%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV406+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:57:36 AM UTC 2026
% Result : Theorem 5.99s 1.36s
% Output : CNFRefutation 5.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of formulae : 420 ( 245 unt; 0 typ; 0 def)
% Number of atoms : 2571 ( 841 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 6331 ( 989 ~; 817 |; 12 &;4437 @)
% ( 32 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 42 usr; 16 con; 0-3 aty)
% Number of variables : 1554 ( 0 ^;1554 !; 0 ?;1554 :)
% 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_sK10_SX0,type,
sK10_SX0: $i ).
thf(tp_sK11_SY199,type,
sK11_SY199: $i ).
thf(tp_sK12_SY217,type,
sK12_SY217: $i ).
thf(tp_sK13_SY225,type,
sK13_SY225: $i ).
thf(tp_sK14_SX2,type,
sK14_SX2: $i > $i > $i ).
thf(tp_sK15_SY233,type,
sK15_SY233: $i > $i > $i ).
thf(tp_sK1_U,type,
sK1_U: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY104,type,
sK3_SY104: $i ).
thf(tp_sK4_SY127,type,
sK4_SY127: $i ).
thf(tp_sK5_SY139,type,
sK5_SY139: $i ).
thf(tp_sK6_SY145,type,
sK6_SY145: $i ).
thf(tp_sK7_SY147,type,
sK7_SY147: $i ).
thf(tp_sK8_SX2,type,
sK8_SX2: $i > $i > $i ).
thf(tp_sK9_SY149,type,
sK9_SY149: $i > $i > $i ).
thf(tp_strictly_less_than,type,
strictly_less_than: $i > $i > $o ).
thf(tp_succ_cpq,type,
succ_cpq: $i > $i > $o ).
thf(tp_triple,type,
triple: $i > $i > $i > $i ).
thf(tp_update_slb,type,
update_slb: $i > $i > $i ).
thf(16,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( strictly_less_than @ X @ Y )
=> ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
<=> $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
thf(17,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( less_than @ Y @ X )
=> ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
<=> ( check_cpq @ ( triple @ U @ V @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax37) ).
thf(18,axiom,
! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).
thf(24,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( less_than @ W @ X )
=> ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax30) ).
thf(28,axiom,
! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
thf(30,axiom,
! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
thf(31,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
<=> ( ( pair_in_list @ U @ W @ Y )
| ( ( V = W )
& ( X = Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
thf(32,axiom,
! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
thf(33,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
<=> ( ( contains_slb @ U @ W )
| ( V = W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
thf(35,axiom,
! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax19) ).
thf(37,axiom,
! [U: $i] : ( less_than @ bottom @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bottom_smallest) ).
thf(38,axiom,
! [U: $i,V: $i] :
( ( strictly_less_than @ U @ V )
<=> ( ( less_than @ U @ V )
& ~ ( less_than @ V @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).
thf(39,axiom,
! [U: $i] : ( less_than @ U @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(40,axiom,
! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
thf(41,axiom,
! [U: $i,V: $i,W: $i] :
( ( ( less_than @ U @ V )
& ( less_than @ V @ W ) )
=> ( less_than @ U @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(42,conjecture,
! [U: $i] :
( ! [V: $i,W: $i] :
( ( check_cpq @ ( triple @ V @ U @ W ) )
<=> ! [X: $i,Y: $i] :
( ( pair_in_list @ U @ X @ Y )
=> ( less_than @ Y @ X ) ) )
=> ! [Z: $i,X1: $i,X2: $i,X3: $i] :
( ( check_cpq @ ( triple @ Z @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ X1 ) )
<=> ! [X4: $i,X5: $i] :
( ( pair_in_list @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ X4 @ X5 )
=> ( less_than @ X5 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l42_co) ).
thf(43,negated_conjecture,
( ( ! [U: $i] :
( ! [V: $i,W: $i] :
( ( check_cpq @ ( triple @ V @ U @ W ) )
<=> ! [X: $i,Y: $i] :
( ( pair_in_list @ U @ X @ Y )
=> ( less_than @ Y @ X ) ) )
=> ! [Z: $i,X1: $i,X2: $i,X3: $i] :
( ( check_cpq @ ( triple @ Z @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ X1 ) )
<=> ! [X4: $i,X5: $i] :
( ( pair_in_list @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ X4 @ X5 )
=> ( less_than @ X5 @ X4 ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[42]) ).
thf(44,plain,
( ( ! [U: $i] :
( ! [V: $i,W: $i] :
( ( check_cpq @ ( triple @ V @ U @ W ) )
<=> ! [X: $i,Y: $i] :
( ( pair_in_list @ U @ X @ Y )
=> ( less_than @ Y @ X ) ) )
=> ! [Z: $i,X1: $i,X2: $i,X3: $i] :
( ( check_cpq @ ( triple @ Z @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ X1 ) )
<=> ! [X4: $i,X5: $i] :
( ( pair_in_list @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ X4 @ X5 )
=> ( less_than @ X5 @ X4 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[43]) ).
thf(45,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(46,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(47,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(48,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(49,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(50,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(51,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(52,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(53,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(54,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(55,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(56,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(57,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(58,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(59,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(60,plain,
( ( ! [SY56: $i,SY57: $i] :
( ( check_cpq @ ( triple @ SY56 @ sK1_U @ SY57 ) )
<=> ! [SY58: $i,SY59: $i] :
( ( pair_in_list @ sK1_U @ SY58 @ SY59 )
=> ( less_than @ SY59 @ SY58 ) ) )
=> ! [SY60: $i,SY61: $i,SY62: $i,SY63: $i] :
( ( check_cpq @ ( triple @ SY60 @ ( insert_slb @ sK1_U @ ( pair @ SY62 @ SY63 ) ) @ SY61 ) )
<=> ! [SY64: $i,SY65: $i] :
( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY62 @ SY63 ) ) @ SY64 @ SY65 )
=> ( less_than @ SY65 @ SY64 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(61,plain,
( ( ! [SY56: $i,SY57: $i] :
( ( check_cpq @ ( triple @ SY56 @ sK1_U @ SY57 ) )
<=> ! [SY58: $i,SY59: $i] :
( ( pair_in_list @ sK1_U @ SY58 @ SY59 )
=> ( less_than @ SY59 @ SY58 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[60]) ).
thf(62,plain,
( ( ! [SY60: $i,SY61: $i,SY62: $i,SY63: $i] :
( ( check_cpq @ ( triple @ SY60 @ ( insert_slb @ sK1_U @ ( pair @ SY62 @ SY63 ) ) @ SY61 ) )
<=> ! [SY64: $i,SY65: $i] :
( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY62 @ SY63 ) ) @ SY64 @ SY65 )
=> ( less_than @ SY65 @ SY64 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[60]) ).
thf(63,plain,
( ( ! [SY60: $i,SY61: $i,SY62: $i,SY63: $i] :
( ( check_cpq @ ( triple @ SY60 @ ( insert_slb @ sK1_U @ ( pair @ SY62 @ SY63 ) ) @ SY61 ) )
=> ! [SY64: $i,SY65: $i] :
( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY62 @ SY63 ) ) @ SY64 @ SY65 )
=> ( less_than @ SY65 @ SY64 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[62]) ).
thf(64,plain,
( ( ! [SY60: $i,SY61: $i,SY62: $i,SY63: $i] :
( ! [SY64: $i,SY65: $i] :
( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY62 @ SY63 ) ) @ SY64 @ SY65 )
=> ( less_than @ SY65 @ SY64 ) )
=> ( check_cpq @ ( triple @ SY60 @ ( insert_slb @ sK1_U @ ( pair @ SY62 @ SY63 ) ) @ SY61 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[62]) ).
thf(65,plain,
( ( ~ ! [SY60: $i,SY61: $i,SY62: $i,SY63: $i] :
( ( check_cpq @ ( triple @ SY60 @ ( insert_slb @ sK1_U @ ( pair @ SY62 @ SY63 ) ) @ SY61 ) )
=> ! [SY64: $i,SY65: $i] :
( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY62 @ SY63 ) ) @ SY64 @ SY65 )
=> ( less_than @ SY65 @ SY64 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[63]) ).
thf(66,plain,
( ( ~ ! [SY60: $i,SY61: $i,SY62: $i,SY63: $i] :
( ! [SY64: $i,SY65: $i] :
( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY62 @ SY63 ) ) @ SY64 @ SY65 )
=> ( less_than @ SY65 @ SY64 ) )
=> ( check_cpq @ ( triple @ SY60 @ ( insert_slb @ sK1_U @ ( pair @ SY62 @ SY63 ) ) @ SY61 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[64]) ).
thf(67,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( less_than @ U @ V )
& ( less_than @ V @ W ) )
=> ( less_than @ U @ W ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(68,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(69,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(70,plain,
( ( ! [U: $i,V: $i] :
( ( strictly_less_than @ U @ V )
<=> ( ( less_than @ U @ V )
& ~ ( less_than @ V @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(71,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(72,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(73,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
<=> ( ( contains_slb @ U @ W )
| ( V = W ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(74,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
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(copy,[status(thm)],[51]) ).
thf(76,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(77,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(78,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)],[48]) ).
thf(79,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(80,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( less_than @ Y @ X )
=> ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
<=> ( check_cpq @ ( triple @ U @ V @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(81,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( strictly_less_than @ X @ Y )
=> ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
<=> $false ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(82,plain,
( ( ! [SY56: $i,SY57: $i] :
( ( check_cpq @ ( triple @ SY56 @ sK1_U @ SY57 ) )
<=> ! [SY58: $i,SY59: $i] :
( ( pair_in_list @ sK1_U @ SY58 @ SY59 )
=> ( less_than @ SY59 @ SY58 ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(83,plain,
( ( ~ ! [SY60: $i,SY61: $i,SY62: $i,SY63: $i] :
( ( check_cpq @ ( triple @ SY60 @ ( insert_slb @ sK1_U @ ( pair @ SY62 @ SY63 ) ) @ SY61 ) )
=> ! [SY64: $i,SY65: $i] :
( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY62 @ SY63 ) ) @ SY64 @ SY65 )
=> ( less_than @ SY65 @ SY64 ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(84,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ sK1_U @ ( pair @ SX2 @ SX3 ) ) @ SX1 ) )
| ! [SX4: $i,SX5: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SX2 @ SX3 ) ) @ SX4 @ SX5 )
| ( less_than @ SX5 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(85,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 )
| ( contains_slb @ SX0 @ SX2 )
| ( SX1 = SX2 ) )
| ~ ( ~ ( ( contains_slb @ SX0 @ SX2 )
| ( SX1 = SX2 ) )
| ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(86,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 )
| ( pair_in_list @ SX0 @ SX2 @ SX4 )
| ~ ( ( SX1 != SX2 )
| ( SX3 != SX4 ) ) )
| ~ ( ~ ( ( pair_in_list @ SX0 @ SX2 @ SX4 )
| ~ ( ( SX1 != SX2 )
| ( SX3 != SX4 ) ) )
| ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(87,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX2 ) )
| ( less_than @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(88,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( ~ ( less_than @ SX0 @ SX1 )
| ~ ~ ( less_than @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SX0 @ SX1 )
| ~ ~ ( less_than @ SX1 @ SX0 ) )
| ( strictly_less_than @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(89,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( strictly_less_than @ SX3 @ SX4 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ SX1 @ ( pair @ SX3 @ SX4 ) ) @ SX2 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ SX1 @ ( pair @ SX3 @ SX4 ) ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(90,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( less_than @ SX2 @ SX3 )
| ( ( update_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 )
= ( insert_slb @ ( update_slb @ SX0 @ SX2 ) @ ( pair @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(91,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) )
| ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) )
| ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(92,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( less_than @ SX4 @ SX3 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ SX1 @ ( pair @ SX3 @ SX4 ) ) @ SX2 ) )
| ( check_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ SX1 @ ( pair @ SX3 @ SX4 ) ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(93,plain,
! [SV1: $i] :
( ( ! [SY66: $i] :
( ( less_than @ SV1 @ SY66 )
| ( less_than @ SY66 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(94,plain,
! [SV2: $i] :
( ( less_than @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(95,plain,
! [SV3: $i] :
( ( less_than @ bottom @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(96,plain,
! [SV4: $i] :
( ( ! [SY67: $i,SY68: $i] : ( isnonempty_slb @ ( insert_slb @ SV4 @ ( pair @ SY67 @ SY68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(97,plain,
! [SV5: $i] :
( ( ! [SY69: $i] :
~ ( pair_in_list @ create_slb @ SV5 @ SY69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(98,plain,
! [SV6: $i] :
( ( ! [SY70: $i,SY71: $i] :
( ( remove_slb @ ( insert_slb @ SV6 @ ( pair @ SY70 @ SY71 ) ) @ SY70 )
= SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(99,plain,
! [SV7: $i] :
( ( ! [SY72: $i,SY73: $i] :
( ( lookup_slb @ ( insert_slb @ SV7 @ ( pair @ SY72 @ SY73 ) ) @ SY72 )
= SY73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(100,plain,
! [SV8: $i] :
( ( ! [SY74: $i] : ( check_cpq @ ( triple @ SV8 @ create_slb @ SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(101,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ sK1_U @ ( pair @ SX2 @ SX3 ) ) @ SX1 ) )
| ! [SX4: $i,SX5: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SX2 @ SX3 ) ) @ SX4 @ SX5 )
| ( less_than @ SX5 @ SX4 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(102,plain,
! [SV9: $i] :
( ( ! [SY75: $i,SY76: $i,SY77: $i] :
~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SY75 @ SY77 ) ) @ SY76 )
| ( contains_slb @ SV9 @ SY76 )
| ( SY75 = SY76 ) )
| ~ ( ~ ( ( contains_slb @ SV9 @ SY76 )
| ( SY75 = SY76 ) )
| ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SY75 @ SY77 ) ) @ SY76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(103,plain,
! [SV10: $i] :
( ( ! [SY78: $i,SY79: $i,SY80: $i,SY81: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SY78 @ SY80 ) ) @ SY79 @ SY81 )
| ( pair_in_list @ SV10 @ SY79 @ SY81 )
| ~ ( ( SY78 != SY79 )
| ( SY80 != SY81 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV10 @ SY79 @ SY81 )
| ~ ( ( SY78 != SY79 )
| ( SY80 != SY81 ) ) )
| ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SY78 @ SY80 ) ) @ SY79 @ SY81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(104,plain,
! [SV11: $i] :
( ( ! [SY82: $i,SY83: $i] :
( ~ ~ ( ~ ( less_than @ SV11 @ SY82 )
| ~ ( less_than @ SY82 @ SY83 ) )
| ( less_than @ SV11 @ SY83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(105,plain,
! [SV12: $i] :
( ( ! [SY84: $i] :
~ ( ~ ( ~ ( strictly_less_than @ SV12 @ SY84 )
| ~ ( ~ ( less_than @ SV12 @ SY84 )
| ~ ~ ( less_than @ SY84 @ SV12 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV12 @ SY84 )
| ~ ~ ( less_than @ SY84 @ SV12 ) )
| ( strictly_less_than @ SV12 @ SY84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(106,plain,
! [SV13: $i] :
( ( ! [SY85: $i,SY86: $i,SY87: $i,SY88: $i] :
( ~ ( strictly_less_than @ SY87 @ SY88 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SY85 @ ( pair @ SY87 @ SY88 ) ) @ SY86 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SY85 @ ( pair @ SY87 @ SY88 ) ) @ SY86 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(107,plain,
! [SV14: $i] :
( ( ! [SY89: $i,SY90: $i,SY91: $i] :
( ~ ( less_than @ SY90 @ SY91 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SY89 @ SY91 ) ) @ SY90 )
= ( insert_slb @ ( update_slb @ SV14 @ SY90 ) @ ( pair @ SY89 @ SY91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(108,plain,
! [SV15: $i] :
( ( ! [SY92: $i] :
~ ( ~ ( ~ ( check_cpq @ ( triple @ SV15 @ sK1_U @ SY92 ) )
| ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) )
| ( check_cpq @ ( triple @ SV15 @ sK1_U @ SY92 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(109,plain,
! [SV16: $i] :
( ( ! [SY97: $i,SY98: $i,SY99: $i,SY100: $i] :
( ~ ( less_than @ SY100 @ SY99 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SY97 @ ( pair @ SY99 @ SY100 ) ) @ SY98 ) )
| ( check_cpq @ ( triple @ SV16 @ SY97 @ SY98 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV16 @ SY97 @ SY98 ) )
| ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SY97 @ ( pair @ SY99 @ SY100 ) ) @ SY98 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(110,plain,
! [SV17: $i,SV1: $i] :
( ( ( less_than @ SV1 @ SV17 )
| ( less_than @ SV17 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(111,plain,
! [SV18: $i,SV4: $i] :
( ( ! [SY101: $i] : ( isnonempty_slb @ ( insert_slb @ SV4 @ ( pair @ SV18 @ SY101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(112,plain,
! [SV19: $i,SV5: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV5 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(113,plain,
! [SV20: $i,SV6: $i] :
( ( ! [SY102: $i] :
( ( remove_slb @ ( insert_slb @ SV6 @ ( pair @ SV20 @ SY102 ) ) @ SV20 )
= SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(114,plain,
! [SV21: $i,SV7: $i] :
( ( ! [SY103: $i] :
( ( lookup_slb @ ( insert_slb @ SV7 @ ( pair @ SV21 @ SY103 ) ) @ SV21 )
= SY103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(115,plain,
! [SV22: $i,SV8: $i] :
( ( check_cpq @ ( triple @ SV8 @ create_slb @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(116,plain,
( ( ! [SY104: $i,SY105: $i,SY106: $i] :
( ~ ( check_cpq @ ( triple @ sK2_SX0 @ ( insert_slb @ sK1_U @ ( pair @ SY105 @ SY106 ) ) @ SY104 ) )
| ! [SX4: $i,SX5: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY105 @ SY106 ) ) @ SX4 @ SX5 )
| ( less_than @ SX5 @ SX4 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[101]) ).
