%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU096+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 10:42:52 AM UTC 2026
% Result : Theorem 0.57s 0.30s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 21
% Syntax : Number of formulae : 278 ( 211 unt; 0 typ; 0 def)
% Number of atoms : 1317 ( 347 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 1806 ( 588 ~; 254 |; 79 &; 845 @)
% ( 0 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 38 usr; 17 con; 0-2 aty)
% Number of variables : 205 ( 0 ^; 172 !; 33 ?; 205 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_being_limit_ordinal,type,
being_limit_ordinal: $i > $o ).
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_finite,type,
finite: $i > $o ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_function_yielding,type,
function_yielding: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_natural,type,
natural: $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_ordinal_yielding,type,
ordinal_yielding: $i > $o ).
thf(tp_positive_rationals,type,
positive_rationals: $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_relation_image,type,
relation_image: $i > $i > $i ).
thf(tp_relation_inverse_image,type,
relation_inverse_image: $i > $i > $i ).
thf(tp_relation_non_empty,type,
relation_non_empty: $i > $o ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_sK10_SX0,type,
sK10_SX0: $i ).
thf(tp_sK11_SX0,type,
sK11_SX0: $i ).
thf(tp_sK12_SX0,type,
sK12_SX0: $i ).
thf(tp_sK13_SX0,type,
sK13_SX0: $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY26,type,
sK2_SY26: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SX0,type,
sK5_SX0: $i ).
thf(tp_sK6_SX0,type,
sK6_SX0: $i ).
thf(tp_sK7_SX0,type,
sK7_SX0: $i ).
thf(tp_sK8_SX0,type,
sK8_SX0: $i ).
thf(tp_sK9_SX0,type,
sK9_SX0: $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_transfinite_sequence,type,
transfinite_sequence: $i > $o ).
thf(tp_with_non_empty_elements,type,
with_non_empty_elements: $i > $o ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( finite @ A )
=> ( finite @ ( relation_image @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_finset_1) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( subset @ A @ ( relation_rng @ B ) )
=> ( ( relation_image @ B @ ( relation_inverse_image @ B @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_funct_1) ).
thf(11,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(12,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_non_empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_funct_1) ).
thf(13,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( transfinite_sequence @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_ordinal1) ).
thf(14,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(15,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(17,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(22,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(25,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(30,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(33,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(34,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( function_yielding @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funcop_1) ).
thf(35,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(37,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(39,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( finite @ B ) )
=> ( finite @ ( relation_image @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_finset_1) ).
thf(54,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(56,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(57,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(60,conjecture,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( subset @ A @ ( relation_rng @ B ) )
& ( finite @ ( relation_inverse_image @ B @ A ) ) )
=> ( finite @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finset_1) ).
thf(61,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( subset @ A @ ( relation_rng @ B ) )
& ( finite @ ( relation_inverse_image @ B @ A ) ) )
=> ( finite @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[60]) ).
thf(62,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( subset @ A @ ( relation_rng @ B ) )
& ( finite @ ( relation_inverse_image @ B @ A ) ) )
=> ( finite @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[61]) ).
thf(63,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( finite @ A )
=> ( finite @ ( relation_image @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(64,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( subset @ A @ ( relation_rng @ B ) )
=> ( ( relation_image @ B @ ( relation_inverse_image @ B @ A ) )
= A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(65,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(66,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_non_empty @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(67,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( transfinite_sequence @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(68,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(69,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(70,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(71,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(72,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(73,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(74,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(75,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( function_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(76,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(77,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(78,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( finite @ B ) )
=> ( finite @ ( relation_image @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(80,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(81,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(82,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(83,plain,
( ( ! [SY26: $i] :
( ( ( relation @ SY26 )
& ( function @ SY26 ) )
=> ( ( ( subset @ sK1_A @ ( relation_rng @ SY26 ) )
& ( finite @ ( relation_inverse_image @ SY26 @ sK1_A ) ) )
=> ( finite @ sK1_A ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[62]) ).
thf(84,plain,
( ( ( ( relation @ sK2_SY26 )
& ( function @ sK2_SY26 ) )
=> ( ( ( subset @ sK1_A @ ( relation_rng @ sK2_SY26 ) )
& ( finite @ ( relation_inverse_image @ sK2_SY26 @ sK1_A ) ) )
=> ( finite @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[83]) ).
