%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV405+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 0.57s 0.27s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 167 ( 117 unt; 0 typ; 0 def)
% Number of atoms : 808 ( 221 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1360 ( 317 ~; 173 |; 8 &; 832 @)
% ( 9 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 9 con; 0-3 aty)
% Number of variables : 306 ( 0 ^; 306 !; 0 ?; 306 :)
% 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_SY19,type,
sK2_SY19: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY31,type,
sK4_SY31: $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(18,axiom,
! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).
thf(26,axiom,
! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
thf(32,axiom,
! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
thf(34,axiom,
! [U: $i] :
~ ( contains_slb @ create_slb @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
thf(36,axiom,
~ ( isnonempty_slb @ create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
thf(37,axiom,
! [U: $i] : ( less_than @ bottom @ U ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).
thf(39,axiom,
! [U: $i] : ( less_than @ U @ U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(40,axiom,
! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(42,conjecture,
! [U: $i,V: $i] :
( ( check_cpq @ ( triple @ U @ create_slb @ V ) )
<=> ! [W: $i,X: $i] :
( ( pair_in_list @ create_slb @ W @ X )
=> ( less_than @ X @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l41_co) ).
thf(43,negated_conjecture,
( ( ! [U: $i,V: $i] :
( ( check_cpq @ ( triple @ U @ create_slb @ V ) )
<=> ! [W: $i,X: $i] :
( ( pair_in_list @ create_slb @ W @ X )
=> ( less_than @ X @ W ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[42]) ).
thf(44,plain,
( ( ! [U: $i,V: $i] :
( ( check_cpq @ ( triple @ U @ create_slb @ V ) )
<=> ! [W: $i,X: $i] :
( ( pair_in_list @ create_slb @ W @ X )
=> ( less_than @ X @ W ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[43]) ).
thf(45,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(46,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(47,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(48,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(49,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(50,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(51,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(52,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(53,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(54,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(55,plain,
( ( ! [SY19: $i] :
( ( check_cpq @ ( triple @ sK1_U @ create_slb @ SY19 ) )
<=> ! [W: $i,X: $i] :
( ( pair_in_list @ create_slb @ W @ X )
=> ( less_than @ X @ W ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(56,plain,
( ( ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY19 ) )
<=> ! [W: $i,X: $i] :
( ( pair_in_list @ create_slb @ W @ X )
=> ( less_than @ X @ W ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[55]) ).
thf(57,plain,
( ( ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY19 ) )
=> ! [W: $i,X: $i] :
( ( pair_in_list @ create_slb @ W @ X )
=> ( less_than @ X @ W ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[56]) ).
thf(58,plain,
( ( ! [W: $i,X: $i] :
( ( pair_in_list @ create_slb @ W @ X )
=> ( less_than @ X @ W ) )
=> ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY19 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[56]) ).
thf(59,plain,
( ( ~ ( ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY19 ) )
=> ! [W: $i,X: $i] :
( ( pair_in_list @ create_slb @ W @ X )
=> ( less_than @ X @ W ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[57]) ).
thf(60,plain,
( ( ~ ( ! [W: $i,X: $i] :
( ( pair_in_list @ create_slb @ W @ X )
=> ( less_than @ X @ W ) )
=> ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY19 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[58]) ).
thf(61,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( less_than @ U @ V )
& ( less_than @ V @ W ) )
=> ( less_than @ U @ W ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(62,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(63,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(64,plain,
( ( ! [U: $i,V: $i] :
( ( strictly_less_than @ U @ V )
<=> ( ( less_than @ U @ V )
& ~ ( less_than @ V @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(65,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(66,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(67,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(68,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(69,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(70,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(71,plain,
( ( ~ ( ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY19 ) )
=> ! [W: $i,X: $i] :
( ( pair_in_list @ create_slb @ W @ X )
=> ( less_than @ X @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(72,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)],[64]) ).
thf(73,plain,
( ( ~ ( ~ ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY19 ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ create_slb @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(74,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)],[61]) ).
