TSTP Solution File: SWV403+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SWV403+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 20:12:20 EDT 2022
% Result : Theorem 0.46s 0.71s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 37
% Syntax : Number of formulae : 256 ( 177 unt; 18 typ; 0 def)
% Number of atoms : 1255 ( 473 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 3177 ( 392 ~; 369 |; 39 &;2346 @)
% ( 6 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 10 con; 0-3 aty)
% Number of variables : 870 ( 0 ^ 870 !; 0 ?; 870 :)
% 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_SY59,type,
sK2_SY59: $i ).
thf(tp_sK3_SY64,type,
sK3_SY64: $i ).
thf(tp_sK4_SY68,type,
sK4_SY68: $i ).
thf(tp_sK5_SY71,type,
sK5_SY71: $i ).
thf(tp_sK6_SY73,type,
sK6_SY73: $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(4,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != W )
& ( contains_slb @ U @ W ) )
=> ( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( lookup_slb @ U @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax27) ).
thf(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(6,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != W )
& ( contains_slb @ U @ W ) )
=> ( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( remove_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).
thf(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(11,axiom,
! [U: $i] :
~ ( contains_slb @ create_slb @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
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(13,axiom,
~ ( isnonempty_slb @ create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
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 )
& ( strictly_less_than @ W @ X ) )
=> ( pair_in_list @ ( update_slb @ U @ X ) @ V @ X ) )
=> ! [Y: $i,Z: $i,X1: $i,X2: $i,X3: $i] :
( ( ( pair_in_list @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ Y @ Z )
& ( strictly_less_than @ Z @ X1 ) )
=> ( pair_in_list @ ( update_slb @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ X1 ) @ Y @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l39_co) ).
thf(20,negated_conjecture,
( ( ! [U: $i] :
( ! [V: $i,W: $i,X: $i] :
( ( ( pair_in_list @ U @ V @ W )
& ( strictly_less_than @ W @ X ) )
=> ( pair_in_list @ ( update_slb @ U @ X ) @ V @ X ) )
=> ! [Y: $i,Z: $i,X1: $i,X2: $i,X3: $i] :
( ( ( pair_in_list @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ Y @ Z )
& ( strictly_less_than @ Z @ X1 ) )
=> ( pair_in_list @ ( update_slb @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ X1 ) @ Y @ X1 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[19]) ).
thf(21,plain,
( ( ! [U: $i] :
( ! [V: $i,W: $i,X: $i] :
( ( ( pair_in_list @ U @ V @ W )
& ( strictly_less_than @ W @ X ) )
=> ( pair_in_list @ ( update_slb @ U @ X ) @ V @ X ) )
=> ! [Y: $i,Z: $i,X1: $i,X2: $i,X3: $i] :
( ( ( pair_in_list @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ Y @ Z )
& ( strictly_less_than @ Z @ X1 ) )
=> ( pair_in_list @ ( update_slb @ ( insert_slb @ U @ ( pair @ X2 @ X3 ) ) @ X1 ) @ Y @ X1 ) ) ) )
= $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,X: $i] :
( ( ( V != W )
& ( contains_slb @ U @ W ) )
=> ( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( lookup_slb @ U @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(26,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(27,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( V != W )
& ( contains_slb @ U @ W ) )
=> ( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( remove_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(28,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(29,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(30,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(31,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(32,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(33,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(34,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(35,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(36,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(37,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(38,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(39,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(40,plain,
( ( ! [SY56: $i,SY57: $i,SY58: $i] :
( ( ( pair_in_list @ sK1_U @ SY56 @ SY57 )
& ( strictly_less_than @ SY57 @ SY58 ) )
=> ( pair_in_list @ ( update_slb @ sK1_U @ SY58 ) @ SY56 @ SY58 ) )
=> ! [SY59: $i,SY60: $i,SY61: $i,SY62: $i,SY63: $i] :
( ( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY62 @ SY63 ) ) @ SY59 @ SY60 )
& ( strictly_less_than @ SY60 @ SY61 ) )
=> ( pair_in_list @ ( update_slb @ ( insert_slb @ sK1_U @ ( pair @ SY62 @ SY63 ) ) @ SY61 ) @ SY59 @ SY61 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(41,plain,
( ( ! [SY56: $i,SY57: $i,SY58: $i] :
( ( ( pair_in_list @ sK1_U @ SY56 @ SY57 )
& ( strictly_less_than @ SY57 @ SY58 ) )
=> ( pair_in_list @ ( update_slb @ sK1_U @ SY58 ) @ SY56 @ SY58 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[40]) ).
thf(42,plain,
( ( ! [SY59: $i,SY60: $i,SY61: $i,SY62: $i,SY63: $i] :
( ( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY62 @ SY63 ) ) @ SY59 @ SY60 )
& ( strictly_less_than @ SY60 @ SY61 ) )
=> ( pair_in_list @ ( update_slb @ ( insert_slb @ sK1_U @ ( pair @ SY62 @ SY63 ) ) @ SY61 ) @ SY59 @ SY61 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[40]) ).
thf(43,plain,
( ( ~ ! [SY59: $i,SY60: $i,SY61: $i,SY62: $i,SY63: $i] :
( ( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY62 @ SY63 ) ) @ SY59 @ SY60 )
& ( strictly_less_than @ SY60 @ SY61 ) )
=> ( pair_in_list @ ( update_slb @ ( insert_slb @ sK1_U @ ( pair @ SY62 @ SY63 ) ) @ SY61 ) @ SY59 @ SY61 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[42]) ).
