TSTP Solution File: SWV397+1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SWV397+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 : n008.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 20:12:19 EDT 2022
% Result : Theorem 0.44s 0.68s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 73
% Syntax : Number of formulae : 466 ( 310 unt; 31 typ; 0 def)
% Number of atoms : 2218 ( 870 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 5650 ( 571 ~; 606 |; 42 &;4372 @)
% ( 14 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 9 con; 0-3 aty)
% Number of variables : 1561 ( 0 ^1561 !; 0 ?;1561 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_bad,type,
bad: $i ).
thf(tp_bottom,type,
bottom: $i ).
thf(tp_check_cpq,type,
check_cpq: $i > $o ).
thf(tp_contains_cpq,type,
contains_cpq: $i > $i > $o ).
thf(tp_contains_slb,type,
contains_slb: $i > $i > $o ).
thf(tp_create_slb,type,
create_slb: $i ).
thf(tp_findmin_cpq_eff,type,
findmin_cpq_eff: $i > $i ).
thf(tp_findmin_cpq_res,type,
findmin_cpq_res: $i > $i ).
thf(tp_findmin_pqp_res,type,
findmin_pqp_res: $i > $i ).
thf(tp_insert_cpq,type,
insert_cpq: $i > $i > $i ).
thf(tp_insert_pqp,type,
insert_pqp: $i > $i > $i ).
thf(tp_insert_slb,type,
insert_slb: $i > $i > $i ).
thf(tp_isnonempty_slb,type,
isnonempty_slb: $i > $o ).
thf(tp_less_than,type,
less_than: $i > $i > $o ).
thf(tp_lookup_slb,type,
lookup_slb: $i > $i > $i ).
thf(tp_ok,type,
ok: $i > $o ).
thf(tp_pair,type,
pair: $i > $i > $i ).
thf(tp_pair_in_list,type,
pair_in_list: $i > $i > $i > $o ).
thf(tp_remove_cpq,type,
remove_cpq: $i > $i > $i ).
thf(tp_remove_pqp,type,
remove_pqp: $i > $i > $i ).
thf(tp_remove_slb,type,
remove_slb: $i > $i > $i ).
thf(tp_removemin_cpq_eff,type,
removemin_cpq_eff: $i > $i ).
thf(tp_removemin_cpq_res,type,
removemin_cpq_res: $i > $i ).
thf(tp_sK1_U,type,
sK1_U: $i ).
thf(tp_sK2_SY121,type,
sK2_SY121: $i ).
thf(tp_sK3_SY124,type,
sK3_SY124: $i ).
thf(tp_sK4_SY126,type,
sK4_SY126: $i ).
thf(tp_strictly_less_than,type,
strictly_less_than: $i > $i > $o ).
thf(tp_succ_cpq,type,
succ_cpq: $i > $i > $o ).
thf(tp_triple,type,
triple: $i > $i > $i > $i ).
thf(tp_update_slb,type,
update_slb: $i > $i > $i ).
thf(1,axiom,
! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax51) ).
thf(4,axiom,
! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax42) ).
thf(13,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ( W = bad ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).
thf(14,axiom,
! [U: $i,V: $i] :
( ( ok @ ( triple @ U @ V @ bad ) )
<=> $false ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax37) ).
thf(18,axiom,
! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax32) ).
thf(23,axiom,
! [U: $i] : ( succ_cpq @ U @ U ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax29) ).
thf(26,axiom,
! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax23) ).
thf(32,axiom,
! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax21) ).
thf(34,axiom,
! [U: $i] :
~ ( contains_slb @ create_slb @ U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
thf(35,axiom,
! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).
thf(36,axiom,
~ ( isnonempty_slb @ create_slb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
thf(37,axiom,
! [U: $i] : ( less_than @ bottom @ U ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',stricly_smaller_definition) ).
thf(39,axiom,
! [U: $i] : ( less_than @ U @ U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(40,axiom,
! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(42,conjecture,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ok @ ( remove_cpq @ ( triple @ U @ V @ W ) @ X ) )
=> ( contains_slb @ V @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l33_co) ).
thf(43,negated_conjecture,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ok @ ( remove_cpq @ ( triple @ U @ V @ W ) @ X ) )
=> ( contains_slb @ V @ X ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[42]) ).
thf(44,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ok @ ( remove_cpq @ ( triple @ U @ V @ W ) @ X ) )
=> ( contains_slb @ V @ X ) ) )
= $false ),
inference(unfold_def,[status(thm)],[43]) ).
thf(45,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(46,plain,
( ( ! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(47,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( V != create_slb )
=> ( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
= ( findmin_pqp_res @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(48,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(49,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != create_slb )
& ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
& ( less_than @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) @ ( findmin_pqp_res @ U ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(50,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != create_slb )
& ( contains_slb @ V @ ( findmin_pqp_res @ U ) )
& ( strictly_less_than @ ( findmin_pqp_res @ U ) @ ( lookup_slb @ V @ ( findmin_pqp_res @ U ) ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(51,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != create_slb )
& ~ ( contains_slb @ V @ ( findmin_pqp_res @ U ) ) )
=> ( ( findmin_cpq_eff @ ( triple @ U @ V @ W ) )
= ( triple @ U @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ bad ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(52,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ create_slb @ V ) )
= ( triple @ U @ create_slb @ bad ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(53,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( contains_slb @ V @ X )
& ( strictly_less_than @ X @ ( lookup_slb @ V @ X ) ) )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ bad ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(54,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( contains_slb @ V @ X )
& ( less_than @ ( lookup_slb @ V @ X ) @ X ) )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(55,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
=> ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ U @ V @ bad ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(56,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( insert_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( insert_pqp @ U @ X ) @ ( insert_slb @ V @ ( pair @ X @ bottom ) ) @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(57,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( ok @ ( triple @ U @ V @ W ) )
=> ( W = bad ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(58,plain,
( ( ! [U: $i,V: $i] :
( ( ok @ ( triple @ U @ V @ bad ) )
<=> $false ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(59,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
<=> ( contains_slb @ V @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(60,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( strictly_less_than @ X @ Y )
=> ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
<=> $false ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(61,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( less_than @ Y @ X )
=> ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
<=> ( check_cpq @ ( triple @ U @ V @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(62,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(63,plain,
( ( ! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(64,plain,
( ( ! [U: $i,V: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(65,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(66,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( succ_cpq @ U @ V )
=> ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(67,plain,
( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(68,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( less_than @ W @ X )
=> ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(69,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( strictly_less_than @ X @ W )
=> ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(70,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(71,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != W )
& ( contains_slb @ U @ W ) )
=> ( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( lookup_slb @ U @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(72,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(73,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != W )
& ( contains_slb @ U @ W ) )
=> ( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( remove_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(74,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(75,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
<=> ( ( pair_in_list @ U @ W @ Y )
| ( ( V = W )
& ( X = Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(76,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(77,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
<=> ( ( contains_slb @ U @ W )
| ( V = W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(78,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(79,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(80,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(81,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(82,plain,
( ( ! [U: $i,V: $i] :
( ( strictly_less_than @ U @ V )
<=> ( ( less_than @ U @ V )
& ~ ( less_than @ V @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(83,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(84,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(85,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( less_than @ U @ V )
& ( less_than @ V @ W ) )
=> ( less_than @ U @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(86,plain,
( ( ! [SY121: $i,SY122: $i,SY123: $i] :
( ( ok @ ( remove_cpq @ ( triple @ sK1_U @ SY121 @ SY122 ) @ SY123 ) )
=> ( contains_slb @ SY121 @ SY123 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(87,plain,
( ( ! [SY124: $i,SY125: $i] :
( ( ok @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY121 @ SY124 ) @ SY125 ) )
=> ( contains_slb @ sK2_SY121 @ SY125 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[86]) ).
thf(88,plain,
( ( ! [SY126: $i] :
( ( ok @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY121 @ sK3_SY124 ) @ SY126 ) )
=> ( contains_slb @ sK2_SY121 @ SY126 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[87]) ).
thf(89,plain,
( ( ( ok @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY121 @ sK3_SY124 ) @ sK4_SY126 ) )
=> ( contains_slb @ sK2_SY121 @ sK4_SY126 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[88]) ).
thf(90,plain,
( ( ok @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY121 @ sK3_SY124 ) @ sK4_SY126 ) )
= $true ),
inference(standard_cnf,[status(thm)],[89]) ).
thf(91,plain,
( ( contains_slb @ sK2_SY121 @ sK4_SY126 )
= $false ),
inference(standard_cnf,[status(thm)],[89]) ).
thf(92,plain,
( ( ~ ( contains_slb @ sK2_SY121 @ sK4_SY126 ) )
= $true ),
inference(polarity_switch,[status(thm)],[91]) ).
thf(93,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)],[47]) ).
thf(94,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)],[49]) ).
thf(95,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)],[50]) ).
thf(96,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)],[51]) ).
thf(97,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)],[53]) ).
thf(98,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)],[54]) ).
thf(99,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)],[55]) ).
thf(100,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( triple @ U @ V @ W ) )
| ( W = bad ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(101,plain,
( ( ! [U: $i,V: $i] :
~ ( ok @ ( triple @ U @ V @ bad ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(102,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)],[59]) ).
thf(103,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)],[60]) ).
thf(104,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)],[61]) ).
thf(105,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[63]) ).
thf(106,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(107,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(108,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(109,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)],[68]) ).
thf(110,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)],[69]) ).
thf(111,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)],[71]) ).
thf(112,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)],[73]) ).
thf(113,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)],[75]) ).
thf(114,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)],[77]) ).
thf(115,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)],[82]) ).
thf(116,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)],[85]) ).
thf(117,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( less_than @ U @ V )
| ~ ( less_than @ V @ W )
| ( less_than @ U @ W ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(118,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(119,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(120,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)],[115]) ).
thf(121,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(122,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(123,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(124,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(125,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)],[114]) ).
thf(126,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(127,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)],[113]) ).
thf(128,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(129,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)],[112]) ).
thf(130,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(131,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)],[111]) ).
thf(132,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(133,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)],[110]) ).
thf(134,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)],[109]) ).
thf(135,plain,
( ( ! [U: $i] : ( succ_cpq @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(136,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( insert_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(137,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ! [W: $i] : ( succ_cpq @ U @ ( remove_cpq @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(138,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( findmin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(139,plain,
( ( ! [U: $i,V: $i] :
( ~ ( succ_cpq @ U @ V )
| ( succ_cpq @ U @ ( removemin_cpq_eff @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(140,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(141,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)],[104]) ).
thf(142,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)],[103]) ).
thf(143,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)],[102]) ).
thf(144,plain,
( ( ! [U: $i,V: $i] :
~ ( ok @ ( triple @ U @ V @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(145,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ok @ ( triple @ U @ V @ W ) )
| ( W = bad ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(146,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( insert_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( insert_pqp @ U @ X ) @ ( insert_slb @ V @ ( pair @ X @ bottom ) ) @ W ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(147,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)],[99]) ).
