%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV401+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 : n001.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 10:57:35 AM UTC 2026
% Result : Theorem 8.37s 1.74s
% Output : CNFRefutation 8.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 187 ( 124 unt; 0 typ; 0 def)
% Number of atoms : 1020 ( 375 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 2449 ( 385 ~; 284 |; 22 &;1723 @)
% ( 9 <=>; 26 =>; 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 : 21 ( 18 usr; 10 con; 0-3 aty)
% Number of variables : 597 ( 0 ^; 597 !; 0 ?; 597 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_bottom,type,
bottom: $i ).
thf(tp_contains_slb,type,
contains_slb: $i > $i > $o ).
thf(tp_create_slb,type,
create_slb: $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_pair,type,
pair: $i > $i > $i ).
thf(tp_pair_in_list,type,
pair_in_list: $i > $i > $i > $o ).
thf(tp_remove_slb,type,
remove_slb: $i > $i > $i ).
thf(tp_sK1_U,type,
sK1_U: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SY92,type,
sK3_SY92: $i ).
thf(tp_sK4_SY103,type,
sK4_SY103: $i ).
thf(tp_sK5_SY108,type,
sK5_SY108: $i ).
thf(tp_sK6_SY110,type,
sK6_SY110: $i ).
thf(tp_strictly_less_than,type,
strictly_less_than: $i > $i > $o ).
thf(tp_update_slb,type,
update_slb: $i > $i > $i ).
thf(1,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(2,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( strictly_less_than @ X @ W )
=> ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax29) ).
thf(3,axiom,
! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
thf(5,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(7,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(8,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(9,axiom,
! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
thf(10,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(12,axiom,
! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax19) ).
thf(14,axiom,
! [U: $i] : ( less_than @ bottom @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bottom_smallest) ).
thf(15,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(16,axiom,
! [U: $i] : ( less_than @ U @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(17,axiom,
! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
thf(18,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(19,conjecture,
! [U: $i] :
( ! [V: $i,W: $i,X: $i] :
( ( ( pair_in_list @ U @ V @ W )
& ( less_than @ X @ W ) )
=> ( pair_in_list @ ( update_slb @ U @ X ) @ V @ W ) )
=> ! [Y: $i,Z: $i,X1: $i,X2: $i,X3: $i] :
( ( ( pair_in_list @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ Y @ Z )
& ( less_than @ X1 @ Z ) )
=> ( pair_in_list @ ( update_slb @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ X1 ) @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l37_co) ).
thf(20,negated_conjecture,
( ( ! [U: $i] :
( ! [V: $i,W: $i,X: $i] :
( ( ( pair_in_list @ U @ V @ W )
& ( less_than @ X @ W ) )
=> ( pair_in_list @ ( update_slb @ U @ X ) @ V @ W ) )
=> ! [Y: $i,Z: $i,X1: $i,X2: $i,X3: $i] :
( ( ( pair_in_list @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ Y @ Z )
& ( less_than @ X1 @ Z ) )
=> ( pair_in_list @ ( update_slb @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ X1 ) @ Y @ Z ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[19]) ).
thf(21,plain,
( ( ! [U: $i] :
( ! [V: $i,W: $i,X: $i] :
( ( ( pair_in_list @ U @ V @ W )
& ( less_than @ X @ W ) )
=> ( pair_in_list @ ( update_slb @ U @ X ) @ V @ W ) )
=> ! [Y: $i,Z: $i,X1: $i,X2: $i,X3: $i] :
( ( ( pair_in_list @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ Y @ Z )
& ( less_than @ X1 @ Z ) )
=> ( pair_in_list @ ( update_slb @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ X1 ) @ Y @ Z ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[20]) ).
thf(22,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)],[1]) ).
thf(23,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( strictly_less_than @ X @ W )
=> ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(24,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(25,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(26,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(27,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)],[8]) ).
thf(28,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(29,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)],[10]) ).
thf(30,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(31,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(32,plain,
( ( ! [U: $i,V: $i] :
( ( strictly_less_than @ U @ V )
<=> ( ( less_than @ U @ V )
& ~ ( less_than @ V @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(33,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(34,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(35,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)],[18]) ).
thf(36,plain,
( ( ! [SY47: $i,SY48: $i,SY49: $i] :
( ( ( pair_in_list @ sK1_U @ SY47 @ SY48 )
& ( less_than @ SY49 @ SY48 ) )
=> ( pair_in_list @ ( update_slb @ sK1_U @ SY49 ) @ SY47 @ SY48 ) )
=> ! [SY50: $i,SY51: $i,SY52: $i,SY53: $i,SY54: $i] :
( ( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY53 @ SY54 ) ) @ SY50 @ SY51 )
& ( less_than @ SY52 @ SY51 ) )
=> ( pair_in_list @ ( update_slb @ ( insert_slb @ sK1_U @ ( pair @ SY53 @ SY54 ) ) @ SY52 ) @ SY50 @ SY51 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(37,plain,
( ( ! [SY47: $i,SY48: $i,SY49: $i] :
( ( ( pair_in_list @ sK1_U @ SY47 @ SY48 )
& ( less_than @ SY49 @ SY48 ) )
=> ( pair_in_list @ ( update_slb @ sK1_U @ SY49 ) @ SY47 @ SY48 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[36]) ).
thf(38,plain,
( ( ! [SY50: $i,SY51: $i,SY52: $i,SY53: $i,SY54: $i] :
( ( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY53 @ SY54 ) ) @ SY50 @ SY51 )
& ( less_than @ SY52 @ SY51 ) )
=> ( pair_in_list @ ( update_slb @ ( insert_slb @ sK1_U @ ( pair @ SY53 @ SY54 ) ) @ SY52 ) @ SY50 @ SY51 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[36]) ).
