,
! [SV237: $i,SV282: $i] :
( ( ( ( SV282 = create_slb )
| ~ ( contains_slb @ SV282 @ ( findmin_pqp_res @ SV237 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV237 ) @ ( lookup_slb @ SV282 @ ( findmin_pqp_res @ SV237 ) ) ) )
= $true )
| ( ( ! [SY531: $i] :
( ( findmin_cpq_eff @ ( triple @ SV237 @ SV282 @ SY531 ) )
= ( triple @ SV237 @ ( update_slb @ SV282 @ ( findmin_pqp_res @ SV237 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1030,plain,
! [SV238: $i,SV283: $i] :
( ( ( ( SV283 = create_slb )
| ~ ( contains_slb @ SV283 @ ( findmin_pqp_res @ SV238 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV283 @ ( findmin_pqp_res @ SV238 ) ) @ ( findmin_pqp_res @ SV238 ) ) )
= $true )
| ( ( ! [SY532: $i] :
( ( findmin_cpq_eff @ ( triple @ SV238 @ SV283 @ SY532 ) )
= ( triple @ SV238 @ ( update_slb @ SV283 @ ( findmin_pqp_res @ SV238 ) ) @ SY532 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(1031,plain,
! [SV318: $i,SV285: $i,SV240: $i] :
( ( ( ( findmin_cpq_res @ ( triple @ SV240 @ SV285 @ SV318 ) )
= ( findmin_pqp_res @ SV240 ) )
= $true )
| ( ( SV285 = create_slb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1032,plain,
! [SV308: $i,SV319: $i,SV287: $i,SV244: $i] :
( ( ! [SY586: $i] :
( ( i @ ( triple @ SV244 @ ( insert_slb @ SV287 @ ( pair @ SV319 @ SY586 ) ) @ SV308 ) )
= ( insert_pq @ ( i @ ( triple @ SV244 @ SV287 @ SV308 ) ) @ SV319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1033,plain,
! [SV320: $i] :
( ( ! [SY587: $i] :
( ~ ( ok @ SY587 )
| ~ ( succ_cpq @ SV320 @ SY587 )
| ~ ( check_cpq @ SY587 ) )
| ( phi @ SV320 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1034,plain,
! [SV321: $i] :
( ( ~ ( phi @ SV321 )
| ~ ( ~ ~ ( ~ ( ok @ ( sK4_V @ SV321 ) )
| ~ ( succ_cpq @ SV321 @ ( sK4_V @ SV321 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SV321 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1035,plain,
! [SV288: $i,SV245: $i] :
( ( ~ ! [SY537: $i,SY538: $i] :
( ~ ( contains_cpq @ ( triple @ SV245 @ SV288 @ SY537 ) @ SY538 )
| ( contains_slb @ SV288 @ SY538 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[984]) ).
thf(1036,plain,
! [SV245: $i,SV288: $i] :
( ( ~ ! [SY539: $i,SY540: $i] :
( ~ ( contains_slb @ SV288 @ SY540 )
| ( contains_cpq @ ( triple @ SV245 @ SV288 @ SY539 ) @ SY540 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[984]) ).
thf(1037,plain,
! [SV322: $i] :
( ( ! [SY588: $i] :
~ ( pi_sharp_find_min @ ( i @ SV322 ) @ SY588 )
| ( pi_find_min @ SV322 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1038,plain,
! [SV323: $i] :
( ( ~ ( pi_find_min @ SV323 )
| ( pi_sharp_find_min @ ( i @ SV323 ) @ ( sK6_V @ SV323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1039,plain,
! [SV324: $i] :
( ( ! [SY589: $i] :
( ~ ( contains_pq @ SV324 @ SY589 )
| ~ ( issmallestelement_pq @ SV324 @ SY589 )
| ( pi_sharp_find_min @ SV324 @ SY589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1040,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)],[988]) ).
thf(1041,plain,
! [SV289: $i,SV246: $i] :
( ( ~ ! [SY541: $i] :
( ! [SY542: $i] :
~ ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY542 ) ) @ SY541 )
| ( SV289 = SY541 )
| ( contains_slb @ SV246 @ SY541 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[989]) ).
thf(1042,plain,
! [SV246: $i,SV289: $i] :
( ( ~ ~ ( ~ ! [SY543: $i] :
( ( SV289 != SY543 )
| ! [SY544: $i] : ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY544 ) ) @ SY543 ) )
| ~ ! [SY545: $i] :
( ~ ( contains_slb @ SV246 @ SY545 )
| ! [SY546: $i] : ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY546 ) ) @ SY545 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[989]) ).
thf(1043,plain,
! [SV325: $i] :
( ( ! [SY590: $i] :
( ~ ( contains_pq @ SV325 @ SY590 )
| ( pi_sharp_remove @ SV325 @ SY590 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1044,plain,
! [SV326: $i] :
( ( ! [SY591: $i] :
( ~ ( pi_sharp_remove @ SV326 @ SY591 )
| ( contains_pq @ SV326 @ SY591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1045,plain,
! [SV327: $i] :
( ( ! [SY592: $i] :
( ~ ( less_than @ SV327 @ SY592 )
| ( less_than @ SY592 @ SV327 )
| ( strictly_less_than @ SV327 @ SY592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1046,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)],[993]) ).
thf(1047,plain,
! [SV328: $i] :
( ( ! [SY593: $i] :
( ~ ( ~ ( contains_pq @ SV328 @ ( sK7_W @ SY593 @ SV328 ) )
| ~ ~ ( less_than @ SY593 @ ( sK7_W @ SY593 @ SV328 ) ) )
| ( issmallestelement_pq @ SV328 @ SY593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1048,plain,
! [SV329: $i] :
( ( ! [SY594: $i] :
( ~ ( issmallestelement_pq @ SV329 @ SY594 )
| ! [SY595: $i] :
( ~ ( contains_pq @ SV329 @ SY595 )
| ( less_than @ SY594 @ SY595 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1049,plain,
! [SV330: $i] :
( ( ! [SY596: $i] :
( ~ ( contains_pq @ SV330 @ SY596 )
| ~ ( issmallestelement_pq @ SV330 @ SY596 )
| ( pi_sharp_removemin @ SV330 @ SY596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1050,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)],[997]) ).
thf(1051,plain,
( ( contains_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY166 ) @ sK3_SY168 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[999]) ).
thf(1052,plain,
! [SV309: $i,SV290: $i,SV247: $i] :
( ( ~ ~ ( ~ ! [SY573: $i,SY574: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY573 ) ) @ SV309 @ SY574 )
| ( SV290 = SV309 )
| ( pair_in_list @ SV247 @ SV309 @ SY574 ) )
| ~ ! [SY575: $i,SY576: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY575 ) ) @ SV309 @ SY576 )
| ( SY575 = SY576 )
| ( pair_in_list @ SV247 @ SV309 @ SY576 ) ) )
| ~ ~ ( ~ ! [SY577: $i,SY578: $i] :
( ( SV290 != SV309 )
| ( SY577 != SY578 )
| ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY577 ) ) @ SV309 @ SY578 ) )
| ~ ! [SY579: $i,SY580: $i] :
( ~ ( pair_in_list @ SV247 @ SV309 @ SY580 )
| ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY579 ) ) @ SV309 @ SY580 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1000]) ).
thf(1053,plain,
! [SV248: $i] :
( ( ! [SY490: $i,SY491: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV248 @ SY490 ) @ SY491 )
| ( SY490 = SY491 )
| ( contains_pq @ SV248 @ SY491 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1001]) ).
thf(1054,plain,
! [SV248: $i] :
( ( ~ ( ~ ! [SY492: $i,SY493: $i] :
( ( SY492 != SY493 )
| ( contains_pq @ ( insert_pq @ SV248 @ SY492 ) @ SY493 ) )
| ~ ! [SY494: $i,SY495: $i] :
( ~ ( contains_pq @ SV248 @ SY495 )
| ( contains_pq @ ( insert_pq @ SV248 @ SY494 ) @ SY495 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1002]) ).
thf(1055,plain,
! [SV331: $i] :
( ( ! [SY597: $i] :
( ~ ( pi_remove @ SV331 @ SY597 )
| ( pi_sharp_remove @ ( i @ SV331 ) @ SY597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1056,plain,
! [SV332: $i] :
( ( ! [SY598: $i] :
( ~ ( pi_sharp_remove @ ( i @ SV332 ) @ SY598 )
| ( pi_remove @ SV332 @ SY598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1057,plain,
! [SV333: $i] :
( ( ! [SY599: $i] :
~ ( pi_sharp_find_min @ ( i @ SV333 ) @ SY599 )
| ( pi_removemin @ SV333 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1058,plain,
! [SV334: $i] :
( ( ~ ( pi_removemin @ SV334 )
| ( pi_sharp_find_min @ ( i @ SV334 ) @ ( sK5_V @ SV334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1059,plain,
! [SV310: $i,SV291: $i,SV249: $i] :
( ( ~ ! [SY581: $i,SY582: $i] :
( ~ ( less_than @ SY582 @ SY581 )
| ~ ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SV291 @ ( pair @ SY581 @ SY582 ) ) @ SV310 ) )
| ( check_cpq @ ( triple @ SV249 @ SV291 @ SV310 ) ) )
| ~ ! [SY583: $i,SY584: $i] :
( ~ ( less_than @ SY584 @ SY583 )
| ~ ( check_cpq @ ( triple @ SV249 @ SV291 @ SV310 ) )
| ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SV291 @ ( pair @ SY583 @ SY584 ) ) @ SV310 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1060,plain,
! [SV292: $i,SV250: $i,SV199: $i] :
( ( ( ~ ( less_than @ SV199 @ SV250 ) )
= $true )
| ( ( ~ ( less_than @ SV250 @ SV292 ) )
= $true )
| ( ( less_than @ SV199 @ SV292 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1008]) ).
thf(1061,plain,
! [SV206: $i,SV293: $i,SV254: $i] :
( ( ( SV254 = SV293 )
= $true )
| ( ( ~ ( contains_pq @ SV206 @ SV293 ) )
= $true )
| ( ( ( remove_pq @ ( insert_pq @ SV206 @ SV254 ) @ SV293 )
= ( insert_pq @ ( remove_pq @ SV206 @ SV293 ) @ SV254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1062,plain,
! [SV255: $i,SV207: $i] :
( ( ( contains_pq @ SV207 @ SV255 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV207 @ SV255 ) )
= $true )
| ( ( ( findmin_pq_eff @ SV207 @ SV255 )
= SV207 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1010]) ).
thf(1063,plain,
! [SV256: $i,SV208: $i] :
( ( ( contains_pq @ SV208 @ SV256 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV208 @ SV256 ) )
= $true )
| ( ( ( findmin_pq_res @ SV208 @ SV256 )
= SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1011]) ).
