TSTP Solution File: SWV390+1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SWV390+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 20:12:17 EDT 2022
% Result : Theorem 4.23s 4.43s
% Output : CNFRefutation 4.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 76
% Syntax : Number of formulae : 497 ( 322 unt; 33 typ; 0 def)
% Number of atoms : 2404 ( 916 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 6217 ( 657 ~; 664 |; 46 &;4788 @)
% ( 16 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 33 usr; 9 con; 0-3 aty)
% Number of variables : 1694 ( 0 ^1694 !; 0 ?;1694 :)
% 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_SY126,type,
sK2_SY126: $i ).
thf(tp_sK3_SY129,type,
sK3_SY129: $i ).
thf(tp_sK4_SY131,type,
sK4_SY131: $i ).
thf(tp_sK5_X,type,
sK5_X: $i > $i > $i ).
thf(tp_sK6_SY132,type,
sK6_SY132: $i > $i > $i ).
thf(tp_strictly_less_than,type,
strictly_less_than: $i > $i > $o ).
thf(tp_succ_cpq,type,
succ_cpq: $i > $i > $o ).
thf(tp_triple,type,
triple: $i > $i > $i > $i ).
thf(tp_update_slb,type,
update_slb: $i > $i > $i ).
thf(1,axiom,
! [U: $i] :
( ( 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,axiom,
! [U: $i,V: $i,W: $i] :
( ( check_cpq @ ( triple @ U @ V @ W ) )
<=> ! [X: $i,Y: $i] :
( ( pair_in_list @ V @ X @ Y )
=> ( less_than @ Y @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l26_li4142) ).
thf(43,conjecture,
! [U: $i,V: $i,W: $i] :
( ~ ( check_cpq @ ( triple @ U @ V @ W ) )
=> ! [X: $i] :
~ ( check_cpq @ ( insert_cpq @ ( triple @ U @ V @ W ) @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l26_co) ).
thf(44,negated_conjecture,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( check_cpq @ ( triple @ U @ V @ W ) )
=> ! [X: $i] :
~ ( check_cpq @ ( insert_cpq @ ( triple @ U @ V @ W ) @ X ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[43]) ).
thf(45,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( check_cpq @ ( triple @ U @ V @ W ) )
=> ! [X: $i] :
~ ( check_cpq @ ( insert_cpq @ ( triple @ U @ V @ W ) @ X ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[44]) ).
thf(46,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(47,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(48,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(49,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(50,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(51,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(52,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(53,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(54,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(55,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(56,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(57,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(58,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ( W = bad ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(59,plain,
( ( ! [U: $i,V: $i] :
( ( ok @ ( triple @ U @ V @ bad ) )
<=> $false ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(60,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(61,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(62,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(63,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(64,plain,
( ( ! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(65,plain,
( ( ! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(66,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(67,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(68,plain,
( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(69,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(70,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(71,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(72,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(73,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(74,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(75,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(76,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(77,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(78,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(79,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(80,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(81,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(82,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(83,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(84,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(85,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(86,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(87,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( check_cpq @ ( triple @ U @ V @ W ) )
<=> ! [X: $i,Y: $i] :
( ( pair_in_list @ V @ X @ Y )
=> ( less_than @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(88,plain,
( ( ! [SY126: $i,SY127: $i] :
( ~ ( check_cpq @ ( triple @ sK1_U @ SY126 @ SY127 ) )
=> ! [SY128: $i] :
~ ( check_cpq @ ( insert_cpq @ ( triple @ sK1_U @ SY126 @ SY127 ) @ SY128 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[45]) ).
thf(89,plain,
( ( ! [SY129: $i] :
( ~ ( check_cpq @ ( triple @ sK1_U @ sK2_SY126 @ SY129 ) )
=> ! [SY130: $i] :
~ ( check_cpq @ ( insert_cpq @ ( triple @ sK1_U @ sK2_SY126 @ SY129 ) @ SY130 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[88]) ).
thf(90,plain,
( ( ~ ( check_cpq @ ( triple @ sK1_U @ sK2_SY126 @ sK3_SY129 ) )
=> ! [SY131: $i] :
~ ( check_cpq @ ( insert_cpq @ ( triple @ sK1_U @ sK2_SY126 @ sK3_SY129 ) @ SY131 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[89]) ).
thf(91,plain,
( ( ~ ( check_cpq @ ( triple @ sK1_U @ sK2_SY126 @ sK3_SY129 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[90]) ).
thf(92,plain,
( ( ! [SY131: $i] :
~ ( check_cpq @ ( insert_cpq @ ( triple @ sK1_U @ sK2_SY126 @ sK3_SY129 ) @ SY131 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[90]) ).
thf(93,plain,
( ( ~ ! [SY131: $i] :
~ ( check_cpq @ ( insert_cpq @ ( triple @ sK1_U @ sK2_SY126 @ sK3_SY129 ) @ SY131 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[92]) ).
thf(94,plain,
( ( check_cpq @ ( insert_cpq @ ( triple @ sK1_U @ sK2_SY126 @ sK3_SY129 ) @ sK4_SY131 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[93]) ).
thf(95,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ! [W: $i] :
( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
= ( findmin_pqp_res @ U ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(96,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
| ~ ( less_than @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) @ ( findmin_pqp_res @ U ) )
| ! [W: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(97,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ U ) @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) )
| ! [W: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(98,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
| ! [W: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(99,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
| ~ ( strictly_less_than @ X @ ( lookup_slb @ V @ X ) )
| ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ bad ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(100,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
| ~ ( less_than @ ( lookup_slb @ V @ X ) @ X )
| ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(101,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_slb @ V @ X )
| ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ U @ V @ bad ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(102,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( triple @ U @ V @ W ) )
| ( W = bad ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(103,plain,
( ( ! [U: $i,V: $i] :
~ ( ok @ ( triple @ U @ V @ bad ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(104,plain,
( ( ! [U: $i,V: $i] :
( ! [W: $i,X: $i] :
( ~ ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
| ( contains_slb @ V @ X ) )
& ! [W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
| ( contains_cpq @ ( triple @ U @ V @ W ) @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(105,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ~ ( strictly_less_than @ X @ Y )
| ~ ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(106,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ! [X: $i,Y: $i] :
( ~ ( less_than @ Y @ X )
| ~ ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
| ( check_cpq @ ( triple @ U @ V @ W ) ) )
& ! [X: $i,Y: $i] :
( ~ ( less_than @ Y @ X )
| ~ ( check_cpq @ ( triple @ U @ V @ W ) )
| ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[62]) ).
thf(107,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(108,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(109,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(110,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(111,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( less_than @ W @ X )
| ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(112,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( strictly_less_than @ X @ W )
| ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(113,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( V = W )
| ~ ( contains_slb @ U @ W )
| ! [X: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( lookup_slb @ U @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[72]) ).
thf(114,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( V = W )
| ~ ( contains_slb @ U @ W )
| ! [X: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( remove_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(115,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
| ( V = W )
| ( pair_in_list @ U @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
| ( X = Y )
| ( pair_in_list @ U @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ( V != W )
| ( X != Y )
| ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ U @ W @ Y )
| ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[76]) ).
thf(116,plain,
( ( ! [U: $i,V: $i] :
( ! [W: $i] :
( ! [X: $i] :
~ ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
| ( V = W )
| ( contains_slb @ U @ W ) )
& ! [W: $i] :
( ( V != W )
| ! [X: $i] : ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W ) )
& ! [W: $i] :
( ~ ( contains_slb @ U @ W )
| ! [X: $i] : ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[78]) ).
thf(117,plain,
( ( ! [U: $i,V: $i] :
( ~ ( less_than @ U @ V )
| ( less_than @ V @ U )
| ( strictly_less_than @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( strictly_less_than @ U @ V )
| ( less_than @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( strictly_less_than @ U @ V )
| ~ ( less_than @ V @ U ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[83]) ).
thf(118,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( less_than @ U @ V )
| ~ ( less_than @ V @ W )
| ( less_than @ U @ W ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[86]) ).
thf(119,plain,
( ( ! [U: $i] :
( ! [V: $i] :
( ( ( pair_in_list @ V @ ( sK5_X @ V @ U ) @ ( sK6_SY132 @ V @ U ) )
& ~ ( less_than @ ( sK6_SY132 @ V @ U ) @ ( sK5_X @ V @ U ) ) )
| ! [W: $i] : ( check_cpq @ ( triple @ U @ V @ W ) ) )
& ! [V: $i] :
( ! [W: $i] :
~ ( check_cpq @ ( triple @ U @ V @ W ) )
| ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ V @ X @ Y )
| ( less_than @ Y @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(120,plain,
( ( ! [U: $i] :
( ! [V: $i] :
( ( ( pair_in_list @ V @ ( sK5_X @ V @ U ) @ ( sK6_SY132 @ V @ U ) )
& ~ ( less_than @ ( sK6_SY132 @ V @ U ) @ ( sK5_X @ V @ U ) ) )
| ! [W: $i] : ( check_cpq @ ( triple @ U @ V @ W ) ) )
& ! [V: $i] :
( ! [W: $i] :
~ ( check_cpq @ ( triple @ U @ V @ W ) )
| ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ V @ X @ Y )
| ( less_than @ Y @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(121,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( less_than @ U @ V )
| ~ ( less_than @ V @ W )
| ( less_than @ U @ W ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(122,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(123,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(124,plain,
( ( ! [U: $i,V: $i] :
( ~ ( less_than @ U @ V )
| ( less_than @ V @ U )
| ( strictly_less_than @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( strictly_less_than @ U @ V )
| ( less_than @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( strictly_less_than @ U @ V )
| ~ ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(125,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(126,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(127,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(128,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(129,plain,
( ( ! [U: $i,V: $i] :
( ! [W: $i] :
( ! [X: $i] :
~ ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
| ( V = W )
| ( contains_slb @ U @ W ) )
& ! [W: $i] :
( ( V != W )
| ! [X: $i] : ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W ) )
& ! [W: $i] :
( ~ ( contains_slb @ U @ W )
| ! [X: $i] : ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(130,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(131,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
| ( V = W )
| ( pair_in_list @ U @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
| ( X = Y )
| ( pair_in_list @ U @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ( V != W )
| ( X != Y )
| ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ U @ W @ Y )
| ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(132,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(133,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( V = W )
| ~ ( contains_slb @ U @ W )
| ! [X: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( remove_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(134,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(135,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( V = W )
| ~ ( contains_slb @ U @ W )
| ! [X: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( lookup_slb @ U @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(136,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(137,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)],[112]) ).
thf(138,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)],[111]) ).
thf(139,plain,
( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(140,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(141,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(142,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(143,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(144,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(145,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ! [X: $i,Y: $i] :
( ~ ( less_than @ Y @ X )
| ~ ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
| ( check_cpq @ ( triple @ U @ V @ W ) ) )
& ! [X: $i,Y: $i] :
( ~ ( less_than @ Y @ X )
| ~ ( check_cpq @ ( triple @ U @ V @ W ) )
| ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(146,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ~ ( strictly_less_than @ X @ Y )
| ~ ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(147,plain,
( ( ! [U: $i,V: $i] :
( ! [W: $i,X: $i] :
( ~ ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
| ( contains_slb @ V @ X ) )
& ! [W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
| ( contains_cpq @ ( triple @ U @ V @ W ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(148,plain,
( ( ! [U: $i,V: $i] :
~ ( ok @ ( triple @ U @ V @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(149,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( triple @ U @ V @ W ) )
| ( W = bad ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(150,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)],[57]) ).
thf(151,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_slb @ V @ X )
| ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ U @ V @ bad ) ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(152,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)],[100]) ).
thf(153,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)],[99]) ).