thf(117,plain,
! [SV23: $i,SV9: $i] :
( ( ! [SY109: $i,SY110: $i] :
~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SY110 ) ) @ SY109 )
| ( contains_slb @ SV9 @ SY109 )
| ( SV23 = SY109 ) )
| ~ ( ~ ( ( contains_slb @ SV9 @ SY109 )
| ( SV23 = SY109 ) )
| ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SY110 ) ) @ SY109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(118,plain,
! [SV24: $i,SV10: $i] :
( ( ! [SY111: $i,SY112: $i,SY113: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SY112 ) ) @ SY111 @ SY113 )
| ( pair_in_list @ SV10 @ SY111 @ SY113 )
| ~ ( ( SV24 != SY111 )
| ( SY112 != SY113 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV10 @ SY111 @ SY113 )
| ~ ( ( SV24 != SY111 )
| ( SY112 != SY113 ) ) )
| ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SY112 ) ) @ SY111 @ SY113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(119,plain,
! [SV25: $i,SV11: $i] :
( ( ! [SY114: $i] :
( ~ ~ ( ~ ( less_than @ SV11 @ SV25 )
| ~ ( less_than @ SV25 @ SY114 ) )
| ( less_than @ SV11 @ SY114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(120,plain,
! [SV26: $i,SV12: $i] :
( ( ~ ( ~ ( ~ ( strictly_less_than @ SV12 @ SV26 )
| ~ ( ~ ( less_than @ SV12 @ SV26 )
| ~ ~ ( less_than @ SV26 @ SV12 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV12 @ SV26 )
| ~ ~ ( less_than @ SV26 @ SV12 ) )
| ( strictly_less_than @ SV12 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(121,plain,
! [SV27: $i,SV13: $i] :
( ( ! [SY115: $i,SY116: $i,SY117: $i] :
( ~ ( strictly_less_than @ SY116 @ SY117 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SV27 @ ( pair @ SY116 @ SY117 ) ) @ SY115 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SV27 @ ( pair @ SY116 @ SY117 ) ) @ SY115 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(122,plain,
! [SV28: $i,SV14: $i] :
( ( ! [SY118: $i,SY119: $i] :
( ~ ( less_than @ SY118 @ SY119 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV28 @ SY119 ) ) @ SY118 )
= ( insert_slb @ ( update_slb @ SV14 @ SY118 ) @ ( pair @ SV28 @ SY119 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(123,plain,
! [SV29: $i,SV15: $i] :
( ( ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV15 @ sK1_U @ SV29 ) )
| ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) )
| ( check_cpq @ ( triple @ SV15 @ sK1_U @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(124,plain,
! [SV30: $i,SV16: $i] :
( ( ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ( less_than @ SY126 @ SY125 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SV30 @ ( pair @ SY125 @ SY126 ) ) @ SY124 ) )
| ( check_cpq @ ( triple @ SV16 @ SV30 @ SY124 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV16 @ SV30 @ SY124 ) )
| ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SV30 @ ( pair @ SY125 @ SY126 ) ) @ SY124 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(125,plain,
! [SV17: $i,SV1: $i] :
( ( ( less_than @ SV1 @ SV17 )
= $true )
| ( ( less_than @ SV17 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(126,plain,
! [SV31: $i,SV18: $i,SV4: $i] :
( ( isnonempty_slb @ ( insert_slb @ SV4 @ ( pair @ SV18 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(127,plain,
! [SV19: $i,SV5: $i] :
( ( pair_in_list @ create_slb @ SV5 @ SV19 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(128,plain,
! [SV32: $i,SV20: $i,SV6: $i] :
( ( ( remove_slb @ ( insert_slb @ SV6 @ ( pair @ SV20 @ SV32 ) ) @ SV20 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(129,plain,
! [SV33: $i,SV21: $i,SV7: $i] :
( ( ( lookup_slb @ ( insert_slb @ SV7 @ ( pair @ SV21 @ SV33 ) ) @ SV21 )
= SV33 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(130,plain,
( ( ! [SY127: $i,SY128: $i] :
( ~ ( check_cpq @ ( triple @ sK2_SX0 @ ( insert_slb @ sK1_U @ ( pair @ SY127 @ SY128 ) ) @ sK3_SY104 ) )
| ! [SX4: $i,SX5: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY127 @ SY128 ) ) @ SX4 @ SX5 )
| ( less_than @ SX5 @ SX4 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[116]) ).
thf(131,plain,
! [SV34: $i,SV23: $i,SV9: $i] :
( ( ! [SY131: $i] :
~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SY131 ) ) @ SV34 )
| ( contains_slb @ SV9 @ SV34 )
| ( SV23 = SV34 ) )
| ~ ( ~ ( ( contains_slb @ SV9 @ SV34 )
| ( SV23 = SV34 ) )
| ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SY131 ) ) @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(132,plain,
! [SV35: $i,SV24: $i,SV10: $i] :
( ( ! [SY132: $i,SY133: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SY132 ) ) @ SV35 @ SY133 )
| ( pair_in_list @ SV10 @ SV35 @ SY133 )
| ~ ( ( SV24 != SV35 )
| ( SY132 != SY133 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV10 @ SV35 @ SY133 )
| ~ ( ( SV24 != SV35 )
| ( SY132 != SY133 ) ) )
| ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SY132 ) ) @ SV35 @ SY133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(133,plain,
! [SV36: $i,SV25: $i,SV11: $i] :
( ( ~ ~ ( ~ ( less_than @ SV11 @ SV25 )
| ~ ( less_than @ SV25 @ SV36 ) )
| ( less_than @ SV11 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(134,plain,
! [SV26: $i,SV12: $i] :
( ( ~ ( ~ ( strictly_less_than @ SV12 @ SV26 )
| ~ ( ~ ( less_than @ SV12 @ SV26 )
| ~ ~ ( less_than @ SV26 @ SV12 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV12 @ SV26 )
| ~ ~ ( less_than @ SV26 @ SV12 ) )
| ( strictly_less_than @ SV12 @ SV26 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(135,plain,
! [SV37: $i,SV27: $i,SV13: $i] :
( ( ! [SY134: $i,SY135: $i] :
( ~ ( strictly_less_than @ SY134 @ SY135 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SV27 @ ( pair @ SY134 @ SY135 ) ) @ SV37 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SV27 @ ( pair @ SY134 @ SY135 ) ) @ SV37 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(136,plain,
! [SV28: $i,SV14: $i,SV38: $i] :
( ( ! [SY136: $i] :
( ~ ( less_than @ SV38 @ SY136 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV28 @ SY136 ) ) @ SV38 )
= ( insert_slb @ ( update_slb @ SV14 @ SV38 ) @ ( pair @ SV28 @ SY136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(137,plain,
! [SV29: $i,SV15: $i] :
( ( ~ ( ~ ( check_cpq @ ( triple @ SV15 @ sK1_U @ SV29 ) )
| ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) )
| ( check_cpq @ ( triple @ SV15 @ sK1_U @ SV29 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(138,plain,
! [SV39: $i,SV30: $i,SV16: $i] :
( ( ! [SY137: $i,SY138: $i] :
( ~ ( less_than @ SY138 @ SY137 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SV30 @ ( pair @ SY137 @ SY138 ) ) @ SV39 ) )
| ( check_cpq @ ( triple @ SV16 @ SV30 @ SV39 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV16 @ SV30 @ SV39 ) )
| ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SV30 @ ( pair @ SY137 @ SY138 ) ) @ SV39 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(139,plain,
( ( ! [SY139: $i] :
( ~ ( check_cpq @ ( triple @ sK2_SX0 @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY127 @ SY139 ) ) @ sK3_SY104 ) )
| ! [SY140: $i,SY141: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY127 @ SY139 ) ) @ SY140 @ SY141 )
| ( less_than @ SY141 @ SY140 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[130]) ).
thf(140,plain,
! [SV34: $i,SV40: $i,SV23: $i,SV9: $i] :
( ( ~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SV40 ) ) @ SV34 )
| ( contains_slb @ SV9 @ SV34 )
| ( SV23 = SV34 ) )
| ~ ( ~ ( ( contains_slb @ SV9 @ SV34 )
| ( SV23 = SV34 ) )
| ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SV40 ) ) @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(141,plain,
! [SV35: $i,SV41: $i,SV24: $i,SV10: $i] :
( ( ! [SY142: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SY142 )
| ( pair_in_list @ SV10 @ SV35 @ SY142 )
| ~ ( ( SV24 != SV35 )
| ( SV41 != SY142 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV10 @ SV35 @ SY142 )
| ~ ( ( SV24 != SV35 )
| ( SV41 != SY142 ) ) )
| ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SY142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(142,plain,
! [SV36: $i,SV25: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( less_than @ SV11 @ SV25 )
| ~ ( less_than @ SV25 @ SV36 ) ) )
= $true )
| ( ( less_than @ SV11 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(143,plain,
! [SV26: $i,SV12: $i] :
( ( ~ ( ~ ( strictly_less_than @ SV12 @ SV26 )
| ~ ( ~ ( less_than @ SV12 @ SV26 )
| ~ ~ ( less_than @ SV26 @ SV12 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(144,plain,
! [SV26: $i,SV12: $i] :
( ( ~ ( ~ ~ ( ~ ( less_than @ SV12 @ SV26 )
| ~ ~ ( less_than @ SV26 @ SV12 ) )
| ( strictly_less_than @ SV12 @ SV26 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[134]) ).
thf(145,plain,
! [SV37: $i,SV27: $i,SV13: $i,SV42: $i] :
( ( ! [SY143: $i] :
( ~ ( strictly_less_than @ SV42 @ SY143 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SV27 @ ( pair @ SV42 @ SY143 ) ) @ SV37 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SV27 @ ( pair @ SV42 @ SY143 ) ) @ SV37 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(146,plain,
! [SV28: $i,SV14: $i,SV43: $i,SV38: $i] :
( ( ~ ( less_than @ SV38 @ SV43 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV28 @ SV43 ) ) @ SV38 )
= ( insert_slb @ ( update_slb @ SV14 @ SV38 ) @ ( pair @ SV28 @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(147,plain,
! [SV29: $i,SV15: $i] :
( ( ~ ( ~ ( check_cpq @ ( triple @ SV15 @ sK1_U @ SV29 ) )
| ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(148,plain,
! [SV29: $i,SV15: $i] :
( ( ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) )
| ( check_cpq @ ( triple @ SV15 @ sK1_U @ SV29 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(149,plain,
! [SV39: $i,SV30: $i,SV16: $i,SV44: $i] :
( ( ! [SY144: $i] :
( ~ ( less_than @ SY144 @ SV44 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SV30 @ ( pair @ SV44 @ SY144 ) ) @ SV39 ) )
| ( check_cpq @ ( triple @ SV16 @ SV30 @ SV39 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV16 @ SV30 @ SV39 ) )
| ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SV30 @ ( pair @ SV44 @ SY144 ) ) @ SV39 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(150,plain,
( ( ~ ( check_cpq @ ( triple @ sK2_SX0 @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY127 @ sK5_SY139 ) ) @ sK3_SY104 ) )
| ! [SY145: $i,SY146: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY127 @ sK5_SY139 ) ) @ SY145 @ SY146 )
| ( less_than @ SY146 @ SY145 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[139]) ).
