%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : MGT085+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 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 : n001.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 10:31:49 AM UTC 2026
% Result : Theorem 22.92s 4.19s
% Output : CNFRefutation 22.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 25
% Syntax : Number of formulae : 265 ( 194 unt; 0 typ; 0 def)
% Number of atoms : 1445 ( 565 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 2859 (1080 ~; 456 |; 60 &;1239 @)
% ( 9 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 13 con; 0-4 aty)
% Number of variables : 373 ( 0 ^; 358 !; 15 ?; 373 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_axis_compatible,type,
axis_compatible: $i > $i > $i > $i > $o ).
thf(tp_axis_conflict,type,
axis_conflict: $i > $i > $i > $i > $o ).
thf(tp_axis_subsumes,type,
axis_subsumes: $i > $i > $i > $i > $o ).
thf(tp_box_verdict,type,
box_verdict: $i > $i > $i ).
thf(tp_compatible,type,
compatible: $i ).
thf(tp_conflict,type,
conflict: $i ).
thf(tp_in_closed,type,
in_closed: $i > $i > $i > $o ).
thf(tp_in_lopen,type,
in_lopen: $i > $i > $i > $o ).
thf(tp_in_open,type,
in_open: $i > $i > $i > $o ).
thf(tp_in_ropen,type,
in_ropen: $i > $i > $i > $o ).
thf(tp_is_verdict,type,
is_verdict: $i > $o ).
thf(tp_leq,type,
leq: $i > $i > $o ).
thf(tp_less,type,
less: $i > $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY41,type,
sK2_SY41: $i ).
thf(tp_sK3_SY44,type,
sK3_SY44: $i ).
thf(tp_unknown,type,
unknown: $i ).
thf(tp_v0,type,
v0: $i ).
thf(tp_v100,type,
v100: $i ).
thf(tp_v200,type,
v200: $i ).
thf(tp_v400,type,
v400: $i ).
thf(tp_v50,type,
v50: $i ).
thf(tp_val,type,
val: $i > $o ).
thf(1,axiom,
( ( v0 != v50 )
& ( v0 != v100 )
& ( v0 != v200 )
& ( v0 != v400 )
& ( v50 != v100 )
& ( v50 != v200 )
& ( v50 != v400 )
& ( v100 != v200 )
& ( v100 != v400 )
& ( v200 != v400 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distinct) ).
thf(2,axiom,
less @ v200 @ v400,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v200_v400) ).
thf(3,axiom,
less @ v100 @ v400,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v100_v400) ).
thf(4,axiom,
less @ v100 @ v200,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v100_v200) ).
thf(5,axiom,
less @ v50 @ v400,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v50_v400) ).
thf(6,axiom,
less @ v50 @ v200,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v50_v200) ).
thf(7,axiom,
less @ v50 @ v100,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v50_v100) ).
thf(8,axiom,
less @ v0 @ v400,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v0_v400) ).
thf(9,axiom,
less @ v0 @ v200,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v0_v200) ).
thf(10,axiom,
less @ v0 @ v100,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v0_v100) ).
thf(11,axiom,
less @ v0 @ v50,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ord_v0_v50) ).
thf(12,axiom,
val @ v400,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',val_v400) ).
thf(13,axiom,
val @ v200,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',val_v200) ).
thf(14,axiom,
val @ v100,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',val_v100) ).
thf(15,axiom,
val @ v50,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',val_v50) ).
thf(16,axiom,
val @ v0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',val_v0) ).
thf(33,axiom,
! [X: $i,A: $i,B: $i] :
( ( in_lopen @ X @ A @ B )
<=> ( ( less @ A @ X )
& ( leq @ X @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_lopen) ).
thf(34,axiom,
! [X: $i,A: $i,B: $i] :
( ( in_closed @ X @ A @ B )
<=> ( ( leq @ A @ X )
& ( leq @ X @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_closed) ).
thf(35,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_trans) ).
thf(36,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( less @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( less @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_leq_trans) ).
thf(37,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( less @ Y @ Z ) )
=> ( less @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_less_trans) ).
thf(38,axiom,
! [X: $i,Y: $i] :
( ( less @ X @ Y )
=> ( leq @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_implies_leq) ).
thf(39,axiom,
! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ X ) )
=> ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_antisym) ).
thf(40,axiom,
! [X: $i,Y: $i] :
( ( leq @ X @ Y )
<=> ( ( less @ X @ Y )
| ( X = Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_def) ).
thf(44,conjecture,
~ ? [X: $i,Y: $i,Z: $i] :
( ( ( in_lopen @ X @ v0 @ v200 )
| ( in_lopen @ Y @ v0 @ v100 )
| ( in_lopen @ Z @ v0 @ v50 ) )
& ( leq @ v400 @ X )
& ( leq @ v200 @ Y )
& ( leq @ v100 @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',odrl445) ).
thf(45,negated_conjecture,
( ( ~ ? [X: $i,Y: $i,Z: $i] :
( ( ( in_lopen @ X @ v0 @ v200 )
| ( in_lopen @ Y @ v0 @ v100 )
| ( in_lopen @ Z @ v0 @ v50 ) )
& ( leq @ v400 @ X )
& ( leq @ v200 @ Y )
& ( leq @ v100 @ Z ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[44]) ).
thf(46,plain,
( ( ~ ? [X: $i,Y: $i,Z: $i] :
( ( ( in_lopen @ X @ v0 @ v200 )
| ( in_lopen @ Y @ v0 @ v100 )
| ( in_lopen @ Z @ v0 @ v50 ) )
& ( leq @ v400 @ X )
& ( leq @ v200 @ Y )
& ( leq @ v100 @ Z ) ) )
= $false ),
inference(unfold_def,[status(thm)],[45]) ).
