%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV366+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 : n011.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 10:57:29 AM UTC 2026
% Result : Theorem 0.58s 0.30s
% Output : CNFRefutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 98 ( 72 unt; 0 typ; 0 def)
% Number of atoms : 511 ( 260 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 1408 ( 162 ~; 154 |; 3 &;1079 @)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 52 usr; 13 con; 0-3 aty)
% Number of variables : 430 ( 0 ^; 430 !; 0 ?; 430 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_bad,type,
bad: $i ).
thf(tp_bottom,type,
bottom: $i ).
thf(tp_check_cpq,type,
check_cpq: $i > $o ).
thf(tp_contains_cpq,type,
contains_cpq: $i > $i > $o ).
thf(tp_contains_pq,type,
contains_pq: $i > $i > $o ).
thf(tp_contains_slb,type,
contains_slb: $i > $i > $o ).
thf(tp_create_pq,type,
create_pq: $i ).
thf(tp_create_slb,type,
create_slb: $i ).
thf(tp_findmin_cpq_eff,type,
findmin_cpq_eff: $i > $i ).
thf(tp_findmin_cpq_res,type,
findmin_cpq_res: $i > $i ).
thf(tp_findmin_pq_eff,type,
findmin_pq_eff: $i > $i > $i ).
thf(tp_findmin_pq_res,type,
findmin_pq_res: $i > $i > $i ).
thf(tp_findmin_pqp_res,type,
findmin_pqp_res: $i > $i ).
thf(tp_i,type,
i: $i > $i ).
thf(tp_insert_cpq,type,
insert_cpq: $i > $i > $i ).
thf(tp_insert_pq,type,
insert_pq: $i > $i > $i ).
thf(tp_insert_pqp,type,
insert_pqp: $i > $i > $i ).
thf(tp_insert_slb,type,
insert_slb: $i > $i > $i ).
thf(tp_isnonempty_pq,type,
isnonempty_pq: $i > $o ).
thf(tp_isnonempty_slb,type,
isnonempty_slb: $i > $o ).
thf(tp_issmallestelement_pq,type,
issmallestelement_pq: $i > $i > $o ).
thf(tp_less_than,type,
less_than: $i > $i > $o ).
thf(tp_lookup_slb,type,
lookup_slb: $i > $i > $i ).
thf(tp_ok,type,
ok: $i > $o ).
thf(tp_pair,type,
pair: $i > $i > $i ).
thf(tp_pair_in_list,type,
pair_in_list: $i > $i > $i > $o ).
thf(tp_phi,type,
phi: $i > $o ).
thf(tp_pi_find_min,type,
pi_find_min: $i > $o ).
thf(tp_pi_remove,type,
pi_remove: $i > $i > $o ).
thf(tp_pi_removemin,type,
pi_removemin: $i > $o ).
thf(tp_pi_sharp_find_min,type,
pi_sharp_find_min: $i > $i > $o ).
thf(tp_pi_sharp_remove,type,
pi_sharp_remove: $i > $i > $o ).
thf(tp_pi_sharp_removemin,type,
pi_sharp_removemin: $i > $i > $o ).
thf(tp_remove_cpq,type,
remove_cpq: $i > $i > $i ).
thf(tp_remove_pq,type,
remove_pq: $i > $i > $i ).
thf(tp_remove_pqp,type,
remove_pqp: $i > $i > $i ).
thf(tp_remove_slb,type,
remove_slb: $i > $i > $i ).
thf(tp_removemin_cpq_eff,type,
removemin_cpq_eff: $i > $i ).
thf(tp_removemin_cpq_res,type,
removemin_cpq_res: $i > $i ).
thf(tp_removemin_pq_eff,type,
removemin_pq_eff: $i > $i > $i ).
thf(tp_removemin_pq_res,type,
removemin_pq_res: $i > $i > $i ).
thf(tp_sK1_U,type,
sK1_U: $i ).
thf(tp_sK2_SY38,type,
sK2_SY38: $i ).
thf(tp_sK3_SY72,type,
sK3_SY72: $i ).
thf(tp_sK4_SY85,type,
sK4_SY85: $i ).
thf(tp_sK5_SY93,type,
sK5_SY93: $i ).
thf(tp_sK6_SY97,type,
sK6_SY97: $i ).
