%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV408+2 : 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 : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:57:36 AM UTC 2026
% Result : Theorem 0.53s 0.36s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 166 ( 108 unt; 0 typ; 0 def)
% Number of atoms : 834 ( 242 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 1788 ( 314 ~; 187 |; 29 &;1230 @)
% ( 6 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 32 usr; 9 con; 0-3 aty)
% Number of variables : 425 ( 0 ^; 412 !; 13 ?; 425 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_bad,type,
bad: $i ).
thf(tp_bottom,type,
bottom: $i ).
thf(tp_check_cpq,type,
check_cpq: $i > $o ).
thf(tp_contains_cpq,type,
contains_cpq: $i > $i > $o ).
thf(tp_contains_slb,type,
contains_slb: $i > $i > $o ).
thf(tp_create_slb,type,
create_slb: $i ).
thf(tp_findmin_cpq_eff,type,
findmin_cpq_eff: $i > $i ).
thf(tp_findmin_cpq_res,type,
findmin_cpq_res: $i > $i ).
thf(tp_findmin_pqp_res,type,
findmin_pqp_res: $i > $i ).
thf(tp_insert_cpq,type,
insert_cpq: $i > $i > $i ).
thf(tp_insert_pqp,type,
insert_pqp: $i > $i > $i ).
thf(tp_insert_slb,type,
insert_slb: $i > $i > $i ).
thf(tp_isnonempty_slb,type,
isnonempty_slb: $i > $o ).
thf(tp_less_than,type,
less_than: $i > $i > $o ).
thf(tp_lookup_slb,type,
lookup_slb: $i > $i > $i ).
thf(tp_ok,type,
ok: $i > $o ).
thf(tp_pair,type,
pair: $i > $i > $i ).
thf(tp_pair_in_list,type,
pair_in_list: $i > $i > $i > $o ).
thf(tp_remove_cpq,type,
remove_cpq: $i > $i > $i ).
thf(tp_remove_pqp,type,
remove_pqp: $i > $i > $i ).
thf(tp_remove_slb,type,
remove_slb: $i > $i > $i ).
thf(tp_removemin_cpq_eff,type,
removemin_cpq_eff: $i > $i ).
thf(tp_removemin_cpq_res,type,
removemin_cpq_res: $i > $i ).
thf(tp_sK1_U,type,
sK1_U: $i ).
thf(tp_sK2_SY38,type,
sK2_SY38: $i ).
thf(tp_sK3_SY42,type,
sK3_SY42: $i ).
thf(tp_sK4_SY45,type,
sK4_SY45: $i ).
thf(tp_sK5_SY72,type,
sK5_SY72: $i > $i > $i ).
thf(tp_strictly_less_than,type,
strictly_less_than: $i > $i > $o ).
thf(tp_succ_cpq,type,
succ_cpq: $i > $i > $o ).
thf(tp_triple,type,
triple: $i > $i > $i > $i ).
thf(tp_update_slb,type,
update_slb: $i > $i > $i ).
thf(1,axiom,
! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).
thf(3,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( V != create_slb )
=> ( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
= ( findmin_pqp_res @ U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).
thf(15,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
<=> ( contains_slb @ V @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).
thf(26,axiom,
! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
thf(32,axiom,
! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
thf(34,axiom,
! [U: $i] :
~ ( contains_slb @ create_slb @ U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
thf(37,axiom,
! [U: $i] : ( less_than @ bottom @ U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bottom_smallest) ).
thf(38,axiom,
! [U: $i,V: $i] :
( ( strictly_less_than @ U @ V )
<=> ( ( less_than @ U @ V )
& ~ ( less_than @ V @ U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stricly_smaller_definition) ).
thf(39,axiom,
! [U: $i] : ( less_than @ U @ U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(40,axiom,
! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality) ).
thf(41,axiom,
! [U: $i,V: $i,W: $i] :
( ( ( less_than @ U @ V )
& ( less_than @ V @ W ) )
=> ( less_than @ U @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(42,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( pair_in_list @ U @ V @ W )
& ( less_than @ X @ W ) )
=> ( pair_in_list @ ( update_slb @ U @ X ) @ V @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l49_li3637) ).
thf(43,axiom,
! [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 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l48_li3839) ).
thf(44,axiom,
! [U: $i,V: $i] :
( ( contains_slb @ U @ V )
=> ? [W: $i] : ( pair_in_list @ U @ V @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_li4647) ).
thf(45,conjecture,
! [U: $i,V: $i,W: $i,X: $i] :
( ( ( contains_slb @ V @ X )
& ( strictly_less_than @ X @ ( findmin_cpq_res @ ( triple @ U @ V @ W ) ) ) )
=> ( ( pair_in_list @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ X @ ( findmin_pqp_res @ U ) )
| ? [Y: $i] :
( ( pair_in_list @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ X @ Y )
& ( less_than @ ( findmin_pqp_res @ U ) @ Y ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l44_co) ).
thf(46,negated_conjecture,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( contains_slb @ V @ X )
& ( strictly_less_than @ X @ ( findmin_cpq_res @ ( triple @ U @ V @ W ) ) ) )
=> ( ( pair_in_list @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ X @ ( findmin_pqp_res @ U ) )
| ? [Y: $i] :
( ( pair_in_list @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ X @ Y )
& ( less_than @ ( findmin_pqp_res @ U ) @ Y ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[45]) ).