thf(85,plain,
( ( relation @ sK2_SY26 )
= $true ),
inference(standard_cnf,[status(thm)],[84]) ).
thf(86,plain,
( ( function @ sK2_SY26 )
= $true ),
inference(standard_cnf,[status(thm)],[84]) ).
thf(87,plain,
( ( subset @ sK1_A @ ( relation_rng @ sK2_SY26 ) )
= $true ),
inference(standard_cnf,[status(thm)],[84]) ).
thf(88,plain,
( ( finite @ ( relation_inverse_image @ sK2_SY26 @ sK1_A ) )
= $true ),
inference(standard_cnf,[status(thm)],[84]) ).
thf(89,plain,
( ( finite @ sK1_A )
= $false ),
inference(standard_cnf,[status(thm)],[84]) ).
thf(90,plain,
( ( ~ ( finite @ sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[89]) ).
thf(91,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(92,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(93,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(94,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( finite @ B ) )
=> ( finite @ ( relation_image @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(95,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(96,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(97,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(98,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( function_yielding @ A ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(99,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(100,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(101,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(102,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(103,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(104,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(105,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(106,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( transfinite_sequence @ A ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(107,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_non_empty @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(108,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(109,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( subset @ A @ ( relation_rng @ B ) )
=> ( ( relation_image @ B @ ( relation_inverse_image @ B @ A ) )
= A ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(110,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( finite @ A )
=> ( finite @ ( relation_image @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(111,plain,
( ( finite @ ( relation_inverse_image @ sK2_SY26 @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(112,plain,
( ( subset @ sK1_A @ ( relation_rng @ sK2_SY26 ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(113,plain,
( ( function @ sK2_SY26 )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(114,plain,
( ( relation @ sK2_SY26 )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(115,plain,
( ( ~ ( finite @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(116,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(117,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(118,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(119,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(120,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( finite @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(121,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( finite @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(122,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX1 )
| ~ ( function @ SX1 ) )
| ~ ( finite @ SX0 )
| ( finite @ ( relation_image @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(123,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_non_empty @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(124,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(125,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( function_yielding @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(126,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(127,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX1 )
| ~ ( function @ SX1 ) )
| ~ ( subset @ SX0 @ ( relation_rng @ SX1 ) )
| ( ( relation_image @ SX1 @ ( relation_inverse_image @ SX1 @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(128,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( finite @ SX1 ) )
| ( finite @ ( relation_image @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(129,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_rng @ SX0 ) )
| ~ ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(130,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(131,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( transfinite_sequence @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(132,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(133,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(134,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(135,plain,
! [SV1: $i] :
( ( ! [SY27: $i] : ( subset @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(136,plain,
( ( finite @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(137,plain,
! [SV2: $i] :
( ( ~ ( empty @ SV2 )
| ( function @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(138,plain,
! [SV3: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV3 )
| ~ ( relation @ SV3 ) )
| ~ ( empty @ ( relation_rng @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(139,plain,
! [SV4: $i] :
( ( ~ ( empty @ SV4 )
| ( relation @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(140,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(141,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( finite @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(142,plain,
! [SV5: $i] :
( ( ~ ( empty @ SV5 )
| ( finite @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(143,plain,
! [SV6: $i] :
( ( ! [SY28: $i] :
( ~ ~ ( ~ ( relation @ SY28 )
| ~ ( function @ SY28 ) )
| ~ ( finite @ SV6 )
| ( finite @ ( relation_image @ SY28 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(144,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_non_empty @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(145,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(146,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( function_yielding @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(147,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(148,plain,
! [SV7: $i] :
( ( ! [SY29: $i] :
( ~ ~ ( ~ ( relation @ SY29 )
| ~ ( function @ SY29 ) )
| ~ ( subset @ SV7 @ ( relation_rng @ SY29 ) )
| ( ( relation_image @ SY29 @ ( relation_inverse_image @ SY29 @ SV7 ) )
= SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(149,plain,
! [SV8: $i] :
( ( ! [SY30: $i] :
( ~ ~ ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) )
| ~ ( finite @ SY30 ) )
| ( finite @ ( relation_image @ SV8 @ SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(150,plain,
! [SV9: $i] :
( ( ~ ( empty @ SV9 )
| ~ ( ~ ( empty @ ( relation_rng @ SV9 ) )
| ~ ( relation @ ( relation_rng @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(151,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(152,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( transfinite_sequence @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(153,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(154,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(155,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(156,plain,
! [SV1: $i] :
( ( subset @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(157,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $true )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(158,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV3 )
| ~ ( relation @ SV3 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(159,plain,
! [SV4: $i] :
( ( ( ~ ( empty @ SV4 ) )
= $true )
| ( ( relation @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(160,plain,
( ( ~ ~ ( ~ ( relation @ sK3_SX0 )
| ~ ( function @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[140]) ).