thf(tp_sK7_SY99,type,
sK7_SY99: $i ).
thf(tp_strictly_less_than,type,
strictly_less_than: $i > $i > $o ).
thf(tp_succ_cpq,type,
succ_cpq: $i > $i > $o ).
thf(tp_triple,type,
triple: $i > $i > $i > $i ).
thf(tp_update_slb,type,
update_slb: $i > $i > $i ).
thf(8,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( i @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
= ( insert_pq @ ( i @ ( triple @ U @ V @ W ) ) @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
thf(37,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(39,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(40,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(42,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(44,axiom,
! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).
thf(63,conjecture,
! [U: $i] :
( ! [V: $i,W: $i,X: $i,Y: $i] :
( ( i @ ( triple @ V @ U @ X ) )
= ( i @ ( triple @ W @ U @ Y ) ) )
=> ! [Z: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( i @ ( triple @ Z @ ( insert_slb @ U @ ( pair @ X4 @ X5 ) ) @ X2 ) )
= ( i @ ( triple @ X1 @ ( insert_slb @ U @ ( pair @ X4 @ X5 ) ) @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_co) ).
thf(64,negated_conjecture,
( ( ! [U: $i] :
( ! [V: $i,W: $i,X: $i,Y: $i] :
( ( i @ ( triple @ V @ U @ X ) )
= ( i @ ( triple @ W @ U @ Y ) ) )
=> ! [Z: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( i @ ( triple @ Z @ ( insert_slb @ U @ ( pair @ X4 @ X5 ) ) @ X2 ) )
= ( i @ ( triple @ X1 @ ( insert_slb @ U @ ( pair @ X4 @ X5 ) ) @ X3 ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[63]) ).
thf(65,plain,
( ( ! [U: $i] :
( ! [V: $i,W: $i,X: $i,Y: $i] :
( ( i @ ( triple @ V @ U @ X ) )
= ( i @ ( triple @ W @ U @ Y ) ) )
=> ! [Z: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( i @ ( triple @ Z @ ( insert_slb @ U @ ( pair @ X4 @ X5 ) ) @ X2 ) )
= ( i @ ( triple @ X1 @ ( insert_slb @ U @ ( pair @ X4 @ X5 ) ) @ X3 ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[64]) ).
thf(66,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( i @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
= ( insert_pq @ ( i @ ( triple @ U @ V @ W ) ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(67,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(68,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(69,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)],[40]) ).
thf(70,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)],[42]) ).
thf(71,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(72,plain,
( ( ! [SY34: $i,SY35: $i,SY36: $i,SY37: $i] :
( ( i @ ( triple @ SY34 @ sK1_U @ SY36 ) )
= ( i @ ( triple @ SY35 @ sK1_U @ SY37 ) ) )
=> ! [SY38: $i,SY39: $i,SY40: $i,SY41: $i,SY42: $i,SY43: $i] :
( ( i @ ( triple @ SY38 @ ( insert_slb @ sK1_U @ ( pair @ SY42 @ SY43 ) ) @ SY40 ) )
= ( i @ ( triple @ SY39 @ ( insert_slb @ sK1_U @ ( pair @ SY42 @ SY43 ) ) @ SY41 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[65]) ).
thf(73,plain,
( ( ! [SY34: $i,SY35: $i,SY36: $i,SY37: $i] :
( ( i @ ( triple @ SY34 @ sK1_U @ SY36 ) )
= ( i @ ( triple @ SY35 @ sK1_U @ SY37 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[72]) ).
thf(74,plain,
( ( ! [SY38: $i,SY39: $i,SY40: $i,SY41: $i,SY42: $i,SY43: $i] :
( ( i @ ( triple @ SY38 @ ( insert_slb @ sK1_U @ ( pair @ SY42 @ SY43 ) ) @ SY40 ) )
= ( i @ ( triple @ SY39 @ ( insert_slb @ sK1_U @ ( pair @ SY42 @ SY43 ) ) @ SY41 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[72]) ).
thf(75,plain,
( ( ~ ! [SY38: $i,SY39: $i,SY40: $i,SY41: $i,SY42: $i,SY43: $i] :
( ( i @ ( triple @ SY38 @ ( insert_slb @ sK1_U @ ( pair @ SY42 @ SY43 ) ) @ SY40 ) )
= ( i @ ( triple @ SY39 @ ( insert_slb @ sK1_U @ ( pair @ SY42 @ SY43 ) ) @ SY41 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[74]) ).