thf(154,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ create_slb @ V ) )
= ( triple @ U @ create_slb @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(155,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
| ! [W: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(156,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ U ) @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) )
| ! [W: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(157,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
| ~ ( less_than @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) @ ( findmin_pqp_res @ U ) )
| ! [W: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(158,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(159,plain,
( ( ! [U: $i,V: $i] :
( ( V = create_slb )
| ! [W: $i] :
( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
= ( findmin_pqp_res @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(160,plain,
( ( ! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(161,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(162,plain,
( ( ~ ( check_cpq @ ( triple @ sK1_U @ sK2_SY126 @ sK3_SY129 ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(163,plain,
( ( check_cpq @ ( insert_cpq @ ( triple @ sK1_U @ sK2_SY126 @ sK3_SY129 ) @ sK4_SY131 ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(164,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( contains_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ SX3 )
| ( contains_slb @ SX1 @ SX3 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( contains_slb @ SX1 @ SX3 )
| ( contains_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(165,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 )
| ( SX1 = SX2 )
| ( contains_slb @ SX0 @ SX2 ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ( SX1 != SX2 )
| ! [SX3: $i] : ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 ) )
| ~ ! [SX2: $i] :
( ~ ( contains_slb @ SX0 @ SX2 )
| ! [SX3: $i] : ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(166,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( pair_in_list @ SX1 @ ( sK5_X @ SX1 @ SX0 ) @ ( sK6_SY132 @ SX1 @ SX0 ) )
| ~ ~ ( less_than @ ( sK6_SY132 @ SX1 @ SX0 ) @ ( sK5_X @ SX1 @ SX0 ) ) )
| ! [SX2: $i] : ( check_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ! [SX2: $i] :
~ ( check_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ SX1 @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(167,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 )
| ( SX1 = SX2 )
| ( pair_in_list @ SX0 @ SX2 @ SX4 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 )
| ( SX3 = SX4 )
| ( pair_in_list @ SX0 @ SX2 @ SX4 ) ) )
| ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ( SX1 != SX2 )
| ( SX3 != SX4 )
| ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( pair_in_list @ SX0 @ SX2 @ SX4 )
| ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(168,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( less_than @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 )
| ( strictly_less_than @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(169,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( less_than @ SX4 @ SX3 )
| ~ ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ SX1 @ ( pair @ SX3 @ SX4 ) ) @ SX2 ) )
| ( check_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( less_than @ SX4 @ SX3 )
| ~ ( check_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ SX1 @ ( pair @ SX3 @ SX4 ) ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(170,plain,
! [SV1: $i] :
( ( ! [SY133: $i,SY134: $i] :
( ~ ( less_than @ SV1 @ SY133 )
| ~ ( less_than @ SY133 @ SY134 )
| ( less_than @ SV1 @ SY134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(171,plain,
! [SV2: $i] :
( ( ! [SY135: $i] :
( ( less_than @ SV2 @ SY135 )
| ( less_than @ SY135 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(172,plain,
! [SV3: $i] :
( ( less_than @ SV3 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(173,plain,
! [SV4: $i] :
( ( less_than @ bottom @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(174,plain,
( ( isnonempty_slb @ create_slb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(175,plain,
! [SV5: $i] :
( ( ! [SY136: $i,SY137: $i] : ( isnonempty_slb @ ( insert_slb @ SV5 @ ( pair @ SY136 @ SY137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(176,plain,
! [SV6: $i] :
( ( ~ ( contains_slb @ create_slb @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(177,plain,
! [SV7: $i] :
( ( ! [SY138: $i] :
~ ( pair_in_list @ create_slb @ SV7 @ SY138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(178,plain,
! [SV8: $i] :
( ( ! [SY139: $i,SY140: $i] :
( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SY139 @ SY140 ) ) @ SY139 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(179,plain,
! [SV9: $i] :
( ( ! [SY141: $i,SY142: $i] :
( ( SY141 = SY142 )
| ~ ( contains_slb @ SV9 @ SY142 )
| ! [SY143: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SY141 @ SY143 ) ) @ SY142 )
= ( insert_slb @ ( remove_slb @ SV9 @ SY142 ) @ ( pair @ SY141 @ SY143 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(180,plain,
! [SV10: $i] :
( ( ! [SY144: $i,SY145: $i] :
( ( lookup_slb @ ( insert_slb @ SV10 @ ( pair @ SY144 @ SY145 ) ) @ SY144 )
= SY145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(181,plain,
! [SV11: $i] :
( ( ! [SY146: $i,SY147: $i] :
( ( SY146 = SY147 )
| ~ ( contains_slb @ SV11 @ SY147 )
| ! [SY148: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SY146 @ SY148 ) ) @ SY147 )
= ( lookup_slb @ SV11 @ SY147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(182,plain,
! [SV12: $i] :
( ( ( update_slb @ create_slb @ SV12 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(183,plain,
! [SV13: $i] :
( ( ! [SY149: $i,SY150: $i,SY151: $i] :
( ~ ( strictly_less_than @ SY151 @ SY150 )
| ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SY149 @ SY151 ) ) @ SY150 )
= ( insert_slb @ ( update_slb @ SV13 @ SY150 ) @ ( pair @ SY149 @ SY150 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(184,plain,
! [SV14: $i] :
( ( ! [SY152: $i,SY153: $i,SY154: $i] :
( ~ ( less_than @ SY153 @ SY154 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SY152 @ SY154 ) ) @ SY153 )
= ( insert_slb @ ( update_slb @ SV14 @ SY153 ) @ ( pair @ SY152 @ SY154 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(185,plain,
! [SV15: $i] :
( ( succ_cpq @ SV15 @ SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(186,plain,
! [SV16: $i] :
( ( ! [SY155: $i] :
( ~ ( succ_cpq @ SV16 @ SY155 )
| ! [SY156: $i] : ( succ_cpq @ SV16 @ ( insert_cpq @ SY155 @ SY156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(187,plain,
! [SV17: $i] :
( ( ! [SY157: $i] :
( ~ ( succ_cpq @ SV17 @ SY157 )
| ! [SY158: $i] : ( succ_cpq @ SV17 @ ( remove_cpq @ SY157 @ SY158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(188,plain,
! [SV18: $i] :
( ( ! [SY159: $i] :
( ~ ( succ_cpq @ SV18 @ SY159 )
| ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SY159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(189,plain,
! [SV19: $i] :
( ( ! [SY160: $i] :
( ~ ( succ_cpq @ SV19 @ SY160 )
| ( succ_cpq @ SV19 @ ( removemin_cpq_eff @ SY160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(190,plain,
! [SV20: $i] :
( ( ! [SY161: $i] : ( check_cpq @ ( triple @ SV20 @ create_slb @ SY161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(191,plain,
! [SV21: $i] :
( ( ! [SY162: $i,SY163: $i,SY164: $i,SY165: $i] :
( ~ ( strictly_less_than @ SY164 @ SY165 )
| ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SY162 @ ( pair @ SY164 @ SY165 ) ) @ SY163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(192,plain,
! [SV22: $i] :
( ( ! [SY166: $i] :
~ ( ok @ ( triple @ SV22 @ SY166 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(193,plain,
! [SV23: $i] :
( ( ! [SY167: $i,SY168: $i] :
( ( ok @ ( triple @ SV23 @ SY167 @ SY168 ) )
| ( SY168 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(194,plain,
! [SV24: $i] :
( ( ! [SY169: $i,SY170: $i,SY171: $i] :
( ( insert_cpq @ ( triple @ SV24 @ SY169 @ SY170 ) @ SY171 )
= ( triple @ ( insert_pqp @ SV24 @ SY171 ) @ ( insert_slb @ SY169 @ ( pair @ SY171 @ bottom ) ) @ SY170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(195,plain,
! [SV25: $i] :
( ( ! [SY172: $i,SY173: $i,SY174: $i] :
( ( contains_slb @ SY172 @ SY174 )
| ( ( remove_cpq @ ( triple @ SV25 @ SY172 @ SY173 ) @ SY174 )
= ( triple @ SV25 @ SY172 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(196,plain,
! [SV26: $i] :
( ( ! [SY175: $i,SY176: $i,SY177: $i] :
( ~ ( contains_slb @ SY175 @ SY177 )
| ~ ( less_than @ ( lookup_slb @ SY175 @ SY177 ) @ SY177 )
| ( ( remove_cpq @ ( triple @ SV26 @ SY175 @ SY176 ) @ SY177 )
= ( triple @ ( remove_pqp @ SV26 @ SY177 ) @ ( remove_slb @ SY175 @ SY177 ) @ SY176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(197,plain,
! [SV27: $i] :
( ( ! [SY178: $i,SY179: $i,SY180: $i] :
( ~ ( contains_slb @ SY178 @ SY180 )
| ~ ( strictly_less_than @ SY180 @ ( lookup_slb @ SY178 @ SY180 ) )
| ( ( remove_cpq @ ( triple @ SV27 @ SY178 @ SY179 ) @ SY180 )
= ( triple @ ( remove_pqp @ SV27 @ SY180 ) @ ( remove_slb @ SY178 @ SY180 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(198,plain,
! [SV28: $i] :
( ( ! [SY181: $i] :
( ( findmin_cpq_eff @ ( triple @ SV28 @ create_slb @ SY181 ) )
= ( triple @ SV28 @ create_slb @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(199,plain,
! [SV29: $i] :
( ( ! [SY182: $i] :
( ( SY182 = create_slb )
| ( contains_slb @ SY182 @ ( findmin_pqp_res @ SV29 ) )
| ! [SY183: $i] :
( ( findmin_cpq_eff @ ( triple @ SV29 @ SY182 @ SY183 ) )
= ( triple @ SV29 @ ( update_slb @ SY182 @ ( findmin_pqp_res @ SV29 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(200,plain,
! [SV30: $i] :
( ( ! [SY184: $i] :
( ( SY184 = create_slb )
| ~ ( contains_slb @ SY184 @ ( findmin_pqp_res @ SV30 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SY184 @ ( findmin_pqp_res @ SV30 ) ) )
| ! [SY185: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SY184 @ SY185 ) )
= ( triple @ SV30 @ ( update_slb @ SY184 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(201,plain,
! [SV31: $i] :
( ( ! [SY186: $i] :
( ( SY186 = create_slb )
| ~ ( contains_slb @ SY186 @ ( findmin_pqp_res @ SV31 ) )
| ~ ( less_than @ ( lookup_slb @ SY186 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) )
| ! [SY187: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SY186 @ SY187 ) )
= ( triple @ SV31 @ ( update_slb @ SY186 @ ( findmin_pqp_res @ SV31 ) ) @ SY187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(202,plain,
! [SV32: $i] :
( ( ! [SY188: $i] :
( ( findmin_cpq_res @ ( triple @ SV32 @ create_slb @ SY188 ) )
= bottom ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(203,plain,
! [SV33: $i] :
( ( ! [SY189: $i] :
( ( SY189 = create_slb )
| ! [SY190: $i] :
( ( findmin_cpq_res @ ( triple @ SV33 @ SY189 @ SY190 ) )
= ( findmin_pqp_res @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(204,plain,
! [SV34: $i] :
( ( ( removemin_cpq_eff @ SV34 )
= ( remove_cpq @ ( findmin_cpq_eff @ SV34 ) @ ( findmin_cpq_res @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(205,plain,
! [SV35: $i] :
( ( ( removemin_cpq_res @ SV35 )
= ( findmin_cpq_res @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(206,plain,
( ( check_cpq @ ( triple @ sK1_U @ sK2_SY126 @ sK3_SY129 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(207,plain,
! [SV36: $i] :
( ( ! [SY191: $i] :
~ ( ~ ! [SY192: $i,SY193: $i] :
( ~ ( contains_cpq @ ( triple @ SV36 @ SY191 @ SY192 ) @ SY193 )
| ( contains_slb @ SY191 @ SY193 ) )
| ~ ! [SY194: $i,SY195: $i] :
( ~ ( contains_slb @ SY191 @ SY195 )
