%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV378+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:57:31 AM UTC 2026
% Result : Theorem 13.46s 2.54s
% Output : CNFRefutation 13.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 42
% Syntax : Number of formulae : 459 ( 281 unt; 0 typ; 0 def)
% Number of atoms : 2512 (1031 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 6421 ( 980 ~; 656 |; 36 &;4664 @)
% ( 21 <=>; 64 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 9 con; 0-3 aty)
% Number of variables : 1497 ( 0 ^;1497 !; 0 ?;1497 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_bad,type,
bad: $i ).
thf(tp_bottom,type,
bottom: $i ).
thf(tp_check_cpq,type,
check_cpq: $i > $o ).
thf(tp_contains_cpq,type,
contains_cpq: $i > $i > $o ).
thf(tp_contains_slb,type,
contains_slb: $i > $i > $o ).
thf(tp_create_slb,type,
create_slb: $i ).
thf(tp_findmin_cpq_eff,type,
findmin_cpq_eff: $i > $i ).
thf(tp_findmin_cpq_res,type,
findmin_cpq_res: $i > $i ).
thf(tp_findmin_pqp_res,type,
findmin_pqp_res: $i > $i ).
thf(tp_insert_cpq,type,
insert_cpq: $i > $i > $i ).
thf(tp_insert_pqp,type,
insert_pqp: $i > $i > $i ).
thf(tp_insert_slb,type,
insert_slb: $i > $i > $i ).
thf(tp_isnonempty_slb,type,
isnonempty_slb: $i > $o ).
thf(tp_less_than,type,
less_than: $i > $i > $o ).
thf(tp_lookup_slb,type,
lookup_slb: $i > $i > $i ).
thf(tp_ok,type,
ok: $i > $o ).
thf(tp_pair,type,
pair: $i > $i > $i ).
thf(tp_pair_in_list,type,
pair_in_list: $i > $i > $i > $o ).
thf(tp_remove_cpq,type,
remove_cpq: $i > $i > $i ).
thf(tp_remove_pqp,type,
remove_pqp: $i > $i > $i ).
thf(tp_remove_slb,type,
remove_slb: $i > $i > $i ).
thf(tp_removemin_cpq_eff,type,
removemin_cpq_eff: $i > $i ).
thf(tp_removemin_cpq_res,type,
removemin_cpq_res: $i > $i ).
thf(tp_sK1_U,type,
sK1_U: $i ).
thf(tp_sK2_SY121,type,
sK2_SY121: $i ).
thf(tp_sK3_SY124,type,
sK3_SY124: $i ).
thf(tp_sK4_SY126,type,
sK4_SY126: $i ).
thf(tp_strictly_less_than,type,
strictly_less_than: $i > $i > $o ).
thf(tp_succ_cpq,type,
succ_cpq: $i > $i > $o ).
thf(tp_triple,type,
triple: $i > $i > $i > $i ).
thf(tp_update_slb,type,
update_slb: $i > $i > $i ).
thf(1,axiom,
! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).
thf(2,axiom,
! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
thf(3,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( V != create_slb )
=> ( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
= ( findmin_pqp_res @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).
thf(4,axiom,
! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax50) ).
thf(5,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != create_slb )
& ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
& ( less_than @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) @ ( findmin_pqp_res @ U ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).
thf(6,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != create_slb )
& ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
& ( strictly_less_than @ ( findmin_pqp_res @ U ) @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax48) ).
thf(7,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != create_slb )
& ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax47) ).
thf(8,axiom,
! [U: $i,V: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ create_slb @ V ) )
= ( triple @ U @ create_slb @ bad ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).
thf(9,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( contains_slb @ V @ X )
& ( strictly_less_than @ X @ ( lookup_slb @ V @ X ) ) )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ bad ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).
thf(10,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( contains_slb @ V @ X )
& ( less_than @ ( lookup_slb @ V @ X ) @ X ) )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax44) ).
thf(11,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ U @ V @ bad ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax43) ).
thf(12,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( insert_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( insert_pqp @ U @ X ) @ ( insert_slb @ V @ ( pair @ X @ bottom ) ) @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).
thf(13,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ( W = bad ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax41) ).
thf(14,axiom,
! [U: $i,V: $i] :
( ( ok @ ( triple @ U @ V @ bad ) )
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax40) ).
thf(15,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
<=> ( contains_slb @ V @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
thf(16,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( strictly_less_than @ X @ Y )
=> ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
<=> $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
thf(17,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( less_than @ Y @ X )
=> ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
<=> ( check_cpq @ ( triple @ U @ V @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax37) ).
thf(18,axiom,
! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).
thf(19,axiom,
! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax35) ).
thf(20,axiom,
! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax34) ).
thf(21,axiom,
! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax33) ).
thf(22,axiom,
! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax32) ).
thf(23,axiom,
! [U: $i] : ( succ_cpq @ U @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).
thf(24,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( less_than @ W @ X )
=> ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax30) ).
thf(25,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( strictly_less_than @ X @ W )
=> ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax29) ).
thf(26,axiom,
! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
thf(27,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != W )
& ( contains_slb @ U @ W ) )
=> ( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( lookup_slb @ U @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax27) ).
thf(28,axiom,
! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
thf(29,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != W )
& ( contains_slb @ U @ W ) )
=> ( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( remove_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).
thf(30,axiom,
! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
thf(31,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
<=> ( ( pair_in_list @ U @ W @ Y )
| ( ( V = W )
& ( X = Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
thf(32,axiom,
! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
thf(33,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
<=> ( ( contains_slb @ U @ W )
| ( V = W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
thf(34,axiom,
! [U: $i] :
~ ( contains_slb @ create_slb @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
thf(35,axiom,
! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax19) ).
thf(36,axiom,
~ ( isnonempty_slb @ create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
thf(37,axiom,
! [U: $i] : ( less_than @ bottom @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bottom_smallest) ).
thf(38,axiom,
! [U: $i,V: $i] :
( ( strictly_less_than @ U @ V )
<=> ( ( less_than @ U @ V )
& ~ ( less_than @ V @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).
thf(39,axiom,
! [U: $i] : ( less_than @ U @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(40,axiom,
! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
thf(41,axiom,
! [U: $i,V: $i,W: $i] :
( ( ( less_than @ U @ V )
& ( less_than @ V @ W ) )
=> ( less_than @ U @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(42,conjecture,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ~ ( ok @ ( remove_cpq @ ( triple @ U @ V @ W ) @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l14_co) ).
thf(43,negated_conjecture,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ~ ( ok @ ( remove_cpq @ ( triple @ U @ V @ W ) @ X ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[42]) ).
thf(44,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ~ ( ok @ ( remove_cpq @ ( triple @ U @ V @ W ) @ X ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[43]) ).
thf(45,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(46,plain,
( ( ! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(47,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( V != create_slb )
=> ( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
= ( findmin_pqp_res @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(48,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(49,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != create_slb )
& ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
& ( less_than @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) @ ( findmin_pqp_res @ U ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(50,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != create_slb )
& ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
& ( strictly_less_than @ ( findmin_pqp_res @ U ) @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(51,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != create_slb )
& ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(52,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ create_slb @ V ) )
= ( triple @ U @ create_slb @ bad ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(53,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( contains_slb @ V @ X )
& ( strictly_less_than @ X @ ( lookup_slb @ V @ X ) ) )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ bad ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(54,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( contains_slb @ V @ X )
& ( less_than @ ( lookup_slb @ V @ X ) @ X ) )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(55,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ U @ V @ bad ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(56,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( insert_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( insert_pqp @ U @ X ) @ ( insert_slb @ V @ ( pair @ X @ bottom ) ) @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(57,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ( W = bad ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(58,plain,
( ( ! [U: $i,V: $i] :
( ( ok @ ( triple @ U @ V @ bad ) )
<=> $false ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(59,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
<=> ( contains_slb @ V @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(60,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( strictly_less_than @ X @ Y )
=> ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
<=> $false ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(61,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( less_than @ Y @ X )
=> ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
<=> ( check_cpq @ ( triple @ U @ V @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(62,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(63,plain,
( ( ! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(64,plain,
( ( ! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(65,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(66,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(67,plain,
( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(68,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( less_than @ W @ X )
=> ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(69,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( strictly_less_than @ X @ W )
=> ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(70,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(71,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != W )
& ( contains_slb @ U @ W ) )
=> ( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( lookup_slb @ U @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(72,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(73,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != W )
& ( contains_slb @ U @ W ) )
=> ( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( remove_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(74,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(75,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
<=> ( ( pair_in_list @ U @ W @ Y )
| ( ( V = W )
& ( X = Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(76,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(77,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
<=> ( ( contains_slb @ U @ W )
| ( V = W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(78,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(79,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(80,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(81,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(82,plain,
( ( ! [U: $i,V: $i] :
( ( strictly_less_than @ U @ V )
<=> ( ( less_than @ U @ V )
& ~ ( less_than @ V @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(83,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(84,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(85,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( less_than @ U @ V )
& ( less_than @ V @ W ) )
=> ( less_than @ U @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(86,plain,
( ( ! [SY121: $i,SY122: $i,SY123: $i] :
( ~ ( ok @ ( triple @ sK1_U @ SY121 @ SY122 ) )
=> ~ ( ok @ ( remove_cpq @ ( triple @ sK1_U @ SY121 @ SY122 ) @ SY123 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(87,plain,
( ( ! [SY124: $i,SY125: $i] :
( ~ ( ok @ ( triple @ sK1_U @ sK2_SY121 @ SY124 ) )
=> ~ ( ok @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY121 @ SY124 ) @ SY125 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[86]) ).
thf(88,plain,
( ( ! [SY126: $i] :
( ~ ( ok @ ( triple @ sK1_U @ sK2_SY121 @ sK3_SY124 ) )
=> ~ ( ok @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY121 @ sK3_SY124 ) @ SY126 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[87]) ).
thf(89,plain,
( ( ~ ( ok @ ( triple @ sK1_U @ sK2_SY121 @ sK3_SY124 ) )
=> ~ ( ok @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY121 @ sK3_SY124 ) @ sK4_SY126 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[88]) ).
thf(90,plain,
( ( ~ ( ok @ ( triple @ sK1_U @ sK2_SY121 @ sK3_SY124 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[89]) ).
thf(91,plain,
( ( ~ ( ok @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY121 @ sK3_SY124 ) @ sK4_SY126 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[89]) ).
thf(92,plain,
( ( ok @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY121 @ sK3_SY124 ) @ sK4_SY126 ) )
= $true ),
inference(polarity_switch,[status(thm)],[91]) ).
thf(93,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( less_than @ U @ V )
& ( less_than @ V @ W ) )
=> ( less_than @ U @ W ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(94,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(95,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(96,plain,
( ( ! [U: $i,V: $i] :
( ( strictly_less_than @ U @ V )
<=> ( ( less_than @ U @ V )
& ~ ( less_than @ V @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(97,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(98,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(99,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(100,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(101,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(copy,[status(thm)],[77]) ).
thf(102,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(103,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(copy,[status(thm)],[75]) ).
thf(104,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(105,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != W )
& ( contains_slb @ U @ W ) )
=> ( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( remove_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(106,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(107,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(copy,[status(thm)],[71]) ).
thf(108,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(109,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)],[69]) ).
thf(110,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( less_than @ W @ X )
=> ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(111,plain,
( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(112,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(113,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(114,plain,
( ( ! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(115,plain,
( ( ! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(116,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(117,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(copy,[status(thm)],[61]) ).
thf(118,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(copy,[status(thm)],[60]) ).
thf(119,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
<=> ( contains_slb @ V @ X ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(120,plain,
( ( ! [U: $i,V: $i] :
( ( ok @ ( triple @ U @ V @ bad ) )
<=> $false ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(121,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ( W = bad ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(122,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( insert_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( insert_pqp @ U @ X ) @ ( insert_slb @ V @ ( pair @ X @ bottom ) ) @ W ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(123,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)],[55]) ).
thf(124,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)],[54]) ).
thf(125,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)],[53]) ).
thf(126,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ create_slb @ V ) )
= ( triple @ U @ create_slb @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(127,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(copy,[status(thm)],[51]) ).
thf(128,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(copy,[status(thm)],[50]) ).
thf(129,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(copy,[status(thm)],[49]) ).
thf(130,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(131,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(copy,[status(thm)],[47]) ).
