%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV411+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 10:57:37 AM UTC 2026
% Result : Theorem 0.09s 0.27s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 138 ( 91 unt; 0 typ; 0 def)
% Number of atoms : 764 ( 352 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 1863 ( 297 ~; 214 |; 9 &;1314 @)
% ( 6 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 8 con; 0-3 aty)
% Number of variables : 494 ( 0 ^; 481 !; 13 ?; 494 :)
% 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_SY75,type,
sK3_SY75: $i ).
thf(tp_sK4_SY83,type,
sK4_SY83: $i ).
thf(tp_sK5_SY62,type,
sK5_SY62: $i > $i ).
thf(tp_strictly_less_than,type,
strictly_less_than: $i > $i > $o ).
thf(tp_update_slb,type,
update_slb: $i > $i > $i ).
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax23) ).
thf(9,axiom,
! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax21) ).
thf(11,axiom,
! [U: $i] :
~ ( contains_slb @ create_slb @ U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
thf(12,axiom,
! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).
thf(19,conjecture,
! [U: $i] :
( ! [V: $i] :
( ( contains_slb @ U @ V )
=> ? [W: $i] : ( pair_in_list @ U @ V @ W ) )
=> ! [X: $i,Y: $i,Z: $i] :
( ( contains_slb @ ( insert_slb @ U @ ( pair @ Y @ Z ) ) @ X )
=> ? [X1: $i] : ( pair_in_list @ ( insert_slb @ U @ ( pair @ Y @ Z ) ) @ X @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l47_co) ).
thf(20,negated_conjecture,
( ( ! [U: $i] :
( ! [V: $i] :
( ( contains_slb @ U @ V )
=> ? [W: $i] : ( pair_in_list @ U @ V @ W ) )
=> ! [X: $i,Y: $i,Z: $i] :
( ( contains_slb @ ( insert_slb @ U @ ( pair @ Y @ Z ) ) @ X )
=> ? [X1: $i] : ( pair_in_list @ ( insert_slb @ U @ ( pair @ Y @ Z ) ) @ X @ X1 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[19]) ).
thf(21,plain,
( ( ! [U: $i] :
( ! [V: $i] :
( ( contains_slb @ U @ V )
=> ? [W: $i] : ( pair_in_list @ U @ V @ W ) )
=> ! [X: $i,Y: $i,Z: $i] :
( ( contains_slb @ ( insert_slb @ U @ ( pair @ Y @ Z ) ) @ X )
=> ? [X1: $i] : ( pair_in_list @ ( insert_slb @ U @ ( pair @ Y @ Z ) ) @ X @ X1 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[20]) ).
thf(22,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(23,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(24,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(25,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(26,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(27,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(28,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(29,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
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,
( ( ! [SY36: $i] :
( ( contains_slb @ sK1_U @ SY36 )
=> ? [SY37: $i] : ( pair_in_list @ sK1_U @ SY36 @ SY37 ) )
=> ! [SY38: $i,SY39: $i,SY40: $i] :
( ( contains_slb @ ( insert_slb @ sK1_U @ ( pair @ SY39 @ SY40 ) ) @ SY38 )
=> ? [SY41: $i] : ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY39 @ SY40 ) ) @ SY38 @ SY41 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[21]) ).
thf(32,plain,
( ( ! [SY36: $i] :
( ( contains_slb @ sK1_U @ SY36 )
=> ? [SY37: $i] : ( pair_in_list @ sK1_U @ SY36 @ SY37 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[31]) ).
thf(33,plain,
( ( ! [SY38: $i,SY39: $i,SY40: $i] :
( ( contains_slb @ ( insert_slb @ sK1_U @ ( pair @ SY39 @ SY40 ) ) @ SY38 )
=> ? [SY41: $i] : ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY39 @ SY40 ) ) @ SY38 @ SY41 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[31]) ).
thf(34,plain,
( ( ~ ! [SY38: $i,SY39: $i,SY40: $i] :
( ( contains_slb @ ( insert_slb @ sK1_U @ ( pair @ SY39 @ SY40 ) ) @ SY38 )
=> ? [SY41: $i] : ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY39 @ SY40 ) ) @ SY38 @ SY41 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[33]) ).
thf(35,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(36,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(37,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)],[28]) ).
thf(38,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(39,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)],[26]) ).
thf(40,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(41,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(copy,[status(thm)],[24]) ).
thf(42,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(43,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(copy,[status(thm)],[22]) ).