thf(161,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK4_SX0 )
| ~ ( finite @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[141]) ).
thf(162,plain,
! [SV5: $i] :
( ( ( ~ ( empty @ SV5 ) )
= $true )
| ( ( finite @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(163,plain,
! [SV6: $i,SV11: $i] :
( ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( function @ SV11 ) )
| ~ ( finite @ SV6 )
| ( finite @ ( relation_image @ SV11 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(164,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( relation_non_empty @ sK5_SX0 ) )
| ~ ( function @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[144]) ).
thf(165,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK6_SX0 )
| ~ ( relation_empty_yielding @ sK6_SX0 ) )
| ~ ( function @ sK6_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[145]) ).
thf(166,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK7_SX0 )
| ~ ( function @ sK7_SX0 ) )
| ~ ( function_yielding @ sK7_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[146]) ).
thf(167,plain,
( ( ~ ~ ( ~ ( empty @ sK8_SX0 )
| ~ ( relation @ sK8_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[147]) ).
thf(168,plain,
! [SV7: $i,SV12: $i] :
( ( ~ ~ ( ~ ( relation @ SV12 )
| ~ ( function @ SV12 ) )
| ~ ( subset @ SV7 @ ( relation_rng @ SV12 ) )
| ( ( relation_image @ SV12 @ ( relation_inverse_image @ SV12 @ SV7 ) )
= SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(169,plain,
! [SV13: $i,SV8: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) )
| ~ ( finite @ SV13 ) )
| ( finite @ ( relation_image @ SV8 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(170,plain,
! [SV9: $i] :
( ( ( ~ ( empty @ SV9 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV9 ) )
| ~ ( relation @ ( relation_rng @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(171,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK9_SX0 )
| ~ ( empty @ sK9_SX0 ) )
| ~ ( function @ sK9_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[151]) ).
thf(172,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK10_SX0 )
| ~ ( function @ sK10_SX0 ) )
| ~ ( transfinite_sequence @ sK10_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[152]) ).
thf(173,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK11_SX0 )
| ~ ( relation @ sK11_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[153]) ).
thf(174,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK12_SX0 )
| ~ ( function @ sK12_SX0 ) )
| ~ ( one_to_one @ sK12_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[154]) ).
thf(175,plain,
( ( ~ ~ ( ~ ( relation @ sK13_SX0 )
| ~ ( relation_empty_yielding @ sK13_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[155]) ).
thf(176,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $false )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(177,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV3 )
| ~ ( relation @ SV3 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_rng @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(178,plain,
! [SV4: $i] :
( ( ( empty @ SV4 )
= $false )
| ( ( relation @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(179,plain,
( ( ~ ( ~ ( relation @ sK3_SX0 )
| ~ ( function @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(180,plain,
( ( ~ ( ~ ~ ( empty @ sK4_SX0 )
| ~ ( finite @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(181,plain,
! [SV5: $i] :
( ( ( empty @ SV5 )
= $false )
| ( ( finite @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(182,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( function @ SV11 ) ) )
= $true )
| ( ( ~ ( finite @ SV6 )
| ( finite @ ( relation_image @ SV11 @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(183,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( relation_non_empty @ sK5_SX0 ) )
| ~ ( function @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(184,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK6_SX0 )
| ~ ( relation_empty_yielding @ sK6_SX0 ) )
| ~ ( function @ sK6_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(185,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK7_SX0 )
| ~ ( function @ sK7_SX0 ) )
| ~ ( function_yielding @ sK7_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(186,plain,
( ( ~ ( ~ ( empty @ sK8_SX0 )
| ~ ( relation @ sK8_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(187,plain,
! [SV7: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV12 )
| ~ ( function @ SV12 ) ) )
= $true )
| ( ( ~ ( subset @ SV7 @ ( relation_rng @ SV12 ) )
| ( ( relation_image @ SV12 @ ( relation_inverse_image @ SV12 @ SV7 ) )
= SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(188,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) )
| ~ ( finite @ SV13 ) ) )
= $true )
| ( ( finite @ ( relation_image @ SV8 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(189,plain,
! [SV9: $i] :