thf(132,plain,
( ( ! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(133,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(134,plain,
( ( ~ ( ok @ ( triple @ sK1_U @ sK2_SY121 @ sK3_SY124 ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(135,plain,
( ( ok @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY121 @ sK3_SY124 ) @ sK4_SY126 ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(136,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( succ_cpq @ SX0 @ SX1 )
| ( succ_cpq @ SX0 @ ( removemin_cpq_eff @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(137,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( succ_cpq @ SX0 @ SX1 )
| ( succ_cpq @ SX0 @ ( findmin_cpq_eff @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(138,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( contains_slb @ SX1 @ SX3 )
| ( ( remove_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ SX3 )
= ( triple @ SX0 @ SX1 @ bad ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(139,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( succ_cpq @ SX0 @ SX1 )
| ( succ_cpq @ SX0 @ ( insert_cpq @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(140,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( succ_cpq @ SX0 @ SX1 )
| ( succ_cpq @ SX0 @ ( remove_cpq @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(141,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( less_than @ SX2 @ SX3 )
| ( ( update_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 )
= ( insert_slb @ ( update_slb @ SX0 @ SX2 ) @ ( pair @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(142,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( ( SX1 != SX2 ) )
| ~ ( contains_slb @ SX0 @ SX2 ) )
| ( ( lookup_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 )
= ( lookup_slb @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(143,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( strictly_less_than @ SX3 @ SX2 )
| ( ( update_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 )
= ( insert_slb @ ( update_slb @ SX0 @ SX2 ) @ ( pair @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(144,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ~ ( ~ ( ( SX1 != create_slb ) )
| ~ ( contains_slb @ SX1 @ ( findmin_pqp_res @ SX0 ) ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SX0 ) @ ( lookup_slb @ SX1 @ ( findmin_pqp_res @ SX0 ) ) ) )
| ( ( findmin_cpq_eff @ ( triple @ SX0 @ SX1 @ SX2 ) )
= ( triple @ SX0 @ ( update_slb @ SX1 @ ( findmin_pqp_res @ SX0 ) ) @ bad ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(145,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( strictly_less_than @ SX3 @ SX4 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ SX1 @ ( pair @ SX3 @ SX4 ) ) @ SX2 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ SX1 @ ( pair @ SX3 @ SX4 ) ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(146,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( ~ ( less_than @ SX0 @ SX1 )
| ~ ~ ( less_than @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SX0 @ SX1 )
| ~ ~ ( less_than @ SX1 @ SX0 ) )
| ( strictly_less_than @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(147,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 )
| ( contains_slb @ SX0 @ SX2 )
| ( SX1 = SX2 ) )
| ~ ( ~ ( ( contains_slb @ SX0 @ SX2 )
| ( SX1 = SX2 ) )
| ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(148,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ~ ( ~ ( ( SX1 != create_slb ) )
| ~ ( contains_slb @ SX1 @ ( findmin_pqp_res @ SX0 ) ) )
| ~ ( less_than @ ( lookup_slb @ SX1 @ ( findmin_pqp_res @ SX0 ) ) @ ( findmin_pqp_res @ SX0 ) ) )
| ( ( findmin_cpq_eff @ ( triple @ SX0 @ SX1 @ SX2 ) )
= ( triple @ SX0 @ ( update_slb @ SX1 @ ( findmin_pqp_res @ SX0 ) ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(149,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( contains_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ SX3 )
| ( contains_slb @ SX1 @ SX3 ) )
| ~ ( ~ ( contains_slb @ SX1 @ SX3 )
| ( contains_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(150,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX2 ) )
| ( less_than @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(151,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ok @ ( triple @ SX0 @ SX1 @ bad ) )
| $false )
| ~ ( ~ $false
| ( ok @ ( triple @ SX0 @ SX1 @ bad ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(152,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( ( SX1 != create_slb ) )
| ~ ~ ( contains_slb @ SX1 @ ( findmin_pqp_res @ SX0 ) ) )
| ( ( findmin_cpq_eff @ ( triple @ SX0 @ SX1 @ SX2 ) )
= ( triple @ SX0 @ ( update_slb @ SX1 @ ( findmin_pqp_res @ SX0 ) ) @ bad ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(153,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 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ SX1 @ ( pair @ SX3 @ SX4 ) ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(154,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( contains_slb @ SX1 @ SX3 )
| ~ ( strictly_less_than @ SX3 @ ( lookup_slb @ SX1 @ SX3 ) ) )
| ( ( remove_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ SX3 )
= ( triple @ ( remove_pqp @ SX0 @ SX3 ) @ ( remove_slb @ SX1 @ SX3 ) @ bad ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(155,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( ( SX1 != SX2 ) )
| ~ ( contains_slb @ SX0 @ SX2 ) )
| ( ( remove_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 )
= ( insert_slb @ ( remove_slb @ SX0 @ SX2 ) @ ( pair @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(156,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ( SX1 != create_slb ) )
| ( ( findmin_cpq_res @ ( triple @ SX0 @ SX1 @ SX2 ) )
= ( findmin_pqp_res @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(157,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( contains_slb @ SX1 @ SX3 )
| ~ ( less_than @ ( lookup_slb @ SX1 @ SX3 ) @ SX3 ) )
| ( ( remove_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ SX3 )
= ( triple @ ( remove_pqp @ SX0 @ SX3 ) @ ( remove_slb @ SX1 @ SX3 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(158,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ok @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ( SX2 = bad ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(159,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 )
| ( pair_in_list @ SX0 @ SX2 @ SX4 )
| ~ ( ( SX1 != SX2 )
| ( SX3 != SX4 ) ) )
| ~ ( ~ ( ( pair_in_list @ SX0 @ SX2 @ SX4 )
| ~ ( ( SX1 != SX2 )
| ( SX3 != SX4 ) ) )
| ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(160,plain,
! [SV1: $i] :
( ( ! [SY127: $i] :
( ( less_than @ SV1 @ SY127 )
| ( less_than @ SY127 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(161,plain,
! [SV2: $i] :
( ( less_than @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(162,plain,
! [SV3: $i] :
( ( less_than @ bottom @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(163,plain,
( ( isnonempty_slb @ create_slb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(164,plain,
! [SV4: $i] :
( ( ! [SY128: $i,SY129: $i] : ( isnonempty_slb @ ( insert_slb @ SV4 @ ( pair @ SY128 @ SY129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(165,plain,
! [SV5: $i] :
( ( ~ ( contains_slb @ create_slb @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(166,plain,
! [SV6: $i] :
( ( ! [SY130: $i] :
~ ( pair_in_list @ create_slb @ SV6 @ SY130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(167,plain,
! [SV7: $i] :
( ( ! [SY131: $i,SY132: $i] :
( ( remove_slb @ ( insert_slb @ SV7 @ ( pair @ SY131 @ SY132 ) ) @ SY131 )
= SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(168,plain,
! [SV8: $i] :
( ( ! [SY133: $i,SY134: $i] :
( ( lookup_slb @ ( insert_slb @ SV8 @ ( pair @ SY133 @ SY134 ) ) @ SY133 )
= SY134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(169,plain,
! [SV9: $i] :
( ( ( update_slb @ create_slb @ SV9 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(170,plain,
! [SV10: $i] :
( ( succ_cpq @ SV10 @ SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(171,plain,
! [SV11: $i] :
( ( ! [SY135: $i] : ( check_cpq @ ( triple @ SV11 @ create_slb @ SY135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(172,plain,
! [SV12: $i] :
( ( ! [SY136: $i,SY137: $i,SY138: $i] :
( ( insert_cpq @ ( triple @ SV12 @ SY136 @ SY137 ) @ SY138 )
= ( triple @ ( insert_pqp @ SV12 @ SY138 ) @ ( insert_slb @ SY136 @ ( pair @ SY138 @ bottom ) ) @ SY137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(173,plain,
! [SV13: $i] :
( ( ! [SY139: $i] :
( ( findmin_cpq_eff @ ( triple @ SV13 @ create_slb @ SY139 ) )
= ( triple @ SV13 @ create_slb @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(174,plain,
! [SV14: $i] :
( ( ! [SY140: $i] :
( ( findmin_cpq_res @ ( triple @ SV14 @ create_slb @ SY140 ) )
= bottom ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(175,plain,
! [SV15: $i] :
( ( ( removemin_cpq_eff @ SV15 )
= ( remove_cpq @ ( findmin_cpq_eff @ SV15 ) @ ( findmin_cpq_res @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(176,plain,
! [SV16: $i] :
( ( ( removemin_cpq_res @ SV16 )
= ( findmin_cpq_res @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(177,plain,
( ( ok @ ( triple @ sK1_U @ sK2_SY121 @ sK3_SY124 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(178,plain,
! [SV17: $i] :
( ( ! [SY141: $i] :
( ~ ( succ_cpq @ SV17 @ SY141 )
| ( succ_cpq @ SV17 @ ( removemin_cpq_eff @ SY141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(179,plain,
! [SV18: $i] :
( ( ! [SY142: $i] :
( ~ ( succ_cpq @ SV18 @ SY142 )
| ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SY142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(180,plain,
! [SV19: $i] :
( ( ! [SY143: $i,SY144: $i,SY145: $i] :
( ~ ~ ( contains_slb @ SY143 @ SY145 )
| ( ( remove_cpq @ ( triple @ SV19 @ SY143 @ SY144 ) @ SY145 )
= ( triple @ SV19 @ SY143 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(181,plain,
! [SV20: $i] :
( ( ! [SY146: $i,SY147: $i] :
( ~ ( succ_cpq @ SV20 @ SY146 )
| ( succ_cpq @ SV20 @ ( insert_cpq @ SY146 @ SY147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(182,plain,
! [SV21: $i] :
( ( ! [SY148: $i,SY149: $i] :
( ~ ( succ_cpq @ SV21 @ SY148 )
| ( succ_cpq @ SV21 @ ( remove_cpq @ SY148 @ SY149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(183,plain,
! [SV22: $i] :
( ( ! [SY150: $i,SY151: $i,SY152: $i] :
( ~ ( less_than @ SY151 @ SY152 )
| ( ( update_slb @ ( insert_slb @ SV22 @ ( pair @ SY150 @ SY152 ) ) @ SY151 )
= ( insert_slb @ ( update_slb @ SV22 @ SY151 ) @ ( pair @ SY150 @ SY152 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(184,plain,
! [SV23: $i] :
( ( ! [SY153: $i,SY154: $i,SY155: $i] :
( ~ ~ ( ~ ( ( SY153 != SY154 ) )
| ~ ( contains_slb @ SV23 @ SY154 ) )
| ( ( lookup_slb @ ( insert_slb @ SV23 @ ( pair @ SY153 @ SY155 ) ) @ SY154 )
= ( lookup_slb @ SV23 @ SY154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(185,plain,
! [SV24: $i] :
( ( ! [SY156: $i,SY157: $i,SY158: $i] :
( ~ ( strictly_less_than @ SY158 @ SY157 )
| ( ( update_slb @ ( insert_slb @ SV24 @ ( pair @ SY156 @ SY158 ) ) @ SY157 )
= ( insert_slb @ ( update_slb @ SV24 @ SY157 ) @ ( pair @ SY156 @ SY157 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(186,plain,
! [SV25: $i] :
( ( ! [SY159: $i,SY160: $i,SY161: $i] :
( ~ ~ ( ~ ~ ( ~ ( ( SY159 != create_slb ) )
| ~ ( contains_slb @ SY159 @ ( findmin_pqp_res @ SV25 ) ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV25 ) @ ( lookup_slb @ SY159 @ ( findmin_pqp_res @ SV25 ) ) ) )
| ( ( findmin_cpq_eff @ ( triple @ SV25 @ SY159 @ SY160 ) )
= ( triple @ SV25 @ ( update_slb @ SY159 @ ( findmin_pqp_res @ SV25 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(187,plain,
! [SV26: $i] :
( ( ! [SY162: $i,SY163: $i,SY164: $i,SY165: $i] :
( ~ ( strictly_less_than @ SY164 @ SY165 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SY162 @ ( pair @ SY164 @ SY165 ) ) @ SY163 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SY162 @ ( pair @ SY164 @ SY165 ) ) @ SY163 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(188,plain,
! [SV27: $i] :
( ( ! [SY166: $i] :
~ ( ~ ( ~ ( strictly_less_than @ SV27 @ SY166 )
| ~ ( ~ ( less_than @ SV27 @ SY166 )
| ~ ~ ( less_than @ SY166 @ SV27 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV27 @ SY166 )
| ~ ~ ( less_than @ SY166 @ SV27 ) )
| ( strictly_less_than @ SV27 @ SY166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(189,plain,
! [SV28: $i] :
( ( ! [SY167: $i,SY168: $i,SY169: $i] :
~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV28 @ ( pair @ SY167 @ SY169 ) ) @ SY168 )
| ( contains_slb @ SV28 @ SY168 )
| ( SY167 = SY168 ) )
| ~ ( ~ ( ( contains_slb @ SV28 @ SY168 )
| ( SY167 = SY168 ) )
| ( contains_slb @ ( insert_slb @ SV28 @ ( pair @ SY167 @ SY169 ) ) @ SY168 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(190,plain,
! [SV29: $i] :
( ( ! [SY170: $i,SY171: $i,SY172: $i] :
( ~ ~ ( ~ ~ ( ~ ( ( SY170 != create_slb ) )
| ~ ( contains_slb @ SY170 @ ( findmin_pqp_res @ SV29 ) ) )
| ~ ( less_than @ ( lookup_slb @ SY170 @ ( findmin_pqp_res @ SV29 ) ) @ ( findmin_pqp_res @ SV29 ) ) )