thf(39,plain,
( ( ~ ! [SY50: $i,SY51: $i,SY52: $i,SY53: $i,SY54: $i] :
( ( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY53 @ SY54 ) ) @ SY50 @ SY51 )
& ( less_than @ SY52 @ SY51 ) )
=> ( pair_in_list @ ( update_slb @ ( insert_slb @ sK1_U @ ( pair @ SY53 @ SY54 ) ) @ SY52 ) @ SY50 @ SY51 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[38]) ).
thf(40,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( less_than @ U @ V )
& ( less_than @ V @ W ) )
=> ( less_than @ U @ W ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(41,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(42,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(43,plain,
( ( ! [U: $i,V: $i] :
( ( strictly_less_than @ U @ V )
<=> ( ( less_than @ U @ V )
& ~ ( less_than @ V @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(44,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(45,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(46,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)],[29]) ).
thf(47,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(48,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)],[27]) ).
thf(49,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(50,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(51,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(52,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( strictly_less_than @ X @ W )
=> ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(53,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)],[22]) ).
thf(54,plain,
( ( ! [SY47: $i,SY48: $i,SY49: $i] :
( ( ( pair_in_list @ sK1_U @ SY47 @ SY48 )
& ( less_than @ SY49 @ SY48 ) )
=> ( pair_in_list @ ( update_slb @ sK1_U @ SY49 ) @ SY47 @ SY48 ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(55,plain,
( ( ~ ! [SY50: $i,SY51: $i,SY52: $i,SY53: $i,SY54: $i] :
( ( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY53 @ SY54 ) ) @ SY50 @ SY51 )
& ( less_than @ SY52 @ SY51 ) )
=> ( pair_in_list @ ( update_slb @ ( insert_slb @ sK1_U @ ( pair @ SY53 @ SY54 ) ) @ SY52 ) @ SY50 @ SY51 ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(56,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)],[43]) ).
thf(57,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)],[46]) ).
thf(58,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)],[53]) ).
thf(59,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( pair_in_list @ sK1_U @ SX0 @ SX1 )
| ~ ( less_than @ SX2 @ SX1 ) )
| ( pair_in_list @ ( update_slb @ sK1_U @ SX2 ) @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(60,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)],[48]) ).
thf(61,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SX3 @ SX4 ) ) @ SX0 @ SX1 )
| ~ ( less_than @ SX2 @ SX1 ) )
| ( pair_in_list @ ( update_slb @ ( insert_slb @ sK1_U @ ( pair @ SX3 @ SX4 ) ) @ SX2 ) @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(62,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( strictly_less_than @ SX3 @ SX2 )
| ( ( update_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 )
= ( insert_slb @ ( update_slb @ SX0 @ SX2 ) @ ( pair @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(63,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)],[40]) ).
thf(64,plain,
! [SV1: $i] :
( ( ! [SY55: $i] :
( ( less_than @ SV1 @ SY55 )
| ( less_than @ SY55 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(65,plain,
! [SV2: $i] :
( ( less_than @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(66,plain,
! [SV3: $i] :
( ( less_than @ bottom @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(67,plain,
! [SV4: $i] :
( ( ! [SY56: $i,SY57: $i] : ( isnonempty_slb @ ( insert_slb @ SV4 @ ( pair @ SY56 @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(68,plain,
! [SV5: $i] :
( ( ! [SY58: $i] :
~ ( pair_in_list @ create_slb @ SV5 @ SY58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(69,plain,
! [SV6: $i] :
( ( ! [SY59: $i,SY60: $i] :
( ( remove_slb @ ( insert_slb @ SV6 @ ( pair @ SY59 @ SY60 ) ) @ SY59 )
= SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(70,plain,
! [SV7: $i] :
( ( ! [SY61: $i,SY62: $i] :
( ( lookup_slb @ ( insert_slb @ SV7 @ ( pair @ SY61 @ SY62 ) ) @ SY61 )
= SY62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(71,plain,
! [SV8: $i] :
( ( ( update_slb @ create_slb @ SV8 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(72,plain,
! [SV9: $i] :
( ( ! [SY63: $i] :
~ ( ~ ( ~ ( strictly_less_than @ SV9 @ SY63 )
| ~ ( ~ ( less_than @ SV9 @ SY63 )
| ~ ~ ( less_than @ SY63 @ SV9 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV9 @ SY63 )
| ~ ~ ( less_than @ SY63 @ SV9 ) )
| ( strictly_less_than @ SV9 @ SY63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(73,plain,
! [SV10: $i] :
( ( ! [SY64: $i,SY65: $i,SY66: $i] :
~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV10 @ ( pair @ SY64 @ SY66 ) ) @ SY65 )
| ( contains_slb @ SV10 @ SY65 )