thf(148,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)],[98]) ).
thf(149,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( contains_slb @ V @ X )
| ~ ( strictly_less_than @ X @ ( lookup_slb @ V @ X ) )
| ( ( remove_cpq @ ( triple @ U @ V @ W ) @ X )
= ( triple @ ( remove_pqp @ U @ X ) @ ( remove_slb @ V @ X ) @ bad ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(150,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_eff @ ( triple @ U @ create_slb @ V ) )
= ( triple @ U @ create_slb @ bad ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(151,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)],[96]) ).
thf(152,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)],[95]) ).
thf(153,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)],[94]) ).
thf(154,plain,
( ( ! [U: $i,V: $i] :
( ( findmin_cpq_res @ ( triple @ U @ create_slb @ V ) )
= bottom ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(155,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)],[93]) ).
thf(156,plain,
( ( ! [U: $i] :
( ( removemin_cpq_eff @ U )
= ( remove_cpq @ ( findmin_cpq_eff @ U ) @ ( findmin_cpq_res @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(157,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(158,plain,
( ( ok @ ( remove_cpq @ ( triple @ sK1_U @ sK2_SY121 @ sK3_SY124 ) @ sK4_SY126 ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(159,plain,
( ( ~ ( contains_slb @ sK2_SY121 @ sK4_SY126 ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(160,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)],[120]) ).
thf(161,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)],[127]) ).
thf(162,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)],[143]) ).
thf(163,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)],[125]) ).
thf(164,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)],[141]) ).
thf(165,plain,
! [SV1: $i] :
( ( ! [SY127: $i,SY128: $i] :
( ~ ( less_than @ SV1 @ SY127 )
| ~ ( less_than @ SY127 @ SY128 )
| ( less_than @ SV1 @ SY128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(166,plain,
! [SV2: $i] :
( ( ! [SY129: $i] :
( ( less_than @ SV2 @ SY129 )
| ( less_than @ SY129 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(167,plain,
! [SV3: $i] :
( ( less_than @ SV3 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(168,plain,
! [SV4: $i] :
( ( less_than @ bottom @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(169,plain,
( ( isnonempty_slb @ create_slb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(170,plain,
! [SV5: $i] :
( ( ! [SY130: $i,SY131: $i] : ( isnonempty_slb @ ( insert_slb @ SV5 @ ( pair @ SY130 @ SY131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(171,plain,
! [SV6: $i] :
( ( ~ ( contains_slb @ create_slb @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(172,plain,
! [SV7: $i] :
( ( ! [SY132: $i] :
~ ( pair_in_list @ create_slb @ SV7 @ SY132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(173,plain,
! [SV8: $i] :
( ( ! [SY133: $i,SY134: $i] :
( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SY133 @ SY134 ) ) @ SY133 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(174,plain,
! [SV9: $i] :
( ( ! [SY135: $i,SY136: $i] :
( ( SY135 = SY136 )
| ~ ( contains_slb @ SV9 @ SY136 )
| ! [SY137: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SY135 @ SY137 ) ) @ SY136 )
= ( insert_slb @ ( remove_slb @ SV9 @ SY136 ) @ ( pair @ SY135 @ SY137 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(175,plain,
! [SV10: $i] :
( ( ! [SY138: $i,SY139: $i] :
( ( lookup_slb @ ( insert_slb @ SV10 @ ( pair @ SY138 @ SY139 ) ) @ SY138 )
= SY139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(176,plain,
! [SV11: $i] :
( ( ! [SY140: $i,SY141: $i] :
( ( SY140 = SY141 )
| ~ ( contains_slb @ SV11 @ SY141 )
| ! [SY142: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SY140 @ SY142 ) ) @ SY141 )
= ( lookup_slb @ SV11 @ SY141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(177,plain,
! [SV12: $i] :
( ( ( update_slb @ create_slb @ SV12 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(178,plain,
! [SV13: $i] :
( ( ! [SY143: $i,SY144: $i,SY145: $i] :
( ~ ( strictly_less_than @ SY145 @ SY144 )
| ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SY143 @ SY145 ) ) @ SY144 )
= ( insert_slb @ ( update_slb @ SV13 @ SY144 ) @ ( pair @ SY143 @ SY144 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(179,plain,
! [SV14: $i] :
( ( ! [SY146: $i,SY147: $i,SY148: $i] :
( ~ ( less_than @ SY147 @ SY148 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SY146 @ SY148 ) ) @ SY147 )
= ( insert_slb @ ( update_slb @ SV14 @ SY147 ) @ ( pair @ SY146 @ SY148 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(180,plain,
! [SV15: $i] :
( ( succ_cpq @ SV15 @ SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(181,plain,
! [SV16: $i] :
( ( ! [SY149: $i] :
( ~ ( succ_cpq @ SV16 @ SY149 )
| ! [SY150: $i] : ( succ_cpq @ SV16 @ ( insert_cpq @ SY149 @ SY150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(182,plain,
! [SV17: $i] :
( ( ! [SY151: $i] :
( ~ ( succ_cpq @ SV17 @ SY151 )
| ! [SY152: $i] : ( succ_cpq @ SV17 @ ( remove_cpq @ SY151 @ SY152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(183,plain,
! [SV18: $i] :
( ( ! [SY153: $i] :
( ~ ( succ_cpq @ SV18 @ SY153 )
| ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SY153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(184,plain,
! [SV19: $i] :
( ( ! [SY154: $i] :
( ~ ( succ_cpq @ SV19 @ SY154 )
| ( succ_cpq @ SV19 @ ( removemin_cpq_eff @ SY154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(185,plain,
! [SV20: $i] :
( ( ! [SY155: $i] : ( check_cpq @ ( triple @ SV20 @ create_slb @ SY155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(186,plain,
! [SV21: $i] :
( ( ! [SY156: $i,SY157: $i,SY158: $i,SY159: $i] :
( ~ ( strictly_less_than @ SY158 @ SY159 )
| ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SY156 @ ( pair @ SY158 @ SY159 ) ) @ SY157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(187,plain,
! [SV22: $i] :
( ( ! [SY160: $i] :
~ ( ok @ ( triple @ SV22 @ SY160 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(188,plain,
! [SV23: $i] :
( ( ! [SY161: $i,SY162: $i] :
( ( ok @ ( triple @ SV23 @ SY161 @ SY162 ) )
| ( SY162 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(189,plain,
! [SV24: $i] :
( ( ! [SY163: $i,SY164: $i,SY165: $i] :
( ( insert_cpq @ ( triple @ SV24 @ SY163 @ SY164 ) @ SY165 )
= ( triple @ ( insert_pqp @ SV24 @ SY165 ) @ ( insert_slb @ SY163 @ ( pair @ SY165 @ bottom ) ) @ SY164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(190,plain,
! [SV25: $i] :
( ( ! [SY166: $i,SY167: $i,SY168: $i] :
( ( contains_slb @ SY166 @ SY168 )
| ( ( remove_cpq @ ( triple @ SV25 @ SY166 @ SY167 ) @ SY168 )
= ( triple @ SV25 @ SY166 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(191,plain,
! [SV26: $i] :
( ( ! [SY169: $i,SY170: $i,SY171: $i] :
( ~ ( contains_slb @ SY169 @ SY171 )
| ~ ( less_than @ ( lookup_slb @ SY169 @ SY171 ) @ SY171 )
| ( ( remove_cpq @ ( triple @ SV26 @ SY169 @ SY170 ) @ SY171 )
= ( triple @ ( remove_pqp @ SV26 @ SY171 ) @ ( remove_slb @ SY169 @ SY171 ) @ SY170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(192,plain,
! [SV27: $i] :
( ( ! [SY172: $i,SY173: $i,SY174: $i] :
( ~ ( contains_slb @ SY172 @ SY174 )
| ~ ( strictly_less_than @ SY174 @ ( lookup_slb @ SY172 @ SY174 ) )
| ( ( remove_cpq @ ( triple @ SV27 @ SY172 @ SY173 ) @ SY174 )
= ( triple @ ( remove_pqp @ SV27 @ SY174 ) @ ( remove_slb @ SY172 @ SY174 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(193,plain,
! [SV28: $i] :
( ( ! [SY175: $i] :
( ( findmin_cpq_eff @ ( triple @ SV28 @ create_slb @ SY175 ) )
= ( triple @ SV28 @ create_slb @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(194,plain,
! [SV29: $i] :
( ( ! [SY176: $i] :
( ( SY176 = create_slb )
| ( contains_slb @ SY176 @ ( findmin_pqp_res @ SV29 ) )
| ! [SY177: $i] :
( ( findmin_cpq_eff @ ( triple @ SV29 @ SY176 @ SY177 ) )
= ( triple @ SV29 @ ( update_slb @ SY176 @ ( findmin_pqp_res @ SV29 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(195,plain,
! [SV30: $i] :
( ( ! [SY178: $i] :
( ( SY178 = create_slb )
| ~ ( contains_slb @ SY178 @ ( findmin_pqp_res @ SV30 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SY178 @ ( findmin_pqp_res @ SV30 ) ) )
| ! [SY179: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SY178 @ SY179 ) )
= ( triple @ SV30 @ ( update_slb @ SY178 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(196,plain,
! [SV31: $i] :
( ( ! [SY180: $i] :
( ( SY180 = create_slb )
| ~ ( contains_slb @ SY180 @ ( findmin_pqp_res @ SV31 ) )
| ~ ( less_than @ ( lookup_slb @ SY180 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) )
| ! [SY181: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SY180 @ SY181 ) )
= ( triple @ SV31 @ ( update_slb @ SY180 @ ( findmin_pqp_res @ SV31 ) ) @ SY181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(197,plain,
! [SV32: $i] :
( ( ! [SY182: $i] :
( ( findmin_cpq_res @ ( triple @ SV32 @ create_slb @ SY182 ) )
= bottom ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(198,plain,
! [SV33: $i] :
( ( ! [SY183: $i] :
( ( SY183 = create_slb )
| ! [SY184: $i] :
( ( findmin_cpq_res @ ( triple @ SV33 @ SY183 @ SY184 ) )
= ( findmin_pqp_res @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(199,plain,
! [SV34: $i] :
( ( ( removemin_cpq_eff @ SV34 )
= ( remove_cpq @ ( findmin_cpq_eff @ SV34 ) @ ( findmin_cpq_res @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(200,plain,
! [SV35: $i] :
( ( ( removemin_cpq_res @ SV35 )
= ( findmin_cpq_res @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(201,plain,
( ( contains_slb @ sK2_SY121 @ sK4_SY126 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(202,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)],[160]) ).