| ( contains_cpq @ ( triple @ SV36 @ SY191 @ SY194 ) @ SY195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(208,plain,
! [SV37: $i] :
( ( ! [SY196: $i] :
~ ( ~ ! [SY197: $i] :
( ! [SY198: $i] :
~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SY196 @ SY198 ) ) @ SY197 )
| ( SY196 = SY197 )
| ( contains_slb @ SV37 @ SY197 ) )
| ~ ~ ( ~ ! [SY199: $i] :
( ( SY196 != SY199 )
| ! [SY200: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SY196 @ SY200 ) ) @ SY199 ) )
| ~ ! [SY201: $i] :
( ~ ( contains_slb @ SV37 @ SY201 )
| ! [SY202: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SY196 @ SY202 ) ) @ SY201 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(209,plain,
! [SV38: $i] :
( ( ~ ( ~ ! [SY203: $i] :
( ~ ( ~ ( pair_in_list @ SY203 @ ( sK5_X @ SY203 @ SV38 ) @ ( sK6_SY132 @ SY203 @ SV38 ) )
| ~ ~ ( less_than @ ( sK6_SY132 @ SY203 @ SV38 ) @ ( sK5_X @ SY203 @ SV38 ) ) )
| ! [SY204: $i] : ( check_cpq @ ( triple @ SV38 @ SY203 @ SY204 ) ) )
| ~ ! [SY205: $i] :
( ! [SY206: $i] :
~ ( check_cpq @ ( triple @ SV38 @ SY205 @ SY206 ) )
| ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ SY205 @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(210,plain,
! [SV39: $i] :
( ( ! [SY209: $i,SY210: $i] :
~ ( ~ ~ ( ~ ! [SY211: $i,SY212: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SY209 @ SY211 ) ) @ SY210 @ SY212 )
| ( SY209 = SY210 )
| ( pair_in_list @ SV39 @ SY210 @ SY212 ) )
| ~ ! [SY213: $i,SY214: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SY209 @ SY213 ) ) @ SY210 @ SY214 )
| ( SY213 = SY214 )
| ( pair_in_list @ SV39 @ SY210 @ SY214 ) ) )
| ~ ~ ( ~ ! [SY215: $i,SY216: $i] :
( ( SY209 != SY210 )
| ( SY215 != SY216 )
| ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SY209 @ SY215 ) ) @ SY210 @ SY216 ) )
| ~ ! [SY217: $i,SY218: $i] :
( ~ ( pair_in_list @ SV39 @ SY210 @ SY218 )
| ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SY209 @ SY217 ) ) @ SY210 @ SY218 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(211,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( less_than @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 )
| ( strictly_less_than @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(212,plain,
! [SV40: $i] :
( ( ! [SY219: $i,SY220: $i] :
~ ( ~ ! [SY221: $i,SY222: $i] :
( ~ ( less_than @ SY222 @ SY221 )
| ~ ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SY219 @ ( pair @ SY221 @ SY222 ) ) @ SY220 ) )
| ( check_cpq @ ( triple @ SV40 @ SY219 @ SY220 ) ) )
| ~ ! [SY223: $i,SY224: $i] :
( ~ ( less_than @ SY224 @ SY223 )
| ~ ( check_cpq @ ( triple @ SV40 @ SY219 @ SY220 ) )
| ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SY219 @ ( pair @ SY223 @ SY224 ) ) @ SY220 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(213,plain,
! [SV41: $i,SV1: $i] :
( ( ! [SY225: $i] :
( ~ ( less_than @ SV1 @ SV41 )
| ~ ( less_than @ SV41 @ SY225 )
| ( less_than @ SV1 @ SY225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(214,plain,
! [SV42: $i,SV2: $i] :
( ( ( less_than @ SV2 @ SV42 )
| ( less_than @ SV42 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(215,plain,
! [SV43: $i,SV5: $i] :
( ( ! [SY226: $i] : ( isnonempty_slb @ ( insert_slb @ SV5 @ ( pair @ SV43 @ SY226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(216,plain,
! [SV6: $i] :
( ( contains_slb @ create_slb @ SV6 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(217,plain,
! [SV44: $i,SV7: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV7 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(218,plain,
! [SV45: $i,SV8: $i] :
( ( ! [SY227: $i] :
( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SV45 @ SY227 ) ) @ SV45 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(219,plain,
! [SV9: $i,SV46: $i] :
( ( ! [SY228: $i] :
( ( SV46 = SY228 )
| ~ ( contains_slb @ SV9 @ SY228 )
| ! [SY229: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV46 @ SY229 ) ) @ SY228 )
= ( insert_slb @ ( remove_slb @ SV9 @ SY228 ) @ ( pair @ SV46 @ SY229 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(220,plain,
! [SV47: $i,SV10: $i] :
( ( ! [SY230: $i] :
( ( lookup_slb @ ( insert_slb @ SV10 @ ( pair @ SV47 @ SY230 ) ) @ SV47 )
= SY230 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(221,plain,
! [SV11: $i,SV48: $i] :
( ( ! [SY231: $i] :
( ( SV48 = SY231 )
| ~ ( contains_slb @ SV11 @ SY231 )
| ! [SY232: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV48 @ SY232 ) ) @ SY231 )
= ( lookup_slb @ SV11 @ SY231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(222,plain,
! [SV49: $i,SV13: $i] :
( ( ! [SY233: $i,SY234: $i] :
( ~ ( strictly_less_than @ SY234 @ SY233 )
| ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV49 @ SY234 ) ) @ SY233 )
= ( insert_slb @ ( update_slb @ SV13 @ SY233 ) @ ( pair @ SV49 @ SY233 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(223,plain,
! [SV50: $i,SV14: $i] :
( ( ! [SY235: $i,SY236: $i] :
( ~ ( less_than @ SY235 @ SY236 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV50 @ SY236 ) ) @ SY235 )
= ( insert_slb @ ( update_slb @ SV14 @ SY235 ) @ ( pair @ SV50 @ SY236 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(224,plain,
! [SV51: $i,SV16: $i] :
( ( ~ ( succ_cpq @ SV16 @ SV51 )
| ! [SY237: $i] : ( succ_cpq @ SV16 @ ( insert_cpq @ SV51 @ SY237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(225,plain,
! [SV52: $i,SV17: $i] :
( ( ~ ( succ_cpq @ SV17 @ SV52 )
| ! [SY238: $i] : ( succ_cpq @ SV17 @ ( remove_cpq @ SV52 @ SY238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(226,plain,
! [SV53: $i,SV18: $i] :
( ( ~ ( succ_cpq @ SV18 @ SV53 )
| ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(227,plain,
! [SV54: $i,SV19: $i] :
( ( ~ ( succ_cpq @ SV19 @ SV54 )
| ( succ_cpq @ SV19 @ ( removemin_cpq_eff @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(228,plain,
! [SV55: $i,SV20: $i] :
( ( check_cpq @ ( triple @ SV20 @ create_slb @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(229,plain,
! [SV56: $i,SV21: $i] :
( ( ! [SY239: $i,SY240: $i,SY241: $i] :
( ~ ( strictly_less_than @ SY240 @ SY241 )
| ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV56 @ ( pair @ SY240 @ SY241 ) ) @ SY239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(230,plain,
! [SV57: $i,SV22: $i] :
( ( ~ ( ok @ ( triple @ SV22 @ SV57 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(231,plain,
! [SV58: $i,SV23: $i] :
( ( ! [SY242: $i] :
( ( ok @ ( triple @ SV23 @ SV58 @ SY242 ) )
| ( SY242 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(232,plain,
! [SV59: $i,SV24: $i] :
( ( ! [SY243: $i,SY244: $i] :
( ( insert_cpq @ ( triple @ SV24 @ SV59 @ SY243 ) @ SY244 )
= ( triple @ ( insert_pqp @ SV24 @ SY244 ) @ ( insert_slb @ SV59 @ ( pair @ SY244 @ bottom ) ) @ SY243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(233,plain,
! [SV25: $i,SV60: $i] :
( ( ! [SY245: $i,SY246: $i] :
( ( contains_slb @ SV60 @ SY246 )
| ( ( remove_cpq @ ( triple @ SV25 @ SV60 @ SY245 ) @ SY246 )
= ( triple @ SV25 @ SV60 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(234,plain,
! [SV26: $i,SV61: $i] :
( ( ! [SY247: $i,SY248: $i] :
( ~ ( contains_slb @ SV61 @ SY248 )
| ~ ( less_than @ ( lookup_slb @ SV61 @ SY248 ) @ SY248 )
| ( ( remove_cpq @ ( triple @ SV26 @ SV61 @ SY247 ) @ SY248 )
= ( triple @ ( remove_pqp @ SV26 @ SY248 ) @ ( remove_slb @ SV61 @ SY248 ) @ SY247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(235,plain,
! [SV27: $i,SV62: $i] :
( ( ! [SY249: $i,SY250: $i] :
( ~ ( contains_slb @ SV62 @ SY250 )
| ~ ( strictly_less_than @ SY250 @ ( lookup_slb @ SV62 @ SY250 ) )
| ( ( remove_cpq @ ( triple @ SV27 @ SV62 @ SY249 ) @ SY250 )
= ( triple @ ( remove_pqp @ SV27 @ SY250 ) @ ( remove_slb @ SV62 @ SY250 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(236,plain,
! [SV63: $i,SV28: $i] :
( ( ( findmin_cpq_eff @ ( triple @ SV28 @ create_slb @ SV63 ) )
= ( triple @ SV28 @ create_slb @ bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(237,plain,
! [SV29: $i,SV64: $i] :
( ( ( SV64 = create_slb )
| ( contains_slb @ SV64 @ ( findmin_pqp_res @ SV29 ) )
| ! [SY251: $i] :
( ( findmin_cpq_eff @ ( triple @ SV29 @ SV64 @ SY251 ) )
= ( triple @ SV29 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV29 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(238,plain,
! [SV30: $i,SV65: $i] :
( ( ( SV65 = create_slb )
| ~ ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) ) )
| ! [SY252: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV65 @ SY252 ) )
= ( triple @ SV30 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(239,plain,
! [SV31: $i,SV66: $i] :
( ( ( SV66 = create_slb )
| ~ ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) )
| ~ ( less_than @ ( lookup_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) )
| ! [SY253: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV66 @ SY253 ) )
= ( triple @ SV31 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) @ SY253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(240,plain,
! [SV67: $i,SV32: $i] :
( ( ( findmin_cpq_res @ ( triple @ SV32 @ create_slb @ SV67 ) )
= bottom )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(241,plain,
! [SV33: $i,SV68: $i] :
( ( ( SV68 = create_slb )
| ! [SY254: $i] :
( ( findmin_cpq_res @ ( triple @ SV33 @ SV68 @ SY254 ) )
= ( findmin_pqp_res @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(242,plain,
! [SV69: $i,SV36: $i] :
( ( ~ ( ~ ! [SY255: $i,SY256: $i] :
( ~ ( contains_cpq @ ( triple @ SV36 @ SV69 @ SY255 ) @ SY256 )
| ( contains_slb @ SV69 @ SY256 ) )
| ~ ! [SY257: $i,SY258: $i] :
( ~ ( contains_slb @ SV69 @ SY258 )
| ( contains_cpq @ ( triple @ SV36 @ SV69 @ SY257 ) @ SY258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(243,plain,
! [SV70: $i,SV37: $i] :
( ( ~ ( ~ ! [SY259: $i] :
( ! [SY260: $i] :
~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY260 ) ) @ SY259 )
| ( SV70 = SY259 )
| ( contains_slb @ SV37 @ SY259 ) )
| ~ ~ ( ~ ! [SY261: $i] :
( ( SV70 != SY261 )
| ! [SY262: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY262 ) ) @ SY261 ) )
| ~ ! [SY263: $i] :
( ~ ( contains_slb @ SV37 @ SY263 )
| ! [SY264: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY264 ) ) @ SY263 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(244,plain,
! [SV38: $i] :
( ( ~ ! [SY203: $i] :
( ~ ( ~ ( pair_in_list @ SY203 @ ( sK5_X @ SY203 @ SV38 ) @ ( sK6_SY132 @ SY203 @ SV38 ) )
| ~ ~ ( less_than @ ( sK6_SY132 @ SY203 @ SV38 ) @ ( sK5_X @ SY203 @ SV38 ) ) )
| ! [SY204: $i] : ( check_cpq @ ( triple @ SV38 @ SY203 @ SY204 ) ) )
| ~ ! [SY205: $i] :
( ! [SY206: $i] :
~ ( check_cpq @ ( triple @ SV38 @ SY205 @ SY206 ) )
| ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ SY205 @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(245,plain,
! [SV71: $i,SV39: $i] :
( ( ! [SY265: $i] :
~ ( ~ ~ ( ~ ! [SY266: $i,SY267: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY266 ) ) @ SY265 @ SY267 )
| ( SV71 = SY265 )
| ( pair_in_list @ SV39 @ SY265 @ SY267 ) )
| ~ ! [SY268: $i,SY269: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY268 ) ) @ SY265 @ SY269 )
| ( SY268 = SY269 )
| ( pair_in_list @ SV39 @ SY265 @ SY269 ) ) )
| ~ ~ ( ~ ! [SY270: $i,SY271: $i] :
( ( SV71 != SY265 )
| ( SY270 != SY271 )
| ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY270 ) ) @ SY265 @ SY271 ) )
| ~ ! [SY272: $i,SY273: $i] :
( ~ ( pair_in_list @ SV39 @ SY265 @ SY273 )
| ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY272 ) ) @ SY265 @ SY273 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(246,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( less_than @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 )
| ( strictly_less_than @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(247,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[211]) ).