thf(75,plain,
! [SV1: $i] :
( ( ! [SY24: $i] :
( ( less_than @ SV1 @ SY24 )
| ( less_than @ SY24 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(76,plain,
! [SV2: $i] :
( ( less_than @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(77,plain,
! [SV3: $i] :
( ( less_than @ bottom @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(78,plain,
( ( isnonempty_slb @ create_slb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(79,plain,
! [SV4: $i] :
( ( ~ ( contains_slb @ create_slb @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(80,plain,
! [SV5: $i] :
( ( ! [SY25: $i] :
~ ( pair_in_list @ create_slb @ SV5 @ SY25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(81,plain,
! [SV6: $i] :
( ( ( update_slb @ create_slb @ SV6 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(82,plain,
! [SV7: $i] :
( ( ! [SY26: $i] : ( check_cpq @ ( triple @ SV7 @ create_slb @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(83,plain,
! [SV8: $i] :
( ( ! [SY27: $i] :
~ ( ~ ( ~ ( strictly_less_than @ SV8 @ SY27 )
| ~ ( ~ ( less_than @ SV8 @ SY27 )
| ~ ~ ( less_than @ SY27 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV8 @ SY27 )
| ~ ~ ( less_than @ SY27 @ SV8 ) )
| ( strictly_less_than @ SV8 @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(84,plain,
( ( ~ ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY19 ) )
| ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ create_slb @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(85,plain,
! [SV9: $i] :
( ( ! [SY28: $i,SY29: $i] :
( ~ ~ ( ~ ( less_than @ SV9 @ SY28 )
| ~ ( less_than @ SY28 @ SY29 ) )
| ( less_than @ SV9 @ SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(86,plain,
! [SV10: $i,SV1: $i] :
( ( ( less_than @ SV1 @ SV10 )
| ( less_than @ SV10 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(87,plain,
! [SV4: $i] :
( ( contains_slb @ create_slb @ SV4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(88,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV5 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(89,plain,
! [SV12: $i,SV7: $i] :
( ( check_cpq @ ( triple @ SV7 @ create_slb @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(90,plain,
! [SV13: $i,SV8: $i] :
( ( ~ ( ~ ( ~ ( strictly_less_than @ SV8 @ SV13 )
| ~ ( ~ ( less_than @ SV8 @ SV13 )
| ~ ~ ( less_than @ SV13 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV8 @ SV13 )
| ~ ~ ( less_than @ SV13 @ SV8 ) )
| ( strictly_less_than @ SV8 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(91,plain,
( ( ~ ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(92,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ create_slb @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[84]) ).
thf(93,plain,
! [SV14: $i,SV9: $i] :
( ( ! [SY30: $i] :
( ~ ~ ( ~ ( less_than @ SV9 @ SV14 )
| ~ ( less_than @ SV14 @ SY30 ) )
| ( less_than @ SV9 @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(94,plain,
! [SV10: $i,SV1: $i] :
( ( ( less_than @ SV1 @ SV10 )
= $true )
| ( ( less_than @ SV10 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(95,plain,
! [SV11: $i,SV5: $i] :
( ( pair_in_list @ create_slb @ SV5 @ SV11 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(96,plain,
! [SV13: $i,SV8: $i] :
( ( ~ ( ~ ( strictly_less_than @ SV8 @ SV13 )
| ~ ( ~ ( less_than @ SV8 @ SV13 )
| ~ ~ ( less_than @ SV13 @ SV8 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV8 @ SV13 )
| ~ ~ ( less_than @ SV13 @ SV8 ) )
| ( strictly_less_than @ SV8 @ SV13 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(97,plain,
( ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(98,plain,
( ( ! [SY31: $i] :
( ~ ( pair_in_list @ create_slb @ sK3_SX0 @ SY31 )
| ( less_than @ SY31 @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[92]) ).