thf(44,plain,
( ( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY71 @ sK6_SY73 ) ) @ sK2_SY59 @ sK3_SY64 )
& ( strictly_less_than @ sK3_SY64 @ sK4_SY68 )
& ~ ( pair_in_list @ ( update_slb @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY71 @ sK6_SY73 ) ) @ sK4_SY68 ) @ sK2_SY59 @ sK4_SY68 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(45,plain,
( ( ! [SY56: $i,SY57: $i,SY58: $i] :
( ~ ( pair_in_list @ sK1_U @ SY56 @ SY57 )
| ~ ( strictly_less_than @ SY57 @ SY58 )
| ( pair_in_list @ ( update_slb @ sK1_U @ SY58 ) @ SY56 @ SY58 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(46,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( less_than @ W @ X )
| ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(47,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( strictly_less_than @ X @ W )
| ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(48,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( V = W )
| ~ ( contains_slb @ U @ W )
| ! [X: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( lookup_slb @ U @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(49,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( V = W )
| ~ ( contains_slb @ U @ W )
| ! [X: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( remove_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(50,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
| ( V = W )
| ( pair_in_list @ U @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
| ( X = Y )
| ( pair_in_list @ U @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ( V != W )
| ( X != Y )
| ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ U @ W @ Y )
| ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(51,plain,
( ( ! [U: $i,V: $i] :
( ! [W: $i] :
( ! [X: $i] :
~ ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
| ( V = W )
| ( contains_slb @ U @ W ) )
& ! [W: $i] :
( ( V != W )
| ! [X: $i] : ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W ) )
& ! [W: $i] :
( ~ ( contains_slb @ U @ W )
| ! [X: $i] : ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(52,plain,
( ( ! [U: $i,V: $i] :
( ~ ( less_than @ U @ V )
| ( less_than @ V @ U )
| ( strictly_less_than @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( strictly_less_than @ U @ V )
| ( less_than @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( strictly_less_than @ U @ V )
| ~ ( less_than @ V @ U ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(53,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( less_than @ U @ V )
| ~ ( less_than @ V @ W )
| ( less_than @ U @ W ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(54,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( less_than @ U @ V )
| ~ ( less_than @ V @ W )
| ( less_than @ U @ W ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(55,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(56,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(57,plain,
( ( ! [U: $i,V: $i] :
( ~ ( less_than @ U @ V )
| ( less_than @ V @ U )
| ( strictly_less_than @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( strictly_less_than @ U @ V )
| ( less_than @ U @ V ) )
& ! [U: $i,V: $i] :
( ~ ( strictly_less_than @ U @ V )
| ~ ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(58,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(59,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(60,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(61,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(62,plain,
( ( ! [U: $i,V: $i] :
( ! [W: $i] :
( ! [X: $i] :
~ ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
| ( V = W )
| ( contains_slb @ U @ W ) )
& ! [W: $i] :
( ( V != W )
| ! [X: $i] : ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W ) )
& ! [W: $i] :
( ~ ( contains_slb @ U @ W )
| ! [X: $i] : ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(63,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(64,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
| ( V = W )
| ( pair_in_list @ U @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y )
| ( X = Y )
| ( pair_in_list @ U @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ( V != W )
| ( X != Y )
| ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y ) )
& ! [X: $i,Y: $i] :
( ~ ( pair_in_list @ U @ W @ Y )
| ( pair_in_list @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(65,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(66,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( V = W )
| ~ ( contains_slb @ U @ W )
| ! [X: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( remove_slb @ U @ W ) @ ( pair @ V @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(67,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(68,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( V = W )
| ~ ( contains_slb @ U @ W )
| ! [X: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( lookup_slb @ U @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(69,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(70,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( strictly_less_than @ X @ W )
| ( ( update_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
= ( insert_slb @ ( update_slb @ U @ W ) @ ( pair @ V @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(71,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)],[46]) ).
thf(72,plain,
( ( ! [SY56: $i,SY57: $i,SY58: $i] :
( ~ ( pair_in_list @ sK1_U @ SY56 @ SY57 )
| ~ ( strictly_less_than @ SY57 @ SY58 )
| ( pair_in_list @ ( update_slb @ sK1_U @ SY58 ) @ SY56 @ SY58 ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(73,plain,
( ( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY71 @ sK6_SY73 ) ) @ sK2_SY59 @ sK3_SY64 )
& ( strictly_less_than @ sK3_SY64 @ sK4_SY68 )
& ~ ( pair_in_list @ ( update_slb @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY71 @ sK6_SY73 ) ) @ sK4_SY68 ) @ sK2_SY59 @ sK4_SY68 ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(74,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 )
| ( SX1 = SX2 )
| ( pair_in_list @ SX0 @ SX2 @ SX4 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 )
| ( SX3 = SX4 )
| ( pair_in_list @ SX0 @ SX2 @ SX4 ) ) )
| ~ ~ ( ~ ! [SX3: $i,SX4: $i] :
( ( SX1 != SX2 )
| ( SX3 != SX4 )
| ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 ) )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ( pair_in_list @ SX0 @ SX2 @ SX4 )
| ( pair_in_list @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(75,plain,
( ( ~ ( ~ ~ ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY71 @ sK6_SY73 ) ) @ sK2_SY59 @ sK3_SY64 )
| ~ ( strictly_less_than @ sK3_SY64 @ sK4_SY68 ) )
| ~ ~ ( pair_in_list @ ( update_slb @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY71 @ sK6_SY73 ) ) @ sK4_SY68 ) @ sK2_SY59 @ sK4_SY68 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(76,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( less_than @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 )