thf(248,plain,
! [SV72: $i,SV40: $i] :
( ( ! [SY274: $i] :
~ ( ~ ! [SY275: $i,SY276: $i] :
( ~ ( less_than @ SY276 @ SY275 )
| ~ ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SV72 @ ( pair @ SY275 @ SY276 ) ) @ SY274 ) )
| ( check_cpq @ ( triple @ SV40 @ SV72 @ SY274 ) ) )
| ~ ! [SY277: $i,SY278: $i] :
( ~ ( less_than @ SY278 @ SY277 )
| ~ ( check_cpq @ ( triple @ SV40 @ SV72 @ SY274 ) )
| ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SV72 @ ( pair @ SY277 @ SY278 ) ) @ SY274 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(249,plain,
! [SV73: $i,SV41: $i,SV1: $i] :
( ( ~ ( less_than @ SV1 @ SV41 )
| ~ ( less_than @ SV41 @ SV73 )
| ( less_than @ SV1 @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(250,plain,
! [SV42: $i,SV2: $i] :
( ( ( less_than @ SV2 @ SV42 )
= $true )
| ( ( less_than @ SV42 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(251,plain,
! [SV74: $i,SV43: $i,SV5: $i] :
( ( isnonempty_slb @ ( insert_slb @ SV5 @ ( pair @ SV43 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(252,plain,
! [SV44: $i,SV7: $i] :
( ( pair_in_list @ create_slb @ SV7 @ SV44 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(253,plain,
! [SV75: $i,SV45: $i,SV8: $i] :
( ( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SV45 @ SV75 ) ) @ SV45 )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(254,plain,
! [SV9: $i,SV76: $i,SV46: $i] :
( ( ( SV46 = SV76 )
| ~ ( contains_slb @ SV9 @ SV76 )
| ! [SY279: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV46 @ SY279 ) ) @ SV76 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV76 ) @ ( pair @ SV46 @ SY279 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(255,plain,
! [SV77: $i,SV47: $i,SV10: $i] :
( ( ( lookup_slb @ ( insert_slb @ SV10 @ ( pair @ SV47 @ SV77 ) ) @ SV47 )
= SV77 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(256,plain,
! [SV11: $i,SV78: $i,SV48: $i] :
( ( ( SV48 = SV78 )
| ~ ( contains_slb @ SV11 @ SV78 )
| ! [SY280: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV48 @ SY280 ) ) @ SV78 )
= ( lookup_slb @ SV11 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(257,plain,
! [SV49: $i,SV13: $i,SV79: $i] :
( ( ! [SY281: $i] :
( ~ ( strictly_less_than @ SY281 @ SV79 )
| ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV49 @ SY281 ) ) @ SV79 )
= ( insert_slb @ ( update_slb @ SV13 @ SV79 ) @ ( pair @ SV49 @ SV79 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(258,plain,
! [SV50: $i,SV14: $i,SV80: $i] :
( ( ! [SY282: $i] :
( ~ ( less_than @ SV80 @ SY282 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV50 @ SY282 ) ) @ SV80 )
= ( insert_slb @ ( update_slb @ SV14 @ SV80 ) @ ( pair @ SV50 @ SY282 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(259,plain,
! [SV51: $i,SV16: $i] :
( ( ( ~ ( succ_cpq @ SV16 @ SV51 ) )
= $true )
| ( ( ! [SY237: $i] : ( succ_cpq @ SV16 @ ( insert_cpq @ SV51 @ SY237 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(260,plain,
! [SV52: $i,SV17: $i] :
( ( ( ~ ( succ_cpq @ SV17 @ SV52 ) )
= $true )
| ( ( ! [SY238: $i] : ( succ_cpq @ SV17 @ ( remove_cpq @ SV52 @ SY238 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(261,plain,
! [SV53: $i,SV18: $i] :
( ( ( ~ ( succ_cpq @ SV18 @ SV53 ) )
= $true )
| ( ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(262,plain,
! [SV54: $i,SV19: $i] :
( ( ( ~ ( succ_cpq @ SV19 @ SV54 ) )
= $true )
| ( ( succ_cpq @ SV19 @ ( removemin_cpq_eff @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(263,plain,
! [SV81: $i,SV56: $i,SV21: $i] :
( ( ! [SY283: $i,SY284: $i] :
( ~ ( strictly_less_than @ SY283 @ SY284 )
| ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV56 @ ( pair @ SY283 @ SY284 ) ) @ SV81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(264,plain,
! [SV57: $i,SV22: $i] :
( ( ok @ ( triple @ SV22 @ SV57 @ bad ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(265,plain,
! [SV82: $i,SV58: $i,SV23: $i] :
( ( ( ok @ ( triple @ SV23 @ SV58 @ SV82 ) )
| ( SV82 = bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(266,plain,
! [SV83: $i,SV59: $i,SV24: $i] :
( ( ! [SY285: $i] :
( ( insert_cpq @ ( triple @ SV24 @ SV59 @ SV83 ) @ SY285 )
= ( triple @ ( insert_pqp @ SV24 @ SY285 ) @ ( insert_slb @ SV59 @ ( pair @ SY285 @ bottom ) ) @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(267,plain,
! [SV84: $i,SV25: $i,SV60: $i] :
( ( ! [SY286: $i] :
( ( contains_slb @ SV60 @ SY286 )
| ( ( remove_cpq @ ( triple @ SV25 @ SV60 @ SV84 ) @ SY286 )
= ( triple @ SV25 @ SV60 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(268,plain,
! [SV85: $i,SV26: $i,SV61: $i] :
( ( ! [SY287: $i] :
( ~ ( contains_slb @ SV61 @ SY287 )
| ~ ( less_than @ ( lookup_slb @ SV61 @ SY287 ) @ SY287 )
| ( ( remove_cpq @ ( triple @ SV26 @ SV61 @ SV85 ) @ SY287 )
= ( triple @ ( remove_pqp @ SV26 @ SY287 ) @ ( remove_slb @ SV61 @ SY287 ) @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(269,plain,
! [SV86: $i,SV27: $i,SV62: $i] :
( ( ! [SY288: $i] :
( ~ ( contains_slb @ SV62 @ SY288 )
| ~ ( strictly_less_than @ SY288 @ ( lookup_slb @ SV62 @ SY288 ) )
| ( ( remove_cpq @ ( triple @ SV27 @ SV62 @ SV86 ) @ SY288 )
= ( triple @ ( remove_pqp @ SV27 @ SY288 ) @ ( remove_slb @ SV62 @ SY288 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(270,plain,
! [SV29: $i,SV64: $i] :
( ( ( ( SV64 = create_slb )
| ( contains_slb @ SV64 @ ( findmin_pqp_res @ SV29 ) ) )
= $true )
| ( ( ! [SY251: $i] :
( ( findmin_cpq_eff @ ( triple @ SV29 @ SV64 @ SY251 ) )
= ( triple @ SV29 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV29 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(271,plain,
! [SV30: $i,SV65: $i] :
( ( ( ( SV65 = create_slb )
| ~ ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) ) ) )
= $true )
| ( ( ! [SY252: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV65 @ SY252 ) )
= ( triple @ SV30 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(272,plain,
! [SV31: $i,SV66: $i] :
( ( ( ( SV66 = create_slb )
| ~ ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) )
| ~ ( less_than @ ( lookup_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) ) )
= $true )
| ( ( ! [SY253: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV66 @ SY253 ) )
= ( triple @ SV31 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) @ SY253 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(273,plain,
! [SV33: $i,SV68: $i] :
( ( ( SV68 = create_slb )
= $true )
| ( ( ! [SY254: $i] :
( ( findmin_cpq_res @ ( triple @ SV33 @ SV68 @ SY254 ) )
= ( findmin_pqp_res @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(274,plain,
! [SV69: $i,SV36: $i] :
( ( ~ ! [SY255: $i,SY256: $i] :
( ~ ( contains_cpq @ ( triple @ SV36 @ SV69 @ SY255 ) @ SY256 )
| ( contains_slb @ SV69 @ SY256 ) )
| ~ ! [SY257: $i,SY258: $i] :
( ~ ( contains_slb @ SV69 @ SY258 )
| ( contains_cpq @ ( triple @ SV36 @ SV69 @ SY257 ) @ SY258 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(275,plain,
! [SV70: $i,SV37: $i] :
( ( ~ ! [SY259: $i] :
( ! [SY260: $i] :
~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY260 ) ) @ SY259 )
| ( SV70 = SY259 )
| ( contains_slb @ SV37 @ SY259 ) )
| ~ ~ ( ~ ! [SY261: $i] :
( ( SV70 != SY261 )
| ! [SY262: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY262 ) ) @ SY261 ) )
| ~ ! [SY263: $i] :
( ~ ( contains_slb @ SV37 @ SY263 )
| ! [SY264: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY264 ) ) @ SY263 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(276,plain,
! [SV38: $i] :
( ( ~ ! [SY203: $i] :
( ~ ( ~ ( pair_in_list @ SY203 @ ( sK5_X @ SY203 @ SV38 ) @ ( sK6_SY132 @ SY203 @ SV38 ) )
| ~ ~ ( less_than @ ( sK6_SY132 @ SY203 @ SV38 ) @ ( sK5_X @ SY203 @ SV38 ) ) )
| ! [SY204: $i] : ( check_cpq @ ( triple @ SV38 @ SY203 @ SY204 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(277,plain,
! [SV38: $i] :
( ( ~ ! [SY205: $i] :
( ! [SY206: $i] :
~ ( check_cpq @ ( triple @ SV38 @ SY205 @ SY206 ) )
| ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ SY205 @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(278,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY289: $i,SY290: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY289 ) ) @ SV87 @ SY290 )
| ( SV71 = SV87 )
| ( pair_in_list @ SV39 @ SV87 @ SY290 ) )
| ~ ! [SY291: $i,SY292: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY291 ) ) @ SV87 @ SY292 )
| ( SY291 = SY292 )
| ( pair_in_list @ SV39 @ SV87 @ SY292 ) ) )
| ~ ~ ( ~ ! [SY293: $i,SY294: $i] :
( ( SV71 != SV87 )
| ( SY293 != SY294 )
| ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY293 ) ) @ SV87 @ SY294 ) )
| ~ ! [SY295: $i,SY296: $i] :
( ~ ( pair_in_list @ SV39 @ SV87 @ SY296 )
| ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY295 ) ) @ SV87 @ SY296 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(279,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( less_than @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 )
| ( strictly_less_than @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(280,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(281,plain,
! [SV88: $i,SV72: $i,SV40: $i] :
( ( ~ ( ~ ! [SY297: $i,SY298: $i] :
( ~ ( less_than @ SY298 @ SY297 )
| ~ ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SV72 @ ( pair @ SY297 @ SY298 ) ) @ SV88 ) )
| ( check_cpq @ ( triple @ SV40 @ SV72 @ SV88 ) ) )
| ~ ! [SY299: $i,SY300: $i] :
( ~ ( less_than @ SY300 @ SY299 )
| ~ ( check_cpq @ ( triple @ SV40 @ SV72 @ SV88 ) )
| ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SV72 @ ( pair @ SY299 @ SY300 ) ) @ SV88 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(282,plain,
! [SV73: $i,SV41: $i,SV1: $i] :
( ( ( ~ ( less_than @ SV1 @ SV41 )
| ~ ( less_than @ SV41 @ SV73 ) )
= $true )
| ( ( less_than @ SV1 @ SV73 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(283,plain,
! [SV9: $i,SV76: $i,SV46: $i] :
( ( ( ( SV46 = SV76 )
| ~ ( contains_slb @ SV9 @ SV76 ) )
= $true )
| ( ( ! [SY279: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV46 @ SY279 ) ) @ SV76 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV76 ) @ ( pair @ SV46 @ SY279 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(284,plain,
! [SV11: $i,SV78: $i,SV48: $i] :
( ( ( ( SV48 = SV78 )
| ~ ( contains_slb @ SV11 @ SV78 ) )
= $true )
| ( ( ! [SY280: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV48 @ SY280 ) ) @ SV78 )
= ( lookup_slb @ SV11 @ SV78 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(285,plain,
! [SV49: $i,SV13: $i,SV79: $i,SV89: $i] :
( ( ~ ( strictly_less_than @ SV89 @ SV79 )
| ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV49 @ SV89 ) ) @ SV79 )
= ( insert_slb @ ( update_slb @ SV13 @ SV79 ) @ ( pair @ SV49 @ SV79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(286,plain,
! [SV50: $i,SV14: $i,SV90: $i,SV80: $i] :
( ( ~ ( less_than @ SV80 @ SV90 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV50 @ SV90 ) ) @ SV80 )
= ( insert_slb @ ( update_slb @ SV14 @ SV80 ) @ ( pair @ SV50 @ SV90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(287,plain,
! [SV51: $i,SV16: $i] :
( ( ( succ_cpq @ SV16 @ SV51 )
= $false )
| ( ( ! [SY237: $i] : ( succ_cpq @ SV16 @ ( insert_cpq @ SV51 @ SY237 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(288,plain,
! [SV52: $i,SV17: $i] :
( ( ( succ_cpq @ SV17 @ SV52 )
= $false )
| ( ( ! [SY238: $i] : ( succ_cpq @ SV17 @ ( remove_cpq @ SV52 @ SY238 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(289,plain,
! [SV53: $i,SV18: $i] :
( ( ( succ_cpq @ SV18 @ SV53 )
= $false )
| ( ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(290,plain,
! [SV54: $i,SV19: $i] :
( ( ( succ_cpq @ SV19 @ SV54 )
= $false )
| ( ( succ_cpq @ SV19 @ ( removemin_cpq_eff @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(291,plain,
! [SV81: $i,SV56: $i,SV21: $i,SV91: $i] :
( ( ! [SY301: $i] :
( ~ ( strictly_less_than @ SV91 @ SY301 )
| ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV56 @ ( pair @ SV91 @ SY301 ) ) @ SV81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(292,plain,
! [SV82: $i,SV58: $i,SV23: $i] :
( ( ( ok @ ( triple @ SV23 @ SV58 @ SV82 ) )
= $true )
| ( ( SV82 = bad )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(293,plain,
! [SV92: $i,SV83: $i,SV59: $i,SV24: $i] :
( ( ( insert_cpq @ ( triple @ SV24 @ SV59 @ SV83 ) @ SV92 )
= ( triple @ ( insert_pqp @ SV24 @ SV92 ) @ ( insert_slb @ SV59 @ ( pair @ SV92 @ bottom ) ) @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(294,plain,
! [SV84: $i,SV25: $i,SV93: $i,SV60: $i] :
( ( ( contains_slb @ SV60 @ SV93 )
| ( ( remove_cpq @ ( triple @ SV25 @ SV60 @ SV84 ) @ SV93 )
= ( triple @ SV25 @ SV60 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(295,plain,
! [SV85: $i,SV26: $i,SV94: $i,SV61: $i] :
( ( ~ ( contains_slb @ SV61 @ SV94 )
| ~ ( less_than @ ( lookup_slb @ SV61 @ SV94 ) @ SV94 )
| ( ( remove_cpq @ ( triple @ SV26 @ SV61 @ SV85 ) @ SV94 )
= ( triple @ ( remove_pqp @ SV26 @ SV94 ) @ ( remove_slb @ SV61 @ SV94 ) @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(296,plain,
! [SV86: $i,SV27: $i,SV95: $i,SV62: $i] :
( ( ~ ( contains_slb @ SV62 @ SV95 )
| ~ ( strictly_less_than @ SV95 @ ( lookup_slb @ SV62 @ SV95 ) )
| ( ( remove_cpq @ ( triple @ SV27 @ SV62 @ SV86 ) @ SV95 )
= ( triple @ ( remove_pqp @ SV27 @ SV95 ) @ ( remove_slb @ SV62 @ SV95 ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(297,plain,
! [SV29: $i,SV64: $i] :
( ( ( SV64 = create_slb )
= $true )
| ( ( contains_slb @ SV64 @ ( findmin_pqp_res @ SV29 ) )
= $true )
| ( ( ! [SY251: $i] :
( ( findmin_cpq_eff @ ( triple @ SV29 @ SV64 @ SY251 ) )
= ( triple @ SV29 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV29 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(298,plain,
! [SV30: $i,SV65: $i] :
( ( ( ( SV65 = create_slb )
| ~ ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) ) ) )
= $true )
| ( ( ! [SY252: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV65 @ SY252 ) )
= ( triple @ SV30 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(299,plain,
! [SV31: $i,SV66: $i] :
( ( ( ( SV66 = create_slb )
| ~ ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) ) )
= $true )
| ( ( ! [SY253: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV66 @ SY253 ) )
= ( triple @ SV31 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) @ SY253 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(300,plain,
! [SV96: $i,SV68: $i,SV33: $i] :
( ( ( ( findmin_cpq_res @ ( triple @ SV33 @ SV68 @ SV96 ) )
= ( findmin_pqp_res @ SV33 ) )
= $true )
| ( ( SV68 = create_slb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(301,plain,
! [SV69: $i,SV36: $i] :
( ( ~ ! [SY255: $i,SY256: $i] :
( ~ ( contains_cpq @ ( triple @ SV36 @ SV69 @ SY255 ) @ SY256 )
| ( contains_slb @ SV69 @ SY256 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[274]) ).
