%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM390+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n010.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 10:33:35 AM UTC 2026
% Result : Theorem 0.09s 0.27s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 185 ( 110 unt; 0 typ; 0 def)
% Number of atoms : 1013 ( 280 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 1484 ( 389 ~; 235 |; 31 &; 771 @)
% ( 6 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 7 con; 0-2 aty)
% Number of variables : 294 ( 0 ^; 291 !; 3 ?; 294 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_epsilon_connected,type,
epsilon_connected: $i > $o ).
thf(tp_epsilon_transitive,type,
epsilon_transitive: $i > $o ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_relation_non_empty,type,
relation_non_empty: $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY39,type,
sK4_SY39: $i ).
thf(tp_sK5_SY34,type,
sK5_SY34: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( subset @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(9,axiom,
! [A: $i] :
( ( epsilon_transitive @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( ( proper_subset @ A @ B )
=> ( in @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_ordinal1) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(12,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(22,axiom,
? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
thf(30,axiom,
! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
thf(31,axiom,
! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(34,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(38,conjecture,
! [A: $i] :
( ( epsilon_transitive @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ! [C: $i] :
( ( ordinal @ C )
=> ( ( ( subset @ A @ B )
& ( in @ B @ C ) )
=> ( in @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_ordinal1) ).
thf(39,negated_conjecture,
( ( ! [A: $i] :
( ( epsilon_transitive @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ! [C: $i] :
( ( ordinal @ C )
=> ( ( ( subset @ A @ B )
& ( in @ B @ C ) )
=> ( in @ A @ C ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[38]) ).
thf(40,plain,
( ( ! [A: $i] :
( ( epsilon_transitive @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ! [C: $i] :
( ( ordinal @ C )
=> ( ( ( subset @ A @ B )
& ( in @ B @ C ) )
=> ( in @ A @ C ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[39]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(42,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(43,plain,
( ( ! [A: $i] :
( ( epsilon_transitive @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( ( proper_subset @ A @ B )
=> ( in @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(44,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(45,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(46,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(47,plain,
( ( ? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(48,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(49,plain,
( ( ! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(50,plain,
( ( ! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(51,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(52,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(53,plain,
( ( ( epsilon_transitive @ sK1_A )
=> ! [SY25: $i] :
( ( ordinal @ SY25 )
=> ! [SY26: $i] :
( ( ordinal @ SY26 )
=> ( ( ( subset @ sK1_A @ SY25 )
& ( in @ SY25 @ SY26 ) )
=> ( in @ sK1_A @ SY26 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(54,plain,
( ( epsilon_transitive @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[53]) ).
thf(55,plain,
( ( ! [SY25: $i] :
( ( ordinal @ SY25 )
=> ! [SY26: $i] :
( ( ordinal @ SY26 )
=> ( ( ( subset @ sK1_A @ SY25 )
& ( in @ SY25 @ SY26 ) )
=> ( in @ sK1_A @ SY26 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[53]) ).
thf(56,plain,
( ( ~ ! [SY25: $i] :
( ( ordinal @ SY25 )
=> ! [SY26: $i] :
( ( ordinal @ SY26 )
=> ( ( ( subset @ sK1_A @ SY25 )
& ( in @ SY25 @ SY26 ) )
=> ( in @ sK1_A @ SY26 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[55]) ).