thf(76,plain,
( ( ! [U: $i,V: $i,W: $i] : ( isnonempty_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(77,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_slb @ ( insert_slb @ U @ ( pair @ V @ X ) ) @ W )
<=> ( ( contains_slb @ U @ W )
| ( V = W ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(78,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)],[69]) ).
thf(79,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( remove_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= U ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(80,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( lookup_slb @ ( insert_slb @ U @ ( pair @ V @ W ) ) @ V )
= W ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(81,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i] :
( ( i @ ( triple @ U @ ( insert_slb @ V @ ( pair @ X @ Y ) ) @ W ) )
= ( insert_pq @ ( i @ ( triple @ U @ V @ W ) ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(82,plain,
( ( ! [SY34: $i,SY35: $i,SY36: $i,SY37: $i] :
( ( i @ ( triple @ SY34 @ sK1_U @ SY36 ) )
= ( i @ ( triple @ SY35 @ sK1_U @ SY37 ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(83,plain,
( ( ~ ! [SY38: $i,SY39: $i,SY40: $i,SY41: $i,SY42: $i,SY43: $i] :
( ( i @ ( triple @ SY38 @ ( insert_slb @ sK1_U @ ( pair @ SY42 @ SY43 ) ) @ SY40 ) )
= ( i @ ( triple @ SY39 @ ( insert_slb @ sK1_U @ ( pair @ SY42 @ SY43 ) ) @ SY41 ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(84,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)],[77]) ).
thf(85,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)],[78]) ).
thf(86,plain,
! [SV1: $i] :
( ( ! [SY44: $i,SY45: $i] : ( isnonempty_slb @ ( insert_slb @ SV1 @ ( pair @ SY44 @ SY45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(87,plain,
! [SV2: $i] :
( ( ! [SY46: $i,SY47: $i] :
( ( remove_slb @ ( insert_slb @ SV2 @ ( pair @ SY46 @ SY47 ) ) @ SY46 )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(88,plain,
! [SV3: $i] :
( ( ! [SY48: $i,SY49: $i] :
( ( lookup_slb @ ( insert_slb @ SV3 @ ( pair @ SY48 @ SY49 ) ) @ SY48 )
= SY49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(89,plain,
! [SV4: $i] :
( ( ! [SY50: $i,SY51: $i,SY52: $i,SY53: $i] :
( ( i @ ( triple @ SV4 @ ( insert_slb @ SY50 @ ( pair @ SY52 @ SY53 ) ) @ SY51 ) )
= ( insert_pq @ ( i @ ( triple @ SV4 @ SY50 @ SY51 ) ) @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(90,plain,
! [SV5: $i] :
( ( ! [SY54: $i,SY55: $i,SY56: $i] :
( ( i @ ( triple @ SV5 @ sK1_U @ SY55 ) )
= ( i @ ( triple @ SY54 @ sK1_U @ SY56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(91,plain,
( ( ! [SY38: $i,SY39: $i,SY40: $i,SY41: $i,SY42: $i,SY43: $i] :
( ( i @ ( triple @ SY38 @ ( insert_slb @ sK1_U @ ( pair @ SY42 @ SY43 ) ) @ SY40 ) )
= ( i @ ( triple @ SY39 @ ( insert_slb @ sK1_U @ ( pair @ SY42 @ SY43 ) ) @ SY41 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(92,plain,
! [SV6: $i] :
( ( ! [SY57: $i,SY58: $i,SY59: $i] :
~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV6 @ ( pair @ SY57 @ SY59 ) ) @ SY58 )
| ( contains_slb @ SV6 @ SY58 )
| ( SY57 = SY58 ) )
| ~ ( ~ ( ( contains_slb @ SV6 @ SY58 )
| ( SY57 = SY58 ) )
| ( contains_slb @ ( insert_slb @ SV6 @ ( pair @ SY57 @ SY59 ) ) @ SY58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(93,plain,
! [SV7: $i] :
( ( ! [SY60: $i,SY61: $i,SY62: $i,SY63: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SY60 @ SY62 ) ) @ SY61 @ SY63 )
| ( pair_in_list @ SV7 @ SY61 @ SY63 )
| ~ ( ( SY60 != SY61 )
| ( SY62 != SY63 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV7 @ SY61 @ SY63 )