thf(302,plain,
! [SV36: $i,SV69: $i] :
( ( ~ ! [SY257: $i,SY258: $i] :
( ~ ( contains_slb @ SV69 @ SY258 )
| ( contains_cpq @ ( triple @ SV36 @ SV69 @ SY257 ) @ SY258 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[274]) ).
thf(303,plain,
! [SV70: $i,SV37: $i] :
( ( ~ ! [SY259: $i] :
( ! [SY260: $i] :
~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY260 ) ) @ SY259 )
| ( SV70 = SY259 )
| ( contains_slb @ SV37 @ SY259 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[275]) ).
thf(304,plain,
! [SV37: $i,SV70: $i] :
( ( ~ ~ ( ~ ! [SY261: $i] :
( ( SV70 != SY261 )
| ! [SY262: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY262 ) ) @ SY261 ) )
| ~ ! [SY263: $i] :
( ~ ( contains_slb @ SV37 @ SY263 )
| ! [SY264: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY264 ) ) @ SY263 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[275]) ).
thf(305,plain,
! [SV38: $i] :
( ( ! [SY203: $i] :
( ~ ( ~ ( pair_in_list @ SY203 @ ( sK5_X @ SY203 @ SV38 ) @ ( sK6_SY132 @ SY203 @ SV38 ) )
| ~ ~ ( less_than @ ( sK6_SY132 @ SY203 @ SV38 ) @ ( sK5_X @ SY203 @ SV38 ) ) )
| ! [SY204: $i] : ( check_cpq @ ( triple @ SV38 @ SY203 @ SY204 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[276]) ).
thf(306,plain,
! [SV38: $i] :
( ( ! [SY205: $i] :
( ! [SY206: $i] :
~ ( check_cpq @ ( triple @ SV38 @ SY205 @ SY206 ) )
| ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ SY205 @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(307,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ~ ~ ( ~ ! [SY289: $i,SY290: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY289 ) ) @ SV87 @ SY290 )
| ( SV71 = SV87 )
| ( pair_in_list @ SV39 @ SV87 @ SY290 ) )
| ~ ! [SY291: $i,SY292: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY291 ) ) @ SV87 @ SY292 )
| ( SY291 = SY292 )
| ( pair_in_list @ SV39 @ SV87 @ SY292 ) ) )
| ~ ~ ( ~ ! [SY293: $i,SY294: $i] :
( ( SV71 != SV87 )
| ( SY293 != SY294 )
| ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY293 ) ) @ SV87 @ SY294 ) )
| ~ ! [SY295: $i,SY296: $i] :
( ~ ( pair_in_list @ SV39 @ SV87 @ SY296 )
| ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY295 ) ) @ SV87 @ SY296 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(308,plain,
! [SV97: $i] :
( ( ! [SY302: $i] :
( ~ ( less_than @ SV97 @ SY302 )
| ( less_than @ SY302 @ SV97 )
| ( strictly_less_than @ SV97 @ SY302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(309,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(310,plain,
! [SV88: $i,SV72: $i,SV40: $i] :
( ( ~ ! [SY297: $i,SY298: $i] :
( ~ ( less_than @ SY298 @ SY297 )
| ~ ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SV72 @ ( pair @ SY297 @ SY298 ) ) @ SV88 ) )
| ( check_cpq @ ( triple @ SV40 @ SV72 @ SV88 ) ) )
| ~ ! [SY299: $i,SY300: $i] :
( ~ ( less_than @ SY300 @ SY299 )
| ~ ( check_cpq @ ( triple @ SV40 @ SV72 @ SV88 ) )
| ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SV72 @ ( pair @ SY299 @ SY300 ) ) @ SV88 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(311,plain,
! [SV73: $i,SV41: $i,SV1: $i] :
( ( ( ~ ( less_than @ SV1 @ SV41 ) )
= $true )
| ( ( ~ ( less_than @ SV41 @ SV73 ) )
= $true )
| ( ( less_than @ SV1 @ SV73 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(312,plain,
! [SV9: $i,SV76: $i,SV46: $i] :
( ( ( SV46 = SV76 )
= $true )
| ( ( ~ ( contains_slb @ SV9 @ SV76 ) )
= $true )
| ( ( ! [SY279: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV46 @ SY279 ) ) @ SV76 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV76 ) @ ( pair @ SV46 @ SY279 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(313,plain,
! [SV11: $i,SV78: $i,SV48: $i] :
( ( ( SV48 = SV78 )
= $true )
| ( ( ~ ( contains_slb @ SV11 @ SV78 ) )
= $true )
| ( ( ! [SY280: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV48 @ SY280 ) ) @ SV78 )
= ( lookup_slb @ SV11 @ SV78 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(314,plain,
! [SV49: $i,SV13: $i,SV79: $i,SV89: $i] :
( ( ( ~ ( strictly_less_than @ SV89 @ SV79 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV49 @ SV89 ) ) @ SV79 )
= ( insert_slb @ ( update_slb @ SV13 @ SV79 ) @ ( pair @ SV49 @ SV79 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(315,plain,
! [SV50: $i,SV14: $i,SV90: $i,SV80: $i] :
( ( ( ~ ( less_than @ SV80 @ SV90 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV50 @ SV90 ) ) @ SV80 )
= ( insert_slb @ ( update_slb @ SV14 @ SV80 ) @ ( pair @ SV50 @ SV90 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(316,plain,
! [SV98: $i,SV51: $i,SV16: $i] :
( ( ( succ_cpq @ SV16 @ ( insert_cpq @ SV51 @ SV98 ) )
= $true )
| ( ( succ_cpq @ SV16 @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(317,plain,
! [SV99: $i,SV52: $i,SV17: $i] :
( ( ( succ_cpq @ SV17 @ ( remove_cpq @ SV52 @ SV99 ) )
= $true )
| ( ( succ_cpq @ SV17 @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(318,plain,
! [SV81: $i,SV56: $i,SV21: $i,SV100: $i,SV91: $i] :
( ( ~ ( strictly_less_than @ SV91 @ SV100 )
| ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV56 @ ( pair @ SV91 @ SV100 ) ) @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(319,plain,
! [SV84: $i,SV25: $i,SV93: $i,SV60: $i] :
( ( ( contains_slb @ SV60 @ SV93 )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV25 @ SV60 @ SV84 ) @ SV93 )
= ( triple @ SV25 @ SV60 @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(320,plain,
! [SV85: $i,SV26: $i,SV94: $i,SV61: $i] :
( ( ( ~ ( contains_slb @ SV61 @ SV94 )
| ~ ( less_than @ ( lookup_slb @ SV61 @ SV94 ) @ SV94 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV26 @ SV61 @ SV85 ) @ SV94 )
= ( triple @ ( remove_pqp @ SV26 @ SV94 ) @ ( remove_slb @ SV61 @ SV94 ) @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(321,plain,
! [SV86: $i,SV27: $i,SV95: $i,SV62: $i] :
( ( ( ~ ( contains_slb @ SV62 @ SV95 )
| ~ ( strictly_less_than @ SV95 @ ( lookup_slb @ SV62 @ SV95 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV27 @ SV62 @ SV86 ) @ SV95 )
= ( triple @ ( remove_pqp @ SV27 @ SV95 ) @ ( remove_slb @ SV62 @ SV95 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(322,plain,
! [SV101: $i,SV64: $i,SV29: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV29 @ SV64 @ SV101 ) )
= ( triple @ SV29 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV29 ) ) @ bad ) )
= $true )
| ( ( contains_slb @ SV64 @ ( findmin_pqp_res @ SV29 ) )
= $true )
| ( ( SV64 = create_slb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(323,plain,
! [SV30: $i,SV65: $i] :
( ( ( SV65 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) ) ) )
= $true )
| ( ( ! [SY252: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV65 @ SY252 ) )
= ( triple @ SV30 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(324,plain,
! [SV31: $i,SV66: $i] :
( ( ( SV66 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) ) )
= $true )
| ( ( ! [SY253: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV66 @ SY253 ) )
= ( triple @ SV31 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) @ SY253 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(325,plain,
! [SV69: $i,SV36: $i] :
( ( ! [SY255: $i,SY256: $i] :
( ~ ( contains_cpq @ ( triple @ SV36 @ SV69 @ SY255 ) @ SY256 )
| ( contains_slb @ SV69 @ SY256 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(326,plain,
! [SV36: $i,SV69: $i] :
( ( ! [SY257: $i,SY258: $i] :
( ~ ( contains_slb @ SV69 @ SY258 )
| ( contains_cpq @ ( triple @ SV36 @ SV69 @ SY257 ) @ SY258 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(327,plain,
! [SV70: $i,SV37: $i] :
( ( ! [SY259: $i] :
( ! [SY260: $i] :
~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY260 ) ) @ SY259 )
| ( SV70 = SY259 )
| ( contains_slb @ SV37 @ SY259 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[303]) ).
thf(328,plain,
! [SV37: $i,SV70: $i] :
( ( ~ ( ~ ! [SY261: $i] :
( ( SV70 != SY261 )
| ! [SY262: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY262 ) ) @ SY261 ) )
| ~ ! [SY263: $i] :
( ~ ( contains_slb @ SV37 @ SY263 )
| ! [SY264: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY264 ) ) @ SY263 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[304]) ).
thf(329,plain,
! [SV38: $i,SV102: $i] :
( ( ~ ( ~ ( pair_in_list @ SV102 @ ( sK5_X @ SV102 @ SV38 ) @ ( sK6_SY132 @ SV102 @ SV38 ) )
| ~ ~ ( less_than @ ( sK6_SY132 @ SV102 @ SV38 ) @ ( sK5_X @ SV102 @ SV38 ) ) )
| ! [SY303: $i] : ( check_cpq @ ( triple @ SV38 @ SV102 @ SY303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(330,plain,
! [SV103: $i,SV38: $i] :
( ( ! [SY304: $i] :
~ ( check_cpq @ ( triple @ SV38 @ SV103 @ SY304 ) )
| ! [SY305: $i,SY306: $i] :
( ~ ( pair_in_list @ SV103 @ SY305 @ SY306 )
| ( less_than @ SY306 @ SY305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(331,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ~ ~ ( ~ ! [SY289: $i,SY290: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY289 ) ) @ SV87 @ SY290 )
| ( SV71 = SV87 )
| ( pair_in_list @ SV39 @ SV87 @ SY290 ) )
| ~ ! [SY291: $i,SY292: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY291 ) ) @ SV87 @ SY292 )
| ( SY291 = SY292 )
| ( pair_in_list @ SV39 @ SV87 @ SY292 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(332,plain,
! [SV39: $i,SV87: $i,SV71: $i] :
( ( ~ ~ ( ~ ! [SY293: $i,SY294: $i] :
( ( SV71 != SV87 )
| ( SY293 != SY294 )
| ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY293 ) ) @ SV87 @ SY294 ) )
| ~ ! [SY295: $i,SY296: $i] :
( ~ ( pair_in_list @ SV39 @ SV87 @ SY296 )
| ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY295 ) ) @ SV87 @ SY296 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(333,plain,
! [SV104: $i,SV97: $i] :
( ( ~ ( less_than @ SV97 @ SV104 )
| ( less_than @ SV104 @ SV97 )
| ( strictly_less_than @ SV97 @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(334,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[309]) ).