| ( ( findmin_cpq_eff @ ( triple @ SV29 @ SY170 @ SY171 ) )
= ( triple @ SV29 @ ( update_slb @ SY170 @ ( findmin_pqp_res @ SV29 ) ) @ SY171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(191,plain,
! [SV30: $i] :
( ( ! [SY173: $i,SY174: $i,SY175: $i] :
~ ( ~ ( ~ ( contains_cpq @ ( triple @ SV30 @ SY173 @ SY174 ) @ SY175 )
| ( contains_slb @ SY173 @ SY175 ) )
| ~ ( ~ ( contains_slb @ SY173 @ SY175 )
| ( contains_cpq @ ( triple @ SV30 @ SY173 @ SY174 ) @ SY175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(192,plain,
! [SV31: $i] :
( ( ! [SY176: $i,SY177: $i] :
( ~ ~ ( ~ ( less_than @ SV31 @ SY176 )
| ~ ( less_than @ SY176 @ SY177 ) )
| ( less_than @ SV31 @ SY177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(193,plain,
! [SV32: $i] :
( ( ! [SY178: $i] :
~ ( ~ ( ~ ( ok @ ( triple @ SV32 @ SY178 @ bad ) )
| $false )
| ~ ( ~ $false
| ( ok @ ( triple @ SV32 @ SY178 @ bad ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(194,plain,
! [SV33: $i] :
( ( ! [SY179: $i,SY180: $i,SY181: $i] :
( ~ ~ ( ~ ( ( SY179 != create_slb ) )
| ~ ~ ( contains_slb @ SY179 @ ( findmin_pqp_res @ SV33 ) ) )
| ( ( findmin_cpq_eff @ ( triple @ SV33 @ SY179 @ SY180 ) )
= ( triple @ SV33 @ ( update_slb @ SY179 @ ( findmin_pqp_res @ SV33 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(195,plain,
! [SV34: $i] :
( ( ! [SY182: $i,SY183: $i,SY184: $i,SY185: $i] :
( ~ ( less_than @ SY185 @ SY184 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SY182 @ ( pair @ SY184 @ SY185 ) ) @ SY183 ) )
| ( check_cpq @ ( triple @ SV34 @ SY182 @ SY183 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV34 @ SY182 @ SY183 ) )
| ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SY182 @ ( pair @ SY184 @ SY185 ) ) @ SY183 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(196,plain,
! [SV35: $i] :
( ( ! [SY186: $i,SY187: $i,SY188: $i] :
( ~ ~ ( ~ ( contains_slb @ SY186 @ SY188 )
| ~ ( strictly_less_than @ SY188 @ ( lookup_slb @ SY186 @ SY188 ) ) )
| ( ( remove_cpq @ ( triple @ SV35 @ SY186 @ SY187 ) @ SY188 )
= ( triple @ ( remove_pqp @ SV35 @ SY188 ) @ ( remove_slb @ SY186 @ SY188 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(197,plain,
! [SV36: $i] :
( ( ! [SY189: $i,SY190: $i,SY191: $i] :
( ~ ~ ( ~ ( ( SY189 != SY190 ) )
| ~ ( contains_slb @ SV36 @ SY190 ) )
| ( ( remove_slb @ ( insert_slb @ SV36 @ ( pair @ SY189 @ SY191 ) ) @ SY190 )
= ( insert_slb @ ( remove_slb @ SV36 @ SY190 ) @ ( pair @ SY189 @ SY191 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(198,plain,
! [SV37: $i] :
( ( ! [SY192: $i,SY193: $i,SY194: $i] :
( ~ ( ( SY192 != create_slb ) )
| ( ( findmin_cpq_res @ ( triple @ SV37 @ SY192 @ SY193 ) )
= ( findmin_pqp_res @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(199,plain,
! [SV38: $i] :
( ( ! [SY195: $i,SY196: $i,SY197: $i] :
( ~ ~ ( ~ ( contains_slb @ SY195 @ SY197 )
| ~ ( less_than @ ( lookup_slb @ SY195 @ SY197 ) @ SY197 ) )
| ( ( remove_cpq @ ( triple @ SV38 @ SY195 @ SY196 ) @ SY197 )
= ( triple @ ( remove_pqp @ SV38 @ SY197 ) @ ( remove_slb @ SY195 @ SY197 ) @ SY196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(200,plain,
! [SV39: $i] :
( ( ! [SY198: $i,SY199: $i] :
( ~ ~ ( ok @ ( triple @ SV39 @ SY198 @ SY199 ) )
| ( SY199 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(201,plain,
! [SV40: $i] :
( ( ! [SY200: $i,SY201: $i,SY202: $i,SY203: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SY200 @ SY202 ) ) @ SY201 @ SY203 )
| ( pair_in_list @ SV40 @ SY201 @ SY203 )
| ~ ( ( SY200 != SY201 )
| ( SY202 != SY203 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV40 @ SY201 @ SY203 )
| ~ ( ( SY200 != SY201 )
| ( SY202 != SY203 ) ) )
| ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SY200 @ SY202 ) ) @ SY201 @ SY203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(202,plain,
! [SV41: $i,SV1: $i] :
( ( ( less_than @ SV1 @ SV41 )
| ( less_than @ SV41 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(203,plain,
! [SV42: $i,SV4: $i] :
( ( ! [SY204: $i] : ( isnonempty_slb @ ( insert_slb @ SV4 @ ( pair @ SV42 @ SY204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(204,plain,
! [SV5: $i] :
( ( contains_slb @ create_slb @ SV5 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(205,plain,
! [SV43: $i,SV6: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV6 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(206,plain,
! [SV44: $i,SV7: $i] :
( ( ! [SY205: $i] :
( ( remove_slb @ ( insert_slb @ SV7 @ ( pair @ SV44 @ SY205 ) ) @ SV44 )
= SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(207,plain,
! [SV45: $i,SV8: $i] :
( ( ! [SY206: $i] :
( ( lookup_slb @ ( insert_slb @ SV8 @ ( pair @ SV45 @ SY206 ) ) @ SV45 )
= SY206 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(208,plain,
! [SV46: $i,SV11: $i] :
( ( check_cpq @ ( triple @ SV11 @ create_slb @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(209,plain,
! [SV47: $i,SV12: $i] :
( ( ! [SY207: $i,SY208: $i] :
( ( insert_cpq @ ( triple @ SV12 @ SV47 @ SY207 ) @ SY208 )
= ( triple @ ( insert_pqp @ SV12 @ SY208 ) @ ( insert_slb @ SV47 @ ( pair @ SY208 @ bottom ) ) @ SY207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(210,plain,
! [SV48: $i,SV13: $i] :
( ( ( findmin_cpq_eff @ ( triple @ SV13 @ create_slb @ SV48 ) )
= ( triple @ SV13 @ create_slb @ bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(211,plain,
! [SV49: $i,SV14: $i] :
( ( ( findmin_cpq_res @ ( triple @ SV14 @ create_slb @ SV49 ) )
= bottom )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(212,plain,
! [SV50: $i,SV17: $i] :
( ( ~ ( succ_cpq @ SV17 @ SV50 )
| ( succ_cpq @ SV17 @ ( removemin_cpq_eff @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(213,plain,
! [SV51: $i,SV18: $i] :
( ( ~ ( succ_cpq @ SV18 @ SV51 )
| ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(214,plain,
! [SV19: $i,SV52: $i] :
( ( ! [SY209: $i,SY210: $i] :
( ~ ~ ( contains_slb @ SV52 @ SY210 )
| ( ( remove_cpq @ ( triple @ SV19 @ SV52 @ SY209 ) @ SY210 )
= ( triple @ SV19 @ SV52 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(215,plain,
! [SV53: $i,SV20: $i] :
( ( ! [SY211: $i] :
( ~ ( succ_cpq @ SV20 @ SV53 )
| ( succ_cpq @ SV20 @ ( insert_cpq @ SV53 @ SY211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(216,plain,
! [SV54: $i,SV21: $i] :
( ( ! [SY212: $i] :
( ~ ( succ_cpq @ SV21 @ SV54 )
| ( succ_cpq @ SV21 @ ( remove_cpq @ SV54 @ SY212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(217,plain,
! [SV55: $i,SV22: $i] :
( ( ! [SY213: $i,SY214: $i] :
( ~ ( less_than @ SY213 @ SY214 )
| ( ( update_slb @ ( insert_slb @ SV22 @ ( pair @ SV55 @ SY214 ) ) @ SY213 )
= ( insert_slb @ ( update_slb @ SV22 @ SY213 ) @ ( pair @ SV55 @ SY214 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(218,plain,
! [SV23: $i,SV56: $i] :
( ( ! [SY215: $i,SY216: $i] :
( ~ ~ ( ~ ( ( SV56 != SY215 ) )
| ~ ( contains_slb @ SV23 @ SY215 ) )
| ( ( lookup_slb @ ( insert_slb @ SV23 @ ( pair @ SV56 @ SY216 ) ) @ SY215 )
= ( lookup_slb @ SV23 @ SY215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(219,plain,
! [SV57: $i,SV24: $i] :
( ( ! [SY217: $i,SY218: $i] :
( ~ ( strictly_less_than @ SY218 @ SY217 )
| ( ( update_slb @ ( insert_slb @ SV24 @ ( pair @ SV57 @ SY218 ) ) @ SY217 )
= ( insert_slb @ ( update_slb @ SV24 @ SY217 ) @ ( pair @ SV57 @ SY217 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(220,plain,
! [SV25: $i,SV58: $i] :
( ( ! [SY219: $i,SY220: $i] :
( ~ ~ ( ~ ~ ( ~ ( ( SV58 != create_slb ) )
| ~ ( contains_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV25 ) @ ( lookup_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) ) )
| ( ( findmin_cpq_eff @ ( triple @ SV25 @ SV58 @ SY219 ) )
= ( triple @ SV25 @ ( update_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(221,plain,
! [SV59: $i,SV26: $i] :
( ( ! [SY221: $i,SY222: $i,SY223: $i] :
( ~ ( strictly_less_than @ SY222 @ SY223 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SV59 @ ( pair @ SY222 @ SY223 ) ) @ SY221 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SV59 @ ( pair @ SY222 @ SY223 ) ) @ SY221 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(222,plain,
! [SV60: $i,SV27: $i] :
( ( ~ ( ~ ( ~ ( strictly_less_than @ SV27 @ SV60 )
| ~ ( ~ ( less_than @ SV27 @ SV60 )
| ~ ~ ( less_than @ SV60 @ SV27 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV27 @ SV60 )
| ~ ~ ( less_than @ SV60 @ SV27 ) )
| ( strictly_less_than @ SV27 @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(223,plain,
! [SV61: $i,SV28: $i] :
( ( ! [SY224: $i,SY225: $i] :
~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV28 @ ( pair @ SV61 @ SY225 ) ) @ SY224 )
| ( contains_slb @ SV28 @ SY224 )
| ( SV61 = SY224 ) )
| ~ ( ~ ( ( contains_slb @ SV28 @ SY224 )
| ( SV61 = SY224 ) )
| ( contains_slb @ ( insert_slb @ SV28 @ ( pair @ SV61 @ SY225 ) ) @ SY224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(224,plain,
! [SV29: $i,SV62: $i] :
( ( ! [SY226: $i,SY227: $i] :
( ~ ~ ( ~ ~ ( ~ ( ( SV62 != create_slb ) )
| ~ ( contains_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) )
| ~ ( less_than @ ( lookup_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ ( findmin_pqp_res @ SV29 ) ) )
| ( ( findmin_cpq_eff @ ( triple @ SV29 @ SV62 @ SY226 ) )
= ( triple @ SV29 @ ( update_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ SY226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(225,plain,
! [SV63: $i,SV30: $i] :
( ( ! [SY228: $i,SY229: $i] :
~ ( ~ ( ~ ( contains_cpq @ ( triple @ SV30 @ SV63 @ SY228 ) @ SY229 )
| ( contains_slb @ SV63 @ SY229 ) )
| ~ ( ~ ( contains_slb @ SV63 @ SY229 )
| ( contains_cpq @ ( triple @ SV30 @ SV63 @ SY228 ) @ SY229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(226,plain,
! [SV64: $i,SV31: $i] :
( ( ! [SY230: $i] :
( ~ ~ ( ~ ( less_than @ SV31 @ SV64 )
| ~ ( less_than @ SV64 @ SY230 ) )
| ( less_than @ SV31 @ SY230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(227,plain,
! [SV65: $i,SV32: $i] :
( ( ~ ( ~ ( ~ ( ok @ ( triple @ SV32 @ SV65 @ bad ) )
| $false )
| ~ ( ~ $false
| ( ok @ ( triple @ SV32 @ SV65 @ bad ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(228,plain,
! [SV33: $i,SV66: $i] :
( ( ! [SY231: $i,SY232: $i] :
( ~ ~ ( ~ ( ( SV66 != create_slb ) )
| ~ ~ ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV33 ) ) )
| ( ( findmin_cpq_eff @ ( triple @ SV33 @ SV66 @ SY231 ) )
= ( triple @ SV33 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV33 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(229,plain,
! [SV67: $i,SV34: $i] :
( ( ! [SY233: $i,SY234: $i,SY235: $i] :
( ~ ( less_than @ SY235 @ SY234 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SV67 @ ( pair @ SY234 @ SY235 ) ) @ SY233 ) )
| ( check_cpq @ ( triple @ SV34 @ SV67 @ SY233 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV34 @ SV67 @ SY233 ) )
| ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SV67 @ ( pair @ SY234 @ SY235 ) ) @ SY233 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(230,plain,
! [SV35: $i,SV68: $i] :
( ( ! [SY236: $i,SY237: $i] :
( ~ ~ ( ~ ( contains_slb @ SV68 @ SY237 )
| ~ ( strictly_less_than @ SY237 @ ( lookup_slb @ SV68 @ SY237 ) ) )
| ( ( remove_cpq @ ( triple @ SV35 @ SV68 @ SY236 ) @ SY237 )
= ( triple @ ( remove_pqp @ SV35 @ SY237 ) @ ( remove_slb @ SV68 @ SY237 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(231,plain,
! [SV36: $i,SV69: $i] :
( ( ! [SY238: $i,SY239: $i] :
( ~ ~ ( ~ ( ( SV69 != SY238 ) )
| ~ ( contains_slb @ SV36 @ SY238 ) )
| ( ( remove_slb @ ( insert_slb @ SV36 @ ( pair @ SV69 @ SY239 ) ) @ SY238 )
= ( insert_slb @ ( remove_slb @ SV36 @ SY238 ) @ ( pair @ SV69 @ SY239 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(232,plain,
! [SV37: $i,SV70: $i] :
( ( ! [SY240: $i,SY241: $i] :
( ~ ( ( SV70 != create_slb ) )
| ( ( findmin_cpq_res @ ( triple @ SV37 @ SV70 @ SY240 ) )
= ( findmin_pqp_res @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(233,plain,
! [SV38: $i,SV71: $i] :
( ( ! [SY242: $i,SY243: $i] :
( ~ ~ ( ~ ( contains_slb @ SV71 @ SY243 )
| ~ ( less_than @ ( lookup_slb @ SV71 @ SY243 ) @ SY243 ) )
| ( ( remove_cpq @ ( triple @ SV38 @ SV71 @ SY242 ) @ SY243 )
= ( triple @ ( remove_pqp @ SV38 @ SY243 ) @ ( remove_slb @ SV71 @ SY243 ) @ SY242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(234,plain,
! [SV72: $i,SV39: $i] :
( ( ! [SY244: $i] :
( ~ ~ ( ok @ ( triple @ SV39 @ SV72 @ SY244 ) )
| ( SY244 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(235,plain,
! [SV73: $i,SV40: $i] :
( ( ! [SY245: $i,SY246: $i,SY247: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SY246 ) ) @ SY245 @ SY247 )
| ( pair_in_list @ SV40 @ SY245 @ SY247 )
| ~ ( ( SV73 != SY245 )
| ( SY246 != SY247 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV40 @ SY245 @ SY247 )
| ~ ( ( SV73 != SY245 )
| ( SY246 != SY247 ) ) )
| ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SY246 ) ) @ SY245 @ SY247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(236,plain,
! [SV41: $i,SV1: $i] :
( ( ( less_than @ SV1 @ SV41 )
= $true )
| ( ( less_than @ SV41 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(237,plain,