| ~ ( ( SY60 != SY61 )
| ( SY62 != SY63 ) ) )
| ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SY60 @ SY62 ) ) @ SY61 @ SY63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(94,plain,
! [SV8: $i,SV1: $i] :
( ( ! [SY64: $i] : ( isnonempty_slb @ ( insert_slb @ SV1 @ ( pair @ SV8 @ SY64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(95,plain,
! [SV9: $i,SV2: $i] :
( ( ! [SY65: $i] :
( ( remove_slb @ ( insert_slb @ SV2 @ ( pair @ SV9 @ SY65 ) ) @ SV9 )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(96,plain,
! [SV10: $i,SV3: $i] :
( ( ! [SY66: $i] :
( ( lookup_slb @ ( insert_slb @ SV3 @ ( pair @ SV10 @ SY66 ) ) @ SV10 )
= SY66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(97,plain,
! [SV11: $i,SV4: $i] :
( ( ! [SY67: $i,SY68: $i,SY69: $i] :
( ( i @ ( triple @ SV4 @ ( insert_slb @ SV11 @ ( pair @ SY68 @ SY69 ) ) @ SY67 ) )
= ( insert_pq @ ( i @ ( triple @ SV4 @ SV11 @ SY67 ) ) @ SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(98,plain,
! [SV12: $i,SV5: $i] :
( ( ! [SY70: $i,SY71: $i] :
( ( i @ ( triple @ SV5 @ sK1_U @ SY70 ) )
= ( i @ ( triple @ SV12 @ sK1_U @ SY71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(99,plain,
( ( ! [SY72: $i,SY73: $i,SY74: $i,SY75: $i,SY76: $i] :
( ( i @ ( triple @ sK2_SY38 @ ( insert_slb @ sK1_U @ ( pair @ SY75 @ SY76 ) ) @ SY73 ) )
= ( i @ ( triple @ SY72 @ ( insert_slb @ sK1_U @ ( pair @ SY75 @ SY76 ) ) @ SY74 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[91]) ).
thf(100,plain,
! [SV13: $i,SV6: $i] :
( ( ! [SY77: $i,SY78: $i] :
~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV6 @ ( pair @ SV13 @ SY78 ) ) @ SY77 )
| ( contains_slb @ SV6 @ SY77 )
| ( SV13 = SY77 ) )
| ~ ( ~ ( ( contains_slb @ SV6 @ SY77 )
| ( SV13 = SY77 ) )
| ( contains_slb @ ( insert_slb @ SV6 @ ( pair @ SV13 @ SY78 ) ) @ SY77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(101,plain,
! [SV14: $i,SV7: $i] :
( ( ! [SY79: $i,SY80: $i,SY81: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SY80 ) ) @ SY79 @ SY81 )
| ( pair_in_list @ SV7 @ SY79 @ SY81 )
| ~ ( ( SV14 != SY79 )
| ( SY80 != SY81 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV7 @ SY79 @ SY81 )
| ~ ( ( SV14 != SY79 )
| ( SY80 != SY81 ) ) )
| ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SY80 ) ) @ SY79 @ SY81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(102,plain,
! [SV15: $i,SV8: $i,SV1: $i] :
( ( isnonempty_slb @ ( insert_slb @ SV1 @ ( pair @ SV8 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(103,plain,
! [SV16: $i,SV9: $i,SV2: $i] :
( ( ( remove_slb @ ( insert_slb @ SV2 @ ( pair @ SV9 @ SV16 ) ) @ SV9 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(104,plain,
! [SV17: $i,SV10: $i,SV3: $i] :
( ( ( lookup_slb @ ( insert_slb @ SV3 @ ( pair @ SV10 @ SV17 ) ) @ SV10 )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(105,plain,
! [SV18: $i,SV11: $i,SV4: $i] :
( ( ! [SY82: $i,SY83: $i] :
( ( i @ ( triple @ SV4 @ ( insert_slb @ SV11 @ ( pair @ SY82 @ SY83 ) ) @ SV18 ) )
= ( insert_pq @ ( i @ ( triple @ SV4 @ SV11 @ SV18 ) ) @ SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(106,plain,
! [SV12: $i,SV19: $i,SV5: $i] :
( ( ! [SY84: $i] :
( ( i @ ( triple @ SV5 @ sK1_U @ SV19 ) )
= ( i @ ( triple @ SV12 @ sK1_U @ SY84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(107,plain,
( ( ! [SY85: $i,SY86: $i,SY87: $i,SY88: $i] :
( ( i @ ( triple @ sK2_SY38 @ ( insert_slb @ sK1_U @ ( pair @ SY87 @ SY88 ) ) @ SY85 ) )
= ( i @ ( triple @ sK3_SY72 @ ( insert_slb @ sK1_U @ ( pair @ SY87 @ SY88 ) ) @ SY86 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[99]) ).