thf(203,plain,
! [SV36: $i] :
( ( ! [SY185: $i,SY186: $i] :
~ ( ~ ~ ( ~ ! [SY187: $i,SY188: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SY185 @ SY187 ) ) @ SY186 @ SY188 )
| ( SY185 = SY186 )
| ( pair_in_list @ SV36 @ SY186 @ SY188 ) )
| ~ ! [SY189: $i,SY190: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SY185 @ SY189 ) ) @ SY186 @ SY190 )
| ( SY189 = SY190 )
| ( pair_in_list @ SV36 @ SY186 @ SY190 ) ) )
| ~ ~ ( ~ ! [SY191: $i,SY192: $i] :
( ( SY185 != SY186 )
| ( SY191 != SY192 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SY185 @ SY191 ) ) @ SY186 @ SY192 ) )
| ~ ! [SY193: $i,SY194: $i] :
( ~ ( pair_in_list @ SV36 @ SY186 @ SY194 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SY185 @ SY193 ) ) @ SY186 @ SY194 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(204,plain,
! [SV37: $i] :
( ( ! [SY195: $i] :
~ ( ~ ! [SY196: $i,SY197: $i] :
( ~ ( contains_cpq @ ( triple @ SV37 @ SY195 @ SY196 ) @ SY197 )
| ( contains_slb @ SY195 @ SY197 ) )
| ~ ! [SY198: $i,SY199: $i] :
( ~ ( contains_slb @ SY195 @ SY199 )
| ( contains_cpq @ ( triple @ SV37 @ SY195 @ SY198 ) @ SY199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(205,plain,
! [SV38: $i] :
( ( ! [SY200: $i] :
~ ( ~ ! [SY201: $i] :
( ! [SY202: $i] :
~ ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SY200 @ SY202 ) ) @ SY201 )
| ( SY200 = SY201 )
| ( contains_slb @ SV38 @ SY201 ) )
| ~ ~ ( ~ ! [SY203: $i] :
( ( SY200 != SY203 )
| ! [SY204: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SY200 @ SY204 ) ) @ SY203 ) )
| ~ ! [SY205: $i] :
( ~ ( contains_slb @ SV38 @ SY205 )
| ! [SY206: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SY200 @ SY206 ) ) @ SY205 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(206,plain,
! [SV39: $i] :
( ( ! [SY207: $i,SY208: $i] :
~ ( ~ ! [SY209: $i,SY210: $i] :
( ~ ( less_than @ SY210 @ SY209 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SY207 @ ( pair @ SY209 @ SY210 ) ) @ SY208 ) )
| ( check_cpq @ ( triple @ SV39 @ SY207 @ SY208 ) ) )
| ~ ! [SY211: $i,SY212: $i] :
( ~ ( less_than @ SY212 @ SY211 )
| ~ ( check_cpq @ ( triple @ SV39 @ SY207 @ SY208 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SY207 @ ( pair @ SY211 @ SY212 ) ) @ SY208 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(207,plain,
! [SV40: $i,SV1: $i] :
( ( ! [SY213: $i] :
( ~ ( less_than @ SV1 @ SV40 )
| ~ ( less_than @ SV40 @ SY213 )
| ( less_than @ SV1 @ SY213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(208,plain,
! [SV41: $i,SV2: $i] :
( ( ( less_than @ SV2 @ SV41 )
| ( less_than @ SV41 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(209,plain,
! [SV42: $i,SV5: $i] :
( ( ! [SY214: $i] : ( isnonempty_slb @ ( insert_slb @ SV5 @ ( pair @ SV42 @ SY214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(210,plain,
! [SV6: $i] :
( ( contains_slb @ create_slb @ SV6 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(211,plain,
! [SV43: $i,SV7: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV7 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(212,plain,
! [SV44: $i,SV8: $i] :
( ( ! [SY215: $i] :
( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SV44 @ SY215 ) ) @ SV44 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(213,plain,
! [SV9: $i,SV45: $i] :
( ( ! [SY216: $i] :
( ( SV45 = SY216 )
| ~ ( contains_slb @ SV9 @ SY216 )
| ! [SY217: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV45 @ SY217 ) ) @ SY216 )
= ( insert_slb @ ( remove_slb @ SV9 @ SY216 ) @ ( pair @ SV45 @ SY217 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(214,plain,
! [SV46: $i,SV10: $i] :
( ( ! [SY218: $i] :
( ( lookup_slb @ ( insert_slb @ SV10 @ ( pair @ SV46 @ SY218 ) ) @ SV46 )
= SY218 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(215,plain,
! [SV11: $i,SV47: $i] :
( ( ! [SY219: $i] :
( ( SV47 = SY219 )
| ~ ( contains_slb @ SV11 @ SY219 )
| ! [SY220: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV47 @ SY220 ) ) @ SY219 )
= ( lookup_slb @ SV11 @ SY219 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(216,plain,
! [SV48: $i,SV13: $i] :
( ( ! [SY221: $i,SY222: $i] :
( ~ ( strictly_less_than @ SY222 @ SY221 )
| ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV48 @ SY222 ) ) @ SY221 )
= ( insert_slb @ ( update_slb @ SV13 @ SY221 ) @ ( pair @ SV48 @ SY221 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(217,plain,
! [SV49: $i,SV14: $i] :
( ( ! [SY223: $i,SY224: $i] :
( ~ ( less_than @ SY223 @ SY224 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV49 @ SY224 ) ) @ SY223 )
= ( insert_slb @ ( update_slb @ SV14 @ SY223 ) @ ( pair @ SV49 @ SY224 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(218,plain,
! [SV50: $i,SV16: $i] :
( ( ~ ( succ_cpq @ SV16 @ SV50 )
| ! [SY225: $i] : ( succ_cpq @ SV16 @ ( insert_cpq @ SV50 @ SY225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(219,plain,
! [SV51: $i,SV17: $i] :
( ( ~ ( succ_cpq @ SV17 @ SV51 )
| ! [SY226: $i] : ( succ_cpq @ SV17 @ ( remove_cpq @ SV51 @ SY226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(220,plain,
! [SV52: $i,SV18: $i] :
( ( ~ ( succ_cpq @ SV18 @ SV52 )
| ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(221,plain,
! [SV53: $i,SV19: $i] :
( ( ~ ( succ_cpq @ SV19 @ SV53 )
| ( succ_cpq @ SV19 @ ( removemin_cpq_eff @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(222,plain,
! [SV54: $i,SV20: $i] :
( ( check_cpq @ ( triple @ SV20 @ create_slb @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(223,plain,
! [SV55: $i,SV21: $i] :
( ( ! [SY227: $i,SY228: $i,SY229: $i] :
( ~ ( strictly_less_than @ SY228 @ SY229 )
| ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV55 @ ( pair @ SY228 @ SY229 ) ) @ SY227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(224,plain,
! [SV56: $i,SV22: $i] :
( ( ~ ( ok @ ( triple @ SV22 @ SV56 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(225,plain,
! [SV57: $i,SV23: $i] :
( ( ! [SY230: $i] :
( ( ok @ ( triple @ SV23 @ SV57 @ SY230 ) )
| ( SY230 = bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(226,plain,
! [SV58: $i,SV24: $i] :
( ( ! [SY231: $i,SY232: $i] :
( ( insert_cpq @ ( triple @ SV24 @ SV58 @ SY231 ) @ SY232 )
= ( triple @ ( insert_pqp @ SV24 @ SY232 ) @ ( insert_slb @ SV58 @ ( pair @ SY232 @ bottom ) ) @ SY231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(227,plain,
! [SV25: $i,SV59: $i] :
( ( ! [SY233: $i,SY234: $i] :
( ( contains_slb @ SV59 @ SY234 )
| ( ( remove_cpq @ ( triple @ SV25 @ SV59 @ SY233 ) @ SY234 )
= ( triple @ SV25 @ SV59 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(228,plain,
! [SV26: $i,SV60: $i] :
( ( ! [SY235: $i,SY236: $i] :
( ~ ( contains_slb @ SV60 @ SY236 )
| ~ ( less_than @ ( lookup_slb @ SV60 @ SY236 ) @ SY236 )
| ( ( remove_cpq @ ( triple @ SV26 @ SV60 @ SY235 ) @ SY236 )
= ( triple @ ( remove_pqp @ SV26 @ SY236 ) @ ( remove_slb @ SV60 @ SY236 ) @ SY235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(229,plain,
! [SV27: $i,SV61: $i] :
( ( ! [SY237: $i,SY238: $i] :
( ~ ( contains_slb @ SV61 @ SY238 )
| ~ ( strictly_less_than @ SY238 @ ( lookup_slb @ SV61 @ SY238 ) )
| ( ( remove_cpq @ ( triple @ SV27 @ SV61 @ SY237 ) @ SY238 )
= ( triple @ ( remove_pqp @ SV27 @ SY238 ) @ ( remove_slb @ SV61 @ SY238 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(230,plain,
! [SV62: $i,SV28: $i] :
( ( ( findmin_cpq_eff @ ( triple @ SV28 @ create_slb @ SV62 ) )
= ( triple @ SV28 @ create_slb @ bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(231,plain,
! [SV29: $i,SV63: $i] :
( ( ( SV63 = create_slb )
| ( contains_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) )
| ! [SY239: $i] :
( ( findmin_cpq_eff @ ( triple @ SV29 @ SV63 @ SY239 ) )
= ( triple @ SV29 @ ( update_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(232,plain,
! [SV30: $i,SV64: $i] :
( ( ( SV64 = create_slb )
| ~ ( contains_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) )
| ! [SY240: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY240 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(233,plain,
! [SV31: $i,SV65: $i] :
( ( ( SV65 = create_slb )
| ~ ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) )
| ~ ( less_than @ ( lookup_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) )
| ! [SY241: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY241 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(234,plain,
! [SV66: $i,SV32: $i] :
( ( ( findmin_cpq_res @ ( triple @ SV32 @ create_slb @ SV66 ) )
= bottom )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(235,plain,
! [SV33: $i,SV67: $i] :
( ( ( SV67 = create_slb )
| ! [SY242: $i] :
( ( findmin_cpq_res @ ( triple @ SV33 @ SV67 @ SY242 ) )
= ( findmin_pqp_res @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(236,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)],[202]) ).
thf(237,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)],[202]) ).