thf(57,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(58,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(59,plain,
( ( ! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(60,plain,
( ( ! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(61,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(62,plain,
( ( ? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(63,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(64,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(65,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(66,plain,
( ( ! [A: $i] :
( ( epsilon_transitive @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( ( proper_subset @ A @ B )
=> ( in @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(68,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(69,plain,
( ( epsilon_transitive @ sK1_A )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(70,plain,
( ( ~ ! [SY25: $i] :
( ( ordinal @ SY25 )
=> ! [SY26: $i] :
( ( ordinal @ SY26 )
=> ( ( ( subset @ sK1_A @ SY25 )
& ( in @ SY25 @ SY26 ) )
=> ( in @ sK1_A @ SY26 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(71,plain,
( ( ! [SX0: $i] :
( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( ordinal @ SX1 )
| ~ ( proper_subset @ SX0 @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(72,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(73,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 ) )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(74,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ~ ( epsilon_transitive @ SX0 )
| ~ ( epsilon_connected @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(75,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( proper_subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( proper_subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(76,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( epsilon_transitive @ SX0 )
| ~ ( epsilon_connected @ SX0 ) )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(77,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( epsilon_transitive @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) )
| ( epsilon_transitive @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(78,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(79,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(80,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(81,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ! [SX1: $i] :
( ~ ( ordinal @ SX1 )
| ~ ~ ( ~ ( subset @ sK1_A @ SX0 )
| ~ ( in @ SX0 @ SX1 ) )
| ( in @ sK1_A @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(82,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( epsilon_transitive @ SX0 )
| ~ ( epsilon_connected @ SX0 ) )
| ~ ( ordinal @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(83,plain,
! [SV1: $i] :
( ( ! [SY27: $i] : ( subset @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(84,plain,
! [SV2: $i] :
( ( ~ ( epsilon_transitive @ SV2 )
| ! [SY28: $i] :
( ~ ( ordinal @ SY28 )
| ~ ( proper_subset @ SV2 @ SY28 )
| ( in @ SV2 @ SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(85,plain,
! [SV3: $i] :
( ( ! [SY29: $i] :
( ~ ( in @ SV3 @ SY29 )
| ( element @ SV3 @ SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(86,plain,
! [SV4: $i] :
( ( ! [SY30: $i,SY31: $i] :
( ~ ~ ( ~ ( subset @ SV4 @ SY30 )
| ~ ( subset @ SY30 @ SY31 ) )
| ( subset @ SV4 @ SY31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(87,plain,
! [SV5: $i] :
( ( ~ ( ordinal @ SV5 )
| ~ ( ~ ( epsilon_transitive @ SV5 )
| ~ ( epsilon_connected @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(88,plain,
! [SV6: $i] :
( ( ! [SY32: $i] :
~ ( ~ ( ~ ( proper_subset @ SV6 @ SY32 )
| ~ ( ~ ( subset @ SV6 @ SY32 )
| ~ ( ( SV6 != SY32 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV6 @ SY32 )
| ~ ( ( SV6 != SY32 ) ) )
| ( proper_subset @ SV6 @ SY32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(89,plain,
! [SV7: $i] :
( ( ~ ~ ( ~ ( epsilon_transitive @ SV7 )
| ~ ( epsilon_connected @ SV7 ) )
| ( ordinal @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(90,plain,
! [SV8: $i] :
( ( ~ ( ~ ( ~ ( epsilon_transitive @ SV8 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ SV8 )