thf(44,plain,
( ( ! [SY36: $i] :
( ( contains_slb @ sK1_U @ SY36 )
=> ? [SY37: $i] : ( pair_in_list @ sK1_U @ SY36 @ SY37 ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(45,plain,
( ( ~ ! [SY38: $i,SY39: $i,SY40: $i] :
( ( contains_slb @ ( insert_slb @ sK1_U @ ( pair @ SY39 @ SY40 ) ) @ SY38 )
=> ? [SY41: $i] : ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY39 @ SY40 ) ) @ SY38 @ SY41 ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(46,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( ( SX1 != SX2 ) )
| ~ ( contains_slb @ SX0 @ SX2 ) )
| ( ( lookup_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 )
= ( lookup_slb @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(47,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)],[39]) ).
thf(48,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( ( SX1 != SX2 ) )
| ~ ( contains_slb @ SX0 @ SX2 ) )
| ( ( remove_slb @ ( insert_slb @ SX0 @ ( pair @ SX1 @ SX3 ) ) @ SX2 )
= ( insert_slb @ ( remove_slb @ SX0 @ SX2 ) @ ( pair @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(49,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)],[37]) ).
thf(50,plain,
( ( ! [SX0: $i] :
( ~ ( contains_slb @ sK1_U @ SX0 )
| ~ ! [SX1: $i] :
~ ( pair_in_list @ sK1_U @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(51,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( contains_slb @ ( insert_slb @ sK1_U @ ( pair @ SX1 @ SX2 ) ) @ SX0 )
| ~ ! [SX3: $i] :
~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SX1 @ SX2 ) ) @ SX0 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(52,plain,
! [SV1: $i] :
( ( ! [SY42: $i,SY43: $i] : ( isnonempty_slb @ ( insert_slb @ SV1 @ ( pair @ SY42 @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(53,plain,
! [SV2: $i] :
( ( ~ ( contains_slb @ create_slb @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(54,plain,
! [SV3: $i] :
( ( ! [SY44: $i] :
~ ( pair_in_list @ create_slb @ SV3 @ SY44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(55,plain,
! [SV4: $i] :
( ( ! [SY45: $i,SY46: $i] :
( ( remove_slb @ ( insert_slb @ SV4 @ ( pair @ SY45 @ SY46 ) ) @ SY45 )
= SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(56,plain,
! [SV5: $i] :
( ( ! [SY47: $i,SY48: $i] :
( ( lookup_slb @ ( insert_slb @ SV5 @ ( pair @ SY47 @ SY48 ) ) @ SY47 )
= SY48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(57,plain,
! [SV6: $i] :
( ( ! [SY49: $i,SY50: $i,SY51: $i] :
( ~ ~ ( ~ ( ( SY49 != SY50 ) )
| ~ ( contains_slb @ SV6 @ SY50 ) )
| ( ( lookup_slb @ ( insert_slb @ SV6 @ ( pair @ SY49 @ SY51 ) ) @ SY50 )
= ( lookup_slb @ SV6 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(58,plain,
! [SV7: $i] :
( ( ! [SY52: $i,SY53: $i,SY54: $i,SY55: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SY52 @ SY54 ) ) @ SY53 @ SY55 )
| ( pair_in_list @ SV7 @ SY53 @ SY55 )
| ~ ( ( SY52 != SY53 )
| ( SY54 != SY55 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV7 @ SY53 @ SY55 )
| ~ ( ( SY52 != SY53 )
| ( SY54 != SY55 ) ) )
| ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SY52 @ SY54 ) ) @ SY53 @ SY55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(59,plain,
! [SV8: $i] :
( ( ! [SY56: $i,SY57: $i,SY58: $i] :
( ~ ~ ( ~ ( ( SY56 != SY57 ) )
| ~ ( contains_slb @ SV8 @ SY57 ) )
| ( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SY56 @ SY58 ) ) @ SY57 )
= ( insert_slb @ ( remove_slb @ SV8 @ SY57 ) @ ( pair @ SY56 @ SY58 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(60,plain,
! [SV9: $i] :
( ( ! [SY59: $i,SY60: $i,SY61: $i] :