thf(108,plain,
! [SV20: $i,SV13: $i,SV6: $i] :
( ( ! [SY89: $i] :
~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV6 @ ( pair @ SV13 @ SY89 ) ) @ SV20 )
| ( contains_slb @ SV6 @ SV20 )
| ( SV13 = SV20 ) )
| ~ ( ~ ( ( contains_slb @ SV6 @ SV20 )
| ( SV13 = SV20 ) )
| ( contains_slb @ ( insert_slb @ SV6 @ ( pair @ SV13 @ SY89 ) ) @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(109,plain,
! [SV21: $i,SV14: $i,SV7: $i] :
( ( ! [SY90: $i,SY91: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SY90 ) ) @ SV21 @ SY91 )
| ( pair_in_list @ SV7 @ SV21 @ SY91 )
| ~ ( ( SV14 != SV21 )
| ( SY90 != SY91 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV7 @ SV21 @ SY91 )
| ~ ( ( SV14 != SV21 )
| ( SY90 != SY91 ) ) )
| ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SY90 ) ) @ SV21 @ SY91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(110,plain,
! [SV18: $i,SV22: $i,SV11: $i,SV4: $i] :
( ( ! [SY92: $i] :
( ( i @ ( triple @ SV4 @ ( insert_slb @ SV11 @ ( pair @ SV22 @ SY92 ) ) @ SV18 ) )
= ( insert_pq @ ( i @ ( triple @ SV4 @ SV11 @ SV18 ) ) @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(111,plain,
! [SV23: $i,SV12: $i,SV19: $i,SV5: $i] :
( ( ( i @ ( triple @ SV5 @ sK1_U @ SV19 ) )
= ( i @ ( triple @ SV12 @ sK1_U @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(112,plain,
( ( ! [SY93: $i,SY94: $i,SY95: $i] :
( ( i @ ( triple @ sK2_SY38 @ ( insert_slb @ sK1_U @ ( pair @ SY94 @ SY95 ) ) @ sK4_SY85 ) )
= ( i @ ( triple @ sK3_SY72 @ ( insert_slb @ sK1_U @ ( pair @ SY94 @ SY95 ) ) @ SY93 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[107]) ).
thf(113,plain,
! [SV20: $i,SV24: $i,SV13: $i,SV6: $i] :
( ( ~ ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV6 @ ( pair @ SV13 @ SV24 ) ) @ SV20 )
| ( contains_slb @ SV6 @ SV20 )
| ( SV13 = SV20 ) )
| ~ ( ~ ( ( contains_slb @ SV6 @ SV20 )
| ( SV13 = SV20 ) )
| ( contains_slb @ ( insert_slb @ SV6 @ ( pair @ SV13 @ SV24 ) ) @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(114,plain,
! [SV21: $i,SV25: $i,SV14: $i,SV7: $i] :
( ( ! [SY96: $i] :
~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SY96 )
| ( pair_in_list @ SV7 @ SV21 @ SY96 )
| ~ ( ( SV14 != SV21 )
| ( SV25 != SY96 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV7 @ SV21 @ SY96 )
| ~ ( ( SV14 != SV21 )
| ( SV25 != SY96 ) ) )
| ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SY96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(115,plain,
! [SV18: $i,SV26: $i,SV22: $i,SV11: $i,SV4: $i] :
( ( ( i @ ( triple @ SV4 @ ( insert_slb @ SV11 @ ( pair @ SV22 @ SV26 ) ) @ SV18 ) )
= ( insert_pq @ ( i @ ( triple @ SV4 @ SV11 @ SV18 ) ) @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(116,plain,
( ( ! [SY97: $i,SY98: $i] :
( ( i @ ( triple @ sK2_SY38 @ ( insert_slb @ sK1_U @ ( pair @ SY97 @ SY98 ) ) @ sK4_SY85 ) )
= ( i @ ( triple @ sK3_SY72 @ ( insert_slb @ sK1_U @ ( pair @ SY97 @ SY98 ) ) @ sK5_SY93 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[112]) ).