thf(47,plain,
( ( ( v0 != v50 )
& ( v0 != v100 )
& ( v0 != v200 )
& ( v0 != v400 )
& ( v50 != v100 )
& ( v50 != v200 )
& ( v50 != v400 )
& ( v100 != v200 )
& ( v100 != v400 )
& ( v200 != v400 ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(48,plain,
( ( less @ v200 @ v400 )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(49,plain,
( ( less @ v100 @ v400 )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(50,plain,
( ( less @ v100 @ v200 )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(51,plain,
( ( less @ v50 @ v400 )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(52,plain,
( ( less @ v50 @ v200 )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(53,plain,
( ( less @ v50 @ v100 )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(54,plain,
( ( less @ v0 @ v400 )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(55,plain,
( ( less @ v0 @ v200 )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(56,plain,
( ( less @ v0 @ v100 )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(57,plain,
( ( less @ v0 @ v50 )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(58,plain,
( ( val @ v400 )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(59,plain,
( ( val @ v200 )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(60,plain,
( ( val @ v100 )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(61,plain,
( ( val @ v50 )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(62,plain,
( ( val @ v0 )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(63,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( in_lopen @ X @ A @ B )
<=> ( ( less @ A @ X )
& ( leq @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(64,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( in_closed @ X @ A @ B )
<=> ( ( leq @ A @ X )
& ( leq @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(65,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(66,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( less @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( less @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(67,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( less @ Y @ Z ) )
=> ( less @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(68,plain,
( ( ! [X: $i,Y: $i] :
( ( less @ X @ Y )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(69,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ X ) )
=> ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(70,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
<=> ( ( less @ X @ Y )
| ( X = Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(71,plain,
( ( ? [X: $i,Y: $i,Z: $i] :
( ( ( in_lopen @ X @ v0 @ v200 )
| ( in_lopen @ Y @ v0 @ v100 )
| ( in_lopen @ Z @ v0 @ v50 ) )
& ( leq @ v400 @ X )
& ( leq @ v200 @ Y )
& ( leq @ v100 @ Z ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[46]) ).
thf(72,plain,
( ( ! [X: $i,Y: $i] :
( ( leq @ X @ Y )
<=> ( ( less @ X @ Y )
| ( X = Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(73,plain,
( ( ! [X: $i,Y: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ X ) )
=> ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(74,plain,
( ( ! [X: $i,Y: $i] :
( ( less @ X @ Y )
=> ( leq @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(75,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( less @ Y @ Z ) )
=> ( less @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(76,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( less @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( less @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(77,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( leq @ X @ Y )
& ( leq @ Y @ Z ) )
=> ( leq @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(78,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( in_closed @ X @ A @ B )
<=> ( ( leq @ A @ X )
& ( leq @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(79,plain,
( ( ! [X: $i,A: $i,B: $i] :
( ( in_lopen @ X @ A @ B )
<=> ( ( less @ A @ X )
& ( leq @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(80,plain,
( ( val @ v0 )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(81,plain,
( ( val @ v50 )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(82,plain,
( ( val @ v100 )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(83,plain,
( ( val @ v200 )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(84,plain,
( ( val @ v400 )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(85,plain,
( ( less @ v0 @ v50 )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(86,plain,
( ( less @ v0 @ v100 )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(87,plain,
( ( less @ v0 @ v200 )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(88,plain,
( ( less @ v0 @ v400 )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(89,plain,
( ( less @ v50 @ v100 )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(90,plain,
( ( less @ v50 @ v200 )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(91,plain,
( ( less @ v50 @ v400 )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(92,plain,
( ( less @ v100 @ v200 )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(93,plain,
( ( less @ v100 @ v400 )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(94,plain,
( ( less @ v200 @ v400 )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(95,plain,
( ( ( v0 != v50 )
& ( v0 != v100 )
& ( v0 != v200 )
& ( v0 != v400 )
& ( v50 != v100 )
& ( v50 != v200 )
& ( v50 != v400 )
& ( v100 != v200 )
& ( v100 != v400 )
& ( v200 != v400 ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(96,plain,
( ( ? [X: $i,Y: $i,Z: $i] :
( ( ( in_lopen @ X @ v0 @ v200 )
| ( in_lopen @ Y @ v0 @ v100 )
| ( in_lopen @ Z @ v0 @ v50 ) )
& ( leq @ v400 @ X )
& ( leq @ v200 @ Y )
& ( leq @ v100 @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(97,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
| ~ ( ( v0 != v200 ) ) )
| ~ ( ( v0 != v400 ) ) )
| ~ ( ( v50 != v100 ) ) )
| ~ ( ( v50 != v200 ) ) )
| ~ ( ( v50 != v400 ) ) )
| ~ ( ( v100 != v200 ) ) )
| ~ ( ( v100 != v400 ) ) )
| ~ ( ( v200 != v400 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(98,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( leq @ SX0 @ SX1 )