thf(1064,plain,
! [SV257: $i,SV209: $i] :
( ( ( contains_pq @ SV209 @ SV257 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV209 @ SV257 ) )
= $true )
| ( ( ( removemin_pq_eff @ SV209 @ SV257 )
= ( remove_pq @ SV209 @ SV257 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1012]) ).
thf(1065,plain,
! [SV258: $i,SV210: $i] :
( ( ( contains_pq @ SV210 @ SV258 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV210 @ SV258 ) )
= $true )
| ( ( ( removemin_pq_res @ SV210 @ SV258 )
= SV258 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1066,plain,
! [SV216: $i,SV297: $i,SV263: $i] :
( ( ( SV263 = SV297 )
= $true )
| ( ( ~ ( contains_slb @ SV216 @ SV297 ) )
= $true )
| ( ( ! [SY561: $i] :
( ( remove_slb @ ( insert_slb @ SV216 @ ( pair @ SV263 @ SY561 ) ) @ SV297 )
= ( insert_slb @ ( remove_slb @ SV216 @ SV297 ) @ ( pair @ SV263 @ SY561 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1014]) ).
thf(1067,plain,
! [SV218: $i,SV299: $i,SV265: $i] :
( ( ( SV265 = SV299 )
= $true )
| ( ( ~ ( contains_slb @ SV218 @ SV299 ) )
= $true )
| ( ( ! [SY562: $i] :
( ( lookup_slb @ ( insert_slb @ SV218 @ ( pair @ SV265 @ SY562 ) ) @ SV299 )
= ( lookup_slb @ SV218 @ SV299 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1015]) ).
thf(1068,plain,
! [SV266: $i,SV220: $i,SV300: $i,SV311: $i] :
( ( ( ~ ( strictly_less_than @ SV311 @ SV300 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV220 @ ( pair @ SV266 @ SV311 ) ) @ SV300 )
= ( insert_slb @ ( update_slb @ SV220 @ SV300 ) @ ( pair @ SV266 @ SV300 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1016]) ).
thf(1069,plain,
! [SV267: $i,SV221: $i,SV312: $i,SV301: $i] :
( ( ( ~ ( less_than @ SV301 @ SV312 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV221 @ ( pair @ SV267 @ SV312 ) ) @ SV301 )
= ( insert_slb @ ( update_slb @ SV221 @ SV301 ) @ ( pair @ SV267 @ SV312 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1017]) ).
thf(1070,plain,
! [SV335: $i,SV268: $i,SV223: $i] :
( ( ( succ_cpq @ SV223 @ ( insert_cpq @ SV268 @ SV335 ) )
= $true )
| ( ( succ_cpq @ SV223 @ SV268 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1071,plain,
! [SV336: $i,SV269: $i,SV224: $i] :
( ( ( succ_cpq @ SV224 @ ( remove_cpq @ SV269 @ SV336 ) )
= $true )
| ( ( succ_cpq @ SV224 @ SV269 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1072,plain,
! [SV302: $i,SV273: $i,SV228: $i,SV337: $i,SV313: $i] :
( ( ~ ( strictly_less_than @ SV313 @ SV337 )
| ~ ( check_cpq @ ( triple @ SV228 @ ( insert_slb @ SV273 @ ( pair @ SV313 @ SV337 ) ) @ SV302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1073,plain,
! [SV305: $i,SV232: $i,SV315: $i,SV277: $i] :
( ( ( contains_slb @ SV277 @ SV315 )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV232 @ SV277 @ SV305 ) @ SV315 )
= ( triple @ SV232 @ SV277 @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1025]) ).
thf(1074,plain,
! [SV306: $i,SV233: $i,SV316: $i,SV278: $i] :
( ( ( ~ ( contains_slb @ SV278 @ SV316 )
| ~ ( less_than @ ( lookup_slb @ SV278 @ SV316 ) @ SV316 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV233 @ SV278 @ SV306 ) @ SV316 )
= ( triple @ ( remove_pqp @ SV233 @ SV316 ) @ ( remove_slb @ SV278 @ SV316 ) @ SV306 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1026]) ).
thf(1075,plain,
! [SV307: $i,SV234: $i,SV317: $i,SV279: $i] :
( ( ( ~ ( contains_slb @ SV279 @ SV317 )
| ~ ( strictly_less_than @ SV317 @ ( lookup_slb @ SV279 @ SV317 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV234 @ SV279 @ SV307 ) @ SV317 )
= ( triple @ ( remove_pqp @ SV234 @ SV317 ) @ ( remove_slb @ SV279 @ SV317 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1027]) ).
thf(1076,plain,
! [SV338: $i,SV281: $i,SV236: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV236 @ SV281 @ SV338 ) )
= ( triple @ SV236 @ ( update_slb @ SV281 @ ( findmin_pqp_res @ SV236 ) ) @ bad ) )
= $true )
| ( ( contains_slb @ SV281 @ ( findmin_pqp_res @ SV236 ) )
= $true )
| ( ( SV281 = create_slb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1077,plain,
! [SV237: $i,SV282: $i] :
( ( ( SV282 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV282 @ ( findmin_pqp_res @ SV237 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV237 ) @ ( lookup_slb @ SV282 @ ( findmin_pqp_res @ SV237 ) ) ) )
= $true )
| ( ( ! [SY531: $i] :
( ( findmin_cpq_eff @ ( triple @ SV237 @ SV282 @ SY531 ) )
= ( triple @ SV237 @ ( update_slb @ SV282 @ ( findmin_pqp_res @ SV237 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1029]) ).
thf(1078,plain,
! [SV238: $i,SV283: $i] :
( ( ( SV283 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV283 @ ( findmin_pqp_res @ SV238 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV283 @ ( findmin_pqp_res @ SV238 ) ) @ ( findmin_pqp_res @ SV238 ) ) )
= $true )
| ( ( ! [SY532: $i] :
( ( findmin_cpq_eff @ ( triple @ SV238 @ SV283 @ SY532 ) )
= ( triple @ SV238 @ ( update_slb @ SV283 @ ( findmin_pqp_res @ SV238 ) ) @ SY532 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1079,plain,
! [SV308: $i,SV339: $i,SV319: $i,SV287: $i,SV244: $i] :
( ( ( i @ ( triple @ SV244 @ ( insert_slb @ SV287 @ ( pair @ SV319 @ SV339 ) ) @ SV308 ) )
= ( insert_pq @ ( i @ ( triple @ SV244 @ SV287 @ SV308 ) ) @ SV319 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1080,plain,
! [SV320: $i] :
( ( ( ! [SY587: $i] :
( ~ ( ok @ SY587 )
| ~ ( succ_cpq @ SV320 @ SY587 )
| ~ ( check_cpq @ SY587 ) ) )
= $true )
| ( ( phi @ SV320 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1033]) ).
thf(1081,plain,
! [SV321: $i] :
( ( ( ~ ( phi @ SV321 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ok @ ( sK4_V @ SV321 ) )
| ~ ( succ_cpq @ SV321 @ ( sK4_V @ SV321 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SV321 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1034]) ).
thf(1082,plain,
! [SV288: $i,SV245: $i] :
( ( ! [SY537: $i,SY538: $i] :
( ~ ( contains_cpq @ ( triple @ SV245 @ SV288 @ SY537 ) @ SY538 )
| ( contains_slb @ SV288 @ SY538 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1035]) ).
thf(1083,plain,
! [SV245: $i,SV288: $i] :
( ( ! [SY539: $i,SY540: $i] :
( ~ ( contains_slb @ SV288 @ SY540 )
| ( contains_cpq @ ( triple @ SV245 @ SV288 @ SY539 ) @ SY540 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1036]) ).
thf(1084,plain,
! [SV322: $i] :
( ( ( ! [SY588: $i] :
~ ( pi_sharp_find_min @ ( i @ SV322 ) @ SY588 ) )
= $true )
| ( ( pi_find_min @ SV322 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1037]) ).
thf(1085,plain,
! [SV323: $i] :
( ( ( ~ ( pi_find_min @ SV323 ) )
= $true )
| ( ( pi_sharp_find_min @ ( i @ SV323 ) @ ( sK6_V @ SV323 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1038]) ).
thf(1086,plain,
! [SV340: $i,SV324: $i] :
( ( ~ ( contains_pq @ SV324 @ SV340 )
| ~ ( issmallestelement_pq @ SV324 @ SV340 )
| ( pi_sharp_find_min @ SV324 @ SV340 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1087,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1040]) ).
thf(1088,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1040]) ).
thf(1089,plain,
! [SV289: $i,SV246: $i] :
( ( ! [SY541: $i] :
( ! [SY542: $i] :
~ ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY542 ) ) @ SY541 )
| ( SV289 = SY541 )
| ( contains_slb @ SV246 @ SY541 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1041]) ).
thf(1090,plain,
! [SV246: $i,SV289: $i] :
( ( ~ ( ~ ! [SY543: $i] :
( ( SV289 != SY543 )
| ! [SY544: $i] : ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY544 ) ) @ SY543 ) )
| ~ ! [SY545: $i] :
( ~ ( contains_slb @ SV246 @ SY545 )
| ! [SY546: $i] : ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY546 ) ) @ SY545 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1042]) ).
thf(1091,plain,
! [SV341: $i,SV325: $i] :
( ( ~ ( contains_pq @ SV325 @ SV341 )
| ( pi_sharp_remove @ SV325 @ SV341 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1092,plain,
! [SV342: $i,SV326: $i] :
( ( ~ ( pi_sharp_remove @ SV326 @ SV342 )
| ( contains_pq @ SV326 @ SV342 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1093,plain,
! [SV343: $i,SV327: $i] :
( ( ~ ( less_than @ SV327 @ SV343 )
| ( less_than @ SV343 @ SV327 )
| ( strictly_less_than @ SV327 @ SV343 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1094,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1046]) ).
thf(1095,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1046]) ).
thf(1096,plain,
! [SV344: $i,SV328: $i] :
( ( ~ ( ~ ( contains_pq @ SV328 @ ( sK7_W @ SV344 @ SV328 ) )
| ~ ~ ( less_than @ SV344 @ ( sK7_W @ SV344 @ SV328 ) ) )
| ( issmallestelement_pq @ SV328 @ SV344 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1097,plain,
! [SV345: $i,SV329: $i] :
( ( ~ ( issmallestelement_pq @ SV329 @ SV345 )
| ! [SY600: $i] :
( ~ ( contains_pq @ SV329 @ SY600 )
| ( less_than @ SV345 @ SY600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1098,plain,
! [SV346: $i,SV330: $i] :
( ( ~ ( contains_pq @ SV330 @ SV346 )
| ~ ( issmallestelement_pq @ SV330 @ SV346 )
| ( pi_sharp_removemin @ SV330 @ SV346 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1099,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1050]) ).