( ( ( empty @ SV9 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV9 ) )
| ~ ( relation @ ( relation_rng @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(190,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK9_SX0 )
| ~ ( empty @ sK9_SX0 ) )
| ~ ( function @ sK9_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(191,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK10_SX0 )
| ~ ( function @ sK10_SX0 ) )
| ~ ( transfinite_sequence @ sK10_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(192,plain,
( ( ~ ( ~ ~ ( empty @ sK11_SX0 )
| ~ ( relation @ sK11_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(193,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK12_SX0 )
| ~ ( function @ sK12_SX0 ) )
| ~ ( one_to_one @ sK12_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(194,plain,
( ( ~ ( ~ ( relation @ sK13_SX0 )
| ~ ( relation_empty_yielding @ sK13_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(195,plain,
! [SV3: $i] :
( ( ( ~ ~ ( empty @ SV3 )
| ~ ( relation @ SV3 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(196,plain,
( ( ~ ( relation @ sK3_SX0 )
| ~ ( function @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(197,plain,
( ( ~ ~ ( empty @ sK4_SX0 )
| ~ ( finite @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(198,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ( ~ ( relation @ SV11 )
| ~ ( function @ SV11 ) ) )
= $false )
| ( ( ~ ( finite @ SV6 )
| ( finite @ ( relation_image @ SV11 @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(199,plain,
( ( ~ ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( relation_non_empty @ sK5_SX0 ) )
| ~ ( function @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(200,plain,
( ( ~ ~ ( ~ ( relation @ sK6_SX0 )
| ~ ( relation_empty_yielding @ sK6_SX0 ) )
| ~ ( function @ sK6_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(201,plain,
( ( ~ ~ ( ~ ( relation @ sK7_SX0 )
| ~ ( function @ sK7_SX0 ) )
| ~ ( function_yielding @ sK7_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(202,plain,
( ( ~ ( empty @ sK8_SX0 )
| ~ ( relation @ sK8_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(203,plain,
! [SV7: $i,SV12: $i] :
( ( ( ~ ( ~ ( relation @ SV12 )
| ~ ( function @ SV12 ) ) )
= $false )
| ( ( ~ ( subset @ SV7 @ ( relation_rng @ SV12 ) )
| ( ( relation_image @ SV12 @ ( relation_inverse_image @ SV12 @ SV7 ) )
= SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(204,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) )
| ~ ( finite @ SV13 ) ) )
= $false )
| ( ( finite @ ( relation_image @ SV8 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(205,plain,
! [SV9: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV9 ) )
| ~ ( relation @ ( relation_rng @ SV9 ) ) )
= $false )
| ( ( empty @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(206,plain,
( ( ~ ~ ( ~ ( relation @ sK9_SX0 )
| ~ ( empty @ sK9_SX0 ) )
| ~ ( function @ sK9_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(207,plain,
( ( ~ ~ ( ~ ( relation @ sK10_SX0 )
| ~ ( function @ sK10_SX0 ) )
| ~ ( transfinite_sequence @ sK10_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(208,plain,
( ( ~ ~ ( empty @ sK11_SX0 )
| ~ ( relation @ sK11_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(209,plain,
( ( ~ ~ ( ~ ( relation @ sK12_SX0 )
| ~ ( function @ sK12_SX0 ) )
| ~ ( one_to_one @ sK12_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(210,plain,
( ( ~ ( relation @ sK13_SX0 )
| ~ ( relation_empty_yielding @ sK13_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(211,plain,
! [SV3: $i] :
( ( ( ~ ~ ( empty @ SV3 ) )
= $true )
| ( ( ~ ( relation @ SV3 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(212,plain,
( ( ~ ( relation @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(213,plain,
( ( ~ ( function @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(214,plain,
( ( ~ ~ ( empty @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(215,plain,
( ( ~ ( finite @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(216,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ( relation @ SV11 )
| ~ ( function @ SV11 ) )
= $true )
| ( ( ~ ( finite @ SV6 )
| ( finite @ ( relation_image @ SV11 @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(217,plain,
( ( ~ ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( relation_non_empty @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(218,plain,
( ( ~ ( function @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(219,plain,
( ( ~ ~ ( ~ ( relation @ sK6_SX0 )
| ~ ( relation_empty_yielding @ sK6_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(220,plain,
( ( ~ ( function @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(221,plain,
( ( ~ ~ ( ~ ( relation @ sK7_SX0 )
| ~ ( function @ sK7_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(222,plain,
( ( ~ ( function_yielding @ sK7_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[201]) ).