thf(238,plain,
! [SV68: $i,SV36: $i] :
( ( ! [SY243: $i] :
~ ( ~ ~ ( ~ ! [SY244: $i,SY245: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY244 ) ) @ SY243 @ SY245 )
| ( SV68 = SY243 )
| ( pair_in_list @ SV36 @ SY243 @ SY245 ) )
| ~ ! [SY246: $i,SY247: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY246 ) ) @ SY243 @ SY247 )
| ( SY246 = SY247 )
| ( pair_in_list @ SV36 @ SY243 @ SY247 ) ) )
| ~ ~ ( ~ ! [SY248: $i,SY249: $i] :
( ( SV68 != SY243 )
| ( SY248 != SY249 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY248 ) ) @ SY243 @ SY249 ) )
| ~ ! [SY250: $i,SY251: $i] :
( ~ ( pair_in_list @ SV36 @ SY243 @ SY251 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY250 ) ) @ SY243 @ SY251 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(239,plain,
! [SV69: $i,SV37: $i] :
( ( ~ ( ~ ! [SY252: $i,SY253: $i] :
( ~ ( contains_cpq @ ( triple @ SV37 @ SV69 @ SY252 ) @ SY253 )
| ( contains_slb @ SV69 @ SY253 ) )
| ~ ! [SY254: $i,SY255: $i] :
( ~ ( contains_slb @ SV69 @ SY255 )
| ( contains_cpq @ ( triple @ SV37 @ SV69 @ SY254 ) @ SY255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(240,plain,
! [SV70: $i,SV38: $i] :
( ( ~ ( ~ ! [SY256: $i] :
( ! [SY257: $i] :
~ ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY257 ) ) @ SY256 )
| ( SV70 = SY256 )
| ( contains_slb @ SV38 @ SY256 ) )
| ~ ~ ( ~ ! [SY258: $i] :
( ( SV70 != SY258 )
| ! [SY259: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY259 ) ) @ SY258 ) )
| ~ ! [SY260: $i] :
( ~ ( contains_slb @ SV38 @ SY260 )
| ! [SY261: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY261 ) ) @ SY260 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(241,plain,
! [SV71: $i,SV39: $i] :
( ( ! [SY262: $i] :
~ ( ~ ! [SY263: $i,SY264: $i] :
( ~ ( less_than @ SY264 @ SY263 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY263 @ SY264 ) ) @ SY262 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SY262 ) ) )
| ~ ! [SY265: $i,SY266: $i] :
( ~ ( less_than @ SY266 @ SY265 )
| ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SY262 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY265 @ SY266 ) ) @ SY262 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(242,plain,
! [SV72: $i,SV40: $i,SV1: $i] :
( ( ~ ( less_than @ SV1 @ SV40 )
| ~ ( less_than @ SV40 @ SV72 )
| ( less_than @ SV1 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(243,plain,
! [SV41: $i,SV2: $i] :
( ( ( less_than @ SV2 @ SV41 )
= $true )
| ( ( less_than @ SV41 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(244,plain,
! [SV73: $i,SV42: $i,SV5: $i] :
( ( isnonempty_slb @ ( insert_slb @ SV5 @ ( pair @ SV42 @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(245,plain,
! [SV43: $i,SV7: $i] :
( ( pair_in_list @ create_slb @ SV7 @ SV43 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(246,plain,
! [SV74: $i,SV44: $i,SV8: $i] :
( ( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SV44 @ SV74 ) ) @ SV44 )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(247,plain,
! [SV9: $i,SV75: $i,SV45: $i] :
( ( ( SV45 = SV75 )
| ~ ( contains_slb @ SV9 @ SV75 )
| ! [SY267: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV45 @ SY267 ) ) @ SV75 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV75 ) @ ( pair @ SV45 @ SY267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(248,plain,
! [SV76: $i,SV46: $i,SV10: $i] :
( ( ( lookup_slb @ ( insert_slb @ SV10 @ ( pair @ SV46 @ SV76 ) ) @ SV46 )
= SV76 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(249,plain,
! [SV11: $i,SV77: $i,SV47: $i] :
( ( ( SV47 = SV77 )
| ~ ( contains_slb @ SV11 @ SV77 )
| ! [SY268: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV47 @ SY268 ) ) @ SV77 )
= ( lookup_slb @ SV11 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(250,plain,
! [SV48: $i,SV13: $i,SV78: $i] :
( ( ! [SY269: $i] :
( ~ ( strictly_less_than @ SY269 @ SV78 )
| ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV48 @ SY269 ) ) @ SV78 )
= ( insert_slb @ ( update_slb @ SV13 @ SV78 ) @ ( pair @ SV48 @ SV78 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(251,plain,
! [SV49: $i,SV14: $i,SV79: $i] :
( ( ! [SY270: $i] :
( ~ ( less_than @ SV79 @ SY270 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV49 @ SY270 ) ) @ SV79 )
= ( insert_slb @ ( update_slb @ SV14 @ SV79 ) @ ( pair @ SV49 @ SY270 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(252,plain,
! [SV50: $i,SV16: $i] :
( ( ( ~ ( succ_cpq @ SV16 @ SV50 ) )
= $true )
| ( ( ! [SY225: $i] : ( succ_cpq @ SV16 @ ( insert_cpq @ SV50 @ SY225 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(253,plain,
! [SV51: $i,SV17: $i] :
( ( ( ~ ( succ_cpq @ SV17 @ SV51 ) )
= $true )
| ( ( ! [SY226: $i] : ( succ_cpq @ SV17 @ ( remove_cpq @ SV51 @ SY226 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(254,plain,
! [SV52: $i,SV18: $i] :
( ( ( ~ ( succ_cpq @ SV18 @ SV52 ) )
= $true )
| ( ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(255,plain,
! [SV53: $i,SV19: $i] :
( ( ( ~ ( succ_cpq @ SV19 @ SV53 ) )
= $true )
| ( ( succ_cpq @ SV19 @ ( removemin_cpq_eff @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(256,plain,
! [SV80: $i,SV55: $i,SV21: $i] :
( ( ! [SY271: $i,SY272: $i] :
( ~ ( strictly_less_than @ SY271 @ SY272 )
| ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV55 @ ( pair @ SY271 @ SY272 ) ) @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(257,plain,
! [SV56: $i,SV22: $i] :
( ( ok @ ( triple @ SV22 @ SV56 @ bad ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(258,plain,
! [SV81: $i,SV57: $i,SV23: $i] :
( ( ( ok @ ( triple @ SV23 @ SV57 @ SV81 ) )
| ( SV81 = bad ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(259,plain,
! [SV82: $i,SV58: $i,SV24: $i] :
( ( ! [SY273: $i] :
( ( insert_cpq @ ( triple @ SV24 @ SV58 @ SV82 ) @ SY273 )
= ( triple @ ( insert_pqp @ SV24 @ SY273 ) @ ( insert_slb @ SV58 @ ( pair @ SY273 @ bottom ) ) @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(260,plain,
! [SV83: $i,SV25: $i,SV59: $i] :
( ( ! [SY274: $i] :
( ( contains_slb @ SV59 @ SY274 )
| ( ( remove_cpq @ ( triple @ SV25 @ SV59 @ SV83 ) @ SY274 )
= ( triple @ SV25 @ SV59 @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(261,plain,
! [SV84: $i,SV26: $i,SV60: $i] :
( ( ! [SY275: $i] :
( ~ ( contains_slb @ SV60 @ SY275 )
| ~ ( less_than @ ( lookup_slb @ SV60 @ SY275 ) @ SY275 )
| ( ( remove_cpq @ ( triple @ SV26 @ SV60 @ SV84 ) @ SY275 )
= ( triple @ ( remove_pqp @ SV26 @ SY275 ) @ ( remove_slb @ SV60 @ SY275 ) @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(262,plain,
! [SV85: $i,SV27: $i,SV61: $i] :
( ( ! [SY276: $i] :
( ~ ( contains_slb @ SV61 @ SY276 )
| ~ ( strictly_less_than @ SY276 @ ( lookup_slb @ SV61 @ SY276 ) )
| ( ( remove_cpq @ ( triple @ SV27 @ SV61 @ SV85 ) @ SY276 )
= ( triple @ ( remove_pqp @ SV27 @ SY276 ) @ ( remove_slb @ SV61 @ SY276 ) @ bad ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(263,plain,
! [SV29: $i,SV63: $i] :
( ( ( ( SV63 = create_slb )
| ( contains_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) ) )
= $true )
| ( ( ! [SY239: $i] :
( ( findmin_cpq_eff @ ( triple @ SV29 @ SV63 @ SY239 ) )
= ( triple @ SV29 @ ( update_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(264,plain,
! [SV30: $i,SV64: $i] :
( ( ( ( SV64 = create_slb )
| ~ ( contains_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) )
| ~ ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) ) )
= $true )
| ( ( ! [SY240: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY240 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(265,plain,
! [SV31: $i,SV65: $i] :
( ( ( ( SV65 = create_slb )
| ~ ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) )
| ~ ( less_than @ ( lookup_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) ) )
= $true )
| ( ( ! [SY241: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY241 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(266,plain,
! [SV33: $i,SV67: $i] :
( ( ( SV67 = create_slb )
= $true )
| ( ( ! [SY242: $i] :
( ( findmin_cpq_res @ ( triple @ SV33 @ SV67 @ SY242 ) )
= ( findmin_pqp_res @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(267,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)],[236]) ).
thf(268,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)],[237]) ).
