%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU062+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 : n004.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 10:42:50 AM UTC 2026
% Result : Theorem 0.09s 0.29s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of formulae : 201 ( 132 unt; 0 typ; 0 def)
% Number of atoms : 951 ( 295 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 1373 ( 344 ~; 181 |; 31 &; 777 @)
% ( 6 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 9 con; 0-2 aty)
% Number of variables : 254 ( 0 ^; 242 !; 12 ?; 254 :)
% 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_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_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_inverse_image,type,
relation_inverse_image: $i > $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY25,type,
sK2_SY25: $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_SY37,type,
sK7_SY37: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(3,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( in @ A @ ( relation_rng @ B ) )
<=> ( ( relation_inverse_image @ B @ ( singleton @ A ) )
!= empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_funct_1) ).
thf(10,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(11,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(15,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(19,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(20,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(21,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(22,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(23,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(24,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(25,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(31,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(34,conjecture,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ! [C: $i] :
~ ( ( in @ C @ A )
& ( ( relation_inverse_image @ B @ ( singleton @ C ) )
= empty_set ) )
=> ( subset @ A @ ( relation_rng @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t143_funct_1) ).
thf(35,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ! [C: $i] :
~ ( ( in @ C @ A )
& ( ( relation_inverse_image @ B @ ( singleton @ C ) )
= empty_set ) )
=> ( subset @ A @ ( relation_rng @ B ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[34]) ).
thf(36,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ! [C: $i] :
~ ( ( in @ C @ A )
& ( ( relation_inverse_image @ B @ ( singleton @ C ) )
= empty_set ) )
=> ( subset @ A @ ( relation_rng @ B ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[35]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(38,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(40,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( in @ A @ ( relation_rng @ B ) )
<=> ( ( relation_inverse_image @ B @ ( singleton @ A ) )
!= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(42,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(43,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(44,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(45,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(46,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(47,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(48,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(49,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(50,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(51,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(52,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(53,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(54,plain,
( ( ! [SY25: $i] :
( ( relation @ SY25 )
=> ( ! [SY26: $i] :
~ ( ( in @ SY26 @ sK1_A )
& ( ( relation_inverse_image @ SY25 @ ( singleton @ SY26 ) )
= empty_set ) )
=> ( subset @ sK1_A @ ( relation_rng @ SY25 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[36]) ).
thf(55,plain,
( ( ( relation @ sK2_SY25 )
=> ( ! [SY27: $i] :
~ ( ( in @ SY27 @ sK1_A )
& ( ( relation_inverse_image @ sK2_SY25 @ ( singleton @ SY27 ) )
= empty_set ) )
=> ( subset @ sK1_A @ ( relation_rng @ sK2_SY25 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[54]) ).
thf(56,plain,
( ( relation @ sK2_SY25 )
= $true ),
inference(standard_cnf,[status(thm)],[55]) ).
thf(57,plain,
( ( ! [SY27: $i] :
~ ( ( in @ SY27 @ sK1_A )
& ( ( relation_inverse_image @ sK2_SY25 @ ( singleton @ SY27 ) )
= empty_set ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[55]) ).
thf(58,plain,
( ( subset @ sK1_A @ ( relation_rng @ sK2_SY25 ) )
= $false ),
inference(standard_cnf,[status(thm)],[55]) ).
thf(59,plain,
( ( ~ ( subset @ sK1_A @ ( relation_rng @ sK2_SY25 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[58]) ).