thf(47,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( contains_slb @ V @ X )
& ( strictly_less_than @ X @ ( findmin_cpq_res @ ( triple @ U @ V @ W ) ) ) )
=> ( ( pair_in_list @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ X @ ( findmin_pqp_res @ U ) )
| ? [Y: $i] :
( ( pair_in_list @ ( update_slb @ V @ ( findmin_pqp_res @ U ) ) @ X @ Y )
& ( less_than @ ( findmin_pqp_res @ U ) @ Y ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[46]) ).
thf(48,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(49,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( V != create_slb )
=> ( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
= ( findmin_pqp_res @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(50,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
<=> ( contains_slb @ V @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(51,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(52,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(53,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(54,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(55,plain,
( ( ! [U: $i,V: $i] :
( ( strictly_less_than @ U @ V )
<=> ( ( less_than @ U @ V )
& ~ ( less_than @ V @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(56,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(57,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(58,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( less_than @ U @ V )
& ( less_than @ V @ W ) )
=> ( less_than @ U @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(59,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( pair_in_list @ U @ V @ W )
& ( less_than @ X @ W ) )
=> ( pair_in_list @ ( update_slb @ U @ X ) @ V @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(60,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 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(61,plain,
( ( ! [U: $i,V: $i] :
( ( contains_slb @ U @ V )
=> ? [W: $i] : ( pair_in_list @ U @ V @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(62,plain,
( ( ! [SY38: $i,SY39: $i,SY40: $i] :
( ( ( contains_slb @ SY38 @ SY40 )
& ( strictly_less_than @ SY40 @ ( findmin_cpq_res @ ( triple @ sK1_U @ SY38 @ SY39 ) ) ) )
=> ( ( pair_in_list @ ( update_slb @ SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ SY40 @ ( findmin_pqp_res @ sK1_U ) )
| ? [SY41: $i] :
( ( pair_in_list @ ( update_slb @ SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ SY40 @ SY41 )
& ( less_than @ ( findmin_pqp_res @ sK1_U ) @ SY41 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[47]) ).
thf(63,plain,
( ( ! [SY42: $i,SY43: $i] :
( ( ( contains_slb @ sK2_SY38 @ SY43 )
& ( strictly_less_than @ SY43 @ ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY38 @ SY42 ) ) ) )
=> ( ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ SY43 @ ( findmin_pqp_res @ sK1_U ) )
| ? [SY44: $i] :
( ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ SY43 @ SY44 )
& ( less_than @ ( findmin_pqp_res @ sK1_U ) @ SY44 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[62]) ).
thf(64,plain,
( ( ! [SY45: $i] :
( ( ( contains_slb @ sK2_SY38 @ SY45 )
& ( strictly_less_than @ SY45 @ ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY38 @ sK3_SY42 ) ) ) )
=> ( ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ SY45 @ ( findmin_pqp_res @ sK1_U ) )
| ? [SY44: $i] :
( ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ SY45 @ SY44 )
& ( less_than @ ( findmin_pqp_res @ sK1_U ) @ SY44 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[63]) ).
thf(65,plain,
( ( ( ( contains_slb @ sK2_SY38 @ sK4_SY45 )
& ( strictly_less_than @ sK4_SY45 @ ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY38 @ sK3_SY42 ) ) ) )
=> ( ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ sK4_SY45 @ ( findmin_pqp_res @ sK1_U ) )
| ? [SY47: $i] :
( ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ sK4_SY45 @ SY47 )
& ( less_than @ ( findmin_pqp_res @ sK1_U ) @ SY47 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[64]) ).
thf(66,plain,
( ( contains_slb @ sK2_SY38 @ sK4_SY45 )
= $true ),
inference(standard_cnf,[status(thm)],[65]) ).
thf(67,plain,
( ( strictly_less_than @ sK4_SY45 @ ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY38 @ sK3_SY42 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[65]) ).
thf(68,plain,
( ( ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ sK4_SY45 @ ( findmin_pqp_res @ sK1_U ) )
| ? [SY47: $i] :
( ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ sK4_SY45 @ SY47 )
& ( less_than @ ( findmin_pqp_res @ sK1_U ) @ SY47 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[65]) ).
thf(69,plain,
( ( ~ ( ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ sK4_SY45 @ ( findmin_pqp_res @ sK1_U ) )
| ? [SY47: $i] :
( ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ sK4_SY45 @ SY47 )
& ( less_than @ ( findmin_pqp_res @ sK1_U ) @ SY47 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[68]) ).