| ( less @ SX0 @ SX1 )
| ( SX0 = SX1 ) )
| ~ ( ~ ( ( less @ SX0 @ SX1 )
| ( SX0 = SX1 ) )
| ( leq @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(99,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(100,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( less @ SX1 @ SX2 ) )
| ( less @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(101,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( less @ SX0 @ SX1 )
| ( leq @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(102,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( less @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX2 ) )
| ( less @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(103,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( leq @ SX0 @ SX1 )
| ~ ( leq @ SX1 @ SX2 ) )
| ( leq @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(104,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( in_closed @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ( leq @ SX1 @ SX0 )
| ~ ( leq @ SX0 @ SX2 ) ) )
| ~ ( ~ ~ ( ~ ( leq @ SX1 @ SX0 )
| ~ ( leq @ SX0 @ SX2 ) )
| ( in_closed @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(105,plain,
( ( ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( in_lopen @ SX0 @ v0 @ v200 )
| ( in_lopen @ SX1 @ v0 @ v100 )
| ( in_lopen @ SX2 @ v0 @ v50 ) )
| ~ ( leq @ v400 @ SX0 ) )
| ~ ( leq @ v200 @ SX1 ) )
| ~ ( leq @ v100 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(106,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( in_lopen @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ( less @ SX1 @ SX0 )
| ~ ( leq @ SX0 @ SX2 ) ) )
| ~ ( ~ ~ ( ~ ( less @ SX1 @ SX0 )
| ~ ( leq @ SX0 @ SX2 ) )
| ( in_lopen @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(107,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
| ~ ( ( v0 != v200 ) ) )
| ~ ( ( v0 != v400 ) ) )
| ~ ( ( v50 != v100 ) ) )
| ~ ( ( v50 != v200 ) ) )
| ~ ( ( v50 != v400 ) ) )
| ~ ( ( v100 != v200 ) ) )
| ~ ( ( v100 != v400 ) ) )
| ~ ( ( v200 != v400 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(108,plain,
! [SV1: $i] :
( ( ! [SY24: $i] :
~ ( ~ ( ~ ( leq @ SV1 @ SY24 )
| ( less @ SV1 @ SY24 )
| ( SV1 = SY24 ) )
| ~ ( ~ ( ( less @ SV1 @ SY24 )
| ( SV1 = SY24 ) )
| ( leq @ SV1 @ SY24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(109,plain,
! [SV2: $i] :
( ( ! [SY25: $i] :
( ~ ~ ( ~ ( leq @ SV2 @ SY25 )
| ~ ( leq @ SY25 @ SV2 ) )
| ( SV2 = SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(110,plain,
! [SV3: $i] :
( ( ! [SY26: $i,SY27: $i] :
( ~ ~ ( ~ ( leq @ SV3 @ SY26 )
| ~ ( less @ SY26 @ SY27 ) )
| ( less @ SV3 @ SY27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(111,plain,
! [SV4: $i] :
( ( ! [SY28: $i] :
( ~ ( less @ SV4 @ SY28 )
| ( leq @ SV4 @ SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(112,plain,
! [SV5: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ~ ~ ( ~ ( less @ SV5 @ SY29 )
| ~ ( leq @ SY29 @ SY30 ) )
| ( less @ SV5 @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(113,plain,
! [SV6: $i] :
( ( ! [SY31: $i,SY32: $i] :
( ~ ~ ( ~ ( leq @ SV6 @ SY31 )
| ~ ( leq @ SY31 @ SY32 ) )
| ( leq @ SV6 @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(114,plain,
! [SV7: $i] :
( ( ! [SY33: $i,SY34: $i] :
~ ( ~ ( ~ ( in_closed @ SV7 @ SY33 @ SY34 )
| ~ ( ~ ( leq @ SY33 @ SV7 )
| ~ ( leq @ SV7 @ SY34 ) ) )
| ~ ( ~ ~ ( ~ ( leq @ SY33 @ SV7 )
| ~ ( leq @ SV7 @ SY34 ) )
| ( in_closed @ SV7 @ SY33 @ SY34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(115,plain,
( ( ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( in_lopen @ SX0 @ v0 @ v200 )
| ( in_lopen @ SX1 @ v0 @ v100 )
| ( in_lopen @ SX2 @ v0 @ v50 ) )
| ~ ( leq @ v400 @ SX0 ) )
| ~ ( leq @ v200 @ SX1 ) )
| ~ ( leq @ v100 @ SX2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(116,plain,
! [SV8: $i] :
( ( ! [SY35: $i,SY36: $i] :
~ ( ~ ( ~ ( in_lopen @ SV8 @ SY35 @ SY36 )
| ~ ( ~ ( less @ SY35 @ SV8 )
| ~ ( leq @ SV8 @ SY36 ) ) )
| ~ ( ~ ~ ( ~ ( less @ SY35 @ SV8 )
| ~ ( leq @ SV8 @ SY36 ) )
| ( in_lopen @ SV8 @ SY35 @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(117,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
| ~ ( ( v0 != v200 ) ) )
| ~ ( ( v0 != v400 ) ) )
| ~ ( ( v50 != v100 ) ) )
| ~ ( ( v50 != v200 ) ) )
| ~ ( ( v50 != v400 ) ) )
| ~ ( ( v100 != v200 ) ) )
| ~ ( ( v100 != v400 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(118,plain,
( ( ~ ( ( v200 != v400 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(119,plain,
! [SV9: $i,SV1: $i] :
( ( ~ ( ~ ( ~ ( leq @ SV1 @ SV9 )
| ( less @ SV1 @ SV9 )
| ( SV1 = SV9 ) )
| ~ ( ~ ( ( less @ SV1 @ SV9 )
| ( SV1 = SV9 ) )
| ( leq @ SV1 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(120,plain,
! [SV10: $i,SV2: $i] :
( ( ~ ~ ( ~ ( leq @ SV2 @ SV10 )
| ~ ( leq @ SV10 @ SV2 ) )
| ( SV2 = SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(121,plain,
! [SV11: $i,SV3: $i] :
( ( ! [SY37: $i] :
( ~ ~ ( ~ ( leq @ SV3 @ SV11 )
| ~ ( less @ SV11 @ SY37 ) )
| ( less @ SV3 @ SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(122,plain,
! [SV12: $i,SV4: $i] :
( ( ~ ( less @ SV4 @ SV12 )
| ( leq @ SV4 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(123,plain,
! [SV13: $i,SV5: $i] :
( ( ! [SY38: $i] :
( ~ ~ ( ~ ( less @ SV5 @ SV13 )
| ~ ( leq @ SV13 @ SY38 ) )
| ( less @ SV5 @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(124,plain,
! [SV14: $i,SV6: $i] :
( ( ! [SY39: $i] :
( ~ ~ ( ~ ( leq @ SV6 @ SV14 )
| ~ ( leq @ SV14 @ SY39 ) )
| ( leq @ SV6 @ SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(125,plain,
! [SV15: $i,SV7: $i] :
( ( ! [SY40: $i] :
~ ( ~ ( ~ ( in_closed @ SV7 @ SV15 @ SY40 )
| ~ ( ~ ( leq @ SV15 @ SV7 )
| ~ ( leq @ SV7 @ SY40 ) ) )
| ~ ( ~ ~ ( ~ ( leq @ SV15 @ SV7 )
| ~ ( leq @ SV7 @ SY40 ) )
| ( in_closed @ SV7 @ SV15 @ SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(126,plain,
( ( ~ ~ ! [SY41: $i] :
~ ~ ! [SY42: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( in_lopen @ sK1_SX0 @ v0 @ v200 )
| ( in_lopen @ SY41 @ v0 @ v100 )
| ( in_lopen @ SY42 @ v0 @ v50 ) )
| ~ ( leq @ v400 @ sK1_SX0 ) )
| ~ ( leq @ v200 @ SY41 ) )
| ~ ( leq @ v100 @ SY42 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[115]) ).