thf(335,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[309]) ).
thf(336,plain,
! [SV88: $i,SV72: $i,SV40: $i] :
( ( ~ ! [SY297: $i,SY298: $i] :
( ~ ( less_than @ SY298 @ SY297 )
| ~ ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SV72 @ ( pair @ SY297 @ SY298 ) ) @ SV88 ) )
| ( check_cpq @ ( triple @ SV40 @ SV72 @ SV88 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(337,plain,
! [SV88: $i,SV72: $i,SV40: $i] :
( ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( less_than @ SY300 @ SY299 )
| ~ ( check_cpq @ ( triple @ SV40 @ SV72 @ SV88 ) )
| ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SV72 @ ( pair @ SY299 @ SY300 ) ) @ SV88 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(338,plain,
! [SV73: $i,SV41: $i,SV1: $i] :
( ( ( less_than @ SV1 @ SV41 )
= $false )
| ( ( ~ ( less_than @ SV41 @ SV73 ) )
= $true )
| ( ( less_than @ SV1 @ SV73 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(339,plain,
! [SV46: $i,SV76: $i,SV9: $i] :
( ( ( contains_slb @ SV9 @ SV76 )
= $false )
| ( ( SV46 = SV76 )
= $true )
| ( ( ! [SY279: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV46 @ SY279 ) ) @ SV76 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV76 ) @ ( pair @ SV46 @ SY279 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(340,plain,
! [SV48: $i,SV78: $i,SV11: $i] :
( ( ( contains_slb @ SV11 @ SV78 )
= $false )
| ( ( SV48 = SV78 )
= $true )
| ( ( ! [SY280: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV48 @ SY280 ) ) @ SV78 )
= ( lookup_slb @ SV11 @ SV78 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(341,plain,
! [SV49: $i,SV13: $i,SV79: $i,SV89: $i] :
( ( ( strictly_less_than @ SV89 @ SV79 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV49 @ SV89 ) ) @ SV79 )
= ( insert_slb @ ( update_slb @ SV13 @ SV79 ) @ ( pair @ SV49 @ SV79 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(342,plain,
! [SV50: $i,SV14: $i,SV90: $i,SV80: $i] :
( ( ( less_than @ SV80 @ SV90 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV50 @ SV90 ) ) @ SV80 )
= ( insert_slb @ ( update_slb @ SV14 @ SV80 ) @ ( pair @ SV50 @ SV90 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(343,plain,
! [SV81: $i,SV56: $i,SV21: $i,SV100: $i,SV91: $i] :
( ( ( ~ ( strictly_less_than @ SV91 @ SV100 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV56 @ ( pair @ SV91 @ SV100 ) ) @ SV81 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(344,plain,
! [SV85: $i,SV26: $i,SV94: $i,SV61: $i] :
( ( ( ~ ( contains_slb @ SV61 @ SV94 ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV61 @ SV94 ) @ SV94 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV26 @ SV61 @ SV85 ) @ SV94 )
= ( triple @ ( remove_pqp @ SV26 @ SV94 ) @ ( remove_slb @ SV61 @ SV94 ) @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(345,plain,
! [SV86: $i,SV27: $i,SV95: $i,SV62: $i] :
( ( ( ~ ( contains_slb @ SV62 @ SV95 ) )
= $true )
| ( ( ~ ( strictly_less_than @ SV95 @ ( lookup_slb @ SV62 @ SV95 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV27 @ SV62 @ SV86 ) @ SV95 )
= ( triple @ ( remove_pqp @ SV27 @ SV95 ) @ ( remove_slb @ SV62 @ SV95 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(346,plain,
! [SV30: $i,SV65: $i] :
( ( ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) )
= $false )
| ( ( SV65 = create_slb )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) ) ) )
= $true )
| ( ( ! [SY252: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV65 @ SY252 ) )
= ( triple @ SV30 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(347,plain,
! [SV31: $i,SV66: $i] :
( ( ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) )
= $false )
| ( ( SV66 = create_slb )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) ) )
= $true )
| ( ( ! [SY253: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV66 @ SY253 ) )
= ( triple @ SV31 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) @ SY253 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(348,plain,
! [SV105: $i,SV69: $i,SV36: $i] :
( ( ! [SY307: $i] :
( ~ ( contains_cpq @ ( triple @ SV36 @ SV69 @ SV105 ) @ SY307 )
| ( contains_slb @ SV69 @ SY307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(349,plain,
! [SV106: $i,SV36: $i,SV69: $i] :
( ( ! [SY308: $i] :
( ~ ( contains_slb @ SV69 @ SY308 )
| ( contains_cpq @ ( triple @ SV36 @ SV69 @ SV106 ) @ SY308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(350,plain,
! [SV107: $i,SV70: $i,SV37: $i] :
( ( ! [SY309: $i] :
~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY309 ) ) @ SV107 )
| ( SV70 = SV107 )
| ( contains_slb @ SV37 @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(351,plain,
! [SV37: $i,SV70: $i] :
( ( ~ ! [SY261: $i] :
( ( SV70 != SY261 )
| ! [SY262: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY262 ) ) @ SY261 ) )
| ~ ! [SY263: $i] :
( ~ ( contains_slb @ SV37 @ SY263 )
| ! [SY264: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY264 ) ) @ SY263 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(352,plain,
! [SV38: $i,SV102: $i] :
( ( ( ~ ( ~ ( pair_in_list @ SV102 @ ( sK5_X @ SV102 @ SV38 ) @ ( sK6_SY132 @ SV102 @ SV38 ) )
| ~ ~ ( less_than @ ( sK6_SY132 @ SV102 @ SV38 ) @ ( sK5_X @ SV102 @ SV38 ) ) ) )
= $true )
| ( ( ! [SY303: $i] : ( check_cpq @ ( triple @ SV38 @ SV102 @ SY303 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(353,plain,
! [SV103: $i,SV38: $i] :
( ( ( ! [SY304: $i] :
~ ( check_cpq @ ( triple @ SV38 @ SV103 @ SY304 ) ) )
= $true )
| ( ( ! [SY305: $i,SY306: $i] :
( ~ ( pair_in_list @ SV103 @ SY305 @ SY306 )
| ( less_than @ SY306 @ SY305 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(354,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ~ ( ~ ! [SY289: $i,SY290: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY289 ) ) @ SV87 @ SY290 )
| ( SV71 = SV87 )
| ( pair_in_list @ SV39 @ SV87 @ SY290 ) )
| ~ ! [SY291: $i,SY292: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY291 ) ) @ SV87 @ SY292 )
| ( SY291 = SY292 )
| ( pair_in_list @ SV39 @ SV87 @ SY292 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(355,plain,
! [SV39: $i,SV87: $i,SV71: $i] :
( ( ~ ( ~ ! [SY293: $i,SY294: $i] :
( ( SV71 != SV87 )
| ( SY293 != SY294 )
| ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY293 ) ) @ SV87 @ SY294 ) )
| ~ ! [SY295: $i,SY296: $i] :
( ~ ( pair_in_list @ SV39 @ SV87 @ SY296 )
| ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY295 ) ) @ SV87 @ SY296 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(356,plain,
! [SV104: $i,SV97: $i] :
( ( ( ~ ( less_than @ SV97 @ SV104 )
| ( less_than @ SV104 @ SV97 ) )
= $true )
| ( ( strictly_less_than @ SV97 @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(357,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[334]) ).
thf(358,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(359,plain,
! [SV88: $i,SV72: $i,SV40: $i] :
( ( ! [SY297: $i,SY298: $i] :
( ~ ( less_than @ SY298 @ SY297 )
| ~ ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SV72 @ ( pair @ SY297 @ SY298 ) ) @ SV88 ) )
| ( check_cpq @ ( triple @ SV40 @ SV72 @ SV88 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[336]) ).
thf(360,plain,
! [SV88: $i,SV72: $i,SV40: $i] :
( ( ! [SY299: $i,SY300: $i] :
( ~ ( less_than @ SY300 @ SY299 )
| ~ ( check_cpq @ ( triple @ SV40 @ SV72 @ SV88 ) )
| ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SV72 @ ( pair @ SY299 @ SY300 ) ) @ SV88 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(361,plain,
! [SV1: $i,SV73: $i,SV41: $i] :
( ( ( less_than @ SV41 @ SV73 )
= $false )
| ( ( less_than @ SV1 @ SV41 )
= $false )
| ( ( less_than @ SV1 @ SV73 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(362,plain,
! [SV76: $i,SV108: $i,SV46: $i,SV9: $i] :
( ( ( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV46 @ SV108 ) ) @ SV76 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV76 ) @ ( pair @ SV46 @ SV108 ) ) )
= $true )
| ( ( SV46 = SV76 )
= $true )
| ( ( contains_slb @ SV9 @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(363,plain,
! [SV78: $i,SV109: $i,SV48: $i,SV11: $i] :
( ( ( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV48 @ SV109 ) ) @ SV78 )
= ( lookup_slb @ SV11 @ SV78 ) )
= $true )
| ( ( SV48 = SV78 )
= $true )
| ( ( contains_slb @ SV11 @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(364,plain,
! [SV81: $i,SV56: $i,SV21: $i,SV100: $i,SV91: $i] :
( ( ( strictly_less_than @ SV91 @ SV100 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV56 @ ( pair @ SV91 @ SV100 ) ) @ SV81 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(365,plain,
! [SV85: $i,SV26: $i,SV94: $i,SV61: $i] :
( ( ( contains_slb @ SV61 @ SV94 )
= $false )
| ( ( ~ ( less_than @ ( lookup_slb @ SV61 @ SV94 ) @ SV94 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV26 @ SV61 @ SV85 ) @ SV94 )
= ( triple @ ( remove_pqp @ SV26 @ SV94 ) @ ( remove_slb @ SV61 @ SV94 ) @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(366,plain,
! [SV86: $i,SV27: $i,SV95: $i,SV62: $i] :
( ( ( contains_slb @ SV62 @ SV95 )
= $false )
| ( ( ~ ( strictly_less_than @ SV95 @ ( lookup_slb @ SV62 @ SV95 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV27 @ SV62 @ SV86 ) @ SV95 )
= ( triple @ ( remove_pqp @ SV27 @ SV95 ) @ ( remove_slb @ SV62 @ SV95 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(367,plain,
! [SV65: $i,SV30: $i] :
( ( ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) ) )
= $false )
| ( ( SV65 = create_slb )
= $true )
| ( ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) )
= $false )
| ( ( ! [SY252: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV65 @ SY252 ) )
= ( triple @ SV30 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(368,plain,
! [SV31: $i,SV66: $i] :
( ( ( less_than @ ( lookup_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) )
= $false )
| ( ( SV66 = create_slb )
= $true )
| ( ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) )
= $false )
| ( ( ! [SY253: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV66 @ SY253 ) )
= ( triple @ SV31 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) @ SY253 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(369,plain,
! [SV110: $i,SV105: $i,SV69: $i,SV36: $i] :
( ( ~ ( contains_cpq @ ( triple @ SV36 @ SV69 @ SV105 ) @ SV110 )
| ( contains_slb @ SV69 @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(370,plain,
! [SV106: $i,SV36: $i,SV111: $i,SV69: $i] :
( ( ~ ( contains_slb @ SV69 @ SV111 )
| ( contains_cpq @ ( triple @ SV36 @ SV69 @ SV106 ) @ SV111 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(371,plain,
! [SV107: $i,SV70: $i,SV37: $i] :
( ( ( ! [SY309: $i] :
~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY309 ) ) @ SV107 ) )
= $true )
| ( ( ( SV70 = SV107 )
| ( contains_slb @ SV37 @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(372,plain,
! [SV37: $i,SV70: $i] :
( ( ~ ! [SY261: $i] :
( ( SV70 != SY261 )
| ! [SY262: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY262 ) ) @ SY261 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[351]) ).
thf(373,plain,
! [SV70: $i,SV37: $i] :
( ( ~ ! [SY263: $i] :
( ~ ( contains_slb @ SV37 @ SY263 )
| ! [SY264: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY264 ) ) @ SY263 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[351]) ).