~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SY59 @ SY61 ) ) @ SY60 )
| ( contains_slb @ SV9 @ SY60 )
| ( SY59 = SY60 ) )
| ~ ( ~ ( ( contains_slb @ SV9 @ SY60 )
| ( SY59 = SY60 ) )
| ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SY59 @ SY61 ) ) @ SY60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(61,plain,
! [SV10: $i] :
( ( ~ ( contains_slb @ sK1_U @ SV10 )
| ~ ! [SY62: $i] :
~ ( pair_in_list @ sK1_U @ SV10 @ SY62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(62,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( contains_slb @ ( insert_slb @ sK1_U @ ( pair @ SX1 @ SX2 ) ) @ SX0 )
| ~ ! [SX3: $i] :
~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SX1 @ SX2 ) ) @ SX0 @ SX3 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(63,plain,
! [SV11: $i,SV1: $i] :
( ( ! [SY63: $i] : ( isnonempty_slb @ ( insert_slb @ SV1 @ ( pair @ SV11 @ SY63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(64,plain,
! [SV2: $i] :
( ( contains_slb @ create_slb @ SV2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(65,plain,
! [SV12: $i,SV3: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV3 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(66,plain,
! [SV13: $i,SV4: $i] :
( ( ! [SY64: $i] :
( ( remove_slb @ ( insert_slb @ SV4 @ ( pair @ SV13 @ SY64 ) ) @ SV13 )
= SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(67,plain,
! [SV14: $i,SV5: $i] :
( ( ! [SY65: $i] :
( ( lookup_slb @ ( insert_slb @ SV5 @ ( pair @ SV14 @ SY65 ) ) @ SV14 )
= SY65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(68,plain,
! [SV6: $i,SV15: $i] :
( ( ! [SY66: $i,SY67: $i] :
( ~ ~ ( ~ ( ( SV15 != SY66 ) )
| ~ ( contains_slb @ SV6 @ SY66 ) )
| ( ( lookup_slb @ ( insert_slb @ SV6 @ ( pair @ SV15 @ SY67 ) ) @ SY66 )
= ( lookup_slb @ SV6 @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(69,plain,
! [SV16: $i,SV7: $i] :
( ( ! [SY68: $i,SY69: $i,SY70: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SY69 ) ) @ SY68 @ SY70 )
| ( pair_in_list @ SV7 @ SY68 @ SY70 )
| ~ ( ( SV16 != SY68 )
| ( SY69 != SY70 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV7 @ SY68 @ SY70 )
| ~ ( ( SV16 != SY68 )
| ( SY69 != SY70 ) ) )
| ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SY69 ) ) @ SY68 @ SY70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(70,plain,
! [SV8: $i,SV17: $i] :
( ( ! [SY71: $i,SY72: $i] :
( ~ ~ ( ~ ( ( SV17 != SY71 ) )
| ~ ( contains_slb @ SV8 @ SY71 ) )
| ( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SV17 @ SY72 ) ) @ SY71 )
= ( insert_slb @ ( remove_slb @ SV8 @ SY71 ) @ ( pair @ SV17 @ SY72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(71,plain,
! [SV18: $i,SV9: $i] :
( ( ! [SY73: $i,SY74: $i] :
~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV18 @ SY74 ) ) @ SY73 )
| ( contains_slb @ SV9 @ SY73 )
| ( SV18 = SY73 ) )
| ~ ( ~ ( ( contains_slb @ SV9 @ SY73 )
| ( SV18 = SY73 ) )
| ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV18 @ SY74 ) ) @ SY73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(72,plain,
! [SV10: $i] :
( ( ( ~ ( contains_slb @ sK1_U @ SV10 ) )
= $true )
| ( ( ~ ! [SY62: $i] :
~ ( pair_in_list @ sK1_U @ SV10 @ SY62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(73,plain,
( ( ! [SY75: $i,SY76: $i] :
( ~ ( contains_slb @ ( insert_slb @ sK1_U @ ( pair @ SY75 @ SY76 ) ) @ sK2_SX0 )
| ~ ! [SY77: $i] :
~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ SY75 @ SY76 ) ) @ sK2_SX0 @ SY77 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[62]) ).