thf(127,plain,
! [SV16: $i,SV8: $i] :
( ( ! [SY43: $i] :
~ ( ~ ( ~ ( in_lopen @ SV8 @ SV16 @ SY43 )
| ~ ( ~ ( less @ SV16 @ SV8 )
| ~ ( leq @ SV8 @ SY43 ) ) )
| ~ ( ~ ~ ( ~ ( less @ SV16 @ SV8 )
| ~ ( leq @ SV8 @ SY43 ) )
| ( in_lopen @ SV8 @ SV16 @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(128,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
| ~ ( ( v0 != v200 ) ) )
| ~ ( ( v0 != v400 ) ) )
| ~ ( ( v50 != v100 ) ) )
| ~ ( ( v50 != v200 ) ) )
| ~ ( ( v50 != v400 ) ) )
| ~ ( ( v100 != v200 ) ) )
| ~ ( ( v100 != v400 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(129,plain,
( ( v200 != v400 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(130,plain,
! [SV9: $i,SV1: $i] :
( ( ~ ( ~ ( leq @ SV1 @ SV9 )
| ( less @ SV1 @ SV9 )
| ( SV1 = SV9 ) )
| ~ ( ~ ( ( less @ SV1 @ SV9 )
| ( SV1 = SV9 ) )
| ( leq @ SV1 @ SV9 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(131,plain,
! [SV10: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV2 @ SV10 )
| ~ ( leq @ SV10 @ SV2 ) ) )
= $true )
| ( ( SV2 = SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(132,plain,
! [SV17: $i,SV11: $i,SV3: $i] :
( ( ~ ~ ( ~ ( leq @ SV3 @ SV11 )
| ~ ( less @ SV11 @ SV17 ) )
| ( less @ SV3 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(133,plain,
! [SV12: $i,SV4: $i] :
( ( ( ~ ( less @ SV4 @ SV12 ) )
= $true )
| ( ( leq @ SV4 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(134,plain,
! [SV18: $i,SV13: $i,SV5: $i] :
( ( ~ ~ ( ~ ( less @ SV5 @ SV13 )
| ~ ( leq @ SV13 @ SV18 ) )
| ( less @ SV5 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(135,plain,
! [SV19: $i,SV14: $i,SV6: $i] :
( ( ~ ~ ( ~ ( leq @ SV6 @ SV14 )
| ~ ( leq @ SV14 @ SV19 ) )
| ( leq @ SV6 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(136,plain,
! [SV20: $i,SV15: $i,SV7: $i] :
( ( ~ ( ~ ( ~ ( in_closed @ SV7 @ SV15 @ SV20 )
| ~ ( ~ ( leq @ SV15 @ SV7 )
| ~ ( leq @ SV7 @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( leq @ SV15 @ SV7 )
| ~ ( leq @ SV7 @ SV20 ) )
| ( in_closed @ SV7 @ SV15 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(137,plain,
( ( ~ ! [SY41: $i] :
~ ~ ! [SY42: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( in_lopen @ sK1_SX0 @ v0 @ v200 )
| ( in_lopen @ SY41 @ v0 @ v100 )
| ( in_lopen @ SY42 @ v0 @ v50 ) )
| ~ ( leq @ v400 @ sK1_SX0 ) )
| ~ ( leq @ v200 @ SY41 ) )
| ~ ( leq @ v100 @ SY42 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(138,plain,
! [SV21: $i,SV16: $i,SV8: $i] :
( ( ~ ( ~ ( ~ ( in_lopen @ SV8 @ SV16 @ SV21 )
| ~ ( ~ ( less @ SV16 @ SV8 )
| ~ ( leq @ SV8 @ SV21 ) ) )
| ~ ( ~ ~ ( ~ ( less @ SV16 @ SV8 )
| ~ ( leq @ SV8 @ SV21 ) )
| ( in_lopen @ SV8 @ SV16 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(139,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
| ~ ( ( v0 != v200 ) ) )
| ~ ( ( v0 != v400 ) ) )
| ~ ( ( v50 != v100 ) ) )
| ~ ( ( v50 != v200 ) ) )
| ~ ( ( v50 != v400 ) ) )
| ~ ( ( v100 != v200 ) ) )
| ~ ( ( v100 != v400 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(140,plain,
( ( v200 = v400 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(141,plain,
! [SV9: $i,SV1: $i] :
( ( ~ ( ~ ( leq @ SV1 @ SV9 )
| ( less @ SV1 @ SV9 )
| ( SV1 = SV9 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(142,plain,
! [SV9: $i,SV1: $i] :
( ( ~ ( ~ ( ( less @ SV1 @ SV9 )
| ( SV1 = SV9 ) )
| ( leq @ SV1 @ SV9 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(143,plain,
! [SV10: $i,SV2: $i] :
( ( ( ~ ( ~ ( leq @ SV2 @ SV10 )
| ~ ( leq @ SV10 @ SV2 ) ) )
= $false )
| ( ( SV2 = SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(144,plain,
! [SV17: $i,SV11: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV3 @ SV11 )
| ~ ( less @ SV11 @ SV17 ) ) )
= $true )
| ( ( less @ SV3 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(145,plain,
! [SV12: $i,SV4: $i] :
( ( ( less @ SV4 @ SV12 )
= $false )
| ( ( leq @ SV4 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(146,plain,
! [SV18: $i,SV13: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( less @ SV5 @ SV13 )
| ~ ( leq @ SV13 @ SV18 ) ) )
= $true )
| ( ( less @ SV5 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(147,plain,
! [SV19: $i,SV14: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV6 @ SV14 )
| ~ ( leq @ SV14 @ SV19 ) ) )
= $true )
| ( ( leq @ SV6 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(148,plain,
! [SV20: $i,SV15: $i,SV7: $i] :
( ( ~ ( ~ ( in_closed @ SV7 @ SV15 @ SV20 )
| ~ ( ~ ( leq @ SV15 @ SV7 )
| ~ ( leq @ SV7 @ SV20 ) ) )
| ~ ( ~ ~ ( ~ ( leq @ SV15 @ SV7 )
| ~ ( leq @ SV7 @ SV20 ) )
| ( in_closed @ SV7 @ SV15 @ SV20 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(149,plain,
( ( ! [SY41: $i] :
~ ~ ! [SY42: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( in_lopen @ sK1_SX0 @ v0 @ v200 )
| ( in_lopen @ SY41 @ v0 @ v100 )
| ( in_lopen @ SY42 @ v0 @ v50 ) )
| ~ ( leq @ v400 @ sK1_SX0 ) )
| ~ ( leq @ v200 @ SY41 ) )
| ~ ( leq @ v100 @ SY42 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(150,plain,
! [SV21: $i,SV16: $i,SV8: $i] :
( ( ~ ( ~ ( in_lopen @ SV8 @ SV16 @ SV21 )
| ~ ( ~ ( less @ SV16 @ SV8 )
| ~ ( leq @ SV8 @ SV21 ) ) )
| ~ ( ~ ~ ( ~ ( less @ SV16 @ SV8 )
| ~ ( leq @ SV8 @ SV21 ) )
| ( in_lopen @ SV8 @ SV16 @ SV21 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(151,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
| ~ ( ( v0 != v200 ) ) )
| ~ ( ( v0 != v400 ) ) )
| ~ ( ( v50 != v100 ) ) )
| ~ ( ( v50 != v200 ) ) )
| ~ ( ( v50 != v400 ) ) )
| ~ ( ( v100 != v200 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(152,plain,
( ( ~ ( ( v100 != v400 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(153,plain,
! [SV9: $i,SV1: $i] :
( ( ~ ( leq @ SV1 @ SV9 )
| ( less @ SV1 @ SV9 )
| ( SV1 = SV9 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(154,plain,
! [SV9: $i,SV1: $i] :
( ( ~ ( ( less @ SV1 @ SV9 )
| ( SV1 = SV9 ) )
| ( leq @ SV1 @ SV9 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(155,plain,
! [SV10: $i,SV2: $i] :
( ( ( ~ ( leq @ SV2 @ SV10 )
| ~ ( leq @ SV10 @ SV2 ) )
= $true )
| ( ( SV2 = SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(156,plain,
! [SV17: $i,SV11: $i,SV3: $i] :
( ( ( ~ ( ~ ( leq @ SV3 @ SV11 )
| ~ ( less @ SV11 @ SV17 ) ) )
= $false )
| ( ( less @ SV3 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(157,plain,
! [SV18: $i,SV13: $i,SV5: $i] :
( ( ( ~ ( ~ ( less @ SV5 @ SV13 )
| ~ ( leq @ SV13 @ SV18 ) ) )
= $false )
| ( ( less @ SV5 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(158,plain,
! [SV19: $i,SV14: $i,SV6: $i] :
( ( ( ~ ( ~ ( leq @ SV6 @ SV14 )
| ~ ( leq @ SV14 @ SV19 ) ) )
= $false )
| ( ( leq @ SV6 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(159,plain,
! [SV20: $i,SV15: $i,SV7: $i] :
( ( ~ ( ~ ( in_closed @ SV7 @ SV15 @ SV20 )
| ~ ( ~ ( leq @ SV15 @ SV7 )
| ~ ( leq @ SV7 @ SV20 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[148]) ).