thf(374,plain,
! [SV38: $i,SV102: $i] :
( ( ( ~ ( pair_in_list @ SV102 @ ( sK5_X @ SV102 @ SV38 ) @ ( sK6_SY132 @ SV102 @ SV38 ) )
| ~ ~ ( less_than @ ( sK6_SY132 @ SV102 @ SV38 ) @ ( sK5_X @ SV102 @ SV38 ) ) )
= $false )
| ( ( ! [SY303: $i] : ( check_cpq @ ( triple @ SV38 @ SV102 @ SY303 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(375,plain,
! [SV112: $i,SV103: $i,SV38: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV38 @ SV103 @ SV112 ) ) )
= $true )
| ( ( ! [SY305: $i,SY306: $i] :
( ~ ( pair_in_list @ SV103 @ SY305 @ SY306 )
| ( less_than @ SY306 @ SY305 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(376,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ~ ! [SY289: $i,SY290: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY289 ) ) @ SV87 @ SY290 )
| ( SV71 = SV87 )
| ( pair_in_list @ SV39 @ SV87 @ SY290 ) )
| ~ ! [SY291: $i,SY292: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY291 ) ) @ SV87 @ SY292 )
| ( SY291 = SY292 )
| ( pair_in_list @ SV39 @ SV87 @ SY292 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(377,plain,
! [SV39: $i,SV87: $i,SV71: $i] :
( ( ~ ! [SY293: $i,SY294: $i] :
( ( SV71 != SV87 )
| ( SY293 != SY294 )
| ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY293 ) ) @ SV87 @ SY294 ) )
| ~ ! [SY295: $i,SY296: $i] :
( ~ ( pair_in_list @ SV39 @ SV87 @ SY296 )
| ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY295 ) ) @ SV87 @ SY296 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(378,plain,
! [SV104: $i,SV97: $i] :
( ( ( ~ ( less_than @ SV97 @ SV104 ) )
= $true )
| ( ( less_than @ SV104 @ SV97 )
= $true )
| ( ( strictly_less_than @ SV97 @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(379,plain,
! [SV113: $i] :
( ( ! [SY310: $i] :
( ~ ( strictly_less_than @ SV113 @ SY310 )
| ( less_than @ SV113 @ SY310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(380,plain,
! [SV114: $i] :
( ( ! [SY311: $i] :
( ~ ( strictly_less_than @ SV114 @ SY311 )
| ~ ( less_than @ SY311 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(381,plain,
! [SV88: $i,SV72: $i,SV40: $i,SV115: $i] :
( ( ! [SY312: $i] :
( ~ ( less_than @ SY312 @ SV115 )
| ~ ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SV72 @ ( pair @ SV115 @ SY312 ) ) @ SV88 ) )
| ( check_cpq @ ( triple @ SV40 @ SV72 @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(382,plain,
! [SV88: $i,SV72: $i,SV40: $i,SV116: $i] :
( ( ! [SY313: $i] :
( ~ ( less_than @ SY313 @ SV116 )
| ~ ( check_cpq @ ( triple @ SV40 @ SV72 @ SV88 ) )
| ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SV72 @ ( pair @ SV116 @ SY313 ) ) @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(383,plain,
! [SV81: $i,SV100: $i,SV91: $i,SV56: $i,SV21: $i] :
( ( ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV56 @ ( pair @ SV91 @ SV100 ) ) @ SV81 ) )
= $false )
| ( ( strictly_less_than @ SV91 @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(384,plain,
! [SV85: $i,SV26: $i,SV94: $i,SV61: $i] :
( ( ( less_than @ ( lookup_slb @ SV61 @ SV94 ) @ SV94 )
= $false )
| ( ( contains_slb @ SV61 @ SV94 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV26 @ SV61 @ SV85 ) @ SV94 )
= ( triple @ ( remove_pqp @ SV26 @ SV94 ) @ ( remove_slb @ SV61 @ SV94 ) @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(385,plain,
! [SV86: $i,SV27: $i,SV62: $i,SV95: $i] :
( ( ( strictly_less_than @ SV95 @ ( lookup_slb @ SV62 @ SV95 ) )
= $false )
| ( ( contains_slb @ SV62 @ SV95 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV27 @ SV62 @ SV86 ) @ SV95 )
= ( triple @ ( remove_pqp @ SV27 @ SV95 ) @ ( remove_slb @ SV62 @ SV95 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(386,plain,
! [SV117: $i,SV65: $i,SV30: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV30 @ SV65 @ SV117 ) )
= ( triple @ SV30 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) )
= $true )
| ( ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) )
= $false )
| ( ( SV65 = create_slb )
= $true )
| ( ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SV65 @ ( findmin_pqp_res @ SV30 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(387,plain,
! [SV118: $i,SV66: $i,SV31: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV31 @ SV66 @ SV118 ) )
= ( triple @ SV31 @ ( update_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) @ SV118 ) )
= $true )
| ( ( contains_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) )
= $false )
| ( ( SV66 = create_slb )
= $true )
| ( ( less_than @ ( lookup_slb @ SV66 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(388,plain,
! [SV110: $i,SV105: $i,SV69: $i,SV36: $i] :
( ( ( ~ ( contains_cpq @ ( triple @ SV36 @ SV69 @ SV105 ) @ SV110 ) )
= $true )
| ( ( contains_slb @ SV69 @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(389,plain,
! [SV106: $i,SV36: $i,SV111: $i,SV69: $i] :
( ( ( ~ ( contains_slb @ SV69 @ SV111 ) )
= $true )
| ( ( contains_cpq @ ( triple @ SV36 @ SV69 @ SV106 ) @ SV111 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(390,plain,
! [SV107: $i,SV119: $i,SV70: $i,SV37: $i] :
( ( ( ~ ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SV119 ) ) @ SV107 ) )
= $true )
| ( ( ( SV70 = SV107 )
| ( contains_slb @ SV37 @ SV107 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(391,plain,
! [SV37: $i,SV70: $i] :
( ( ! [SY261: $i] :
( ( SV70 != SY261 )
| ! [SY262: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY262 ) ) @ SY261 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(392,plain,
! [SV70: $i,SV37: $i] :
( ( ! [SY263: $i] :
( ~ ( contains_slb @ SV37 @ SY263 )
| ! [SY264: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY264 ) ) @ SY263 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(393,plain,
! [SV38: $i,SV102: $i] :
( ( ( ~ ( pair_in_list @ SV102 @ ( sK5_X @ SV102 @ SV38 ) @ ( sK6_SY132 @ SV102 @ SV38 ) ) )
= $false )
| ( ( ! [SY303: $i] : ( check_cpq @ ( triple @ SV38 @ SV102 @ SY303 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[374]) ).
thf(394,plain,
! [SV38: $i,SV102: $i] :
( ( ( ~ ~ ( less_than @ ( sK6_SY132 @ SV102 @ SV38 ) @ ( sK5_X @ SV102 @ SV38 ) ) )
= $false )
| ( ( ! [SY303: $i] : ( check_cpq @ ( triple @ SV38 @ SV102 @ SY303 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[374]) ).
thf(395,plain,
! [SV112: $i,SV103: $i,SV38: $i] :
( ( ( check_cpq @ ( triple @ SV38 @ SV103 @ SV112 ) )
= $false )
| ( ( ! [SY305: $i,SY306: $i] :
( ~ ( pair_in_list @ SV103 @ SY305 @ SY306 )
| ( less_than @ SY306 @ SY305 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(396,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ~ ! [SY289: $i,SY290: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY289 ) ) @ SV87 @ SY290 )
| ( SV71 = SV87 )
| ( pair_in_list @ SV39 @ SV87 @ SY290 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[376]) ).
thf(397,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ~ ! [SY291: $i,SY292: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY291 ) ) @ SV87 @ SY292 )
| ( SY291 = SY292 )
| ( pair_in_list @ SV39 @ SV87 @ SY292 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[376]) ).
thf(398,plain,
! [SV39: $i,SV87: $i,SV71: $i] :
( ( ~ ! [SY293: $i,SY294: $i] :
( ( SV71 != SV87 )
| ( SY293 != SY294 )
| ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY293 ) ) @ SV87 @ SY294 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[377]) ).
thf(399,plain,
! [SV71: $i,SV87: $i,SV39: $i] :
( ( ~ ! [SY295: $i,SY296: $i] :
( ~ ( pair_in_list @ SV39 @ SV87 @ SY296 )
| ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY295 ) ) @ SV87 @ SY296 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[377]) ).
thf(400,plain,
! [SV104: $i,SV97: $i] :
( ( ( less_than @ SV97 @ SV104 )
= $false )
| ( ( less_than @ SV104 @ SV97 )
= $true )
| ( ( strictly_less_than @ SV97 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(401,plain,
! [SV120: $i,SV113: $i] :
( ( ~ ( strictly_less_than @ SV113 @ SV120 )
| ( less_than @ SV113 @ SV120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(402,plain,
! [SV121: $i,SV114: $i] :
( ( ~ ( strictly_less_than @ SV114 @ SV121 )
| ~ ( less_than @ SV121 @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(403,plain,
! [SV88: $i,SV72: $i,SV40: $i,SV115: $i,SV122: $i] :
( ( ~ ( less_than @ SV122 @ SV115 )
| ~ ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SV72 @ ( pair @ SV115 @ SV122 ) ) @ SV88 ) )
| ( check_cpq @ ( triple @ SV40 @ SV72 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(404,plain,
! [SV88: $i,SV72: $i,SV40: $i,SV116: $i,SV123: $i] :
( ( ~ ( less_than @ SV123 @ SV116 )
| ~ ( check_cpq @ ( triple @ SV40 @ SV72 @ SV88 ) )
| ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SV72 @ ( pair @ SV116 @ SV123 ) ) @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(405,plain,
! [SV110: $i,SV105: $i,SV69: $i,SV36: $i] :
( ( ( contains_cpq @ ( triple @ SV36 @ SV69 @ SV105 ) @ SV110 )
= $false )
| ( ( contains_slb @ SV69 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(406,plain,
! [SV106: $i,SV36: $i,SV111: $i,SV69: $i] :
( ( ( contains_slb @ SV69 @ SV111 )
= $false )
| ( ( contains_cpq @ ( triple @ SV36 @ SV69 @ SV106 ) @ SV111 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(407,plain,
! [SV107: $i,SV119: $i,SV70: $i,SV37: $i] :
( ( ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SV119 ) ) @ SV107 )
= $false )
| ( ( ( SV70 = SV107 )
| ( contains_slb @ SV37 @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(408,plain,
! [SV37: $i,SV124: $i,SV70: $i] :
( ( ( SV70 != SV124 )
| ! [SY314: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY314 ) ) @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(409,plain,
! [SV70: $i,SV125: $i,SV37: $i] :
( ( ~ ( contains_slb @ SV37 @ SV125 )
| ! [SY315: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY315 ) ) @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(410,plain,
! [SV38: $i,SV102: $i] :
( ( ( pair_in_list @ SV102 @ ( sK5_X @ SV102 @ SV38 ) @ ( sK6_SY132 @ SV102 @ SV38 ) )
= $true )
| ( ( ! [SY303: $i] : ( check_cpq @ ( triple @ SV38 @ SV102 @ SY303 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[393]) ).
thf(411,plain,
! [SV38: $i,SV102: $i] :
( ( ( ~ ( less_than @ ( sK6_SY132 @ SV102 @ SV38 ) @ ( sK5_X @ SV102 @ SV38 ) ) )
= $true )
| ( ( ! [SY303: $i] : ( check_cpq @ ( triple @ SV38 @ SV102 @ SY303 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[394]) ).
thf(412,plain,
! [SV112: $i,SV38: $i,SV126: $i,SV103: $i] :
( ( ( ! [SY316: $i] :
( ~ ( pair_in_list @ SV103 @ SV126 @ SY316 )
| ( less_than @ SY316 @ SV126 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV38 @ SV103 @ SV112 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(413,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ! [SY289: $i,SY290: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY289 ) ) @ SV87 @ SY290 )
| ( SV71 = SV87 )
| ( pair_in_list @ SV39 @ SV87 @ SY290 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[396]) ).
thf(414,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ! [SY291: $i,SY292: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY291 ) ) @ SV87 @ SY292 )
| ( SY291 = SY292 )
| ( pair_in_list @ SV39 @ SV87 @ SY292 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[397]) ).
thf(415,plain,
! [SV39: $i,SV87: $i,SV71: $i] :
( ( ! [SY293: $i,SY294: $i] :
( ( SV71 != SV87 )
| ( SY293 != SY294 )
| ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY293 ) ) @ SV87 @ SY294 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[398]) ).
thf(416,plain,
! [SV71: $i,SV87: $i,SV39: $i] :
( ( ! [SY295: $i,SY296: $i] :
( ~ ( pair_in_list @ SV39 @ SV87 @ SY296 )
| ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SY295 ) ) @ SV87 @ SY296 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[399]) ).