| ( strictly_less_than @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(77,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 )
| ( SX1 = SX2 )
| ( contains_slb @ SX0 @ SX2 ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ( SX1 != SX2 )
| ! [SX3: $i] : ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 ) )
| ~ ! [SX2: $i] :
( ~ ( contains_slb @ SX0 @ SX2 )
| ! [SX3: $i] : ( contains_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(78,plain,
! [SV1: $i] :
( ( ! [SY74: $i,SY75: $i] :
( ~ ( less_than @ SV1 @ SY74 )
| ~ ( less_than @ SY74 @ SY75 )
| ( less_than @ SV1 @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(79,plain,
! [SV2: $i] :
( ( ! [SY76: $i] :
( ( less_than @ SV2 @ SY76 )
| ( less_than @ SY76 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(80,plain,
! [SV3: $i] :
( ( less_than @ SV3 @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(81,plain,
! [SV4: $i] :
( ( less_than @ bottom @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(82,plain,
( ( isnonempty_slb @ create_slb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(83,plain,
! [SV5: $i] :
( ( ! [SY77: $i,SY78: $i] : ( isnonempty_slb @ ( insert_slb @ SV5 @ ( pair @ SY77 @ SY78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(84,plain,
! [SV6: $i] :
( ( ~ ( contains_slb @ create_slb @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(85,plain,
! [SV7: $i] :
( ( ! [SY79: $i] :
~ ( pair_in_list @ create_slb @ SV7 @ SY79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(86,plain,
! [SV8: $i] :
( ( ! [SY80: $i,SY81: $i] :
( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SY80 @ SY81 ) ) @ SY80 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(87,plain,
! [SV9: $i] :
( ( ! [SY82: $i,SY83: $i] :
( ( SY82 = SY83 )
| ~ ( contains_slb @ SV9 @ SY83 )
| ! [SY84: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SY82 @ SY84 ) ) @ SY83 )
= ( insert_slb @ ( remove_slb @ SV9 @ SY83 ) @ ( pair @ SY82 @ SY84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(88,plain,
! [SV10: $i] :
( ( ! [SY85: $i,SY86: $i] :
( ( lookup_slb @ ( insert_slb @ SV10 @ ( pair @ SY85 @ SY86 ) ) @ SY85 )
= SY86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(89,plain,
! [SV11: $i] :
( ( ! [SY87: $i,SY88: $i] :
( ( SY87 = SY88 )
| ~ ( contains_slb @ SV11 @ SY88 )
| ! [SY89: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SY87 @ SY89 ) ) @ SY88 )
= ( lookup_slb @ SV11 @ SY88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(90,plain,
! [SV12: $i] :
( ( ( update_slb @ create_slb @ SV12 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(91,plain,
! [SV13: $i] :
( ( ! [SY90: $i,SY91: $i,SY92: $i] :
( ~ ( strictly_less_than @ SY92 @ SY91 )
| ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SY90 @ SY92 ) ) @ SY91 )
= ( insert_slb @ ( update_slb @ SV13 @ SY91 ) @ ( pair @ SY90 @ SY91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(92,plain,
! [SV14: $i] :
( ( ! [SY93: $i,SY94: $i,SY95: $i] :
( ~ ( less_than @ SY94 @ SY95 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SY93 @ SY95 ) ) @ SY94 )
= ( insert_slb @ ( update_slb @ SV14 @ SY94 ) @ ( pair @ SY93 @ SY95 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(93,plain,
! [SV15: $i] :
( ( ! [SY96: $i,SY97: $i] :
( ~ ( pair_in_list @ sK1_U @ SV15 @ SY96 )
| ~ ( strictly_less_than @ SY96 @ SY97 )
| ( pair_in_list @ ( update_slb @ sK1_U @ SY97 ) @ SV15 @ SY97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(94,plain,
! [SV16: $i] :
( ( ! [SY98: $i,SY99: $i] :
~ ( ~ ~ ( ~ ! [SY100: $i,SY101: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SY98 @ SY100 ) ) @ SY99 @ SY101 )
| ( SY98 = SY99 )
| ( pair_in_list @ SV16 @ SY99 @ SY101 ) )
| ~ ! [SY102: $i,SY103: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SY98 @ SY102 ) ) @ SY99 @ SY103 )
| ( SY102 = SY103 )
| ( pair_in_list @ SV16 @ SY99 @ SY103 ) ) )
| ~ ~ ( ~ ! [SY104: $i,SY105: $i] :
( ( SY98 != SY99 )
| ( SY104 != SY105 )
| ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SY98 @ SY104 ) ) @ SY99 @ SY105 ) )
| ~ ! [SY106: $i,SY107: $i] :
( ~ ( pair_in_list @ SV16 @ SY99 @ SY107 )
| ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SY98 @ SY106 ) ) @ SY99 @ SY107 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(95,plain,
( ( ~ ~ ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY71 @ sK6_SY73 ) ) @ sK2_SY59 @ sK3_SY64 )
| ~ ( strictly_less_than @ sK3_SY64 @ sK4_SY68 ) )
| ~ ~ ( pair_in_list @ ( update_slb @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY71 @ sK6_SY73 ) ) @ sK4_SY68 ) @ sK2_SY59 @ sK4_SY68 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(96,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( less_than @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 )
| ( strictly_less_than @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(97,plain,
! [SV17: $i] :
( ( ! [SY108: $i] :
~ ( ~ ! [SY109: $i] :
( ! [SY110: $i] :
~ ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SY108 @ SY110 ) ) @ SY109 )
| ( SY108 = SY109 )
| ( contains_slb @ SV17 @ SY109 ) )
| ~ ~ ( ~ ! [SY111: $i] :
( ( SY108 != SY111 )
| ! [SY112: $i] : ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SY108 @ SY112 ) ) @ SY111 ) )
| ~ ! [SY113: $i] :
( ~ ( contains_slb @ SV17 @ SY113 )
| ! [SY114: $i] : ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SY108 @ SY114 ) ) @ SY113 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(98,plain,
! [SV18: $i,SV1: $i] :
( ( ! [SY115: $i] :
( ~ ( less_than @ SV1 @ SV18 )
| ~ ( less_than @ SV18 @ SY115 )
| ( less_than @ SV1 @ SY115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(99,plain,
! [SV19: $i,SV2: $i] :
( ( ( less_than @ SV2 @ SV19 )
| ( less_than @ SV19 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(100,plain,
! [SV20: $i,SV5: $i] :
( ( ! [SY116: $i] : ( isnonempty_slb @ ( insert_slb @ SV5 @ ( pair @ SV20 @ SY116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(101,plain,
! [SV6: $i] :
( ( contains_slb @ create_slb @ SV6 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(102,plain,
! [SV21: $i,SV7: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV7 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(103,plain,
! [SV22: $i,SV8: $i] :
( ( ! [SY117: $i] :
( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SV22 @ SY117 ) ) @ SV22 )
= SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(104,plain,
! [SV9: $i,SV23: $i] :
( ( ! [SY118: $i] :
( ( SV23 = SY118 )
| ~ ( contains_slb @ SV9 @ SY118 )
| ! [SY119: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SY119 ) ) @ SY118 )
= ( insert_slb @ ( remove_slb @ SV9 @ SY118 ) @ ( pair @ SV23 @ SY119 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(105,plain,
! [SV24: $i,SV10: $i] :
( ( ! [SY120: $i] :
( ( lookup_slb @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SY120 ) ) @ SV24 )
= SY120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(106,plain,
! [SV11: $i,SV25: $i] :
( ( ! [SY121: $i] :