thf(70,plain,
( ( ! [U: $i,V: $i] :
( ( contains_slb @ U @ V )
=> ? [W: $i] : ( pair_in_list @ U @ V @ W ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(71,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 ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(72,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( ( pair_in_list @ U @ V @ W )
& ( less_than @ X @ W ) )
=> ( pair_in_list @ ( update_slb @ U @ X ) @ V @ W ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(73,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( less_than @ U @ V )
& ( less_than @ V @ W ) )
=> ( less_than @ U @ W ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(74,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(75,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(76,plain,
( ( ! [U: $i,V: $i] :
( ( strictly_less_than @ U @ V )
<=> ( ( less_than @ U @ V )
& ~ ( less_than @ V @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(77,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(78,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(79,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(80,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(81,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( contains_cpq @ ( triple @ U @ V @ W ) @ X )
<=> ( contains_slb @ V @ X ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(82,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ( V != create_slb )
=> ( ( findmin_cpq_res @ ( triple @ U @ V @ W ) )
= ( findmin_pqp_res @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(83,plain,
( ( ! [U: $i] :
( ( removemin_cpq_res @ U )
= ( findmin_cpq_res @ U ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(84,plain,
( ( strictly_less_than @ sK4_SY45 @ ( findmin_cpq_res @ ( triple @ sK1_U @ sK2_SY38 @ sK3_SY42 ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(85,plain,
( ( contains_slb @ sK2_SY38 @ sK4_SY45 )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(86,plain,
( ( ~ ( ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ sK4_SY45 @ ( findmin_pqp_res @ sK1_U ) )
| ? [SY47: $i] :
( ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ sK4_SY45 @ SY47 )
& ( less_than @ ( findmin_pqp_res @ sK1_U ) @ SY47 ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(87,plain,
( ( ~ ( ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ sK4_SY45 @ ( findmin_pqp_res @ sK1_U ) )
| ~ ! [SX0: $i] :
~ ~ ( ~ ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ sK4_SY45 @ SX0 )
| ~ ( less_than @ ( findmin_pqp_res @ sK1_U ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(88,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( pair_in_list @ SX0 @ SX1 @ SX2 )
| ~ ( less_than @ SX3 @ SX2 ) )
| ( pair_in_list @ ( update_slb @ SX0 @ SX3 ) @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(89,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( less_than @ SX0 @ SX1 )
| ~ ( less_than @ SX1 @ SX2 ) )
| ( less_than @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(90,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( pair_in_list @ SX0 @ SX1 @ SX2 )
| ~ ( strictly_less_than @ SX2 @ SX3 ) )
| ( pair_in_list @ ( update_slb @ SX0 @ SX3 ) @ SX1 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(91,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( strictly_less_than @ SX0 @ SX1 )
| ~ ( ~ ( less_than @ SX0 @ SX1 )
| ~ ~ ( less_than @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SX0 @ SX1 )
| ~ ~ ( less_than @ SX1 @ SX0 ) )
| ( strictly_less_than @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(92,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( contains_slb @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ( pair_in_list @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(93,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( contains_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ SX3 )
| ( contains_slb @ SX1 @ SX3 ) )
| ~ ( ~ ( contains_slb @ SX1 @ SX3 )
| ( contains_cpq @ ( triple @ SX0 @ SX1 @ SX2 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(94,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( ( SX1 != create_slb ) )
| ( ( findmin_cpq_res @ ( triple @ SX0 @ SX1 @ SX2 ) )
= ( findmin_pqp_res @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(95,plain,
! [SV1: $i] :
( ( ! [SY48: $i] :
( ( less_than @ SV1 @ SY48 )
| ( less_than @ SY48 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(96,plain,
! [SV2: $i] :
( ( less_than @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(97,plain,
! [SV3: $i] :