thf(117,plain,
! [SV20: $i,SV24: $i,SV13: $i,SV6: $i] :
( ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV6 @ ( pair @ SV13 @ SV24 ) ) @ SV20 )
| ( contains_slb @ SV6 @ SV20 )
| ( SV13 = SV20 ) )
| ~ ( ~ ( ( contains_slb @ SV6 @ SV20 )
| ( SV13 = SV20 ) )
| ( contains_slb @ ( insert_slb @ SV6 @ ( pair @ SV13 @ SV24 ) ) @ SV20 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(118,plain,
! [SV27: $i,SV21: $i,SV25: $i,SV14: $i,SV7: $i] :
( ( ~ ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 )
| ( pair_in_list @ SV7 @ SV21 @ SV27 )
| ~ ( ( SV14 != SV21 )
| ( SV25 != SV27 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV7 @ SV21 @ SV27 )
| ~ ( ( SV14 != SV21 )
| ( SV25 != SV27 ) ) )
| ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(119,plain,
( ( ! [SY99: $i] :
( ( i @ ( triple @ sK2_SY38 @ ( insert_slb @ sK1_U @ ( pair @ sK6_SY97 @ SY99 ) ) @ sK4_SY85 ) )
= ( i @ ( triple @ sK3_SY72 @ ( insert_slb @ sK1_U @ ( pair @ sK6_SY97 @ SY99 ) ) @ sK5_SY93 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[116]) ).
thf(120,plain,
! [SV20: $i,SV24: $i,SV13: $i,SV6: $i] :
( ( ~ ( ~ ( contains_slb @ ( insert_slb @ SV6 @ ( pair @ SV13 @ SV24 ) ) @ SV20 )
| ( contains_slb @ SV6 @ SV20 )
| ( SV13 = SV20 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(121,plain,
! [SV24: $i,SV13: $i,SV20: $i,SV6: $i] :
( ( ~ ( ~ ( ( contains_slb @ SV6 @ SV20 )
| ( SV13 = SV20 ) )
| ( contains_slb @ ( insert_slb @ SV6 @ ( pair @ SV13 @ SV24 ) ) @ SV20 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(122,plain,
! [SV27: $i,SV21: $i,SV25: $i,SV14: $i,SV7: $i] :
( ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 )
| ( pair_in_list @ SV7 @ SV21 @ SV27 )
| ~ ( ( SV14 != SV21 )
| ( SV25 != SV27 ) ) )
| ~ ( ~ ( ( pair_in_list @ SV7 @ SV21 @ SV27 )
| ~ ( ( SV14 != SV21 )
| ( SV25 != SV27 ) ) )
| ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(123,plain,
( ( ( i @ ( triple @ sK2_SY38 @ ( insert_slb @ sK1_U @ ( pair @ sK6_SY97 @ sK7_SY99 ) ) @ sK4_SY85 ) )
= ( i @ ( triple @ sK3_SY72 @ ( insert_slb @ sK1_U @ ( pair @ sK6_SY97 @ sK7_SY99 ) ) @ sK5_SY93 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[119]) ).