thf(99,plain,
! [SV15: $i,SV14: $i,SV9: $i] :
( ( ~ ~ ( ~ ( less_than @ SV9 @ SV14 )
| ~ ( less_than @ SV14 @ SV15 ) )
| ( less_than @ SV9 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(100,plain,
! [SV13: $i,SV8: $i] :
( ( ~ ( ~ ( strictly_less_than @ SV8 @ SV13 )
| ~ ( ~ ( less_than @ SV8 @ SV13 )
| ~ ~ ( less_than @ SV13 @ SV8 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(101,plain,
! [SV13: $i,SV8: $i] :
( ( ~ ( ~ ~ ( ~ ( less_than @ SV8 @ SV13 )
| ~ ~ ( less_than @ SV13 @ SV8 ) )
| ( strictly_less_than @ SV8 @ SV13 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(102,plain,
( ( ~ ( pair_in_list @ create_slb @ sK3_SX0 @ sK4_SY31 )
| ( less_than @ sK4_SY31 @ sK3_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[98]) ).
thf(103,plain,
! [SV15: $i,SV14: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( less_than @ SV9 @ SV14 )
| ~ ( less_than @ SV14 @ SV15 ) ) )
= $true )
| ( ( less_than @ SV9 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(104,plain,
! [SV13: $i,SV8: $i] :
( ( ~ ( strictly_less_than @ SV8 @ SV13 )
| ~ ( ~ ( less_than @ SV8 @ SV13 )
| ~ ~ ( less_than @ SV13 @ SV8 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(105,plain,
! [SV13: $i,SV8: $i] :
( ( ~ ~ ( ~ ( less_than @ SV8 @ SV13 )
| ~ ~ ( less_than @ SV13 @ SV8 ) )
| ( strictly_less_than @ SV8 @ SV13 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(106,plain,
( ( ~ ( pair_in_list @ create_slb @ sK3_SX0 @ sK4_SY31 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(107,plain,
( ( less_than @ sK4_SY31 @ sK3_SX0 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(108,plain,
! [SV15: $i,SV14: $i,SV9: $i] :
( ( ( ~ ( ~ ( less_than @ SV9 @ SV14 )
| ~ ( less_than @ SV14 @ SV15 ) ) )
= $false )
| ( ( less_than @ SV9 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(109,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( strictly_less_than @ SV8 @ SV13 ) )
= $true )
| ( ( ~ ( ~ ( less_than @ SV8 @ SV13 )
| ~ ~ ( less_than @ SV13 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(110,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( less_than @ SV8 @ SV13 )
| ~ ~ ( less_than @ SV13 @ SV8 ) ) )
= $true )
| ( ( strictly_less_than @ SV8 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(111,plain,
( ( pair_in_list @ create_slb @ sK3_SX0 @ sK4_SY31 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(112,plain,
! [SV15: $i,SV14: $i,SV9: $i] :
( ( ( ~ ( less_than @ SV9 @ SV14 )
| ~ ( less_than @ SV14 @ SV15 ) )
= $true )
| ( ( less_than @ SV9 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(113,plain,
! [SV13: $i,SV8: $i] :
( ( ( strictly_less_than @ SV8 @ SV13 )
= $false )
| ( ( ~ ( ~ ( less_than @ SV8 @ SV13 )
| ~ ~ ( less_than @ SV13 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(114,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( ~ ( less_than @ SV8 @ SV13 )
| ~ ~ ( less_than @ SV13 @ SV8 ) ) )
= $false )
| ( ( strictly_less_than @ SV8 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(115,plain,
! [SV15: $i,SV14: $i,SV9: $i] :
( ( ( ~ ( less_than @ SV9 @ SV14 ) )
= $true )
| ( ( ~ ( less_than @ SV14 @ SV15 ) )
= $true )
| ( ( less_than @ SV9 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(116,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( less_than @ SV8 @ SV13 )
| ~ ~ ( less_than @ SV13 @ SV8 ) )
= $false )
| ( ( strictly_less_than @ SV8 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(117,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( less_than @ SV8 @ SV13 )
| ~ ~ ( less_than @ SV13 @ SV8 ) )
= $true )
| ( ( strictly_less_than @ SV8 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(118,plain,
! [SV15: $i,SV14: $i,SV9: $i] :
( ( ( less_than @ SV9 @ SV14 )
= $false )
| ( ( ~ ( less_than @ SV14 @ SV15 ) )
= $true )
| ( ( less_than @ SV9 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(119,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( less_than @ SV8 @ SV13 ) )
= $false )
| ( ( strictly_less_than @ SV8 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(120,plain,
! [SV8: $i,SV13: $i] :
( ( ( ~ ~ ( less_than @ SV13 @ SV8 ) )
= $false )
| ( ( strictly_less_than @ SV8 @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[116]) ).