thf(151,plain,
! [SV34: $i,SV40: $i,SV23: $i,SV9: $i] :
( ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SV40 ) ) @ SV34 )
| ( contains_slb @ SV9 @ SV34 )
| ( SV23 = SV34 ) )
| ~ ( ~ ( ( contains_slb @ SV9 @ SV34 )
| ( SV23 = SV34 ) )
| ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SV40 ) ) @ SV34 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(152,plain,
! [SV45: $i,SV35: $i,SV41: $i,SV24: $i,SV10: $i] :
( ( ~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 )
| ( pair_in_list @ SV10 @ SV35 @ SV45 )
| ~ ( ( SV24 != SV35 )
| ( SV41 != SV45 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV10 @ SV35 @ SV45 )
| ~ ( ( SV24 != SV35 )
| ( SV41 != SV45 ) ) )
| ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(153,plain,
! [SV36: $i,SV25: $i,SV11: $i] :
( ( ( ~ ( ~ ( less_than @ SV11 @ SV25 )
| ~ ( less_than @ SV25 @ SV36 ) ) )
= $false )
| ( ( less_than @ SV11 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(154,plain,
! [SV26: $i,SV12: $i] :
( ( ~ ( strictly_less_than @ SV12 @ SV26 )
| ~ ( ~ ( less_than @ SV12 @ SV26 )
| ~ ~ ( less_than @ SV26 @ SV12 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(155,plain,
! [SV26: $i,SV12: $i] :
( ( ~ ~ ( ~ ( less_than @ SV12 @ SV26 )
| ~ ~ ( less_than @ SV26 @ SV12 ) )
| ( strictly_less_than @ SV12 @ SV26 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(156,plain,
! [SV37: $i,SV27: $i,SV13: $i,SV46: $i,SV42: $i] :
( ( ~ ( strictly_less_than @ SV42 @ SV46 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SV27 @ ( pair @ SV42 @ SV46 ) ) @ SV37 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SV27 @ ( pair @ SV42 @ SV46 ) ) @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(157,plain,
! [SV28: $i,SV14: $i,SV43: $i,SV38: $i] :
( ( ( ~ ( less_than @ SV38 @ SV43 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV28 @ SV43 ) ) @ SV38 )
= ( insert_slb @ ( update_slb @ SV14 @ SV38 ) @ ( pair @ SV28 @ SV43 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(158,plain,
! [SV29: $i,SV15: $i] :
( ( ~ ( check_cpq @ ( triple @ SV15 @ sK1_U @ SV29 ) )
| ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(159,plain,
! [SV29: $i,SV15: $i] :
( ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) )
| ( check_cpq @ ( triple @ SV15 @ sK1_U @ SV29 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(160,plain,
! [SV39: $i,SV30: $i,SV16: $i,SV44: $i,SV47: $i] :
( ( ~ ( less_than @ SV47 @ SV44 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SV30 @ ( pair @ SV44 @ SV47 ) ) @ SV39 ) )
| ( check_cpq @ ( triple @ SV16 @ SV30 @ SV39 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV16 @ SV30 @ SV39 ) )
| ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SV30 @ ( pair @ SV44 @ SV47 ) ) @ SV39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(161,plain,
( ( ~ ( check_cpq @ ( triple @ sK2_SX0 @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY127 @ sK5_SY139 ) ) @ sK3_SY104 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(162,plain,
( ( ! [SY145: $i,SY146: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY127 @ sK5_SY139 ) ) @ SY145 @ SY146 )
| ( less_than @ SY146 @ SY145 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(163,plain,
! [SV34: $i,SV40: $i,SV23: $i,SV9: $i] :
( ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SV40 ) ) @ SV34 )
| ( contains_slb @ SV9 @ SV34 )
| ( SV23 = SV34 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(164,plain,
! [SV40: $i,SV23: $i,SV34: $i,SV9: $i] :
( ( ~ ( ~ ( ( contains_slb @ SV9 @ SV34 )
| ( SV23 = SV34 ) )
| ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SV40 ) ) @ SV34 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(165,plain,
! [SV45: $i,SV35: $i,SV41: $i,SV24: $i,SV10: $i] :
( ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 )
| ( pair_in_list @ SV10 @ SV35 @ SV45 )
| ~ ( ( SV24 != SV35 )
| ( SV41 != SV45 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV10 @ SV35 @ SV45 )
| ~ ( ( SV24 != SV35 )
| ( SV41 != SV45 ) ) )
| ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(166,plain,
! [SV36: $i,SV25: $i,SV11: $i] :
( ( ( ~ ( less_than @ SV11 @ SV25 )
| ~ ( less_than @ SV25 @ SV36 ) )
= $true )
| ( ( less_than @ SV11 @ SV36 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(167,plain,
! [SV26: $i,SV12: $i] :
( ( ( ~ ( strictly_less_than @ SV12 @ SV26 ) )
= $true )
| ( ( ~ ( ~ ( less_than @ SV12 @ SV26 )
| ~ ~ ( less_than @ SV26 @ SV12 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(168,plain,
! [SV26: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( less_than @ SV12 @ SV26 )
| ~ ~ ( less_than @ SV26 @ SV12 ) ) )
= $true )
| ( ( strictly_less_than @ SV12 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(169,plain,
! [SV37: $i,SV27: $i,SV13: $i,SV46: $i,SV42: $i] :
( ( ( ~ ( strictly_less_than @ SV42 @ SV46 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SV27 @ ( pair @ SV42 @ SV46 ) ) @ SV37 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SV27 @ ( pair @ SV42 @ SV46 ) ) @ SV37 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(170,plain,
! [SV28: $i,SV14: $i,SV43: $i,SV38: $i] :
( ( ( less_than @ SV38 @ SV43 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV28 @ SV43 ) ) @ SV38 )
= ( insert_slb @ ( update_slb @ SV14 @ SV38 ) @ ( pair @ SV28 @ SV43 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(171,plain,
! [SV29: $i,SV15: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV15 @ sK1_U @ SV29 ) ) )
= $true )
| ( ( ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(172,plain,
! [SV29: $i,SV15: $i] :
( ( ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV15 @ sK1_U @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(173,plain,
! [SV39: $i,SV30: $i,SV16: $i,SV44: $i,SV47: $i] :
( ( ( ~ ( less_than @ SV47 @ SV44 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SV30 @ ( pair @ SV44 @ SV47 ) ) @ SV39 ) )
| ( check_cpq @ ( triple @ SV16 @ SV30 @ SV39 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV16 @ SV30 @ SV39 ) )
| ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SV30 @ ( pair @ SV44 @ SV47 ) ) @ SV39 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(174,plain,
( ( check_cpq @ ( triple @ sK2_SX0 @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY127 @ sK5_SY139 ) ) @ sK3_SY104 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(175,plain,
( ( ! [SY147: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY127 @ sK5_SY139 ) ) @ sK6_SY145 @ SY147 )
| ( less_than @ SY147 @ sK6_SY145 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[162]) ).
thf(176,plain,
! [SV34: $i,SV40: $i,SV23: $i,SV9: $i] :
( ( ~ ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SV40 ) ) @ SV34 )
| ( contains_slb @ SV9 @ SV34 )
| ( SV23 = SV34 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(177,plain,
! [SV40: $i,SV23: $i,SV34: $i,SV9: $i] :
( ( ~ ( ( contains_slb @ SV9 @ SV34 )
| ( SV23 = SV34 ) )
| ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SV40 ) ) @ SV34 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(178,plain,
! [SV45: $i,SV35: $i,SV41: $i,SV24: $i,SV10: $i] :
( ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 )
| ( pair_in_list @ SV10 @ SV35 @ SV45 )
| ~ ( ( SV24 != SV35 )
| ( SV41 != SV45 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(179,plain,
! [SV41: $i,SV24: $i,SV45: $i,SV35: $i,SV10: $i] :
( ( ~ ( ~ ( ( pair_in_list @ SV10 @ SV35 @ SV45 )
| ~ ( ( SV24 != SV35 )
| ( SV41 != SV45 ) ) )
| ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(180,plain,
! [SV36: $i,SV25: $i,SV11: $i] :
( ( ( ~ ( less_than @ SV11 @ SV25 ) )
= $true )
| ( ( ~ ( less_than @ SV25 @ SV36 ) )
= $true )
| ( ( less_than @ SV11 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(181,plain,
! [SV26: $i,SV12: $i] :
( ( ( strictly_less_than @ SV12 @ SV26 )
= $false )
| ( ( ~ ( ~ ( less_than @ SV12 @ SV26 )
| ~ ~ ( less_than @ SV26 @ SV12 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(182,plain,
! [SV26: $i,SV12: $i] :
( ( ( ~ ( ~ ( less_than @ SV12 @ SV26 )
| ~ ~ ( less_than @ SV26 @ SV12 ) ) )
= $false )
| ( ( strictly_less_than @ SV12 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(183,plain,
! [SV37: $i,SV27: $i,SV13: $i,SV46: $i,SV42: $i] :
( ( ( strictly_less_than @ SV42 @ SV46 )
= $false )
| ( ( ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SV27 @ ( pair @ SV42 @ SV46 ) ) @ SV37 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SV27 @ ( pair @ SV42 @ SV46 ) ) @ SV37 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(184,plain,
! [SV29: $i,SV15: $i] :
( ( ( check_cpq @ ( triple @ SV15 @ sK1_U @ SV29 ) )
= $false )
| ( ( ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(185,plain,
! [SV29: $i,SV15: $i] :
( ( ( ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) )
= $false )
| ( ( check_cpq @ ( triple @ SV15 @ sK1_U @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(186,plain,
! [SV39: $i,SV30: $i,SV16: $i,SV44: $i,SV47: $i] :
( ( ( less_than @ SV47 @ SV44 )
= $false )
| ( ( ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SV30 @ ( pair @ SV44 @ SV47 ) ) @ SV39 ) )
| ( check_cpq @ ( triple @ SV16 @ SV30 @ SV39 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV16 @ SV30 @ SV39 ) )
| ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SV30 @ ( pair @ SV44 @ SV47 ) ) @ SV39 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(187,plain,
( ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY127 @ sK5_SY139 ) ) @ sK6_SY145 @ sK7_SY147 )
| ( less_than @ sK7_SY147 @ sK6_SY145 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[175]) ).
thf(188,plain,
! [SV34: $i,SV40: $i,SV23: $i,SV9: $i] :
( ( ( ~ ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SV40 ) ) @ SV34 ) )
= $true )
| ( ( ( contains_slb @ SV9 @ SV34 )
| ( SV23 = SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(189,plain,
! [SV40: $i,SV23: $i,SV34: $i,SV9: $i] :
( ( ( ~ ( ( contains_slb @ SV9 @ SV34 )
| ( SV23 = SV34 ) ) )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SV40 ) ) @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(190,plain,
! [SV45: $i,SV35: $i,SV41: $i,SV24: $i,SV10: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 )
| ( pair_in_list @ SV10 @ SV35 @ SV45 )
| ~ ( ( SV24 != SV35 )
| ( SV41 != SV45 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(191,plain,
! [SV41: $i,SV24: $i,SV45: $i,SV35: $i,SV10: $i] :
( ( ~ ( ( pair_in_list @ SV10 @ SV35 @ SV45 )
| ~ ( ( SV24 != SV35 )
| ( SV41 != SV45 ) ) )
| ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(192,plain,
! [SV36: $i,SV25: $i,SV11: $i] :
( ( ( less_than @ SV11 @ SV25 )
= $false )
| ( ( ~ ( less_than @ SV25 @ SV36 ) )
= $true )
| ( ( less_than @ SV11 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(193,plain,
! [SV26: $i,SV12: $i] :
( ( ( ~ ( less_than @ SV12 @ SV26 )
| ~ ~ ( less_than @ SV26 @ SV12 ) )
= $false )
| ( ( strictly_less_than @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(194,plain,
! [SV26: $i,SV12: $i] :
( ( ( ~ ( less_than @ SV12 @ SV26 )
| ~ ~ ( less_than @ SV26 @ SV12 ) )
= $true )
| ( ( strictly_less_than @ SV12 @ SV26 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(195,plain,
! [SV37: $i,SV46: $i,SV42: $i,SV27: $i,SV13: $i] :
( ( ( ~ ( ~ ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SV27 @ ( pair @ SV42 @ SV46 ) ) @ SV37 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SV27 @ ( pair @ SV42 @ SV46 ) ) @ SV37 ) ) ) )
= $false )
| ( ( strictly_less_than @ SV42 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(196,plain,
! [SV29: $i,SV15: $i,SV48: $i] :
( ( ( ! [SY148: $i] :
( ~ ( pair_in_list @ sK1_U @ SV48 @ SY148 )
| ( less_than @ SY148 @ SV48 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV15 @ sK1_U @ SV29 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(197,plain,
! [SV15: $i,SV29: $i] :
( ( ( ! [SY149: $i] :
( ~ ( pair_in_list @ sK1_U @ ( sK8_SX2 @ SV29 @ SV15 ) @ SY149 )
| ( less_than @ SY149 @ ( sK8_SX2 @ SV29 @ SV15 ) ) ) )
= $false )
| ( ( check_cpq @ ( triple @ SV15 @ sK1_U @ SV29 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[185]) ).