( ( SV25 = SY121 )
| ~ ( contains_slb @ SV11 @ SY121 )
| ! [SY122: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV25 @ SY122 ) ) @ SY121 )
= ( lookup_slb @ SV11 @ SY121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(107,plain,
! [SV26: $i,SV13: $i] :
( ( ! [SY123: $i,SY124: $i] :
( ~ ( strictly_less_than @ SY124 @ SY123 )
| ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV26 @ SY124 ) ) @ SY123 )
= ( insert_slb @ ( update_slb @ SV13 @ SY123 ) @ ( pair @ SV26 @ SY123 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(108,plain,
! [SV27: $i,SV14: $i] :
( ( ! [SY125: $i,SY126: $i] :
( ~ ( less_than @ SY125 @ SY126 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV27 @ SY126 ) ) @ SY125 )
= ( insert_slb @ ( update_slb @ SV14 @ SY125 ) @ ( pair @ SV27 @ SY126 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(109,plain,
! [SV28: $i,SV15: $i] :
( ( ! [SY127: $i] :
( ~ ( pair_in_list @ sK1_U @ SV15 @ SV28 )
| ~ ( strictly_less_than @ SV28 @ SY127 )
| ( pair_in_list @ ( update_slb @ sK1_U @ SY127 ) @ SV15 @ SY127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(110,plain,
! [SV29: $i,SV16: $i] :
( ( ! [SY128: $i] :
~ ( ~ ~ ( ~ ! [SY129: $i,SY130: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY129 ) ) @ SY128 @ SY130 )
| ( SV29 = SY128 )
| ( pair_in_list @ SV16 @ SY128 @ SY130 ) )
| ~ ! [SY131: $i,SY132: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY131 ) ) @ SY128 @ SY132 )
| ( SY131 = SY132 )
| ( pair_in_list @ SV16 @ SY128 @ SY132 ) ) )
| ~ ~ ( ~ ! [SY133: $i,SY134: $i] :
( ( SV29 != SY128 )
| ( SY133 != SY134 )
| ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY133 ) ) @ SY128 @ SY134 ) )
| ~ ! [SY135: $i,SY136: $i] :
( ~ ( pair_in_list @ SV16 @ SY128 @ SY136 )
| ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY135 ) ) @ SY128 @ SY136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(111,plain,
( ( ~ ~ ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY71 @ sK6_SY73 ) ) @ sK2_SY59 @ sK3_SY64 )
| ~ ( strictly_less_than @ sK3_SY64 @ sK4_SY68 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(112,plain,
( ( ~ ~ ( pair_in_list @ ( update_slb @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY71 @ sK6_SY73 ) ) @ sK4_SY68 ) @ sK2_SY59 @ sK4_SY68 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(113,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( less_than @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 )
| ( strictly_less_than @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(114,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(115,plain,
! [SV30: $i,SV17: $i] :
( ( ~ ( ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY138 ) ) @ SY137 )
| ( SV30 = SY137 )
| ( contains_slb @ SV17 @ SY137 ) )
| ~ ~ ( ~ ! [SY139: $i] :
( ( SV30 != SY139 )
| ! [SY140: $i] : ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY140 ) ) @ SY139 ) )
| ~ ! [SY141: $i] :
( ~ ( contains_slb @ SV17 @ SY141 )
| ! [SY142: $i] : ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY142 ) ) @ SY141 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(116,plain,
! [SV31: $i,SV18: $i,SV1: $i] :
( ( ~ ( less_than @ SV1 @ SV18 )
| ~ ( less_than @ SV18 @ SV31 )
| ( less_than @ SV1 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(117,plain,
! [SV19: $i,SV2: $i] :
( ( ( less_than @ SV2 @ SV19 )
= $true )
| ( ( less_than @ SV19 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(118,plain,
! [SV32: $i,SV20: $i,SV5: $i] :
( ( isnonempty_slb @ ( insert_slb @ SV5 @ ( pair @ SV20 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(119,plain,
! [SV21: $i,SV7: $i] :
( ( pair_in_list @ create_slb @ SV7 @ SV21 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(120,plain,
! [SV33: $i,SV22: $i,SV8: $i] :
( ( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SV22 @ SV33 ) ) @ SV22 )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(121,plain,
! [SV9: $i,SV34: $i,SV23: $i] :
( ( ( SV23 = SV34 )
| ~ ( contains_slb @ SV9 @ SV34 )
| ! [SY143: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SY143 ) ) @ SV34 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV34 ) @ ( pair @ SV23 @ SY143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(122,plain,
! [SV35: $i,SV24: $i,SV10: $i] :
( ( ( lookup_slb @ ( insert_slb @ SV10 @ ( pair @ SV24 @ SV35 ) ) @ SV24 )
= SV35 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(123,plain,
! [SV11: $i,SV36: $i,SV25: $i] :
( ( ( SV25 = SV36 )
| ~ ( contains_slb @ SV11 @ SV36 )
| ! [SY144: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV25 @ SY144 ) ) @ SV36 )
= ( lookup_slb @ SV11 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(124,plain,
! [SV26: $i,SV13: $i,SV37: $i] :
( ( ! [SY145: $i] :
( ~ ( strictly_less_than @ SY145 @ SV37 )
| ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV26 @ SY145 ) ) @ SV37 )
= ( insert_slb @ ( update_slb @ SV13 @ SV37 ) @ ( pair @ SV26 @ SV37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(125,plain,
! [SV27: $i,SV14: $i,SV38: $i] :
( ( ! [SY146: $i] :
( ~ ( less_than @ SV38 @ SY146 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV27 @ SY146 ) ) @ SV38 )
= ( insert_slb @ ( update_slb @ SV14 @ SV38 ) @ ( pair @ SV27 @ SY146 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(126,plain,
! [SV39: $i,SV28: $i,SV15: $i] :
( ( ~ ( pair_in_list @ sK1_U @ SV15 @ SV28 )
| ~ ( strictly_less_than @ SV28 @ SV39 )
| ( pair_in_list @ ( update_slb @ sK1_U @ SV39 ) @ SV15 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(127,plain,
! [SV40: $i,SV29: $i,SV16: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY147: $i,SY148: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY147 ) ) @ SV40 @ SY148 )
| ( SV29 = SV40 )
| ( pair_in_list @ SV16 @ SV40 @ SY148 ) )
| ~ ! [SY149: $i,SY150: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY149 ) ) @ SV40 @ SY150 )
| ( SY149 = SY150 )
| ( pair_in_list @ SV16 @ SV40 @ SY150 ) ) )
| ~ ~ ( ~ ! [SY151: $i,SY152: $i] :
( ( SV29 != SV40 )
| ( SY151 != SY152 )
| ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY151 ) ) @ SV40 @ SY152 ) )
| ~ ! [SY153: $i,SY154: $i] :
( ~ ( pair_in_list @ SV16 @ SV40 @ SY154 )
| ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY153 ) ) @ SV40 @ SY154 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(128,plain,
( ( ~ ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY71 @ sK6_SY73 ) ) @ sK2_SY59 @ sK3_SY64 )
| ~ ( strictly_less_than @ sK3_SY64 @ sK4_SY68 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(129,plain,
( ( ~ ( pair_in_list @ ( update_slb @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY71 @ sK6_SY73 ) ) @ sK4_SY68 ) @ sK2_SY59 @ sK4_SY68 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(130,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( less_than @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 )
| ( strictly_less_than @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(131,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(132,plain,