thf(1100,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1050]) ).
thf(1101,plain,
! [SV309: $i,SV290: $i,SV247: $i] :
( ( ~ ~ ( ~ ! [SY573: $i,SY574: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY573 ) ) @ SV309 @ SY574 )
| ( SV290 = SV309 )
| ( pair_in_list @ SV247 @ SV309 @ SY574 ) )
| ~ ! [SY575: $i,SY576: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY575 ) ) @ SV309 @ SY576 )
| ( SY575 = SY576 )
| ( pair_in_list @ SV247 @ SV309 @ SY576 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1102,plain,
! [SV247: $i,SV309: $i,SV290: $i] :
( ( ~ ~ ( ~ ! [SY577: $i,SY578: $i] :
( ( SV290 != SV309 )
| ( SY577 != SY578 )
| ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY577 ) ) @ SV309 @ SY578 ) )
| ~ ! [SY579: $i,SY580: $i] :
( ~ ( pair_in_list @ SV247 @ SV309 @ SY580 )
| ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY579 ) ) @ SV309 @ SY580 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1103,plain,
! [SV347: $i,SV248: $i] :
( ( ! [SY601: $i] :
( ~ ( contains_pq @ ( insert_pq @ SV248 @ SV347 ) @ SY601 )
| ( SV347 = SY601 )
| ( contains_pq @ SV248 @ SY601 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1104,plain,
! [SV248: $i] :
( ( ~ ! [SY492: $i,SY493: $i] :
( ( SY492 != SY493 )
| ( contains_pq @ ( insert_pq @ SV248 @ SY492 ) @ SY493 ) )
| ~ ! [SY494: $i,SY495: $i] :
( ~ ( contains_pq @ SV248 @ SY495 )
| ( contains_pq @ ( insert_pq @ SV248 @ SY494 ) @ SY495 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1054]) ).
thf(1105,plain,
! [SV348: $i,SV331: $i] :
( ( ~ ( pi_remove @ SV331 @ SV348 )
| ( pi_sharp_remove @ ( i @ SV331 ) @ SV348 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1106,plain,
! [SV349: $i,SV332: $i] :
( ( ~ ( pi_sharp_remove @ ( i @ SV332 ) @ SV349 )
| ( pi_remove @ SV332 @ SV349 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1107,plain,
! [SV333: $i] :
( ( ( ! [SY599: $i] :
~ ( pi_sharp_find_min @ ( i @ SV333 ) @ SY599 ) )
= $true )
| ( ( pi_removemin @ SV333 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1057]) ).
thf(1108,plain,
! [SV334: $i] :
( ( ( ~ ( pi_removemin @ SV334 ) )
= $true )
| ( ( pi_sharp_find_min @ ( i @ SV334 ) @ ( sK5_V @ SV334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1058]) ).
thf(1109,plain,
! [SV310: $i,SV291: $i,SV249: $i] :
( ( ~ ! [SY581: $i,SY582: $i] :
( ~ ( less_than @ SY582 @ SY581 )
| ~ ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SV291 @ ( pair @ SY581 @ SY582 ) ) @ SV310 ) )
| ( check_cpq @ ( triple @ SV249 @ SV291 @ SV310 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1059]) ).
thf(1110,plain,
! [SV310: $i,SV291: $i,SV249: $i] :
( ( ~ ! [SY583: $i,SY584: $i] :
( ~ ( less_than @ SY584 @ SY583 )
| ~ ( check_cpq @ ( triple @ SV249 @ SV291 @ SV310 ) )
| ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SV291 @ ( pair @ SY583 @ SY584 ) ) @ SV310 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1059]) ).
thf(1111,plain,
! [SV292: $i,SV250: $i,SV199: $i] :
( ( ( less_than @ SV199 @ SV250 )
= $false )
| ( ( ~ ( less_than @ SV250 @ SV292 ) )
= $true )
| ( ( less_than @ SV199 @ SV292 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1060]) ).
thf(1112,plain,
! [SV254: $i,SV293: $i,SV206: $i] :
( ( ( contains_pq @ SV206 @ SV293 )
= $false )
| ( ( SV254 = SV293 )
= $true )
| ( ( ( remove_pq @ ( insert_pq @ SV206 @ SV254 ) @ SV293 )
= ( insert_pq @ ( remove_pq @ SV206 @ SV293 ) @ SV254 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1061]) ).
thf(1113,plain,
! [SV255: $i,SV207: $i] :
( ( ( issmallestelement_pq @ SV207 @ SV255 )
= $false )
| ( ( contains_pq @ SV207 @ SV255 )
= $false )
| ( ( ( findmin_pq_eff @ SV207 @ SV255 )
= SV207 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1062]) ).
thf(1114,plain,
! [SV256: $i,SV208: $i] :
( ( ( issmallestelement_pq @ SV208 @ SV256 )
= $false )
| ( ( contains_pq @ SV208 @ SV256 )
= $false )
| ( ( ( findmin_pq_res @ SV208 @ SV256 )
= SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1063]) ).
thf(1115,plain,
! [SV257: $i,SV209: $i] :
( ( ( issmallestelement_pq @ SV209 @ SV257 )
= $false )
| ( ( contains_pq @ SV209 @ SV257 )
= $false )
| ( ( ( removemin_pq_eff @ SV209 @ SV257 )
= ( remove_pq @ SV209 @ SV257 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1064]) ).
thf(1116,plain,
! [SV258: $i,SV210: $i] :
( ( ( issmallestelement_pq @ SV210 @ SV258 )
= $false )
| ( ( contains_pq @ SV210 @ SV258 )
= $false )
| ( ( ( removemin_pq_res @ SV210 @ SV258 )
= SV258 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1065]) ).
thf(1117,plain,
! [SV263: $i,SV297: $i,SV216: $i] :
( ( ( contains_slb @ SV216 @ SV297 )
= $false )
| ( ( SV263 = SV297 )
= $true )
| ( ( ! [SY561: $i] :
( ( remove_slb @ ( insert_slb @ SV216 @ ( pair @ SV263 @ SY561 ) ) @ SV297 )
= ( insert_slb @ ( remove_slb @ SV216 @ SV297 ) @ ( pair @ SV263 @ SY561 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1066]) ).
thf(1118,plain,
! [SV265: $i,SV299: $i,SV218: $i] :
( ( ( contains_slb @ SV218 @ SV299 )
= $false )
| ( ( SV265 = SV299 )
= $true )
| ( ( ! [SY562: $i] :
( ( lookup_slb @ ( insert_slb @ SV218 @ ( pair @ SV265 @ SY562 ) ) @ SV299 )
= ( lookup_slb @ SV218 @ SV299 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1119,plain,
! [SV266: $i,SV220: $i,SV300: $i,SV311: $i] :
( ( ( strictly_less_than @ SV311 @ SV300 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV220 @ ( pair @ SV266 @ SV311 ) ) @ SV300 )
= ( insert_slb @ ( update_slb @ SV220 @ SV300 ) @ ( pair @ SV266 @ SV300 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1068]) ).
thf(1120,plain,
! [SV267: $i,SV221: $i,SV312: $i,SV301: $i] :
( ( ( less_than @ SV301 @ SV312 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV221 @ ( pair @ SV267 @ SV312 ) ) @ SV301 )
= ( insert_slb @ ( update_slb @ SV221 @ SV301 ) @ ( pair @ SV267 @ SV312 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1069]) ).
thf(1121,plain,
! [SV302: $i,SV273: $i,SV228: $i,SV337: $i,SV313: $i] :
( ( ( ~ ( strictly_less_than @ SV313 @ SV337 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV228 @ ( insert_slb @ SV273 @ ( pair @ SV313 @ SV337 ) ) @ SV302 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1072]) ).
thf(1122,plain,
! [SV306: $i,SV233: $i,SV316: $i,SV278: $i] :
( ( ( ~ ( contains_slb @ SV278 @ SV316 ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV278 @ SV316 ) @ SV316 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV233 @ SV278 @ SV306 ) @ SV316 )
= ( triple @ ( remove_pqp @ SV233 @ SV316 ) @ ( remove_slb @ SV278 @ SV316 ) @ SV306 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1074]) ).
thf(1123,plain,
! [SV307: $i,SV234: $i,SV317: $i,SV279: $i] :
( ( ( ~ ( contains_slb @ SV279 @ SV317 ) )
= $true )
| ( ( ~ ( strictly_less_than @ SV317 @ ( lookup_slb @ SV279 @ SV317 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV234 @ SV279 @ SV307 ) @ SV317 )
= ( triple @ ( remove_pqp @ SV234 @ SV317 ) @ ( remove_slb @ SV279 @ SV317 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1075]) ).
thf(1124,plain,
! [SV237: $i,SV282: $i] :
( ( ( contains_slb @ SV282 @ ( findmin_pqp_res @ SV237 ) )
= $false )
| ( ( SV282 = create_slb )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV237 ) @ ( lookup_slb @ SV282 @ ( findmin_pqp_res @ SV237 ) ) ) )
= $true )
| ( ( ! [SY531: $i] :
( ( findmin_cpq_eff @ ( triple @ SV237 @ SV282 @ SY531 ) )
= ( triple @ SV237 @ ( update_slb @ SV282 @ ( findmin_pqp_res @ SV237 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1077]) ).
thf(1125,plain,
! [SV238: $i,SV283: $i] :
( ( ( contains_slb @ SV283 @ ( findmin_pqp_res @ SV238 ) )
= $false )
| ( ( SV283 = create_slb )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV283 @ ( findmin_pqp_res @ SV238 ) ) @ ( findmin_pqp_res @ SV238 ) ) )
= $true )
| ( ( ! [SY532: $i] :
( ( findmin_cpq_eff @ ( triple @ SV238 @ SV283 @ SY532 ) )
= ( triple @ SV238 @ ( update_slb @ SV283 @ ( findmin_pqp_res @ SV238 ) ) @ SY532 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1126,plain,
! [SV320: $i,SV350: $i] :
( ( ( ~ ( ok @ SV350 )
| ~ ( succ_cpq @ SV320 @ SV350 )
| ~ ( check_cpq @ SV350 ) )
= $true )
| ( ( phi @ SV320 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1127,plain,
! [SV321: $i] :
( ( ( phi @ SV321 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( ok @ ( sK4_V @ SV321 ) )
| ~ ( succ_cpq @ SV321 @ ( sK4_V @ SV321 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SV321 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1128,plain,
! [SV351: $i,SV288: $i,SV245: $i] :
( ( ! [SY602: $i] :
( ~ ( contains_cpq @ ( triple @ SV245 @ SV288 @ SV351 ) @ SY602 )
| ( contains_slb @ SV288 @ SY602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1129,plain,
! [SV352: $i,SV245: $i,SV288: $i] :
( ( ! [SY603: $i] :
( ~ ( contains_slb @ SV288 @ SY603 )
| ( contains_cpq @ ( triple @ SV245 @ SV288 @ SV352 ) @ SY603 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1130,plain,
! [SV353: $i,SV322: $i] :
( ( ( ~ ( pi_sharp_find_min @ ( i @ SV322 ) @ SV353 ) )
= $true )
| ( ( pi_find_min @ SV322 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1131,plain,
! [SV323: $i] :
( ( ( pi_find_min @ SV323 )
= $false )
| ( ( pi_sharp_find_min @ ( i @ SV323 ) @ ( sK6_V @ SV323 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1132,plain,
! [SV340: $i,SV324: $i] :
( ( ( ~ ( contains_pq @ SV324 @ SV340 )
| ~ ( issmallestelement_pq @ SV324 @ SV340 ) )
= $true )
| ( ( pi_sharp_find_min @ SV324 @ SV340 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1086]) ).