| ( subset @ SY33 @ SV8 ) ) )
| ~ ( ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ SV8 )
| ( subset @ SY34 @ SV8 ) )
| ( epsilon_transitive @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(91,plain,
! [SV9: $i] :
( ( ! [SY35: $i] :
~ ~ ( ~ ( in @ SV9 @ SY35 )
| ~ ( empty @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(92,plain,
! [SV10: $i] :
( ( ! [SY36: $i] :
~ ~ ( ~ ( in @ SV10 @ SY36 )
| ~ ( subset @ SY36 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(93,plain,
! [SV11: $i] :
( ( ! [SY37: $i] :
( ~ ( in @ SV11 @ SY37 )
| ~ ( in @ SY37 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(94,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ! [SX1: $i] :
( ~ ( ordinal @ SX1 )
| ~ ~ ( ~ ( subset @ sK1_A @ SX0 )
| ~ ( in @ SX0 @ SX1 ) )
| ( in @ sK1_A @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(95,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( epsilon_transitive @ SX0 )
| ~ ( epsilon_connected @ SX0 ) )
| ~ ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(96,plain,
! [SV1: $i] :
( ( subset @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(97,plain,
! [SV2: $i] :
( ( ( ~ ( epsilon_transitive @ SV2 ) )
= $true )
| ( ( ! [SY28: $i] :
( ~ ( ordinal @ SY28 )
| ~ ( proper_subset @ SV2 @ SY28 )
| ( in @ SV2 @ SY28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(98,plain,
! [SV13: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ SV13 )
| ( element @ SV3 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(99,plain,
! [SV14: $i,SV4: $i] :
( ( ! [SY38: $i] :
( ~ ~ ( ~ ( subset @ SV4 @ SV14 )
| ~ ( subset @ SV14 @ SY38 ) )
| ( subset @ SV4 @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(100,plain,
! [SV5: $i] :
( ( ( ~ ( ordinal @ SV5 ) )
= $true )
| ( ( ~ ( ~ ( epsilon_transitive @ SV5 )
| ~ ( epsilon_connected @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(101,plain,
! [SV15: $i,SV6: $i] :
( ( ~ ( ~ ( ~ ( proper_subset @ SV6 @ SV15 )
| ~ ( ~ ( subset @ SV6 @ SV15 )
| ~ ( ( SV6 != SV15 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV6 @ SV15 )
| ~ ( ( SV6 != SV15 ) ) )
| ( proper_subset @ SV6 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(102,plain,
! [SV7: $i] :
( ( ( ~ ~ ( ~ ( epsilon_transitive @ SV7 )
| ~ ( epsilon_connected @ SV7 ) ) )
= $true )
| ( ( ordinal @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(103,plain,
! [SV8: $i] :
( ( ~ ( ~ ( epsilon_transitive @ SV8 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ SV8 )
| ( subset @ SY33 @ SV8 ) ) )
| ~ ( ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ SV8 )
| ( subset @ SY34 @ SV8 ) )
| ( epsilon_transitive @ SV8 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(104,plain,
! [SV16: $i,SV9: $i] :
( ( ~ ~ ( ~ ( in @ SV9 @ SV16 )
| ~ ( empty @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(105,plain,
! [SV17: $i,SV10: $i] :
( ( ~ ~ ( ~ ( in @ SV10 @ SV17 )
| ~ ( subset @ SV17 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(106,plain,
! [SV18: $i,SV11: $i] :
( ( ~ ( in @ SV11 @ SV18 )
| ~ ( in @ SV18 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(107,plain,
( ( ~ ( ordinal @ sK2_SX0 )
| ! [SY39: $i] :
( ~ ( ordinal @ SY39 )
| ~ ~ ( ~ ( subset @ sK1_A @ sK2_SX0 )
| ~ ( in @ sK2_SX0 @ SY39 ) )
| ( in @ sK1_A @ SY39 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[94]) ).
thf(108,plain,
( ( ~ ~ ( ~ ~ ( ~ ( epsilon_transitive @ sK3_SX0 )
| ~ ( epsilon_connected @ sK3_SX0 ) )
| ~ ( ordinal @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[95]) ).
thf(109,plain,
! [SV2: $i] :
( ( ( epsilon_transitive @ SV2 )
= $false )
| ( ( ! [SY28: $i] :
( ~ ( ordinal @ SY28 )
| ~ ( proper_subset @ SV2 @ SY28 )
| ( in @ SV2 @ SY28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(110,plain,
! [SV13: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV13 ) )
= $true )
| ( ( element @ SV3 @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(111,plain,
! [SV19: $i,SV14: $i,SV4: $i] :
( ( ~ ~ ( ~ ( subset @ SV4 @ SV14 )
| ~ ( subset @ SV14 @ SV19 ) )
| ( subset @ SV4 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(112,plain,
! [SV5: $i] :
( ( ( ordinal @ SV5 )
= $false )
| ( ( ~ ( ~ ( epsilon_transitive @ SV5 )
| ~ ( epsilon_connected @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(113,plain,