! [SV74: $i,SV42: $i,SV4: $i] :
( ( isnonempty_slb @ ( insert_slb @ SV4 @ ( pair @ SV42 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(238,plain,
! [SV43: $i,SV6: $i] :
( ( pair_in_list @ create_slb @ SV6 @ SV43 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(239,plain,
! [SV75: $i,SV44: $i,SV7: $i] :
( ( ( remove_slb @ ( insert_slb @ SV7 @ ( pair @ SV44 @ SV75 ) ) @ SV44 )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(240,plain,
! [SV76: $i,SV45: $i,SV8: $i] :
( ( ( lookup_slb @ ( insert_slb @ SV8 @ ( pair @ SV45 @ SV76 ) ) @ SV45 )
= SV76 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(241,plain,
! [SV77: $i,SV47: $i,SV12: $i] :
( ( ! [SY248: $i] :
( ( insert_cpq @ ( triple @ SV12 @ SV47 @ SV77 ) @ SY248 )
= ( triple @ ( insert_pqp @ SV12 @ SY248 ) @ ( insert_slb @ SV47 @ ( pair @ SY248 @ bottom ) ) @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(242,plain,
! [SV50: $i,SV17: $i] :
( ( ( ~ ( succ_cpq @ SV17 @ SV50 ) )
= $true )
| ( ( succ_cpq @ SV17 @ ( removemin_cpq_eff @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(243,plain,
! [SV51: $i,SV18: $i] :
( ( ( ~ ( succ_cpq @ SV18 @ SV51 ) )
= $true )
| ( ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(244,plain,
! [SV78: $i,SV19: $i,SV52: $i] :
( ( ! [SY249: $i] :
( ~ ~ ( contains_slb @ SV52 @ SY249 )
| ( ( remove_cpq @ ( triple @ SV19 @ SV52 @ SV78 ) @ SY249 )
= ( triple @ SV19 @ SV52 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(245,plain,
! [SV79: $i,SV53: $i,SV20: $i] :
( ( ~ ( succ_cpq @ SV20 @ SV53 )
| ( succ_cpq @ SV20 @ ( insert_cpq @ SV53 @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(246,plain,
! [SV80: $i,SV54: $i,SV21: $i] :
( ( ~ ( succ_cpq @ SV21 @ SV54 )
| ( succ_cpq @ SV21 @ ( remove_cpq @ SV54 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(247,plain,
! [SV55: $i,SV22: $i,SV81: $i] :
( ( ! [SY250: $i] :
( ~ ( less_than @ SV81 @ SY250 )
| ( ( update_slb @ ( insert_slb @ SV22 @ ( pair @ SV55 @ SY250 ) ) @ SV81 )
= ( insert_slb @ ( update_slb @ SV22 @ SV81 ) @ ( pair @ SV55 @ SY250 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(248,plain,
! [SV23: $i,SV82: $i,SV56: $i] :
( ( ! [SY251: $i] :
( ~ ~ ( ~ ( ( SV56 != SV82 ) )
| ~ ( contains_slb @ SV23 @ SV82 ) )
| ( ( lookup_slb @ ( insert_slb @ SV23 @ ( pair @ SV56 @ SY251 ) ) @ SV82 )
= ( lookup_slb @ SV23 @ SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(249,plain,
! [SV57: $i,SV24: $i,SV83: $i] :
( ( ! [SY252: $i] :
( ~ ( strictly_less_than @ SY252 @ SV83 )
| ( ( update_slb @ ( insert_slb @ SV24 @ ( pair @ SV57 @ SY252 ) ) @ SV83 )
= ( insert_slb @ ( update_slb @ SV24 @ SV83 ) @ ( pair @ SV57 @ SV83 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(250,plain,
! [SV84: $i,SV25: $i,SV58: $i] :
( ( ! [SY253: $i] :
( ~ ~ ( ~ ~ ( ~ ( ( SV58 != create_slb ) )
| ~ ( contains_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV25 ) @ ( lookup_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) ) )
| ( ( findmin_cpq_eff @ ( triple @ SV25 @ SV58 @ SV84 ) )
= ( triple @ SV25 @ ( update_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(251,plain,
! [SV85: $i,SV59: $i,SV26: $i] :
( ( ! [SY254: $i,SY255: $i] :
( ~ ( strictly_less_than @ SY254 @ SY255 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SV59 @ ( pair @ SY254 @ SY255 ) ) @ SV85 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SV59 @ ( pair @ SY254 @ SY255 ) ) @ SV85 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(252,plain,
! [SV60: $i,SV27: $i] :
( ( ~ ( ~ ( strictly_less_than @ SV27 @ SV60 )
| ~ ( ~ ( less_than @ SV27 @ SV60 )
| ~ ~ ( less_than @ SV60 @ SV27 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV27 @ SV60 )
| ~ ~ ( less_than @ SV60 @ SV27 ) )
| ( strictly_less_than @ SV27 @ SV60 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(253,plain,
! [SV86: $i,SV61: $i,SV28: $i] :
( ( ! [SY256: $i] :
~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV28 @ ( pair @ SV61 @ SY256 ) ) @ SV86 )
| ( contains_slb @ SV28 @ SV86 )
| ( SV61 = SV86 ) )
| ~ ( ~ ( ( contains_slb @ SV28 @ SV86 )
| ( SV61 = SV86 ) )
| ( contains_slb @ ( insert_slb @ SV28 @ ( pair @ SV61 @ SY256 ) ) @ SV86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(254,plain,
! [SV87: $i,SV29: $i,SV62: $i] :
( ( ! [SY257: $i] :
( ~ ~ ( ~ ~ ( ~ ( ( SV62 != create_slb ) )
| ~ ( contains_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) )
| ~ ( less_than @ ( lookup_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ ( findmin_pqp_res @ SV29 ) ) )
| ( ( findmin_cpq_eff @ ( triple @ SV29 @ SV62 @ SV87 ) )
= ( triple @ SV29 @ ( update_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(255,plain,
! [SV88: $i,SV63: $i,SV30: $i] :
( ( ! [SY258: $i] :
~ ( ~ ( ~ ( contains_cpq @ ( triple @ SV30 @ SV63 @ SV88 ) @ SY258 )
| ( contains_slb @ SV63 @ SY258 ) )
| ~ ( ~ ( contains_slb @ SV63 @ SY258 )
| ( contains_cpq @ ( triple @ SV30 @ SV63 @ SV88 ) @ SY258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(256,plain,
! [SV89: $i,SV64: $i,SV31: $i] :
( ( ~ ~ ( ~ ( less_than @ SV31 @ SV64 )
| ~ ( less_than @ SV64 @ SV89 ) )
| ( less_than @ SV31 @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(257,plain,
! [SV65: $i,SV32: $i] :
( ( ~ ( ~ ( ok @ ( triple @ SV32 @ SV65 @ bad ) )
| $false )
| ~ ( ~ $false
| ( ok @ ( triple @ SV32 @ SV65 @ bad ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(258,plain,
! [SV90: $i,SV33: $i,SV66: $i] :
( ( ! [SY259: $i] :
( ~ ~ ( ~ ( ( SV66 != create_slb ) )
| ~ ~ ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV33 ) ) )
| ( ( findmin_cpq_eff @ ( triple @ SV33 @ SV66 @ SV90 ) )
= ( triple @ SV33 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV33 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(259,plain,
! [SV91: $i,SV67: $i,SV34: $i] :
( ( ! [SY260: $i,SY261: $i] :
( ~ ( less_than @ SY261 @ SY260 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SV67 @ ( pair @ SY260 @ SY261 ) ) @ SV91 ) )
| ( check_cpq @ ( triple @ SV34 @ SV67 @ SV91 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV34 @ SV67 @ SV91 ) )
| ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SV67 @ ( pair @ SY260 @ SY261 ) ) @ SV91 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(260,plain,
! [SV92: $i,SV35: $i,SV68: $i] :
( ( ! [SY262: $i] :
( ~ ~ ( ~ ( contains_slb @ SV68 @ SY262 )
| ~ ( strictly_less_than @ SY262 @ ( lookup_slb @ SV68 @ SY262 ) ) )
| ( ( remove_cpq @ ( triple @ SV35 @ SV68 @ SV92 ) @ SY262 )
= ( triple @ ( remove_pqp @ SV35 @ SY262 ) @ ( remove_slb @ SV68 @ SY262 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(261,plain,
! [SV36: $i,SV93: $i,SV69: $i] :
( ( ! [SY263: $i] :
( ~ ~ ( ~ ( ( SV69 != SV93 ) )
| ~ ( contains_slb @ SV36 @ SV93 ) )
| ( ( remove_slb @ ( insert_slb @ SV36 @ ( pair @ SV69 @ SY263 ) ) @ SV93 )
= ( insert_slb @ ( remove_slb @ SV36 @ SV93 ) @ ( pair @ SV69 @ SY263 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(262,plain,
! [SV94: $i,SV37: $i,SV70: $i] :
( ( ! [SY264: $i] :
( ~ ( ( SV70 != create_slb ) )
| ( ( findmin_cpq_res @ ( triple @ SV37 @ SV70 @ SV94 ) )
= ( findmin_pqp_res @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(263,plain,
! [SV95: $i,SV38: $i,SV71: $i] :
( ( ! [SY265: $i] :
( ~ ~ ( ~ ( contains_slb @ SV71 @ SY265 )
| ~ ( less_than @ ( lookup_slb @ SV71 @ SY265 ) @ SY265 ) )
| ( ( remove_cpq @ ( triple @ SV38 @ SV71 @ SV95 ) @ SY265 )
= ( triple @ ( remove_pqp @ SV38 @ SY265 ) @ ( remove_slb @ SV71 @ SY265 ) @ SV95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(264,plain,
! [SV96: $i,SV72: $i,SV39: $i] :
( ( ~ ~ ( ok @ ( triple @ SV39 @ SV72 @ SV96 ) )
| ( SV96 = bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(265,plain,
! [SV97: $i,SV73: $i,SV40: $i] :
( ( ! [SY266: $i,SY267: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SY266 ) ) @ SV97 @ SY267 )
| ( pair_in_list @ SV40 @ SV97 @ SY267 )
| ~ ( ( SV73 != SV97 )
| ( SY266 != SY267 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV40 @ SV97 @ SY267 )
| ~ ( ( SV73 != SV97 )
| ( SY266 != SY267 ) ) )
| ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SY266 ) ) @ SV97 @ SY267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(266,plain,
! [SV98: $i,SV77: $i,SV47: $i,SV12: $i] :
( ( ( insert_cpq @ ( triple @ SV12 @ SV47 @ SV77 ) @ SV98 )
= ( triple @ ( insert_pqp @ SV12 @ SV98 ) @ ( insert_slb @ SV47 @ ( pair @ SV98 @ bottom ) ) @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(267,plain,
! [SV50: $i,SV17: $i] :
( ( ( succ_cpq @ SV17 @ SV50 )
= $false )
| ( ( succ_cpq @ SV17 @ ( removemin_cpq_eff @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(268,plain,
! [SV51: $i,SV18: $i] :
( ( ( succ_cpq @ SV18 @ SV51 )
= $false )
| ( ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(269,plain,
! [SV78: $i,SV19: $i,SV99: $i,SV52: $i] :
( ( ~ ~ ( contains_slb @ SV52 @ SV99 )
| ( ( remove_cpq @ ( triple @ SV19 @ SV52 @ SV78 ) @ SV99 )
= ( triple @ SV19 @ SV52 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(270,plain,
! [SV79: $i,SV53: $i,SV20: $i] :
( ( ( ~ ( succ_cpq @ SV20 @ SV53 ) )
= $true )
| ( ( succ_cpq @ SV20 @ ( insert_cpq @ SV53 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(271,plain,
! [SV80: $i,SV54: $i,SV21: $i] :
( ( ( ~ ( succ_cpq @ SV21 @ SV54 ) )
= $true )
| ( ( succ_cpq @ SV21 @ ( remove_cpq @ SV54 @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(272,plain,
! [SV55: $i,SV22: $i,SV100: $i,SV81: $i] :
( ( ~ ( less_than @ SV81 @ SV100 )
| ( ( update_slb @ ( insert_slb @ SV22 @ ( pair @ SV55 @ SV100 ) ) @ SV81 )
= ( insert_slb @ ( update_slb @ SV22 @ SV81 ) @ ( pair @ SV55 @ SV100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(273,plain,
! [SV101: $i,SV23: $i,SV82: $i,SV56: $i] :
( ( ~ ~ ( ~ ( ( SV56 != SV82 ) )
| ~ ( contains_slb @ SV23 @ SV82 ) )
| ( ( lookup_slb @ ( insert_slb @ SV23 @ ( pair @ SV56 @ SV101 ) ) @ SV82 )
= ( lookup_slb @ SV23 @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(274,plain,
! [SV57: $i,SV24: $i,SV83: $i,SV102: $i] :
( ( ~ ( strictly_less_than @ SV102 @ SV83 )
| ( ( update_slb @ ( insert_slb @ SV24 @ ( pair @ SV57 @ SV102 ) ) @ SV83 )
= ( insert_slb @ ( update_slb @ SV24 @ SV83 ) @ ( pair @ SV57 @ SV83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(275,plain,
! [SV84: $i,SV25: $i,SV58: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ( SV58 != create_slb ) )
| ~ ( contains_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV25 ) @ ( lookup_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) ) )
| ( ( findmin_cpq_eff @ ( triple @ SV25 @ SV58 @ SV84 ) )
= ( triple @ SV25 @ ( update_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(276,plain,
! [SV85: $i,SV59: $i,SV26: $i,SV104: $i] :
( ( ! [SY268: $i] :
( ~ ( strictly_less_than @ SV104 @ SY268 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SV59 @ ( pair @ SV104 @ SY268 ) ) @ SV85 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SV59 @ ( pair @ SV104 @ SY268 ) ) @ SV85 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(277,plain,
! [SV60: $i,SV27: $i] :
( ( ~ ( ~ ( strictly_less_than @ SV27 @ SV60 )
| ~ ( ~ ( less_than @ SV27 @ SV60 )
| ~ ~ ( less_than @ SV60 @ SV27 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(278,plain,
! [SV60: $i,SV27: $i] :
( ( ~ ( ~ ~ ( ~ ( less_than @ SV27 @ SV60 )
| ~ ~ ( less_than @ SV60 @ SV27 ) )
| ( strictly_less_than @ SV27 @ SV60 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(279,plain,
! [SV86: $i,SV105: $i,SV61: $i,SV28: $i] :
( ( ~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV28 @ ( pair @ SV61 @ SV105 ) ) @ SV86 )
| ( contains_slb @ SV28 @ SV86 )
| ( SV61 = SV86 ) )
| ~ ( ~ ( ( contains_slb @ SV28 @ SV86 )
| ( SV61 = SV86 ) )
| ( contains_slb @ ( insert_slb @ SV28 @ ( pair @ SV61 @ SV105 ) ) @ SV86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(280,plain,
! [SV87: $i,SV29: $i,SV62: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ( SV62 != create_slb ) )
| ~ ( contains_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) )
| ~ ( less_than @ ( lookup_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ ( findmin_pqp_res @ SV29 ) ) )
| ( ( findmin_cpq_eff @ ( triple @ SV29 @ SV62 @ SV87 ) )
= ( triple @ SV29 @ ( update_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(281,plain,
! [SV107: $i,SV88: $i,SV63: $i,SV30: $i] :
( ( ~ ( ~ ( ~ ( contains_cpq @ ( triple @ SV30 @ SV63 @ SV88 ) @ SV107 )
| ( contains_slb @ SV63 @ SV107 ) )
| ~ ( ~ ( contains_slb @ SV63 @ SV107 )
| ( contains_cpq @ ( triple @ SV30 @ SV63 @ SV88 ) @ SV107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(282,plain,
! [SV89: $i,SV64: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( less_than @ SV31 @ SV64 )
| ~ ( less_than @ SV64 @ SV89 ) ) )
= $true )
| ( ( less_than @ SV31 @ SV89 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(283,plain,
! [SV65: $i,SV32: $i] :
( ( ~ ( ~ ( ok @ ( triple @ SV32 @ SV65 @ bad ) )
| $false ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[257]) ).
thf(284,plain,
! [SV65: $i,SV32: $i] :
( ( ~ ( ~ $false
| ( ok @ ( triple @ SV32 @ SV65 @ bad ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[257]) ).