( ( less_than @ bottom @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(98,plain,
! [SV4: $i] :
( ( ~ ( contains_slb @ create_slb @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(99,plain,
! [SV5: $i] :
( ( ! [SY49: $i] :
~ ( pair_in_list @ create_slb @ SV5 @ SY49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(100,plain,
! [SV6: $i] :
( ( ( update_slb @ create_slb @ SV6 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(101,plain,
! [SV7: $i] :
( ( ( removemin_cpq_res @ SV7 )
= ( findmin_cpq_res @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(102,plain,
( ( ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ sK4_SY45 @ ( findmin_pqp_res @ sK1_U ) )
| ~ ! [SX0: $i] :
~ ~ ( ~ ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ sK4_SY45 @ SX0 )
| ~ ( less_than @ ( findmin_pqp_res @ sK1_U ) @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(103,plain,
! [SV8: $i] :
( ( ! [SY50: $i,SY51: $i,SY52: $i] :
( ~ ~ ( ~ ( pair_in_list @ SV8 @ SY50 @ SY51 )
| ~ ( less_than @ SY52 @ SY51 ) )
| ( pair_in_list @ ( update_slb @ SV8 @ SY52 ) @ SY50 @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(104,plain,
! [SV9: $i] :
( ( ! [SY53: $i,SY54: $i] :
( ~ ~ ( ~ ( less_than @ SV9 @ SY53 )
| ~ ( less_than @ SY53 @ SY54 ) )
| ( less_than @ SV9 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(105,plain,
! [SV10: $i] :
( ( ! [SY55: $i,SY56: $i,SY57: $i] :
( ~ ~ ( ~ ( pair_in_list @ SV10 @ SY55 @ SY56 )
| ~ ( strictly_less_than @ SY56 @ SY57 ) )
| ( pair_in_list @ ( update_slb @ SV10 @ SY57 ) @ SY55 @ SY57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(106,plain,
! [SV11: $i] :
( ( ! [SY58: $i] :
~ ( ~ ( ~ ( strictly_less_than @ SV11 @ SY58 )
| ~ ( ~ ( less_than @ SV11 @ SY58 )
| ~ ~ ( less_than @ SY58 @ SV11 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV11 @ SY58 )
| ~ ~ ( less_than @ SY58 @ SV11 ) )
| ( strictly_less_than @ SV11 @ SY58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(107,plain,
! [SV12: $i] :
( ( ! [SY59: $i] :
( ~ ( contains_slb @ SV12 @ SY59 )
| ~ ! [SY60: $i] :
~ ( pair_in_list @ SV12 @ SY59 @ SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(108,plain,
! [SV13: $i] :
( ( ! [SY61: $i,SY62: $i,SY63: $i] :
~ ( ~ ( ~ ( contains_cpq @ ( triple @ SV13 @ SY61 @ SY62 ) @ SY63 )
| ( contains_slb @ SY61 @ SY63 ) )
| ~ ( ~ ( contains_slb @ SY61 @ SY63 )
| ( contains_cpq @ ( triple @ SV13 @ SY61 @ SY62 ) @ SY63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(109,plain,
! [SV14: $i] :
( ( ! [SY64: $i,SY65: $i,SY66: $i] :
( ~ ( ( SY64 != create_slb ) )
| ( ( findmin_cpq_res @ ( triple @ SV14 @ SY64 @ SY65 ) )
= ( findmin_pqp_res @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(110,plain,
! [SV15: $i,SV1: $i] :
( ( ( less_than @ SV1 @ SV15 )
| ( less_than @ SV15 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(111,plain,
! [SV4: $i] :
( ( contains_slb @ create_slb @ SV4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(112,plain,
! [SV16: $i,SV5: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV5 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(113,plain,
( ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ sK4_SY45 @ ( findmin_pqp_res @ sK1_U ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(114,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ sK4_SY45 @ SX0 )
| ~ ( less_than @ ( findmin_pqp_res @ sK1_U ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(115,plain,
! [SV17: $i,SV8: $i] :
( ( ! [SY67: $i,SY68: $i] :
( ~ ~ ( ~ ( pair_in_list @ SV8 @ SV17 @ SY67 )
| ~ ( less_than @ SY68 @ SY67 ) )
| ( pair_in_list @ ( update_slb @ SV8 @ SY68 ) @ SV17 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(116,plain,
! [SV18: $i,SV9: $i] :
( ( ! [SY69: $i] :
( ~ ~ ( ~ ( less_than @ SV9 @ SV18 )
| ~ ( less_than @ SV18 @ SY69 ) )
| ( less_than @ SV9 @ SY69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(117,plain,
! [SV19: $i,SV10: $i] :
( ( ! [SY70: $i,SY71: $i] :
( ~ ~ ( ~ ( pair_in_list @ SV10 @ SV19 @ SY70 )
| ~ ( strictly_less_than @ SY70 @ SY71 ) )
| ( pair_in_list @ ( update_slb @ SV10 @ SY71 ) @ SV19 @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(118,plain,
! [SV20: $i,SV11: $i] :
( ( ~ ( ~ ( ~ ( strictly_less_than @ SV11 @ SV20 )
| ~ ( ~ ( less_than @ SV11 @ SV20 )
| ~ ~ ( less_than @ SV20 @ SV11 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV11 @ SV20 )
| ~ ~ ( less_than @ SV20 @ SV11 ) )
| ( strictly_less_than @ SV11 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(119,plain,
! [SV21: $i,SV12: $i] :
( ( ~ ( contains_slb @ SV12 @ SV21 )
| ~ ! [SY72: $i] :