| ( SY64 = SY65 ) )
| ~ ( ~ ( ( contains_slb @ SV10 @ SY65 )
| ( SY64 = SY65 ) )
| ( contains_slb @ ( insert_slb @ SV10 @ ( pair @ SY64 @ SY66 ) ) @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(74,plain,
! [SV11: $i] :
( ( ! [SY67: $i,SY68: $i,SY69: $i] :
( ~ ( less_than @ SY68 @ SY69 )
| ( ( update_slb @ ( insert_slb @ SV11 @ ( pair @ SY67 @ SY69 ) ) @ SY68 )
= ( insert_slb @ ( update_slb @ SV11 @ SY68 ) @ ( pair @ SY67 @ SY69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(75,plain,
! [SV12: $i] :
( ( ! [SY70: $i,SY71: $i] :
( ~ ~ ( ~ ( pair_in_list @ sK1_U @ SV12 @ SY70 )
| ~ ( less_than @ SY71 @ SY70 ) )
| ( pair_in_list @ ( update_slb @ sK1_U @ SY71 ) @ SV12 @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(76,plain,
! [SV13: $i] :
( ( ! [SY72: $i,SY73: $i,SY74: $i,SY75: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SY72 @ SY74 ) ) @ SY73 @ SY75 )
| ( pair_in_list @ SV13 @ SY73 @ SY75 )
| ~ ( ( SY72 != SY73 )
| ( SY74 != SY75 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV13 @ SY73 @ SY75 )
| ~ ( ( SY72 != SY73 )
| ( SY74 != SY75 ) ) )
| ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SY72 @ SY74 ) ) @ SY73 @ SY75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(77,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SX3 @ SX4 ) ) @ SX0 @ SX1 )
| ~ ( less_than @ SX2 @ SX1 ) )
| ( pair_in_list @ ( update_slb @ ( insert_slb @ sK1_U @ ( pair @ SX3 @ SX4 ) ) @ SX2 ) @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(78,plain,
! [SV14: $i] :
( ( ! [SY76: $i,SY77: $i,SY78: $i] :
( ~ ( strictly_less_than @ SY78 @ SY77 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SY76 @ SY78 ) ) @ SY77 )
= ( insert_slb @ ( update_slb @ SV14 @ SY77 ) @ ( pair @ SY76 @ SY77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(79,plain,
! [SV15: $i] :
( ( ! [SY79: $i,SY80: $i] :
( ~ ~ ( ~ ( less_than @ SV15 @ SY79 )
| ~ ( less_than @ SY79 @ SY80 ) )
| ( less_than @ SV15 @ SY80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(80,plain,
! [SV16: $i,SV1: $i] :
( ( ( less_than @ SV1 @ SV16 )
| ( less_than @ SV16 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(81,plain,
! [SV17: $i,SV4: $i] :
( ( ! [SY81: $i] : ( isnonempty_slb @ ( insert_slb @ SV4 @ ( pair @ SV17 @ SY81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(82,plain,
! [SV18: $i,SV5: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV5 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(83,plain,
! [SV19: $i,SV6: $i] :
( ( ! [SY82: $i] :
( ( remove_slb @ ( insert_slb @ SV6 @ ( pair @ SV19 @ SY82 ) ) @ SV19 )
= SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(84,plain,
! [SV20: $i,SV7: $i] :
( ( ! [SY83: $i] :
( ( lookup_slb @ ( insert_slb @ SV7 @ ( pair @ SV20 @ SY83 ) ) @ SV20 )
= SY83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(85,plain,
! [SV21: $i,SV9: $i] :
( ( ~ ( ~ ( ~ ( strictly_less_than @ SV9 @ SV21 )
| ~ ( ~ ( less_than @ SV9 @ SV21 )
| ~ ~ ( less_than @ SV21 @ SV9 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV9 @ SV21 )
| ~ ~ ( less_than @ SV21 @ SV9 ) )
| ( strictly_less_than @ SV9 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(86,plain,
! [SV22: $i,SV10: $i] :
( ( ! [SY84: $i,SY85: $i] :
~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV10 @ ( pair @ SV22 @ SY85 ) ) @ SY84 )
| ( contains_slb @ SV10 @ SY84 )
| ( SV22 = SY84 ) )
| ~ ( ~ ( ( contains_slb @ SV10 @ SY84 )
| ( SV22 = SY84 ) )
| ( contains_slb @ ( insert_slb @ SV10 @ ( pair @ SV22 @ SY85 ) ) @ SY84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(87,plain,
! [SV23: $i,SV11: $i] :
( ( ! [SY86: $i,SY87: $i] :
( ~ ( less_than @ SY86 @ SY87 )
| ( ( update_slb @ ( insert_slb @ SV11 @ ( pair @ SV23 @ SY87 ) ) @ SY86 )
= ( insert_slb @ ( update_slb @ SV11 @ SY86 ) @ ( pair @ SV23 @ SY87 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(88,plain,
! [SV24: $i,SV12: $i] :
( ( ! [SY88: $i] :
( ~ ~ ( ~ ( pair_in_list @ sK1_U @ SV12 @ SV24 )
| ~ ( less_than @ SY88 @ SV24 ) )
| ( pair_in_list @ ( update_slb @ sK1_U @ SY88 ) @ SV12 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(89,plain,
! [SV25: $i,SV13: $i] :
( ( ! [SY89: $i,SY90: $i,SY91: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SY90 ) ) @ SY89 @ SY91 )
| ( pair_in_list @ SV13 @ SY89 @ SY91 )
| ~ ( ( SV25 != SY89 )
| ( SY90 != SY91 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV13 @ SY89 @ SY91 )
| ~ ( ( SV25 != SY89 )
| ( SY90 != SY91 ) ) )
| ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SY90 ) ) @ SY89 @ SY91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(90,plain,
( ( ! [SY92: $i,SY93: $i,SY94: $i,SY95: $i] :
( ~ ~ ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY94 @ SY95 ) ) @ sK2_SX0 @ SY92 )
| ~ ( less_than @ SY93 @ SY92 ) )
| ( pair_in_list @ ( update_slb @ ( insert_slb @ sK1_U @ ( pair @ SY94 @ SY95 ) ) @ SY93 ) @ sK2_SX0 @ SY92 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[77]) ).