thf(1133,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1087]) ).
thf(1134,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_find_min @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1088]) ).
thf(1135,plain,
! [SV354: $i,SV289: $i,SV246: $i] :
( ( ! [SY604: $i] :
~ ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY604 ) ) @ SV354 )
| ( SV289 = SV354 )
| ( contains_slb @ SV246 @ SV354 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1136,plain,
! [SV246: $i,SV289: $i] :
( ( ~ ! [SY543: $i] :
( ( SV289 != SY543 )
| ! [SY544: $i] : ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY544 ) ) @ SY543 ) )
| ~ ! [SY545: $i] :
( ~ ( contains_slb @ SV246 @ SY545 )
| ! [SY546: $i] : ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY546 ) ) @ SY545 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1090]) ).
thf(1137,plain,
! [SV341: $i,SV325: $i] :
( ( ( ~ ( contains_pq @ SV325 @ SV341 ) )
= $true )
| ( ( pi_sharp_remove @ SV325 @ SV341 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1091]) ).
thf(1138,plain,
! [SV342: $i,SV326: $i] :
( ( ( ~ ( pi_sharp_remove @ SV326 @ SV342 ) )
= $true )
| ( ( contains_pq @ SV326 @ SV342 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1092]) ).
thf(1139,plain,
! [SV343: $i,SV327: $i] :
( ( ( ~ ( less_than @ SV327 @ SV343 )
| ( less_than @ SV343 @ SV327 ) )
= $true )
| ( ( strictly_less_than @ SV327 @ SV343 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1093]) ).
thf(1140,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1094]) ).
thf(1141,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1095]) ).
thf(1142,plain,
! [SV344: $i,SV328: $i] :
( ( ( ~ ( ~ ( contains_pq @ SV328 @ ( sK7_W @ SV344 @ SV328 ) )
| ~ ~ ( less_than @ SV344 @ ( sK7_W @ SV344 @ SV328 ) ) ) )
= $true )
| ( ( issmallestelement_pq @ SV328 @ SV344 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1096]) ).
thf(1143,plain,
! [SV345: $i,SV329: $i] :
( ( ( ~ ( issmallestelement_pq @ SV329 @ SV345 ) )
= $true )
| ( ( ! [SY600: $i] :
( ~ ( contains_pq @ SV329 @ SY600 )
| ( less_than @ SV345 @ SY600 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1097]) ).
thf(1144,plain,
! [SV346: $i,SV330: $i] :
( ( ( ~ ( contains_pq @ SV330 @ SV346 )
| ~ ( issmallestelement_pq @ SV330 @ SV346 ) )
= $true )
| ( ( pi_sharp_removemin @ SV330 @ SV346 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1098]) ).
thf(1145,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( contains_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1099]) ).
thf(1146,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pi_sharp_removemin @ SX0 @ SX1 )
| ( issmallestelement_pq @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1100]) ).
thf(1147,plain,
! [SV309: $i,SV290: $i,SV247: $i] :
( ( ~ ( ~ ! [SY573: $i,SY574: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY573 ) ) @ SV309 @ SY574 )
| ( SV290 = SV309 )
| ( pair_in_list @ SV247 @ SV309 @ SY574 ) )
| ~ ! [SY575: $i,SY576: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY575 ) ) @ SV309 @ SY576 )
| ( SY575 = SY576 )
| ( pair_in_list @ SV247 @ SV309 @ SY576 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1101]) ).
thf(1148,plain,
! [SV247: $i,SV309: $i,SV290: $i] :
( ( ~ ( ~ ! [SY577: $i,SY578: $i] :
( ( SV290 != SV309 )
| ( SY577 != SY578 )
| ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY577 ) ) @ SV309 @ SY578 ) )
| ~ ! [SY579: $i,SY580: $i] :
( ~ ( pair_in_list @ SV247 @ SV309 @ SY580 )
| ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY579 ) ) @ SV309 @ SY580 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1102]) ).
thf(1149,plain,
! [SV355: $i,SV347: $i,SV248: $i] :
( ( ~ ( contains_pq @ ( insert_pq @ SV248 @ SV347 ) @ SV355 )
| ( SV347 = SV355 )
| ( contains_pq @ SV248 @ SV355 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1150,plain,
! [SV248: $i] :
( ( ~ ! [SY492: $i,SY493: $i] :
( ( SY492 != SY493 )
| ( contains_pq @ ( insert_pq @ SV248 @ SY492 ) @ SY493 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1104]) ).
thf(1151,plain,
! [SV248: $i] :
( ( ~ ! [SY494: $i,SY495: $i] :
( ~ ( contains_pq @ SV248 @ SY495 )
| ( contains_pq @ ( insert_pq @ SV248 @ SY494 ) @ SY495 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1104]) ).
thf(1152,plain,
! [SV348: $i,SV331: $i] :
( ( ( ~ ( pi_remove @ SV331 @ SV348 ) )
= $true )
| ( ( pi_sharp_remove @ ( i @ SV331 ) @ SV348 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1105]) ).
thf(1153,plain,
! [SV349: $i,SV332: $i] :
( ( ( ~ ( pi_sharp_remove @ ( i @ SV332 ) @ SV349 ) )
= $true )
| ( ( pi_remove @ SV332 @ SV349 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1106]) ).
thf(1154,plain,
! [SV356: $i,SV333: $i] :
( ( ( ~ ( pi_sharp_find_min @ ( i @ SV333 ) @ SV356 ) )
= $true )
| ( ( pi_removemin @ SV333 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1155,plain,
! [SV334: $i] :
( ( ( pi_removemin @ SV334 )
= $false )
| ( ( pi_sharp_find_min @ ( i @ SV334 ) @ ( sK5_V @ SV334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1108]) ).
thf(1156,plain,
! [SV310: $i,SV291: $i,SV249: $i] :
( ( ! [SY581: $i,SY582: $i] :
( ~ ( less_than @ SY582 @ SY581 )
| ~ ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SV291 @ ( pair @ SY581 @ SY582 ) ) @ SV310 ) )
| ( check_cpq @ ( triple @ SV249 @ SV291 @ SV310 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1109]) ).
thf(1157,plain,
! [SV310: $i,SV291: $i,SV249: $i] :
( ( ! [SY583: $i,SY584: $i] :
( ~ ( less_than @ SY584 @ SY583 )
| ~ ( check_cpq @ ( triple @ SV249 @ SV291 @ SV310 ) )
| ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SV291 @ ( pair @ SY583 @ SY584 ) ) @ SV310 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1110]) ).
thf(1158,plain,
! [SV199: $i,SV292: $i,SV250: $i] :
( ( ( less_than @ SV250 @ SV292 )
= $false )
| ( ( less_than @ SV199 @ SV250 )
= $false )
| ( ( less_than @ SV199 @ SV292 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1159,plain,
! [SV297: $i,SV357: $i,SV263: $i,SV216: $i] :
( ( ( ( remove_slb @ ( insert_slb @ SV216 @ ( pair @ SV263 @ SV357 ) ) @ SV297 )
= ( insert_slb @ ( remove_slb @ SV216 @ SV297 ) @ ( pair @ SV263 @ SV357 ) ) )
= $true )
| ( ( SV263 = SV297 )
= $true )
| ( ( contains_slb @ SV216 @ SV297 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1160,plain,
! [SV299: $i,SV358: $i,SV265: $i,SV218: $i] :
( ( ( ( lookup_slb @ ( insert_slb @ SV218 @ ( pair @ SV265 @ SV358 ) ) @ SV299 )
= ( lookup_slb @ SV218 @ SV299 ) )
= $true )
| ( ( SV265 = SV299 )
= $true )
| ( ( contains_slb @ SV218 @ SV299 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1161,plain,
! [SV302: $i,SV273: $i,SV228: $i,SV337: $i,SV313: $i] :
( ( ( strictly_less_than @ SV313 @ SV337 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV228 @ ( insert_slb @ SV273 @ ( pair @ SV313 @ SV337 ) ) @ SV302 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1162,plain,
! [SV306: $i,SV233: $i,SV316: $i,SV278: $i] :
( ( ( contains_slb @ SV278 @ SV316 )
= $false )
| ( ( ~ ( less_than @ ( lookup_slb @ SV278 @ SV316 ) @ SV316 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV233 @ SV278 @ SV306 ) @ SV316 )
= ( triple @ ( remove_pqp @ SV233 @ SV316 ) @ ( remove_slb @ SV278 @ SV316 ) @ SV306 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1163,plain,
! [SV307: $i,SV234: $i,SV317: $i,SV279: $i] :
( ( ( contains_slb @ SV279 @ SV317 )
= $false )
| ( ( ~ ( strictly_less_than @ SV317 @ ( lookup_slb @ SV279 @ SV317 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV234 @ SV279 @ SV307 ) @ SV317 )
= ( triple @ ( remove_pqp @ SV234 @ SV317 ) @ ( remove_slb @ SV279 @ SV317 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1123]) ).
thf(1164,plain,
! [SV282: $i,SV237: $i] :
( ( ( strictly_less_than @ ( findmin_pqp_res @ SV237 ) @ ( lookup_slb @ SV282 @ ( findmin_pqp_res @ SV237 ) ) )
= $false )
| ( ( SV282 = create_slb )
= $true )
| ( ( contains_slb @ SV282 @ ( findmin_pqp_res @ SV237 ) )
= $false )
| ( ( ! [SY531: $i] :
( ( findmin_cpq_eff @ ( triple @ SV237 @ SV282 @ SY531 ) )
= ( triple @ SV237 @ ( update_slb @ SV282 @ ( findmin_pqp_res @ SV237 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1124]) ).