thf(121,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( less_than @ SV8 @ SV13 ) )
= $true )
| ( ( ~ ~ ( less_than @ SV13 @ SV8 ) )
= $true )
| ( ( strictly_less_than @ SV8 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(122,plain,
! [SV9: $i,SV15: $i,SV14: $i] :
( ( ( less_than @ SV14 @ SV15 )
= $false )
| ( ( less_than @ SV9 @ SV14 )
= $false )
| ( ( less_than @ SV9 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(123,plain,
! [SV13: $i,SV8: $i] :
( ( ( less_than @ SV8 @ SV13 )
= $true )
| ( ( strictly_less_than @ SV8 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(124,plain,
! [SV8: $i,SV13: $i] :
( ( ( ~ ( less_than @ SV13 @ SV8 ) )
= $true )
| ( ( strictly_less_than @ SV8 @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(125,plain,
! [SV13: $i,SV8: $i] :
( ( ( less_than @ SV8 @ SV13 )
= $false )
| ( ( ~ ~ ( less_than @ SV13 @ SV8 ) )
= $true )
| ( ( strictly_less_than @ SV8 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(126,plain,
! [SV8: $i,SV13: $i] :
( ( ( less_than @ SV13 @ SV8 )
= $false )
| ( ( strictly_less_than @ SV8 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(127,plain,
! [SV8: $i,SV13: $i] :
( ( ( ~ ( less_than @ SV13 @ SV8 ) )
= $false )
| ( ( less_than @ SV8 @ SV13 )
= $false )
| ( ( strictly_less_than @ SV8 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(128,plain,
! [SV8: $i,SV13: $i] :
( ( ( less_than @ SV13 @ SV8 )
= $true )
| ( ( less_than @ SV8 @ SV13 )
= $false )
| ( ( strictly_less_than @ SV8 @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(129,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[76,128,126,123,122,111,107,97,95,94,89,87,81,78,77]) ).
thf(130,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ( ( less_than @ U @ V )
& ( less_than @ V @ W ) )
=> ( less_than @ U @ W ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(131,plain,
( ( ! [U: $i,V: $i] :
( ( less_than @ U @ V )
| ( less_than @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(132,plain,
( ( ! [U: $i] : ( less_than @ U @ U ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(133,plain,
( ( ! [U: $i,V: $i] :
( ( strictly_less_than @ U @ V )
<=> ( ( less_than @ U @ V )
& ~ ( less_than @ V @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(134,plain,
( ( ! [U: $i] : ( less_than @ bottom @ U ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(135,plain,
( ( ~ ( isnonempty_slb @ create_slb ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(136,plain,
( ( ! [U: $i] :
~ ( contains_slb @ create_slb @ U ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(137,plain,
( ( ! [U: $i,V: $i] :
~ ( pair_in_list @ create_slb @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(138,plain,
( ( ! [U: $i] :
( ( update_slb @ create_slb @ U )
= create_slb ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(139,plain,
( ( ! [U: $i,V: $i] : ( check_cpq @ ( triple @ U @ create_slb @ V ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(140,plain,
( ( ~ ( ! [W: $i,X: $i] :
( ( pair_in_list @ create_slb @ W @ X )
=> ( less_than @ X @ W ) )
=> ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY19 ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(141,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)],[133]) ).
thf(142,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)],[130]) ).