thf(269,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY277: $i,SY278: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY277 ) ) @ SV86 @ SY278 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY278 ) )
| ~ ! [SY279: $i,SY280: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY279 ) ) @ SV86 @ SY280 )
| ( SY279 = SY280 )
| ( pair_in_list @ SV36 @ SV86 @ SY280 ) ) )
| ~ ~ ( ~ ! [SY281: $i,SY282: $i] :
( ( SV68 != SV86 )
| ( SY281 != SY282 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY281 ) ) @ SV86 @ SY282 ) )
| ~ ! [SY283: $i,SY284: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY284 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY283 ) ) @ SV86 @ SY284 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(270,plain,
! [SV69: $i,SV37: $i] :
( ( ~ ! [SY252: $i,SY253: $i] :
( ~ ( contains_cpq @ ( triple @ SV37 @ SV69 @ SY252 ) @ SY253 )
| ( contains_slb @ SV69 @ SY253 ) )
| ~ ! [SY254: $i,SY255: $i] :
( ~ ( contains_slb @ SV69 @ SY255 )
| ( contains_cpq @ ( triple @ SV37 @ SV69 @ SY254 ) @ SY255 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(271,plain,
! [SV70: $i,SV38: $i] :
( ( ~ ! [SY256: $i] :
( ! [SY257: $i] :
~ ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY257 ) ) @ SY256 )
| ( SV70 = SY256 )
| ( contains_slb @ SV38 @ SY256 ) )
| ~ ~ ( ~ ! [SY258: $i] :
( ( SV70 != SY258 )
| ! [SY259: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY259 ) ) @ SY258 ) )
| ~ ! [SY260: $i] :
( ~ ( contains_slb @ SV38 @ SY260 )
| ! [SY261: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY261 ) ) @ SY260 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(272,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ~ ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( less_than @ SY286 @ SY285 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY285 @ SY286 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) )
| ~ ! [SY287: $i,SY288: $i] :
( ~ ( less_than @ SY288 @ SY287 )
| ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY287 @ SY288 ) ) @ SV87 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(273,plain,
! [SV72: $i,SV40: $i,SV1: $i] :
( ( ( ~ ( less_than @ SV1 @ SV40 )
| ~ ( less_than @ SV40 @ SV72 ) )
= $true )
| ( ( less_than @ SV1 @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(274,plain,
! [SV9: $i,SV75: $i,SV45: $i] :
( ( ( ( SV45 = SV75 )
| ~ ( contains_slb @ SV9 @ SV75 ) )
= $true )
| ( ( ! [SY267: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV45 @ SY267 ) ) @ SV75 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV75 ) @ ( pair @ SV45 @ SY267 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(275,plain,
! [SV11: $i,SV77: $i,SV47: $i] :
( ( ( ( SV47 = SV77 )
| ~ ( contains_slb @ SV11 @ SV77 ) )
= $true )
| ( ( ! [SY268: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV47 @ SY268 ) ) @ SV77 )
= ( lookup_slb @ SV11 @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(276,plain,
! [SV48: $i,SV13: $i,SV78: $i,SV88: $i] :
( ( ~ ( strictly_less_than @ SV88 @ SV78 )
| ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV48 @ SV88 ) ) @ SV78 )
= ( insert_slb @ ( update_slb @ SV13 @ SV78 ) @ ( pair @ SV48 @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(277,plain,
! [SV49: $i,SV14: $i,SV89: $i,SV79: $i] :
( ( ~ ( less_than @ SV79 @ SV89 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV49 @ SV89 ) ) @ SV79 )
= ( insert_slb @ ( update_slb @ SV14 @ SV79 ) @ ( pair @ SV49 @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(278,plain,
! [SV50: $i,SV16: $i] :
( ( ( succ_cpq @ SV16 @ SV50 )
= $false )
| ( ( ! [SY225: $i] : ( succ_cpq @ SV16 @ ( insert_cpq @ SV50 @ SY225 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(279,plain,
! [SV51: $i,SV17: $i] :
( ( ( succ_cpq @ SV17 @ SV51 )
= $false )
| ( ( ! [SY226: $i] : ( succ_cpq @ SV17 @ ( remove_cpq @ SV51 @ SY226 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(280,plain,
! [SV52: $i,SV18: $i] :
( ( ( succ_cpq @ SV18 @ SV52 )
= $false )
| ( ( succ_cpq @ SV18 @ ( findmin_cpq_eff @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(281,plain,
! [SV53: $i,SV19: $i] :
( ( ( succ_cpq @ SV19 @ SV53 )
= $false )
| ( ( succ_cpq @ SV19 @ ( removemin_cpq_eff @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(282,plain,
! [SV80: $i,SV55: $i,SV21: $i,SV90: $i] :
( ( ! [SY289: $i] :
( ~ ( strictly_less_than @ SV90 @ SY289 )
| ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV55 @ ( pair @ SV90 @ SY289 ) ) @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(283,plain,
! [SV81: $i,SV57: $i,SV23: $i] :
( ( ( ok @ ( triple @ SV23 @ SV57 @ SV81 ) )
= $true )
| ( ( SV81 = bad )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(284,plain,
! [SV91: $i,SV82: $i,SV58: $i,SV24: $i] :
( ( ( insert_cpq @ ( triple @ SV24 @ SV58 @ SV82 ) @ SV91 )
= ( triple @ ( insert_pqp @ SV24 @ SV91 ) @ ( insert_slb @ SV58 @ ( pair @ SV91 @ bottom ) ) @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(285,plain,
! [SV83: $i,SV25: $i,SV92: $i,SV59: $i] :
( ( ( contains_slb @ SV59 @ SV92 )
| ( ( remove_cpq @ ( triple @ SV25 @ SV59 @ SV83 ) @ SV92 )
= ( triple @ SV25 @ SV59 @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(286,plain,
! [SV84: $i,SV26: $i,SV93: $i,SV60: $i] :
( ( ~ ( contains_slb @ SV60 @ SV93 )
| ~ ( less_than @ ( lookup_slb @ SV60 @ SV93 ) @ SV93 )
| ( ( remove_cpq @ ( triple @ SV26 @ SV60 @ SV84 ) @ SV93 )
= ( triple @ ( remove_pqp @ SV26 @ SV93 ) @ ( remove_slb @ SV60 @ SV93 ) @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(287,plain,
! [SV85: $i,SV27: $i,SV94: $i,SV61: $i] :
( ( ~ ( contains_slb @ SV61 @ SV94 )
| ~ ( strictly_less_than @ SV94 @ ( lookup_slb @ SV61 @ SV94 ) )
| ( ( remove_cpq @ ( triple @ SV27 @ SV61 @ SV85 ) @ SV94 )
= ( triple @ ( remove_pqp @ SV27 @ SV94 ) @ ( remove_slb @ SV61 @ SV94 ) @ bad ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(288,plain,
! [SV29: $i,SV63: $i] :
( ( ( SV63 = create_slb )
= $true )
| ( ( contains_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) )
= $true )
| ( ( ! [SY239: $i] :
( ( findmin_cpq_eff @ ( triple @ SV29 @ SV63 @ SY239 ) )
= ( triple @ SV29 @ ( update_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(289,plain,
! [SV30: $i,SV64: $i] :
( ( ( ( SV64 = create_slb )
| ~ ( contains_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) ) )
= $true )
| ( ( ! [SY240: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY240 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(290,plain,
! [SV31: $i,SV65: $i] :
( ( ( ( SV65 = create_slb )
| ~ ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) ) )
= $true )
| ( ( ! [SY241: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY241 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(291,plain,
! [SV95: $i,SV67: $i,SV33: $i] :
( ( ( ( findmin_cpq_res @ ( triple @ SV33 @ SV67 @ SV95 ) )
= ( findmin_pqp_res @ SV33 ) )
= $true )
| ( ( SV67 = create_slb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(292,plain,
! [SV96: $i] :
( ( ! [SY290: $i] :
( ~ ( less_than @ SV96 @ SY290 )
| ( less_than @ SY290 @ SV96 )
| ( strictly_less_than @ SV96 @ SY290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(293,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)],[268]) ).
thf(294,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ~ ~ ( ~ ! [SY277: $i,SY278: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY277 ) ) @ SV86 @ SY278 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY278 ) )
| ~ ! [SY279: $i,SY280: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY279 ) ) @ SV86 @ SY280 )
| ( SY279 = SY280 )
| ( pair_in_list @ SV36 @ SV86 @ SY280 ) ) )
| ~ ~ ( ~ ! [SY281: $i,SY282: $i] :
( ( SV68 != SV86 )
| ( SY281 != SY282 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY281 ) ) @ SV86 @ SY282 ) )
| ~ ! [SY283: $i,SY284: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY284 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY283 ) ) @ SV86 @ SY284 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(295,plain,
! [SV69: $i,SV37: $i] :
( ( ~ ! [SY252: $i,SY253: $i] :
( ~ ( contains_cpq @ ( triple @ SV37 @ SV69 @ SY252 ) @ SY253 )
| ( contains_slb @ SV69 @ SY253 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[270]) ).
thf(296,plain,
! [SV37: $i,SV69: $i] :
( ( ~ ! [SY254: $i,SY255: $i] :
( ~ ( contains_slb @ SV69 @ SY255 )
| ( contains_cpq @ ( triple @ SV37 @ SV69 @ SY254 ) @ SY255 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[270]) ).
thf(297,plain,
! [SV70: $i,SV38: $i] :
( ( ~ ! [SY256: $i] :
( ! [SY257: $i] :
~ ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY257 ) ) @ SY256 )
| ( SV70 = SY256 )
| ( contains_slb @ SV38 @ SY256 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[271]) ).
thf(298,plain,
! [SV38: $i,SV70: $i] :
( ( ~ ~ ( ~ ! [SY258: $i] :
( ( SV70 != SY258 )
| ! [SY259: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY259 ) ) @ SY258 ) )
| ~ ! [SY260: $i] :
( ~ ( contains_slb @ SV38 @ SY260 )
| ! [SY261: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY261 ) ) @ SY260 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[271]) ).
thf(299,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( less_than @ SY286 @ SY285 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY285 @ SY286 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) )
| ~ ! [SY287: $i,SY288: $i] :
( ~ ( less_than @ SY288 @ SY287 )
| ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY287 @ SY288 ) ) @ SV87 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(300,plain,
! [SV72: $i,SV40: $i,SV1: $i] :
( ( ( ~ ( less_than @ SV1 @ SV40 ) )
= $true )
| ( ( ~ ( less_than @ SV40 @ SV72 ) )
= $true )
| ( ( less_than @ SV1 @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(301,plain,
! [SV9: $i,SV75: $i,SV45: $i] :
( ( ( SV45 = SV75 )
= $true )
| ( ( ~ ( contains_slb @ SV9 @ SV75 ) )
= $true )
| ( ( ! [SY267: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV45 @ SY267 ) ) @ SV75 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV75 ) @ ( pair @ SV45 @ SY267 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(302,plain,
! [SV11: $i,SV77: $i,SV47: $i] :
( ( ( SV47 = SV77 )
= $true )
| ( ( ~ ( contains_slb @ SV11 @ SV77 ) )
= $true )
| ( ( ! [SY268: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV47 @ SY268 ) ) @ SV77 )
= ( lookup_slb @ SV11 @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(303,plain,
! [SV48: $i,SV13: $i,SV78: $i,SV88: $i] :
( ( ( ~ ( strictly_less_than @ SV88 @ SV78 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV48 @ SV88 ) ) @ SV78 )
= ( insert_slb @ ( update_slb @ SV13 @ SV78 ) @ ( pair @ SV48 @ SV78 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(304,plain,
! [SV49: $i,SV14: $i,SV89: $i,SV79: $i] :
( ( ( ~ ( less_than @ SV79 @ SV89 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV49 @ SV89 ) ) @ SV79 )
= ( insert_slb @ ( update_slb @ SV14 @ SV79 ) @ ( pair @ SV49 @ SV89 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(305,plain,
! [SV97: $i,SV50: $i,SV16: $i] :
( ( ( succ_cpq @ SV16 @ ( insert_cpq @ SV50 @ SV97 ) )
= $true )
| ( ( succ_cpq @ SV16 @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(306,plain,
! [SV98: $i,SV51: $i,SV17: $i] :
( ( ( succ_cpq @ SV17 @ ( remove_cpq @ SV51 @ SV98 ) )
= $true )
| ( ( succ_cpq @ SV17 @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(307,plain,
! [SV80: $i,SV55: $i,SV21: $i,SV99: $i,SV90: $i] :
( ( ~ ( strictly_less_than @ SV90 @ SV99 )
| ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV55 @ ( pair @ SV90 @ SV99 ) ) @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(308,plain,
! [SV83: $i,SV25: $i,SV92: $i,SV59: $i] :
( ( ( contains_slb @ SV59 @ SV92 )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV25 @ SV59 @ SV83 ) @ SV92 )
= ( triple @ SV25 @ SV59 @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(309,plain,
! [SV84: $i,SV26: $i,SV93: $i,SV60: $i] :
( ( ( ~ ( contains_slb @ SV60 @ SV93 )
| ~ ( less_than @ ( lookup_slb @ SV60 @ SV93 ) @ SV93 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV26 @ SV60 @ SV84 ) @ SV93 )
= ( triple @ ( remove_pqp @ SV26 @ SV93 ) @ ( remove_slb @ SV60 @ SV93 ) @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(310,plain,
! [SV85: $i,SV27: $i,SV94: $i,SV61: $i] :
( ( ( ~ ( contains_slb @ SV61 @ SV94 )
| ~ ( strictly_less_than @ SV94 @ ( lookup_slb @ SV61 @ SV94 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV27 @ SV61 @ SV85 ) @ SV94 )
= ( triple @ ( remove_pqp @ SV27 @ SV94 ) @ ( remove_slb @ SV61 @ SV94 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(311,plain,
! [SV100: $i,SV63: $i,SV29: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV29 @ SV63 @ SV100 ) )
= ( triple @ SV29 @ ( update_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) ) @ bad ) )
= $true )
| ( ( contains_slb @ SV63 @ ( findmin_pqp_res @ SV29 ) )
= $true )
| ( ( SV63 = create_slb )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(312,plain,
! [SV30: $i,SV64: $i] :
( ( ( SV64 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) ) )
= $true )
| ( ( ! [SY240: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY240 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(313,plain,
! [SV31: $i,SV65: $i] :
( ( ( SV65 = create_slb )
= $true )
| ( ( ~ ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) ) )
= $true )
| ( ( ! [SY241: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY241 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(314,plain,
! [SV101: $i,SV96: $i] :
( ( ~ ( less_than @ SV96 @ SV101 )
| ( less_than @ SV101 @ SV96 )
| ( strictly_less_than @ SV96 @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(315,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(316,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(317,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ~ ~ ( ~ ! [SY277: $i,SY278: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY277 ) ) @ SV86 @ SY278 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY278 ) )
| ~ ! [SY279: $i,SY280: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY279 ) ) @ SV86 @ SY280 )
| ( SY279 = SY280 )
| ( pair_in_list @ SV36 @ SV86 @ SY280 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(318,plain,
! [SV36: $i,SV86: $i,SV68: $i] :
( ( ~ ~ ( ~ ! [SY281: $i,SY282: $i] :
( ( SV68 != SV86 )
| ( SY281 != SY282 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY281 ) ) @ SV86 @ SY282 ) )
| ~ ! [SY283: $i,SY284: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY284 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY283 ) ) @ SV86 @ SY284 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(319,plain,
! [SV69: $i,SV37: $i] :
( ( ! [SY252: $i,SY253: $i] :
( ~ ( contains_cpq @ ( triple @ SV37 @ SV69 @ SY252 ) @ SY253 )
| ( contains_slb @ SV69 @ SY253 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(320,plain,
! [SV37: $i,SV69: $i] :
( ( ! [SY254: $i,SY255: $i] :
( ~ ( contains_slb @ SV69 @ SY255 )
| ( contains_cpq @ ( triple @ SV37 @ SV69 @ SY254 ) @ SY255 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(321,plain,
! [SV70: $i,SV38: $i] :
( ( ! [SY256: $i] :
( ! [SY257: $i] :
~ ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY257 ) ) @ SY256 )
| ( SV70 = SY256 )
| ( contains_slb @ SV38 @ SY256 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(322,plain,
! [SV38: $i,SV70: $i] :
( ( ~ ( ~ ! [SY258: $i] :
( ( SV70 != SY258 )
| ! [SY259: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY259 ) ) @ SY258 ) )
| ~ ! [SY260: $i] :
( ~ ( contains_slb @ SV38 @ SY260 )
| ! [SY261: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY261 ) ) @ SY260 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(323,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( less_than @ SY286 @ SY285 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY285 @ SY286 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[299]) ).