thf(1165,plain,
! [SV238: $i,SV283: $i] :
( ( ( less_than @ ( lookup_slb @ SV283 @ ( findmin_pqp_res @ SV238 ) ) @ ( findmin_pqp_res @ SV238 ) )
= $false )
| ( ( SV283 = create_slb )
= $true )
| ( ( contains_slb @ SV283 @ ( findmin_pqp_res @ SV238 ) )
= $false )
| ( ( ! [SY532: $i] :
( ( findmin_cpq_eff @ ( triple @ SV238 @ SV283 @ SY532 ) )
= ( triple @ SV238 @ ( update_slb @ SV283 @ ( findmin_pqp_res @ SV238 ) ) @ SY532 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1166,plain,
! [SV320: $i,SV350: $i] :
( ( ( ~ ( ok @ SV350 )
| ~ ( succ_cpq @ SV320 @ SV350 ) )
= $true )
| ( ( ~ ( check_cpq @ SV350 ) )
= $true )
| ( ( phi @ SV320 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1126]) ).
thf(1167,plain,
! [SV321: $i] :
( ( ( ~ ~ ( ~ ( ok @ ( sK4_V @ SV321 ) )
| ~ ( succ_cpq @ SV321 @ ( sK4_V @ SV321 ) ) )
| ~ ( check_cpq @ ( sK4_V @ SV321 ) ) )
= $false )
| ( ( phi @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1127]) ).
thf(1168,plain,
! [SV359: $i,SV351: $i,SV288: $i,SV245: $i] :
( ( ~ ( contains_cpq @ ( triple @ SV245 @ SV288 @ SV351 ) @ SV359 )
| ( contains_slb @ SV288 @ SV359 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1169,plain,
! [SV352: $i,SV245: $i,SV360: $i,SV288: $i] :
( ( ~ ( contains_slb @ SV288 @ SV360 )
| ( contains_cpq @ ( triple @ SV245 @ SV288 @ SV352 ) @ SV360 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1170,plain,
! [SV353: $i,SV322: $i] :
( ( ( pi_sharp_find_min @ ( i @ SV322 ) @ SV353 )
= $false )
| ( ( pi_find_min @ SV322 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1171,plain,
! [SV340: $i,SV324: $i] :
( ( ( ~ ( contains_pq @ SV324 @ SV340 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV324 @ SV340 ) )
= $true )
| ( ( pi_sharp_find_min @ SV324 @ SV340 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1132]) ).
thf(1172,plain,
! [SV361: $i] :
( ( ! [SY605: $i] :
( ~ ( pi_sharp_find_min @ SV361 @ SY605 )
| ( contains_pq @ SV361 @ SY605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1173,plain,
! [SV362: $i] :
( ( ! [SY606: $i] :
( ~ ( pi_sharp_find_min @ SV362 @ SY606 )
| ( issmallestelement_pq @ SV362 @ SY606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1174,plain,
! [SV354: $i,SV289: $i,SV246: $i] :
( ( ( ! [SY604: $i] :
~ ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY604 ) ) @ SV354 ) )
= $true )
| ( ( ( SV289 = SV354 )
| ( contains_slb @ SV246 @ SV354 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1135]) ).
thf(1175,plain,
! [SV246: $i,SV289: $i] :
( ( ~ ! [SY543: $i] :
( ( SV289 != SY543 )
| ! [SY544: $i] : ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY544 ) ) @ SY543 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1136]) ).
thf(1176,plain,
! [SV289: $i,SV246: $i] :
( ( ~ ! [SY545: $i] :
( ~ ( contains_slb @ SV246 @ SY545 )
| ! [SY546: $i] : ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY546 ) ) @ SY545 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1136]) ).
thf(1177,plain,
! [SV341: $i,SV325: $i] :
( ( ( contains_pq @ SV325 @ SV341 )
= $false )
| ( ( pi_sharp_remove @ SV325 @ SV341 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1178,plain,
! [SV342: $i,SV326: $i] :
( ( ( pi_sharp_remove @ SV326 @ SV342 )
= $false )
| ( ( contains_pq @ SV326 @ SV342 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1179,plain,
! [SV343: $i,SV327: $i] :
( ( ( ~ ( less_than @ SV327 @ SV343 ) )
= $true )
| ( ( less_than @ SV343 @ SV327 )
= $true )
| ( ( strictly_less_than @ SV327 @ SV343 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1139]) ).
thf(1180,plain,
! [SV363: $i] :
( ( ! [SY607: $i] :
( ~ ( strictly_less_than @ SV363 @ SY607 )
| ( less_than @ SV363 @ SY607 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1181,plain,
! [SV364: $i] :
( ( ! [SY608: $i] :
( ~ ( strictly_less_than @ SV364 @ SY608 )
| ~ ( less_than @ SY608 @ SV364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1182,plain,
! [SV344: $i,SV328: $i] :
( ( ( ~ ( contains_pq @ SV328 @ ( sK7_W @ SV344 @ SV328 ) )
| ~ ~ ( less_than @ SV344 @ ( sK7_W @ SV344 @ SV328 ) ) )
= $false )
| ( ( issmallestelement_pq @ SV328 @ SV344 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1142]) ).
thf(1183,plain,
! [SV345: $i,SV329: $i] :
( ( ( issmallestelement_pq @ SV329 @ SV345 )
= $false )
| ( ( ! [SY600: $i] :
( ~ ( contains_pq @ SV329 @ SY600 )
| ( less_than @ SV345 @ SY600 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1184,plain,
! [SV346: $i,SV330: $i] :
( ( ( ~ ( contains_pq @ SV330 @ SV346 ) )
= $true )
| ( ( ~ ( issmallestelement_pq @ SV330 @ SV346 ) )
= $true )
| ( ( pi_sharp_removemin @ SV330 @ SV346 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1144]) ).
thf(1185,plain,
! [SV365: $i] :
( ( ! [SY609: $i] :
( ~ ( pi_sharp_removemin @ SV365 @ SY609 )
| ( contains_pq @ SV365 @ SY609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1186,plain,
! [SV366: $i] :
( ( ! [SY610: $i] :
( ~ ( pi_sharp_removemin @ SV366 @ SY610 )
| ( issmallestelement_pq @ SV366 @ SY610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1187,plain,
! [SV309: $i,SV290: $i,SV247: $i] :
( ( ~ ! [SY573: $i,SY574: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY573 ) ) @ SV309 @ SY574 )
| ( SV290 = SV309 )
| ( pair_in_list @ SV247 @ SV309 @ SY574 ) )
| ~ ! [SY575: $i,SY576: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY575 ) ) @ SV309 @ SY576 )
| ( SY575 = SY576 )
| ( pair_in_list @ SV247 @ SV309 @ SY576 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1188,plain,
! [SV247: $i,SV309: $i,SV290: $i] :
( ( ~ ! [SY577: $i,SY578: $i] :
( ( SV290 != SV309 )
| ( SY577 != SY578 )
| ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY577 ) ) @ SV309 @ SY578 ) )
| ~ ! [SY579: $i,SY580: $i] :
( ~ ( pair_in_list @ SV247 @ SV309 @ SY580 )
| ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY579 ) ) @ SV309 @ SY580 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1189,plain,
! [SV355: $i,SV347: $i,SV248: $i] :
( ( ( ~ ( contains_pq @ ( insert_pq @ SV248 @ SV347 ) @ SV355 ) )
= $true )
| ( ( ( SV347 = SV355 )
| ( contains_pq @ SV248 @ SV355 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1149]) ).
thf(1190,plain,
! [SV248: $i] :
( ( ! [SY492: $i,SY493: $i] :
( ( SY492 != SY493 )
| ( contains_pq @ ( insert_pq @ SV248 @ SY492 ) @ SY493 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1150]) ).
thf(1191,plain,
! [SV248: $i] :
( ( ! [SY494: $i,SY495: $i] :
( ~ ( contains_pq @ SV248 @ SY495 )
| ( contains_pq @ ( insert_pq @ SV248 @ SY494 ) @ SY495 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1151]) ).
thf(1192,plain,
! [SV348: $i,SV331: $i] :
( ( ( pi_remove @ SV331 @ SV348 )
= $false )
| ( ( pi_sharp_remove @ ( i @ SV331 ) @ SV348 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1152]) ).
thf(1193,plain,
! [SV349: $i,SV332: $i] :
( ( ( pi_sharp_remove @ ( i @ SV332 ) @ SV349 )
= $false )
| ( ( pi_remove @ SV332 @ SV349 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1194,plain,
! [SV356: $i,SV333: $i] :
( ( ( pi_sharp_find_min @ ( i @ SV333 ) @ SV356 )
= $false )
| ( ( pi_removemin @ SV333 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1154]) ).
thf(1195,plain,
! [SV310: $i,SV291: $i,SV249: $i,SV367: $i] :
( ( ! [SY611: $i] :
( ~ ( less_than @ SY611 @ SV367 )
| ~ ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SV291 @ ( pair @ SV367 @ SY611 ) ) @ SV310 ) )
| ( check_cpq @ ( triple @ SV249 @ SV291 @ SV310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1196,plain,
! [SV310: $i,SV291: $i,SV249: $i,SV368: $i] :
( ( ! [SY612: $i] :
( ~ ( less_than @ SY612 @ SV368 )
| ~ ( check_cpq @ ( triple @ SV249 @ SV291 @ SV310 ) )
| ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SV291 @ ( pair @ SV368 @ SY612 ) ) @ SV310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1197,plain,
! [SV302: $i,SV337: $i,SV313: $i,SV273: $i,SV228: $i] :
( ( ( check_cpq @ ( triple @ SV228 @ ( insert_slb @ SV273 @ ( pair @ SV313 @ SV337 ) ) @ SV302 ) )
= $false )
| ( ( strictly_less_than @ SV313 @ SV337 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1198,plain,
! [SV306: $i,SV233: $i,SV316: $i,SV278: $i] :
( ( ( less_than @ ( lookup_slb @ SV278 @ SV316 ) @ SV316 )
= $false )
| ( ( contains_slb @ SV278 @ SV316 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV233 @ SV278 @ SV306 ) @ SV316 )
= ( triple @ ( remove_pqp @ SV233 @ SV316 ) @ ( remove_slb @ SV278 @ SV316 ) @ SV306 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1162]) ).
thf(1199,plain,
! [SV307: $i,SV234: $i,SV279: $i,SV317: $i] :
( ( ( strictly_less_than @ SV317 @ ( lookup_slb @ SV279 @ SV317 ) )
= $false )
| ( ( contains_slb @ SV279 @ SV317 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV234 @ SV279 @ SV307 ) @ SV317 )
= ( triple @ ( remove_pqp @ SV234 @ SV317 ) @ ( remove_slb @ SV279 @ SV317 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1163]) ).