thf(160,plain,
! [SV20: $i,SV7: $i,SV15: $i] :
( ( ~ ( ~ ~ ( ~ ( leq @ SV15 @ SV7 )
| ~ ( leq @ SV7 @ SV20 ) )
| ( in_closed @ SV7 @ SV15 @ SV20 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[148]) ).
thf(161,plain,
( ( ~ ~ ! [SY44: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( in_lopen @ sK1_SX0 @ v0 @ v200 )
| ( in_lopen @ sK2_SY41 @ v0 @ v100 )
| ( in_lopen @ SY44 @ v0 @ v50 ) )
| ~ ( leq @ v400 @ sK1_SX0 ) )
| ~ ( leq @ v200 @ sK2_SY41 ) )
| ~ ( leq @ v100 @ SY44 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[149]) ).
thf(162,plain,
! [SV21: $i,SV16: $i,SV8: $i] :
( ( ~ ( ~ ( in_lopen @ SV8 @ SV16 @ SV21 )
| ~ ( ~ ( less @ SV16 @ SV8 )
| ~ ( leq @ SV8 @ SV21 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(163,plain,
! [SV21: $i,SV8: $i,SV16: $i] :
( ( ~ ( ~ ~ ( ~ ( less @ SV16 @ SV8 )
| ~ ( leq @ SV8 @ SV21 ) )
| ( in_lopen @ SV8 @ SV16 @ SV21 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(164,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
| ~ ( ( v0 != v200 ) ) )
| ~ ( ( v0 != v400 ) ) )
| ~ ( ( v50 != v100 ) ) )
| ~ ( ( v50 != v200 ) ) )
| ~ ( ( v50 != v400 ) ) )
| ~ ( ( v100 != v200 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(165,plain,
( ( v100 != v400 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(166,plain,
! [SV9: $i,SV1: $i] :
( ( ( ~ ( leq @ SV1 @ SV9 ) )
= $true )
| ( ( ( less @ SV1 @ SV9 )
| ( SV1 = SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(167,plain,
! [SV9: $i,SV1: $i] :
( ( ( ~ ( ( less @ SV1 @ SV9 )
| ( SV1 = SV9 ) ) )
= $true )
| ( ( leq @ SV1 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(168,plain,
! [SV10: $i,SV2: $i] :
( ( ( ~ ( leq @ SV2 @ SV10 ) )
= $true )
| ( ( ~ ( leq @ SV10 @ SV2 ) )
= $true )
| ( ( SV2 = SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(169,plain,
! [SV17: $i,SV11: $i,SV3: $i] :
( ( ( ~ ( leq @ SV3 @ SV11 )
| ~ ( less @ SV11 @ SV17 ) )
= $true )
| ( ( less @ SV3 @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(170,plain,
! [SV18: $i,SV13: $i,SV5: $i] :
( ( ( ~ ( less @ SV5 @ SV13 )
| ~ ( leq @ SV13 @ SV18 ) )
= $true )
| ( ( less @ SV5 @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(171,plain,
! [SV19: $i,SV14: $i,SV6: $i] :
( ( ( ~ ( leq @ SV6 @ SV14 )
| ~ ( leq @ SV14 @ SV19 ) )
= $true )
| ( ( leq @ SV6 @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(172,plain,
! [SV20: $i,SV15: $i,SV7: $i] :
( ( ~ ( in_closed @ SV7 @ SV15 @ SV20 )
| ~ ( ~ ( leq @ SV15 @ SV7 )
| ~ ( leq @ SV7 @ SV20 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(173,plain,
! [SV20: $i,SV7: $i,SV15: $i] :
( ( ~ ~ ( ~ ( leq @ SV15 @ SV7 )
| ~ ( leq @ SV7 @ SV20 ) )
| ( in_closed @ SV7 @ SV15 @ SV20 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(174,plain,
( ( ~ ! [SY44: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( in_lopen @ sK1_SX0 @ v0 @ v200 )
| ( in_lopen @ sK2_SY41 @ v0 @ v100 )
| ( in_lopen @ SY44 @ v0 @ v50 ) )
| ~ ( leq @ v400 @ sK1_SX0 ) )
| ~ ( leq @ v200 @ sK2_SY41 ) )
| ~ ( leq @ v100 @ SY44 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(175,plain,
! [SV21: $i,SV16: $i,SV8: $i] :
( ( ~ ( in_lopen @ SV8 @ SV16 @ SV21 )
| ~ ( ~ ( less @ SV16 @ SV8 )
| ~ ( leq @ SV8 @ SV21 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(176,plain,
! [SV21: $i,SV8: $i,SV16: $i] :
( ( ~ ~ ( ~ ( less @ SV16 @ SV8 )
| ~ ( leq @ SV8 @ SV21 ) )
| ( in_lopen @ SV8 @ SV16 @ SV21 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(177,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
| ~ ( ( v0 != v200 ) ) )
| ~ ( ( v0 != v400 ) ) )
| ~ ( ( v50 != v100 ) ) )
| ~ ( ( v50 != v200 ) ) )
| ~ ( ( v50 != v400 ) ) )
| ~ ( ( v100 != v200 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(178,plain,
( ( v100 = v400 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(179,plain,
! [SV9: $i,SV1: $i] :
( ( ( leq @ SV1 @ SV9 )
= $false )
| ( ( ( less @ SV1 @ SV9 )
| ( SV1 = SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(180,plain,
! [SV9: $i,SV1: $i] :
( ( ( ( less @ SV1 @ SV9 )
| ( SV1 = SV9 ) )
= $false )
| ( ( leq @ SV1 @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(181,plain,
! [SV10: $i,SV2: $i] :
( ( ( leq @ SV2 @ SV10 )