thf(223,plain,
( ( ~ ( empty @ sK8_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(224,plain,
( ( ~ ( relation @ sK8_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(225,plain,
! [SV7: $i,SV12: $i] :
( ( ( ~ ( relation @ SV12 )
| ~ ( function @ SV12 ) )
= $true )
| ( ( ~ ( subset @ SV7 @ ( relation_rng @ SV12 ) )
| ( ( relation_image @ SV12 @ ( relation_inverse_image @ SV12 @ SV7 ) )
= SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(226,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) )
| ~ ( finite @ SV13 ) )
= $true )
| ( ( finite @ ( relation_image @ SV8 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(227,plain,
! [SV9: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV9 ) ) )
= $false )
| ( ( empty @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(228,plain,
! [SV9: $i] :
( ( ( ~ ( relation @ ( relation_rng @ SV9 ) ) )
= $false )
| ( ( empty @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(229,plain,
( ( ~ ~ ( ~ ( relation @ sK9_SX0 )
| ~ ( empty @ sK9_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[206]) ).
thf(230,plain,
( ( ~ ( function @ sK9_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[206]) ).
thf(231,plain,
( ( ~ ~ ( ~ ( relation @ sK10_SX0 )
| ~ ( function @ sK10_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(232,plain,
( ( ~ ( transfinite_sequence @ sK10_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(233,plain,
( ( ~ ~ ( empty @ sK11_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(234,plain,
( ( ~ ( relation @ sK11_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(235,plain,
( ( ~ ~ ( ~ ( relation @ sK12_SX0 )
| ~ ( function @ sK12_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(236,plain,
( ( ~ ( one_to_one @ sK12_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(237,plain,
( ( ~ ( relation @ sK13_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(238,plain,
( ( ~ ( relation_empty_yielding @ sK13_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(239,plain,
! [SV3: $i] :
( ( ( ~ ( empty @ SV3 ) )
= $false )
| ( ( ~ ( relation @ SV3 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(240,plain,
( ( relation @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(241,plain,
( ( function @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(242,plain,
( ( ~ ( empty @ sK4_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(243,plain,
( ( finite @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(244,plain,
! [SV6: $i,SV11: $i] :
( ( ( ~ ( relation @ SV11 ) )
= $true )
| ( ( ~ ( function @ SV11 ) )
= $true )
| ( ( ~ ( finite @ SV6 )
| ( finite @ ( relation_image @ SV11 @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(245,plain,
( ( ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( relation_non_empty @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(246,plain,
( ( function @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(247,plain,
( ( ~ ( ~ ( relation @ sK6_SX0 )
| ~ ( relation_empty_yielding @ sK6_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(248,plain,
( ( function @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(249,plain,
( ( ~ ( ~ ( relation @ sK7_SX0 )
| ~ ( function @ sK7_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(250,plain,
( ( function_yielding @ sK7_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(251,plain,
( ( empty @ sK8_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(252,plain,
( ( relation @ sK8_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(253,plain,
! [SV7: $i,SV12: $i] :
( ( ( ~ ( relation @ SV12 ) )
= $true )
| ( ( ~ ( function @ SV12 ) )
= $true )
| ( ( ~ ( subset @ SV7 @ ( relation_rng @ SV12 ) )
| ( ( relation_image @ SV12 @ ( relation_inverse_image @ SV12 @ SV7 ) )
= SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(254,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) ) )
= $true )
| ( ( ~ ( finite @ SV13 ) )
= $true )
| ( ( finite @ ( relation_image @ SV8 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(255,plain,
! [SV9: $i] :
( ( ( empty @ ( relation_rng @ SV9 ) )
= $true )
| ( ( empty @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(256,plain,
! [SV9: $i] :
( ( ( relation @ ( relation_rng @ SV9 ) )
= $true )
| ( ( empty @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(257,plain,
( ( ~ ( ~ ( relation @ sK9_SX0 )
| ~ ( empty @ sK9_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(258,plain,