thf(91,plain,
! [SV26: $i,SV14: $i] :
( ( ! [SY96: $i,SY97: $i] :
( ~ ( strictly_less_than @ SY97 @ SY96 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV26 @ SY97 ) ) @ SY96 )
= ( insert_slb @ ( update_slb @ SV14 @ SY96 ) @ ( pair @ SV26 @ SY96 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(92,plain,
! [SV27: $i,SV15: $i] :
( ( ! [SY98: $i] :
( ~ ~ ( ~ ( less_than @ SV15 @ SV27 )
| ~ ( less_than @ SV27 @ SY98 ) )
| ( less_than @ SV15 @ SY98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(93,plain,
! [SV16: $i,SV1: $i] :
( ( ( less_than @ SV1 @ SV16 )
= $true )
| ( ( less_than @ SV16 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(94,plain,
! [SV28: $i,SV17: $i,SV4: $i] :
( ( isnonempty_slb @ ( insert_slb @ SV4 @ ( pair @ SV17 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(95,plain,
! [SV18: $i,SV5: $i] :
( ( pair_in_list @ create_slb @ SV5 @ SV18 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(96,plain,
! [SV29: $i,SV19: $i,SV6: $i] :
( ( ( remove_slb @ ( insert_slb @ SV6 @ ( pair @ SV19 @ SV29 ) ) @ SV19 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(97,plain,
! [SV30: $i,SV20: $i,SV7: $i] :
( ( ( lookup_slb @ ( insert_slb @ SV7 @ ( pair @ SV20 @ SV30 ) ) @ SV20 )
= SV30 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(98,plain,
! [SV21: $i,SV9: $i] :
( ( ~ ( ~ ( strictly_less_than @ SV9 @ SV21 )
| ~ ( ~ ( less_than @ SV9 @ SV21 )
| ~ ~ ( less_than @ SV21 @ SV9 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV9 @ SV21 )
| ~ ~ ( less_than @ SV21 @ SV9 ) )
| ( strictly_less_than @ SV9 @ SV21 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(99,plain,
! [SV31: $i,SV22: $i,SV10: $i] :
( ( ! [SY99: $i] :
~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV10 @ ( pair @ SV22 @ SY99 ) ) @ SV31 )
| ( contains_slb @ SV10 @ SV31 )
| ( SV22 = SV31 ) )
| ~ ( ~ ( ( contains_slb @ SV10 @ SV31 )
| ( SV22 = SV31 ) )
| ( contains_slb @ ( insert_slb @ SV10 @ ( pair @ SV22 @ SY99 ) ) @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(100,plain,
! [SV23: $i,SV11: $i,SV32: $i] :
( ( ! [SY100: $i] :
( ~ ( less_than @ SV32 @ SY100 )
| ( ( update_slb @ ( insert_slb @ SV11 @ ( pair @ SV23 @ SY100 ) ) @ SV32 )
= ( insert_slb @ ( update_slb @ SV11 @ SV32 ) @ ( pair @ SV23 @ SY100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(101,plain,
! [SV33: $i,SV24: $i,SV12: $i] :
( ( ~ ~ ( ~ ( pair_in_list @ sK1_U @ SV12 @ SV24 )
| ~ ( less_than @ SV33 @ SV24 ) )
| ( pair_in_list @ ( update_slb @ sK1_U @ SV33 ) @ SV12 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(102,plain,
! [SV34: $i,SV25: $i,SV13: $i] :
( ( ! [SY101: $i,SY102: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SY101 ) ) @ SV34 @ SY102 )
| ( pair_in_list @ SV13 @ SV34 @ SY102 )
| ~ ( ( SV25 != SV34 )
| ( SY101 != SY102 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV13 @ SV34 @ SY102 )
| ~ ( ( SV25 != SV34 )
| ( SY101 != SY102 ) ) )
| ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SY101 ) ) @ SV34 @ SY102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(103,plain,
( ( ! [SY103: $i,SY104: $i,SY105: $i] :
( ~ ~ ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY104 @ SY105 ) ) @ sK2_SX0 @ sK3_SY92 )
| ~ ( less_than @ SY103 @ sK3_SY92 ) )
| ( pair_in_list @ ( update_slb @ ( insert_slb @ sK1_U @ ( pair @ SY104 @ SY105 ) ) @ SY103 ) @ sK2_SX0 @ sK3_SY92 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[90]) ).
thf(104,plain,
! [SV26: $i,SV14: $i,SV35: $i] :
( ( ! [SY106: $i] :
( ~ ( strictly_less_than @ SY106 @ SV35 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV26 @ SY106 ) ) @ SV35 )
= ( insert_slb @ ( update_slb @ SV14 @ SV35 ) @ ( pair @ SV26 @ SV35 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(105,plain,
! [SV36: $i,SV27: $i,SV15: $i] :
( ( ~ ~ ( ~ ( less_than @ SV15 @ SV27 )
| ~ ( less_than @ SV27 @ SV36 ) )
| ( less_than @ SV15 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(106,plain,
! [SV21: $i,SV9: $i] :
( ( ~ ( ~ ( strictly_less_than @ SV9 @ SV21 )
| ~ ( ~ ( less_than @ SV9 @ SV21 )
| ~ ~ ( less_than @ SV21 @ SV9 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(107,plain,
! [SV21: $i,SV9: $i] :
( ( ~ ( ~ ~ ( ~ ( less_than @ SV9 @ SV21 )
| ~ ~ ( less_than @ SV21 @ SV9 ) )
| ( strictly_less_than @ SV9 @ SV21 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(108,plain,
! [SV31: $i,SV37: $i,SV22: $i,SV10: $i] :
( ( ~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV10 @ ( pair @ SV22 @ SV37 ) ) @ SV31 )
| ( contains_slb @ SV10 @ SV31 )
| ( SV22 = SV31 ) )
| ~ ( ~ ( ( contains_slb @ SV10 @ SV31 )
| ( SV22 = SV31 ) )
| ( contains_slb @ ( insert_slb @ SV10 @ ( pair @ SV22 @ SV37 ) ) @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(109,plain,
! [SV23: $i,SV11: $i,SV38: $i,SV32: $i] :
( ( ~ ( less_than @ SV32 @ SV38 )
| ( ( update_slb @ ( insert_slb @ SV11 @ ( pair @ SV23 @ SV38 ) ) @ SV32 )
= ( insert_slb @ ( update_slb @ SV11 @ SV32 ) @ ( pair @ SV23 @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(110,plain,
! [SV33: $i,SV24: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( pair_in_list @ sK1_U @ SV12 @ SV24 )
| ~ ( less_than @ SV33 @ SV24 ) ) )
= $true )
| ( ( pair_in_list @ ( update_slb @ sK1_U @ SV33 ) @ SV12 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(111,plain,
! [SV34: $i,SV39: $i,SV25: $i,SV13: $i] :
( ( ! [SY107: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SY107 )
| ( pair_in_list @ SV13 @ SV34 @ SY107 )
| ~ ( ( SV25 != SV34 )
| ( SV39 != SY107 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV13 @ SV34 @ SY107 )
| ~ ( ( SV25 != SV34 )
| ( SV39 != SY107 ) ) )
| ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SY107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(112,plain,
( ( ! [SY108: $i,SY109: $i] :
( ~ ~ ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY108 @ SY109 ) ) @ sK2_SX0 @ sK3_SY92 )
| ~ ( less_than @ sK4_SY103 @ sK3_SY92 ) )
| ( pair_in_list @ ( update_slb @ ( insert_slb @ sK1_U @ ( pair @ SY108 @ SY109 ) ) @ sK4_SY103 ) @ sK2_SX0 @ sK3_SY92 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[103]) ).