~ ( pair_in_list @ SV12 @ SV21 @ SY72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(120,plain,
! [SV22: $i,SV13: $i] :
( ( ! [SY73: $i,SY74: $i] :
~ ( ~ ( ~ ( contains_cpq @ ( triple @ SV13 @ SV22 @ SY73 ) @ SY74 )
| ( contains_slb @ SV22 @ SY74 ) )
| ~ ( ~ ( contains_slb @ SV22 @ SY74 )
| ( contains_cpq @ ( triple @ SV13 @ SV22 @ SY73 ) @ SY74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(121,plain,
! [SV14: $i,SV23: $i] :
( ( ! [SY75: $i,SY76: $i] :
( ~ ( ( SV23 != create_slb ) )
| ( ( findmin_cpq_res @ ( triple @ SV14 @ SV23 @ SY75 ) )
= ( findmin_pqp_res @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(122,plain,
! [SV15: $i,SV1: $i] :
( ( ( less_than @ SV1 @ SV15 )
= $true )
| ( ( less_than @ SV15 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(123,plain,
! [SV16: $i,SV5: $i] :
( ( pair_in_list @ create_slb @ SV5 @ SV16 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(124,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ sK4_SY45 @ SX0 )
| ~ ( less_than @ ( findmin_pqp_res @ sK1_U ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(125,plain,
! [SV24: $i,SV17: $i,SV8: $i] :
( ( ! [SY77: $i] :
( ~ ~ ( ~ ( pair_in_list @ SV8 @ SV17 @ SV24 )
| ~ ( less_than @ SY77 @ SV24 ) )
| ( pair_in_list @ ( update_slb @ SV8 @ SY77 ) @ SV17 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(126,plain,
! [SV25: $i,SV18: $i,SV9: $i] :
( ( ~ ~ ( ~ ( less_than @ SV9 @ SV18 )
| ~ ( less_than @ SV18 @ SV25 ) )
| ( less_than @ SV9 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(127,plain,
! [SV26: $i,SV19: $i,SV10: $i] :
( ( ! [SY78: $i] :
( ~ ~ ( ~ ( pair_in_list @ SV10 @ SV19 @ SV26 )
| ~ ( strictly_less_than @ SV26 @ SY78 ) )
| ( pair_in_list @ ( update_slb @ SV10 @ SY78 ) @ SV19 @ SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(128,plain,
! [SV20: $i,SV11: $i] :
( ( ~ ( ~ ( strictly_less_than @ SV11 @ SV20 )
| ~ ( ~ ( less_than @ SV11 @ SV20 )
| ~ ~ ( less_than @ SV20 @ SV11 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV11 @ SV20 )
| ~ ~ ( less_than @ SV20 @ SV11 ) )
| ( strictly_less_than @ SV11 @ SV20 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(129,plain,
! [SV21: $i,SV12: $i] :
( ( ( ~ ( contains_slb @ SV12 @ SV21 ) )
= $true )
| ( ( ~ ! [SY72: $i] :
~ ( pair_in_list @ SV12 @ SV21 @ SY72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(130,plain,
! [SV27: $i,SV22: $i,SV13: $i] :
( ( ! [SY79: $i] :
~ ( ~ ( ~ ( contains_cpq @ ( triple @ SV13 @ SV22 @ SV27 ) @ SY79 )
| ( contains_slb @ SV22 @ SY79 ) )
| ~ ( ~ ( contains_slb @ SV22 @ SY79 )
| ( contains_cpq @ ( triple @ SV13 @ SV22 @ SV27 ) @ SY79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(131,plain,
! [SV28: $i,SV14: $i,SV23: $i] :
( ( ! [SY80: $i] :
( ~ ( ( SV23 != create_slb ) )
| ( ( findmin_cpq_res @ ( triple @ SV14 @ SV23 @ SV28 ) )
= ( findmin_pqp_res @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(132,plain,
! [SV29: $i] :
( ( ~ ~ ( ~ ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ sK4_SY45 @ SV29 )
| ~ ( less_than @ ( findmin_pqp_res @ sK1_U ) @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(133,plain,
! [SV30: $i,SV24: $i,SV17: $i,SV8: $i] :
( ( ~ ~ ( ~ ( pair_in_list @ SV8 @ SV17 @ SV24 )
| ~ ( less_than @ SV30 @ SV24 ) )
| ( pair_in_list @ ( update_slb @ SV8 @ SV30 ) @ SV17 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(134,plain,
! [SV25: $i,SV18: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( less_than @ SV9 @ SV18 )
| ~ ( less_than @ SV18 @ SV25 ) ) )
= $true )
| ( ( less_than @ SV9 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(135,plain,
! [SV31: $i,SV26: $i,SV19: $i,SV10: $i] :
( ( ~ ~ ( ~ ( pair_in_list @ SV10 @ SV19 @ SV26 )
| ~ ( strictly_less_than @ SV26 @ SV31 ) )
| ( pair_in_list @ ( update_slb @ SV10 @ SV31 ) @ SV19 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(136,plain,
! [SV20: $i,SV11: $i] :
( ( ~ ( ~ ( strictly_less_than @ SV11 @ SV20 )
| ~ ( ~ ( less_than @ SV11 @ SV20 )
| ~ ~ ( less_than @ SV20 @ SV11 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(137,plain,
! [SV20: $i,SV11: $i] :
( ( ~ ( ~ ~ ( ~ ( less_than @ SV11 @ SV20 )
| ~ ~ ( less_than @ SV20 @ SV11 ) )
| ( strictly_less_than @ SV11 @ SV20 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(138,plain,
! [SV21: $i,SV12: $i] :
( ( ( contains_slb @ SV12 @ SV21 )
= $false )
| ( ( ~ ! [SY72: $i] :
~ ( pair_in_list @ SV12 @ SV21 @ SY72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(139,plain,
! [SV32: $i,SV27: $i,SV22: $i,SV13: $i] :
( ( ~ ( ~ ( ~ ( contains_cpq @ ( triple @ SV13 @ SV22 @ SV27 ) @ SV32 )
| ( contains_slb @ SV22 @ SV32 ) )