! [SV15: $i,SV6: $i] :
( ( ~ ( ~ ( proper_subset @ SV6 @ SV15 )
| ~ ( ~ ( subset @ SV6 @ SV15 )
| ~ ( ( SV6 != SV15 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV6 @ SV15 )
| ~ ( ( SV6 != SV15 ) ) )
| ( proper_subset @ SV6 @ SV15 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(114,plain,
! [SV7: $i] :
( ( ( ~ ( ~ ( epsilon_transitive @ SV7 )
| ~ ( epsilon_connected @ SV7 ) ) )
= $false )
| ( ( ordinal @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(115,plain,
! [SV8: $i] :
( ( ~ ( ~ ( epsilon_transitive @ SV8 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ SV8 )
| ( subset @ SY33 @ SV8 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(116,plain,
! [SV8: $i] :
( ( ~ ( ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ SV8 )
| ( subset @ SY34 @ SV8 ) )
| ( epsilon_transitive @ SV8 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(117,plain,
! [SV16: $i,SV9: $i] :
( ( ~ ( ~ ( in @ SV9 @ SV16 )
| ~ ( empty @ SV16 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(118,plain,
! [SV17: $i,SV10: $i] :
( ( ~ ( ~ ( in @ SV10 @ SV17 )
| ~ ( subset @ SV17 @ SV10 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(119,plain,
! [SV18: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV18 ) )
= $true )
| ( ( ~ ( in @ SV18 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(120,plain,
( ( ~ ( ordinal @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(121,plain,
( ( ! [SY39: $i] :
( ~ ( ordinal @ SY39 )
| ~ ~ ( ~ ( subset @ sK1_A @ sK2_SX0 )
| ~ ( in @ sK2_SX0 @ SY39 ) )
| ( in @ sK1_A @ SY39 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(122,plain,
( ( ~ ( ~ ~ ( ~ ( epsilon_transitive @ sK3_SX0 )
| ~ ( epsilon_connected @ sK3_SX0 ) )
| ~ ( ordinal @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(123,plain,
! [SV2: $i,SV20: $i] :
( ( ( ~ ( ordinal @ SV20 )
| ~ ( proper_subset @ SV2 @ SV20 )
| ( in @ SV2 @ SV20 ) )
= $true )
| ( ( epsilon_transitive @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(124,plain,
! [SV13: $i,SV3: $i] :
( ( ( in @ SV3 @ SV13 )
= $false )
| ( ( element @ SV3 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(125,plain,
! [SV19: $i,SV14: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV4 @ SV14 )
| ~ ( subset @ SV14 @ SV19 ) ) )
= $true )
| ( ( subset @ SV4 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(126,plain,
! [SV5: $i] :
( ( ( ~ ( epsilon_transitive @ SV5 )
| ~ ( epsilon_connected @ SV5 ) )
= $false )
| ( ( ordinal @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(127,plain,
! [SV15: $i,SV6: $i] :
( ( ~ ( ~ ( proper_subset @ SV6 @ SV15 )
| ~ ( ~ ( subset @ SV6 @ SV15 )
| ~ ( ( SV6 != SV15 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(128,plain,
! [SV15: $i,SV6: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV6 @ SV15 )
| ~ ( ( SV6 != SV15 ) ) )
| ( proper_subset @ SV6 @ SV15 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[113]) ).
thf(129,plain,
! [SV7: $i] :
( ( ( ~ ( epsilon_transitive @ SV7 )
| ~ ( epsilon_connected @ SV7 ) )
= $true )
| ( ( ordinal @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(130,plain,
! [SV8: $i] :
( ( ~ ( epsilon_transitive @ SV8 )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ SV8 )
| ( subset @ SY33 @ SV8 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(131,plain,
! [SV8: $i] :
( ( ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ SV8 )
| ( subset @ SY34 @ SV8 ) )
| ( epsilon_transitive @ SV8 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(132,plain,
! [SV16: $i,SV9: $i] :
( ( ~ ( in @ SV9 @ SV16 )
| ~ ( empty @ SV16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(133,plain,
! [SV17: $i,SV10: $i] :
( ( ~ ( in @ SV10 @ SV17 )
| ~ ( subset @ SV17 @ SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(134,plain,
! [SV18: $i,SV11: $i] :
( ( ( in @ SV11 @ SV18 )
= $false )
| ( ( ~ ( in @ SV18 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(135,plain,
( ( ordinal @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(136,plain,
( ( ~ ( ordinal @ sK4_SY39 )
| ~ ~ ( ~ ( subset @ sK1_A @ sK2_SX0 )
| ~ ( in @ sK2_SX0 @ sK4_SY39 ) )
| ( in @ sK1_A @ sK4_SY39 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[121]) ).