thf(324,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ~ ! [SY287: $i,SY288: $i] :
( ~ ( less_than @ SY288 @ SY287 )
| ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY287 @ SY288 ) ) @ SV87 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[299]) ).
thf(325,plain,
! [SV72: $i,SV40: $i,SV1: $i] :
( ( ( less_than @ SV1 @ SV40 )
= $false )
| ( ( ~ ( less_than @ SV40 @ SV72 ) )
= $true )
| ( ( less_than @ SV1 @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(326,plain,
! [SV45: $i,SV75: $i,SV9: $i] :
( ( ( contains_slb @ SV9 @ SV75 )
= $false )
| ( ( SV45 = SV75 )
= $true )
| ( ( ! [SY267: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV45 @ SY267 ) ) @ SV75 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV75 ) @ ( pair @ SV45 @ SY267 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(327,plain,
! [SV47: $i,SV77: $i,SV11: $i] :
( ( ( contains_slb @ SV11 @ SV77 )
= $false )
| ( ( SV47 = SV77 )
= $true )
| ( ( ! [SY268: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV47 @ SY268 ) ) @ SV77 )
= ( lookup_slb @ SV11 @ SV77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(328,plain,
! [SV48: $i,SV13: $i,SV78: $i,SV88: $i] :
( ( ( strictly_less_than @ SV88 @ SV78 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV48 @ SV88 ) ) @ SV78 )
= ( insert_slb @ ( update_slb @ SV13 @ SV78 ) @ ( pair @ SV48 @ SV78 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(329,plain,
! [SV49: $i,SV14: $i,SV89: $i,SV79: $i] :
( ( ( less_than @ SV79 @ SV89 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV49 @ SV89 ) ) @ SV79 )
= ( insert_slb @ ( update_slb @ SV14 @ SV79 ) @ ( pair @ SV49 @ SV89 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(330,plain,
! [SV80: $i,SV55: $i,SV21: $i,SV99: $i,SV90: $i] :
( ( ( ~ ( strictly_less_than @ SV90 @ SV99 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV55 @ ( pair @ SV90 @ SV99 ) ) @ SV80 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(331,plain,
! [SV84: $i,SV26: $i,SV93: $i,SV60: $i] :
( ( ( ~ ( contains_slb @ SV60 @ SV93 ) )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV60 @ SV93 ) @ SV93 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV26 @ SV60 @ SV84 ) @ SV93 )
= ( triple @ ( remove_pqp @ SV26 @ SV93 ) @ ( remove_slb @ SV60 @ SV93 ) @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(332,plain,
! [SV85: $i,SV27: $i,SV94: $i,SV61: $i] :
( ( ( ~ ( contains_slb @ SV61 @ SV94 ) )
= $true )
| ( ( ~ ( strictly_less_than @ SV94 @ ( lookup_slb @ SV61 @ SV94 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV27 @ SV61 @ SV85 ) @ SV94 )
= ( triple @ ( remove_pqp @ SV27 @ SV94 ) @ ( remove_slb @ SV61 @ SV94 ) @ bad ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(333,plain,
! [SV30: $i,SV64: $i] :
( ( ( contains_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) )
= $false )
| ( ( SV64 = create_slb )
= $true )
| ( ( ~ ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) ) )
= $true )
| ( ( ! [SY240: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY240 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(334,plain,
! [SV31: $i,SV65: $i] :
( ( ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) )
= $false )
| ( ( SV65 = create_slb )
= $true )
| ( ( ~ ( less_than @ ( lookup_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) ) )
= $true )
| ( ( ! [SY241: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY241 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY241 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(335,plain,
! [SV101: $i,SV96: $i] :
( ( ( ~ ( less_than @ SV96 @ SV101 )
| ( less_than @ SV101 @ SV96 ) )
= $true )
| ( ( strictly_less_than @ SV96 @ SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(336,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(337,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(338,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ~ ( ~ ! [SY277: $i,SY278: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY277 ) ) @ SV86 @ SY278 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY278 ) )
| ~ ! [SY279: $i,SY280: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY279 ) ) @ SV86 @ SY280 )
| ( SY279 = SY280 )
| ( pair_in_list @ SV36 @ SV86 @ SY280 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[317]) ).
thf(339,plain,
! [SV36: $i,SV86: $i,SV68: $i] :
( ( ~ ( ~ ! [SY281: $i,SY282: $i] :
( ( SV68 != SV86 )
| ( SY281 != SY282 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY281 ) ) @ SV86 @ SY282 ) )
| ~ ! [SY283: $i,SY284: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY284 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY283 ) ) @ SV86 @ SY284 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[318]) ).
thf(340,plain,
! [SV102: $i,SV69: $i,SV37: $i] :
( ( ! [SY291: $i] :
( ~ ( contains_cpq @ ( triple @ SV37 @ SV69 @ SV102 ) @ SY291 )
| ( contains_slb @ SV69 @ SY291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(341,plain,
! [SV103: $i,SV37: $i,SV69: $i] :
( ( ! [SY292: $i] :
( ~ ( contains_slb @ SV69 @ SY292 )
| ( contains_cpq @ ( triple @ SV37 @ SV69 @ SV103 ) @ SY292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(342,plain,
! [SV104: $i,SV70: $i,SV38: $i] :
( ( ! [SY293: $i] :
~ ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY293 ) ) @ SV104 )
| ( SV70 = SV104 )
| ( contains_slb @ SV38 @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(343,plain,
! [SV38: $i,SV70: $i] :
( ( ~ ! [SY258: $i] :
( ( SV70 != SY258 )
| ! [SY259: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY259 ) ) @ SY258 ) )
| ~ ! [SY260: $i] :
( ~ ( contains_slb @ SV38 @ SY260 )
| ! [SY261: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY261 ) ) @ SY260 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(344,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ! [SY285: $i,SY286: $i] :
( ~ ( less_than @ SY286 @ SY285 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY285 @ SY286 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(345,plain,
! [SV87: $i,SV71: $i,SV39: $i] :
( ( ! [SY287: $i,SY288: $i] :
( ~ ( less_than @ SY288 @ SY287 )
| ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SY287 @ SY288 ) ) @ SV87 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[324]) ).