thf(285,plain,
! [SV90: $i,SV33: $i,SV66: $i] :
( ( ~ ~ ( ~ ( ( SV66 != create_slb ) )
| ~ ~ ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV33 ) ) )
| ( ( findmin_cpq_eff @ ( triple @ SV33 @ SV66 @ SV90 ) )
= ( triple @ SV33 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV33 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(286,plain,
! [SV91: $i,SV67: $i,SV34: $i,SV109: $i] :
( ( ! [SY269: $i] :
( ~ ( less_than @ SY269 @ SV109 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SV67 @ ( pair @ SV109 @ SY269 ) ) @ SV91 ) )
| ( check_cpq @ ( triple @ SV34 @ SV67 @ SV91 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV34 @ SV67 @ SV91 ) )
| ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SV67 @ ( pair @ SV109 @ SY269 ) ) @ SV91 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(287,plain,
! [SV92: $i,SV35: $i,SV110: $i,SV68: $i] :
( ( ~ ~ ( ~ ( contains_slb @ SV68 @ SV110 )
| ~ ( strictly_less_than @ SV110 @ ( lookup_slb @ SV68 @ SV110 ) ) )
| ( ( remove_cpq @ ( triple @ SV35 @ SV68 @ SV92 ) @ SV110 )
= ( triple @ ( remove_pqp @ SV35 @ SV110 ) @ ( remove_slb @ SV68 @ SV110 ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(288,plain,
! [SV111: $i,SV36: $i,SV93: $i,SV69: $i] :
( ( ~ ~ ( ~ ( ( SV69 != SV93 ) )
| ~ ( contains_slb @ SV36 @ SV93 ) )
| ( ( remove_slb @ ( insert_slb @ SV36 @ ( pair @ SV69 @ SV111 ) ) @ SV93 )
= ( insert_slb @ ( remove_slb @ SV36 @ SV93 ) @ ( pair @ SV69 @ SV111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(289,plain,
! [SV94: $i,SV37: $i,SV70: $i] :
( ( ~ ( ( SV70 != create_slb ) )
| ( ( findmin_cpq_res @ ( triple @ SV37 @ SV70 @ SV94 ) )
= ( findmin_pqp_res @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(290,plain,
! [SV95: $i,SV38: $i,SV113: $i,SV71: $i] :
( ( ~ ~ ( ~ ( contains_slb @ SV71 @ SV113 )
| ~ ( less_than @ ( lookup_slb @ SV71 @ SV113 ) @ SV113 ) )
| ( ( remove_cpq @ ( triple @ SV38 @ SV71 @ SV95 ) @ SV113 )
= ( triple @ ( remove_pqp @ SV38 @ SV113 ) @ ( remove_slb @ SV71 @ SV113 ) @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(291,plain,
! [SV96: $i,SV72: $i,SV39: $i] :
( ( ( ~ ~ ( ok @ ( triple @ SV39 @ SV72 @ SV96 ) ) )
= $true )
| ( ( SV96 = bad )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(292,plain,
! [SV97: $i,SV114: $i,SV73: $i,SV40: $i] :
( ( ! [SY270: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SY270 )
| ( pair_in_list @ SV40 @ SV97 @ SY270 )
| ~ ( ( SV73 != SV97 )
| ( SV114 != SY270 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV40 @ SV97 @ SY270 )
| ~ ( ( SV73 != SV97 )
| ( SV114 != SY270 ) ) )
| ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SY270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(293,plain,
! [SV78: $i,SV19: $i,SV99: $i,SV52: $i] :
( ( ( ~ ~ ( contains_slb @ SV52 @ SV99 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV19 @ SV52 @ SV78 ) @ SV99 )
= ( triple @ SV19 @ SV52 @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(294,plain,
! [SV79: $i,SV53: $i,SV20: $i] :
( ( ( succ_cpq @ SV20 @ SV53 )
= $false )
| ( ( succ_cpq @ SV20 @ ( insert_cpq @ SV53 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(295,plain,
! [SV80: $i,SV54: $i,SV21: $i] :
( ( ( succ_cpq @ SV21 @ SV54 )
= $false )
| ( ( succ_cpq @ SV21 @ ( remove_cpq @ SV54 @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(296,plain,
! [SV55: $i,SV22: $i,SV100: $i,SV81: $i] :
( ( ( ~ ( less_than @ SV81 @ SV100 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV22 @ ( pair @ SV55 @ SV100 ) ) @ SV81 )
= ( insert_slb @ ( update_slb @ SV22 @ SV81 ) @ ( pair @ SV55 @ SV100 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(297,plain,
! [SV101: $i,SV23: $i,SV82: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ( ( SV56 != SV82 ) )
| ~ ( contains_slb @ SV23 @ SV82 ) ) )
= $true )
| ( ( ( lookup_slb @ ( insert_slb @ SV23 @ ( pair @ SV56 @ SV101 ) ) @ SV82 )
= ( lookup_slb @ SV23 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(298,plain,
! [SV57: $i,SV24: $i,SV83: $i,SV102: $i] :
( ( ( ~ ( strictly_less_than @ SV102 @ SV83 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV24 @ ( pair @ SV57 @ SV102 ) ) @ SV83 )
= ( insert_slb @ ( update_slb @ SV24 @ SV83 ) @ ( pair @ SV57 @ SV83 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(299,plain,
! [SV84: $i,SV25: $i,SV58: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV58 != create_slb ) )
| ~ ( contains_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV25 ) @ ( lookup_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) ) ) )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV25 @ SV58 @ SV84 ) )
= ( triple @ SV25 @ ( update_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(300,plain,
! [SV85: $i,SV59: $i,SV26: $i,SV115: $i,SV104: $i] :
( ( ~ ( strictly_less_than @ SV104 @ SV115 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SV59 @ ( pair @ SV104 @ SV115 ) ) @ SV85 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SV59 @ ( pair @ SV104 @ SV115 ) ) @ SV85 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(301,plain,
! [SV60: $i,SV27: $i] :
( ( ~ ( strictly_less_than @ SV27 @ SV60 )
| ~ ( ~ ( less_than @ SV27 @ SV60 )
| ~ ~ ( less_than @ SV60 @ SV27 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(302,plain,
! [SV60: $i,SV27: $i] :
( ( ~ ~ ( ~ ( less_than @ SV27 @ SV60 )
| ~ ~ ( less_than @ SV60 @ SV27 ) )
| ( strictly_less_than @ SV27 @ SV60 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(303,plain,
! [SV86: $i,SV105: $i,SV61: $i,SV28: $i] :
( ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV28 @ ( pair @ SV61 @ SV105 ) ) @ SV86 )
| ( contains_slb @ SV28 @ SV86 )
| ( SV61 = SV86 ) )
| ~ ( ~ ( ( contains_slb @ SV28 @ SV86 )
| ( SV61 = SV86 ) )
| ( contains_slb @ ( insert_slb @ SV28 @ ( pair @ SV61 @ SV105 ) ) @ SV86 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(304,plain,
! [SV87: $i,SV29: $i,SV62: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ( SV62 != create_slb ) )
| ~ ( contains_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) )
| ~ ( less_than @ ( lookup_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ ( findmin_pqp_res @ SV29 ) ) ) )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV29 @ SV62 @ SV87 ) )
= ( triple @ SV29 @ ( update_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(305,plain,
! [SV107: $i,SV88: $i,SV63: $i,SV30: $i] :
( ( ~ ( ~ ( contains_cpq @ ( triple @ SV30 @ SV63 @ SV88 ) @ SV107 )
| ( contains_slb @ SV63 @ SV107 ) )
| ~ ( ~ ( contains_slb @ SV63 @ SV107 )
| ( contains_cpq @ ( triple @ SV30 @ SV63 @ SV88 ) @ SV107 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(306,plain,
! [SV89: $i,SV64: $i,SV31: $i] :
( ( ( ~ ( ~ ( less_than @ SV31 @ SV64 )
| ~ ( less_than @ SV64 @ SV89 ) ) )
= $false )
| ( ( less_than @ SV31 @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(307,plain,
! [SV65: $i,SV32: $i] :
( ( ~ ( ok @ ( triple @ SV32 @ SV65 @ bad ) )
| $false )
= $true ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(308,plain,
! [SV65: $i,SV32: $i] :
( ( ~ $false
| ( ok @ ( triple @ SV32 @ SV65 @ bad ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(309,plain,
! [SV90: $i,SV33: $i,SV66: $i] :
( ( ( ~ ~ ( ~ ( ( SV66 != create_slb ) )
| ~ ~ ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV33 ) ) ) )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV33 @ SV66 @ SV90 ) )
= ( triple @ SV33 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV33 ) ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(310,plain,
! [SV91: $i,SV67: $i,SV34: $i,SV109: $i,SV116: $i] :
( ( ~ ( less_than @ SV116 @ SV109 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SV67 @ ( pair @ SV109 @ SV116 ) ) @ SV91 ) )
| ( check_cpq @ ( triple @ SV34 @ SV67 @ SV91 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV34 @ SV67 @ SV91 ) )
| ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SV67 @ ( pair @ SV109 @ SV116 ) ) @ SV91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(311,plain,
! [SV92: $i,SV35: $i,SV110: $i,SV68: $i] :
( ( ( ~ ~ ( ~ ( contains_slb @ SV68 @ SV110 )
| ~ ( strictly_less_than @ SV110 @ ( lookup_slb @ SV68 @ SV110 ) ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV35 @ SV68 @ SV92 ) @ SV110 )
= ( triple @ ( remove_pqp @ SV35 @ SV110 ) @ ( remove_slb @ SV68 @ SV110 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(312,plain,
! [SV111: $i,SV36: $i,SV93: $i,SV69: $i] :
( ( ( ~ ~ ( ~ ( ( SV69 != SV93 ) )
| ~ ( contains_slb @ SV36 @ SV93 ) ) )
= $true )
| ( ( ( remove_slb @ ( insert_slb @ SV36 @ ( pair @ SV69 @ SV111 ) ) @ SV93 )
= ( insert_slb @ ( remove_slb @ SV36 @ SV93 ) @ ( pair @ SV69 @ SV111 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(313,plain,
! [SV94: $i,SV37: $i,SV70: $i] :
( ( ( ~ ( ( SV70 != create_slb ) ) )
= $true )
| ( ( ( findmin_cpq_res @ ( triple @ SV37 @ SV70 @ SV94 ) )
= ( findmin_pqp_res @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(314,plain,
! [SV95: $i,SV38: $i,SV113: $i,SV71: $i] :
( ( ( ~ ~ ( ~ ( contains_slb @ SV71 @ SV113 )
| ~ ( less_than @ ( lookup_slb @ SV71 @ SV113 ) @ SV113 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV38 @ SV71 @ SV95 ) @ SV113 )
= ( triple @ ( remove_pqp @ SV38 @ SV113 ) @ ( remove_slb @ SV71 @ SV113 ) @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(315,plain,
! [SV96: $i,SV72: $i,SV39: $i] :
( ( ( ~ ( ok @ ( triple @ SV39 @ SV72 @ SV96 ) ) )
= $false )
| ( ( SV96 = bad )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(316,plain,
! [SV117: $i,SV97: $i,SV114: $i,SV73: $i,SV40: $i] :
( ( ~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 )
| ( pair_in_list @ SV40 @ SV97 @ SV117 )
| ~ ( ( SV73 != SV97 )
| ( SV114 != SV117 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV40 @ SV97 @ SV117 )
| ~ ( ( SV73 != SV97 )
| ( SV114 != SV117 ) ) )
| ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(317,plain,
! [SV78: $i,SV19: $i,SV99: $i,SV52: $i] :
( ( ( ~ ( contains_slb @ SV52 @ SV99 ) )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV19 @ SV52 @ SV78 ) @ SV99 )
= ( triple @ SV19 @ SV52 @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(318,plain,
! [SV55: $i,SV22: $i,SV100: $i,SV81: $i] :
( ( ( less_than @ SV81 @ SV100 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV22 @ ( pair @ SV55 @ SV100 ) ) @ SV81 )
= ( insert_slb @ ( update_slb @ SV22 @ SV81 ) @ ( pair @ SV55 @ SV100 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(319,plain,
! [SV101: $i,SV23: $i,SV82: $i,SV56: $i] :
( ( ( ~ ( ~ ( ( SV56 != SV82 ) )
| ~ ( contains_slb @ SV23 @ SV82 ) ) )
= $false )
| ( ( ( lookup_slb @ ( insert_slb @ SV23 @ ( pair @ SV56 @ SV101 ) ) @ SV82 )
= ( lookup_slb @ SV23 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(320,plain,
! [SV57: $i,SV24: $i,SV83: $i,SV102: $i] :
( ( ( strictly_less_than @ SV102 @ SV83 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV24 @ ( pair @ SV57 @ SV102 ) ) @ SV83 )
= ( insert_slb @ ( update_slb @ SV24 @ SV83 ) @ ( pair @ SV57 @ SV83 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(321,plain,
! [SV84: $i,SV25: $i,SV58: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV58 != create_slb ) )
| ~ ( contains_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV25 ) @ ( lookup_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) ) ) )
= $false )
| ( ( ( findmin_cpq_eff @ ( triple @ SV25 @ SV58 @ SV84 ) )
= ( triple @ SV25 @ ( update_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(322,plain,
! [SV85: $i,SV59: $i,SV26: $i,SV115: $i,SV104: $i] :
( ( ( ~ ( strictly_less_than @ SV104 @ SV115 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SV59 @ ( pair @ SV104 @ SV115 ) ) @ SV85 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SV59 @ ( pair @ SV104 @ SV115 ) ) @ SV85 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(323,plain,
! [SV60: $i,SV27: $i] :
( ( ( ~ ( strictly_less_than @ SV27 @ SV60 ) )
= $true )
| ( ( ~ ( ~ ( less_than @ SV27 @ SV60 )
| ~ ~ ( less_than @ SV60 @ SV27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(324,plain,
! [SV60: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( less_than @ SV27 @ SV60 )
| ~ ~ ( less_than @ SV60 @ SV27 ) ) )
= $true )
| ( ( strictly_less_than @ SV27 @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(325,plain,
! [SV86: $i,SV105: $i,SV61: $i,SV28: $i] :
( ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV28 @ ( pair @ SV61 @ SV105 ) ) @ SV86 )
| ( contains_slb @ SV28 @ SV86 )
| ( SV61 = SV86 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(326,plain,
! [SV105: $i,SV61: $i,SV86: $i,SV28: $i] :
( ( ~ ( ~ ( ( contains_slb @ SV28 @ SV86 )
| ( SV61 = SV86 ) )
| ( contains_slb @ ( insert_slb @ SV28 @ ( pair @ SV61 @ SV105 ) ) @ SV86 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(327,plain,
! [SV87: $i,SV29: $i,SV62: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ( SV62 != create_slb ) )
| ~ ( contains_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) )
| ~ ( less_than @ ( lookup_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ ( findmin_pqp_res @ SV29 ) ) ) )
= $false )
| ( ( ( findmin_cpq_eff @ ( triple @ SV29 @ SV62 @ SV87 ) )
= ( triple @ SV29 @ ( update_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(328,plain,
! [SV107: $i,SV88: $i,SV63: $i,SV30: $i] :
( ( ~ ( ~ ( contains_cpq @ ( triple @ SV30 @ SV63 @ SV88 ) @ SV107 )
| ( contains_slb @ SV63 @ SV107 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(329,plain,
! [SV88: $i,SV30: $i,SV107: $i,SV63: $i] :
( ( ~ ( ~ ( contains_slb @ SV63 @ SV107 )
| ( contains_cpq @ ( triple @ SV30 @ SV63 @ SV88 ) @ SV107 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(330,plain,
! [SV89: $i,SV64: $i,SV31: $i] :
( ( ( ~ ( less_than @ SV31 @ SV64 )
| ~ ( less_than @ SV64 @ SV89 ) )
= $true )
| ( ( less_than @ SV31 @ SV89 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[306]) ).