thf(124,plain,
! [SV20: $i,SV24: $i,SV13: $i,SV6: $i] :
( ( ~ ( contains_slb @ ( insert_slb @ SV6 @ ( pair @ SV13 @ SV24 ) ) @ SV20 )
| ( contains_slb @ SV6 @ SV20 )
| ( SV13 = SV20 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(125,plain,
! [SV24: $i,SV13: $i,SV20: $i,SV6: $i] :
( ( ~ ( ( contains_slb @ SV6 @ SV20 )
| ( SV13 = SV20 ) )
| ( contains_slb @ ( insert_slb @ SV6 @ ( pair @ SV13 @ SV24 ) ) @ SV20 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(126,plain,
! [SV27: $i,SV21: $i,SV25: $i,SV14: $i,SV7: $i] :
( ( ~ ( ~ ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 )
| ( pair_in_list @ SV7 @ SV21 @ SV27 )
| ~ ( ( SV14 != SV21 )
| ( SV25 != SV27 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(127,plain,
! [SV25: $i,SV14: $i,SV27: $i,SV21: $i,SV7: $i] :
( ( ~ ( ~ ( ( pair_in_list @ SV7 @ SV21 @ SV27 )
| ~ ( ( SV14 != SV21 )
| ( SV25 != SV27 ) ) )
| ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(128,plain,
! [SV20: $i,SV24: $i,SV13: $i,SV6: $i] :
( ( ( ~ ( contains_slb @ ( insert_slb @ SV6 @ ( pair @ SV13 @ SV24 ) ) @ SV20 ) )
= $true )
| ( ( ( contains_slb @ SV6 @ SV20 )
| ( SV13 = SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(129,plain,
! [SV24: $i,SV13: $i,SV20: $i,SV6: $i] :
( ( ( ~ ( ( contains_slb @ SV6 @ SV20 )
| ( SV13 = SV20 ) ) )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV6 @ ( pair @ SV13 @ SV24 ) ) @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(130,plain,
! [SV27: $i,SV21: $i,SV25: $i,SV14: $i,SV7: $i] :
( ( ~ ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 )
| ( pair_in_list @ SV7 @ SV21 @ SV27 )
| ~ ( ( SV14 != SV21 )
| ( SV25 != SV27 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(131,plain,
! [SV25: $i,SV14: $i,SV27: $i,SV21: $i,SV7: $i] :
( ( ~ ( ( pair_in_list @ SV7 @ SV21 @ SV27 )
| ~ ( ( SV14 != SV21 )
| ( SV25 != SV27 ) ) )
| ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(132,plain,
! [SV20: $i,SV24: $i,SV13: $i,SV6: $i] :
( ( ( contains_slb @ ( insert_slb @ SV6 @ ( pair @ SV13 @ SV24 ) ) @ SV20 )
= $false )
| ( ( ( contains_slb @ SV6 @ SV20 )
| ( SV13 = SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(133,plain,
! [SV24: $i,SV13: $i,SV20: $i,SV6: $i] :
( ( ( ( contains_slb @ SV6 @ SV20 )
| ( SV13 = SV20 ) )
= $false )
| ( ( contains_slb @ ( insert_slb @ SV6 @ ( pair @ SV13 @ SV24 ) ) @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(134,plain,
! [SV27: $i,SV21: $i,SV25: $i,SV14: $i,SV7: $i] :
( ( ( ~ ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 ) )
= $true )
| ( ( ( pair_in_list @ SV7 @ SV21 @ SV27 )
| ~ ( ( SV14 != SV21 )
| ( SV25 != SV27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(135,plain,
! [SV25: $i,SV14: $i,SV27: $i,SV21: $i,SV7: $i] :
( ( ( ~ ( ( pair_in_list @ SV7 @ SV21 @ SV27 )
| ~ ( ( SV14 != SV21 )
| ( SV25 != SV27 ) ) ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(136,plain,
! [SV24: $i,SV13: $i,SV20: $i,SV6: $i] :
( ( ( contains_slb @ SV6 @ SV20 )
= $true )
| ( ( SV13 = SV20 )
= $true )
| ( ( contains_slb @ ( insert_slb @ SV6 @ ( pair @ SV13 @ SV24 ) ) @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(137,plain,
! [SV24: $i,SV13: $i,SV20: $i,SV6: $i] :
( ( ( contains_slb @ SV6 @ SV20 )
= $false )
| ( ( contains_slb @ ( insert_slb @ SV6 @ ( pair @ SV13 @ SV24 ) ) @ SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(138,plain,
! [SV24: $i,SV6: $i,SV20: $i,SV13: $i] :
( ( ( SV13 = SV20 )
= $false )
| ( ( contains_slb @ ( insert_slb @ SV6 @ ( pair @ SV13 @ SV24 ) ) @ SV20 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(139,plain,
! [SV27: $i,SV21: $i,SV25: $i,SV14: $i,SV7: $i] :
( ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 )
= $false )
| ( ( ( pair_in_list @ SV7 @ SV21 @ SV27 )
| ~ ( ( SV14 != SV21 )
| ( SV25 != SV27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(140,plain,
! [SV25: $i,SV14: $i,SV27: $i,SV21: $i,SV7: $i] :
( ( ( ( pair_in_list @ SV7 @ SV21 @ SV27 )
| ~ ( ( SV14 != SV21 )
| ( SV25 != SV27 ) ) )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(141,plain,
! [SV25: $i,SV14: $i,SV27: $i,SV21: $i,SV7: $i] :
( ( ( pair_in_list @ SV7 @ SV21 @ SV27 )
= $true )
| ( ( ~ ( ( SV14 != SV21 )
| ( SV25 != SV27 ) ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(142,plain,
! [SV25: $i,SV14: $i,SV27: $i,SV21: $i,SV7: $i] :
( ( ( pair_in_list @ SV7 @ SV21 @ SV27 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(143,plain,
! [SV7: $i,SV27: $i,SV25: $i,SV21: $i,SV14: $i] :
( ( ( ~ ( ( SV14 != SV21 )
| ( SV25 != SV27 ) ) )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[140]) ).