! [SV30: $i,SV17: $i] :
( ( ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY138 ) ) @ SY137 )
| ( SV30 = SY137 )
| ( contains_slb @ SV17 @ SY137 ) )
| ~ ~ ( ~ ! [SY139: $i] :
( ( SV30 != SY139 )
| ! [SY140: $i] : ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY140 ) ) @ SY139 ) )
| ~ ! [SY141: $i] :
( ~ ( contains_slb @ SV17 @ SY141 )
| ! [SY142: $i] : ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY142 ) ) @ SY141 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(133,plain,
! [SV31: $i,SV18: $i,SV1: $i] :
( ( ( ~ ( less_than @ SV1 @ SV18 )
| ~ ( less_than @ SV18 @ SV31 ) )
= $true )
| ( ( less_than @ SV1 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(134,plain,
! [SV9: $i,SV34: $i,SV23: $i] :
( ( ( ( SV23 = SV34 )
| ~ ( contains_slb @ SV9 @ SV34 ) )
= $true )
| ( ( ! [SY143: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SY143 ) ) @ SV34 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV34 ) @ ( pair @ SV23 @ SY143 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(135,plain,
! [SV11: $i,SV36: $i,SV25: $i] :
( ( ( ( SV25 = SV36 )
| ~ ( contains_slb @ SV11 @ SV36 ) )
= $true )
| ( ( ! [SY144: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV25 @ SY144 ) ) @ SV36 )
= ( lookup_slb @ SV11 @ SV36 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(136,plain,
! [SV26: $i,SV13: $i,SV37: $i,SV41: $i] :
( ( ~ ( strictly_less_than @ SV41 @ SV37 )
| ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV26 @ SV41 ) ) @ SV37 )
= ( insert_slb @ ( update_slb @ SV13 @ SV37 ) @ ( pair @ SV26 @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(137,plain,
! [SV27: $i,SV14: $i,SV42: $i,SV38: $i] :
( ( ~ ( less_than @ SV38 @ SV42 )
| ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV27 @ SV42 ) ) @ SV38 )
= ( insert_slb @ ( update_slb @ SV14 @ SV38 ) @ ( pair @ SV27 @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(138,plain,
! [SV39: $i,SV28: $i,SV15: $i] :
( ( ( ~ ( pair_in_list @ sK1_U @ SV15 @ SV28 )
| ~ ( strictly_less_than @ SV28 @ SV39 ) )
= $true )
| ( ( pair_in_list @ ( update_slb @ sK1_U @ SV39 ) @ SV15 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(139,plain,
! [SV40: $i,SV29: $i,SV16: $i] :
( ( ~ ~ ( ~ ! [SY147: $i,SY148: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY147 ) ) @ SV40 @ SY148 )
| ( SV29 = SV40 )
| ( pair_in_list @ SV16 @ SV40 @ SY148 ) )
| ~ ! [SY149: $i,SY150: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY149 ) ) @ SV40 @ SY150 )
| ( SY149 = SY150 )
| ( pair_in_list @ SV16 @ SV40 @ SY150 ) ) )
| ~ ~ ( ~ ! [SY151: $i,SY152: $i] :
( ( SV29 != SV40 )
| ( SY151 != SY152 )
| ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY151 ) ) @ SV40 @ SY152 ) )
| ~ ! [SY153: $i,SY154: $i] :
( ~ ( pair_in_list @ SV16 @ SV40 @ SY154 )
| ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY153 ) ) @ SV40 @ SY154 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(140,plain,
( ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY71 @ sK6_SY73 ) ) @ sK2_SY59 @ sK3_SY64 )
| ~ ( strictly_less_than @ sK3_SY64 @ sK4_SY68 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(141,plain,
( ( pair_in_list @ ( update_slb @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY71 @ sK6_SY73 ) ) @ sK4_SY68 ) @ sK2_SY59 @ sK4_SY68 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(142,plain,
! [SV43: $i] :
( ( ! [SY155: $i] :
( ~ ( less_than @ SV43 @ SY155 )
| ( less_than @ SY155 @ SV43 )
| ( strictly_less_than @ SV43 @ SY155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(143,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(144,plain,
! [SV30: $i,SV17: $i] :
( ( ~ ! [SY137: $i] :
( ! [SY138: $i] :
~ ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY138 ) ) @ SY137 )
| ( SV30 = SY137 )
| ( contains_slb @ SV17 @ SY137 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(145,plain,
! [SV17: $i,SV30: $i] :
( ( ~ ~ ( ~ ! [SY139: $i] :
( ( SV30 != SY139 )
| ! [SY140: $i] : ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY140 ) ) @ SY139 ) )
| ~ ! [SY141: $i] :
( ~ ( contains_slb @ SV17 @ SY141 )
| ! [SY142: $i] : ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY142 ) ) @ SY141 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(146,plain,
! [SV31: $i,SV18: $i,SV1: $i] :
( ( ( ~ ( less_than @ SV1 @ SV18 ) )
= $true )
| ( ( ~ ( less_than @ SV18 @ SV31 ) )
= $true )
| ( ( less_than @ SV1 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(147,plain,
! [SV9: $i,SV34: $i,SV23: $i] :
( ( ( SV23 = SV34 )
= $true )
| ( ( ~ ( contains_slb @ SV9 @ SV34 ) )
= $true )
| ( ( ! [SY143: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SY143 ) ) @ SV34 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV34 ) @ ( pair @ SV23 @ SY143 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(148,plain,
! [SV11: $i,SV36: $i,SV25: $i] :
( ( ( SV25 = SV36 )
= $true )
| ( ( ~ ( contains_slb @ SV11 @ SV36 ) )
= $true )
| ( ( ! [SY144: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV25 @ SY144 ) ) @ SV36 )
= ( lookup_slb @ SV11 @ SV36 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(149,plain,
! [SV26: $i,SV13: $i,SV37: $i,SV41: $i] :
( ( ( ~ ( strictly_less_than @ SV41 @ SV37 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV26 @ SV41 ) ) @ SV37 )
= ( insert_slb @ ( update_slb @ SV13 @ SV37 ) @ ( pair @ SV26 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(150,plain,
! [SV27: $i,SV14: $i,SV42: $i,SV38: $i] :
( ( ( ~ ( less_than @ SV38 @ SV42 ) )
= $true )
| ( ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV27 @ SV42 ) ) @ SV38 )
= ( insert_slb @ ( update_slb @ SV14 @ SV38 ) @ ( pair @ SV27 @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(151,plain,
! [SV39: $i,SV28: $i,SV15: $i] :
( ( ( ~ ( pair_in_list @ sK1_U @ SV15 @ SV28 ) )
= $true )
| ( ( ~ ( strictly_less_than @ SV28 @ SV39 ) )
= $true )
| ( ( pair_in_list @ ( update_slb @ sK1_U @ SV39 ) @ SV15 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(152,plain,
! [SV40: $i,SV29: $i,SV16: $i] :
( ( ~ ~ ( ~ ! [SY147: $i,SY148: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY147 ) ) @ SV40 @ SY148 )
| ( SV29 = SV40 )
| ( pair_in_list @ SV16 @ SV40 @ SY148 ) )
| ~ ! [SY149: $i,SY150: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY149 ) ) @ SV40 @ SY150 )
| ( SY149 = SY150 )
| ( pair_in_list @ SV16 @ SV40 @ SY150 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(153,plain,
! [SV16: $i,SV40: $i,SV29: $i] :
( ( ~ ~ ( ~ ! [SY151: $i,SY152: $i] :
( ( SV29 != SV40 )
| ( SY151 != SY152 )
| ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY151 ) ) @ SV40 @ SY152 ) )
| ~ ! [SY153: $i,SY154: $i] :
( ~ ( pair_in_list @ SV16 @ SV40 @ SY154 )
| ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY153 ) ) @ SV40 @ SY154 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(154,plain,
( ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY71 @ sK6_SY73 ) ) @ sK2_SY59 @ sK3_SY64 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(155,plain,