= $false )
| ( ( ~ ( leq @ SV10 @ SV2 ) )
= $true )
| ( ( SV2 = SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(182,plain,
! [SV17: $i,SV11: $i,SV3: $i] :
( ( ( ~ ( leq @ SV3 @ SV11 ) )
= $true )
| ( ( ~ ( less @ SV11 @ SV17 ) )
= $true )
| ( ( less @ SV3 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(183,plain,
! [SV18: $i,SV13: $i,SV5: $i] :
( ( ( ~ ( less @ SV5 @ SV13 ) )
= $true )
| ( ( ~ ( leq @ SV13 @ SV18 ) )
= $true )
| ( ( less @ SV5 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(184,plain,
! [SV19: $i,SV14: $i,SV6: $i] :
( ( ( ~ ( leq @ SV6 @ SV14 ) )
= $true )
| ( ( ~ ( leq @ SV14 @ SV19 ) )
= $true )
| ( ( leq @ SV6 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(185,plain,
! [SV20: $i,SV15: $i,SV7: $i] :
( ( ( ~ ( in_closed @ SV7 @ SV15 @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( leq @ SV15 @ SV7 )
| ~ ( leq @ SV7 @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(186,plain,
! [SV20: $i,SV7: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( leq @ SV15 @ SV7 )
| ~ ( leq @ SV7 @ SV20 ) ) )
= $true )
| ( ( in_closed @ SV7 @ SV15 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(187,plain,
( ( ! [SY44: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( in_lopen @ sK1_SX0 @ v0 @ v200 )
| ( in_lopen @ sK2_SY41 @ v0 @ v100 )
| ( in_lopen @ SY44 @ v0 @ v50 ) )
| ~ ( leq @ v400 @ sK1_SX0 ) )
| ~ ( leq @ v200 @ sK2_SY41 ) )
| ~ ( leq @ v100 @ SY44 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(188,plain,
! [SV21: $i,SV16: $i,SV8: $i] :
( ( ( ~ ( in_lopen @ SV8 @ SV16 @ SV21 ) )
= $true )
| ( ( ~ ( ~ ( less @ SV16 @ SV8 )
| ~ ( leq @ SV8 @ SV21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(189,plain,
! [SV21: $i,SV8: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( less @ SV16 @ SV8 )
| ~ ( leq @ SV8 @ SV21 ) ) )
= $true )
| ( ( in_lopen @ SV8 @ SV16 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(190,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
| ~ ( ( v0 != v200 ) ) )
| ~ ( ( v0 != v400 ) ) )
| ~ ( ( v50 != v100 ) ) )
| ~ ( ( v50 != v200 ) ) )
| ~ ( ( v50 != v400 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(191,plain,
( ( ~ ( ( v100 != v200 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(192,plain,
! [SV9: $i,SV1: $i] :
( ( ( less @ SV1 @ SV9 )
= $true )
| ( ( SV1 = SV9 )
= $true )
| ( ( leq @ SV1 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(193,plain,
! [SV9: $i,SV1: $i] :
( ( ( less @ SV1 @ SV9 )
= $false )
| ( ( leq @ SV1 @ SV9 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(194,plain,
! [SV9: $i,SV1: $i] :
( ( ( SV1 = SV9 )
= $false )
| ( ( leq @ SV1 @ SV9 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(195,plain,
! [SV2: $i,SV10: $i] :
( ( ( leq @ SV10 @ SV2 )
= $false )
| ( ( leq @ SV2 @ SV10 )
= $false )
| ( ( SV2 = SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(196,plain,
! [SV17: $i,SV11: $i,SV3: $i] :
( ( ( leq @ SV3 @ SV11 )
= $false )
| ( ( ~ ( less @ SV11 @ SV17 ) )
= $true )
| ( ( less @ SV3 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(197,plain,
! [SV18: $i,SV13: $i,SV5: $i] :
( ( ( less @ SV5 @ SV13 )
= $false )
| ( ( ~ ( leq @ SV13 @ SV18 ) )
= $true )
| ( ( less @ SV5 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(198,plain,
! [SV19: $i,SV14: $i,SV6: $i] :
( ( ( leq @ SV6 @ SV14 )
= $false )
| ( ( ~ ( leq @ SV14 @ SV19 ) )
= $true )
| ( ( leq @ SV6 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(199,plain,
! [SV20: $i,SV15: $i,SV7: $i] :
( ( ( in_closed @ SV7 @ SV15 @ SV20 )
= $false )
| ( ( ~ ( ~ ( leq @ SV15 @ SV7 )
| ~ ( leq @ SV7 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(200,plain,
! [SV20: $i,SV7: $i,SV15: $i] :
( ( ( ~ ( ~ ( leq @ SV15 @ SV7 )
| ~ ( leq @ SV7 @ SV20 ) ) )
= $false )
| ( ( in_closed @ SV7 @ SV15 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(201,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( in_lopen @ sK1_SX0 @ v0 @ v200 )
| ( in_lopen @ sK2_SY41 @ v0 @ v100 )
| ( in_lopen @ sK3_SY44 @ v0 @ v50 ) )
| ~ ( leq @ v400 @ sK1_SX0 ) )
| ~ ( leq @ v200 @ sK2_SY41 ) )
| ~ ( leq @ v100 @ sK3_SY44 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[187]) ).