thf(113,plain,
! [SV26: $i,SV14: $i,SV35: $i,SV40: $i] :
( ( ~ ( strictly_less_than @ SV40 @ SV35 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV26 @ SV40 ) ) @ SV35 )
= ( insert_slb @ ( update_slb @ SV14 @ SV35 ) @ ( pair @ SV26 @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(114,plain,
! [SV36: $i,SV27: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( less_than @ SV15 @ SV27 )
| ~ ( less_than @ SV27 @ SV36 ) ) )
= $true )
| ( ( less_than @ SV15 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(115,plain,
! [SV21: $i,SV9: $i] :
( ( ~ ( strictly_less_than @ SV9 @ SV21 )
| ~ ( ~ ( less_than @ SV9 @ SV21 )
| ~ ~ ( less_than @ SV21 @ SV9 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(116,plain,
! [SV21: $i,SV9: $i] :
( ( ~ ~ ( ~ ( less_than @ SV9 @ SV21 )
| ~ ~ ( less_than @ SV21 @ SV9 ) )
| ( strictly_less_than @ SV9 @ SV21 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(117,plain,
! [SV31: $i,SV37: $i,SV22: $i,SV10: $i] :
( ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV10 @ ( pair @ SV22 @ SV37 ) ) @ SV31 )
| ( contains_slb @ SV10 @ SV31 )
| ( SV22 = SV31 ) )
| ~ ( ~ ( ( contains_slb @ SV10 @ SV31 )
| ( SV22 = SV31 ) )
| ( contains_slb @ ( insert_slb @ SV10 @ ( pair @ SV22 @ SV37 ) ) @ SV31 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(118,plain,
! [SV23: $i,SV11: $i,SV38: $i,SV32: $i] :
( ( ( ~ ( less_than @ SV32 @ SV38 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV11 @ ( pair @ SV23 @ SV38 ) ) @ SV32 )
= ( insert_slb @ ( update_slb @ SV11 @ SV32 ) @ ( pair @ SV23 @ SV38 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(119,plain,
! [SV33: $i,SV24: $i,SV12: $i] :
( ( ( ~ ( ~ ( pair_in_list @ sK1_U @ SV12 @ SV24 )
| ~ ( less_than @ SV33 @ SV24 ) ) )
= $false )
| ( ( pair_in_list @ ( update_slb @ sK1_U @ SV33 ) @ SV12 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(120,plain,
! [SV41: $i,SV34: $i,SV39: $i,SV25: $i,SV13: $i] :
( ( ~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 )
| ( pair_in_list @ SV13 @ SV34 @ SV41 )
| ~ ( ( SV25 != SV34 )
| ( SV39 != SV41 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV13 @ SV34 @ SV41 )
| ~ ( ( SV25 != SV34 )
| ( SV39 != SV41 ) ) )
| ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(121,plain,
( ( ! [SY110: $i] :
( ~ ~ ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY108 @ SY110 ) ) @ sK2_SX0 @ sK3_SY92 )
| ~ ( less_than @ sK4_SY103 @ sK3_SY92 ) )
| ( pair_in_list @ ( update_slb @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY108 @ SY110 ) ) @ sK4_SY103 ) @ sK2_SX0 @ sK3_SY92 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[112]) ).
thf(122,plain,
! [SV26: $i,SV14: $i,SV35: $i,SV40: $i] :
( ( ( ~ ( strictly_less_than @ SV40 @ SV35 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV26 @ SV40 ) ) @ SV35 )
= ( insert_slb @ ( update_slb @ SV14 @ SV35 ) @ ( pair @ SV26 @ SV35 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(123,plain,
! [SV36: $i,SV27: $i,SV15: $i] :
( ( ( ~ ( ~ ( less_than @ SV15 @ SV27 )
| ~ ( less_than @ SV27 @ SV36 ) ) )
= $false )
| ( ( less_than @ SV15 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(124,plain,
! [SV21: $i,SV9: $i] :
( ( ( ~ ( strictly_less_than @ SV9 @ SV21 ) )
= $true )
| ( ( ~ ( ~ ( less_than @ SV9 @ SV21 )
| ~ ~ ( less_than @ SV21 @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(125,plain,
! [SV21: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( less_than @ SV9 @ SV21 )
| ~ ~ ( less_than @ SV21 @ SV9 ) ) )
= $true )
| ( ( strictly_less_than @ SV9 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(126,plain,
! [SV31: $i,SV37: $i,SV22: $i,SV10: $i] :
( ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV10 @ ( pair @ SV22 @ SV37 ) ) @ SV31 )
| ( contains_slb @ SV10 @ SV31 )
| ( SV22 = SV31 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(127,plain,
! [SV37: $i,SV22: $i,SV31: $i,SV10: $i] :
( ( ~ ( ~ ( ( contains_slb @ SV10 @ SV31 )
| ( SV22 = SV31 ) )
| ( contains_slb @ ( insert_slb @ SV10 @ ( pair @ SV22 @ SV37 ) ) @ SV31 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(128,plain,
! [SV23: $i,SV11: $i,SV38: $i,SV32: $i] :
( ( ( less_than @ SV32 @ SV38 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV11 @ ( pair @ SV23 @ SV38 ) ) @ SV32 )
= ( insert_slb @ ( update_slb @ SV11 @ SV32 ) @ ( pair @ SV23 @ SV38 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(129,plain,
! [SV33: $i,SV24: $i,SV12: $i] :
( ( ( ~ ( pair_in_list @ sK1_U @ SV12 @ SV24 )
| ~ ( less_than @ SV33 @ SV24 ) )
= $true )
| ( ( pair_in_list @ ( update_slb @ sK1_U @ SV33 ) @ SV12 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(130,plain,
! [SV41: $i,SV34: $i,SV39: $i,SV25: $i,SV13: $i] :
( ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 )
| ( pair_in_list @ SV13 @ SV34 @ SV41 )
| ~ ( ( SV25 != SV34 )
| ( SV39 != SV41 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV13 @ SV34 @ SV41 )
| ~ ( ( SV25 != SV34 )
| ( SV39 != SV41 ) ) )
| ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(131,plain,
( ( ~ ~ ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY108 @ sK6_SY110 ) ) @ sK2_SX0 @ sK3_SY92 )
| ~ ( less_than @ sK4_SY103 @ sK3_SY92 ) )
| ( pair_in_list @ ( update_slb @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY108 @ sK6_SY110 ) ) @ sK4_SY103 ) @ sK2_SX0 @ sK3_SY92 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[121]) ).