thf(137,plain,
( ( ~ ~ ( ~ ( epsilon_transitive @ sK3_SX0 )
| ~ ( epsilon_connected @ sK3_SX0 ) )
| ~ ( ordinal @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(138,plain,
! [SV2: $i,SV20: $i] :
( ( ( ~ ( ordinal @ SV20 ) )
= $true )
| ( ( ~ ( proper_subset @ SV2 @ SV20 )
| ( in @ SV2 @ SV20 ) )
= $true )
| ( ( epsilon_transitive @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(139,plain,
! [SV19: $i,SV14: $i,SV4: $i] :
( ( ( ~ ( ~ ( subset @ SV4 @ SV14 )
| ~ ( subset @ SV14 @ SV19 ) ) )
= $false )
| ( ( subset @ SV4 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(140,plain,
! [SV5: $i] :
( ( ( ~ ( epsilon_transitive @ SV5 ) )
= $false )
| ( ( ordinal @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(141,plain,
! [SV5: $i] :
( ( ( ~ ( epsilon_connected @ SV5 ) )
= $false )
| ( ( ordinal @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(142,plain,
! [SV15: $i,SV6: $i] :
( ( ~ ( proper_subset @ SV6 @ SV15 )
| ~ ( ~ ( subset @ SV6 @ SV15 )
| ~ ( ( SV6 != SV15 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(143,plain,
! [SV15: $i,SV6: $i] :
( ( ~ ~ ( ~ ( subset @ SV6 @ SV15 )
| ~ ( ( SV6 != SV15 ) ) )
| ( proper_subset @ SV6 @ SV15 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(144,plain,
! [SV7: $i] :
( ( ( ~ ( epsilon_transitive @ SV7 ) )
= $true )
| ( ( ~ ( epsilon_connected @ SV7 ) )
= $true )
| ( ( ordinal @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(145,plain,
! [SV8: $i] :
( ( ( ~ ( epsilon_transitive @ SV8 ) )
= $true )
| ( ( ! [SY33: $i] :
( ~ ( in @ SY33 @ SV8 )
| ( subset @ SY33 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(146,plain,
! [SV8: $i] :
( ( ( ~ ! [SY34: $i] :
( ~ ( in @ SY34 @ SV8 )
| ( subset @ SY34 @ SV8 ) ) )
= $true )
| ( ( epsilon_transitive @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(147,plain,
! [SV16: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV16 ) )
= $true )
| ( ( ~ ( empty @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(148,plain,
! [SV17: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV17 ) )
= $true )
| ( ( ~ ( subset @ SV17 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(149,plain,
! [SV11: $i,SV18: $i] :
( ( ( in @ SV18 @ SV11 )
= $false )
| ( ( in @ SV11 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(150,plain,
( ( ~ ( ordinal @ sK4_SY39 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(151,plain,
( ( ~ ~ ( ~ ( subset @ sK1_A @ sK2_SX0 )
| ~ ( in @ sK2_SX0 @ sK4_SY39 ) )
| ( in @ sK1_A @ sK4_SY39 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(152,plain,
( ( ~ ~ ( ~ ( epsilon_transitive @ sK3_SX0 )
| ~ ( epsilon_connected @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(153,plain,
( ( ~ ( ordinal @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(154,plain,
! [SV2: $i,SV20: $i] :
( ( ( ordinal @ SV20 )
= $false )
| ( ( ~ ( proper_subset @ SV2 @ SV20 )
| ( in @ SV2 @ SV20 ) )
= $true )
| ( ( epsilon_transitive @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(155,plain,
! [SV19: $i,SV14: $i,SV4: $i] :
( ( ( ~ ( subset @ SV4 @ SV14 )
| ~ ( subset @ SV14 @ SV19 ) )
= $true )
| ( ( subset @ SV4 @ SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(156,plain,
! [SV5: $i] :
( ( ( epsilon_transitive @ SV5 )
= $true )
| ( ( ordinal @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(157,plain,
! [SV5: $i] :
( ( ( epsilon_connected @ SV5 )
= $true )
| ( ( ordinal @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(158,plain,
! [SV15: $i,SV6: $i] :
( ( ( ~ ( proper_subset @ SV6 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV6 @ SV15 )
| ~ ( ( SV6 != SV15 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(159,plain,
! [SV15: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV6 @ SV15 )
| ~ ( ( SV6 != SV15 ) ) ) )
= $true )
| ( ( proper_subset @ SV6 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(160,plain,
! [SV7: $i] :
( ( ( epsilon_transitive @ SV7 )
= $false )
| ( ( ~ ( epsilon_connected @ SV7 ) )
= $true )
| ( ( ordinal @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(161,plain,
! [SV8: $i] :
( ( ( epsilon_transitive @ SV8 )
= $false )
| ( ( ! [SY33: $i] :
( ~ ( in @ SY33 @ SV8 )
| ( subset @ SY33 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(162,plain,
! [SV8: $i] :
( ( ( ! [SY34: $i] :
( ~ ( in @ SY34 @ SV8 )
| ( subset @ SY34 @ SV8 ) ) )