thf(74,plain,
! [SV19: $i,SV11: $i,SV1: $i] :
( ( isnonempty_slb @ ( insert_slb @ SV1 @ ( pair @ SV11 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(75,plain,
! [SV12: $i,SV3: $i] :
( ( pair_in_list @ create_slb @ SV3 @ SV12 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(76,plain,
! [SV20: $i,SV13: $i,SV4: $i] :
( ( ( remove_slb @ ( insert_slb @ SV4 @ ( pair @ SV13 @ SV20 ) ) @ SV13 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(77,plain,
! [SV21: $i,SV14: $i,SV5: $i] :
( ( ( lookup_slb @ ( insert_slb @ SV5 @ ( pair @ SV14 @ SV21 ) ) @ SV14 )
= SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(78,plain,
! [SV6: $i,SV22: $i,SV15: $i] :
( ( ! [SY78: $i] :
( ~ ~ ( ~ ( ( SV15 != SV22 ) )
| ~ ( contains_slb @ SV6 @ SV22 ) )
| ( ( lookup_slb @ ( insert_slb @ SV6 @ ( pair @ SV15 @ SY78 ) ) @ SV22 )
= ( lookup_slb @ SV6 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(79,plain,
! [SV23: $i,SV16: $i,SV7: $i] :
( ( ! [SY79: $i,SY80: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SY79 ) ) @ SV23 @ SY80 )
| ( pair_in_list @ SV7 @ SV23 @ SY80 )
| ~ ( ( SV16 != SV23 )
| ( SY79 != SY80 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV7 @ SV23 @ SY80 )
| ~ ( ( SV16 != SV23 )
| ( SY79 != SY80 ) ) )
| ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SY79 ) ) @ SV23 @ SY80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(80,plain,
! [SV8: $i,SV24: $i,SV17: $i] :
( ( ! [SY81: $i] :
( ~ ~ ( ~ ( ( SV17 != SV24 ) )
| ~ ( contains_slb @ SV8 @ SV24 ) )
| ( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SV17 @ SY81 ) ) @ SV24 )
= ( insert_slb @ ( remove_slb @ SV8 @ SV24 ) @ ( pair @ SV17 @ SY81 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(81,plain,
! [SV25: $i,SV18: $i,SV9: $i] :
( ( ! [SY82: $i] :
~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV18 @ SY82 ) ) @ SV25 )
| ( contains_slb @ SV9 @ SV25 )
| ( SV18 = SV25 ) )
| ~ ( ~ ( ( contains_slb @ SV9 @ SV25 )
| ( SV18 = SV25 ) )
| ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV18 @ SY82 ) ) @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(82,plain,
! [SV10: $i] :
( ( ( contains_slb @ sK1_U @ SV10 )
= $false )
| ( ( ~ ! [SY62: $i] :
~ ( pair_in_list @ sK1_U @ SV10 @ SY62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(83,plain,
( ( ! [SY83: $i] :
( ~ ( contains_slb @ ( insert_slb @ sK1_U @ ( pair @ sK3_SY75 @ SY83 ) ) @ sK2_SX0 )
| ~ ! [SY84: $i] :
~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK3_SY75 @ SY83 ) ) @ sK2_SX0 @ SY84 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[73]) ).
thf(84,plain,
! [SV26: $i,SV6: $i,SV22: $i,SV15: $i] :
( ( ~ ~ ( ~ ( ( SV15 != SV22 ) )
| ~ ( contains_slb @ SV6 @ SV22 ) )
| ( ( lookup_slb @ ( insert_slb @ SV6 @ ( pair @ SV15 @ SV26 ) ) @ SV22 )
= ( lookup_slb @ SV6 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(85,plain,
! [SV23: $i,SV27: $i,SV16: $i,SV7: $i] :
( ( ! [SY85: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SY85 )
| ( pair_in_list @ SV7 @ SV23 @ SY85 )
| ~ ( ( SV16 != SV23 )
| ( SV27 != SY85 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV7 @ SV23 @ SY85 )
| ~ ( ( SV16 != SV23 )
| ( SV27 != SY85 ) ) )
| ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SY85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(86,plain,
! [SV28: $i,SV8: $i,SV24: $i,SV17: $i] :
( ( ~ ~ ( ~ ( ( SV17 != SV24 ) )
| ~ ( contains_slb @ SV8 @ SV24 ) )
| ( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SV17 @ SV28 ) ) @ SV24 )
= ( insert_slb @ ( remove_slb @ SV8 @ SV24 ) @ ( pair @ SV17 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(87,plain,
! [SV25: $i,SV29: $i,SV18: $i,SV9: $i] :
( ( ~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV18 @ SV29 ) ) @ SV25 )
| ( contains_slb @ SV9 @ SV25 )
| ( SV18 = SV25 ) )
| ~ ( ~ ( ( contains_slb @ SV9 @ SV25 )
| ( SV18 = SV25 ) )
| ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV18 @ SV29 ) ) @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(88,plain,
! [SV10: $i] :
( ( ( ! [SY62: $i] :
~ ( pair_in_list @ sK1_U @ SV10 @ SY62 ) )
= $false )
| ( ( contains_slb @ sK1_U @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(89,plain,
( ( ~ ( contains_slb @ ( insert_slb @ sK1_U @ ( pair @ sK3_SY75 @ sK4_SY83 ) ) @ sK2_SX0 )
| ~ ! [SY86: $i] :
~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK3_SY75 @ sK4_SY83 ) ) @ sK2_SX0 @ SY86 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[83]) ).