| ~ ( ~ ( contains_slb @ SV22 @ SV32 )
| ( contains_cpq @ ( triple @ SV13 @ SV22 @ SV27 ) @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(140,plain,
! [SV28: $i,SV14: $i,SV23: $i] :
( ( ~ ( ( SV23 != create_slb ) )
| ( ( findmin_cpq_res @ ( triple @ SV14 @ SV23 @ SV28 ) )
= ( findmin_pqp_res @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(141,plain,
! [SV29: $i] :
( ( ~ ( ~ ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ sK4_SY45 @ SV29 )
| ~ ( less_than @ ( findmin_pqp_res @ sK1_U ) @ SV29 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(142,plain,
! [SV30: $i,SV24: $i,SV17: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( pair_in_list @ SV8 @ SV17 @ SV24 )
| ~ ( less_than @ SV30 @ SV24 ) ) )
= $true )
| ( ( pair_in_list @ ( update_slb @ SV8 @ SV30 ) @ SV17 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(143,plain,
! [SV25: $i,SV18: $i,SV9: $i] :
( ( ( ~ ( ~ ( less_than @ SV9 @ SV18 )
| ~ ( less_than @ SV18 @ SV25 ) ) )
= $false )
| ( ( less_than @ SV9 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(144,plain,
! [SV31: $i,SV26: $i,SV19: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( pair_in_list @ SV10 @ SV19 @ SV26 )
| ~ ( strictly_less_than @ SV26 @ SV31 ) ) )
= $true )
| ( ( pair_in_list @ ( update_slb @ SV10 @ SV31 ) @ SV19 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(145,plain,
! [SV20: $i,SV11: $i] :
( ( ~ ( strictly_less_than @ SV11 @ SV20 )
| ~ ( ~ ( less_than @ SV11 @ SV20 )
| ~ ~ ( less_than @ SV20 @ SV11 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(146,plain,
! [SV20: $i,SV11: $i] :
( ( ~ ~ ( ~ ( less_than @ SV11 @ SV20 )
| ~ ~ ( less_than @ SV20 @ SV11 ) )
| ( strictly_less_than @ SV11 @ SV20 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(147,plain,
! [SV21: $i,SV12: $i] :
( ( ( ! [SY72: $i] :
~ ( pair_in_list @ SV12 @ SV21 @ SY72 ) )
= $false )
| ( ( contains_slb @ SV12 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(148,plain,
! [SV32: $i,SV27: $i,SV22: $i,SV13: $i] :
( ( ~ ( ~ ( contains_cpq @ ( triple @ SV13 @ SV22 @ SV27 ) @ SV32 )
| ( contains_slb @ SV22 @ SV32 ) )
| ~ ( ~ ( contains_slb @ SV22 @ SV32 )
| ( contains_cpq @ ( triple @ SV13 @ SV22 @ SV27 ) @ SV32 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(149,plain,
! [SV28: $i,SV14: $i,SV23: $i] :
( ( ( ~ ( ( SV23 != create_slb ) ) )
= $true )
| ( ( ( findmin_cpq_res @ ( triple @ SV14 @ SV23 @ SV28 ) )
= ( findmin_pqp_res @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(150,plain,
! [SV29: $i] :
( ( ~ ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ sK4_SY45 @ SV29 )
| ~ ( less_than @ ( findmin_pqp_res @ sK1_U ) @ SV29 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(151,plain,
! [SV30: $i,SV24: $i,SV17: $i,SV8: $i] :
( ( ( ~ ( ~ ( pair_in_list @ SV8 @ SV17 @ SV24 )
| ~ ( less_than @ SV30 @ SV24 ) ) )
= $false )
| ( ( pair_in_list @ ( update_slb @ SV8 @ SV30 ) @ SV17 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(152,plain,
! [SV25: $i,SV18: $i,SV9: $i] :
( ( ( ~ ( less_than @ SV9 @ SV18 )
| ~ ( less_than @ SV18 @ SV25 ) )
= $true )
| ( ( less_than @ SV9 @ SV25 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(153,plain,
! [SV31: $i,SV26: $i,SV19: $i,SV10: $i] :
( ( ( ~ ( ~ ( pair_in_list @ SV10 @ SV19 @ SV26 )
| ~ ( strictly_less_than @ SV26 @ SV31 ) ) )
= $false )
| ( ( pair_in_list @ ( update_slb @ SV10 @ SV31 ) @ SV19 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(154,plain,
! [SV20: $i,SV11: $i] :
( ( ( ~ ( strictly_less_than @ SV11 @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( less_than @ SV11 @ SV20 )
| ~ ~ ( less_than @ SV20 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(155,plain,
! [SV20: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( less_than @ SV11 @ SV20 )
| ~ ~ ( less_than @ SV20 @ SV11 ) ) )
= $true )
| ( ( strictly_less_than @ SV11 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(156,plain,
! [SV21: $i,SV12: $i] :
( ( ( ~ ( pair_in_list @ SV12 @ SV21 @ ( sK5_SY72 @ SV21 @ SV12 ) ) )
= $false )
| ( ( contains_slb @ SV12 @ SV21 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[147]) ).
thf(157,plain,
! [SV32: $i,SV27: $i,SV22: $i,SV13: $i] :
( ( ~ ( ~ ( contains_cpq @ ( triple @ SV13 @ SV22 @ SV27 ) @ SV32 )
| ( contains_slb @ SV22 @ SV32 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[148]) ).
thf(158,plain,
! [SV27: $i,SV13: $i,SV32: $i,SV22: $i] :
( ( ~ ( ~ ( contains_slb @ SV22 @ SV32 )
| ( contains_cpq @ ( triple @ SV13 @ SV22 @ SV27 ) @ SV32 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[148]) ).