thf(143,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ create_slb @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) )
| ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY19 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(144,plain,
! [SV16: $i] :
( ( ! [SY32: $i] :
( ( less_than @ SV16 @ SY32 )
| ( less_than @ SY32 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(145,plain,
! [SV17: $i] :
( ( less_than @ SV17 @ SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(146,plain,
! [SV18: $i] :
( ( less_than @ bottom @ SV18 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(147,plain,
( ( isnonempty_slb @ create_slb )
= $false ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(148,plain,
! [SV19: $i] :
( ( ~ ( contains_slb @ create_slb @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(149,plain,
! [SV20: $i] :
( ( ! [SY33: $i] :
~ ( pair_in_list @ create_slb @ SV20 @ SY33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(150,plain,
! [SV21: $i] :
( ( ( update_slb @ create_slb @ SV21 )
= create_slb )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(151,plain,
! [SV22: $i] :
( ( ! [SY34: $i] : ( check_cpq @ ( triple @ SV22 @ create_slb @ SY34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(152,plain,
! [SV23: $i] :
( ( ! [SY35: $i] :
~ ( ~ ( ~ ( strictly_less_than @ SV23 @ SY35 )
| ~ ( ~ ( less_than @ SV23 @ SY35 )
| ~ ~ ( less_than @ SY35 @ SV23 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV23 @ SY35 )
| ~ ~ ( less_than @ SY35 @ SV23 ) )
| ( strictly_less_than @ SV23 @ SY35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(153,plain,
! [SV24: $i] :
( ( ! [SY36: $i,SY37: $i] :
( ~ ~ ( ~ ( less_than @ SV24 @ SY36 )
| ~ ( less_than @ SY36 @ SY37 ) )
| ( less_than @ SV24 @ SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(154,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ create_slb @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) )
| ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY19 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(155,plain,
! [SV25: $i,SV16: $i] :
( ( ( less_than @ SV16 @ SV25 )
| ( less_than @ SV25 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(156,plain,
! [SV19: $i] :
( ( contains_slb @ create_slb @ SV19 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(157,plain,
! [SV26: $i,SV20: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV20 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(158,plain,
! [SV27: $i,SV22: $i] :
( ( check_cpq @ ( triple @ SV22 @ create_slb @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(159,plain,
! [SV28: $i,SV23: $i] :
( ( ~ ( ~ ( ~ ( strictly_less_than @ SV23 @ SV28 )
| ~ ( ~ ( less_than @ SV23 @ SV28 )
| ~ ~ ( less_than @ SV28 @ SV23 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV23 @ SV28 )
| ~ ~ ( less_than @ SV28 @ SV23 ) )
| ( strictly_less_than @ SV23 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(160,plain,
! [SV29: $i,SV24: $i] :
( ( ! [SY38: $i] :
( ~ ~ ( ~ ( less_than @ SV24 @ SV29 )
| ~ ( less_than @ SV29 @ SY38 ) )
| ( less_than @ SV24 @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(161,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ create_slb @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(162,plain,
( ( check_cpq @ ( triple @ sK1_U @ create_slb @ sK2_SY19 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(163,plain,
! [SV25: $i,SV16: $i] :
( ( ( less_than @ SV16 @ SV25 )
= $true )
| ( ( less_than @ SV25 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(164,plain,
! [SV26: $i,SV20: $i] :
( ( pair_in_list @ create_slb @ SV20 @ SV26 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(165,plain,
! [SV28: $i,SV23: $i] :
( ( ~ ( ~ ( strictly_less_than @ SV23 @ SV28 )
| ~ ( ~ ( less_than @ SV23 @ SV28 )
| ~ ~ ( less_than @ SV28 @ SV23 ) ) )