thf(198,plain,
! [SV39: $i,SV47: $i,SV44: $i,SV30: $i,SV16: $i] :
( ( ( ~ ( ~ ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SV30 @ ( pair @ SV44 @ SV47 ) ) @ SV39 ) )
| ( check_cpq @ ( triple @ SV16 @ SV30 @ SV39 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV16 @ SV30 @ SV39 ) )
| ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SV30 @ ( pair @ SV44 @ SV47 ) ) @ SV39 ) ) ) )
= $false )
| ( ( less_than @ SV47 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(199,plain,
( ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY127 @ sK5_SY139 ) ) @ sK6_SY145 @ sK7_SY147 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(200,plain,
( ( less_than @ sK7_SY147 @ sK6_SY145 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[187]) ).
thf(201,plain,
! [SV34: $i,SV40: $i,SV23: $i,SV9: $i] :
( ( ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SV40 ) ) @ SV34 )
= $false )
| ( ( ( contains_slb @ SV9 @ SV34 )
| ( SV23 = SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(202,plain,
! [SV40: $i,SV23: $i,SV34: $i,SV9: $i] :
( ( ( ( contains_slb @ SV9 @ SV34 )
| ( SV23 = SV34 ) )
= $false )
| ( ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SV40 ) ) @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(203,plain,
! [SV45: $i,SV35: $i,SV41: $i,SV24: $i,SV10: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 ) )
= $true )
| ( ( ( pair_in_list @ SV10 @ SV35 @ SV45 )
| ~ ( ( SV24 != SV35 )
| ( SV41 != SV45 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(204,plain,
! [SV41: $i,SV24: $i,SV45: $i,SV35: $i,SV10: $i] :
( ( ( ~ ( ( pair_in_list @ SV10 @ SV35 @ SV45 )
| ~ ( ( SV24 != SV35 )
| ( SV41 != SV45 ) ) ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(205,plain,
! [SV11: $i,SV36: $i,SV25: $i] :
( ( ( less_than @ SV25 @ SV36 )
= $false )
| ( ( less_than @ SV11 @ SV25 )
= $false )
| ( ( less_than @ SV11 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(206,plain,
! [SV26: $i,SV12: $i] :
( ( ( ~ ( less_than @ SV12 @ SV26 ) )
= $false )
| ( ( strictly_less_than @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(207,plain,
! [SV12: $i,SV26: $i] :
( ( ( ~ ~ ( less_than @ SV26 @ SV12 ) )
= $false )
| ( ( strictly_less_than @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(208,plain,
! [SV26: $i,SV12: $i] :
( ( ( ~ ( less_than @ SV12 @ SV26 ) )
= $true )
| ( ( ~ ~ ( less_than @ SV26 @ SV12 ) )
= $true )
| ( ( strictly_less_than @ SV12 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(209,plain,
! [SV37: $i,SV46: $i,SV42: $i,SV27: $i,SV13: $i] :
( ( ( ~ ( ~ ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SV27 @ ( pair @ SV42 @ SV46 ) ) @ SV37 ) )
| $false ) )
= $false )
| ( ( strictly_less_than @ SV42 @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[195]) ).
thf(210,plain,
! [SV37: $i,SV46: $i,SV42: $i,SV27: $i,SV13: $i] :
( ( ( ~ ( ~ $false
| ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SV27 @ ( pair @ SV42 @ SV46 ) ) @ SV37 ) ) ) )
= $false )
| ( ( strictly_less_than @ SV42 @ SV46 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[195]) ).
thf(211,plain,
! [SV29: $i,SV15: $i,SV49: $i,SV48: $i] :
( ( ( ~ ( pair_in_list @ sK1_U @ SV48 @ SV49 )
| ( less_than @ SV49 @ SV48 ) )
= $true )
| ( ( check_cpq @ ( triple @ SV15 @ sK1_U @ SV29 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(212,plain,
! [SV15: $i,SV29: $i] :
( ( ( ~ ( pair_in_list @ sK1_U @ ( sK8_SX2 @ SV29 @ SV15 ) @ ( sK9_SY149 @ SV15 @ SV29 ) )
| ( less_than @ ( sK9_SY149 @ SV15 @ SV29 ) @ ( sK8_SX2 @ SV29 @ SV15 ) ) )
= $false )
| ( ( check_cpq @ ( triple @ SV15 @ sK1_U @ SV29 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[197]) ).
thf(213,plain,
! [SV39: $i,SV47: $i,SV44: $i,SV30: $i,SV16: $i] :
( ( ( ~ ( ~ ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SV30 @ ( pair @ SV44 @ SV47 ) ) @ SV39 ) )
| ( check_cpq @ ( triple @ SV16 @ SV30 @ SV39 ) ) ) )
= $false )
| ( ( less_than @ SV47 @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(214,plain,
! [SV47: $i,SV44: $i,SV39: $i,SV30: $i,SV16: $i] :
( ( ( ~ ( ~ ( check_cpq @ ( triple @ SV16 @ SV30 @ SV39 ) )
| ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SV30 @ ( pair @ SV44 @ SV47 ) ) @ SV39 ) ) ) )
= $false )
| ( ( less_than @ SV47 @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[198]) ).
thf(215,plain,
( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK4_SY127 @ sK5_SY139 ) ) @ sK6_SY145 @ sK7_SY147 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(216,plain,
! [SV40: $i,SV23: $i,SV34: $i,SV9: $i] :
( ( ( contains_slb @ SV9 @ SV34 )
= $true )
| ( ( SV23 = SV34 )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SV40 ) ) @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(217,plain,
! [SV40: $i,SV23: $i,SV34: $i,SV9: $i] :
( ( ( contains_slb @ SV9 @ SV34 )
= $false )
| ( ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SV40 ) ) @ SV34 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(218,plain,
! [SV40: $i,SV9: $i,SV34: $i,SV23: $i] :
( ( ( SV23 = SV34 )
= $false )
| ( ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SV40 ) ) @ SV34 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(219,plain,
! [SV45: $i,SV35: $i,SV41: $i,SV24: $i,SV10: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 )
= $false )
| ( ( ( pair_in_list @ SV10 @ SV35 @ SV45 )
| ~ ( ( SV24 != SV35 )
| ( SV41 != SV45 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(220,plain,
! [SV41: $i,SV24: $i,SV45: $i,SV35: $i,SV10: $i] :
( ( ( ( pair_in_list @ SV10 @ SV35 @ SV45 )
| ~ ( ( SV24 != SV35 )
| ( SV41 != SV45 ) ) )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(221,plain,
! [SV26: $i,SV12: $i] :
( ( ( less_than @ SV12 @ SV26 )
= $true )
| ( ( strictly_less_than @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(222,plain,
! [SV12: $i,SV26: $i] :
( ( ( ~ ( less_than @ SV26 @ SV12 ) )
= $true )
| ( ( strictly_less_than @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(223,plain,
! [SV26: $i,SV12: $i] :
( ( ( less_than @ SV12 @ SV26 )
= $false )
| ( ( ~ ~ ( less_than @ SV26 @ SV12 ) )
= $true )
| ( ( strictly_less_than @ SV12 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(224,plain,
! [SV37: $i,SV46: $i,SV42: $i,SV27: $i,SV13: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SV27 @ ( pair @ SV42 @ SV46 ) ) @ SV37 ) )
| $false )
= $true )
| ( ( strictly_less_than @ SV42 @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(225,plain,
! [SV37: $i,SV46: $i,SV42: $i,SV27: $i,SV13: $i] :
( ( ( ~ $false
| ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SV27 @ ( pair @ SV42 @ SV46 ) ) @ SV37 ) ) )
= $true )
| ( ( strictly_less_than @ SV42 @ SV46 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(226,plain,
! [SV29: $i,SV15: $i,SV49: $i,SV48: $i] :
( ( ( ~ ( pair_in_list @ sK1_U @ SV48 @ SV49 ) )
= $true )
| ( ( less_than @ SV49 @ SV48 )
= $true )
| ( ( check_cpq @ ( triple @ SV15 @ sK1_U @ SV29 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(227,plain,
! [SV15: $i,SV29: $i] :
( ( ( ~ ( pair_in_list @ sK1_U @ ( sK8_SX2 @ SV29 @ SV15 ) @ ( sK9_SY149 @ SV15 @ SV29 ) ) )
= $false )
| ( ( check_cpq @ ( triple @ SV15 @ sK1_U @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(228,plain,
! [SV29: $i,SV15: $i] :
( ( ( less_than @ ( sK9_SY149 @ SV15 @ SV29 ) @ ( sK8_SX2 @ SV29 @ SV15 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV15 @ sK1_U @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(229,plain,
! [SV39: $i,SV47: $i,SV44: $i,SV30: $i,SV16: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SV30 @ ( pair @ SV44 @ SV47 ) ) @ SV39 ) )
| ( check_cpq @ ( triple @ SV16 @ SV30 @ SV39 ) ) )
= $true )
| ( ( less_than @ SV47 @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(230,plain,
! [SV47: $i,SV44: $i,SV39: $i,SV30: $i,SV16: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV16 @ SV30 @ SV39 ) )
| ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SV30 @ ( pair @ SV44 @ SV47 ) ) @ SV39 ) ) )
= $true )
| ( ( less_than @ SV47 @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(231,plain,
! [SV41: $i,SV24: $i,SV45: $i,SV35: $i,SV10: $i] :
( ( ( pair_in_list @ SV10 @ SV35 @ SV45 )
= $true )
| ( ( ~ ( ( SV24 != SV35 )
| ( SV41 != SV45 ) ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(232,plain,
! [SV41: $i,SV24: $i,SV45: $i,SV35: $i,SV10: $i] :
( ( ( pair_in_list @ SV10 @ SV35 @ SV45 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(233,plain,
! [SV10: $i,SV45: $i,SV41: $i,SV35: $i,SV24: $i] :
( ( ( ~ ( ( SV24 != SV35 )
| ( SV41 != SV45 ) ) )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[220]) ).
thf(234,plain,
! [SV12: $i,SV26: $i] :
( ( ( less_than @ SV26 @ SV12 )
= $false )
| ( ( strictly_less_than @ SV12 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(235,plain,
! [SV12: $i,SV26: $i] :
( ( ( ~ ( less_than @ SV26 @ SV12 ) )
= $false )
| ( ( less_than @ SV12 @ SV26 )
= $false )
| ( ( strictly_less_than @ SV12 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(236,plain,
! [SV37: $i,SV46: $i,SV42: $i,SV27: $i,SV13: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SV27 @ ( pair @ SV42 @ SV46 ) ) @ SV37 ) ) )
= $true )
| ( $false = $true )
| ( ( strictly_less_than @ SV42 @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(237,plain,
! [SV37: $i,SV46: $i,SV42: $i,SV27: $i,SV13: $i] :
( ( ( ~ $false ) = $true )
| ( ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SV27 @ ( pair @ SV42 @ SV46 ) ) @ SV37 ) )
= $true )
| ( ( strictly_less_than @ SV42 @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(238,plain,
! [SV29: $i,SV15: $i,SV49: $i,SV48: $i] :
( ( ( pair_in_list @ sK1_U @ SV48 @ SV49 )
= $false )
| ( ( less_than @ SV49 @ SV48 )
= $true )
| ( ( check_cpq @ ( triple @ SV15 @ sK1_U @ SV29 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(239,plain,
! [SV15: $i,SV29: $i] :
( ( ( pair_in_list @ sK1_U @ ( sK8_SX2 @ SV29 @ SV15 ) @ ( sK9_SY149 @ SV15 @ SV29 ) )
= $true )
| ( ( check_cpq @ ( triple @ SV15 @ sK1_U @ SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(240,plain,
! [SV39: $i,SV47: $i,SV44: $i,SV30: $i,SV16: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SV30 @ ( pair @ SV44 @ SV47 ) ) @ SV39 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV16 @ SV30 @ SV39 ) )
= $true )
| ( ( less_than @ SV47 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(241,plain,
! [SV47: $i,SV44: $i,SV39: $i,SV30: $i,SV16: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV16 @ SV30 @ SV39 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SV30 @ ( pair @ SV44 @ SV47 ) ) @ SV39 ) )
= $true )
| ( ( less_than @ SV47 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(242,plain,
! [SV10: $i,SV45: $i,SV41: $i,SV35: $i,SV24: $i] :
( ( ( ( SV24 != SV35 )
| ( SV41 != SV45 ) )
= $false )
| ( ( pair_in_list @ SV10 @ SV35 @ SV45 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(243,plain,
! [SV10: $i,SV45: $i,SV41: $i,SV35: $i,SV24: $i] :
( ( ( ( SV24 != SV35 )
| ( SV41 != SV45 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(244,plain,
! [SV12: $i,SV26: $i] :
( ( ( less_than @ SV26 @ SV12 )
= $true )
| ( ( less_than @ SV12 @ SV26 )
= $false )
| ( ( strictly_less_than @ SV12 @ SV26 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(245,plain,
! [SV37: $i,SV46: $i,SV42: $i,SV27: $i,SV13: $i] :
( ( ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SV27 @ ( pair @ SV42 @ SV46 ) ) @ SV37 ) )
= $false )
| ( $false = $true )
| ( ( strictly_less_than @ SV42 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(246,plain,
! [SV37: $i,SV46: $i,SV42: $i,SV27: $i,SV13: $i] :
( ( $false = $false )
| ( ( check_cpq @ ( triple @ SV13 @ ( insert_slb @ SV27 @ ( pair @ SV42 @ SV46 ) ) @ SV37 ) )
= $true )
| ( ( strictly_less_than @ SV42 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(247,plain,
! [SV39: $i,SV47: $i,SV44: $i,SV30: $i,SV16: $i] :
( ( ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SV30 @ ( pair @ SV44 @ SV47 ) ) @ SV39 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV16 @ SV30 @ SV39 ) )
= $true )
| ( ( less_than @ SV47 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(248,plain,
! [SV47: $i,SV44: $i,SV39: $i,SV30: $i,SV16: $i] :
( ( ( check_cpq @ ( triple @ SV16 @ SV30 @ SV39 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV16 @ ( insert_slb @ SV30 @ ( pair @ SV44 @ SV47 ) ) @ SV39 ) )
= $true )
| ( ( less_than @ SV47 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(249,plain,
! [SV41: $i,SV45: $i,SV10: $i,SV35: $i,SV24: $i] :
( ( ( SV24 != SV35 )
= $false )
| ( ( pair_in_list @ SV10 @ SV35 @ SV45 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(250,plain,
! [SV24: $i,SV35: $i,SV10: $i,SV45: $i,SV41: $i] :
( ( ( SV41 != SV45 )
= $false )
| ( ( pair_in_list @ SV10 @ SV35 @ SV45 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(251,plain,
! [SV10: $i,SV45: $i,SV41: $i,SV35: $i,SV24: $i] :
( ( ( SV24 != SV35 )
= $true )
| ( ( SV41 != SV45 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(252,plain,
! [SV41: $i,SV45: $i,SV10: $i,SV35: $i,SV24: $i] :
( ( ( SV24 = SV35 )
= $true )
| ( ( pair_in_list @ SV10 @ SV35 @ SV45 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(253,plain,
! [SV24: $i,SV35: $i,SV10: $i,SV45: $i,SV41: $i] :
( ( ( SV41 = SV45 )
= $true )
| ( ( pair_in_list @ SV10 @ SV35 @ SV45 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(254,plain,
! [SV10: $i,SV45: $i,SV41: $i,SV35: $i,SV24: $i] :
( ( ( SV24 = SV35 )
= $false )
| ( ( SV41 != SV45 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(255,plain,
! [SV10: $i,SV35: $i,SV24: $i,SV45: $i,SV41: $i] :
( ( ( SV41 = SV45 )
= $false )
| ( ( SV24 = SV35 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV41 ) ) @ SV35 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(256,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[94,255,253,252,248,247,246,245,244,239,238,234,232,228,221,218,217,216,215,205,200,174,170,129,128,127,126,125,115,95]) ).