thf(202,plain,
! [SV21: $i,SV16: $i,SV8: $i] :
( ( ( in_lopen @ SV8 @ SV16 @ SV21 )
= $false )
| ( ( ~ ( ~ ( less @ SV16 @ SV8 )
| ~ ( leq @ SV8 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(203,plain,
! [SV21: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( ~ ( less @ SV16 @ SV8 )
| ~ ( leq @ SV8 @ SV21 ) ) )
= $false )
| ( ( in_lopen @ SV8 @ SV16 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(204,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
| ~ ( ( v0 != v200 ) ) )
| ~ ( ( v0 != v400 ) ) )
| ~ ( ( v50 != v100 ) ) )
| ~ ( ( v50 != v200 ) ) )
| ~ ( ( v50 != v400 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(205,plain,
( ( v100 != v200 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(206,plain,
! [SV3: $i,SV17: $i,SV11: $i] :
( ( ( less @ SV11 @ SV17 )
= $false )
| ( ( leq @ SV3 @ SV11 )
= $false )
| ( ( less @ SV3 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(207,plain,
! [SV5: $i,SV18: $i,SV13: $i] :
( ( ( leq @ SV13 @ SV18 )
= $false )
| ( ( less @ SV5 @ SV13 )
= $false )
| ( ( less @ SV5 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(208,plain,
! [SV6: $i,SV19: $i,SV14: $i] :
( ( ( leq @ SV14 @ SV19 )
= $false )
| ( ( leq @ SV6 @ SV14 )
= $false )
| ( ( leq @ SV6 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(209,plain,
! [SV20: $i,SV7: $i,SV15: $i] :
( ( ( ~ ( leq @ SV15 @ SV7 )
| ~ ( leq @ SV7 @ SV20 ) )
= $false )
| ( ( in_closed @ SV7 @ SV15 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(210,plain,
! [SV20: $i,SV7: $i,SV15: $i] :
( ( ( ~ ( leq @ SV15 @ SV7 )
| ~ ( leq @ SV7 @ SV20 ) )
= $true )
| ( ( in_closed @ SV7 @ SV15 @ SV20 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(211,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( in_lopen @ sK1_SX0 @ v0 @ v200 )
| ( in_lopen @ sK2_SY41 @ v0 @ v100 )
| ( in_lopen @ sK3_SY44 @ v0 @ v50 ) )
| ~ ( leq @ v400 @ sK1_SX0 ) )
| ~ ( leq @ v200 @ sK2_SY41 ) )
| ~ ( leq @ v100 @ sK3_SY44 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(212,plain,
! [SV21: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( less @ SV16 @ SV8 )
| ~ ( leq @ SV8 @ SV21 ) )
= $false )
| ( ( in_lopen @ SV8 @ SV16 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(213,plain,
! [SV21: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( less @ SV16 @ SV8 )
| ~ ( leq @ SV8 @ SV21 ) )
= $true )
| ( ( in_lopen @ SV8 @ SV16 @ SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(214,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
| ~ ( ( v0 != v200 ) ) )
| ~ ( ( v0 != v400 ) ) )
| ~ ( ( v50 != v100 ) ) )
| ~ ( ( v50 != v200 ) ) )
| ~ ( ( v50 != v400 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(215,plain,
( ( v100 = v200 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(216,plain,
! [SV20: $i,SV7: $i,SV15: $i] :
( ( ( ~ ( leq @ SV15 @ SV7 ) )
= $false )
| ( ( in_closed @ SV7 @ SV15 @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(217,plain,
! [SV15: $i,SV20: $i,SV7: $i] :
( ( ( ~ ( leq @ SV7 @ SV20 ) )
= $false )
| ( ( in_closed @ SV7 @ SV15 @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(218,plain,
! [SV20: $i,SV7: $i,SV15: $i] :
( ( ( ~ ( leq @ SV15 @ SV7 ) )
= $true )
| ( ( ~ ( leq @ SV7 @ SV20 ) )
= $true )
| ( ( in_closed @ SV7 @ SV15 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(219,plain,
( ( ~ ~ ( ~ ~ ( ~ ( ( in_lopen @ sK1_SX0 @ v0 @ v200 )
| ( in_lopen @ sK2_SY41 @ v0 @ v100 )
| ( in_lopen @ sK3_SY44 @ v0 @ v50 ) )
| ~ ( leq @ v400 @ sK1_SX0 ) )
| ~ ( leq @ v200 @ sK2_SY41 ) )
| ~ ( leq @ v100 @ sK3_SY44 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(220,plain,
! [SV21: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( less @ SV16 @ SV8 ) )
= $false )
| ( ( in_lopen @ SV8 @ SV16 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(221,plain,
! [SV16: $i,SV21: $i,SV8: $i] :
( ( ( ~ ( leq @ SV8 @ SV21 ) )
= $false )
| ( ( in_lopen @ SV8 @ SV16 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(222,plain,
! [SV21: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( less @ SV16 @ SV8 ) )
= $true )
| ( ( ~ ( leq @ SV8 @ SV21 ) )
= $true )
| ( ( in_lopen @ SV8 @ SV16 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(223,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
| ~ ( ( v0 != v200 ) ) )
| ~ ( ( v0 != v400 ) ) )
| ~ ( ( v50 != v100 ) ) )
| ~ ( ( v50 != v200 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(224,plain,
( ( ~ ( ( v50 != v400 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(225,plain,
! [SV20: $i,SV7: $i,SV15: $i] :
( ( ( leq @ SV15 @ SV7 )
= $true )
| ( ( in_closed @ SV7 @ SV15 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(226,plain,
! [SV15: $i,SV20: $i,SV7: $i] :
( ( ( leq @ SV7 @ SV20 )
= $true )
| ( ( in_closed @ SV7 @ SV15 @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(227,plain,
! [SV20: $i,SV7: $i,SV15: $i] :
( ( ( leq @ SV15 @ SV7 )
= $false )
| ( ( ~ ( leq @ SV7 @ SV20 ) )
= $true )
| ( ( in_closed @ SV7 @ SV15 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(228,plain,
( ( ~ ~ ( ~ ~ ( ~ ( ( in_lopen @ sK1_SX0 @ v0 @ v200 )
| ( in_lopen @ sK2_SY41 @ v0 @ v100 )
| ( in_lopen @ sK3_SY44 @ v0 @ v50 ) )
| ~ ( leq @ v400 @ sK1_SX0 ) )
| ~ ( leq @ v200 @ sK2_SY41 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(229,plain,
( ( ~ ( leq @ v100 @ sK3_SY44 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(230,plain,
! [SV21: $i,SV8: $i,SV16: $i] :
( ( ( less @ SV16 @ SV8 )
= $true )
| ( ( in_lopen @ SV8 @ SV16 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(231,plain,
! [SV16: $i,SV21: $i,SV8: $i] :
( ( ( leq @ SV8 @ SV21 )
= $true )
| ( ( in_lopen @ SV8 @ SV16 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(232,plain,
! [SV21: $i,SV8: $i,SV16: $i] :
( ( ( less @ SV16 @ SV8 )
= $false )
| ( ( ~ ( leq @ SV8 @ SV21 ) )
= $true )
| ( ( in_lopen @ SV8 @ SV16 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(233,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
| ~ ( ( v0 != v200 ) ) )
| ~ ( ( v0 != v400 ) ) )
| ~ ( ( v50 != v100 ) ) )
| ~ ( ( v50 != v200 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(234,plain,
( ( v50 != v400 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(235,plain,
! [SV15: $i,SV20: $i,SV7: $i] :
( ( ( leq @ SV7 @ SV20 )
= $false )
| ( ( leq @ SV15 @ SV7 )
= $false )
| ( ( in_closed @ SV7 @ SV15 @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(236,plain,
( ( ~ ( ~ ~ ( ~ ( ( in_lopen @ sK1_SX0 @ v0 @ v200 )
| ( in_lopen @ sK2_SY41 @ v0 @ v100 )
| ( in_lopen @ sK3_SY44 @ v0 @ v50 ) )
| ~ ( leq @ v400 @ sK1_SX0 ) )
| ~ ( leq @ v200 @ sK2_SY41 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(237,plain,
( ( leq @ v100 @ sK3_SY44 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(238,plain,
! [SV16: $i,SV21: $i,SV8: $i] :
( ( ( leq @ SV8 @ SV21 )
= $false )
| ( ( less @ SV16 @ SV8 )
= $false )
| ( ( in_lopen @ SV8 @ SV16 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(239,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
| ~ ( ( v0 != v200 ) ) )