thf(132,plain,
! [SV26: $i,SV14: $i,SV35: $i,SV40: $i] :
( ( ( strictly_less_than @ SV40 @ SV35 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV26 @ SV40 ) ) @ SV35 )
= ( insert_slb @ ( update_slb @ SV14 @ SV35 ) @ ( pair @ SV26 @ SV35 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(133,plain,
! [SV36: $i,SV27: $i,SV15: $i] :
( ( ( ~ ( less_than @ SV15 @ SV27 )
| ~ ( less_than @ SV27 @ SV36 ) )
= $true )
| ( ( less_than @ SV15 @ SV36 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(134,plain,
! [SV21: $i,SV9: $i] :
( ( ( strictly_less_than @ SV9 @ SV21 )
= $false )
| ( ( ~ ( ~ ( less_than @ SV9 @ SV21 )
| ~ ~ ( less_than @ SV21 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(135,plain,
! [SV21: $i,SV9: $i] :
( ( ( ~ ( ~ ( less_than @ SV9 @ SV21 )
| ~ ~ ( less_than @ SV21 @ SV9 ) ) )
= $false )
| ( ( strictly_less_than @ SV9 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(136,plain,
! [SV31: $i,SV37: $i,SV22: $i,SV10: $i] :
( ( ~ ( contains_slb @ ( insert_slb @ SV10 @ ( pair @ SV22 @ SV37 ) ) @ SV31 )
| ( contains_slb @ SV10 @ SV31 )
| ( SV22 = SV31 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(137,plain,
! [SV37: $i,SV22: $i,SV31: $i,SV10: $i] :
( ( ~ ( ( contains_slb @ SV10 @ SV31 )
| ( SV22 = SV31 ) )
| ( contains_slb @ ( insert_slb @ SV10 @ ( pair @ SV22 @ SV37 ) ) @ SV31 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(138,plain,
! [SV33: $i,SV24: $i,SV12: $i] :
( ( ( ~ ( pair_in_list @ sK1_U @ SV12 @ SV24 ) )
= $true )
| ( ( ~ ( less_than @ SV33 @ SV24 ) )
= $true )
| ( ( pair_in_list @ ( update_slb @ sK1_U @ SV33 ) @ SV12 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(139,plain,
! [SV41: $i,SV34: $i,SV39: $i,SV25: $i,SV13: $i] :
( ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 )
| ( pair_in_list @ SV13 @ SV34 @ SV41 )
| ~ ( ( SV25 != SV34 )
| ( SV39 != SV41 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(140,plain,
! [SV39: $i,SV25: $i,SV41: $i,SV34: $i,SV13: $i] :
( ( ~ ( ~ ( ( pair_in_list @ SV13 @ SV34 @ SV41 )
| ~ ( ( SV25 != SV34 )
| ( SV39 != SV41 ) ) )
| ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(141,plain,
( ( ~ ~ ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY108 @ sK6_SY110 ) ) @ sK2_SX0 @ sK3_SY92 )
| ~ ( less_than @ sK4_SY103 @ sK3_SY92 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(142,plain,
( ( pair_in_list @ ( update_slb @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY108 @ sK6_SY110 ) ) @ sK4_SY103 ) @ sK2_SX0 @ sK3_SY92 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(143,plain,
! [SV36: $i,SV27: $i,SV15: $i] :
( ( ( ~ ( less_than @ SV15 @ SV27 ) )
= $true )
| ( ( ~ ( less_than @ SV27 @ SV36 ) )
= $true )
| ( ( less_than @ SV15 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(144,plain,
! [SV21: $i,SV9: $i] :
( ( ( ~ ( less_than @ SV9 @ SV21 )
| ~ ~ ( less_than @ SV21 @ SV9 ) )
= $false )
| ( ( strictly_less_than @ SV9 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(145,plain,
! [SV21: $i,SV9: $i] :
( ( ( ~ ( less_than @ SV9 @ SV21 )
| ~ ~ ( less_than @ SV21 @ SV9 ) )
= $true )
| ( ( strictly_less_than @ SV9 @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(146,plain,
! [SV31: $i,SV37: $i,SV22: $i,SV10: $i] :
( ( ( ~ ( contains_slb @ ( insert_slb @ SV10 @ ( pair @ SV22 @ SV37 ) ) @ SV31 ) )
= $true )
| ( ( ( contains_slb @ SV10 @ SV31 )
| ( SV22 = SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(147,plain,
! [SV37: $i,SV22: $i,SV31: $i,SV10: $i] :
( ( ( ~ ( ( contains_slb @ SV10 @ SV31 )
| ( SV22 = SV31 ) ) )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV10 @ ( pair @ SV22 @ SV37 ) ) @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(148,plain,
! [SV33: $i,SV24: $i,SV12: $i] :
( ( ( pair_in_list @ sK1_U @ SV12 @ SV24 )
= $false )
| ( ( ~ ( less_than @ SV33 @ SV24 ) )
= $true )
| ( ( pair_in_list @ ( update_slb @ sK1_U @ SV33 ) @ SV12 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(149,plain,
! [SV41: $i,SV34: $i,SV39: $i,SV25: $i,SV13: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 )
| ( pair_in_list @ SV13 @ SV34 @ SV41 )
| ~ ( ( SV25 != SV34 )
| ( SV39 != SV41 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(150,plain,
! [SV39: $i,SV25: $i,SV41: $i,SV34: $i,SV13: $i] :
( ( ~ ( ( pair_in_list @ SV13 @ SV34 @ SV41 )
| ~ ( ( SV25 != SV34 )
| ( SV39 != SV41 ) ) )
| ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(151,plain,
( ( ~ ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY108 @ sK6_SY110 ) ) @ sK2_SX0 @ sK3_SY92 )