thf(257,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( less_than @ U @ V )
& ( less_than @ V @ W ) )
=> ( less_than @ U @ W ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(258,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(259,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(260,plain,
( ( ! [U: $i,V: $i] :
( ( strictly_less_than @ U @ V )
<=> ( ( less_than @ U @ V )
& ~ ( less_than @ V @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(261,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(262,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(263,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
<=> ( ( contains_slb @ U @ W )
| ( V = W ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(264,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(265,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
<=> ( ( pair_in_list @ U @ W @ Y )
| ( ( V = W )
& ( X = Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(266,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(267,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(268,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)],[48]) ).
thf(269,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(270,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( less_than @ Y @ X )
=> ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
<=> ( check_cpq @ ( triple @ U @ V @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(271,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( strictly_less_than @ X @ Y )
=> ( ( check_cpq @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
<=> $false ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(272,plain,
( ( ! [SY56: $i,SY57: $i] :
( ( check_cpq @ ( triple @ SY56 @ sK1_U @ SY57 ) )
<=> ! [SY58: $i,SY59: $i] :
( ( pair_in_list @ sK1_U @ SY58 @ SY59 )
=> ( less_than @ SY59 @ SY58 ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(273,plain,
( ( ~ ! [SY60: $i,SY61: $i,SY62: $i,SY63: $i] :
( ! [SY64: $i,SY65: $i] :
( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY62 @ SY63 ) ) @ SY64 @ SY65 )
=> ( less_than @ SY65 @ SY64 ) )
=> ( check_cpq @ ( triple @ SY60 @ ( insert_slb @ sK1_U @ ( pair @ SY62 @ SY63 ) ) @ SY61 ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(274,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 )
| ( contains_slb @ SX0 @ SX2 )
| ( SX1 = SX2 ) )
| ~ ( ~ ( ( contains_slb @ SX0 @ SX2 )
| ( SX1 = SX2 ) )
| ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(275,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 )
| ( pair_in_list @ SX0 @ SX2 @ SX4 )
| ~ ( ( SX1 != SX2 )
| ( SX3 != SX4 ) ) )
| ~ ( ~ ( ( pair_in_list @ SX0 @ SX2 @ SX4 )
| ~ ( ( SX1 != SX2 )
| ( SX3 != SX4 ) ) )
| ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(276,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( ~ ( less_than @ SX0 @ SX1 )
| ~ ~ ( less_than @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SX0 @ SX1 )
| ~ ~ ( less_than @ SX1 @ SX0 ) )
| ( strictly_less_than @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(277,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( less_than @ SX2 @ SX3 )
| ( ( update_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 )
= ( insert_slb @ ( update_slb @ SX0 @ SX2 ) @ ( pair @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(278,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( strictly_less_than @ SX3 @ SX4 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ SX1 @ ( pair @ SX3 @ SX4 ) ) @ SX2 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ SX1 @ ( pair @ SX3 @ SX4 ) ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(279,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX2 ) )
| ( less_than @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(280,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ! [SX4: $i,SX5: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SX2 @ SX3 ) ) @ SX4 @ SX5 )
| ( less_than @ SX5 @ SX4 ) )
| ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ sK1_U @ ( pair @ SX2 @ SX3 ) ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(281,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( less_than @ SX4 @ SX3 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ SX1 @ ( pair @ SX3 @ SX4 ) ) @ SX2 ) )
| ( check_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) )
| ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ SX1 @ ( pair @ SX3 @ SX4 ) ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(282,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) )
| ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) )
| ( check_cpq @ ( triple @ SX0 @ sK1_U @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(283,plain,
! [SV50: $i] :
( ( ! [SY150: $i] :
( ( less_than @ SV50 @ SY150 )
| ( less_than @ SY150 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(284,plain,
! [SV51: $i] :
( ( less_than @ SV51 @ SV51 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(285,plain,
! [SV52: $i] :
( ( less_than @ bottom @ SV52 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(286,plain,
! [SV53: $i] :
( ( ! [SY151: $i,SY152: $i] : ( isnonempty_slb @ ( insert_slb @ SV53 @ ( pair @ SY151 @ SY152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(287,plain,
! [SV54: $i] :
( ( ! [SY153: $i] :
~ ( pair_in_list @ create_slb @ SV54 @ SY153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(288,plain,
! [SV55: $i] :
( ( ! [SY154: $i,SY155: $i] :
( ( remove_slb @ ( insert_slb @ SV55 @ ( pair @ SY154 @ SY155 ) ) @ SY154 )
= SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(289,plain,
! [SV56: $i] :
( ( ! [SY156: $i,SY157: $i] :
( ( lookup_slb @ ( insert_slb @ SV56 @ ( pair @ SY156 @ SY157 ) ) @ SY156 )
= SY157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(290,plain,
! [SV57: $i] :
( ( ! [SY158: $i] : ( check_cpq @ ( triple @ SV57 @ create_slb @ SY158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(291,plain,
! [SV58: $i] :
( ( ! [SY159: $i,SY160: $i,SY161: $i] :
~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV58 @ ( pair @ SY159 @ SY161 ) ) @ SY160 )
| ( contains_slb @ SV58 @ SY160 )
| ( SY159 = SY160 ) )
| ~ ( ~ ( ( contains_slb @ SV58 @ SY160 )
| ( SY159 = SY160 ) )
| ( contains_slb @ ( insert_slb @ SV58 @ ( pair @ SY159 @ SY161 ) ) @ SY160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(292,plain,
! [SV59: $i] :
( ( ! [SY162: $i,SY163: $i,SY164: $i,SY165: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SY162 @ SY164 ) ) @ SY163 @ SY165 )
| ( pair_in_list @ SV59 @ SY163 @ SY165 )
| ~ ( ( SY162 != SY163 )
| ( SY164 != SY165 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV59 @ SY163 @ SY165 )
| ~ ( ( SY162 != SY163 )
| ( SY164 != SY165 ) ) )
| ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SY162 @ SY164 ) ) @ SY163 @ SY165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(293,plain,
! [SV60: $i] :
( ( ! [SY166: $i] :
~ ( ~ ( ~ ( strictly_less_than @ SV60 @ SY166 )
| ~ ( ~ ( less_than @ SV60 @ SY166 )
| ~ ~ ( less_than @ SY166 @ SV60 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV60 @ SY166 )
| ~ ~ ( less_than @ SY166 @ SV60 ) )
| ( strictly_less_than @ SV60 @ SY166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(294,plain,
! [SV61: $i] :
( ( ! [SY167: $i,SY168: $i,SY169: $i] :
( ~ ( less_than @ SY168 @ SY169 )
| ( ( update_slb @ ( insert_slb @ SV61 @ ( pair @ SY167 @ SY169 ) ) @ SY168 )
= ( insert_slb @ ( update_slb @ SV61 @ SY168 ) @ ( pair @ SY167 @ SY169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(295,plain,
! [SV62: $i] :
( ( ! [SY170: $i,SY171: $i,SY172: $i,SY173: $i] :
( ~ ( strictly_less_than @ SY172 @ SY173 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SY170 @ ( pair @ SY172 @ SY173 ) ) @ SY171 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SY170 @ ( pair @ SY172 @ SY173 ) ) @ SY171 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(296,plain,
! [SV63: $i] :
( ( ! [SY174: $i,SY175: $i] :
( ~ ~ ( ~ ( less_than @ SV63 @ SY174 )
| ~ ( less_than @ SY174 @ SY175 ) )
| ( less_than @ SV63 @ SY175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(297,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ! [SX4: $i,SX5: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SX2 @ SX3 ) ) @ SX4 @ SX5 )
| ( less_than @ SX5 @ SX4 ) )
| ( check_cpq @ ( triple @ SX0 @ ( insert_slb @ sK1_U @ ( pair @ SX2 @ SX3 ) ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(298,plain,
! [SV64: $i] :
( ( ! [SY176: $i,SY177: $i,SY178: $i,SY179: $i] :
( ~ ( less_than @ SY179 @ SY178 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SY176 @ ( pair @ SY178 @ SY179 ) ) @ SY177 ) )
| ( check_cpq @ ( triple @ SV64 @ SY176 @ SY177 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV64 @ SY176 @ SY177 ) )
| ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SY176 @ ( pair @ SY178 @ SY179 ) ) @ SY177 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(299,plain,
! [SV65: $i] :
( ( ! [SY180: $i] :
~ ( ~ ( ~ ( check_cpq @ ( triple @ SV65 @ sK1_U @ SY180 ) )
| ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) )
| ( check_cpq @ ( triple @ SV65 @ sK1_U @ SY180 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(300,plain,
! [SV66: $i,SV50: $i] :
( ( ( less_than @ SV50 @ SV66 )
| ( less_than @ SV66 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(301,plain,
! [SV67: $i,SV53: $i] :
( ( ! [SY185: $i] : ( isnonempty_slb @ ( insert_slb @ SV53 @ ( pair @ SV67 @ SY185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(302,plain,
! [SV68: $i,SV54: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV54 @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(303,plain,
! [SV69: $i,SV55: $i] :
( ( ! [SY186: $i] :
( ( remove_slb @ ( insert_slb @ SV55 @ ( pair @ SV69 @ SY186 ) ) @ SV69 )
= SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(304,plain,
! [SV70: $i,SV56: $i] :
( ( ! [SY187: $i] :
( ( lookup_slb @ ( insert_slb @ SV56 @ ( pair @ SV70 @ SY187 ) ) @ SV70 )
= SY187 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(305,plain,
! [SV71: $i,SV57: $i] :
( ( check_cpq @ ( triple @ SV57 @ create_slb @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(306,plain,
! [SV72: $i,SV58: $i] :
( ( ! [SY188: $i,SY189: $i] :
~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV58 @ ( pair @ SV72 @ SY189 ) ) @ SY188 )
| ( contains_slb @ SV58 @ SY188 )
| ( SV72 = SY188 ) )
| ~ ( ~ ( ( contains_slb @ SV58 @ SY188 )
| ( SV72 = SY188 ) )
| ( contains_slb @ ( insert_slb @ SV58 @ ( pair @ SV72 @ SY189 ) ) @ SY188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(307,plain,
! [SV73: $i,SV59: $i] :
( ( ! [SY190: $i,SY191: $i,SY192: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SY191 ) ) @ SY190 @ SY192 )
| ( pair_in_list @ SV59 @ SY190 @ SY192 )
| ~ ( ( SV73 != SY190 )
| ( SY191 != SY192 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV59 @ SY190 @ SY192 )
| ~ ( ( SV73 != SY190 )
| ( SY191 != SY192 ) ) )
| ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SY191 ) ) @ SY190 @ SY192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(308,plain,
! [SV74: $i,SV60: $i] :
( ( ~ ( ~ ( ~ ( strictly_less_than @ SV60 @ SV74 )
| ~ ( ~ ( less_than @ SV60 @ SV74 )
| ~ ~ ( less_than @ SV74 @ SV60 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV60 @ SV74 )
| ~ ~ ( less_than @ SV74 @ SV60 ) )
| ( strictly_less_than @ SV60 @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(309,plain,
! [SV75: $i,SV61: $i] :
( ( ! [SY193: $i,SY194: $i] :
( ~ ( less_than @ SY193 @ SY194 )
| ( ( update_slb @ ( insert_slb @ SV61 @ ( pair @ SV75 @ SY194 ) ) @ SY193 )
= ( insert_slb @ ( update_slb @ SV61 @ SY193 ) @ ( pair @ SV75 @ SY194 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(310,plain,
! [SV76: $i,SV62: $i] :
( ( ! [SY195: $i,SY196: $i,SY197: $i] :
( ~ ( strictly_less_than @ SY196 @ SY197 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SV76 @ ( pair @ SY196 @ SY197 ) ) @ SY195 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SV76 @ ( pair @ SY196 @ SY197 ) ) @ SY195 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(311,plain,
! [SV77: $i,SV63: $i] :
( ( ! [SY198: $i] :
( ~ ~ ( ~ ( less_than @ SV63 @ SV77 )
| ~ ( less_than @ SV77 @ SY198 ) )
| ( less_than @ SV63 @ SY198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(312,plain,
( ( ! [SY199: $i,SY200: $i,SY201: $i] :
( ~ ! [SX4: $i,SX5: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY200 @ SY201 ) ) @ SX4 @ SX5 )
| ( less_than @ SX5 @ SX4 ) )
| ( check_cpq @ ( triple @ sK10_SX0 @ ( insert_slb @ sK1_U @ ( pair @ SY200 @ SY201 ) ) @ SY199 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[297]) ).