( ( ~ ( strictly_less_than @ sK3_SY64 @ sK4_SY68 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(156,plain,
! [SV44: $i,SV43: $i] :
( ( ~ ( less_than @ SV43 @ SV44 )
| ( less_than @ SV44 @ SV43 )
| ( strictly_less_than @ SV43 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(157,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(158,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(159,plain,
! [SV30: $i,SV17: $i] :
( ( ! [SY137: $i] :
( ! [SY138: $i] :
~ ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY138 ) ) @ SY137 )
| ( SV30 = SY137 )
| ( contains_slb @ SV17 @ SY137 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(160,plain,
! [SV17: $i,SV30: $i] :
( ( ~ ( ~ ! [SY139: $i] :
( ( SV30 != SY139 )
| ! [SY140: $i] : ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY140 ) ) @ SY139 ) )
| ~ ! [SY141: $i] :
( ~ ( contains_slb @ SV17 @ SY141 )
| ! [SY142: $i] : ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY142 ) ) @ SY141 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(161,plain,
! [SV31: $i,SV18: $i,SV1: $i] :
( ( ( less_than @ SV1 @ SV18 )
= $false )
| ( ( ~ ( less_than @ SV18 @ SV31 ) )
= $true )
| ( ( less_than @ SV1 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(162,plain,
! [SV23: $i,SV34: $i,SV9: $i] :
( ( ( contains_slb @ SV9 @ SV34 )
= $false )
| ( ( SV23 = SV34 )
= $true )
| ( ( ! [SY143: $i] :
( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SY143 ) ) @ SV34 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV34 ) @ ( pair @ SV23 @ SY143 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(163,plain,
! [SV25: $i,SV36: $i,SV11: $i] :
( ( ( contains_slb @ SV11 @ SV36 )
= $false )
| ( ( SV25 = SV36 )
= $true )
| ( ( ! [SY144: $i] :
( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV25 @ SY144 ) ) @ SV36 )
= ( lookup_slb @ SV11 @ SV36 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(164,plain,
! [SV26: $i,SV13: $i,SV37: $i,SV41: $i] :
( ( ( strictly_less_than @ SV41 @ SV37 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV13 @ ( pair @ SV26 @ SV41 ) ) @ SV37 )
= ( insert_slb @ ( update_slb @ SV13 @ SV37 ) @ ( pair @ SV26 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(165,plain,
! [SV27: $i,SV14: $i,SV42: $i,SV38: $i] :
( ( ( less_than @ SV38 @ SV42 )
= $false )
| ( ( ( update_slb @ ( insert_slb @ SV14 @ ( pair @ SV27 @ SV42 ) ) @ SV38 )
= ( insert_slb @ ( update_slb @ SV14 @ SV38 ) @ ( pair @ SV27 @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(166,plain,
! [SV39: $i,SV28: $i,SV15: $i] :
( ( ( pair_in_list @ sK1_U @ SV15 @ SV28 )
= $false )
| ( ( ~ ( strictly_less_than @ SV28 @ SV39 ) )
= $true )
| ( ( pair_in_list @ ( update_slb @ sK1_U @ SV39 ) @ SV15 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(167,plain,
! [SV40: $i,SV29: $i,SV16: $i] :
( ( ~ ( ~ ! [SY147: $i,SY148: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY147 ) ) @ SV40 @ SY148 )
| ( SV29 = SV40 )
| ( pair_in_list @ SV16 @ SV40 @ SY148 ) )
| ~ ! [SY149: $i,SY150: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY149 ) ) @ SV40 @ SY150 )
| ( SY149 = SY150 )
| ( pair_in_list @ SV16 @ SV40 @ SY150 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(168,plain,
! [SV16: $i,SV40: $i,SV29: $i] :
( ( ~ ( ~ ! [SY151: $i,SY152: $i] :
( ( SV29 != SV40 )
| ( SY151 != SY152 )
| ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY151 ) ) @ SV40 @ SY152 ) )
| ~ ! [SY153: $i,SY154: $i] :
( ~ ( pair_in_list @ SV16 @ SV40 @ SY154 )
| ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY153 ) ) @ SV40 @ SY154 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(169,plain,
( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK5_SY71 @ sK6_SY73 ) ) @ sK2_SY59 @ sK3_SY64 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(170,plain,
( ( strictly_less_than @ sK3_SY64 @ sK4_SY68 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[155]) ).
thf(171,plain,
! [SV44: $i,SV43: $i] :
( ( ( ~ ( less_than @ SV43 @ SV44 )
| ( less_than @ SV44 @ SV43 ) )
= $true )
| ( ( strictly_less_than @ SV43 @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(172,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ( less_than @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(173,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(174,plain,
! [SV45: $i,SV30: $i,SV17: $i] :
( ( ! [SY156: $i] :
~ ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY156 ) ) @ SV45 )
| ( SV30 = SV45 )
| ( contains_slb @ SV17 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(175,plain,
! [SV17: $i,SV30: $i] :
( ( ~ ! [SY139: $i] :
( ( SV30 != SY139 )
| ! [SY140: $i] : ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY140 ) ) @ SY139 ) )
| ~ ! [SY141: $i] :
( ~ ( contains_slb @ SV17 @ SY141 )
| ! [SY142: $i] : ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY142 ) ) @ SY141 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(176,plain,
! [SV1: $i,SV31: $i,SV18: $i] :
( ( ( less_than @ SV18 @ SV31 )
= $false )
| ( ( less_than @ SV1 @ SV18 )
= $false )
| ( ( less_than @ SV1 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(177,plain,
! [SV34: $i,SV46: $i,SV23: $i,SV9: $i] :
( ( ( ( remove_slb @ ( insert_slb @ SV9 @ ( pair @ SV23 @ SV46 ) ) @ SV34 )
= ( insert_slb @ ( remove_slb @ SV9 @ SV34 ) @ ( pair @ SV23 @ SV46 ) ) )
= $true )
| ( ( SV23 = SV34 )
= $true )
| ( ( contains_slb @ SV9 @ SV34 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(178,plain,
! [SV36: $i,SV47: $i,SV25: $i,SV11: $i] :
( ( ( ( lookup_slb @ ( insert_slb @ SV11 @ ( pair @ SV25 @ SV47 ) ) @ SV36 )
= ( lookup_slb @ SV11 @ SV36 ) )
= $true )
| ( ( SV25 = SV36 )
= $true )
| ( ( contains_slb @ SV11 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(179,plain,
! [SV15: $i,SV39: $i,SV28: $i] :
( ( ( strictly_less_than @ SV28 @ SV39 )
= $false )
| ( ( pair_in_list @ sK1_U @ SV15 @ SV28 )
= $false )
| ( ( pair_in_list @ ( update_slb @ sK1_U @ SV39 ) @ SV15 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(180,plain,
! [SV40: $i,SV29: $i,SV16: $i] :
( ( ~ ! [SY147: $i,SY148: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY147 ) ) @ SV40 @ SY148 )
| ( SV29 = SV40 )
| ( pair_in_list @ SV16 @ SV40 @ SY148 ) )
| ~ ! [SY149: $i,SY150: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY149 ) ) @ SV40 @ SY150 )
| ( SY149 = SY150 )
| ( pair_in_list @ SV16 @ SV40 @ SY150 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(181,plain,
! [SV16: $i,SV40: $i,SV29: $i] :
( ( ~ ! [SY151: $i,SY152: $i] :
( ( SV29 != SV40 )
| ( SY151 != SY152 )
| ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY151 ) ) @ SV40 @ SY152 ) )
| ~ ! [SY153: $i,SY154: $i] :
( ~ ( pair_in_list @ SV16 @ SV40 @ SY154 )
| ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY153 ) ) @ SV40 @ SY154 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(182,plain,
! [SV44: $i,SV43: $i] :
( ( ( ~ ( less_than @ SV43 @ SV44 ) )
= $true )