( ( function @ sK9_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(259,plain,
( ( ~ ( ~ ( relation @ sK10_SX0 )
| ~ ( function @ sK10_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(260,plain,
( ( transfinite_sequence @ sK10_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(261,plain,
( ( ~ ( empty @ sK11_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(262,plain,
( ( relation @ sK11_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(263,plain,
( ( ~ ( ~ ( relation @ sK12_SX0 )
| ~ ( function @ sK12_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(264,plain,
( ( one_to_one @ sK12_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(265,plain,
( ( relation @ sK13_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(266,plain,
( ( relation_empty_yielding @ sK13_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(267,plain,
! [SV3: $i] :
( ( ( empty @ SV3 )
= $true )
| ( ( ~ ( relation @ SV3 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(268,plain,
( ( empty @ sK4_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(269,plain,
! [SV6: $i,SV11: $i] :
( ( ( relation @ SV11 )
= $false )
| ( ( ~ ( function @ SV11 ) )
= $true )
| ( ( ~ ( finite @ SV6 )
| ( finite @ ( relation_image @ SV11 @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(270,plain,
( ( ~ ( relation @ sK5_SX0 )
| ~ ( relation_non_empty @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(271,plain,
( ( ~ ( relation @ sK6_SX0 )
| ~ ( relation_empty_yielding @ sK6_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(272,plain,
( ( ~ ( relation @ sK7_SX0 )
| ~ ( function @ sK7_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(273,plain,
! [SV7: $i,SV12: $i] :
( ( ( relation @ SV12 )
= $false )
| ( ( ~ ( function @ SV12 ) )
= $true )
| ( ( ~ ( subset @ SV7 @ ( relation_rng @ SV12 ) )
| ( ( relation_image @ SV12 @ ( relation_inverse_image @ SV12 @ SV7 ) )
= SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(274,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) ) )
= $false )
| ( ( ~ ( finite @ SV13 ) )
= $true )
| ( ( finite @ ( relation_image @ SV8 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(275,plain,
( ( ~ ( relation @ sK9_SX0 )
| ~ ( empty @ sK9_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(276,plain,
( ( ~ ( relation @ sK10_SX0 )
| ~ ( function @ sK10_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(277,plain,
( ( empty @ sK11_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(278,plain,
( ( ~ ( relation @ sK12_SX0 )
| ~ ( function @ sK12_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(279,plain,
! [SV3: $i] :
( ( ( relation @ SV3 )
= $false )
| ( ( empty @ SV3 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(280,plain,
! [SV6: $i,SV11: $i] :
( ( ( function @ SV11 )
= $false )
| ( ( relation @ SV11 )
= $false )
| ( ( ~ ( finite @ SV6 )
| ( finite @ ( relation_image @ SV11 @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(281,plain,
( ( ~ ( relation @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[270]) ).
thf(282,plain,
( ( ~ ( relation_non_empty @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[270]) ).
thf(283,plain,
( ( ~ ( relation @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[271]) ).
thf(284,plain,
( ( ~ ( relation_empty_yielding @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[271]) ).
thf(285,plain,
( ( ~ ( relation @ sK7_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[272]) ).
thf(286,plain,
( ( ~ ( function @ sK7_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[272]) ).
thf(287,plain,
! [SV7: $i,SV12: $i] :
( ( ( function @ SV12 )
= $false )
| ( ( relation @ SV12 )
= $false )
| ( ( ~ ( subset @ SV7 @ ( relation_rng @ SV12 ) )
| ( ( relation_image @ SV12 @ ( relation_inverse_image @ SV12 @ SV7 ) )
= SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(288,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) )
= $true )
| ( ( ~ ( finite @ SV13 ) )
= $true )
| ( ( finite @ ( relation_image @ SV8 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(289,plain,
( ( ~ ( relation @ sK9_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[275]) ).
thf(290,plain,
( ( ~ ( empty @ sK9_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[275]) ).
thf(291,plain,
( ( ~ ( relation @ sK10_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[276]) ).
thf(292,plain,
( ( ~ ( function @ sK10_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[276]) ).