thf(313,plain,
! [SV78: $i,SV64: $i] :
( ( ! [SY204: $i,SY205: $i,SY206: $i] :
( ~ ( less_than @ SY206 @ SY205 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SV78 @ ( pair @ SY205 @ SY206 ) ) @ SY204 ) )
| ( check_cpq @ ( triple @ SV64 @ SV78 @ SY204 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV64 @ SV78 @ SY204 ) )
| ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SV78 @ ( pair @ SY205 @ SY206 ) ) @ SY204 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(314,plain,
! [SV79: $i,SV65: $i] :
( ( ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV65 @ sK1_U @ SV79 ) )
| ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) )
| ( check_cpq @ ( triple @ SV65 @ sK1_U @ SV79 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(315,plain,
! [SV66: $i,SV50: $i] :
( ( ( less_than @ SV50 @ SV66 )
= $true )
| ( ( less_than @ SV66 @ SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(316,plain,
! [SV80: $i,SV67: $i,SV53: $i] :
( ( isnonempty_slb @ ( insert_slb @ SV53 @ ( pair @ SV67 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(317,plain,
! [SV68: $i,SV54: $i] :
( ( pair_in_list @ create_slb @ SV54 @ SV68 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(318,plain,
! [SV81: $i,SV69: $i,SV55: $i] :
( ( ( remove_slb @ ( insert_slb @ SV55 @ ( pair @ SV69 @ SV81 ) ) @ SV69 )
= SV55 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(319,plain,
! [SV82: $i,SV70: $i,SV56: $i] :
( ( ( lookup_slb @ ( insert_slb @ SV56 @ ( pair @ SV70 @ SV82 ) ) @ SV70 )
= SV82 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(320,plain,
! [SV83: $i,SV72: $i,SV58: $i] :
( ( ! [SY211: $i] :
~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV58 @ ( pair @ SV72 @ SY211 ) ) @ SV83 )
| ( contains_slb @ SV58 @ SV83 )
| ( SV72 = SV83 ) )
| ~ ( ~ ( ( contains_slb @ SV58 @ SV83 )
| ( SV72 = SV83 ) )
| ( contains_slb @ ( insert_slb @ SV58 @ ( pair @ SV72 @ SY211 ) ) @ SV83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(321,plain,
! [SV84: $i,SV73: $i,SV59: $i] :
( ( ! [SY212: $i,SY213: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SY212 ) ) @ SV84 @ SY213 )
| ( pair_in_list @ SV59 @ SV84 @ SY213 )
| ~ ( ( SV73 != SV84 )
| ( SY212 != SY213 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV59 @ SV84 @ SY213 )
| ~ ( ( SV73 != SV84 )
| ( SY212 != SY213 ) ) )
| ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SY212 ) ) @ SV84 @ SY213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(322,plain,
! [SV74: $i,SV60: $i] :
( ( ~ ( ~ ( strictly_less_than @ SV60 @ SV74 )
| ~ ( ~ ( less_than @ SV60 @ SV74 )
| ~ ~ ( less_than @ SV74 @ SV60 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV60 @ SV74 )
| ~ ~ ( less_than @ SV74 @ SV60 ) )
| ( strictly_less_than @ SV60 @ SV74 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(323,plain,
! [SV75: $i,SV61: $i,SV85: $i] :
( ( ! [SY214: $i] :
( ~ ( less_than @ SV85 @ SY214 )
| ( ( update_slb @ ( insert_slb @ SV61 @ ( pair @ SV75 @ SY214 ) ) @ SV85 )
= ( insert_slb @ ( update_slb @ SV61 @ SV85 ) @ ( pair @ SV75 @ SY214 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(324,plain,
! [SV86: $i,SV76: $i,SV62: $i] :
( ( ! [SY215: $i,SY216: $i] :
( ~ ( strictly_less_than @ SY215 @ SY216 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SV76 @ ( pair @ SY215 @ SY216 ) ) @ SV86 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SV76 @ ( pair @ SY215 @ SY216 ) ) @ SV86 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(325,plain,
! [SV87: $i,SV77: $i,SV63: $i] :
( ( ~ ~ ( ~ ( less_than @ SV63 @ SV77 )
| ~ ( less_than @ SV77 @ SV87 ) )
| ( less_than @ SV63 @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(326,plain,
( ( ! [SY217: $i,SY218: $i] :
( ~ ! [SX4: $i,SX5: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY217 @ SY218 ) ) @ SX4 @ SX5 )
| ( less_than @ SX5 @ SX4 ) )
| ( check_cpq @ ( triple @ sK10_SX0 @ ( insert_slb @ sK1_U @ ( pair @ SY217 @ SY218 ) ) @ sK11_SY199 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[312]) ).
thf(327,plain,
! [SV88: $i,SV78: $i,SV64: $i] :
( ( ! [SY221: $i,SY222: $i] :
( ~ ( less_than @ SY222 @ SY221 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SV78 @ ( pair @ SY221 @ SY222 ) ) @ SV88 ) )
| ( check_cpq @ ( triple @ SV64 @ SV78 @ SV88 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV64 @ SV78 @ SV88 ) )
| ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SV78 @ ( pair @ SY221 @ SY222 ) ) @ SV88 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(328,plain,
! [SV79: $i,SV65: $i] :
( ( ~ ( ~ ( check_cpq @ ( triple @ SV65 @ sK1_U @ SV79 ) )
| ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) )
| ( check_cpq @ ( triple @ SV65 @ sK1_U @ SV79 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(329,plain,
! [SV83: $i,SV89: $i,SV72: $i,SV58: $i] :
( ( ~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV58 @ ( pair @ SV72 @ SV89 ) ) @ SV83 )
| ( contains_slb @ SV58 @ SV83 )
| ( SV72 = SV83 ) )
| ~ ( ~ ( ( contains_slb @ SV58 @ SV83 )
| ( SV72 = SV83 ) )
| ( contains_slb @ ( insert_slb @ SV58 @ ( pair @ SV72 @ SV89 ) ) @ SV83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(330,plain,
! [SV84: $i,SV90: $i,SV73: $i,SV59: $i] :
( ( ! [SY223: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SY223 )
| ( pair_in_list @ SV59 @ SV84 @ SY223 )
| ~ ( ( SV73 != SV84 )
| ( SV90 != SY223 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV59 @ SV84 @ SY223 )
| ~ ( ( SV73 != SV84 )
| ( SV90 != SY223 ) ) )
| ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SY223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(331,plain,
! [SV74: $i,SV60: $i] :
( ( ~ ( ~ ( strictly_less_than @ SV60 @ SV74 )
| ~ ( ~ ( less_than @ SV60 @ SV74 )
| ~ ~ ( less_than @ SV74 @ SV60 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(332,plain,
! [SV74: $i,SV60: $i] :
( ( ~ ( ~ ~ ( ~ ( less_than @ SV60 @ SV74 )
| ~ ~ ( less_than @ SV74 @ SV60 ) )
| ( strictly_less_than @ SV60 @ SV74 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(333,plain,
! [SV75: $i,SV61: $i,SV91: $i,SV85: $i] :
( ( ~ ( less_than @ SV85 @ SV91 )
| ( ( update_slb @ ( insert_slb @ SV61 @ ( pair @ SV75 @ SV91 ) ) @ SV85 )
= ( insert_slb @ ( update_slb @ SV61 @ SV85 ) @ ( pair @ SV75 @ SV91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(334,plain,
! [SV86: $i,SV76: $i,SV62: $i,SV92: $i] :
( ( ! [SY224: $i] :
( ~ ( strictly_less_than @ SV92 @ SY224 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SV76 @ ( pair @ SV92 @ SY224 ) ) @ SV86 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SV76 @ ( pair @ SV92 @ SY224 ) ) @ SV86 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(335,plain,
! [SV87: $i,SV77: $i,SV63: $i] :
( ( ( ~ ~ ( ~ ( less_than @ SV63 @ SV77 )
| ~ ( less_than @ SV77 @ SV87 ) ) )
= $true )
| ( ( less_than @ SV63 @ SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(336,plain,
( ( ! [SY225: $i] :
( ~ ! [SY226: $i,SY227: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK12_SY217 @ SY225 ) ) @ SY226 @ SY227 )
| ( less_than @ SY227 @ SY226 ) )
| ( check_cpq @ ( triple @ sK10_SX0 @ ( insert_slb @ sK1_U @ ( pair @ sK12_SY217 @ SY225 ) ) @ sK11_SY199 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[326]) ).
thf(337,plain,
! [SV88: $i,SV78: $i,SV64: $i,SV93: $i] :
( ( ! [SY228: $i] :
( ~ ( less_than @ SY228 @ SV93 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SV78 @ ( pair @ SV93 @ SY228 ) ) @ SV88 ) )
| ( check_cpq @ ( triple @ SV64 @ SV78 @ SV88 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV64 @ SV78 @ SV88 ) )
| ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SV78 @ ( pair @ SV93 @ SY228 ) ) @ SV88 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(338,plain,
! [SV79: $i,SV65: $i] :
( ( ~ ( ~ ( check_cpq @ ( triple @ SV65 @ sK1_U @ SV79 ) )
| ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[328]) ).
thf(339,plain,
! [SV79: $i,SV65: $i] :
( ( ~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) )
| ( check_cpq @ ( triple @ SV65 @ sK1_U @ SV79 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[328]) ).
thf(340,plain,
! [SV83: $i,SV89: $i,SV72: $i,SV58: $i] :
( ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV58 @ ( pair @ SV72 @ SV89 ) ) @ SV83 )
| ( contains_slb @ SV58 @ SV83 )
| ( SV72 = SV83 ) )
| ~ ( ~ ( ( contains_slb @ SV58 @ SV83 )
| ( SV72 = SV83 ) )
| ( contains_slb @ ( insert_slb @ SV58 @ ( pair @ SV72 @ SV89 ) ) @ SV83 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(341,plain,
! [SV94: $i,SV84: $i,SV90: $i,SV73: $i,SV59: $i] :
( ( ~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 )
| ( pair_in_list @ SV59 @ SV84 @ SV94 )
| ~ ( ( SV73 != SV84 )
| ( SV90 != SV94 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV59 @ SV84 @ SV94 )
| ~ ( ( SV73 != SV84 )
| ( SV90 != SV94 ) ) )
| ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(342,plain,
! [SV74: $i,SV60: $i] :
( ( ~ ( strictly_less_than @ SV60 @ SV74 )
| ~ ( ~ ( less_than @ SV60 @ SV74 )
| ~ ~ ( less_than @ SV74 @ SV60 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(343,plain,
! [SV74: $i,SV60: $i] :
( ( ~ ~ ( ~ ( less_than @ SV60 @ SV74 )
| ~ ~ ( less_than @ SV74 @ SV60 ) )
| ( strictly_less_than @ SV60 @ SV74 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(344,plain,
! [SV75: $i,SV61: $i,SV91: $i,SV85: $i] :
( ( ( ~ ( less_than @ SV85 @ SV91 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV61 @ ( pair @ SV75 @ SV91 ) ) @ SV85 )
= ( insert_slb @ ( update_slb @ SV61 @ SV85 ) @ ( pair @ SV75 @ SV91 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(345,plain,
! [SV86: $i,SV76: $i,SV62: $i,SV95: $i,SV92: $i] :
( ( ~ ( strictly_less_than @ SV92 @ SV95 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SV76 @ ( pair @ SV92 @ SV95 ) ) @ SV86 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SV76 @ ( pair @ SV92 @ SV95 ) ) @ SV86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(346,plain,
! [SV87: $i,SV77: $i,SV63: $i] :
( ( ( ~ ( ~ ( less_than @ SV63 @ SV77 )
| ~ ( less_than @ SV77 @ SV87 ) ) )
= $false )
| ( ( less_than @ SV63 @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(347,plain,
( ( ~ ! [SY229: $i,SY230: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK12_SY217 @ sK13_SY225 ) ) @ SY229 @ SY230 )
| ( less_than @ SY230 @ SY229 ) )
| ( check_cpq @ ( triple @ sK10_SX0 @ ( insert_slb @ sK1_U @ ( pair @ sK12_SY217 @ sK13_SY225 ) ) @ sK11_SY199 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[336]) ).
thf(348,plain,
! [SV88: $i,SV78: $i,SV64: $i,SV93: $i,SV96: $i] :
( ( ~ ( less_than @ SV96 @ SV93 )
| ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SV78 @ ( pair @ SV93 @ SV96 ) ) @ SV88 ) )
| ( check_cpq @ ( triple @ SV64 @ SV78 @ SV88 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV64 @ SV78 @ SV88 ) )
| ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SV78 @ ( pair @ SV93 @ SV96 ) ) @ SV88 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(349,plain,
! [SV79: $i,SV65: $i] :
( ( ~ ( check_cpq @ ( triple @ SV65 @ sK1_U @ SV79 ) )
| ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(350,plain,
! [SV79: $i,SV65: $i] :
( ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) )
| ( check_cpq @ ( triple @ SV65 @ sK1_U @ SV79 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(351,plain,
! [SV83: $i,SV89: $i,SV72: $i,SV58: $i] :
( ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV58 @ ( pair @ SV72 @ SV89 ) ) @ SV83 )
| ( contains_slb @ SV58 @ SV83 )
| ( SV72 = SV83 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(352,plain,
! [SV89: $i,SV72: $i,SV83: $i,SV58: $i] :
( ( ~ ( ~ ( ( contains_slb @ SV58 @ SV83 )
| ( SV72 = SV83 ) )
| ( contains_slb @ ( insert_slb @ SV58 @ ( pair @ SV72 @ SV89 ) ) @ SV83 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(353,plain,
! [SV94: $i,SV84: $i,SV90: $i,SV73: $i,SV59: $i] :
( ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 )
| ( pair_in_list @ SV59 @ SV84 @ SV94 )
| ~ ( ( SV73 != SV84 )
| ( SV90 != SV94 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV59 @ SV84 @ SV94 )
| ~ ( ( SV73 != SV84 )
| ( SV90 != SV94 ) ) )
| ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(354,plain,
! [SV74: $i,SV60: $i] :
( ( ( ~ ( strictly_less_than @ SV60 @ SV74 ) )
= $true )
| ( ( ~ ( ~ ( less_than @ SV60 @ SV74 )
| ~ ~ ( less_than @ SV74 @ SV60 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(355,plain,
! [SV74: $i,SV60: $i] :
( ( ( ~ ~ ( ~ ( less_than @ SV60 @ SV74 )
| ~ ~ ( less_than @ SV74 @ SV60 ) ) )
= $true )
| ( ( strictly_less_than @ SV60 @ SV74 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(356,plain,
! [SV75: $i,SV61: $i,SV91: $i,SV85: $i] :
( ( ( less_than @ SV85 @ SV91 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV61 @ ( pair @ SV75 @ SV91 ) ) @ SV85 )
= ( insert_slb @ ( update_slb @ SV61 @ SV85 ) @ ( pair @ SV75 @ SV91 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(357,plain,
! [SV86: $i,SV76: $i,SV62: $i,SV95: $i,SV92: $i] :
( ( ( ~ ( strictly_less_than @ SV92 @ SV95 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SV76 @ ( pair @ SV92 @ SV95 ) ) @ SV86 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SV76 @ ( pair @ SV92 @ SV95 ) ) @ SV86 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(358,plain,
! [SV87: $i,SV77: $i,SV63: $i] :
( ( ( ~ ( less_than @ SV63 @ SV77 )
| ~ ( less_than @ SV77 @ SV87 ) )
= $true )
| ( ( less_than @ SV63 @ SV87 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(359,plain,
( ( ~ ! [SY229: $i,SY230: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK12_SY217 @ sK13_SY225 ) ) @ SY229 @ SY230 )
| ( less_than @ SY230 @ SY229 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[347]) ).