thf(159,plain,
! [SV28: $i,SV14: $i,SV23: $i] :
( ( ( SV23 != create_slb )
= $false )
| ( ( ( findmin_cpq_res @ ( triple @ SV14 @ SV23 @ SV28 ) )
= ( findmin_pqp_res @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(160,plain,
! [SV29: $i] :
( ( ( ~ ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ sK4_SY45 @ SV29 ) )
= $true )
| ( ( ~ ( less_than @ ( findmin_pqp_res @ sK1_U ) @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(161,plain,
! [SV30: $i,SV24: $i,SV17: $i,SV8: $i] :
( ( ( ~ ( pair_in_list @ SV8 @ SV17 @ SV24 )
| ~ ( less_than @ SV30 @ SV24 ) )
= $true )
| ( ( pair_in_list @ ( update_slb @ SV8 @ SV30 ) @ SV17 @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(162,plain,
! [SV25: $i,SV18: $i,SV9: $i] :
( ( ( ~ ( less_than @ SV9 @ SV18 ) )
= $true )
| ( ( ~ ( less_than @ SV18 @ SV25 ) )
= $true )
| ( ( less_than @ SV9 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(163,plain,
! [SV31: $i,SV26: $i,SV19: $i,SV10: $i] :
( ( ( ~ ( pair_in_list @ SV10 @ SV19 @ SV26 )
| ~ ( strictly_less_than @ SV26 @ SV31 ) )
= $true )
| ( ( pair_in_list @ ( update_slb @ SV10 @ SV31 ) @ SV19 @ SV31 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(164,plain,
! [SV20: $i,SV11: $i] :
( ( ( strictly_less_than @ SV11 @ SV20 )
= $false )
| ( ( ~ ( ~ ( less_than @ SV11 @ SV20 )
| ~ ~ ( less_than @ SV20 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(165,plain,
! [SV20: $i,SV11: $i] :
( ( ( ~ ( ~ ( less_than @ SV11 @ SV20 )
| ~ ~ ( less_than @ SV20 @ SV11 ) ) )
= $false )
| ( ( strictly_less_than @ SV11 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(166,plain,
! [SV21: $i,SV12: $i] :
( ( ( pair_in_list @ SV12 @ SV21 @ ( sK5_SY72 @ SV21 @ SV12 ) )
= $true )
| ( ( contains_slb @ SV12 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(167,plain,
! [SV32: $i,SV27: $i,SV22: $i,SV13: $i] :
( ( ~ ( contains_cpq @ ( triple @ SV13 @ SV22 @ SV27 ) @ SV32 )
| ( contains_slb @ SV22 @ SV32 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(168,plain,
! [SV27: $i,SV13: $i,SV32: $i,SV22: $i] :
( ( ~ ( contains_slb @ SV22 @ SV32 )
| ( contains_cpq @ ( triple @ SV13 @ SV22 @ SV27 ) @ SV32 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(169,plain,
! [SV28: $i,SV14: $i,SV23: $i] :
( ( ( SV23 = create_slb )
= $true )
| ( ( ( findmin_cpq_res @ ( triple @ SV14 @ SV23 @ SV28 ) )
= ( findmin_pqp_res @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(170,plain,
! [SV29: $i] :
( ( ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ sK4_SY45 @ SV29 )
= $false )
| ( ( ~ ( less_than @ ( findmin_pqp_res @ sK1_U ) @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(171,plain,
! [SV30: $i,SV24: $i,SV17: $i,SV8: $i] :
( ( ( ~ ( pair_in_list @ SV8 @ SV17 @ SV24 ) )
= $true )
| ( ( ~ ( less_than @ SV30 @ SV24 ) )
= $true )
| ( ( pair_in_list @ ( update_slb @ SV8 @ SV30 ) @ SV17 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(172,plain,
! [SV25: $i,SV18: $i,SV9: $i] :
( ( ( less_than @ SV9 @ SV18 )
= $false )
| ( ( ~ ( less_than @ SV18 @ SV25 ) )
= $true )
| ( ( less_than @ SV9 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(173,plain,
! [SV31: $i,SV26: $i,SV19: $i,SV10: $i] :
( ( ( ~ ( pair_in_list @ SV10 @ SV19 @ SV26 ) )
= $true )
| ( ( ~ ( strictly_less_than @ SV26 @ SV31 ) )
= $true )
| ( ( pair_in_list @ ( update_slb @ SV10 @ SV31 ) @ SV19 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(174,plain,
! [SV20: $i,SV11: $i] :
( ( ( ~ ( less_than @ SV11 @ SV20 )
| ~ ~ ( less_than @ SV20 @ SV11 ) )
= $false )
| ( ( strictly_less_than @ SV11 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(175,plain,
! [SV20: $i,SV11: $i] :
( ( ( ~ ( less_than @ SV11 @ SV20 )
| ~ ~ ( less_than @ SV20 @ SV11 ) )
= $true )
| ( ( strictly_less_than @ SV11 @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(176,plain,
! [SV32: $i,SV27: $i,SV22: $i,SV13: $i] :
( ( ( ~ ( contains_cpq @ ( triple @ SV13 @ SV22 @ SV27 ) @ SV32 ) )
= $true )
| ( ( contains_slb @ SV22 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(177,plain,
! [SV27: $i,SV13: $i,SV32: $i,SV22: $i] :
( ( ( ~ ( contains_slb @ SV22 @ SV32 ) )
= $true )
| ( ( contains_cpq @ ( triple @ SV13 @ SV22 @ SV27 ) @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(178,plain,
! [SV29: $i] :
( ( ( less_than @ ( findmin_pqp_res @ sK1_U ) @ SV29 )
= $false )
| ( ( pair_in_list @ ( update_slb @ sK2_SY38 @ ( findmin_pqp_res @ sK1_U ) ) @ sK4_SY45 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(179,plain,
! [SV30: $i,SV24: $i,SV17: $i,SV8: $i] :
( ( ( pair_in_list @ SV8 @ SV17 @ SV24 )
= $false )
| ( ( ~ ( less_than @ SV30 @ SV24 ) )
= $true )