| ( ( less_than @ SV44 @ SV43 )
= $true )
| ( ( strictly_less_than @ SV43 @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(183,plain,
! [SV48: $i] :
( ( ! [SY157: $i] :
( ~ ( strictly_less_than @ SV48 @ SY157 )
| ( less_than @ SV48 @ SY157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(184,plain,
! [SV49: $i] :
( ( ! [SY158: $i] :
( ~ ( strictly_less_than @ SV49 @ SY158 )
| ~ ( less_than @ SY158 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(185,plain,
! [SV45: $i,SV30: $i,SV17: $i] :
( ( ( ! [SY156: $i] :
~ ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY156 ) ) @ SV45 ) )
= $true )
| ( ( ( SV30 = SV45 )
| ( contains_slb @ SV17 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(186,plain,
! [SV17: $i,SV30: $i] :
( ( ~ ! [SY139: $i] :
( ( SV30 != SY139 )
| ! [SY140: $i] : ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY140 ) ) @ SY139 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(187,plain,
! [SV30: $i,SV17: $i] :
( ( ~ ! [SY141: $i] :
( ~ ( contains_slb @ SV17 @ SY141 )
| ! [SY142: $i] : ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY142 ) ) @ SY141 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(188,plain,
! [SV40: $i,SV29: $i,SV16: $i] :
( ( ~ ! [SY147: $i,SY148: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY147 ) ) @ SV40 @ SY148 )
| ( SV29 = SV40 )
| ( pair_in_list @ SV16 @ SV40 @ SY148 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(189,plain,
! [SV40: $i,SV29: $i,SV16: $i] :
( ( ~ ! [SY149: $i,SY150: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY149 ) ) @ SV40 @ SY150 )
| ( SY149 = SY150 )
| ( pair_in_list @ SV16 @ SV40 @ SY150 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(190,plain,
! [SV16: $i,SV40: $i,SV29: $i] :
( ( ~ ! [SY151: $i,SY152: $i] :
( ( SV29 != SV40 )
| ( SY151 != SY152 )
| ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY151 ) ) @ SV40 @ SY152 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(191,plain,
! [SV29: $i,SV40: $i,SV16: $i] :
( ( ~ ! [SY153: $i,SY154: $i] :
( ~ ( pair_in_list @ SV16 @ SV40 @ SY154 )
| ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY153 ) ) @ SV40 @ SY154 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(192,plain,
! [SV44: $i,SV43: $i] :
( ( ( less_than @ SV43 @ SV44 )
= $false )
| ( ( less_than @ SV44 @ SV43 )
= $true )
| ( ( strictly_less_than @ SV43 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(193,plain,
! [SV50: $i,SV48: $i] :
( ( ~ ( strictly_less_than @ SV48 @ SV50 )
| ( less_than @ SV48 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(194,plain,
! [SV51: $i,SV49: $i] :
( ( ~ ( strictly_less_than @ SV49 @ SV51 )
| ~ ( less_than @ SV51 @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(195,plain,
! [SV45: $i,SV52: $i,SV30: $i,SV17: $i] :
( ( ( ~ ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SV52 ) ) @ SV45 ) )
= $true )
| ( ( ( SV30 = SV45 )
| ( contains_slb @ SV17 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(196,plain,
! [SV17: $i,SV30: $i] :
( ( ! [SY139: $i] :
( ( SV30 != SY139 )
| ! [SY140: $i] : ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY140 ) ) @ SY139 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(197,plain,
! [SV30: $i,SV17: $i] :
( ( ! [SY141: $i] :
( ~ ( contains_slb @ SV17 @ SY141 )
| ! [SY142: $i] : ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY142 ) ) @ SY141 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(198,plain,
! [SV40: $i,SV29: $i,SV16: $i] :
( ( ! [SY147: $i,SY148: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY147 ) ) @ SV40 @ SY148 )
| ( SV29 = SV40 )
| ( pair_in_list @ SV16 @ SV40 @ SY148 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(199,plain,
! [SV40: $i,SV29: $i,SV16: $i] :
( ( ! [SY149: $i,SY150: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY149 ) ) @ SV40 @ SY150 )
| ( SY149 = SY150 )
| ( pair_in_list @ SV16 @ SV40 @ SY150 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(200,plain,
! [SV16: $i,SV40: $i,SV29: $i] :
( ( ! [SY151: $i,SY152: $i] :
( ( SV29 != SV40 )
| ( SY151 != SY152 )
| ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY151 ) ) @ SV40 @ SY152 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(201,plain,
! [SV29: $i,SV40: $i,SV16: $i] :
( ( ! [SY153: $i,SY154: $i] :
( ~ ( pair_in_list @ SV16 @ SV40 @ SY154 )
| ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SY153 ) ) @ SV40 @ SY154 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(202,plain,
! [SV50: $i,SV48: $i] :
( ( ( ~ ( strictly_less_than @ SV48 @ SV50 ) )
= $true )
| ( ( less_than @ SV48 @ SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(203,plain,
! [SV51: $i,SV49: $i] :
( ( ( ~ ( strictly_less_than @ SV49 @ SV51 ) )
= $true )
| ( ( ~ ( less_than @ SV51 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(204,plain,
! [SV45: $i,SV52: $i,SV30: $i,SV17: $i] :
( ( ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SV52 ) ) @ SV45 )
= $false )
| ( ( ( SV30 = SV45 )
| ( contains_slb @ SV17 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(205,plain,
! [SV17: $i,SV53: $i,SV30: $i] :
( ( ( SV30 != SV53 )
| ! [SY159: $i] : ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY159 ) ) @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(206,plain,
! [SV30: $i,SV54: $i,SV17: $i] :
( ( ~ ( contains_slb @ SV17 @ SV54 )
| ! [SY160: $i] : ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY160 ) ) @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(207,plain,
! [SV40: $i,SV55: $i,SV29: $i,SV16: $i] :
( ( ! [SY161: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SV55 ) ) @ SV40 @ SY161 )
| ( SV29 = SV40 )
| ( pair_in_list @ SV16 @ SV40 @ SY161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(208,plain,
! [SV40: $i,SV56: $i,SV29: $i,SV16: $i] :
( ( ! [SY162: $i] :
( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SV56 ) ) @ SV40 @ SY162 )
| ( SV56 = SY162 )
| ( pair_in_list @ SV16 @ SV40 @ SY162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(209,plain,
! [SV16: $i,SV57: $i,SV40: $i,SV29: $i] :
( ( ! [SY163: $i] :
( ( SV29 != SV40 )
| ( SV57 != SY163 )
| ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SV57 ) ) @ SV40 @ SY163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(210,plain,
! [SV58: $i,SV29: $i,SV40: $i,SV16: $i] :
( ( ! [SY164: $i] :
( ~ ( pair_in_list @ SV16 @ SV40 @ SY164 )
| ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SV58 ) ) @ SV40 @ SY164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(211,plain,
! [SV50: $i,SV48: $i] :
( ( ( strictly_less_than @ SV48 @ SV50 )
= $false )
| ( ( less_than @ SV48 @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(212,plain,
! [SV51: $i,SV49: $i] :
( ( ( strictly_less_than @ SV49 @ SV51 )
= $false )
| ( ( ~ ( less_than @ SV51 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(213,plain,
! [SV52: $i,SV17: $i,SV45: $i,SV30: $i] :
( ( ( SV30 = SV45 )
= $true )