= $false )
| ( ( epsilon_transitive @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(163,plain,
! [SV16: $i,SV9: $i] :
( ( ( in @ SV9 @ SV16 )
= $false )
| ( ( ~ ( empty @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(164,plain,
! [SV17: $i,SV10: $i] :
( ( ( in @ SV10 @ SV17 )
= $false )
| ( ( ~ ( subset @ SV17 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(165,plain,
( ( ordinal @ sK4_SY39 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(166,plain,
( ( ~ ~ ( ~ ( subset @ sK1_A @ sK2_SX0 )
| ~ ( in @ sK2_SX0 @ sK4_SY39 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(167,plain,
( ( in @ sK1_A @ sK4_SY39 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(168,plain,
( ( ~ ( ~ ( epsilon_transitive @ sK3_SX0 )
| ~ ( epsilon_connected @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(169,plain,
( ( ordinal @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(170,plain,
! [SV20: $i,SV2: $i] :
( ( ( ~ ( proper_subset @ SV2 @ SV20 ) )
= $true )
| ( ( in @ SV2 @ SV20 )
= $true )
| ( ( ordinal @ SV20 )
= $false )
| ( ( epsilon_transitive @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(171,plain,
! [SV19: $i,SV14: $i,SV4: $i] :
( ( ( ~ ( subset @ SV4 @ SV14 ) )
= $true )
| ( ( ~ ( subset @ SV14 @ SV19 ) )
= $true )
| ( ( subset @ SV4 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(172,plain,
! [SV15: $i,SV6: $i] :
( ( ( proper_subset @ SV6 @ SV15 )
= $false )
| ( ( ~ ( ~ ( subset @ SV6 @ SV15 )
| ~ ( ( SV6 != SV15 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(173,plain,
! [SV15: $i,SV6: $i] :
( ( ( ~ ( ~ ( subset @ SV6 @ SV15 )
| ~ ( ( SV6 != SV15 ) ) ) )
= $false )
| ( ( proper_subset @ SV6 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(174,plain,
! [SV7: $i] :
( ( ( epsilon_connected @ SV7 )
= $false )
| ( ( epsilon_transitive @ SV7 )
= $false )
| ( ( ordinal @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(175,plain,
! [SV8: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ SV8 )
| ( subset @ SV21 @ SV8 ) )
= $true )
| ( ( epsilon_transitive @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(176,plain,
! [SV8: $i] :
( ( ( ~ ( in @ ( sK5_SY34 @ SV8 ) @ SV8 )
| ( subset @ ( sK5_SY34 @ SV8 ) @ SV8 ) )
= $false )
| ( ( epsilon_transitive @ SV8 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[162]) ).
thf(177,plain,
! [SV9: $i,SV16: $i] :
( ( ( empty @ SV16 )
= $false )
| ( ( in @ SV9 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(178,plain,
! [SV10: $i,SV17: $i] :
( ( ( subset @ SV17 @ SV10 )
= $false )
| ( ( in @ SV10 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(179,plain,
( ( ~ ( ~ ( subset @ sK1_A @ sK2_SX0 )
| ~ ( in @ sK2_SX0 @ sK4_SY39 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(180,plain,
( ( ~ ( epsilon_transitive @ sK3_SX0 )
| ~ ( epsilon_connected @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(181,plain,
! [SV20: $i,SV2: $i] :
( ( ( proper_subset @ SV2 @ SV20 )
= $false )
| ( ( in @ SV2 @ SV20 )
= $true )
| ( ( ordinal @ SV20 )
= $false )
| ( ( epsilon_transitive @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(182,plain,
! [SV19: $i,SV14: $i,SV4: $i] :
( ( ( subset @ SV4 @ SV14 )
= $false )
| ( ( ~ ( subset @ SV14 @ SV19 ) )
= $true )
| ( ( subset @ SV4 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(183,plain,
! [SV15: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV15 )
| ~ ( ( SV6 != SV15 ) ) )
= $false )
| ( ( proper_subset @ SV6 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(184,plain,
! [SV15: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV15 )
| ~ ( ( SV6 != SV15 ) ) )
= $true )
| ( ( proper_subset @ SV6 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(185,plain,
! [SV8: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ SV8 ) )
= $true )
| ( ( subset @ SV21 @ SV8 )
= $true )
| ( ( epsilon_transitive @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(186,plain,
! [SV8: $i] :
( ( ( ~ ( in @ ( sK5_SY34 @ SV8 ) @ SV8 ) )
= $false )
| ( ( epsilon_transitive @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(187,plain,
! [SV8: $i] :
( ( ( subset @ ( sK5_SY34 @ SV8 ) @ SV8 )
= $false )
| ( ( epsilon_transitive @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(188,plain,
( ( ~ ( subset @ sK1_A @ sK2_SX0 )
| ~ ( in @ sK2_SX0 @ sK4_SY39 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(189,plain,