| ( ( pair_in_list @ ( update_slb @ SV8 @ SV30 ) @ SV17 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(180,plain,
! [SV9: $i,SV25: $i,SV18: $i] :
( ( ( less_than @ SV18 @ SV25 )
= $false )
| ( ( less_than @ SV9 @ SV18 )
= $false )
| ( ( less_than @ SV9 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(181,plain,
! [SV31: $i,SV26: $i,SV19: $i,SV10: $i] :
( ( ( pair_in_list @ SV10 @ SV19 @ SV26 )
= $false )
| ( ( ~ ( strictly_less_than @ SV26 @ SV31 ) )
= $true )
| ( ( pair_in_list @ ( update_slb @ SV10 @ SV31 ) @ SV19 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(182,plain,
! [SV20: $i,SV11: $i] :
( ( ( ~ ( less_than @ SV11 @ SV20 ) )
= $false )
| ( ( strictly_less_than @ SV11 @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(183,plain,
! [SV11: $i,SV20: $i] :
( ( ( ~ ~ ( less_than @ SV20 @ SV11 ) )
= $false )
| ( ( strictly_less_than @ SV11 @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(184,plain,
! [SV20: $i,SV11: $i] :
( ( ( ~ ( less_than @ SV11 @ SV20 ) )
= $true )
| ( ( ~ ~ ( less_than @ SV20 @ SV11 ) )
= $true )
| ( ( strictly_less_than @ SV11 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(185,plain,
! [SV32: $i,SV27: $i,SV22: $i,SV13: $i] :
( ( ( contains_cpq @ ( triple @ SV13 @ SV22 @ SV27 ) @ SV32 )
= $false )
| ( ( contains_slb @ SV22 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(186,plain,
! [SV27: $i,SV13: $i,SV32: $i,SV22: $i] :
( ( ( contains_slb @ SV22 @ SV32 )
= $false )
| ( ( contains_cpq @ ( triple @ SV13 @ SV22 @ SV27 ) @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(187,plain,
! [SV17: $i,SV8: $i,SV24: $i,SV30: $i] :
( ( ( less_than @ SV30 @ SV24 )
= $false )
| ( ( pair_in_list @ SV8 @ SV17 @ SV24 )
= $false )
| ( ( pair_in_list @ ( update_slb @ SV8 @ SV30 ) @ SV17 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(188,plain,
! [SV19: $i,SV10: $i,SV31: $i,SV26: $i] :
( ( ( strictly_less_than @ SV26 @ SV31 )
= $false )
| ( ( pair_in_list @ SV10 @ SV19 @ SV26 )
= $false )
| ( ( pair_in_list @ ( update_slb @ SV10 @ SV31 ) @ SV19 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(189,plain,
! [SV20: $i,SV11: $i] :
( ( ( less_than @ SV11 @ SV20 )
= $true )
| ( ( strictly_less_than @ SV11 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(190,plain,
! [SV11: $i,SV20: $i] :
( ( ( ~ ( less_than @ SV20 @ SV11 ) )
= $true )
| ( ( strictly_less_than @ SV11 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(191,plain,
! [SV20: $i,SV11: $i] :
( ( ( less_than @ SV11 @ SV20 )
= $false )
| ( ( ~ ~ ( less_than @ SV20 @ SV11 ) )
= $true )
| ( ( strictly_less_than @ SV11 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(192,plain,
! [SV11: $i,SV20: $i] :
( ( ( less_than @ SV20 @ SV11 )
= $false )
| ( ( strictly_less_than @ SV11 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(193,plain,
! [SV11: $i,SV20: $i] :
( ( ( ~ ( less_than @ SV20 @ SV11 ) )
= $false )
| ( ( less_than @ SV11 @ SV20 )
= $false )
| ( ( strictly_less_than @ SV11 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(194,plain,
! [SV11: $i,SV20: $i] :
( ( ( less_than @ SV20 @ SV11 )
= $true )
| ( ( less_than @ SV11 @ SV20 )
= $false )
| ( ( strictly_less_than @ SV11 @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(195,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[84,194,192,189,188,187,186,185,180,178,169,166,123,122,113,111,101,100,97,96,85]) ).
thf(196,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV408+2 : 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
% 0.08/0.18 % Computer : n005.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 16:27:44 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.53/0.36
% 0.53/0.36 No.of.Axioms: 14
% 0.53/0.36
% 0.53/0.36 Length.of.Defs: 0
% 0.53/0.36
% 0.53/0.36 Contains.Choice.Funs: false
% 0.53/0.36 .....
% 0.53/0.36
% 0.53/0.36 ********************************
% 0.53/0.36 * All subproblems solved! *
% 0.53/0.36 ********************************
% 0.53/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:16,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:195,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.53/0.36
% 0.53/0.36 %**** Beginning of derivation protocol ****
% 0.53/0.36 % SZS output start CNFRefutation
% See solution above
% 0.53/0.36
% 0.53/0.36 %**** End of derivation protocol ****
% 0.53/0.36 %**** no. of clauses in derivation: 166 ****
% 0.53/0.36 %**** clause counter: 195 ****
% 0.53/0.36
% 0.53/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:16,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:195,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------