thf(346,plain,
! [SV1: $i,SV72: $i,SV40: $i] :
( ( ( less_than @ SV40 @ SV72 )
= $false )
| ( ( less_than @ SV1 @ SV40 )
= $false )
| ( ( less_than @ SV1 @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(347,plain,
! [SV75: $i,SV105: $i,SV45: $i,SV9: $i] :
( ( ( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV45 @ SV105 ) ) @ SV75 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV75 ) @ ( pair @ SV45 @ SV105 ) ) )
= $true )
| ( ( SV45 = SV75 )
= $true )
| ( ( contains_slb @ SV9 @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(348,plain,
! [SV77: $i,SV106: $i,SV47: $i,SV11: $i] :
( ( ( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV47 @ SV106 ) ) @ SV77 )
= ( lookup_slb @ SV11 @ SV77 ) )
= $true )
| ( ( SV47 = SV77 )
= $true )
| ( ( contains_slb @ SV11 @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(349,plain,
! [SV80: $i,SV55: $i,SV21: $i,SV99: $i,SV90: $i] :
( ( ( strictly_less_than @ SV90 @ SV99 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV55 @ ( pair @ SV90 @ SV99 ) ) @ SV80 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(350,plain,
! [SV84: $i,SV26: $i,SV93: $i,SV60: $i] :
( ( ( contains_slb @ SV60 @ SV93 )
= $false )
| ( ( ~ ( less_than @ ( lookup_slb @ SV60 @ SV93 ) @ SV93 ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV26 @ SV60 @ SV84 ) @ SV93 )
= ( triple @ ( remove_pqp @ SV26 @ SV93 ) @ ( remove_slb @ SV60 @ SV93 ) @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(351,plain,
! [SV85: $i,SV27: $i,SV94: $i,SV61: $i] :
( ( ( contains_slb @ SV61 @ SV94 )
= $false )
| ( ( ~ ( strictly_less_than @ SV94 @ ( lookup_slb @ SV61 @ SV94 ) ) )
= $true )
| ( ( ( remove_cpq @ ( triple @ SV27 @ SV61 @ SV85 ) @ SV94 )
= ( triple @ ( remove_pqp @ SV27 @ SV94 ) @ ( remove_slb @ SV61 @ SV94 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(352,plain,
! [SV64: $i,SV30: $i] :
( ( ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) )
= $false )
| ( ( SV64 = create_slb )
= $true )
| ( ( contains_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) )
= $false )
| ( ( ! [SY240: $i] :
( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SY240 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(353,plain,
! [SV31: $i,SV65: $i] :
( ( ( less_than @ ( lookup_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) )
= $false )
| ( ( SV65 = create_slb )
= $true )
| ( ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) )
= $false )
| ( ( ! [SY241: $i] :
( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SY241 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SY241 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(354,plain,
! [SV101: $i,SV96: $i] :
( ( ( ~ ( less_than @ SV96 @ SV101 ) )
= $true )
| ( ( less_than @ SV101 @ SV96 )
= $true )
| ( ( strictly_less_than @ SV96 @ SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(355,plain,
! [SV107: $i] :
( ( ! [SY294: $i] :
( ~ ( strictly_less_than @ SV107 @ SY294 )
| ( less_than @ SV107 @ SY294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(356,plain,
! [SV108: $i] :
( ( ! [SY295: $i] :
( ~ ( strictly_less_than @ SV108 @ SY295 )
| ~ ( less_than @ SY295 @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(357,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ~ ! [SY277: $i,SY278: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY277 ) ) @ SV86 @ SY278 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY278 ) )
| ~ ! [SY279: $i,SY280: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY279 ) ) @ SV86 @ SY280 )
| ( SY279 = SY280 )
| ( pair_in_list @ SV36 @ SV86 @ SY280 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(358,plain,
! [SV36: $i,SV86: $i,SV68: $i] :
( ( ~ ! [SY281: $i,SY282: $i] :
( ( SV68 != SV86 )
| ( SY281 != SY282 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY281 ) ) @ SV86 @ SY282 ) )
| ~ ! [SY283: $i,SY284: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY284 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY283 ) ) @ SV86 @ SY284 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(359,plain,
! [SV109: $i,SV102: $i,SV69: $i,SV37: $i] :
( ( ~ ( contains_cpq @ ( triple @ SV37 @ SV69 @ SV102 ) @ SV109 )
| ( contains_slb @ SV69 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(360,plain,
! [SV103: $i,SV37: $i,SV110: $i,SV69: $i] :
( ( ~ ( contains_slb @ SV69 @ SV110 )
| ( contains_cpq @ ( triple @ SV37 @ SV69 @ SV103 ) @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(361,plain,
! [SV104: $i,SV70: $i,SV38: $i] :
( ( ( ! [SY293: $i] :
~ ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY293 ) ) @ SV104 ) )
= $true )
| ( ( ( SV70 = SV104 )
| ( contains_slb @ SV38 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(362,plain,
! [SV38: $i,SV70: $i] :
( ( ~ ! [SY258: $i] :
( ( SV70 != SY258 )
| ! [SY259: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY259 ) ) @ SY258 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[343]) ).
thf(363,plain,
! [SV70: $i,SV38: $i] :
( ( ~ ! [SY260: $i] :
( ~ ( contains_slb @ SV38 @ SY260 )
| ! [SY261: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY261 ) ) @ SY260 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[343]) ).
thf(364,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV111: $i] :
( ( ! [SY296: $i] :
( ~ ( less_than @ SY296 @ SV111 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV111 @ SY296 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(365,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV112: $i] :
( ( ! [SY297: $i] :
( ~ ( less_than @ SY297 @ SV112 )
| ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV112 @ SY297 ) ) @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(366,plain,
! [SV80: $i,SV99: $i,SV90: $i,SV55: $i,SV21: $i] :
( ( ( check_cpq @ ( triple @ SV21 @ ( insert_slb @ SV55 @ ( pair @ SV90 @ SV99 ) ) @ SV80 ) )
= $false )
| ( ( strictly_less_than @ SV90 @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(367,plain,
! [SV84: $i,SV26: $i,SV93: $i,SV60: $i] :
( ( ( less_than @ ( lookup_slb @ SV60 @ SV93 ) @ SV93 )
= $false )
| ( ( contains_slb @ SV60 @ SV93 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV26 @ SV60 @ SV84 ) @ SV93 )
= ( triple @ ( remove_pqp @ SV26 @ SV93 ) @ ( remove_slb @ SV60 @ SV93 ) @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(368,plain,
! [SV85: $i,SV27: $i,SV61: $i,SV94: $i] :
( ( ( strictly_less_than @ SV94 @ ( lookup_slb @ SV61 @ SV94 ) )
= $false )
| ( ( contains_slb @ SV61 @ SV94 )
= $false )
| ( ( ( remove_cpq @ ( triple @ SV27 @ SV61 @ SV85 ) @ SV94 )
= ( triple @ ( remove_pqp @ SV27 @ SV94 ) @ ( remove_slb @ SV61 @ SV94 ) @ bad ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(369,plain,
! [SV113: $i,SV64: $i,SV30: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV30 @ SV64 @ SV113 ) )
= ( triple @ SV30 @ ( update_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) @ bad ) )
= $true )
| ( ( contains_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) )
= $false )
| ( ( SV64 = create_slb )
= $true )
| ( ( strictly_less_than @ ( findmin_pqp_res @ SV30 ) @ ( lookup_slb @ SV64 @ ( findmin_pqp_res @ SV30 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(370,plain,
! [SV114: $i,SV65: $i,SV31: $i] :
( ( ( ( findmin_cpq_eff @ ( triple @ SV31 @ SV65 @ SV114 ) )
= ( triple @ SV31 @ ( update_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ SV114 ) )
= $true )
| ( ( contains_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) )
= $false )
| ( ( SV65 = create_slb )
= $true )
| ( ( less_than @ ( lookup_slb @ SV65 @ ( findmin_pqp_res @ SV31 ) ) @ ( findmin_pqp_res @ SV31 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(371,plain,
! [SV101: $i,SV96: $i] :
( ( ( less_than @ SV96 @ SV101 )
= $false )
| ( ( less_than @ SV101 @ SV96 )
= $true )
| ( ( strictly_less_than @ SV96 @ SV101 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(372,plain,
! [SV115: $i,SV107: $i] :
( ( ~ ( strictly_less_than @ SV107 @ SV115 )
| ( less_than @ SV107 @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(373,plain,
! [SV116: $i,SV108: $i] :
( ( ~ ( strictly_less_than @ SV108 @ SV116 )
| ~ ( less_than @ SV116 @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(374,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ~ ! [SY277: $i,SY278: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY277 ) ) @ SV86 @ SY278 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY278 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[357]) ).
thf(375,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ~ ! [SY279: $i,SY280: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY279 ) ) @ SV86 @ SY280 )
| ( SY279 = SY280 )
| ( pair_in_list @ SV36 @ SV86 @ SY280 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[357]) ).
thf(376,plain,
! [SV36: $i,SV86: $i,SV68: $i] :
( ( ~ ! [SY281: $i,SY282: $i] :
( ( SV68 != SV86 )
| ( SY281 != SY282 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY281 ) ) @ SV86 @ SY282 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(377,plain,
! [SV68: $i,SV86: $i,SV36: $i] :
( ( ~ ! [SY283: $i,SY284: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY284 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY283 ) ) @ SV86 @ SY284 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(378,plain,
! [SV109: $i,SV102: $i,SV69: $i,SV37: $i] :
( ( ( ~ ( contains_cpq @ ( triple @ SV37 @ SV69 @ SV102 ) @ SV109 ) )
= $true )
| ( ( contains_slb @ SV69 @ SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[359]) ).
thf(379,plain,
! [SV103: $i,SV37: $i,SV110: $i,SV69: $i] :
( ( ( ~ ( contains_slb @ SV69 @ SV110 ) )
= $true )
| ( ( contains_cpq @ ( triple @ SV37 @ SV69 @ SV103 ) @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(380,plain,
! [SV104: $i,SV117: $i,SV70: $i,SV38: $i] :
( ( ( ~ ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV117 ) ) @ SV104 ) )
= $true )
| ( ( ( SV70 = SV104 )
| ( contains_slb @ SV38 @ SV104 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(381,plain,
! [SV38: $i,SV70: $i] :
( ( ! [SY258: $i] :
( ( SV70 != SY258 )
| ! [SY259: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY259 ) ) @ SY258 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[362]) ).
thf(382,plain,
! [SV70: $i,SV38: $i] :
( ( ! [SY260: $i] :
( ~ ( contains_slb @ SV38 @ SY260 )
| ! [SY261: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY261 ) ) @ SY260 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[363]) ).
thf(383,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV111: $i,SV118: $i] :
( ( ~ ( less_than @ SV118 @ SV111 )
| ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV111 @ SV118 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(384,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV112: $i,SV119: $i] :
( ( ~ ( less_than @ SV119 @ SV112 )
| ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV112 @ SV119 ) ) @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(385,plain,
! [SV115: $i,SV107: $i] :
( ( ( ~ ( strictly_less_than @ SV107 @ SV115 ) )
= $true )
| ( ( less_than @ SV107 @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(386,plain,
! [SV116: $i,SV108: $i] :
( ( ( ~ ( strictly_less_than @ SV108 @ SV116 ) )
= $true )
| ( ( ~ ( less_than @ SV116 @ SV108 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(387,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ! [SY277: $i,SY278: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY277 ) ) @ SV86 @ SY278 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY278 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[374]) ).
thf(388,plain,
! [SV86: $i,SV68: $i,SV36: $i] :
( ( ! [SY279: $i,SY280: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY279 ) ) @ SV86 @ SY280 )
| ( SY279 = SY280 )
| ( pair_in_list @ SV36 @ SV86 @ SY280 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[375]) ).
thf(389,plain,
! [SV36: $i,SV86: $i,SV68: $i] :
( ( ! [SY281: $i,SY282: $i] :
( ( SV68 != SV86 )
| ( SY281 != SY282 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY281 ) ) @ SV86 @ SY282 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[376]) ).