thf(331,plain,
! [SV65: $i,SV32: $i] :
( ( ( ~ ( ok @ ( triple @ SV32 @ SV65 @ bad ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(332,plain,
! [SV65: $i,SV32: $i] :
( ( ( ~ $false ) = $true )
| ( ( ok @ ( triple @ SV32 @ SV65 @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(333,plain,
! [SV90: $i,SV33: $i,SV66: $i] :
( ( ( ~ ( ~ ( ( SV66 != create_slb ) )
| ~ ~ ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV33 ) ) ) )
= $false )
| ( ( ( findmin_cpq_eff @ ( triple @ SV33 @ SV66 @ SV90 ) )
= ( triple @ SV33 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV33 ) ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(334,plain,
! [SV91: $i,SV67: $i,SV34: $i,SV109: $i,SV116: $i] :
( ( ( ~ ( less_than @ SV116 @ SV109 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SV67 @ ( pair @ SV109 @ SV116 ) ) @ SV91 ) )
| ( check_cpq @ ( triple @ SV34 @ SV67 @ SV91 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV34 @ SV67 @ SV91 ) )
| ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SV67 @ ( pair @ SV109 @ SV116 ) ) @ SV91 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(335,plain,
! [SV92: $i,SV35: $i,SV110: $i,SV68: $i] :
( ( ( ~ ( ~ ( contains_slb @ SV68 @ SV110 )
| ~ ( strictly_less_than @ SV110 @ ( lookup_slb @ SV68 @ SV110 ) ) ) )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV35 @ SV68 @ SV92 ) @ SV110 )
= ( triple @ ( remove_pqp @ SV35 @ SV110 ) @ ( remove_slb @ SV68 @ SV110 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(336,plain,
! [SV111: $i,SV36: $i,SV93: $i,SV69: $i] :
( ( ( ~ ( ~ ( ( SV69 != SV93 ) )
| ~ ( contains_slb @ SV36 @ SV93 ) ) )
= $false )
| ( ( ( remove_slb @ ( insert_slb @ SV36 @ ( pair @ SV69 @ SV111 ) ) @ SV93 )
= ( insert_slb @ ( remove_slb @ SV36 @ SV93 ) @ ( pair @ SV69 @ SV111 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(337,plain,
! [SV94: $i,SV37: $i,SV70: $i] :
( ( ( SV70 != create_slb )
= $false )
| ( ( ( findmin_cpq_res @ ( triple @ SV37 @ SV70 @ SV94 ) )
= ( findmin_pqp_res @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(338,plain,
! [SV95: $i,SV38: $i,SV113: $i,SV71: $i] :
( ( ( ~ ( ~ ( contains_slb @ SV71 @ SV113 )
| ~ ( less_than @ ( lookup_slb @ SV71 @ SV113 ) @ SV113 ) ) )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV38 @ SV71 @ SV95 ) @ SV113 )
= ( triple @ ( remove_pqp @ SV38 @ SV113 ) @ ( remove_slb @ SV71 @ SV113 ) @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(339,plain,
! [SV96: $i,SV72: $i,SV39: $i] :
( ( ( ok @ ( triple @ SV39 @ SV72 @ SV96 ) )
= $true )
| ( ( SV96 = bad )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(340,plain,
! [SV117: $i,SV97: $i,SV114: $i,SV73: $i,SV40: $i] :
( ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 )
| ( pair_in_list @ SV40 @ SV97 @ SV117 )
| ~ ( ( SV73 != SV97 )
| ( SV114 != SV117 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV40 @ SV97 @ SV117 )
| ~ ( ( SV73 != SV97 )
| ( SV114 != SV117 ) ) )
| ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(341,plain,
! [SV78: $i,SV19: $i,SV99: $i,SV52: $i] :
( ( ( contains_slb @ SV52 @ SV99 )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV19 @ SV52 @ SV78 ) @ SV99 )
= ( triple @ SV19 @ SV52 @ bad ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[317]) ).
thf(342,plain,
! [SV101: $i,SV23: $i,SV82: $i,SV56: $i] :
( ( ( ~ ( ( SV56 != SV82 ) )
| ~ ( contains_slb @ SV23 @ SV82 ) )
= $true )
| ( ( ( lookup_slb @ ( insert_slb @ SV23 @ ( pair @ SV56 @ SV101 ) ) @ SV82 )
= ( lookup_slb @ SV23 @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[319]) ).
thf(343,plain,
! [SV84: $i,SV25: $i,SV58: $i] :
( ( ( ~ ~ ( ~ ( ( SV58 != create_slb ) )
| ~ ( contains_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV25 ) @ ( lookup_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) ) )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV25 @ SV58 @ SV84 ) )
= ( triple @ SV25 @ ( update_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) @ bad ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(344,plain,
! [SV85: $i,SV59: $i,SV26: $i,SV115: $i,SV104: $i] :
( ( ( strictly_less_than @ SV104 @ SV115 )
= $false )
| ( ( ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SV59 @ ( pair @ SV104 @ SV115 ) ) @ SV85 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SV59 @ ( pair @ SV104 @ SV115 ) ) @ SV85 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(345,plain,
! [SV60: $i,SV27: $i] :
( ( ( strictly_less_than @ SV27 @ SV60 )
= $false )
| ( ( ~ ( ~ ( less_than @ SV27 @ SV60 )
| ~ ~ ( less_than @ SV60 @ SV27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(346,plain,
! [SV60: $i,SV27: $i] :
( ( ( ~ ( ~ ( less_than @ SV27 @ SV60 )
| ~ ~ ( less_than @ SV60 @ SV27 ) ) )
= $false )
| ( ( strictly_less_than @ SV27 @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(347,plain,
! [SV86: $i,SV105: $i,SV61: $i,SV28: $i] :
( ( ~ ( contains_slb @ ( insert_slb @ SV28 @ ( pair @ SV61 @ SV105 ) ) @ SV86 )
| ( contains_slb @ SV28 @ SV86 )
| ( SV61 = SV86 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[325]) ).
thf(348,plain,
! [SV105: $i,SV61: $i,SV86: $i,SV28: $i] :
( ( ~ ( ( contains_slb @ SV28 @ SV86 )
| ( SV61 = SV86 ) )
| ( contains_slb @ ( insert_slb @ SV28 @ ( pair @ SV61 @ SV105 ) ) @ SV86 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(349,plain,
! [SV87: $i,SV29: $i,SV62: $i] :
( ( ( ~ ~ ( ~ ( ( SV62 != create_slb ) )
| ~ ( contains_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) )
| ~ ( less_than @ ( lookup_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ ( findmin_pqp_res @ SV29 ) ) )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV29 @ SV62 @ SV87 ) )
= ( triple @ SV29 @ ( update_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ SV87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[327]) ).
thf(350,plain,
! [SV107: $i,SV88: $i,SV63: $i,SV30: $i] :
( ( ~ ( contains_cpq @ ( triple @ SV30 @ SV63 @ SV88 ) @ SV107 )
| ( contains_slb @ SV63 @ SV107 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(351,plain,
! [SV88: $i,SV30: $i,SV107: $i,SV63: $i] :
( ( ~ ( contains_slb @ SV63 @ SV107 )
| ( contains_cpq @ ( triple @ SV30 @ SV63 @ SV88 ) @ SV107 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(352,plain,
! [SV89: $i,SV64: $i,SV31: $i] :
( ( ( ~ ( less_than @ SV31 @ SV64 ) )
= $true )
| ( ( ~ ( less_than @ SV64 @ SV89 ) )
= $true )
| ( ( less_than @ SV31 @ SV89 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(353,plain,
! [SV65: $i,SV32: $i] :
( ( ( ok @ ( triple @ SV32 @ SV65 @ bad ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(354,plain,
! [SV65: $i,SV32: $i] :
( ( $false = $false )
| ( ( ok @ ( triple @ SV32 @ SV65 @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(355,plain,
! [SV90: $i,SV33: $i,SV66: $i] :
( ( ( ~ ( ( SV66 != create_slb ) )
| ~ ~ ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV33 ) ) )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV33 @ SV66 @ SV90 ) )
= ( triple @ SV33 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV33 ) ) @ bad ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[333]) ).
thf(356,plain,
! [SV91: $i,SV67: $i,SV34: $i,SV109: $i,SV116: $i] :
( ( ( less_than @ SV116 @ SV109 )
= $false )
| ( ( ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SV67 @ ( pair @ SV109 @ SV116 ) ) @ SV91 ) )
| ( check_cpq @ ( triple @ SV34 @ SV67 @ SV91 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV34 @ SV67 @ SV91 ) )
| ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SV67 @ ( pair @ SV109 @ SV116 ) ) @ SV91 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(357,plain,
! [SV92: $i,SV35: $i,SV110: $i,SV68: $i] :
( ( ( ~ ( contains_slb @ SV68 @ SV110 )
| ~ ( strictly_less_than @ SV110 @ ( lookup_slb @ SV68 @ SV110 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV35 @ SV68 @ SV92 ) @ SV110 )
= ( triple @ ( remove_pqp @ SV35 @ SV110 ) @ ( remove_slb @ SV68 @ SV110 ) @ bad ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(358,plain,
! [SV111: $i,SV36: $i,SV93: $i,SV69: $i] :
( ( ( ~ ( ( SV69 != SV93 ) )
| ~ ( contains_slb @ SV36 @ SV93 ) )
= $true )
| ( ( ( remove_slb @ ( insert_slb @ SV36 @ ( pair @ SV69 @ SV111 ) ) @ SV93 )
= ( insert_slb @ ( remove_slb @ SV36 @ SV93 ) @ ( pair @ SV69 @ SV111 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[336]) ).
thf(359,plain,
! [SV94: $i,SV37: $i,SV70: $i] :
( ( ( SV70 = create_slb )
= $true )
| ( ( ( findmin_cpq_res @ ( triple @ SV37 @ SV70 @ SV94 ) )
= ( findmin_pqp_res @ SV37 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(360,plain,
! [SV95: $i,SV38: $i,SV113: $i,SV71: $i] :
( ( ( ~ ( contains_slb @ SV71 @ SV113 )
| ~ ( less_than @ ( lookup_slb @ SV71 @ SV113 ) @ SV113 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV38 @ SV71 @ SV95 ) @ SV113 )
= ( triple @ ( remove_pqp @ SV38 @ SV113 ) @ ( remove_slb @ SV71 @ SV113 ) @ SV95 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(361,plain,
! [SV117: $i,SV97: $i,SV114: $i,SV73: $i,SV40: $i] :
( ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 )
| ( pair_in_list @ SV40 @ SV97 @ SV117 )
| ~ ( ( SV73 != SV97 )
| ( SV114 != SV117 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(362,plain,
! [SV114: $i,SV73: $i,SV117: $i,SV97: $i,SV40: $i] :
( ( ~ ( ~ ( ( pair_in_list @ SV40 @ SV97 @ SV117 )
| ~ ( ( SV73 != SV97 )
| ( SV114 != SV117 ) ) )
| ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(363,plain,
! [SV101: $i,SV23: $i,SV82: $i,SV56: $i] :
( ( ( ~ ( ( SV56 != SV82 ) ) )
= $true )
| ( ( ~ ( contains_slb @ SV23 @ SV82 ) )
= $true )
| ( ( ( lookup_slb @ ( insert_slb @ SV23 @ ( pair @ SV56 @ SV101 ) ) @ SV82 )
= ( lookup_slb @ SV23 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(364,plain,
! [SV84: $i,SV25: $i,SV58: $i] :
( ( ( ~ ~ ( ~ ( ( SV58 != create_slb ) )
| ~ ( contains_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV25 ) @ ( lookup_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) ) )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV25 @ SV58 @ SV84 ) )
= ( triple @ SV25 @ ( update_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(365,plain,
! [SV85: $i,SV115: $i,SV104: $i,SV59: $i,SV26: $i] :
( ( ( ~ ( ~ ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SV59 @ ( pair @ SV104 @ SV115 ) ) @ SV85 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SV59 @ ( pair @ SV104 @ SV115 ) ) @ SV85 ) ) ) )
= $false )
| ( ( strictly_less_than @ SV104 @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(366,plain,
! [SV60: $i,SV27: $i] :
( ( ( ~ ( less_than @ SV27 @ SV60 )
| ~ ~ ( less_than @ SV60 @ SV27 ) )
= $false )
| ( ( strictly_less_than @ SV27 @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(367,plain,
! [SV60: $i,SV27: $i] :
( ( ( ~ ( less_than @ SV27 @ SV60 )
| ~ ~ ( less_than @ SV60 @ SV27 ) )
= $true )
| ( ( strictly_less_than @ SV27 @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(368,plain,
! [SV86: $i,SV105: $i,SV61: $i,SV28: $i] :
( ( ( ~ ( contains_slb @ ( insert_slb @ SV28 @ ( pair @ SV61 @ SV105 ) ) @ SV86 ) )
= $true )
| ( ( ( contains_slb @ SV28 @ SV86 )
| ( SV61 = SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(369,plain,
! [SV105: $i,SV61: $i,SV86: $i,SV28: $i] :
( ( ( ~ ( ( contains_slb @ SV28 @ SV86 )
| ( SV61 = SV86 ) ) )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV28 @ ( pair @ SV61 @ SV105 ) ) @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(370,plain,
! [SV87: $i,SV29: $i,SV62: $i] :
( ( ( ~ ~ ( ~ ( ( SV62 != create_slb ) )
| ~ ( contains_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ ( findmin_pqp_res @ SV29 ) ) )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV29 @ SV62 @ SV87 ) )
= ( triple @ SV29 @ ( update_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(371,plain,
! [SV107: $i,SV88: $i,SV63: $i,SV30: $i] :
( ( ( ~ ( contains_cpq @ ( triple @ SV30 @ SV63 @ SV88 ) @ SV107 ) )
= $true )
| ( ( contains_slb @ SV63 @ SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(372,plain,
! [SV88: $i,SV30: $i,SV107: $i,SV63: $i] :
( ( ( ~ ( contains_slb @ SV63 @ SV107 ) )
= $true )
| ( ( contains_cpq @ ( triple @ SV30 @ SV63 @ SV88 ) @ SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(373,plain,
! [SV89: $i,SV64: $i,SV31: $i] :
( ( ( less_than @ SV31 @ SV64 )
= $false )
| ( ( ~ ( less_than @ SV64 @ SV89 ) )
= $true )
| ( ( less_than @ SV31 @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(374,plain,
! [SV90: $i,SV33: $i,SV66: $i] :
( ( ( ~ ( ( SV66 != create_slb ) ) )
= $true )
| ( ( ~ ~ ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV33 ) ) )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV33 @ SV66 @ SV90 ) )
= ( triple @ SV33 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV33 ) ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(375,plain,
! [SV91: $i,SV116: $i,SV109: $i,SV67: $i,SV34: $i] :
( ( ( ~ ( ~ ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SV67 @ ( pair @ SV109 @ SV116 ) ) @ SV91 ) )
| ( check_cpq @ ( triple @ SV34 @ SV67 @ SV91 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV34 @ SV67 @ SV91 ) )
| ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SV67 @ ( pair @ SV109 @ SV116 ) ) @ SV91 ) ) ) )
= $false )
| ( ( less_than @ SV116 @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(376,plain,
! [SV92: $i,SV35: $i,SV110: $i,SV68: $i] :
( ( ( ~ ( contains_slb @ SV68 @ SV110 ) )
= $true )
| ( ( ~ ( strictly_less_than @ SV110 @ ( lookup_slb @ SV68 @ SV110 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV35 @ SV68 @ SV92 ) @ SV110 )
= ( triple @ ( remove_pqp @ SV35 @ SV110 ) @ ( remove_slb @ SV68 @ SV110 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(377,plain,
! [SV111: $i,SV36: $i,SV93: $i,SV69: $i] :
( ( ( ~ ( ( SV69 != SV93 ) ) )
= $true )
| ( ( ~ ( contains_slb @ SV36 @ SV93 ) )
= $true )
| ( ( ( remove_slb @ ( insert_slb @ SV36 @ ( pair @ SV69 @ SV111 ) ) @ SV93 )
= ( insert_slb @ ( remove_slb @ SV36 @ SV93 ) @ ( pair @ SV69 @ SV111 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(378,plain,
! [SV95: $i,SV38: $i,SV113: $i,SV71: $i] :
( ( ( ~ ( contains_slb @ SV71 @ SV113 ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV71 @ SV113 ) @ SV113 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV38 @ SV71 @ SV95 ) @ SV113 )
= ( triple @ ( remove_pqp @ SV38 @ SV113 ) @ ( remove_slb @ SV71 @ SV113 ) @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(379,plain,
! [SV117: $i,SV97: $i,SV114: $i,SV73: $i,SV40: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 )
| ( pair_in_list @ SV40 @ SV97 @ SV117 )
| ~ ( ( SV73 != SV97 )
| ( SV114 != SV117 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[361]) ).