| ~ ( less_than @ sK4_SY103 @ sK3_SY92 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(152,plain,
! [SV36: $i,SV27: $i,SV15: $i] :
( ( ( less_than @ SV15 @ SV27 )
= $false )
| ( ( ~ ( less_than @ SV27 @ SV36 ) )
= $true )
| ( ( less_than @ SV15 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(153,plain,
! [SV21: $i,SV9: $i] :
( ( ( ~ ( less_than @ SV9 @ SV21 ) )
= $false )
| ( ( strictly_less_than @ SV9 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(154,plain,
! [SV9: $i,SV21: $i] :
( ( ( ~ ~ ( less_than @ SV21 @ SV9 ) )
= $false )
| ( ( strictly_less_than @ SV9 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(155,plain,
! [SV21: $i,SV9: $i] :
( ( ( ~ ( less_than @ SV9 @ SV21 ) )
= $true )
| ( ( ~ ~ ( less_than @ SV21 @ SV9 ) )
= $true )
| ( ( strictly_less_than @ SV9 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(156,plain,
! [SV31: $i,SV37: $i,SV22: $i,SV10: $i] :
( ( ( contains_slb @ ( insert_slb @ SV10 @ ( pair @ SV22 @ SV37 ) ) @ SV31 )
= $false )
| ( ( ( contains_slb @ SV10 @ SV31 )
| ( SV22 = SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(157,plain,
! [SV37: $i,SV22: $i,SV31: $i,SV10: $i] :
( ( ( ( contains_slb @ SV10 @ SV31 )
| ( SV22 = SV31 ) )
= $false )
| ( ( contains_slb @ ( insert_slb @ SV10 @ ( pair @ SV22 @ SV37 ) ) @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(158,plain,
! [SV12: $i,SV24: $i,SV33: $i] :
( ( ( less_than @ SV33 @ SV24 )
= $false )
| ( ( pair_in_list @ sK1_U @ SV12 @ SV24 )
= $false )
| ( ( pair_in_list @ ( update_slb @ sK1_U @ SV33 ) @ SV12 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(159,plain,
! [SV41: $i,SV34: $i,SV39: $i,SV25: $i,SV13: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 ) )
= $true )
| ( ( ( pair_in_list @ SV13 @ SV34 @ SV41 )
| ~ ( ( SV25 != SV34 )
| ( SV39 != SV41 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(160,plain,
! [SV39: $i,SV25: $i,SV41: $i,SV34: $i,SV13: $i] :
( ( ( ~ ( ( pair_in_list @ SV13 @ SV34 @ SV41 )
| ~ ( ( SV25 != SV34 )
| ( SV39 != SV41 ) ) ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(161,plain,
( ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY108 @ sK6_SY110 ) ) @ sK2_SX0 @ sK3_SY92 )
| ~ ( less_than @ sK4_SY103 @ sK3_SY92 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(162,plain,
! [SV15: $i,SV36: $i,SV27: $i] :
( ( ( less_than @ SV27 @ SV36 )
= $false )
| ( ( less_than @ SV15 @ SV27 )
= $false )
| ( ( less_than @ SV15 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(163,plain,
! [SV21: $i,SV9: $i] :
( ( ( less_than @ SV9 @ SV21 )
= $true )
| ( ( strictly_less_than @ SV9 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(164,plain,
! [SV9: $i,SV21: $i] :
( ( ( ~ ( less_than @ SV21 @ SV9 ) )
= $true )
| ( ( strictly_less_than @ SV9 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(165,plain,
! [SV21: $i,SV9: $i] :
( ( ( less_than @ SV9 @ SV21 )
= $false )
| ( ( ~ ~ ( less_than @ SV21 @ SV9 ) )
= $true )
| ( ( strictly_less_than @ SV9 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(166,plain,
! [SV37: $i,SV22: $i,SV31: $i,SV10: $i] :
( ( ( contains_slb @ SV10 @ SV31 )
= $true )
| ( ( SV22 = SV31 )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV10 @ ( pair @ SV22 @ SV37 ) ) @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(167,plain,
! [SV37: $i,SV22: $i,SV31: $i,SV10: $i] :
( ( ( contains_slb @ SV10 @ SV31 )
= $false )
| ( ( contains_slb @ ( insert_slb @ SV10 @ ( pair @ SV22 @ SV37 ) ) @ SV31 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(168,plain,
! [SV37: $i,SV10: $i,SV31: $i,SV22: $i] :
( ( ( SV22 = SV31 )
= $false )
| ( ( contains_slb @ ( insert_slb @ SV10 @ ( pair @ SV22 @ SV37 ) ) @ SV31 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(169,plain,
! [SV41: $i,SV34: $i,SV39: $i,SV25: $i,SV13: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 )
= $false )
| ( ( ( pair_in_list @ SV13 @ SV34 @ SV41 )
| ~ ( ( SV25 != SV34 )
| ( SV39 != SV41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(170,plain,
! [SV39: $i,SV25: $i,SV41: $i,SV34: $i,SV13: $i] :
( ( ( ( pair_in_list @ SV13 @ SV34 @ SV41 )
| ~ ( ( SV25 != SV34 )
| ( SV39 != SV41 ) ) )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(171,plain,
( ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY108 @ sK6_SY110 ) ) @ sK2_SX0 @ sK3_SY92 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(172,plain,
( ( ~ ( less_than @ sK4_SY103 @ sK3_SY92 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(173,plain,
! [SV9: $i,SV21: $i] :
( ( ( less_than @ SV21 @ SV9 )