| ~ ( ~ ~ ( ~ ( less_than @ SV23 @ SV28 )
| ~ ~ ( less_than @ SV28 @ SV23 ) )
| ( strictly_less_than @ SV23 @ SV28 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(166,plain,
! [SV30: $i,SV29: $i,SV24: $i] :
( ( ~ ~ ( ~ ( less_than @ SV24 @ SV29 )
| ~ ( less_than @ SV29 @ SV30 ) )
| ( less_than @ SV24 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(167,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( pair_in_list @ create_slb @ SX0 @ SX1 )
| ( less_than @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(168,plain,
! [SV28: $i,SV23: $i] :
( ( ~ ( ~ ( strictly_less_than @ SV23 @ SV28 )
| ~ ( ~ ( less_than @ SV23 @ SV28 )
| ~ ~ ( less_than @ SV28 @ SV23 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(169,plain,
! [SV28: $i,SV23: $i] :
( ( ~ ( ~ ~ ( ~ ( less_than @ SV23 @ SV28 )
| ~ ~ ( less_than @ SV28 @ SV23 ) )
| ( strictly_less_than @ SV23 @ SV28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(170,plain,
! [SV30: $i,SV29: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( less_than @ SV24 @ SV29 )
| ~ ( less_than @ SV29 @ SV30 ) ) )
= $true )
| ( ( less_than @ SV24 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(171,plain,
! [SV31: $i] :
( ( ! [SY39: $i] :
( ~ ( pair_in_list @ create_slb @ SV31 @ SY39 )
| ( less_than @ SY39 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(172,plain,
! [SV28: $i,SV23: $i] :
( ( ~ ( strictly_less_than @ SV23 @ SV28 )
| ~ ( ~ ( less_than @ SV23 @ SV28 )
| ~ ~ ( less_than @ SV28 @ SV23 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(173,plain,
! [SV28: $i,SV23: $i] :
( ( ~ ~ ( ~ ( less_than @ SV23 @ SV28 )
| ~ ~ ( less_than @ SV28 @ SV23 ) )
| ( strictly_less_than @ SV23 @ SV28 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(174,plain,
! [SV30: $i,SV29: $i,SV24: $i] :
( ( ( ~ ( ~ ( less_than @ SV24 @ SV29 )
| ~ ( less_than @ SV29 @ SV30 ) ) )
= $false )
| ( ( less_than @ SV24 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(175,plain,
! [SV32: $i,SV31: $i] :
( ( ~ ( pair_in_list @ create_slb @ SV31 @ SV32 )
| ( less_than @ SV32 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(176,plain,
! [SV28: $i,SV23: $i] :
( ( ( ~ ( strictly_less_than @ SV23 @ SV28 ) )
= $true )
| ( ( ~ ( ~ ( less_than @ SV23 @ SV28 )
| ~ ~ ( less_than @ SV28 @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(177,plain,
! [SV28: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( less_than @ SV23 @ SV28 )
| ~ ~ ( less_than @ SV28 @ SV23 ) ) )
= $true )
| ( ( strictly_less_than @ SV23 @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(178,plain,
! [SV30: $i,SV29: $i,SV24: $i] :
( ( ( ~ ( less_than @ SV24 @ SV29 )
| ~ ( less_than @ SV29 @ SV30 ) )
= $true )
| ( ( less_than @ SV24 @ SV30 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(179,plain,
! [SV32: $i,SV31: $i] :
( ( ( ~ ( pair_in_list @ create_slb @ SV31 @ SV32 ) )
= $true )
| ( ( less_than @ SV32 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(180,plain,
! [SV28: $i,SV23: $i] :
( ( ( strictly_less_than @ SV23 @ SV28 )
= $false )
| ( ( ~ ( ~ ( less_than @ SV23 @ SV28 )
| ~ ~ ( less_than @ SV28 @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(181,plain,
! [SV28: $i,SV23: $i] :
( ( ( ~ ( ~ ( less_than @ SV23 @ SV28 )
| ~ ~ ( less_than @ SV28 @ SV23 ) ) )
= $false )
| ( ( strictly_less_than @ SV23 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(182,plain,
! [SV30: $i,SV29: $i,SV24: $i] :
( ( ( ~ ( less_than @ SV24 @ SV29 ) )
= $true )
| ( ( ~ ( less_than @ SV29 @ SV30 ) )
= $true )
| ( ( less_than @ SV24 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(183,plain,
! [SV32: $i,SV31: $i] :
( ( ( pair_in_list @ create_slb @ SV31 @ SV32 )
= $false )
| ( ( less_than @ SV32 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(184,plain,
! [SV28: $i,SV23: $i] :
( ( ( ~ ( less_than @ SV23 @ SV28 )
| ~ ~ ( less_than @ SV28 @ SV23 ) )