thf(1200,plain,
! [SV369: $i,SV282: $i,SV237: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV237 @ SV282 @ SV369 ) )
= ( triple @ SV237 @ ( update_slb @ SV282 @ ( findmin_pqp_res @ SV237 ) ) @ bad ) )
= $true )
| ( ( contains_slb @ SV282 @ ( findmin_pqp_res @ SV237 ) )
= $false )
| ( ( SV282 = create_slb )
= $true )
| ( ( strictly_less_than @ ( findmin_pqp_res @ SV237 ) @ ( lookup_slb @ SV282 @ ( findmin_pqp_res @ SV237 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1201,plain,
! [SV370: $i,SV283: $i,SV238: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV238 @ SV283 @ SV370 ) )
= ( triple @ SV238 @ ( update_slb @ SV283 @ ( findmin_pqp_res @ SV238 ) ) @ SV370 ) )
= $true )
| ( ( contains_slb @ SV283 @ ( findmin_pqp_res @ SV238 ) )
= $false )
| ( ( SV283 = create_slb )
= $true )
| ( ( less_than @ ( lookup_slb @ SV283 @ ( findmin_pqp_res @ SV238 ) ) @ ( findmin_pqp_res @ SV238 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1202,plain,
! [SV320: $i,SV350: $i] :
( ( ( ~ ( ok @ SV350 ) )
= $true )
| ( ( ~ ( succ_cpq @ SV320 @ SV350 ) )
= $true )
| ( ( ~ ( check_cpq @ SV350 ) )
= $true )
| ( ( phi @ SV320 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1166]) ).
thf(1203,plain,
! [SV321: $i] :
( ( ( ~ ~ ( ~ ( ok @ ( sK4_V @ SV321 ) )
| ~ ( succ_cpq @ SV321 @ ( sK4_V @ SV321 ) ) ) )
= $false )
| ( ( phi @ SV321 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1167]) ).
thf(1204,plain,
! [SV321: $i] :
( ( ( ~ ( check_cpq @ ( sK4_V @ SV321 ) ) )
= $false )
| ( ( phi @ SV321 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1167]) ).
thf(1205,plain,
! [SV359: $i,SV351: $i,SV288: $i,SV245: $i] :
( ( ( ~ ( contains_cpq @ ( triple @ SV245 @ SV288 @ SV351 ) @ SV359 ) )
= $true )
| ( ( contains_slb @ SV288 @ SV359 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1168]) ).
thf(1206,plain,
! [SV352: $i,SV245: $i,SV360: $i,SV288: $i] :
( ( ( ~ ( contains_slb @ SV288 @ SV360 ) )
= $true )
| ( ( contains_cpq @ ( triple @ SV245 @ SV288 @ SV352 ) @ SV360 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1169]) ).
thf(1207,plain,
! [SV340: $i,SV324: $i] :
( ( ( contains_pq @ SV324 @ SV340 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV324 @ SV340 ) )
= $true )
| ( ( pi_sharp_find_min @ SV324 @ SV340 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1208,plain,
! [SV371: $i,SV361: $i] :
( ( ~ ( pi_sharp_find_min @ SV361 @ SV371 )
| ( contains_pq @ SV361 @ SV371 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1209,plain,
! [SV372: $i,SV362: $i] :
( ( ~ ( pi_sharp_find_min @ SV362 @ SV372 )
| ( issmallestelement_pq @ SV362 @ SV372 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1210,plain,
! [SV354: $i,SV373: $i,SV289: $i,SV246: $i] :
( ( ( ~ ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SV373 ) ) @ SV354 ) )
= $true )
| ( ( ( SV289 = SV354 )
| ( contains_slb @ SV246 @ SV354 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1211,plain,
! [SV246: $i,SV289: $i] :
( ( ! [SY543: $i] :
( ( SV289 != SY543 )
| ! [SY544: $i] : ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY544 ) ) @ SY543 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1175]) ).
thf(1212,plain,
! [SV289: $i,SV246: $i] :
( ( ! [SY545: $i] :
( ~ ( contains_slb @ SV246 @ SY545 )
| ! [SY546: $i] : ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY546 ) ) @ SY545 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1176]) ).
thf(1213,plain,
! [SV343: $i,SV327: $i] :
( ( ( less_than @ SV327 @ SV343 )
= $false )
| ( ( less_than @ SV343 @ SV327 )
= $true )
| ( ( strictly_less_than @ SV327 @ SV343 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1214,plain,
! [SV374: $i,SV363: $i] :
( ( ~ ( strictly_less_than @ SV363 @ SV374 )
| ( less_than @ SV363 @ SV374 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1215,plain,
! [SV375: $i,SV364: $i] :
( ( ~ ( strictly_less_than @ SV364 @ SV375 )
| ~ ( less_than @ SV375 @ SV364 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1216,plain,
! [SV344: $i,SV328: $i] :
( ( ( ~ ( contains_pq @ SV328 @ ( sK7_W @ SV344 @ SV328 ) ) )
= $false )
| ( ( issmallestelement_pq @ SV328 @ SV344 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1182]) ).
thf(1217,plain,
! [SV328: $i,SV344: $i] :
( ( ( ~ ~ ( less_than @ SV344 @ ( sK7_W @ SV344 @ SV328 ) ) )
= $false )
| ( ( issmallestelement_pq @ SV328 @ SV344 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1182]) ).
thf(1218,plain,
! [SV345: $i,SV376: $i,SV329: $i] :
( ( ( ~ ( contains_pq @ SV329 @ SV376 )
| ( less_than @ SV345 @ SV376 ) )
= $true )
| ( ( issmallestelement_pq @ SV329 @ SV345 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1219,plain,
! [SV346: $i,SV330: $i] :
( ( ( contains_pq @ SV330 @ SV346 )
= $false )
| ( ( ~ ( issmallestelement_pq @ SV330 @ SV346 ) )
= $true )
| ( ( pi_sharp_removemin @ SV330 @ SV346 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1220,plain,
! [SV377: $i,SV365: $i] :
( ( ~ ( pi_sharp_removemin @ SV365 @ SV377 )
| ( contains_pq @ SV365 @ SV377 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1221,plain,
! [SV378: $i,SV366: $i] :
( ( ~ ( pi_sharp_removemin @ SV366 @ SV378 )
| ( issmallestelement_pq @ SV366 @ SV378 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1222,plain,
! [SV309: $i,SV290: $i,SV247: $i] :
( ( ~ ! [SY573: $i,SY574: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY573 ) ) @ SV309 @ SY574 )
| ( SV290 = SV309 )
| ( pair_in_list @ SV247 @ SV309 @ SY574 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1187]) ).
thf(1223,plain,
! [SV309: $i,SV290: $i,SV247: $i] :
( ( ~ ! [SY575: $i,SY576: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY575 ) ) @ SV309 @ SY576 )
| ( SY575 = SY576 )
| ( pair_in_list @ SV247 @ SV309 @ SY576 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1187]) ).
thf(1224,plain,
! [SV247: $i,SV309: $i,SV290: $i] :
( ( ~ ! [SY577: $i,SY578: $i] :
( ( SV290 != SV309 )
| ( SY577 != SY578 )
| ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY577 ) ) @ SV309 @ SY578 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1188]) ).
thf(1225,plain,
! [SV290: $i,SV309: $i,SV247: $i] :
( ( ~ ! [SY579: $i,SY580: $i] :
( ~ ( pair_in_list @ SV247 @ SV309 @ SY580 )
| ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY579 ) ) @ SV309 @ SY580 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1188]) ).
thf(1226,plain,
! [SV355: $i,SV347: $i,SV248: $i] :
( ( ( contains_pq @ ( insert_pq @ SV248 @ SV347 ) @ SV355 )
= $false )
| ( ( ( SV347 = SV355 )
| ( contains_pq @ SV248 @ SV355 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1189]) ).
thf(1227,plain,
! [SV248: $i,SV379: $i] :
( ( ! [SY613: $i] :
( ( SV379 != SY613 )
| ( contains_pq @ ( insert_pq @ SV248 @ SV379 ) @ SY613 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1228,plain,
! [SV380: $i,SV248: $i] :
( ( ! [SY614: $i] :
( ~ ( contains_pq @ SV248 @ SY614 )
| ( contains_pq @ ( insert_pq @ SV248 @ SV380 ) @ SY614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1229,plain,
! [SV310: $i,SV291: $i,SV249: $i,SV367: $i,SV381: $i] :
( ( ~ ( less_than @ SV381 @ SV367 )
| ~ ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SV291 @ ( pair @ SV367 @ SV381 ) ) @ SV310 ) )
| ( check_cpq @ ( triple @ SV249 @ SV291 @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1230,plain,
! [SV310: $i,SV291: $i,SV249: $i,SV368: $i,SV382: $i] :
( ( ~ ( less_than @ SV382 @ SV368 )
| ~ ( check_cpq @ ( triple @ SV249 @ SV291 @ SV310 ) )
| ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SV291 @ ( pair @ SV368 @ SV382 ) ) @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1231,plain,
! [SV320: $i,SV350: $i] :
( ( ( ok @ SV350 )
= $false )
| ( ( ~ ( succ_cpq @ SV320 @ SV350 ) )
= $true )
| ( ( ~ ( check_cpq @ SV350 ) )
= $true )
| ( ( phi @ SV320 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1232,plain,
! [SV321: $i] :
( ( ( ~ ( ~ ( ok @ ( sK4_V @ SV321 ) )
| ~ ( succ_cpq @ SV321 @ ( sK4_V @ SV321 ) ) ) )
= $true )
| ( ( phi @ SV321 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1203]) ).
thf(1233,plain,
! [SV321: $i] :
( ( ( check_cpq @ ( sK4_V @ SV321 ) )
= $true )
| ( ( phi @ SV321 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1204]) ).
thf(1234,plain,
! [SV359: $i,SV351: $i,SV288: $i,SV245: $i] :
( ( ( contains_cpq @ ( triple @ SV245 @ SV288 @ SV351 ) @ SV359 )
= $false )
| ( ( contains_slb @ SV288 @ SV359 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1235,plain,
! [SV352: $i,SV245: $i,SV360: $i,SV288: $i] :
( ( ( contains_slb @ SV288 @ SV360 )
= $false )
| ( ( contains_cpq @ ( triple @ SV245 @ SV288 @ SV352 ) @ SV360 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1236,plain,
! [SV340: $i,SV324: $i] :
( ( ( issmallestelement_pq @ SV324 @ SV340 )
= $false )
| ( ( contains_pq @ SV324 @ SV340 )
= $false )
| ( ( pi_sharp_find_min @ SV324 @ SV340 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1237,plain,
! [SV371: $i,SV361: $i] :
( ( ( ~ ( pi_sharp_find_min @ SV361 @ SV371 ) )
= $true )
| ( ( contains_pq @ SV361 @ SV371 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1238,plain,
! [SV372: $i,SV362: $i] :
( ( ( ~ ( pi_sharp_find_min @ SV362 @ SV372 ) )
= $true )
| ( ( issmallestelement_pq @ SV362 @ SV372 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1239,plain,
! [SV354: $i,SV373: $i,SV289: $i,SV246: $i] :
( ( ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SV373 ) ) @ SV354 )
= $false )
| ( ( ( SV289 = SV354 )
| ( contains_slb @ SV246 @ SV354 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1210]) ).