( ( ~ ( epsilon_transitive @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(190,plain,
( ( ~ ( epsilon_connected @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(191,plain,
! [SV4: $i,SV19: $i,SV14: $i] :
( ( ( subset @ SV14 @ SV19 )
= $false )
| ( ( subset @ SV4 @ SV14 )
= $false )
| ( ( subset @ SV4 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(192,plain,
! [SV15: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV15 ) )
= $false )
| ( ( proper_subset @ SV6 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(193,plain,
! [SV15: $i,SV6: $i] :
( ( ( ~ ( ( SV6 != SV15 ) ) )
= $false )
| ( ( proper_subset @ SV6 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(194,plain,
! [SV15: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV15 ) )
= $true )
| ( ( ~ ( ( SV6 != SV15 ) ) )
= $true )
| ( ( proper_subset @ SV6 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(195,plain,
! [SV8: $i,SV21: $i] :
( ( ( in @ SV21 @ SV8 )
= $false )
| ( ( subset @ SV21 @ SV8 )
= $true )
| ( ( epsilon_transitive @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(196,plain,
! [SV8: $i] :
( ( ( in @ ( sK5_SY34 @ SV8 ) @ SV8 )
= $true )
| ( ( epsilon_transitive @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(197,plain,
( ( ~ ( subset @ sK1_A @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(198,plain,
( ( ~ ( in @ sK2_SX0 @ sK4_SY39 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(199,plain,
( ( epsilon_transitive @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(200,plain,
( ( epsilon_connected @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(201,plain,
! [SV15: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV15 )
= $true )
| ( ( proper_subset @ SV6 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[192]) ).
thf(202,plain,
! [SV15: $i,SV6: $i] :
( ( ( SV6 != SV15 )
= $true )
| ( ( proper_subset @ SV6 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(203,plain,
! [SV15: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV15 )
= $false )
| ( ( ~ ( ( SV6 != SV15 ) ) )
= $true )
| ( ( proper_subset @ SV6 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(204,plain,
( ( subset @ sK1_A @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(205,plain,
( ( in @ sK2_SX0 @ sK4_SY39 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(206,plain,
! [SV15: $i,SV6: $i] :
( ( ( SV6 = SV15 )
= $false )
| ( ( proper_subset @ SV6 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(207,plain,
! [SV15: $i,SV6: $i] :
( ( ( SV6 != SV15 )
= $false )
| ( ( subset @ SV6 @ SV15 )
= $false )
| ( ( proper_subset @ SV6 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(208,plain,
! [SV15: $i,SV6: $i] :
( ( ( SV6 = SV15 )
= $true )
| ( ( subset @ SV6 @ SV15 )
= $false )
| ( ( proper_subset @ SV6 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(209,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[69,208,206,205,204,201,200,199,196,195,191,187,181,178,177,174,169,167,165,157,156,149,135,124,96]) ).
thf(210,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[209]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM390+1 : TPTP v9.3.1. Released v3.2.0.
% 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
% 0.09/0.16 % Computer : n010.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Oct 6 13:11:55 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.27
% 0.09/0.27 No.of.Axioms: 12
% 0.09/0.27
% 0.09/0.27 Length.of.Defs: 0
% 0.09/0.27
% 0.09/0.27 Contains.Choice.Funs: false
% 0.09/0.27 ....
% 0.09/0.27
% 0.09/0.27 ********************************
% 0.09/0.27 * All subproblems solved! *
% 0.09/0.27 ********************************
% 0.09/0.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:13,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:209,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.27
% 0.09/0.27 %**** Beginning of derivation protocol ****
% 0.09/0.27 % SZS output start CNFRefutation
% See solution above
% 0.09/0.28
% 0.09/0.28 %**** End of derivation protocol ****
% 0.09/0.28 %**** no. of clauses in derivation: 185 ****
% 0.09/0.28 %**** clause counter: 209 ****
% 0.09/0.28
% 0.09/0.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:13,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:209,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------