= $false )
| ( ( strictly_less_than @ SV23 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(185,plain,
! [SV28: $i,SV23: $i] :
( ( ( ~ ( less_than @ SV23 @ SV28 )
| ~ ~ ( less_than @ SV28 @ SV23 ) )
= $true )
| ( ( strictly_less_than @ SV23 @ SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(186,plain,
! [SV30: $i,SV29: $i,SV24: $i] :
( ( ( less_than @ SV24 @ SV29 )
= $false )
| ( ( ~ ( less_than @ SV29 @ SV30 ) )
= $true )
| ( ( less_than @ SV24 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(187,plain,
! [SV28: $i,SV23: $i] :
( ( ( ~ ( less_than @ SV23 @ SV28 ) )
= $false )
| ( ( strictly_less_than @ SV23 @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(188,plain,
! [SV23: $i,SV28: $i] :
( ( ( ~ ~ ( less_than @ SV28 @ SV23 ) )
= $false )
| ( ( strictly_less_than @ SV23 @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(189,plain,
! [SV28: $i,SV23: $i] :
( ( ( ~ ( less_than @ SV23 @ SV28 ) )
= $true )
| ( ( ~ ~ ( less_than @ SV28 @ SV23 ) )
= $true )
| ( ( strictly_less_than @ SV23 @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(190,plain,
! [SV24: $i,SV30: $i,SV29: $i] :
( ( ( less_than @ SV29 @ SV30 )
= $false )
| ( ( less_than @ SV24 @ SV29 )
= $false )
| ( ( less_than @ SV24 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(191,plain,
! [SV28: $i,SV23: $i] :
( ( ( less_than @ SV23 @ SV28 )
= $true )
| ( ( strictly_less_than @ SV23 @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(192,plain,
! [SV23: $i,SV28: $i] :
( ( ( ~ ( less_than @ SV28 @ SV23 ) )
= $true )
| ( ( strictly_less_than @ SV23 @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(193,plain,
! [SV28: $i,SV23: $i] :
( ( ( less_than @ SV23 @ SV28 )
= $false )
| ( ( ~ ~ ( less_than @ SV28 @ SV23 ) )
= $true )
| ( ( strictly_less_than @ SV23 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(194,plain,
! [SV23: $i,SV28: $i] :
( ( ( less_than @ SV28 @ SV23 )
= $false )
| ( ( strictly_less_than @ SV23 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(195,plain,
! [SV23: $i,SV28: $i] :
( ( ( ~ ( less_than @ SV28 @ SV23 ) )
= $false )
| ( ( less_than @ SV23 @ SV28 )
= $false )
| ( ( strictly_less_than @ SV23 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(196,plain,
! [SV23: $i,SV28: $i] :
( ( ( less_than @ SV28 @ SV23 )
= $true )
| ( ( less_than @ SV23 @ SV28 )
= $false )
| ( ( strictly_less_than @ SV23 @ SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(197,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[145,196,194,191,190,183,164,163,162,158,156,150,147,146]) ).
thf(198,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[197,129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV405+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.16 % Computer : n007.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Oct 6 16:25:30 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.57/0.27
% 0.57/0.27 No.of.Axioms: 10
% 0.57/0.27
% 0.57/0.27 Length.of.Defs: 0
% 0.57/0.27
% 0.57/0.27 Contains.Choice.Funs: false
% 0.57/0.27 ....
% 0.57/0.27
% 0.57/0.27 ********************************
% 0.57/0.27 * All subproblems solved! *
% 0.57/0.27 ********************************
% 0.57/0.27 % SZS status Theorem for /export/starexec/sandbox/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:197,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.57/0.27
% 0.57/0.27 %**** Beginning of derivation protocol ****
% 0.57/0.27 % SZS output start CNFRefutation
% See solution above
% 0.57/0.27
% 0.57/0.27 %**** End of derivation protocol ****
% 0.57/0.27 %**** no. of clauses in derivation: 167 ****
% 0.57/0.27 %**** clause counter: 197 ****
% 0.57/0.27
% 0.57/0.27 % SZS status Theorem for /export/starexec/sandbox/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:197,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------