thf(1240,plain,
! [SV246: $i,SV383: $i,SV289: $i] :
( ( ( SV289 != SV383 )
| ! [SY615: $i] : ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY615 ) ) @ SV383 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1241,plain,
! [SV289: $i,SV384: $i,SV246: $i] :
( ( ~ ( contains_slb @ SV246 @ SV384 )
| ! [SY616: $i] : ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY616 ) ) @ SV384 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1242,plain,
! [SV374: $i,SV363: $i] :
( ( ( ~ ( strictly_less_than @ SV363 @ SV374 ) )
= $true )
| ( ( less_than @ SV363 @ SV374 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1214]) ).
thf(1243,plain,
! [SV375: $i,SV364: $i] :
( ( ( ~ ( strictly_less_than @ SV364 @ SV375 ) )
= $true )
| ( ( ~ ( less_than @ SV375 @ SV364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1215]) ).
thf(1244,plain,
! [SV344: $i,SV328: $i] :
( ( ( contains_pq @ SV328 @ ( sK7_W @ SV344 @ SV328 ) )
= $true )
| ( ( issmallestelement_pq @ SV328 @ SV344 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1216]) ).
thf(1245,plain,
! [SV328: $i,SV344: $i] :
( ( ( ~ ( less_than @ SV344 @ ( sK7_W @ SV344 @ SV328 ) ) )
= $true )
| ( ( issmallestelement_pq @ SV328 @ SV344 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1217]) ).
thf(1246,plain,
! [SV345: $i,SV376: $i,SV329: $i] :
( ( ( ~ ( contains_pq @ SV329 @ SV376 ) )
= $true )
| ( ( less_than @ SV345 @ SV376 )
= $true )
| ( ( issmallestelement_pq @ SV329 @ SV345 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1218]) ).
thf(1247,plain,
! [SV346: $i,SV330: $i] :
( ( ( issmallestelement_pq @ SV330 @ SV346 )
= $false )
| ( ( contains_pq @ SV330 @ SV346 )
= $false )
| ( ( pi_sharp_removemin @ SV330 @ SV346 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1248,plain,
! [SV377: $i,SV365: $i] :
( ( ( ~ ( pi_sharp_removemin @ SV365 @ SV377 ) )
= $true )
| ( ( contains_pq @ SV365 @ SV377 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1220]) ).
thf(1249,plain,
! [SV378: $i,SV366: $i] :
( ( ( ~ ( pi_sharp_removemin @ SV366 @ SV378 ) )
= $true )
| ( ( issmallestelement_pq @ SV366 @ SV378 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1221]) ).
thf(1250,plain,
! [SV309: $i,SV290: $i,SV247: $i] :
( ( ! [SY573: $i,SY574: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY573 ) ) @ SV309 @ SY574 )
| ( SV290 = SV309 )
| ( pair_in_list @ SV247 @ SV309 @ SY574 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1222]) ).
thf(1251,plain,
! [SV309: $i,SV290: $i,SV247: $i] :
( ( ! [SY575: $i,SY576: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY575 ) ) @ SV309 @ SY576 )
| ( SY575 = SY576 )
| ( pair_in_list @ SV247 @ SV309 @ SY576 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1223]) ).
thf(1252,plain,
! [SV247: $i,SV309: $i,SV290: $i] :
( ( ! [SY577: $i,SY578: $i] :
( ( SV290 != SV309 )
| ( SY577 != SY578 )
| ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY577 ) ) @ SV309 @ SY578 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1224]) ).
thf(1253,plain,
! [SV290: $i,SV309: $i,SV247: $i] :
( ( ! [SY579: $i,SY580: $i] :
( ~ ( pair_in_list @ SV247 @ SV309 @ SY580 )
| ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SY579 ) ) @ SV309 @ SY580 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1225]) ).
thf(1254,plain,
! [SV248: $i,SV355: $i,SV347: $i] :
( ( ( SV347 = SV355 )
= $true )
| ( ( contains_pq @ SV248 @ SV355 )
= $true )
| ( ( contains_pq @ ( insert_pq @ SV248 @ SV347 ) @ SV355 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1226]) ).
thf(1255,plain,
! [SV248: $i,SV385: $i,SV379: $i] :
( ( ( SV379 != SV385 )
| ( contains_pq @ ( insert_pq @ SV248 @ SV379 ) @ SV385 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1256,plain,
! [SV380: $i,SV386: $i,SV248: $i] :
( ( ~ ( contains_pq @ SV248 @ SV386 )
| ( contains_pq @ ( insert_pq @ SV248 @ SV380 ) @ SV386 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1257,plain,
! [SV310: $i,SV291: $i,SV249: $i,SV367: $i,SV381: $i] :
( ( ( ~ ( less_than @ SV381 @ SV367 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SV291 @ ( pair @ SV367 @ SV381 ) ) @ SV310 ) )
| ( check_cpq @ ( triple @ SV249 @ SV291 @ SV310 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1229]) ).
thf(1258,plain,
! [SV310: $i,SV291: $i,SV249: $i,SV368: $i,SV382: $i] :
( ( ( ~ ( less_than @ SV382 @ SV368 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV249 @ SV291 @ SV310 ) )
| ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SV291 @ ( pair @ SV368 @ SV382 ) ) @ SV310 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1230]) ).
thf(1259,plain,
! [SV350: $i,SV320: $i] :
( ( ( succ_cpq @ SV320 @ SV350 )
= $false )
| ( ( ok @ SV350 )
= $false )
| ( ( ~ ( check_cpq @ SV350 ) )
= $true )
| ( ( phi @ SV320 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1260,plain,
! [SV321: $i] :
( ( ( ~ ( ok @ ( sK4_V @ SV321 ) )
| ~ ( succ_cpq @ SV321 @ ( sK4_V @ SV321 ) ) )
= $false )
| ( ( phi @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1261,plain,
! [SV371: $i,SV361: $i] :
( ( ( pi_sharp_find_min @ SV361 @ SV371 )
= $false )
| ( ( contains_pq @ SV361 @ SV371 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1262,plain,
! [SV372: $i,SV362: $i] :
( ( ( pi_sharp_find_min @ SV362 @ SV372 )
= $false )
| ( ( issmallestelement_pq @ SV362 @ SV372 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1238]) ).
thf(1263,plain,
! [SV373: $i,SV246: $i,SV354: $i,SV289: $i] :
( ( ( SV289 = SV354 )
= $true )
| ( ( contains_slb @ SV246 @ SV354 )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SV373 ) ) @ SV354 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1264,plain,
! [SV246: $i,SV383: $i,SV289: $i] :
( ( ( ( SV289 != SV383 ) )
= $true )
| ( ( ! [SY615: $i] : ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY615 ) ) @ SV383 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1240]) ).
thf(1265,plain,
! [SV289: $i,SV384: $i,SV246: $i] :
( ( ( ~ ( contains_slb @ SV246 @ SV384 ) )
= $true )
| ( ( ! [SY616: $i] : ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY616 ) ) @ SV384 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1241]) ).
thf(1266,plain,
! [SV374: $i,SV363: $i] :
( ( ( strictly_less_than @ SV363 @ SV374 )
= $false )
| ( ( less_than @ SV363 @ SV374 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1267,plain,
! [SV375: $i,SV364: $i] :
( ( ( strictly_less_than @ SV364 @ SV375 )
= $false )
| ( ( ~ ( less_than @ SV375 @ SV364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1243]) ).
thf(1268,plain,
! [SV328: $i,SV344: $i] :
( ( ( less_than @ SV344 @ ( sK7_W @ SV344 @ SV328 ) )
= $false )
| ( ( issmallestelement_pq @ SV328 @ SV344 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1245]) ).
thf(1269,plain,
! [SV345: $i,SV376: $i,SV329: $i] :
( ( ( contains_pq @ SV329 @ SV376 )
= $false )
| ( ( less_than @ SV345 @ SV376 )
= $true )
| ( ( issmallestelement_pq @ SV329 @ SV345 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1246]) ).
thf(1270,plain,
! [SV377: $i,SV365: $i] :
( ( ( pi_sharp_removemin @ SV365 @ SV377 )
= $false )
| ( ( contains_pq @ SV365 @ SV377 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1248]) ).
thf(1271,plain,
! [SV378: $i,SV366: $i] :
( ( ( pi_sharp_removemin @ SV366 @ SV378 )
= $false )
| ( ( issmallestelement_pq @ SV366 @ SV378 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1249]) ).
thf(1272,plain,
! [SV309: $i,SV387: $i,SV290: $i,SV247: $i] :
( ( ! [SY617: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SV387 ) ) @ SV309 @ SY617 )
| ( SV290 = SV309 )
| ( pair_in_list @ SV247 @ SV309 @ SY617 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1273,plain,
! [SV309: $i,SV388: $i,SV290: $i,SV247: $i] :
( ( ! [SY618: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SV388 ) ) @ SV309 @ SY618 )
| ( SV388 = SY618 )
| ( pair_in_list @ SV247 @ SV309 @ SY618 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1274,plain,
! [SV247: $i,SV389: $i,SV309: $i,SV290: $i] :
( ( ! [SY619: $i] :
( ( SV290 != SV309 )
| ( SV389 != SY619 )
| ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SV389 ) ) @ SV309 @ SY619 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1275,plain,
! [SV390: $i,SV290: $i,SV309: $i,SV247: $i] :
( ( ! [SY620: $i] :
( ~ ( pair_in_list @ SV247 @ SV309 @ SY620 )
| ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SV390 ) ) @ SV309 @ SY620 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1276,plain,
! [SV248: $i,SV385: $i,SV379: $i] :
( ( ( ( SV379 != SV385 ) )
= $true )
| ( ( contains_pq @ ( insert_pq @ SV248 @ SV379 ) @ SV385 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1255]) ).
thf(1277,plain,
! [SV380: $i,SV386: $i,SV248: $i] :
( ( ( ~ ( contains_pq @ SV248 @ SV386 ) )
= $true )
| ( ( contains_pq @ ( insert_pq @ SV248 @ SV380 ) @ SV386 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1256]) ).
thf(1278,plain,
! [SV310: $i,SV291: $i,SV249: $i,SV367: $i,SV381: $i] :
( ( ( less_than @ SV381 @ SV367 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SV291 @ ( pair @ SV367 @ SV381 ) ) @ SV310 ) )
| ( check_cpq @ ( triple @ SV249 @ SV291 @ SV310 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1257]) ).