thf(90,plain,
! [SV26: $i,SV6: $i,SV22: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( ( SV15 != SV22 ) )
| ~ ( contains_slb @ SV6 @ SV22 ) ) )
= $true )
| ( ( ( lookup_slb @ ( insert_slb @ SV6 @ ( pair @ SV15 @ SV26 ) ) @ SV22 )
= ( lookup_slb @ SV6 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(91,plain,
! [SV30: $i,SV23: $i,SV27: $i,SV16: $i,SV7: $i] :
( ( ~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 )
| ( pair_in_list @ SV7 @ SV23 @ SV30 )
| ~ ( ( SV16 != SV23 )
| ( SV27 != SV30 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV7 @ SV23 @ SV30 )
| ~ ( ( SV16 != SV23 )
| ( SV27 != SV30 ) ) )
| ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(92,plain,
! [SV28: $i,SV8: $i,SV24: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( ( SV17 != SV24 ) )
| ~ ( contains_slb @ SV8 @ SV24 ) ) )
= $true )
| ( ( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SV17 @ SV28 ) ) @ SV24 )
= ( insert_slb @ ( remove_slb @ SV8 @ SV24 ) @ ( pair @ SV17 @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(93,plain,
! [SV25: $i,SV29: $i,SV18: $i,SV9: $i] :
( ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV18 @ SV29 ) ) @ SV25 )
| ( contains_slb @ SV9 @ SV25 )
| ( SV18 = SV25 ) )
| ~ ( ~ ( ( contains_slb @ SV9 @ SV25 )
| ( SV18 = SV25 ) )
| ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV18 @ SV29 ) ) @ SV25 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(94,plain,
! [SV10: $i] :
( ( ( ~ ( pair_in_list @ sK1_U @ SV10 @ ( sK5_SY62 @ SV10 ) ) )
= $false )
| ( ( contains_slb @ sK1_U @ SV10 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[88]) ).
thf(95,plain,
( ( ~ ( contains_slb @ ( insert_slb @ sK1_U @ ( pair @ sK3_SY75 @ sK4_SY83 ) ) @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(96,plain,
( ( ~ ! [SY86: $i] :
~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK3_SY75 @ sK4_SY83 ) ) @ sK2_SX0 @ SY86 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(97,plain,
! [SV26: $i,SV6: $i,SV22: $i,SV15: $i] :
( ( ( ~ ( ~ ( ( SV15 != SV22 ) )
| ~ ( contains_slb @ SV6 @ SV22 ) ) )
= $false )
| ( ( ( lookup_slb @ ( insert_slb @ SV6 @ ( pair @ SV15 @ SV26 ) ) @ SV22 )
= ( lookup_slb @ SV6 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(98,plain,
! [SV30: $i,SV23: $i,SV27: $i,SV16: $i,SV7: $i] :
( ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 )
| ( pair_in_list @ SV7 @ SV23 @ SV30 )
| ~ ( ( SV16 != SV23 )
| ( SV27 != SV30 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV7 @ SV23 @ SV30 )
| ~ ( ( SV16 != SV23 )
| ( SV27 != SV30 ) ) )
| ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(99,plain,
! [SV28: $i,SV8: $i,SV24: $i,SV17: $i] :
( ( ( ~ ( ~ ( ( SV17 != SV24 ) )
| ~ ( contains_slb @ SV8 @ SV24 ) ) )
= $false )
| ( ( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SV17 @ SV28 ) ) @ SV24 )
= ( insert_slb @ ( remove_slb @ SV8 @ SV24 ) @ ( pair @ SV17 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(100,plain,
! [SV25: $i,SV29: $i,SV18: $i,SV9: $i] :
( ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV18 @ SV29 ) ) @ SV25 )
| ( contains_slb @ SV9 @ SV25 )
| ( SV18 = SV25 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(101,plain,
! [SV29: $i,SV18: $i,SV25: $i,SV9: $i] :
( ( ~ ( ~ ( ( contains_slb @ SV9 @ SV25 )
| ( SV18 = SV25 ) )
| ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV18 @ SV29 ) ) @ SV25 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(102,plain,
! [SV10: $i] :
( ( ( pair_in_list @ sK1_U @ SV10 @ ( sK5_SY62 @ SV10 ) )
= $true )
| ( ( contains_slb @ sK1_U @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(103,plain,
( ( contains_slb @ ( insert_slb @ sK1_U @ ( pair @ sK3_SY75 @ sK4_SY83 ) ) @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(104,plain,