thf(360,plain,
( ( check_cpq @ ( triple @ sK10_SX0 @ ( insert_slb @ sK1_U @ ( pair @ sK12_SY217 @ sK13_SY225 ) ) @ sK11_SY199 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[347]) ).
thf(361,plain,
! [SV88: $i,SV78: $i,SV64: $i,SV93: $i,SV96: $i] :
( ( ( ~ ( less_than @ SV96 @ SV93 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SV78 @ ( pair @ SV93 @ SV96 ) ) @ SV88 ) )
| ( check_cpq @ ( triple @ SV64 @ SV78 @ SV88 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV64 @ SV78 @ SV88 ) )
| ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SV78 @ ( pair @ SV93 @ SV96 ) ) @ SV88 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(362,plain,
! [SV79: $i,SV65: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV65 @ sK1_U @ SV79 ) ) )
= $true )
| ( ( ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(363,plain,
! [SV79: $i,SV65: $i] :
( ( ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV65 @ sK1_U @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(364,plain,
! [SV83: $i,SV89: $i,SV72: $i,SV58: $i] :
( ( ~ ( contains_slb @ ( insert_slb @ SV58 @ ( pair @ SV72 @ SV89 ) ) @ SV83 )
| ( contains_slb @ SV58 @ SV83 )
| ( SV72 = SV83 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[351]) ).
thf(365,plain,
! [SV89: $i,SV72: $i,SV83: $i,SV58: $i] :
( ( ~ ( ( contains_slb @ SV58 @ SV83 )
| ( SV72 = SV83 ) )
| ( contains_slb @ ( insert_slb @ SV58 @ ( pair @ SV72 @ SV89 ) ) @ SV83 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(366,plain,
! [SV94: $i,SV84: $i,SV90: $i,SV73: $i,SV59: $i] :
( ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 )
| ( pair_in_list @ SV59 @ SV84 @ SV94 )
| ~ ( ( SV73 != SV84 )
| ( SV90 != SV94 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[353]) ).
thf(367,plain,
! [SV90: $i,SV73: $i,SV94: $i,SV84: $i,SV59: $i] :
( ( ~ ( ~ ( ( pair_in_list @ SV59 @ SV84 @ SV94 )
| ~ ( ( SV73 != SV84 )
| ( SV90 != SV94 ) ) )
| ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[353]) ).
thf(368,plain,
! [SV74: $i,SV60: $i] :
( ( ( strictly_less_than @ SV60 @ SV74 )
= $false )
| ( ( ~ ( ~ ( less_than @ SV60 @ SV74 )
| ~ ~ ( less_than @ SV74 @ SV60 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(369,plain,
! [SV74: $i,SV60: $i] :
( ( ( ~ ( ~ ( less_than @ SV60 @ SV74 )
| ~ ~ ( less_than @ SV74 @ SV60 ) ) )
= $false )
| ( ( strictly_less_than @ SV60 @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(370,plain,
! [SV86: $i,SV76: $i,SV62: $i,SV95: $i,SV92: $i] :
( ( ( strictly_less_than @ SV92 @ SV95 )
= $false )
| ( ( ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SV76 @ ( pair @ SV92 @ SV95 ) ) @ SV86 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SV76 @ ( pair @ SV92 @ SV95 ) ) @ SV86 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(371,plain,
! [SV87: $i,SV77: $i,SV63: $i] :
( ( ( ~ ( less_than @ SV63 @ SV77 ) )
= $true )
| ( ( ~ ( less_than @ SV77 @ SV87 ) )
= $true )
| ( ( less_than @ SV63 @ SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(372,plain,
( ( ! [SY229: $i,SY230: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK12_SY217 @ sK13_SY225 ) ) @ SY229 @ SY230 )
| ( less_than @ SY230 @ SY229 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(373,plain,
! [SV88: $i,SV78: $i,SV64: $i,SV93: $i,SV96: $i] :
( ( ( less_than @ SV96 @ SV93 )
= $false )
| ( ( ~ ( ~ ( ~ ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SV78 @ ( pair @ SV93 @ SV96 ) ) @ SV88 ) )
| ( check_cpq @ ( triple @ SV64 @ SV78 @ SV88 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV64 @ SV78 @ SV88 ) )
| ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SV78 @ ( pair @ SV93 @ SV96 ) ) @ SV88 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(374,plain,
! [SV79: $i,SV65: $i] :
( ( ( check_cpq @ ( triple @ SV65 @ sK1_U @ SV79 ) )
= $false )
| ( ( ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(375,plain,
! [SV79: $i,SV65: $i] :
( ( ( ! [SX2: $i,SX3: $i] :
( ~ ( pair_in_list @ sK1_U @ SX2 @ SX3 )
| ( less_than @ SX3 @ SX2 ) ) )
= $false )
| ( ( check_cpq @ ( triple @ SV65 @ sK1_U @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(376,plain,
! [SV83: $i,SV89: $i,SV72: $i,SV58: $i] :
( ( ( ~ ( contains_slb @ ( insert_slb @ SV58 @ ( pair @ SV72 @ SV89 ) ) @ SV83 ) )
= $true )
| ( ( ( contains_slb @ SV58 @ SV83 )
| ( SV72 = SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(377,plain,
! [SV89: $i,SV72: $i,SV83: $i,SV58: $i] :
( ( ( ~ ( ( contains_slb @ SV58 @ SV83 )
| ( SV72 = SV83 ) ) )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV58 @ ( pair @ SV72 @ SV89 ) ) @ SV83 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(378,plain,
! [SV94: $i,SV84: $i,SV90: $i,SV73: $i,SV59: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 )
| ( pair_in_list @ SV59 @ SV84 @ SV94 )
| ~ ( ( SV73 != SV84 )
| ( SV90 != SV94 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(379,plain,
! [SV90: $i,SV73: $i,SV94: $i,SV84: $i,SV59: $i] :
( ( ~ ( ( pair_in_list @ SV59 @ SV84 @ SV94 )
| ~ ( ( SV73 != SV84 )
| ( SV90 != SV94 ) ) )
| ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(380,plain,
! [SV74: $i,SV60: $i] :
( ( ( ~ ( less_than @ SV60 @ SV74 )
| ~ ~ ( less_than @ SV74 @ SV60 ) )
= $false )
| ( ( strictly_less_than @ SV60 @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(381,plain,
! [SV74: $i,SV60: $i] :
( ( ( ~ ( less_than @ SV60 @ SV74 )
| ~ ~ ( less_than @ SV74 @ SV60 ) )
= $true )
| ( ( strictly_less_than @ SV60 @ SV74 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(382,plain,
! [SV86: $i,SV95: $i,SV92: $i,SV76: $i,SV62: $i] :
( ( ( ~ ( ~ ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SV76 @ ( pair @ SV92 @ SV95 ) ) @ SV86 ) )
| $false )
| ~ ( ~ $false
| ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SV76 @ ( pair @ SV92 @ SV95 ) ) @ SV86 ) ) ) )
= $false )
| ( ( strictly_less_than @ SV92 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(383,plain,
! [SV87: $i,SV77: $i,SV63: $i] :
( ( ( less_than @ SV63 @ SV77 )
= $false )
| ( ( ~ ( less_than @ SV77 @ SV87 ) )
= $true )
| ( ( less_than @ SV63 @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(384,plain,
! [SV97: $i] :
( ( ! [SY231: $i] :
( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK12_SY217 @ sK13_SY225 ) ) @ SV97 @ SY231 )
| ( less_than @ SY231 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(385,plain,
! [SV88: $i,SV96: $i,SV93: $i,SV78: $i,SV64: $i] :
( ( ( ~ ( ~ ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SV78 @ ( pair @ SV93 @ SV96 ) ) @ SV88 ) )
| ( check_cpq @ ( triple @ SV64 @ SV78 @ SV88 ) ) )
| ~ ( ~ ( check_cpq @ ( triple @ SV64 @ SV78 @ SV88 ) )
| ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SV78 @ ( pair @ SV93 @ SV96 ) ) @ SV88 ) ) ) )
= $false )
| ( ( less_than @ SV96 @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(386,plain,
! [SV79: $i,SV65: $i,SV98: $i] :
( ( ( ! [SY232: $i] :
( ~ ( pair_in_list @ sK1_U @ SV98 @ SY232 )
| ( less_than @ SY232 @ SV98 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV65 @ sK1_U @ SV79 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(387,plain,
! [SV65: $i,SV79: $i] :
( ( ( ! [SY233: $i] :
( ~ ( pair_in_list @ sK1_U @ ( sK14_SX2 @ SV79 @ SV65 ) @ SY233 )
| ( less_than @ SY233 @ ( sK14_SX2 @ SV79 @ SV65 ) ) ) )
= $false )
| ( ( check_cpq @ ( triple @ SV65 @ sK1_U @ SV79 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[375]) ).
thf(388,plain,
! [SV83: $i,SV89: $i,SV72: $i,SV58: $i] :
( ( ( contains_slb @ ( insert_slb @ SV58 @ ( pair @ SV72 @ SV89 ) ) @ SV83 )
= $false )
| ( ( ( contains_slb @ SV58 @ SV83 )
| ( SV72 = SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(389,plain,
! [SV89: $i,SV72: $i,SV83: $i,SV58: $i] :
( ( ( ( contains_slb @ SV58 @ SV83 )
| ( SV72 = SV83 ) )
= $false )
| ( ( contains_slb @ ( insert_slb @ SV58 @ ( pair @ SV72 @ SV89 ) ) @ SV83 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(390,plain,
! [SV94: $i,SV84: $i,SV90: $i,SV73: $i,SV59: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 ) )
= $true )
| ( ( ( pair_in_list @ SV59 @ SV84 @ SV94 )
| ~ ( ( SV73 != SV84 )
| ( SV90 != SV94 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(391,plain,
! [SV90: $i,SV73: $i,SV94: $i,SV84: $i,SV59: $i] :
( ( ( ~ ( ( pair_in_list @ SV59 @ SV84 @ SV94 )
| ~ ( ( SV73 != SV84 )
| ( SV90 != SV94 ) ) ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(392,plain,
! [SV74: $i,SV60: $i] :
( ( ( ~ ( less_than @ SV60 @ SV74 ) )
= $false )
| ( ( strictly_less_than @ SV60 @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[380]) ).
thf(393,plain,
! [SV60: $i,SV74: $i] :
( ( ( ~ ~ ( less_than @ SV74 @ SV60 ) )
= $false )
| ( ( strictly_less_than @ SV60 @ SV74 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[380]) ).
thf(394,plain,
! [SV74: $i,SV60: $i] :
( ( ( ~ ( less_than @ SV60 @ SV74 ) )
= $true )
| ( ( ~ ~ ( less_than @ SV74 @ SV60 ) )
= $true )
| ( ( strictly_less_than @ SV60 @ SV74 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(395,plain,
! [SV86: $i,SV95: $i,SV92: $i,SV76: $i,SV62: $i] :
( ( ( ~ ( ~ ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SV76 @ ( pair @ SV92 @ SV95 ) ) @ SV86 ) )
| $false ) )
= $false )
| ( ( strictly_less_than @ SV92 @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[382]) ).
thf(396,plain,
! [SV86: $i,SV95: $i,SV92: $i,SV76: $i,SV62: $i] :
( ( ( ~ ( ~ $false
| ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SV76 @ ( pair @ SV92 @ SV95 ) ) @ SV86 ) ) ) )
= $false )
| ( ( strictly_less_than @ SV92 @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[382]) ).
thf(397,plain,
! [SV63: $i,SV87: $i,SV77: $i] :
( ( ( less_than @ SV77 @ SV87 )
= $false )
| ( ( less_than @ SV63 @ SV77 )
= $false )
| ( ( less_than @ SV63 @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(398,plain,
! [SV99: $i,SV97: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK12_SY217 @ sK13_SY225 ) ) @ SV97 @ SV99 )
| ( less_than @ SV99 @ SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(399,plain,
! [SV88: $i,SV96: $i,SV93: $i,SV78: $i,SV64: $i] :
( ( ( ~ ( ~ ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SV78 @ ( pair @ SV93 @ SV96 ) ) @ SV88 ) )
| ( check_cpq @ ( triple @ SV64 @ SV78 @ SV88 ) ) ) )
= $false )
| ( ( less_than @ SV96 @ SV93 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[385]) ).
thf(400,plain,
! [SV96: $i,SV93: $i,SV88: $i,SV78: $i,SV64: $i] :
( ( ( ~ ( ~ ( check_cpq @ ( triple @ SV64 @ SV78 @ SV88 ) )
| ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SV78 @ ( pair @ SV93 @ SV96 ) ) @ SV88 ) ) ) )
= $false )
| ( ( less_than @ SV96 @ SV93 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[385]) ).