thf(1279,plain,
! [SV310: $i,SV291: $i,SV249: $i,SV368: $i,SV382: $i] :
( ( ( less_than @ SV382 @ SV368 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV249 @ SV291 @ SV310 ) )
| ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SV291 @ ( pair @ SV368 @ SV382 ) ) @ SV310 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1258]) ).
thf(1280,plain,
! [SV320: $i,SV350: $i] :
( ( ( check_cpq @ SV350 )
= $false )
| ( ( ok @ SV350 )
= $false )
| ( ( succ_cpq @ SV320 @ SV350 )
= $false )
| ( ( phi @ SV320 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1259]) ).
thf(1281,plain,
! [SV321: $i] :
( ( ( ~ ( ok @ ( sK4_V @ SV321 ) ) )
= $false )
| ( ( phi @ SV321 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1260]) ).
thf(1282,plain,
! [SV321: $i] :
( ( ( ~ ( succ_cpq @ SV321 @ ( sK4_V @ SV321 ) ) )
= $false )
| ( ( phi @ SV321 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1260]) ).
thf(1283,plain,
! [SV246: $i,SV383: $i,SV289: $i] :
( ( ( SV289 = SV383 )
= $false )
| ( ( ! [SY615: $i] : ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY615 ) ) @ SV383 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1264]) ).
thf(1284,plain,
! [SV289: $i,SV384: $i,SV246: $i] :
( ( ( contains_slb @ SV246 @ SV384 )
= $false )
| ( ( ! [SY616: $i] : ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SY616 ) ) @ SV384 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1285,plain,
! [SV364: $i,SV375: $i] :
( ( ( less_than @ SV375 @ SV364 )
= $false )
| ( ( strictly_less_than @ SV364 @ SV375 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1267]) ).
thf(1286,plain,
! [SV391: $i,SV309: $i,SV387: $i,SV290: $i,SV247: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SV387 ) ) @ SV309 @ SV391 )
| ( SV290 = SV309 )
| ( pair_in_list @ SV247 @ SV309 @ SV391 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1287,plain,
! [SV392: $i,SV309: $i,SV388: $i,SV290: $i,SV247: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SV388 ) ) @ SV309 @ SV392 )
| ( SV388 = SV392 )
| ( pair_in_list @ SV247 @ SV309 @ SV392 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1288,plain,
! [SV247: $i,SV393: $i,SV389: $i,SV309: $i,SV290: $i] :
( ( ( SV290 != SV309 )
| ( SV389 != SV393 )
| ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SV389 ) ) @ SV309 @ SV393 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1289,plain,
! [SV390: $i,SV290: $i,SV394: $i,SV309: $i,SV247: $i] :
( ( ~ ( pair_in_list @ SV247 @ SV309 @ SV394 )
| ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SV390 ) ) @ SV309 @ SV394 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1290,plain,
! [SV248: $i,SV385: $i,SV379: $i] :
( ( ( SV379 = SV385 )
= $false )
| ( ( contains_pq @ ( insert_pq @ SV248 @ SV379 ) @ SV385 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1276]) ).
thf(1291,plain,
! [SV380: $i,SV386: $i,SV248: $i] :
( ( ( contains_pq @ SV248 @ SV386 )
= $false )
| ( ( contains_pq @ ( insert_pq @ SV248 @ SV380 ) @ SV386 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1292,plain,
! [SV310: $i,SV381: $i,SV367: $i,SV291: $i,SV249: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SV291 @ ( pair @ SV367 @ SV381 ) ) @ SV310 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV249 @ SV291 @ SV310 ) )
= $true )
| ( ( less_than @ SV381 @ SV367 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1278]) ).
thf(1293,plain,
! [SV382: $i,SV368: $i,SV310: $i,SV291: $i,SV249: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV249 @ SV291 @ SV310 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SV291 @ ( pair @ SV368 @ SV382 ) ) @ SV310 ) )
= $true )
| ( ( less_than @ SV382 @ SV368 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1279]) ).
thf(1294,plain,
! [SV321: $i] :
( ( ( ok @ ( sK4_V @ SV321 ) )
= $true )
| ( ( phi @ SV321 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1281]) ).
thf(1295,plain,
! [SV321: $i] :
( ( ( succ_cpq @ SV321 @ ( sK4_V @ SV321 ) )
= $true )
| ( ( phi @ SV321 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1282]) ).
thf(1296,plain,
! [SV383: $i,SV395: $i,SV289: $i,SV246: $i] :
( ( ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SV395 ) ) @ SV383 )
= $true )
| ( ( SV289 = SV383 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1297,plain,
! [SV384: $i,SV396: $i,SV289: $i,SV246: $i] :
( ( ( contains_slb @ ( insert_slb @ SV246 @ ( pair @ SV289 @ SV396 ) ) @ SV384 )
= $true )
| ( ( contains_slb @ SV246 @ SV384 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1298,plain,
! [SV391: $i,SV309: $i,SV387: $i,SV290: $i,SV247: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SV387 ) ) @ SV309 @ SV391 ) )
= $true )
| ( ( ( SV290 = SV309 )
| ( pair_in_list @ SV247 @ SV309 @ SV391 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1286]) ).
thf(1299,plain,
! [SV392: $i,SV309: $i,SV388: $i,SV290: $i,SV247: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SV388 ) ) @ SV309 @ SV392 ) )
= $true )
| ( ( ( SV388 = SV392 )
| ( pair_in_list @ SV247 @ SV309 @ SV392 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1287]) ).
thf(1300,plain,
! [SV247: $i,SV393: $i,SV389: $i,SV309: $i,SV290: $i] :
( ( ( ( SV290 != SV309 )
| ( SV389 != SV393 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SV389 ) ) @ SV309 @ SV393 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1288]) ).
thf(1301,plain,
! [SV390: $i,SV290: $i,SV394: $i,SV309: $i,SV247: $i] :
( ( ( ~ ( pair_in_list @ SV247 @ SV309 @ SV394 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SV390 ) ) @ SV309 @ SV394 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1289]) ).
thf(1302,plain,
! [SV310: $i,SV381: $i,SV367: $i,SV291: $i,SV249: $i] :
( ( ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SV291 @ ( pair @ SV367 @ SV381 ) ) @ SV310 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV249 @ SV291 @ SV310 ) )
= $true )
| ( ( less_than @ SV381 @ SV367 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1292]) ).
thf(1303,plain,
! [SV382: $i,SV368: $i,SV310: $i,SV291: $i,SV249: $i] :
( ( ( check_cpq @ ( triple @ SV249 @ SV291 @ SV310 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV249 @ ( insert_slb @ SV291 @ ( pair @ SV368 @ SV382 ) ) @ SV310 ) )
= $true )
| ( ( less_than @ SV382 @ SV368 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1304,plain,
! [SV391: $i,SV309: $i,SV387: $i,SV290: $i,SV247: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SV387 ) ) @ SV309 @ SV391 )
= $false )
| ( ( ( SV290 = SV309 )
| ( pair_in_list @ SV247 @ SV309 @ SV391 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1298]) ).
thf(1305,plain,
! [SV392: $i,SV309: $i,SV388: $i,SV290: $i,SV247: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SV388 ) ) @ SV309 @ SV392 )
= $false )
| ( ( ( SV388 = SV392 )
| ( pair_in_list @ SV247 @ SV309 @ SV392 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1299]) ).
thf(1306,plain,
! [SV247: $i,SV393: $i,SV389: $i,SV309: $i,SV290: $i] :
( ( ( ( SV290 != SV309 ) )
= $true )
| ( ( ( SV389 != SV393 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SV389 ) ) @ SV309 @ SV393 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1300]) ).
thf(1307,plain,
! [SV390: $i,SV290: $i,SV394: $i,SV309: $i,SV247: $i] :
( ( ( pair_in_list @ SV247 @ SV309 @ SV394 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SV390 ) ) @ SV309 @ SV394 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1301]) ).
thf(1308,plain,
! [SV387: $i,SV391: $i,SV247: $i,SV309: $i,SV290: $i] :
( ( ( SV290 = SV309 )
= $true )
| ( ( pair_in_list @ SV247 @ SV309 @ SV391 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SV387 ) ) @ SV309 @ SV391 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1304]) ).
thf(1309,plain,
! [SV290: $i,SV309: $i,SV247: $i,SV392: $i,SV388: $i] :
( ( ( SV388 = SV392 )
= $true )
| ( ( pair_in_list @ SV247 @ SV309 @ SV392 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SV388 ) ) @ SV309 @ SV392 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1305]) ).
thf(1310,plain,
! [SV247: $i,SV393: $i,SV389: $i,SV309: $i,SV290: $i] :
( ( ( SV290 = SV309 )
= $false )
| ( ( ( SV389 != SV393 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SV389 ) ) @ SV309 @ SV393 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1306]) ).
thf(1311,plain,
! [SV247: $i,SV309: $i,SV290: $i,SV393: $i,SV389: $i] :
( ( ( SV389 = SV393 )
= $false )
| ( ( SV290 = SV309 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV247 @ ( pair @ SV290 @ SV389 ) ) @ SV309 @ SV393 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1312,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[824,1311,1309,1308,1307,1303,1302,1297,1296,1295,1294,1291,1290,1285,1280,1271,1270,1269,1268,1266,1263,1262,1261,1254,1247,1244,1236,1235,1234,1233,1213,1201,1200,1199,1198,1197,1194,1193,1192,1178,1177,1170,1160,1159,1158,1155,1131,1120,1119,1116,1115,1114,1113,1112,1079,1076,1073,1071,1070,1051,1031,1024,1023,1021,1020,998,971,962,960,959,958,957,951,923,921,917,909,897,889,888,887,867,866,847,844,836,826,825]) ).
thf(1313,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1312,743]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWV369+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.11 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Wed Jun 15 22:03:59 EDT 2022
% 0.16/0.31 % CPUTime :
% 0.16/0.34 .
% 0.16/0.36
% 0.16/0.36 No.of.Axioms: 62
% 0.16/0.36
% 0.16/0.36 Length.of.Defs: 0
% 0.16/0.36
% 0.16/0.36 Contains.Choice.Funs: false
% 0.16/0.38 ..
% 0.16/0.40 (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)...............................................................................
% 0.67/0.89
% 0.67/0.89 ********************************
% 0.67/0.89 * All subproblems solved! *
% 0.67/0.89 ********************************
% 0.67/0.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:1312,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.27/1.47
% 1.27/1.47 %**** Beginning of derivation protocol ****
% 1.27/1.47 % SZS output start CNFRefutation
% See solution above
% 1.27/1.47
% 1.27/1.47 %**** End of derivation protocol ****
% 1.27/1.47 %**** no. of clauses in derivation: 1313 ****
% 1.27/1.47 %**** clause counter: 1312 ****
% 1.27/1.47
% 1.27/1.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (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:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:1312,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------