( ( ! [SY86: $i] :
~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK3_SY75 @ sK4_SY83 ) ) @ sK2_SX0 @ SY86 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(105,plain,
! [SV26: $i,SV6: $i,SV22: $i,SV15: $i] :
( ( ( ~ ( ( SV15 != SV22 ) )
| ~ ( contains_slb @ SV6 @ SV22 ) )
= $true )
| ( ( ( lookup_slb @ ( insert_slb @ SV6 @ ( pair @ SV15 @ SV26 ) ) @ SV22 )
= ( lookup_slb @ SV6 @ SV22 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(106,plain,
! [SV30: $i,SV23: $i,SV27: $i,SV16: $i,SV7: $i] :
( ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 )
| ( pair_in_list @ SV7 @ SV23 @ SV30 )
| ~ ( ( SV16 != SV23 )
| ( SV27 != SV30 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(107,plain,
! [SV27: $i,SV16: $i,SV30: $i,SV23: $i,SV7: $i] :
( ( ~ ( ~ ( ( pair_in_list @ SV7 @ SV23 @ SV30 )
| ~ ( ( SV16 != SV23 )
| ( SV27 != SV30 ) ) )
| ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(108,plain,
! [SV28: $i,SV8: $i,SV24: $i,SV17: $i] :
( ( ( ~ ( ( SV17 != SV24 ) )
| ~ ( contains_slb @ SV8 @ SV24 ) )
= $true )
| ( ( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SV17 @ SV28 ) ) @ SV24 )
= ( insert_slb @ ( remove_slb @ SV8 @ SV24 ) @ ( pair @ SV17 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(109,plain,
! [SV25: $i,SV29: $i,SV18: $i,SV9: $i] :
( ( ~ ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV18 @ SV29 ) ) @ SV25 )
| ( contains_slb @ SV9 @ SV25 )
| ( SV18 = SV25 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(110,plain,
! [SV29: $i,SV18: $i,SV25: $i,SV9: $i] :
( ( ~ ( ( contains_slb @ SV9 @ SV25 )
| ( SV18 = SV25 ) )
| ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV18 @ SV29 ) ) @ SV25 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(111,plain,
! [SV31: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK3_SY75 @ sK4_SY83 ) ) @ sK2_SX0 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(112,plain,
! [SV26: $i,SV6: $i,SV22: $i,SV15: $i] :
( ( ( ~ ( ( SV15 != SV22 ) ) )
= $true )
| ( ( ~ ( contains_slb @ SV6 @ SV22 ) )
= $true )
| ( ( ( lookup_slb @ ( insert_slb @ SV6 @ ( pair @ SV15 @ SV26 ) ) @ SV22 )
= ( lookup_slb @ SV6 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(113,plain,
! [SV30: $i,SV23: $i,SV27: $i,SV16: $i,SV7: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 )
| ( pair_in_list @ SV7 @ SV23 @ SV30 )
| ~ ( ( SV16 != SV23 )
| ( SV27 != SV30 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(114,plain,
! [SV27: $i,SV16: $i,SV30: $i,SV23: $i,SV7: $i] :
( ( ~ ( ( pair_in_list @ SV7 @ SV23 @ SV30 )
| ~ ( ( SV16 != SV23 )
| ( SV27 != SV30 ) ) )
| ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(115,plain,
! [SV28: $i,SV8: $i,SV24: $i,SV17: $i] :
( ( ( ~ ( ( SV17 != SV24 ) ) )
= $true )
| ( ( ~ ( contains_slb @ SV8 @ SV24 ) )
= $true )
| ( ( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SV17 @ SV28 ) ) @ SV24 )
= ( insert_slb @ ( remove_slb @ SV8 @ SV24 ) @ ( pair @ SV17 @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(116,plain,
! [SV25: $i,SV29: $i,SV18: $i,SV9: $i] :
( ( ( ~ ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV18 @ SV29 ) ) @ SV25 ) )
= $true )
| ( ( ( contains_slb @ SV9 @ SV25 )
| ( SV18 = SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(117,plain,
! [SV29: $i,SV18: $i,SV25: $i,SV9: $i] :
( ( ( ~ ( ( contains_slb @ SV9 @ SV25 )
| ( SV18 = SV25 ) ) )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV18 @ SV29 ) ) @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(118,plain,
! [SV31: $i] :
( ( pair_in_list @ ( insert_slb @ sK1_U @ ( pair @ sK3_SY75 @ sK4_SY83 ) ) @ sK2_SX0 @ SV31 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(119,plain,
! [SV26: $i,SV6: $i,SV22: $i,SV15: $i] :