thf(417,plain,
! [SV120: $i,SV113: $i] :
( ( ( ~ ( strictly_less_than @ SV113 @ SV120 ) )
= $true )
| ( ( less_than @ SV113 @ SV120 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(418,plain,
! [SV121: $i,SV114: $i] :
( ( ( ~ ( strictly_less_than @ SV114 @ SV121 ) )
= $true )
| ( ( ~ ( less_than @ SV121 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(419,plain,
! [SV88: $i,SV72: $i,SV40: $i,SV115: $i,SV122: $i] :
( ( ( ~ ( less_than @ SV122 @ SV115 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SV72 @ ( pair @ SV115 @ SV122 ) ) @ SV88 ) )
| ( check_cpq @ ( triple @ SV40 @ SV72 @ SV88 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(420,plain,
! [SV88: $i,SV72: $i,SV40: $i,SV116: $i,SV123: $i] :
( ( ( ~ ( less_than @ SV123 @ SV116 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV40 @ SV72 @ SV88 ) )
| ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SV72 @ ( pair @ SV116 @ SV123 ) ) @ SV88 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(421,plain,
! [SV119: $i,SV37: $i,SV107: $i,SV70: $i] :
( ( ( SV70 = SV107 )
= $true )
| ( ( contains_slb @ SV37 @ SV107 )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SV119 ) ) @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(422,plain,
! [SV37: $i,SV124: $i,SV70: $i] :
( ( ( ( SV70 != SV124 ) )
= $true )
| ( ( ! [SY314: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY314 ) ) @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(423,plain,
! [SV70: $i,SV125: $i,SV37: $i] :
( ( ( ~ ( contains_slb @ SV37 @ SV125 ) )
= $true )
| ( ( ! [SY315: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY315 ) ) @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(424,plain,
! [SV127: $i,SV102: $i,SV38: $i] :
( ( ( check_cpq @ ( triple @ SV38 @ SV102 @ SV127 ) )
= $true )
| ( ( pair_in_list @ SV102 @ ( sK5_X @ SV102 @ SV38 ) @ ( sK6_SY132 @ SV102 @ SV38 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(425,plain,
! [SV38: $i,SV102: $i] :
( ( ( less_than @ ( sK6_SY132 @ SV102 @ SV38 ) @ ( sK5_X @ SV102 @ SV38 ) )
= $false )
| ( ( ! [SY303: $i] : ( check_cpq @ ( triple @ SV38 @ SV102 @ SY303 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(426,plain,
! [SV112: $i,SV38: $i,SV128: $i,SV126: $i,SV103: $i] :
( ( ( ~ ( pair_in_list @ SV103 @ SV126 @ SV128 )
| ( less_than @ SV128 @ SV126 ) )
= $true )
| ( ( check_cpq @ ( triple @ SV38 @ SV103 @ SV112 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(427,plain,
! [SV87: $i,SV129: $i,SV71: $i,SV39: $i] :
( ( ! [SY317: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SV129 ) ) @ SV87 @ SY317 )
| ( SV71 = SV87 )
| ( pair_in_list @ SV39 @ SV87 @ SY317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(428,plain,
! [SV87: $i,SV130: $i,SV71: $i,SV39: $i] :
( ( ! [SY318: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SV130 ) ) @ SV87 @ SY318 )
| ( SV130 = SY318 )
| ( pair_in_list @ SV39 @ SV87 @ SY318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(429,plain,
! [SV39: $i,SV131: $i,SV87: $i,SV71: $i] :
( ( ! [SY319: $i] :
( ( SV71 != SV87 )
| ( SV131 != SY319 )
| ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SV131 ) ) @ SV87 @ SY319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(430,plain,
! [SV132: $i,SV71: $i,SV87: $i,SV39: $i] :
( ( ! [SY320: $i] :
( ~ ( pair_in_list @ SV39 @ SV87 @ SY320 )
| ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SV132 ) ) @ SV87 @ SY320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(431,plain,
! [SV120: $i,SV113: $i] :
( ( ( strictly_less_than @ SV113 @ SV120 )
= $false )
| ( ( less_than @ SV113 @ SV120 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(432,plain,
! [SV121: $i,SV114: $i] :
( ( ( strictly_less_than @ SV114 @ SV121 )
= $false )
| ( ( ~ ( less_than @ SV121 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(433,plain,
! [SV88: $i,SV72: $i,SV40: $i,SV115: $i,SV122: $i] :
( ( ( less_than @ SV122 @ SV115 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SV72 @ ( pair @ SV115 @ SV122 ) ) @ SV88 ) )
| ( check_cpq @ ( triple @ SV40 @ SV72 @ SV88 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(434,plain,
! [SV88: $i,SV72: $i,SV40: $i,SV116: $i,SV123: $i] :
( ( ( less_than @ SV123 @ SV116 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV40 @ SV72 @ SV88 ) )
| ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SV72 @ ( pair @ SV116 @ SV123 ) ) @ SV88 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(435,plain,
! [SV37: $i,SV124: $i,SV70: $i] :
( ( ( SV70 = SV124 )
= $false )
| ( ( ! [SY314: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY314 ) ) @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(436,plain,
! [SV70: $i,SV125: $i,SV37: $i] :
( ( ( contains_slb @ SV37 @ SV125 )
= $false )
| ( ( ! [SY315: $i] : ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SY315 ) ) @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(437,plain,
! [SV133: $i,SV102: $i,SV38: $i] :
( ( ( check_cpq @ ( triple @ SV38 @ SV102 @ SV133 ) )
= $true )
| ( ( less_than @ ( sK6_SY132 @ SV102 @ SV38 ) @ ( sK5_X @ SV102 @ SV38 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(438,plain,
! [SV112: $i,SV38: $i,SV128: $i,SV126: $i,SV103: $i] :
( ( ( ~ ( pair_in_list @ SV103 @ SV126 @ SV128 ) )
= $true )
| ( ( less_than @ SV128 @ SV126 )
= $true )
| ( ( check_cpq @ ( triple @ SV38 @ SV103 @ SV112 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(439,plain,
! [SV134: $i,SV87: $i,SV129: $i,SV71: $i,SV39: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SV129 ) ) @ SV87 @ SV134 )
| ( SV71 = SV87 )
| ( pair_in_list @ SV39 @ SV87 @ SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(440,plain,
! [SV135: $i,SV87: $i,SV130: $i,SV71: $i,SV39: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SV130 ) ) @ SV87 @ SV135 )
| ( SV130 = SV135 )
| ( pair_in_list @ SV39 @ SV87 @ SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(441,plain,
! [SV39: $i,SV136: $i,SV131: $i,SV87: $i,SV71: $i] :
( ( ( SV71 != SV87 )
| ( SV131 != SV136 )
| ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SV131 ) ) @ SV87 @ SV136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(442,plain,
! [SV132: $i,SV71: $i,SV137: $i,SV87: $i,SV39: $i] :
( ( ~ ( pair_in_list @ SV39 @ SV87 @ SV137 )
| ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SV132 ) ) @ SV87 @ SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(443,plain,
! [SV114: $i,SV121: $i] :
( ( ( less_than @ SV121 @ SV114 )
= $false )
| ( ( strictly_less_than @ SV114 @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(444,plain,
! [SV88: $i,SV122: $i,SV115: $i,SV72: $i,SV40: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SV72 @ ( pair @ SV115 @ SV122 ) ) @ SV88 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV40 @ SV72 @ SV88 ) )
= $true )
| ( ( less_than @ SV122 @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(445,plain,
! [SV123: $i,SV116: $i,SV88: $i,SV72: $i,SV40: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV40 @ SV72 @ SV88 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SV72 @ ( pair @ SV116 @ SV123 ) ) @ SV88 ) )
= $true )
| ( ( less_than @ SV123 @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(446,plain,
! [SV124: $i,SV138: $i,SV70: $i,SV37: $i] :
( ( ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SV138 ) ) @ SV124 )
= $true )
| ( ( SV70 = SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(447,plain,
! [SV125: $i,SV139: $i,SV70: $i,SV37: $i] :
( ( ( contains_slb @ ( insert_slb @ SV37 @ ( pair @ SV70 @ SV139 ) ) @ SV125 )
= $true )
| ( ( contains_slb @ SV37 @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(448,plain,
! [SV112: $i,SV38: $i,SV128: $i,SV126: $i,SV103: $i] :
( ( ( pair_in_list @ SV103 @ SV126 @ SV128 )
= $false )
| ( ( less_than @ SV128 @ SV126 )
= $true )
| ( ( check_cpq @ ( triple @ SV38 @ SV103 @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(449,plain,
! [SV134: $i,SV87: $i,SV129: $i,SV71: $i,SV39: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SV129 ) ) @ SV87 @ SV134 ) )
= $true )
| ( ( ( SV71 = SV87 )
| ( pair_in_list @ SV39 @ SV87 @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(450,plain,
! [SV135: $i,SV87: $i,SV130: $i,SV71: $i,SV39: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SV130 ) ) @ SV87 @ SV135 ) )
= $true )
| ( ( ( SV130 = SV135 )
| ( pair_in_list @ SV39 @ SV87 @ SV135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(451,plain,
! [SV39: $i,SV136: $i,SV131: $i,SV87: $i,SV71: $i] :
( ( ( ( SV71 != SV87 )
| ( SV131 != SV136 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SV131 ) ) @ SV87 @ SV136 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(452,plain,
! [SV132: $i,SV71: $i,SV137: $i,SV87: $i,SV39: $i] :
( ( ( ~ ( pair_in_list @ SV39 @ SV87 @ SV137 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SV132 ) ) @ SV87 @ SV137 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[442]) ).
thf(453,plain,
! [SV88: $i,SV122: $i,SV115: $i,SV72: $i,SV40: $i] :
( ( ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SV72 @ ( pair @ SV115 @ SV122 ) ) @ SV88 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV40 @ SV72 @ SV88 ) )
= $true )
| ( ( less_than @ SV122 @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(454,plain,
! [SV123: $i,SV116: $i,SV88: $i,SV72: $i,SV40: $i] :
( ( ( check_cpq @ ( triple @ SV40 @ SV72 @ SV88 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV40 @ ( insert_slb @ SV72 @ ( pair @ SV116 @ SV123 ) ) @ SV88 ) )
= $true )
| ( ( less_than @ SV123 @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(455,plain,
! [SV134: $i,SV87: $i,SV129: $i,SV71: $i,SV39: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SV129 ) ) @ SV87 @ SV134 )
= $false )
| ( ( ( SV71 = SV87 )
| ( pair_in_list @ SV39 @ SV87 @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(456,plain,
! [SV135: $i,SV87: $i,SV130: $i,SV71: $i,SV39: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SV130 ) ) @ SV87 @ SV135 )
= $false )
| ( ( ( SV130 = SV135 )
| ( pair_in_list @ SV39 @ SV87 @ SV135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(457,plain,
! [SV39: $i,SV136: $i,SV131: $i,SV87: $i,SV71: $i] :
( ( ( ( SV71 != SV87 ) )
= $true )
| ( ( ( SV131 != SV136 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SV131 ) ) @ SV87 @ SV136 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(458,plain,
! [SV132: $i,SV71: $i,SV137: $i,SV87: $i,SV39: $i] :
( ( ( pair_in_list @ SV39 @ SV87 @ SV137 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SV132 ) ) @ SV87 @ SV137 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(459,plain,
! [SV129: $i,SV134: $i,SV39: $i,SV87: $i,SV71: $i] :
( ( ( SV71 = SV87 )
= $true )
| ( ( pair_in_list @ SV39 @ SV87 @ SV134 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SV129 ) ) @ SV87 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(460,plain,
! [SV71: $i,SV87: $i,SV39: $i,SV135: $i,SV130: $i] :
( ( ( SV130 = SV135 )
= $true )
| ( ( pair_in_list @ SV39 @ SV87 @ SV135 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SV130 ) ) @ SV87 @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[456]) ).
thf(461,plain,
! [SV39: $i,SV136: $i,SV131: $i,SV87: $i,SV71: $i] :
( ( ( SV71 = SV87 )
= $false )
| ( ( ( SV131 != SV136 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SV131 ) ) @ SV87 @ SV136 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(462,plain,
! [SV39: $i,SV87: $i,SV71: $i,SV136: $i,SV131: $i] :
( ( ( SV131 = SV136 )
= $false )
| ( ( SV71 = SV87 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV39 @ ( pair @ SV71 @ SV131 ) ) @ SV87 @ SV136 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(463,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[163,462,460,459,458,454,453,448,447,446,443,437,431,424,421,406,405,400,387,386,385,384,383,363,362,361,342,341,322,319,317,316,300,293,292,290,289,264,255,253,252,251,250,240,236,228,216,206,205,204,185,182,174,173,172]) ).
thf(464,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[463]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV390+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 21:46:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.39 .
% 0.13/0.39
% 0.13/0.39 No.of.Axioms: 42
% 0.13/0.39
% 0.13/0.39 Length.of.Defs: 0
% 0.13/0.39
% 0.13/0.39 Contains.Choice.Funs: false
% 0.20/0.44 .
% 0.20/0.44 (rf:0,axioms:42,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:44,loop_count:0,foatp_calls:0,translation:fof_full)...................................
% 4.23/4.43
% 4.23/4.43 ********************************
% 4.23/4.43 * All subproblems solved! *
% 4.23/4.43 ********************************
% 4.23/4.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:43,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:463,loop_count:0,foatp_calls:1,translation:fof_full)
% 4.36/4.54
% 4.36/4.54 %**** Beginning of derivation protocol ****
% 4.36/4.54 % SZS output start CNFRefutation
% See solution above
% 4.36/4.55
% 4.36/4.55 %**** End of derivation protocol ****
% 4.36/4.55 %**** no. of clauses in derivation: 464 ****
% 4.36/4.55 %**** clause counter: 463 ****
% 4.36/4.55
% 4.36/4.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:43,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:463,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------