| ( ( contains_slb @ SV17 @ SV45 )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SV52 ) ) @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(214,plain,
! [SV17: $i,SV53: $i,SV30: $i] :
( ( ( ( SV30 != SV53 ) )
= $true )
| ( ( ! [SY159: $i] : ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY159 ) ) @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(215,plain,
! [SV30: $i,SV54: $i,SV17: $i] :
( ( ( ~ ( contains_slb @ SV17 @ SV54 ) )
= $true )
| ( ( ! [SY160: $i] : ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY160 ) ) @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(216,plain,
! [SV59: $i,SV40: $i,SV55: $i,SV29: $i,SV16: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SV55 ) ) @ SV40 @ SV59 )
| ( SV29 = SV40 )
| ( pair_in_list @ SV16 @ SV40 @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(217,plain,
! [SV60: $i,SV40: $i,SV56: $i,SV29: $i,SV16: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SV56 ) ) @ SV40 @ SV60 )
| ( SV56 = SV60 )
| ( pair_in_list @ SV16 @ SV40 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(218,plain,
! [SV16: $i,SV61: $i,SV57: $i,SV40: $i,SV29: $i] :
( ( ( SV29 != SV40 )
| ( SV57 != SV61 )
| ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SV57 ) ) @ SV40 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(219,plain,
! [SV58: $i,SV29: $i,SV62: $i,SV40: $i,SV16: $i] :
( ( ~ ( pair_in_list @ SV16 @ SV40 @ SV62 )
| ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SV58 ) ) @ SV40 @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(220,plain,
! [SV49: $i,SV51: $i] :
( ( ( less_than @ SV51 @ SV49 )
= $false )
| ( ( strictly_less_than @ SV49 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(221,plain,
! [SV17: $i,SV53: $i,SV30: $i] :
( ( ( SV30 = SV53 )
= $false )
| ( ( ! [SY159: $i] : ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY159 ) ) @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(222,plain,
! [SV30: $i,SV54: $i,SV17: $i] :
( ( ( contains_slb @ SV17 @ SV54 )
= $false )
| ( ( ! [SY160: $i] : ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SY160 ) ) @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(223,plain,
! [SV59: $i,SV40: $i,SV55: $i,SV29: $i,SV16: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SV55 ) ) @ SV40 @ SV59 ) )
= $true )
| ( ( ( SV29 = SV40 )
| ( pair_in_list @ SV16 @ SV40 @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(224,plain,
! [SV60: $i,SV40: $i,SV56: $i,SV29: $i,SV16: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SV56 ) ) @ SV40 @ SV60 ) )
= $true )
| ( ( ( SV56 = SV60 )
| ( pair_in_list @ SV16 @ SV40 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(225,plain,
! [SV16: $i,SV61: $i,SV57: $i,SV40: $i,SV29: $i] :
( ( ( ( SV29 != SV40 )
| ( SV57 != SV61 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SV57 ) ) @ SV40 @ SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(226,plain,
! [SV58: $i,SV29: $i,SV62: $i,SV40: $i,SV16: $i] :
( ( ( ~ ( pair_in_list @ SV16 @ SV40 @ SV62 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SV58 ) ) @ SV40 @ SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(227,plain,
! [SV53: $i,SV63: $i,SV30: $i,SV17: $i] :
( ( ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SV63 ) ) @ SV53 )
= $true )
| ( ( SV30 = SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(228,plain,
! [SV54: $i,SV64: $i,SV30: $i,SV17: $i] :
( ( ( contains_slb @ ( insert_slb @ SV17 @ ( pair @ SV30 @ SV64 ) ) @ SV54 )
= $true )
| ( ( contains_slb @ SV17 @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(229,plain,
! [SV59: $i,SV40: $i,SV55: $i,SV29: $i,SV16: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SV55 ) ) @ SV40 @ SV59 )
= $false )
| ( ( ( SV29 = SV40 )
| ( pair_in_list @ SV16 @ SV40 @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(230,plain,
! [SV60: $i,SV40: $i,SV56: $i,SV29: $i,SV16: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SV56 ) ) @ SV40 @ SV60 )
= $false )
| ( ( ( SV56 = SV60 )
| ( pair_in_list @ SV16 @ SV40 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(231,plain,
! [SV16: $i,SV61: $i,SV57: $i,SV40: $i,SV29: $i] :
( ( ( ( SV29 != SV40 ) )
= $true )
| ( ( ( SV57 != SV61 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SV57 ) ) @ SV40 @ SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(232,plain,
! [SV58: $i,SV29: $i,SV62: $i,SV40: $i,SV16: $i] :
( ( ( pair_in_list @ SV16 @ SV40 @ SV62 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SV58 ) ) @ SV40 @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(233,plain,
! [SV55: $i,SV59: $i,SV16: $i,SV40: $i,SV29: $i] :
( ( ( SV29 = SV40 )
= $true )
| ( ( pair_in_list @ SV16 @ SV40 @ SV59 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SV55 ) ) @ SV40 @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(234,plain,
! [SV29: $i,SV40: $i,SV16: $i,SV60: $i,SV56: $i] :
( ( ( SV56 = SV60 )
= $true )
| ( ( pair_in_list @ SV16 @ SV40 @ SV60 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SV56 ) ) @ SV40 @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(235,plain,
! [SV16: $i,SV61: $i,SV57: $i,SV40: $i,SV29: $i] :
( ( ( SV29 = SV40 )
= $false )
| ( ( ( SV57 != SV61 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SV57 ) ) @ SV40 @ SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(236,plain,
! [SV16: $i,SV40: $i,SV29: $i,SV61: $i,SV57: $i] :
( ( ( SV57 = SV61 )
= $false )
| ( ( SV29 = SV40 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV16 @ ( pair @ SV29 @ SV57 ) ) @ SV40 @ SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(237,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[80,236,234,233,232,228,227,220,213,211,192,179,178,177,176,170,169,165,164,141,122,120,119,118,117,101,90,82,81]) ).
thf(238,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV403+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 20:06:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.36
% 0.12/0.36 No.of.Axioms: 18
% 0.12/0.36
% 0.12/0.36 Length.of.Defs: 0
% 0.12/0.36
% 0.12/0.36 Contains.Choice.Funs: false
% 0.12/0.38 (rf:0,axioms:18,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:20,loop_count:0,foatp_calls:0,translation:fof_full)...................
% 0.46/0.71
% 0.46/0.71 ********************************
% 0.46/0.71 * All subproblems solved! *
% 0.46/0.71 ********************************
% 0.46/0.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:19,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:237,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.54/0.74
% 0.54/0.74 %**** Beginning of derivation protocol ****
% 0.54/0.74 % SZS output start CNFRefutation
% See solution above
% 0.54/0.74
% 0.54/0.74 %**** End of derivation protocol ****
% 0.54/0.74 %**** no. of clauses in derivation: 238 ****
% 0.54/0.74 %**** clause counter: 237 ****
% 0.54/0.74
% 0.54/0.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:19,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:237,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------