thf(380,plain,
! [SV114: $i,SV73: $i,SV117: $i,SV97: $i,SV40: $i] :
( ( ~ ( ( pair_in_list @ SV40 @ SV97 @ SV117 )
| ~ ( ( SV73 != SV97 )
| ( SV114 != SV117 ) ) )
| ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[362]) ).
thf(381,plain,
! [SV101: $i,SV23: $i,SV82: $i,SV56: $i] :
( ( ( SV56 != SV82 )
= $false )
| ( ( ~ ( contains_slb @ SV23 @ SV82 ) )
= $true )
| ( ( ( lookup_slb @ ( insert_slb @ SV23 @ ( pair @ SV56 @ SV101 ) ) @ SV82 )
= ( lookup_slb @ SV23 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(382,plain,
! [SV84: $i,SV25: $i,SV58: $i] :
( ( ( ~ ( ~ ( ( SV58 != create_slb ) )
| ~ ( contains_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) ) )
= $false )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV25 ) @ ( lookup_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) ) )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV25 @ SV58 @ SV84 ) )
= ( triple @ SV25 @ ( update_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(383,plain,
! [SV85: $i,SV115: $i,SV104: $i,SV59: $i,SV26: $i] :
( ( ( ~ ( ~ ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SV59 @ ( pair @ SV104 @ SV115 ) ) @ SV85 ) )
| $false ) )
= $false )
| ( ( strictly_less_than @ SV104 @ SV115 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[365]) ).
thf(384,plain,
! [SV85: $i,SV115: $i,SV104: $i,SV59: $i,SV26: $i] :
( ( ( ~ ( ~ $false
| ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SV59 @ ( pair @ SV104 @ SV115 ) ) @ SV85 ) ) ) )
= $false )
| ( ( strictly_less_than @ SV104 @ SV115 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[365]) ).
thf(385,plain,
! [SV60: $i,SV27: $i] :
( ( ( ~ ( less_than @ SV27 @ SV60 ) )
= $false )
| ( ( strictly_less_than @ SV27 @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[366]) ).
thf(386,plain,
! [SV27: $i,SV60: $i] :
( ( ( ~ ~ ( less_than @ SV60 @ SV27 ) )
= $false )
| ( ( strictly_less_than @ SV27 @ SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[366]) ).
thf(387,plain,
! [SV60: $i,SV27: $i] :
( ( ( ~ ( less_than @ SV27 @ SV60 ) )
= $true )
| ( ( ~ ~ ( less_than @ SV60 @ SV27 ) )
= $true )
| ( ( strictly_less_than @ SV27 @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(388,plain,
! [SV86: $i,SV105: $i,SV61: $i,SV28: $i] :
( ( ( contains_slb @ ( insert_slb @ SV28 @ ( pair @ SV61 @ SV105 ) ) @ SV86 )
= $false )
| ( ( ( contains_slb @ SV28 @ SV86 )
| ( SV61 = SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(389,plain,
! [SV105: $i,SV61: $i,SV86: $i,SV28: $i] :
( ( ( ( contains_slb @ SV28 @ SV86 )
| ( SV61 = SV86 ) )
= $false )
| ( ( contains_slb @ ( insert_slb @ SV28 @ ( pair @ SV61 @ SV105 ) ) @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(390,plain,
! [SV87: $i,SV29: $i,SV62: $i] :
( ( ( ~ ( ~ ( ( SV62 != create_slb ) )
| ~ ( contains_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) ) )
= $false )
| ( ( ~ ( less_than @ ( lookup_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ ( findmin_pqp_res @ SV29 ) ) )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV29 @ SV62 @ SV87 ) )
= ( triple @ SV29 @ ( update_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(391,plain,
! [SV107: $i,SV88: $i,SV63: $i,SV30: $i] :
( ( ( contains_cpq @ ( triple @ SV30 @ SV63 @ SV88 ) @ SV107 )
= $false )
| ( ( contains_slb @ SV63 @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(392,plain,
! [SV88: $i,SV30: $i,SV107: $i,SV63: $i] :
( ( ( contains_slb @ SV63 @ SV107 )
= $false )
| ( ( contains_cpq @ ( triple @ SV30 @ SV63 @ SV88 ) @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(393,plain,
! [SV31: $i,SV89: $i,SV64: $i] :
( ( ( less_than @ SV64 @ SV89 )
= $false )
| ( ( less_than @ SV31 @ SV64 )
= $false )
| ( ( less_than @ SV31 @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(394,plain,
! [SV90: $i,SV33: $i,SV66: $i] :
( ( ( SV66 != create_slb )
= $false )
| ( ( ~ ~ ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV33 ) ) )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV33 @ SV66 @ SV90 ) )
= ( triple @ SV33 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV33 ) ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(395,plain,
! [SV91: $i,SV116: $i,SV109: $i,SV67: $i,SV34: $i] :
( ( ( ~ ( ~ ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SV67 @ ( pair @ SV109 @ SV116 ) ) @ SV91 ) )
| ( check_cpq @ ( triple @ SV34 @ SV67 @ SV91 ) ) ) )
= $false )
| ( ( less_than @ SV116 @ SV109 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[375]) ).
thf(396,plain,
! [SV116: $i,SV109: $i,SV91: $i,SV67: $i,SV34: $i] :
( ( ( ~ ( ~ ( check_cpq @ ( triple @ SV34 @ SV67 @ SV91 ) )
| ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SV67 @ ( pair @ SV109 @ SV116 ) ) @ SV91 ) ) ) )
= $false )
| ( ( less_than @ SV116 @ SV109 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[375]) ).
thf(397,plain,
! [SV92: $i,SV35: $i,SV110: $i,SV68: $i] :
( ( ( contains_slb @ SV68 @ SV110 )
= $false )
| ( ( ~ ( strictly_less_than @ SV110 @ ( lookup_slb @ SV68 @ SV110 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV35 @ SV68 @ SV92 ) @ SV110 )
= ( triple @ ( remove_pqp @ SV35 @ SV110 ) @ ( remove_slb @ SV68 @ SV110 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(398,plain,
! [SV111: $i,SV36: $i,SV93: $i,SV69: $i] :
( ( ( SV69 != SV93 )
= $false )
| ( ( ~ ( contains_slb @ SV36 @ SV93 ) )
= $true )
| ( ( ( remove_slb @ ( insert_slb @ SV36 @ ( pair @ SV69 @ SV111 ) ) @ SV93 )
= ( insert_slb @ ( remove_slb @ SV36 @ SV93 ) @ ( pair @ SV69 @ SV111 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(399,plain,
! [SV95: $i,SV38: $i,SV113: $i,SV71: $i] :
( ( ( contains_slb @ SV71 @ SV113 )
= $false )
| ( ( ~ ( less_than @ ( lookup_slb @ SV71 @ SV113 ) @ SV113 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV38 @ SV71 @ SV95 ) @ SV113 )
= ( triple @ ( remove_pqp @ SV38 @ SV113 ) @ ( remove_slb @ SV71 @ SV113 ) @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(400,plain,
! [SV117: $i,SV97: $i,SV114: $i,SV73: $i,SV40: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 ) )
= $true )
| ( ( ( pair_in_list @ SV40 @ SV97 @ SV117 )
| ~ ( ( SV73 != SV97 )
| ( SV114 != SV117 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(401,plain,
! [SV114: $i,SV73: $i,SV117: $i,SV97: $i,SV40: $i] :
( ( ( ~ ( ( pair_in_list @ SV40 @ SV97 @ SV117 )
| ~ ( ( SV73 != SV97 )
| ( SV114 != SV117 ) ) ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(402,plain,
! [SV101: $i,SV23: $i,SV82: $i,SV56: $i] :
( ( ( SV56 = SV82 )
= $true )
| ( ( ~ ( contains_slb @ SV23 @ SV82 ) )
= $true )
| ( ( ( lookup_slb @ ( insert_slb @ SV23 @ ( pair @ SV56 @ SV101 ) ) @ SV82 )
= ( lookup_slb @ SV23 @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[381]) ).
thf(403,plain,
! [SV84: $i,SV25: $i,SV58: $i] :
( ( ( ~ ( ( SV58 != create_slb ) )
| ~ ( contains_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV25 ) @ ( lookup_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) ) )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV25 @ SV58 @ SV84 ) )
= ( triple @ SV25 @ ( update_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) @ bad ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[382]) ).
thf(404,plain,
! [SV85: $i,SV115: $i,SV104: $i,SV59: $i,SV26: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SV59 @ ( pair @ SV104 @ SV115 ) ) @ SV85 ) )
| $false )
= $true )
| ( ( strictly_less_than @ SV104 @ SV115 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[383]) ).
thf(405,plain,
! [SV85: $i,SV115: $i,SV104: $i,SV59: $i,SV26: $i] :
( ( ( ~ $false
| ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SV59 @ ( pair @ SV104 @ SV115 ) ) @ SV85 ) ) )
= $true )
| ( ( strictly_less_than @ SV104 @ SV115 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[384]) ).
thf(406,plain,
! [SV60: $i,SV27: $i] :
( ( ( less_than @ SV27 @ SV60 )
= $true )
| ( ( strictly_less_than @ SV27 @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[385]) ).
thf(407,plain,
! [SV27: $i,SV60: $i] :
( ( ( ~ ( less_than @ SV60 @ SV27 ) )
= $true )
| ( ( strictly_less_than @ SV27 @ SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[386]) ).
thf(408,plain,
! [SV60: $i,SV27: $i] :
( ( ( less_than @ SV27 @ SV60 )
= $false )
| ( ( ~ ~ ( less_than @ SV60 @ SV27 ) )
= $true )
| ( ( strictly_less_than @ SV27 @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(409,plain,
! [SV105: $i,SV61: $i,SV86: $i,SV28: $i] :
( ( ( contains_slb @ SV28 @ SV86 )
= $true )
| ( ( SV61 = SV86 )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV28 @ ( pair @ SV61 @ SV105 ) ) @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(410,plain,
! [SV105: $i,SV61: $i,SV86: $i,SV28: $i] :
( ( ( contains_slb @ SV28 @ SV86 )
= $false )
| ( ( contains_slb @ ( insert_slb @ SV28 @ ( pair @ SV61 @ SV105 ) ) @ SV86 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(411,plain,
! [SV105: $i,SV28: $i,SV86: $i,SV61: $i] :
( ( ( SV61 = SV86 )
= $false )
| ( ( contains_slb @ ( insert_slb @ SV28 @ ( pair @ SV61 @ SV105 ) ) @ SV86 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(412,plain,
! [SV87: $i,SV29: $i,SV62: $i] :
( ( ( ~ ( ( SV62 != create_slb ) )
| ~ ( contains_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ ( findmin_pqp_res @ SV29 ) ) )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV29 @ SV62 @ SV87 ) )
= ( triple @ SV29 @ ( update_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ SV87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[390]) ).
thf(413,plain,
! [SV90: $i,SV33: $i,SV66: $i] :
( ( ( SV66 = create_slb )
= $true )
| ( ( ~ ~ ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV33 ) ) )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV33 @ SV66 @ SV90 ) )
= ( triple @ SV33 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV33 ) ) @ bad ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[394]) ).
thf(414,plain,
! [SV91: $i,SV116: $i,SV109: $i,SV67: $i,SV34: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SV67 @ ( pair @ SV109 @ SV116 ) ) @ SV91 ) )
| ( check_cpq @ ( triple @ SV34 @ SV67 @ SV91 ) ) )
= $true )
| ( ( less_than @ SV116 @ SV109 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[395]) ).