thf(390,plain,
! [SV68: $i,SV86: $i,SV36: $i] :
( ( ! [SY283: $i,SY284: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY284 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SY283 ) ) @ SV86 @ SY284 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(391,plain,
! [SV109: $i,SV102: $i,SV69: $i,SV37: $i] :
( ( ( contains_cpq @ ( triple @ SV37 @ SV69 @ SV102 ) @ SV109 )
= $false )
| ( ( contains_slb @ SV69 @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(392,plain,
! [SV103: $i,SV37: $i,SV110: $i,SV69: $i] :
( ( ( contains_slb @ SV69 @ SV110 )
= $false )
| ( ( contains_cpq @ ( triple @ SV37 @ SV69 @ SV103 ) @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(393,plain,
! [SV104: $i,SV117: $i,SV70: $i,SV38: $i] :
( ( ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV117 ) ) @ SV104 )
= $false )
| ( ( ( SV70 = SV104 )
| ( contains_slb @ SV38 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(394,plain,
! [SV38: $i,SV120: $i,SV70: $i] :
( ( ( SV70 != SV120 )
| ! [SY298: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY298 ) ) @ SV120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(395,plain,
! [SV70: $i,SV121: $i,SV38: $i] :
( ( ~ ( contains_slb @ SV38 @ SV121 )
| ! [SY299: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY299 ) ) @ SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(396,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV111: $i,SV118: $i] :
( ( ( ~ ( less_than @ SV118 @ SV111 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV111 @ SV118 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(397,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV112: $i,SV119: $i] :
( ( ( ~ ( less_than @ SV119 @ SV112 ) )
= $true )
| ( ( ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV112 @ SV119 ) ) @ SV87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(398,plain,
! [SV115: $i,SV107: $i] :
( ( ( strictly_less_than @ SV107 @ SV115 )
= $false )
| ( ( less_than @ SV107 @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(399,plain,
! [SV116: $i,SV108: $i] :
( ( ( strictly_less_than @ SV108 @ SV116 )
= $false )
| ( ( ~ ( less_than @ SV116 @ SV108 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(400,plain,
! [SV86: $i,SV122: $i,SV68: $i,SV36: $i] :
( ( ! [SY300: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV122 ) ) @ SV86 @ SY300 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SY300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(401,plain,
! [SV86: $i,SV123: $i,SV68: $i,SV36: $i] :
( ( ! [SY301: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV123 ) ) @ SV86 @ SY301 )
| ( SV123 = SY301 )
| ( pair_in_list @ SV36 @ SV86 @ SY301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(402,plain,
! [SV36: $i,SV124: $i,SV86: $i,SV68: $i] :
( ( ! [SY302: $i] :
( ( SV68 != SV86 )
| ( SV124 != SY302 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV124 ) ) @ SV86 @ SY302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(403,plain,
! [SV125: $i,SV68: $i,SV86: $i,SV36: $i] :
( ( ! [SY303: $i] :
( ~ ( pair_in_list @ SV36 @ SV86 @ SY303 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV125 ) ) @ SV86 @ SY303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(404,plain,
! [SV117: $i,SV38: $i,SV104: $i,SV70: $i] :
( ( ( SV70 = SV104 )
= $true )
| ( ( contains_slb @ SV38 @ SV104 )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV117 ) ) @ SV104 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(405,plain,
! [SV38: $i,SV120: $i,SV70: $i] :
( ( ( ( SV70 != SV120 ) )
= $true )
| ( ( ! [SY298: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY298 ) ) @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(406,plain,
! [SV70: $i,SV121: $i,SV38: $i] :
( ( ( ~ ( contains_slb @ SV38 @ SV121 ) )
= $true )
| ( ( ! [SY299: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY299 ) ) @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(407,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV111: $i,SV118: $i] :
( ( ( less_than @ SV118 @ SV111 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV111 @ SV118 ) ) @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(408,plain,
! [SV87: $i,SV71: $i,SV39: $i,SV112: $i,SV119: $i] :
( ( ( less_than @ SV119 @ SV112 )
= $false )
| ( ( ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
| ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV112 @ SV119 ) ) @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(409,plain,
! [SV108: $i,SV116: $i] :
( ( ( less_than @ SV116 @ SV108 )
= $false )
| ( ( strictly_less_than @ SV108 @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(410,plain,
! [SV126: $i,SV86: $i,SV122: $i,SV68: $i,SV36: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV122 ) ) @ SV86 @ SV126 )
| ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(411,plain,
! [SV127: $i,SV86: $i,SV123: $i,SV68: $i,SV36: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV123 ) ) @ SV86 @ SV127 )
| ( SV123 = SV127 )
| ( pair_in_list @ SV36 @ SV86 @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(412,plain,
! [SV36: $i,SV128: $i,SV124: $i,SV86: $i,SV68: $i] :
( ( ( SV68 != SV86 )
| ( SV124 != SV128 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV124 ) ) @ SV86 @ SV128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(413,plain,
! [SV125: $i,SV68: $i,SV129: $i,SV86: $i,SV36: $i] :
( ( ~ ( pair_in_list @ SV36 @ SV86 @ SV129 )
| ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV125 ) ) @ SV86 @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(414,plain,
! [SV38: $i,SV120: $i,SV70: $i] :
( ( ( SV70 = SV120 )
= $false )
| ( ( ! [SY298: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY298 ) ) @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(415,plain,
! [SV70: $i,SV121: $i,SV38: $i] :
( ( ( contains_slb @ SV38 @ SV121 )
= $false )
| ( ( ! [SY299: $i] : ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SY299 ) ) @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(416,plain,
! [SV87: $i,SV118: $i,SV111: $i,SV71: $i,SV39: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV111 @ SV118 ) ) @ SV87 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
= $true )
| ( ( less_than @ SV118 @ SV111 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(417,plain,
! [SV119: $i,SV112: $i,SV87: $i,SV71: $i,SV39: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV112 @ SV119 ) ) @ SV87 ) )
= $true )
| ( ( less_than @ SV119 @ SV112 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(418,plain,
! [SV126: $i,SV86: $i,SV122: $i,SV68: $i,SV36: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV122 ) ) @ SV86 @ SV126 ) )
= $true )
| ( ( ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(419,plain,
! [SV127: $i,SV86: $i,SV123: $i,SV68: $i,SV36: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV123 ) ) @ SV86 @ SV127 ) )
= $true )
| ( ( ( SV123 = SV127 )
| ( pair_in_list @ SV36 @ SV86 @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(420,plain,
! [SV36: $i,SV128: $i,SV124: $i,SV86: $i,SV68: $i] :
( ( ( ( SV68 != SV86 )
| ( SV124 != SV128 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV124 ) ) @ SV86 @ SV128 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(421,plain,
! [SV125: $i,SV68: $i,SV129: $i,SV86: $i,SV36: $i] :
( ( ( ~ ( pair_in_list @ SV36 @ SV86 @ SV129 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV125 ) ) @ SV86 @ SV129 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(422,plain,
! [SV120: $i,SV130: $i,SV70: $i,SV38: $i] :
( ( ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV130 ) ) @ SV120 )
= $true )
| ( ( SV70 = SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(423,plain,
! [SV121: $i,SV131: $i,SV70: $i,SV38: $i] :
( ( ( contains_slb @ ( insert_slb @ SV38 @ ( pair @ SV70 @ SV131 ) ) @ SV121 )
= $true )
| ( ( contains_slb @ SV38 @ SV121 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(424,plain,
! [SV87: $i,SV118: $i,SV111: $i,SV71: $i,SV39: $i] :
( ( ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV111 @ SV118 ) ) @ SV87 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
= $true )
| ( ( less_than @ SV118 @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(425,plain,
! [SV119: $i,SV112: $i,SV87: $i,SV71: $i,SV39: $i] :
( ( ( check_cpq @ ( triple @ SV39 @ SV71 @ SV87 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV39 @ ( insert_slb @ SV71 @ ( pair @ SV112 @ SV119 ) ) @ SV87 ) )
= $true )
| ( ( less_than @ SV119 @ SV112 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(426,plain,
! [SV126: $i,SV86: $i,SV122: $i,SV68: $i,SV36: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV122 ) ) @ SV86 @ SV126 )
= $false )
| ( ( ( SV68 = SV86 )
| ( pair_in_list @ SV36 @ SV86 @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(427,plain,
! [SV127: $i,SV86: $i,SV123: $i,SV68: $i,SV36: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV123 ) ) @ SV86 @ SV127 )
= $false )
| ( ( ( SV123 = SV127 )
| ( pair_in_list @ SV36 @ SV86 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(428,plain,
! [SV36: $i,SV128: $i,SV124: $i,SV86: $i,SV68: $i] :
( ( ( ( SV68 != SV86 ) )
= $true )
| ( ( ( SV124 != SV128 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV124 ) ) @ SV86 @ SV128 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(429,plain,
! [SV125: $i,SV68: $i,SV129: $i,SV86: $i,SV36: $i] :
( ( ( pair_in_list @ SV36 @ SV86 @ SV129 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV125 ) ) @ SV86 @ SV129 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(430,plain,
! [SV122: $i,SV126: $i,SV36: $i,SV86: $i,SV68: $i] :
( ( ( SV68 = SV86 )
= $true )
| ( ( pair_in_list @ SV36 @ SV86 @ SV126 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV122 ) ) @ SV86 @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(431,plain,
! [SV68: $i,SV86: $i,SV36: $i,SV127: $i,SV123: $i] :
( ( ( SV123 = SV127 )
= $true )
| ( ( pair_in_list @ SV36 @ SV86 @ SV127 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV123 ) ) @ SV86 @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(432,plain,
! [SV36: $i,SV128: $i,SV124: $i,SV86: $i,SV68: $i] :
( ( ( SV68 = SV86 )
= $false )
| ( ( ( SV124 != SV128 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV124 ) ) @ SV86 @ SV128 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(433,plain,
! [SV36: $i,SV86: $i,SV68: $i,SV128: $i,SV124: $i] :
( ( ( SV124 = SV128 )
= $false )
| ( ( SV68 = SV86 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV36 @ ( pair @ SV68 @ SV124 ) ) @ SV86 @ SV128 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(434,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[158,433,431,430,429,425,424,423,422,409,404,398,392,391,371,370,369,368,367,366,348,347,346,329,328,311,308,306,305,291,284,283,281,280,257,248,246,245,244,243,234,230,222,210,201,200,199,180,177,169,168,167]) ).
thf(435,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[434]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV397+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 15 18:51:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.39 .
% 0.12/0.39
% 0.12/0.39 No.of.Axioms: 41
% 0.12/0.39
% 0.12/0.39 Length.of.Defs: 0
% 0.12/0.39
% 0.12/0.39 Contains.Choice.Funs: false
% 0.20/0.44 .
% 0.20/0.44 (rf:0,axioms:41,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:43,loop_count:0,foatp_calls:0,translation:fof_full)...............................
% 0.44/0.68
% 0.44/0.68 ********************************
% 0.44/0.68 * All subproblems solved! *
% 0.44/0.68 ********************************
% 0.44/0.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:42,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:434,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.55/0.75
% 0.55/0.75 %**** Beginning of derivation protocol ****
% 0.55/0.75 % SZS output start CNFRefutation
% See solution above
% 0.55/0.75
% 0.55/0.75 %**** End of derivation protocol ****
% 0.55/0.75 %**** no. of clauses in derivation: 435 ****
% 0.55/0.75 %**** clause counter: 434 ****
% 0.55/0.75
% 0.55/0.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:42,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:434,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------