( ( ( SV15 != SV22 )
= $false )
| ( ( ~ ( contains_slb @ SV6 @ SV22 ) )
= $true )
| ( ( ( lookup_slb @ ( insert_slb @ SV6 @ ( pair @ SV15 @ SV26 ) ) @ SV22 )
= ( lookup_slb @ SV6 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(120,plain,
! [SV30: $i,SV23: $i,SV27: $i,SV16: $i,SV7: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 ) )
= $true )
| ( ( ( pair_in_list @ SV7 @ SV23 @ SV30 )
| ~ ( ( SV16 != SV23 )
| ( SV27 != SV30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(121,plain,
! [SV27: $i,SV16: $i,SV30: $i,SV23: $i,SV7: $i] :
( ( ( ~ ( ( pair_in_list @ SV7 @ SV23 @ SV30 )
| ~ ( ( SV16 != SV23 )
| ( SV27 != SV30 ) ) ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(122,plain,
! [SV28: $i,SV8: $i,SV24: $i,SV17: $i] :
( ( ( SV17 != SV24 )
= $false )
| ( ( ~ ( contains_slb @ SV8 @ SV24 ) )
= $true )
| ( ( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SV17 @ SV28 ) ) @ SV24 )
= ( insert_slb @ ( remove_slb @ SV8 @ SV24 ) @ ( pair @ SV17 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(123,plain,
! [SV25: $i,SV29: $i,SV18: $i,SV9: $i] :
( ( ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV18 @ SV29 ) ) @ SV25 )
= $false )
| ( ( ( contains_slb @ SV9 @ SV25 )
| ( SV18 = SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(124,plain,
! [SV29: $i,SV18: $i,SV25: $i,SV9: $i] :
( ( ( ( contains_slb @ SV9 @ SV25 )
| ( SV18 = SV25 ) )
= $false )
| ( ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV18 @ SV29 ) ) @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(125,plain,
! [SV26: $i,SV6: $i,SV22: $i,SV15: $i] :
( ( ( SV15 = SV22 )
= $true )
| ( ( ~ ( contains_slb @ SV6 @ SV22 ) )
= $true )
| ( ( ( lookup_slb @ ( insert_slb @ SV6 @ ( pair @ SV15 @ SV26 ) ) @ SV22 )
= ( lookup_slb @ SV6 @ SV22 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(126,plain,
! [SV30: $i,SV23: $i,SV27: $i,SV16: $i,SV7: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 )
= $false )
| ( ( ( pair_in_list @ SV7 @ SV23 @ SV30 )
| ~ ( ( SV16 != SV23 )
| ( SV27 != SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(127,plain,
! [SV27: $i,SV16: $i,SV30: $i,SV23: $i,SV7: $i] :
( ( ( ( pair_in_list @ SV7 @ SV23 @ SV30 )
| ~ ( ( SV16 != SV23 )
| ( SV27 != SV30 ) ) )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(128,plain,
! [SV28: $i,SV8: $i,SV24: $i,SV17: $i] :
( ( ( SV17 = SV24 )
= $true )
| ( ( ~ ( contains_slb @ SV8 @ SV24 ) )
= $true )
| ( ( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SV17 @ SV28 ) ) @ SV24 )
= ( insert_slb @ ( remove_slb @ SV8 @ SV24 ) @ ( pair @ SV17 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(129,plain,
! [SV29: $i,SV18: $i,SV25: $i,SV9: $i] :
( ( ( contains_slb @ SV9 @ SV25 )
= $true )
| ( ( SV18 = SV25 )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV18 @ SV29 ) ) @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(130,plain,
! [SV29: $i,SV18: $i,SV25: $i,SV9: $i] :
( ( ( contains_slb @ SV9 @ SV25 )
= $false )
| ( ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV18 @ SV29 ) ) @ SV25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(131,plain,
! [SV29: $i,SV9: $i,SV25: $i,SV18: $i] :
( ( ( SV18 = SV25 )
= $false )
| ( ( contains_slb @ ( insert_slb @ SV9 @ ( pair @ SV18 @ SV29 ) ) @ SV25 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(132,plain,
! [SV26: $i,SV15: $i,SV22: $i,SV6: $i] :
( ( ( contains_slb @ SV6 @ SV22 )
= $false )
| ( ( SV15 = SV22 )
= $true )
| ( ( ( lookup_slb @ ( insert_slb @ SV6 @ ( pair @ SV15 @ SV26 ) ) @ SV22 )
= ( lookup_slb @ SV6 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(133,plain,
! [SV27: $i,SV16: $i,SV30: $i,SV23: $i,SV7: $i] :
( ( ( pair_in_list @ SV7 @ SV23 @ SV30 )
= $true )
| ( ( ~ ( ( SV16 != SV23 )