thf(60,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(61,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(62,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(63,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(64,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(65,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(66,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(67,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(68,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(69,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(70,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(71,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(72,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(73,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( in @ A @ ( relation_rng @ B ) )
<=> ( ( relation_inverse_image @ B @ ( singleton @ A ) )
!= empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(74,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(75,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(76,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(77,plain,
( ( ! [SY27: $i] :
~ ( ( in @ SY27 @ sK1_A )
& ( ( relation_inverse_image @ sK2_SY25 @ ( singleton @ SY27 ) )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(78,plain,
( ( relation @ sK2_SY25 )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(79,plain,
( ( ~ ( subset @ sK1_A @ ( relation_rng @ sK2_SY25 ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(80,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(81,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( ~ ( ~ ( in @ SX0 @ ( relation_rng @ SX1 ) )
| ( ( relation_inverse_image @ SX1 @ ( singleton @ SX0 ) )
!= empty_set ) )
| ~ ( ~ ( ( ( relation_inverse_image @ SX1 @ ( singleton @ SX0 ) )
!= empty_set ) )
| ( in @ SX0 @ ( relation_rng @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(82,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(83,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(84,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(85,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(86,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(87,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(88,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_rng @ SX0 ) )
| ~ ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(89,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(90,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(91,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(92,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( in @ SX0 @ sK1_A )
| ( ( relation_inverse_image @ sK2_SY25 @ ( singleton @ SX0 ) )
!= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(93,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(94,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(95,plain,
! [SV1: $i] :
( ( ~ ( empty @ ( singleton @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(96,plain,
! [SV2: $i] :
( ( ! [SY28: $i] : ( subset @ SV2 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(97,plain,
( ( subset @ sK1_A @ ( relation_rng @ sK2_SY25 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(98,plain,
! [SV3: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV3 )
| ~ ( relation @ SV3 ) )
| ~ ( empty @ ( relation_rng @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(99,plain,
! [SV4: $i] :
( ( ! [SY29: $i] :
( ~ ( relation @ SY29 )
| ~ ( ~ ( ~ ( in @ SV4 @ ( relation_rng @ SY29 ) )
| ( ( relation_inverse_image @ SY29 @ ( singleton @ SV4 ) )
!= empty_set ) )
| ~ ( ~ ( ( ( relation_inverse_image @ SY29 @ ( singleton @ SV4 ) )
!= empty_set ) )
| ( in @ SV4 @ ( relation_rng @ SY29 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(100,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(101,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(102,plain,
! [SV5: $i] :
( ( ~ ( empty @ SV5 )
| ( SV5 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(103,plain,
! [SV6: $i] :
( ( ! [SY30: $i] :
( ~ ( in @ SV6 @ SY30 )
| ( element @ SV6 @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(104,plain,
! [SV7: $i] :
( ( ~ ( empty @ SV7 )
| ( relation @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(105,plain,
! [SV8: $i] :
( ( ! [SY31: $i] :
( ~ ( in @ SV8 @ SY31 )
| ~ ( in @ SY31 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(106,plain,
! [SV9: $i] :
( ( ~ ( empty @ SV9 )
| ~ ( ~ ( empty @ ( relation_rng @ SV9 ) )
| ~ ( relation @ ( relation_rng @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(107,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(108,plain,
! [SV10: $i] :
( ( ! [SY32: $i] :
~ ~ ( ~ ( in @ SV10 @ SY32 )
| ~ ( empty @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(109,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(110,plain,
! [SV11: $i] :
( ( ~ ~ ( ~ ( in @ SV11 @ sK1_A )
| ( ( relation_inverse_image @ sK2_SY25 @ ( singleton @ SV11 ) )
!= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(111,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(112,plain,
! [SV12: $i] :
( ( ! [SY33: $i] :
~ ( ~ ( ~ ( subset @ SV12 @ SY33 )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ SV12 )
| ( in @ SY34 @ SY33 ) ) )
| ~ ( ~ ! [SY35: $i] :
( ~ ( in @ SY35 @ SV12 )
| ( in @ SY35 @ SY33 ) )
| ( subset @ SV12 @ SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(113,plain,
! [SV1: $i] :
( ( empty @ ( singleton @ SV1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(114,plain,
! [SV2: $i] :
( ( subset @ SV2 @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(115,plain,
! [SV3: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV3 )
| ~ ( relation @ SV3 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(116,plain,
! [SV4: $i,SV14: $i] :
( ( ~ ( relation @ SV14 )
| ~ ( ~ ( ~ ( in @ SV4 @ ( relation_rng @ SV14 ) )
| ( ( relation_inverse_image @ SV14 @ ( singleton @ SV4 ) )
!= empty_set ) )
| ~ ( ~ ( ( ( relation_inverse_image @ SV14 @ ( singleton @ SV4 ) )
!= empty_set ) )
| ( in @ SV4 @ ( relation_rng @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(117,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(118,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(119,plain,
( ( ~ ~ ( ~ ( relation @ sK3_SX0 )
| ~ ( relation_empty_yielding @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[101]) ).