thf(415,plain,
! [SV116: $i,SV109: $i,SV91: $i,SV67: $i,SV34: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV34 @ SV67 @ SV91 ) )
| ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SV67 @ ( pair @ SV109 @ SV116 ) ) @ SV91 ) ) )
= $true )
| ( ( less_than @ SV116 @ SV109 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[396]) ).
thf(416,plain,
! [SV92: $i,SV35: $i,SV68: $i,SV110: $i] :
( ( ( strictly_less_than @ SV110 @ ( lookup_slb @ SV68 @ SV110 ) )
= $false )
| ( ( contains_slb @ SV68 @ SV110 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV35 @ SV68 @ SV92 ) @ SV110 )
= ( triple @ ( remove_pqp @ SV35 @ SV110 ) @ ( remove_slb @ SV68 @ SV110 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(417,plain,
! [SV111: $i,SV36: $i,SV93: $i,SV69: $i] :
( ( ( SV69 = SV93 )
= $true )
| ( ( ~ ( contains_slb @ SV36 @ SV93 ) )
= $true )
| ( ( ( remove_slb @ ( insert_slb @ SV36 @ ( pair @ SV69 @ SV111 ) ) @ SV93 )
= ( insert_slb @ ( remove_slb @ SV36 @ SV93 ) @ ( pair @ SV69 @ SV111 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[398]) ).
thf(418,plain,
! [SV95: $i,SV38: $i,SV113: $i,SV71: $i] :
( ( ( less_than @ ( lookup_slb @ SV71 @ SV113 ) @ SV113 )
= $false )
| ( ( contains_slb @ SV71 @ SV113 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV38 @ SV71 @ SV95 ) @ SV113 )
= ( triple @ ( remove_pqp @ SV38 @ SV113 ) @ ( remove_slb @ SV71 @ SV113 ) @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(419,plain,
! [SV117: $i,SV97: $i,SV114: $i,SV73: $i,SV40: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 )
= $false )
| ( ( ( pair_in_list @ SV40 @ SV97 @ SV117 )
| ~ ( ( SV73 != SV97 )
| ( SV114 != SV117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(420,plain,
! [SV114: $i,SV73: $i,SV117: $i,SV97: $i,SV40: $i] :
( ( ( ( pair_in_list @ SV40 @ SV97 @ SV117 )
| ~ ( ( SV73 != SV97 )
| ( SV114 != SV117 ) ) )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(421,plain,
! [SV101: $i,SV56: $i,SV82: $i,SV23: $i] :
( ( ( contains_slb @ SV23 @ SV82 )
= $false )
| ( ( SV56 = SV82 )
= $true )
| ( ( ( lookup_slb @ ( insert_slb @ SV23 @ ( pair @ SV56 @ SV101 ) ) @ SV82 )
= ( lookup_slb @ SV23 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(422,plain,
! [SV84: $i,SV25: $i,SV58: $i] :
( ( ( ~ ( ( SV58 != create_slb ) ) )
= $true )
| ( ( ~ ( contains_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV25 ) @ ( lookup_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) ) )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV25 @ SV58 @ SV84 ) )
= ( triple @ SV25 @ ( update_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(423,plain,
! [SV85: $i,SV115: $i,SV104: $i,SV59: $i,SV26: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SV59 @ ( pair @ SV104 @ SV115 ) ) @ SV85 ) ) )
= $true )
| ( $false = $true )
| ( ( strictly_less_than @ SV104 @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(424,plain,
! [SV85: $i,SV115: $i,SV104: $i,SV59: $i,SV26: $i] :
( ( ( ~ $false ) = $true )
| ( ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SV59 @ ( pair @ SV104 @ SV115 ) ) @ SV85 ) )
= $true )
| ( ( strictly_less_than @ SV104 @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(425,plain,
! [SV27: $i,SV60: $i] :
( ( ( less_than @ SV60 @ SV27 )
= $false )
| ( ( strictly_less_than @ SV27 @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(426,plain,
! [SV27: $i,SV60: $i] :
( ( ( ~ ( less_than @ SV60 @ SV27 ) )
= $false )
| ( ( less_than @ SV27 @ SV60 )
= $false )
| ( ( strictly_less_than @ SV27 @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(427,plain,
! [SV87: $i,SV29: $i,SV62: $i] :
( ( ( ~ ( ( SV62 != create_slb ) ) )
= $true )
| ( ( ~ ( contains_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ ( findmin_pqp_res @ SV29 ) ) )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV29 @ SV62 @ SV87 ) )
= ( triple @ SV29 @ ( update_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(428,plain,
! [SV90: $i,SV33: $i,SV66: $i] :
( ( ( ~ ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV33 ) ) )
= $false )
| ( ( SV66 = create_slb )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV33 @ SV66 @ SV90 ) )
= ( triple @ SV33 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV33 ) ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(429,plain,
! [SV91: $i,SV116: $i,SV109: $i,SV67: $i,SV34: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SV67 @ ( pair @ SV109 @ SV116 ) ) @ SV91 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV34 @ SV67 @ SV91 ) )
= $true )
| ( ( less_than @ SV116 @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(430,plain,
! [SV116: $i,SV109: $i,SV91: $i,SV67: $i,SV34: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV34 @ SV67 @ SV91 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SV67 @ ( pair @ SV109 @ SV116 ) ) @ SV91 ) )
= $true )
| ( ( less_than @ SV116 @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(431,plain,
! [SV111: $i,SV69: $i,SV93: $i,SV36: $i] :
( ( ( contains_slb @ SV36 @ SV93 )
= $false )
| ( ( SV69 = SV93 )
= $true )
| ( ( ( remove_slb @ ( insert_slb @ SV36 @ ( pair @ SV69 @ SV111 ) ) @ SV93 )
= ( insert_slb @ ( remove_slb @ SV36 @ SV93 ) @ ( pair @ SV69 @ SV111 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(432,plain,
! [SV114: $i,SV73: $i,SV117: $i,SV97: $i,SV40: $i] :
( ( ( pair_in_list @ SV40 @ SV97 @ SV117 )
= $true )
| ( ( ~ ( ( SV73 != SV97 )
| ( SV114 != SV117 ) ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(433,plain,
! [SV114: $i,SV73: $i,SV117: $i,SV97: $i,SV40: $i] :
( ( ( pair_in_list @ SV40 @ SV97 @ SV117 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[420]) ).
thf(434,plain,
! [SV40: $i,SV117: $i,SV114: $i,SV97: $i,SV73: $i] :
( ( ( ~ ( ( SV73 != SV97 )
| ( SV114 != SV117 ) ) )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[420]) ).
thf(435,plain,
! [SV84: $i,SV25: $i,SV58: $i] :
( ( ( SV58 != create_slb )
= $false )
| ( ( ~ ( contains_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV25 ) @ ( lookup_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) ) )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV25 @ SV58 @ SV84 ) )
= ( triple @ SV25 @ ( update_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(436,plain,
! [SV85: $i,SV115: $i,SV104: $i,SV59: $i,SV26: $i] :
( ( ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SV59 @ ( pair @ SV104 @ SV115 ) ) @ SV85 ) )
= $false )
| ( $false = $true )
| ( ( strictly_less_than @ SV104 @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(437,plain,
! [SV85: $i,SV115: $i,SV104: $i,SV59: $i,SV26: $i] :
( ( $false = $false )
| ( ( check_cpq @ ( triple @ SV26 @ ( insert_slb @ SV59 @ ( pair @ SV104 @ SV115 ) ) @ SV85 ) )
= $true )
| ( ( strictly_less_than @ SV104 @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(438,plain,
! [SV27: $i,SV60: $i] :
( ( ( less_than @ SV60 @ SV27 )
= $true )
| ( ( less_than @ SV27 @ SV60 )
= $false )
| ( ( strictly_less_than @ SV27 @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[426]) ).
thf(439,plain,
! [SV87: $i,SV29: $i,SV62: $i] :
( ( ( SV62 != create_slb )
= $false )
| ( ( ~ ( contains_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ ( findmin_pqp_res @ SV29 ) ) )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV29 @ SV62 @ SV87 ) )
= ( triple @ SV29 @ ( update_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(440,plain,
! [SV90: $i,SV33: $i,SV66: $i] :
( ( ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV33 ) )
= $true )
| ( ( SV66 = create_slb )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV33 @ SV66 @ SV90 ) )
= ( triple @ SV33 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV33 ) ) @ bad ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(441,plain,
! [SV91: $i,SV116: $i,SV109: $i,SV67: $i,SV34: $i] :
( ( ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SV67 @ ( pair @ SV109 @ SV116 ) ) @ SV91 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV34 @ SV67 @ SV91 ) )
= $true )
| ( ( less_than @ SV116 @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(442,plain,
! [SV116: $i,SV109: $i,SV91: $i,SV67: $i,SV34: $i] :
( ( ( check_cpq @ ( triple @ SV34 @ SV67 @ SV91 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV34 @ ( insert_slb @ SV67 @ ( pair @ SV109 @ SV116 ) ) @ SV91 ) )
= $true )
| ( ( less_than @ SV116 @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(443,plain,
! [SV40: $i,SV117: $i,SV114: $i,SV97: $i,SV73: $i] :
( ( ( ( SV73 != SV97 )
| ( SV114 != SV117 ) )
= $false )
| ( ( pair_in_list @ SV40 @ SV97 @ SV117 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(444,plain,
! [SV40: $i,SV117: $i,SV114: $i,SV97: $i,SV73: $i] :
( ( ( ( SV73 != SV97 )
| ( SV114 != SV117 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(445,plain,
! [SV84: $i,SV25: $i,SV58: $i] :
( ( ( SV58 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV25 ) @ ( lookup_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) ) )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV25 @ SV58 @ SV84 ) )
= ( triple @ SV25 @ ( update_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) @ bad ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(446,plain,
! [SV87: $i,SV29: $i,SV62: $i] :
( ( ( SV62 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ ( findmin_pqp_res @ SV29 ) ) )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV29 @ SV62 @ SV87 ) )
= ( triple @ SV29 @ ( update_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ SV87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[439]) ).
thf(447,plain,
! [SV114: $i,SV117: $i,SV40: $i,SV97: $i,SV73: $i] :
( ( ( SV73 != SV97 )
= $false )
| ( ( pair_in_list @ SV40 @ SV97 @ SV117 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(448,plain,
! [SV73: $i,SV97: $i,SV40: $i,SV117: $i,SV114: $i] :
( ( ( SV114 != SV117 )
= $false )
| ( ( pair_in_list @ SV40 @ SV97 @ SV117 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(449,plain,
! [SV40: $i,SV117: $i,SV114: $i,SV97: $i,SV73: $i] :
( ( ( SV73 != SV97 )
= $true )
| ( ( SV114 != SV117 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(450,plain,
! [SV84: $i,SV25: $i,SV58: $i] :
( ( ( contains_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) )
= $false )
| ( ( SV58 = create_slb )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV25 ) @ ( lookup_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) ) )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV25 @ SV58 @ SV84 ) )
= ( triple @ SV25 @ ( update_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(451,plain,
! [SV87: $i,SV29: $i,SV62: $i] :
( ( ( contains_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) )
= $false )
| ( ( SV62 = create_slb )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ ( findmin_pqp_res @ SV29 ) ) )
= $true )
| ( ( ( findmin_cpq_eff @ ( triple @ SV29 @ SV62 @ SV87 ) )
= ( triple @ SV29 @ ( update_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(452,plain,
! [SV114: $i,SV117: $i,SV40: $i,SV97: $i,SV73: $i] :
( ( ( SV73 = SV97 )
= $true )
| ( ( pair_in_list @ SV40 @ SV97 @ SV117 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(453,plain,
! [SV73: $i,SV97: $i,SV40: $i,SV117: $i,SV114: $i] :
( ( ( SV114 = SV117 )
= $true )
| ( ( pair_in_list @ SV40 @ SV97 @ SV117 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(454,plain,
! [SV40: $i,SV117: $i,SV114: $i,SV97: $i,SV73: $i] :
( ( ( SV73 = SV97 )
= $false )
| ( ( SV114 != SV117 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(455,plain,
! [SV84: $i,SV58: $i,SV25: $i] :
( ( ( strictly_less_than @ ( findmin_pqp_res @ SV25 ) @ ( lookup_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) )
= $false )
| ( ( SV58 = create_slb )
= $true )
| ( ( contains_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) )
= $false )
| ( ( ( findmin_cpq_eff @ ( triple @ SV25 @ SV58 @ SV84 ) )
= ( triple @ SV25 @ ( update_slb @ SV58 @ ( findmin_pqp_res @ SV25 ) ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(456,plain,
! [SV87: $i,SV29: $i,SV62: $i] :
( ( ( less_than @ ( lookup_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ ( findmin_pqp_res @ SV29 ) )
= $false )
| ( ( SV62 = create_slb )
= $true )
| ( ( contains_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) )
= $false )
| ( ( ( findmin_cpq_eff @ ( triple @ SV29 @ SV62 @ SV87 ) )
= ( triple @ SV29 @ ( update_slb @ SV62 @ ( findmin_pqp_res @ SV29 ) ) @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(457,plain,
! [SV40: $i,SV97: $i,SV73: $i,SV117: $i,SV114: $i] :
( ( ( SV114 = SV117 )
= $false )
| ( ( SV73 = SV97 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV40 @ ( pair @ SV73 @ SV114 ) ) @ SV97 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(458,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[135,457,456,455,453,452,442,441,440,438,437,436,433,431,425,421,418,416,411,410,409,406,393,392,391,359,354,353,341,339,320,318,295,294,268,267,266,240,239,238,237,236,211,210,208,204,177,176,175,170,169,163,162,161]) ).
thf(459,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[458]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV378+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.20 % Computer : n010.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Oct 6 16:27:40 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.46/2.54
% 13.46/2.54 No.of.Axioms: 41
% 13.46/2.54
% 13.46/2.54 Length.of.Defs: 0
% 13.46/2.54
% 13.46/2.54 Contains.Choice.Funs: false
% 13.46/2.54 .................
% 13.46/2.54
% 13.46/2.54 ********************************
% 13.46/2.54 * All subproblems solved! *
% 13.46/2.54 ********************************
% 13.46/2.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:42,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:458,loop_count:0,foatp_calls:1,translation:fof_full)
% 13.46/2.54
% 13.46/2.54 %**** Beginning of derivation protocol ****
% 13.46/2.54 % SZS output start CNFRefutation
% See solution above
% 13.46/2.54
% 13.46/2.54 %**** End of derivation protocol ****
% 13.46/2.54 %**** no. of clauses in derivation: 459 ****
% 13.46/2.54 %**** clause counter: 458 ****
% 13.46/2.54
% 13.46/2.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:42,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:458,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------