| ( SV27 != SV30 ) ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(134,plain,
! [SV27: $i,SV16: $i,SV30: $i,SV23: $i,SV7: $i] :
( ( ( pair_in_list @ SV7 @ SV23 @ SV30 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(135,plain,
! [SV7: $i,SV30: $i,SV27: $i,SV23: $i,SV16: $i] :
( ( ( ~ ( ( SV16 != SV23 )
| ( SV27 != SV30 ) ) )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(136,plain,
! [SV28: $i,SV17: $i,SV24: $i,SV8: $i] :
( ( ( contains_slb @ SV8 @ SV24 )
= $false )
| ( ( SV17 = SV24 )
= $true )
| ( ( ( remove_slb @ ( insert_slb @ SV8 @ ( pair @ SV17 @ SV28 ) ) @ SV24 )
= ( insert_slb @ ( remove_slb @ SV8 @ SV24 ) @ ( pair @ SV17 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(137,plain,
! [SV7: $i,SV30: $i,SV27: $i,SV23: $i,SV16: $i] :
( ( ( ( SV16 != SV23 )
| ( SV27 != SV30 ) )
= $false )
| ( ( pair_in_list @ SV7 @ SV23 @ SV30 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(138,plain,
! [SV7: $i,SV30: $i,SV27: $i,SV23: $i,SV16: $i] :
( ( ( ( SV16 != SV23 )
| ( SV27 != SV30 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(139,plain,
! [SV27: $i,SV30: $i,SV7: $i,SV23: $i,SV16: $i] :
( ( ( SV16 != SV23 )
= $false )
| ( ( pair_in_list @ SV7 @ SV23 @ SV30 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(140,plain,
! [SV16: $i,SV23: $i,SV7: $i,SV30: $i,SV27: $i] :
( ( ( SV27 != SV30 )
= $false )
| ( ( pair_in_list @ SV7 @ SV23 @ SV30 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(141,plain,
! [SV7: $i,SV30: $i,SV27: $i,SV23: $i,SV16: $i] :
( ( ( SV16 != SV23 )
= $true )
| ( ( SV27 != SV30 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(142,plain,
! [SV27: $i,SV30: $i,SV7: $i,SV23: $i,SV16: $i] :
( ( ( SV16 = SV23 )
= $true )
| ( ( pair_in_list @ SV7 @ SV23 @ SV30 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(143,plain,
! [SV16: $i,SV23: $i,SV7: $i,SV30: $i,SV27: $i] :
( ( ( SV27 = SV30 )
= $true )
| ( ( pair_in_list @ SV7 @ SV23 @ SV30 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(144,plain,
! [SV7: $i,SV30: $i,SV27: $i,SV23: $i,SV16: $i] :
( ( ( SV16 = SV23 )
= $false )
| ( ( SV27 != SV30 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(145,plain,
! [SV7: $i,SV23: $i,SV16: $i,SV30: $i,SV27: $i] :
( ( ( SV27 = SV30 )
= $false )
| ( ( SV16 = SV23 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV16 @ SV27 ) ) @ SV23 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(146,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[64,145,143,142,136,134,132,131,130,129,118,103,102,77,76,75,74]) ).
thf(147,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV411+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n002.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 16:30:42 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.27
% 0.09/0.27 No.of.Axioms: 9
% 0.09/0.27
% 0.09/0.27 Length.of.Defs: 0
% 0.09/0.27
% 0.09/0.27 Contains.Choice.Funs: false
% 0.09/0.27 .....
% 0.09/0.27
% 0.09/0.27 ********************************
% 0.09/0.27 * All subproblems solved! *
% 0.09/0.27 ********************************
% 0.09/0.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:10,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:146,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.27
% 0.09/0.27 %**** Beginning of derivation protocol ****
% 0.09/0.27 % SZS output start CNFRefutation
% See solution above
% 0.09/0.27
% 0.09/0.27 %**** End of derivation protocol ****
% 0.09/0.27 %**** no. of clauses in derivation: 138 ****
% 0.09/0.27 %**** clause counter: 146 ****
% 0.09/0.27
% 0.09/0.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:10,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:146,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------