thf(144,plain,
! [SV7: $i,SV27: $i,SV25: $i,SV21: $i,SV14: $i] :
( ( ( ( SV14 != SV21 )
| ( SV25 != SV27 ) )
= $false )
| ( ( pair_in_list @ SV7 @ SV21 @ SV27 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(145,plain,
! [SV7: $i,SV27: $i,SV25: $i,SV21: $i,SV14: $i] :
( ( ( ( SV14 != SV21 )
| ( SV25 != SV27 ) )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(146,plain,
! [SV25: $i,SV27: $i,SV7: $i,SV21: $i,SV14: $i] :
( ( ( SV14 != SV21 )
= $false )
| ( ( pair_in_list @ SV7 @ SV21 @ SV27 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(147,plain,
! [SV14: $i,SV21: $i,SV7: $i,SV27: $i,SV25: $i] :
( ( ( SV25 != SV27 )
= $false )
| ( ( pair_in_list @ SV7 @ SV21 @ SV27 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(148,plain,
! [SV7: $i,SV27: $i,SV25: $i,SV21: $i,SV14: $i] :
( ( ( SV14 != SV21 )
= $true )
| ( ( SV25 != SV27 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(149,plain,
! [SV25: $i,SV27: $i,SV7: $i,SV21: $i,SV14: $i] :
( ( ( SV14 = SV21 )
= $true )
| ( ( pair_in_list @ SV7 @ SV21 @ SV27 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(150,plain,
! [SV14: $i,SV21: $i,SV7: $i,SV27: $i,SV25: $i] :
( ( ( SV25 = SV27 )
= $true )
| ( ( pair_in_list @ SV7 @ SV21 @ SV27 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(151,plain,
! [SV7: $i,SV27: $i,SV25: $i,SV21: $i,SV14: $i] :
( ( ( SV14 = SV21 )
= $false )
| ( ( SV25 != SV27 )
= $true )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(152,plain,
! [SV7: $i,SV21: $i,SV14: $i,SV27: $i,SV25: $i] :
( ( ( SV25 = SV27 )
= $false )
| ( ( SV14 = SV21 )
= $false )
| ( ( pair_in_list @ ( insert_slb @ SV7 @ ( pair @ SV14 @ SV25 ) ) @ SV21 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(153,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[102,152,150,149,142,138,137,136,123,115,111,104,103]) ).
thf(154,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[153]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV366+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.17 % Computer : n011.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 16:27:21 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.58/0.30
% 0.58/0.30 No.of.Axioms: 6
% 0.58/0.30
% 0.58/0.30 Length.of.Defs: 0
% 0.58/0.30
% 0.58/0.30 Contains.Choice.Funs: false
% 0.58/0.30 ....
% 0.58/0.30
% 0.58/0.30 ********************************
% 0.58/0.30 * All subproblems solved! *
% 0.58/0.30 ********************************
% 0.58/0.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:7,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:153,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.58/0.30
% 0.58/0.30 %**** Beginning of derivation protocol ****
% 0.58/0.30 % SZS output start CNFRefutation
% See solution above
% 0.58/0.30
% 0.58/0.30 %**** End of derivation protocol ****
% 0.58/0.30 %**** no. of clauses in derivation: 98 ****
% 0.58/0.30 %**** clause counter: 153 ****
% 0.58/0.30
% 0.58/0.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:7,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:153,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------