thf(401,plain,
! [SV79: $i,SV65: $i,SV100: $i,SV98: $i] :
( ( ( ~ ( pair_in_list @ sK1_U @ SV98 @ SV100 )
| ( less_than @ SV100 @ SV98 ) )
= $true )
| ( ( check_cpq @ ( triple @ SV65 @ sK1_U @ SV79 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(402,plain,
! [SV65: $i,SV79: $i] :
( ( ( ~ ( pair_in_list @ sK1_U @ ( sK14_SX2 @ SV79 @ SV65 ) @ ( sK15_SY233 @ SV65 @ SV79 ) )
| ( less_than @ ( sK15_SY233 @ SV65 @ SV79 ) @ ( sK14_SX2 @ SV79 @ SV65 ) ) )
= $false )
| ( ( check_cpq @ ( triple @ SV65 @ sK1_U @ SV79 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[387]) ).
thf(403,plain,
! [SV89: $i,SV72: $i,SV83: $i,SV58: $i] :
( ( ( contains_slb @ SV58 @ SV83 )
= $true )
| ( ( SV72 = SV83 )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV58 @ ( pair @ SV72 @ SV89 ) ) @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(404,plain,
! [SV89: $i,SV72: $i,SV83: $i,SV58: $i] :
( ( ( contains_slb @ SV58 @ SV83 )
= $false )
| ( ( contains_slb @ ( insert_slb @ SV58 @ ( pair @ SV72 @ SV89 ) ) @ SV83 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(405,plain,
! [SV89: $i,SV58: $i,SV83: $i,SV72: $i] :
( ( ( SV72 = SV83 )
= $false )
| ( ( contains_slb @ ( insert_slb @ SV58 @ ( pair @ SV72 @ SV89 ) ) @ SV83 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(406,plain,
! [SV94: $i,SV84: $i,SV90: $i,SV73: $i,SV59: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 )
= $false )
| ( ( ( pair_in_list @ SV59 @ SV84 @ SV94 )
| ~ ( ( SV73 != SV84 )
| ( SV90 != SV94 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(407,plain,
! [SV90: $i,SV73: $i,SV94: $i,SV84: $i,SV59: $i] :
( ( ( ( pair_in_list @ SV59 @ SV84 @ SV94 )
| ~ ( ( SV73 != SV84 )
| ( SV90 != SV94 ) ) )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(408,plain,
! [SV74: $i,SV60: $i] :
( ( ( less_than @ SV60 @ SV74 )
= $true )
| ( ( strictly_less_than @ SV60 @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[392]) ).
thf(409,plain,
! [SV60: $i,SV74: $i] :
( ( ( ~ ( less_than @ SV74 @ SV60 ) )
= $true )
| ( ( strictly_less_than @ SV60 @ SV74 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[393]) ).
thf(410,plain,
! [SV74: $i,SV60: $i] :
( ( ( less_than @ SV60 @ SV74 )
= $false )
| ( ( ~ ~ ( less_than @ SV74 @ SV60 ) )
= $true )
| ( ( strictly_less_than @ SV60 @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(411,plain,
! [SV86: $i,SV95: $i,SV92: $i,SV76: $i,SV62: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SV76 @ ( pair @ SV92 @ SV95 ) ) @ SV86 ) )
| $false )
= $true )
| ( ( strictly_less_than @ SV92 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[395]) ).
thf(412,plain,
! [SV86: $i,SV95: $i,SV92: $i,SV76: $i,SV62: $i] :
( ( ( ~ $false
| ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SV76 @ ( pair @ SV92 @ SV95 ) ) @ SV86 ) ) )
= $true )
| ( ( strictly_less_than @ SV92 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[396]) ).
thf(413,plain,
! [SV99: $i,SV97: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK12_SY217 @ sK13_SY225 ) ) @ SV97 @ SV99 ) )
= $true )
| ( ( less_than @ SV99 @ SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[398]) ).
thf(414,plain,
! [SV88: $i,SV96: $i,SV93: $i,SV78: $i,SV64: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SV78 @ ( pair @ SV93 @ SV96 ) ) @ SV88 ) )
| ( check_cpq @ ( triple @ SV64 @ SV78 @ SV88 ) ) )
= $true )
| ( ( less_than @ SV96 @ SV93 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[399]) ).
thf(415,plain,
! [SV96: $i,SV93: $i,SV88: $i,SV78: $i,SV64: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV64 @ SV78 @ SV88 ) )
| ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SV78 @ ( pair @ SV93 @ SV96 ) ) @ SV88 ) ) )
= $true )
| ( ( less_than @ SV96 @ SV93 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[400]) ).
thf(416,plain,
! [SV79: $i,SV65: $i,SV100: $i,SV98: $i] :
( ( ( ~ ( pair_in_list @ sK1_U @ SV98 @ SV100 ) )
= $true )
| ( ( less_than @ SV100 @ SV98 )
= $true )
| ( ( check_cpq @ ( triple @ SV65 @ sK1_U @ SV79 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(417,plain,
! [SV65: $i,SV79: $i] :
( ( ( ~ ( pair_in_list @ sK1_U @ ( sK14_SX2 @ SV79 @ SV65 ) @ ( sK15_SY233 @ SV65 @ SV79 ) ) )
= $false )
| ( ( check_cpq @ ( triple @ SV65 @ sK1_U @ SV79 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[402]) ).
thf(418,plain,
! [SV79: $i,SV65: $i] :
( ( ( less_than @ ( sK15_SY233 @ SV65 @ SV79 ) @ ( sK14_SX2 @ SV79 @ SV65 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV65 @ sK1_U @ SV79 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[402]) ).
thf(419,plain,
! [SV90: $i,SV73: $i,SV94: $i,SV84: $i,SV59: $i] :
( ( ( pair_in_list @ SV59 @ SV84 @ SV94 )
= $true )
| ( ( ~ ( ( SV73 != SV84 )
| ( SV90 != SV94 ) ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[406]) ).
thf(420,plain,
! [SV90: $i,SV73: $i,SV94: $i,SV84: $i,SV59: $i] :
( ( ( pair_in_list @ SV59 @ SV84 @ SV94 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[407]) ).
thf(421,plain,
! [SV59: $i,SV94: $i,SV90: $i,SV84: $i,SV73: $i] :
( ( ( ~ ( ( SV73 != SV84 )
| ( SV90 != SV94 ) ) )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[407]) ).
thf(422,plain,
! [SV60: $i,SV74: $i] :
( ( ( less_than @ SV74 @ SV60 )
= $false )
| ( ( strictly_less_than @ SV60 @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(423,plain,
! [SV60: $i,SV74: $i] :
( ( ( ~ ( less_than @ SV74 @ SV60 ) )
= $false )
| ( ( less_than @ SV60 @ SV74 )
= $false )
| ( ( strictly_less_than @ SV60 @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(424,plain,
! [SV86: $i,SV95: $i,SV92: $i,SV76: $i,SV62: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SV76 @ ( pair @ SV92 @ SV95 ) ) @ SV86 ) ) )
= $true )
| ( $false = $true )
| ( ( strictly_less_than @ SV92 @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(425,plain,
! [SV86: $i,SV95: $i,SV92: $i,SV76: $i,SV62: $i] :
( ( ( ~ $false ) = $true )
| ( ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SV76 @ ( pair @ SV92 @ SV95 ) ) @ SV86 ) )
= $true )
| ( ( strictly_less_than @ SV92 @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(426,plain,
! [SV99: $i,SV97: $i] :
( ( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK12_SY217 @ sK13_SY225 ) ) @ SV97 @ SV99 )
= $false )
| ( ( less_than @ SV99 @ SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(427,plain,
! [SV88: $i,SV96: $i,SV93: $i,SV78: $i,SV64: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SV78 @ ( pair @ SV93 @ SV96 ) ) @ SV88 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV64 @ SV78 @ SV88 ) )
= $true )
| ( ( less_than @ SV96 @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(428,plain,
! [SV96: $i,SV93: $i,SV88: $i,SV78: $i,SV64: $i] :
( ( ( ~ ( check_cpq @ ( triple @ SV64 @ SV78 @ SV88 ) ) )
= $true )
| ( ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SV78 @ ( pair @ SV93 @ SV96 ) ) @ SV88 ) )
= $true )
| ( ( less_than @ SV96 @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(429,plain,
! [SV79: $i,SV65: $i,SV100: $i,SV98: $i] :
( ( ( pair_in_list @ sK1_U @ SV98 @ SV100 )
= $false )
| ( ( less_than @ SV100 @ SV98 )
= $true )
| ( ( check_cpq @ ( triple @ SV65 @ sK1_U @ SV79 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(430,plain,
! [SV65: $i,SV79: $i] :
( ( ( pair_in_list @ sK1_U @ ( sK14_SX2 @ SV79 @ SV65 ) @ ( sK15_SY233 @ SV65 @ SV79 ) )
= $true )
| ( ( check_cpq @ ( triple @ SV65 @ sK1_U @ SV79 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[417]) ).
thf(431,plain,
! [SV59: $i,SV94: $i,SV90: $i,SV84: $i,SV73: $i] :
( ( ( ( SV73 != SV84 )
| ( SV90 != SV94 ) )
= $false )
| ( ( pair_in_list @ SV59 @ SV84 @ SV94 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(432,plain,
! [SV59: $i,SV94: $i,SV90: $i,SV84: $i,SV73: $i] :
( ( ( ( SV73 != SV84 )
| ( SV90 != SV94 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[421]) ).
thf(433,plain,
! [SV60: $i,SV74: $i] :
( ( ( less_than @ SV74 @ SV60 )
= $true )
| ( ( less_than @ SV60 @ SV74 )
= $false )
| ( ( strictly_less_than @ SV60 @ SV74 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[423]) ).
thf(434,plain,
! [SV86: $i,SV95: $i,SV92: $i,SV76: $i,SV62: $i] :
( ( ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SV76 @ ( pair @ SV92 @ SV95 ) ) @ SV86 ) )
= $false )
| ( $false = $true )
| ( ( strictly_less_than @ SV92 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(435,plain,
! [SV86: $i,SV95: $i,SV92: $i,SV76: $i,SV62: $i] :
( ( $false = $false )
| ( ( check_cpq @ ( triple @ SV62 @ ( insert_slb @ SV76 @ ( pair @ SV92 @ SV95 ) ) @ SV86 ) )
= $true )
| ( ( strictly_less_than @ SV92 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(436,plain,
! [SV88: $i,SV96: $i,SV93: $i,SV78: $i,SV64: $i] :
( ( ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SV78 @ ( pair @ SV93 @ SV96 ) ) @ SV88 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV64 @ SV78 @ SV88 ) )
= $true )
| ( ( less_than @ SV96 @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(437,plain,
! [SV96: $i,SV93: $i,SV88: $i,SV78: $i,SV64: $i] :
( ( ( check_cpq @ ( triple @ SV64 @ SV78 @ SV88 ) )
= $false )
| ( ( check_cpq @ ( triple @ SV64 @ ( insert_slb @ SV78 @ ( pair @ SV93 @ SV96 ) ) @ SV88 ) )
= $true )
| ( ( less_than @ SV96 @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(438,plain,
! [SV90: $i,SV94: $i,SV59: $i,SV84: $i,SV73: $i] :
( ( ( SV73 != SV84 )
= $false )
| ( ( pair_in_list @ SV59 @ SV84 @ SV94 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[431]) ).
thf(439,plain,
! [SV73: $i,SV84: $i,SV59: $i,SV94: $i,SV90: $i] :
( ( ( SV90 != SV94 )
= $false )
| ( ( pair_in_list @ SV59 @ SV84 @ SV94 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[431]) ).
thf(440,plain,
! [SV59: $i,SV94: $i,SV90: $i,SV84: $i,SV73: $i] :
( ( ( SV73 != SV84 )
= $true )
| ( ( SV90 != SV94 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(441,plain,
! [SV90: $i,SV94: $i,SV59: $i,SV84: $i,SV73: $i] :
( ( ( SV73 = SV84 )
= $true )
| ( ( pair_in_list @ SV59 @ SV84 @ SV94 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[438]) ).
thf(442,plain,
! [SV73: $i,SV84: $i,SV59: $i,SV94: $i,SV90: $i] :
( ( ( SV90 = SV94 )
= $true )
| ( ( pair_in_list @ SV59 @ SV84 @ SV94 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[439]) ).
thf(443,plain,
! [SV59: $i,SV94: $i,SV90: $i,SV84: $i,SV73: $i] :
( ( ( SV73 = SV84 )
= $false )
| ( ( SV90 != SV94 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(444,plain,
! [SV59: $i,SV84: $i,SV73: $i,SV94: $i,SV90: $i] :
( ( ( SV90 = SV94 )
= $false )
| ( ( SV73 = SV84 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV59 @ ( pair @ SV73 @ SV90 ) ) @ SV84 @ SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(445,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[284,444,442,441,437,436,435,434,433,430,429,426,422,420,418,408,405,404,403,397,360,356,319,318,317,316,315,305,285]) ).
thf(446,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[445,256]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV406+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.18 % Computer : n015.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 16:31:28 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.99/1.36
% 5.99/1.36 No.of.Axioms: 15
% 5.99/1.36
% 5.99/1.36 Length.of.Defs: 0
% 5.99/1.36
% 5.99/1.36 Contains.Choice.Funs: false
% 5.99/1.36 .................
% 5.99/1.36
% 5.99/1.36 ********************************
% 5.99/1.36 * All subproblems solved! *
% 5.99/1.36 ********************************
% 5.99/1.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:16,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:445,loop_count:0,foatp_calls:1,translation:fof_full)
% 5.99/1.36
% 5.99/1.36 %**** Beginning of derivation protocol ****
% 5.99/1.36 % SZS output start CNFRefutation
% See solution above
% 5.99/1.37
% 5.99/1.37 %**** End of derivation protocol ****
% 5.99/1.37 %**** no. of clauses in derivation: 420 ****
% 5.99/1.37 %**** clause counter: 445 ****
% 5.99/1.37
% 5.99/1.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:16,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:445,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------