| ~ ( ( v0 != v400 ) ) )
| ~ ( ( v50 != v100 ) ) )
| ~ ( ( v50 != v200 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(240,plain,
( ( v50 = v400 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(241,plain,
( ( ~ ~ ( ~ ( ( in_lopen @ sK1_SX0 @ v0 @ v200 )
| ( in_lopen @ sK2_SY41 @ v0 @ v100 )
| ( in_lopen @ sK3_SY44 @ v0 @ v50 ) )
| ~ ( leq @ v400 @ sK1_SX0 ) )
| ~ ( leq @ v200 @ sK2_SY41 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(242,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
| ~ ( ( v0 != v200 ) ) )
| ~ ( ( v0 != v400 ) ) )
| ~ ( ( v50 != v100 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(243,plain,
( ( ~ ( ( v50 != v200 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(244,plain,
( ( ~ ~ ( ~ ( ( in_lopen @ sK1_SX0 @ v0 @ v200 )
| ( in_lopen @ sK2_SY41 @ v0 @ v100 )
| ( in_lopen @ sK3_SY44 @ v0 @ v50 ) )
| ~ ( leq @ v400 @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(245,plain,
( ( ~ ( leq @ v200 @ sK2_SY41 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(246,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
| ~ ( ( v0 != v200 ) ) )
| ~ ( ( v0 != v400 ) ) )
| ~ ( ( v50 != v100 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(247,plain,
( ( v50 != v200 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(248,plain,
( ( ~ ( ~ ( ( in_lopen @ sK1_SX0 @ v0 @ v200 )
| ( in_lopen @ sK2_SY41 @ v0 @ v100 )
| ( in_lopen @ sK3_SY44 @ v0 @ v50 ) )
| ~ ( leq @ v400 @ sK1_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(249,plain,
( ( leq @ v200 @ sK2_SY41 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(250,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
| ~ ( ( v0 != v200 ) ) )
| ~ ( ( v0 != v400 ) ) )
| ~ ( ( v50 != v100 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(251,plain,
( ( v50 = v200 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(252,plain,
( ( ~ ( ( in_lopen @ sK1_SX0 @ v0 @ v200 )
| ( in_lopen @ sK2_SY41 @ v0 @ v100 )
| ( in_lopen @ sK3_SY44 @ v0 @ v50 ) )
| ~ ( leq @ v400 @ sK1_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(253,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
| ~ ( ( v0 != v200 ) ) )
| ~ ( ( v0 != v400 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(254,plain,
( ( ~ ( ( v50 != v100 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(255,plain,
( ( ~ ( ( in_lopen @ sK1_SX0 @ v0 @ v200 )
| ( in_lopen @ sK2_SY41 @ v0 @ v100 )
| ( in_lopen @ sK3_SY44 @ v0 @ v50 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(256,plain,
( ( ~ ( leq @ v400 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(257,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
| ~ ( ( v0 != v200 ) ) )
| ~ ( ( v0 != v400 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(258,plain,
( ( v50 != v100 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(259,plain,
( ( ( in_lopen @ sK1_SX0 @ v0 @ v200 )
| ( in_lopen @ sK2_SY41 @ v0 @ v100 )
| ( in_lopen @ sK3_SY44 @ v0 @ v50 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(260,plain,
( ( leq @ v400 @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(261,plain,
( ( ~ ~ ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
| ~ ( ( v0 != v200 ) ) )
| ~ ( ( v0 != v400 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(262,plain,
( ( v50 = v100 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(263,plain,
( ( ( ( in_lopen @ sK1_SX0 @ v0 @ v200 )
| ( in_lopen @ sK2_SY41 @ v0 @ v100 ) )
= $true )
| ( ( in_lopen @ sK3_SY44 @ v0 @ v50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(264,plain,
( ( ~ ~ ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
| ~ ( ( v0 != v200 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[261]) ).
thf(265,plain,
( ( ~ ( ( v0 != v400 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[261]) ).
thf(266,plain,
( ( ( in_lopen @ sK1_SX0 @ v0 @ v200 )
= $true )
| ( ( in_lopen @ sK2_SY41 @ v0 @ v100 )
= $true )
| ( ( in_lopen @ sK3_SY44 @ v0 @ v50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(267,plain,
( ( ~ ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
| ~ ( ( v0 != v200 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(268,plain,
( ( v0 != v400 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[265]) ).
thf(269,plain,
( ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
| ~ ( ( v0 != v200 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(270,plain,
( ( v0 = v400 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(271,plain,
( ( ~ ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(272,plain,
( ( ~ ( ( v0 != v200 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(273,plain,
( ( ~ ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(274,plain,
( ( v0 != v200 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(275,plain,
( ( ~ ( ( v0 != v50 ) )
| ~ ( ( v0 != v100 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(276,plain,
( ( v0 = v200 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(277,plain,
( ( ~ ( ( v0 != v50 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[275]) ).
thf(278,plain,
( ( ~ ( ( v0 != v100 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[275]) ).
thf(279,plain,
( ( v0 != v50 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(280,plain,
( ( v0 != v100 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(281,plain,
( ( v0 = v50 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(282,plain,
( ( v0 = v100 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(283,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[80,282,281,276,270,266,262,260,251,249,240,238,237,235,231,230,226,225,215,208,207,206,195,194,193,192,178,145,140,94,93,92,91,90,89,88,87,86,85,84,83,82,81]) ).
thf(284,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[283]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT085+1 : TPTP v9.3.1. Bugfixed v9.3.1.
% 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
% 0.09/0.18 % Computer : n001.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 12:50:23 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.92/4.19
% 22.92/4.19 No.of.Axioms: 24
% 22.92/4.19
% 22.92/4.19 Length.of.Defs: 0
% 22.92/4.19
% 22.92/4.19 Contains.Choice.Funs: false
% 22.92/4.19 .......
% 22.92/4.19
% 22.92/4.19 ********************************
% 22.92/4.19 * All subproblems solved! *
% 22.92/4.19 ********************************
% 22.92/4.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:24,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:283,loop_count:0,foatp_calls:1,translation:fof_full)
% 22.92/4.19
% 22.92/4.19 %**** Beginning of derivation protocol ****
% 22.92/4.19 % SZS output start CNFRefutation
% See solution above
% 22.92/4.20
% 22.92/4.20 %**** End of derivation protocol ****
% 22.92/4.20 %**** no. of clauses in derivation: 265 ****
% 22.92/4.20 %**** clause counter: 283 ****
% 22.92/4.20
% 22.92/4.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:24,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:283,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------