= $false )
| ( ( strictly_less_than @ SV9 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(174,plain,
! [SV9: $i,SV21: $i] :
( ( ( ~ ( less_than @ SV21 @ SV9 ) )
= $false )
| ( ( less_than @ SV9 @ SV21 )
= $false )
| ( ( strictly_less_than @ SV9 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(175,plain,
! [SV39: $i,SV25: $i,SV41: $i,SV34: $i,SV13: $i] :
( ( ( pair_in_list @ SV13 @ SV34 @ SV41 )
= $true )
| ( ( ~ ( ( SV25 != SV34 )
| ( SV39 != SV41 ) ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(176,plain,
! [SV39: $i,SV25: $i,SV41: $i,SV34: $i,SV13: $i] :
( ( ( pair_in_list @ SV13 @ SV34 @ SV41 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(177,plain,
! [SV13: $i,SV41: $i,SV39: $i,SV34: $i,SV25: $i] :
( ( ( ~ ( ( SV25 != SV34 )
| ( SV39 != SV41 ) ) )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(178,plain,
( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY108 @ sK6_SY110 ) ) @ sK2_SX0 @ sK3_SY92 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(179,plain,
( ( less_than @ sK4_SY103 @ sK3_SY92 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(180,plain,
! [SV9: $i,SV21: $i] :
( ( ( less_than @ SV21 @ SV9 )
= $true )
| ( ( less_than @ SV9 @ SV21 )
= $false )
| ( ( strictly_less_than @ SV9 @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(181,plain,
! [SV13: $i,SV41: $i,SV39: $i,SV34: $i,SV25: $i] :
( ( ( ( SV25 != SV34 )
| ( SV39 != SV41 ) )
= $false )
| ( ( pair_in_list @ SV13 @ SV34 @ SV41 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(182,plain,
! [SV13: $i,SV41: $i,SV39: $i,SV34: $i,SV25: $i] :
( ( ( ( SV25 != SV34 )
| ( SV39 != SV41 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(183,plain,
! [SV39: $i,SV41: $i,SV13: $i,SV34: $i,SV25: $i] :
( ( ( SV25 != SV34 )
= $false )
| ( ( pair_in_list @ SV13 @ SV34 @ SV41 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(184,plain,
! [SV25: $i,SV34: $i,SV13: $i,SV41: $i,SV39: $i] :
( ( ( SV39 != SV41 )
= $false )
| ( ( pair_in_list @ SV13 @ SV34 @ SV41 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(185,plain,
! [SV13: $i,SV41: $i,SV39: $i,SV34: $i,SV25: $i] :
( ( ( SV25 != SV34 )
= $true )
| ( ( SV39 != SV41 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(186,plain,
! [SV39: $i,SV41: $i,SV13: $i,SV34: $i,SV25: $i] :
( ( ( SV25 = SV34 )
= $true )
| ( ( pair_in_list @ SV13 @ SV34 @ SV41 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(187,plain,
! [SV25: $i,SV34: $i,SV13: $i,SV41: $i,SV39: $i] :
( ( ( SV39 = SV41 )
= $true )
| ( ( pair_in_list @ SV13 @ SV34 @ SV41 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(188,plain,
! [SV13: $i,SV41: $i,SV39: $i,SV34: $i,SV25: $i] :
( ( ( SV25 = SV34 )
= $false )
| ( ( SV39 != SV41 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(189,plain,
! [SV13: $i,SV34: $i,SV25: $i,SV41: $i,SV39: $i] :
( ( ( SV39 = SV41 )
= $false )
| ( ( SV25 = SV34 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV13 @ ( pair @ SV25 @ SV39 ) ) @ SV34 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(190,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[65,189,187,186,180,179,178,176,173,168,167,166,163,162,158,142,132,128,97,96,95,94,93,71,66]) ).
thf(191,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[190]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV401+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
% 0.07/0.20 % Computer : n001.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Oct 6 16:33:39 UTC 2026
% 0.07/0.21 % CPUTime :
% 0.07/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.37/1.74
% 8.37/1.74 No.of.Axioms: 14
% 8.37/1.74
% 8.37/1.74 Length.of.Defs: 0
% 8.37/1.74
% 8.37/1.74 Contains.Choice.Funs: false
% 8.37/1.74 .......
% 8.37/1.74
% 8.37/1.74 ********************************
% 8.37/1.74 * All subproblems solved! *
% 8.37/1.74 ********************************
% 8.37/1.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:15,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:190,loop_count:0,foatp_calls:1,translation:fof_full)
% 8.37/1.74
% 8.37/1.74 %**** Beginning of derivation protocol ****
% 8.37/1.74 % SZS output start CNFRefutation
% See solution above
% 8.37/1.74
% 8.37/1.74 %**** End of derivation protocol ****
% 8.37/1.74 %**** no. of clauses in derivation: 187 ****
% 8.37/1.74 %**** clause counter: 190 ****
% 8.37/1.74
% 8.37/1.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:15,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:190,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------