thf(293,plain,
( ( ~ ( relation @ sK12_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[278]) ).
thf(294,plain,
( ( ~ ( function @ sK12_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[278]) ).
thf(295,plain,
! [SV3: $i] :
( ( ( empty @ ( relation_rng @ SV3 ) )
= $false )
| ( ( empty @ SV3 )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(296,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( finite @ SV6 ) )
= $true )
| ( ( finite @ ( relation_image @ SV11 @ SV6 ) )
= $true )
| ( ( relation @ SV11 )
= $false )
| ( ( function @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(297,plain,
( ( relation @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(298,plain,
( ( relation_non_empty @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(299,plain,
( ( relation @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(300,plain,
( ( relation_empty_yielding @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(301,plain,
( ( relation @ sK7_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(302,plain,
( ( function @ sK7_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(303,plain,
! [SV12: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ ( relation_rng @ SV12 ) ) )
= $true )
| ( ( ( relation_image @ SV12 @ ( relation_inverse_image @ SV12 @ SV7 ) )
= SV7 )
= $true )
| ( ( relation @ SV12 )
= $false )
| ( ( function @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(304,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( relation @ SV8 ) )
= $true )
| ( ( ~ ( function @ SV8 ) )
= $true )
| ( ( ~ ( finite @ SV13 ) )
= $true )
| ( ( finite @ ( relation_image @ SV8 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(305,plain,
( ( relation @ sK9_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(306,plain,
( ( empty @ sK9_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(307,plain,
( ( relation @ sK10_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[291]) ).
thf(308,plain,
( ( function @ sK10_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(309,plain,
( ( relation @ sK12_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(310,plain,
( ( function @ sK12_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(311,plain,
! [SV11: $i,SV6: $i] :
( ( ( finite @ SV6 )
= $false )
| ( ( finite @ ( relation_image @ SV11 @ SV6 ) )
= $true )
| ( ( relation @ SV11 )
= $false )
| ( ( function @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(312,plain,
! [SV12: $i,SV7: $i] :
( ( ( subset @ SV7 @ ( relation_rng @ SV12 ) )
= $false )
| ( ( ( relation_image @ SV12 @ ( relation_inverse_image @ SV12 @ SV7 ) )
= SV7 )
= $true )
| ( ( relation @ SV12 )
= $false )
| ( ( function @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(313,plain,
! [SV13: $i,SV8: $i] :
( ( ( relation @ SV8 )
= $false )
| ( ( ~ ( function @ SV8 ) )
= $true )
| ( ( ~ ( finite @ SV13 ) )
= $true )
| ( ( finite @ ( relation_image @ SV8 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(314,plain,
! [SV13: $i,SV8: $i] :
( ( ( function @ SV8 )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( ~ ( finite @ SV13 ) )
= $true )
| ( ( finite @ ( relation_image @ SV8 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(315,plain,
! [SV8: $i,SV13: $i] :
( ( ( finite @ SV13 )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false )
| ( ( finite @ ( relation_image @ SV8 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(316,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[111,315,312,311,310,309,308,307,306,305,302,301,300,299,298,297,295,277,268,266,265,264,262,260,258,256,255,252,251,250,248,246,243,241,240,181,178,176,156,136,114,113,112]) ).
thf(317,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[316]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU096+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n019.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 15:00:16 UTC 2026
% 0.09/0.17 % 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
% 0.57/0.30
% 0.57/0.30 No.of.Axioms: 20
% 0.57/0.30
% 0.57/0.30 Length.of.Defs: 0
% 0.57/0.30
% 0.57/0.30 Contains.Choice.Funs: false
% 0.57/0.30 .....
% 0.57/0.30
% 0.57/0.30 ********************************
% 0.57/0.30 * All subproblems solved! *
% 0.57/0.30 ********************************
% 0.57/0.30 % 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:316,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.57/0.30
% 0.57/0.30 %**** Beginning of derivation protocol ****
% 0.57/0.30 % SZS output start CNFRefutation
% See solution above
% 0.57/0.30
% 0.57/0.30 %**** End of derivation protocol ****
% 0.57/0.30 %**** no. of clauses in derivation: 278 ****
% 0.57/0.30 %**** clause counter: 316 ****
% 0.57/0.30
% 0.57/0.30 % 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:316,loop_count:0,foatp_calls:1,translation:fof_full)
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