thf(120,plain,
! [SV5: $i] :
( ( ( ~ ( empty @ SV5 ) )
= $true )
| ( ( SV5 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(121,plain,
! [SV15: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ SV15 )
| ( element @ SV6 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(122,plain,
! [SV7: $i] :
( ( ( ~ ( empty @ SV7 ) )
= $true )
| ( ( relation @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(123,plain,
! [SV16: $i,SV8: $i] :
( ( ~ ( in @ SV8 @ SV16 )
| ~ ( in @ SV16 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(124,plain,
! [SV9: $i] :
( ( ( ~ ( empty @ SV9 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV9 ) )
| ~ ( relation @ ( relation_rng @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(125,plain,
( ( ~ ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( function @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[107]) ).
thf(126,plain,
! [SV17: $i,SV10: $i] :
( ( ~ ~ ( ~ ( in @ SV10 @ SV17 )
| ~ ( empty @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(127,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK5_SX0 )
| ~ ( relation @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[109]) ).
thf(128,plain,
! [SV11: $i] :
( ( ~ ( ~ ( in @ SV11 @ sK1_A )
| ( ( relation_inverse_image @ sK2_SY25 @ ( singleton @ SV11 ) )
!= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(129,plain,
( ( ~ ~ ( ~ ( empty @ sK6_SX0 )
| ~ ( relation @ sK6_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[111]) ).
thf(130,plain,
! [SV18: $i,SV12: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV12 @ SV18 )
| ! [SY36: $i] :
( ~ ( in @ SY36 @ SV12 )
| ( in @ SY36 @ SV18 ) ) )
| ~ ( ~ ! [SY37: $i] :
( ~ ( in @ SY37 @ SV12 )
| ( in @ SY37 @ SV18 ) )
| ( subset @ SV12 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(131,plain,
! [SV3: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV3 )
| ~ ( relation @ SV3 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_rng @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(132,plain,
! [SV4: $i,SV14: $i] :
( ( ( ~ ( relation @ SV14 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV4 @ ( relation_rng @ SV14 ) )
| ( ( relation_inverse_image @ SV14 @ ( singleton @ SV4 ) )
!= empty_set ) )
| ~ ( ~ ( ( ( relation_inverse_image @ SV14 @ ( singleton @ SV4 ) )
!= empty_set ) )
| ( in @ SV4 @ ( relation_rng @ SV14 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(133,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(134,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(135,plain,
( ( ~ ( ~ ( relation @ sK3_SX0 )
| ~ ( relation_empty_yielding @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(136,plain,
! [SV5: $i] :
( ( ( empty @ SV5 )
= $false )
| ( ( SV5 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(137,plain,
! [SV15: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV15 ) )
= $true )
| ( ( element @ SV6 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(138,plain,
! [SV7: $i] :
( ( ( empty @ SV7 )
= $false )
| ( ( relation @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(139,plain,
! [SV16: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV16 ) )
= $true )
| ( ( ~ ( in @ SV16 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(140,plain,
! [SV9: $i] :
( ( ( empty @ SV9 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV9 ) )
| ~ ( relation @ ( relation_rng @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(141,plain,
( ( ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( function @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(142,plain,
! [SV17: $i,SV10: $i] :
( ( ~ ( ~ ( in @ SV10 @ SV17 )
| ~ ( empty @ SV17 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(143,plain,
( ( ~ ( ~ ~ ( empty @ sK5_SX0 )
| ~ ( relation @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(144,plain,
! [SV11: $i] :
( ( ~ ( in @ SV11 @ sK1_A )
| ( ( relation_inverse_image @ sK2_SY25 @ ( singleton @ SV11 ) )
!= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(145,plain,
( ( ~ ( ~ ( empty @ sK6_SX0 )
| ~ ( relation @ sK6_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(146,plain,
! [SV18: $i,SV12: $i] :
( ( ~ ( ~ ( subset @ SV12 @ SV18 )
| ! [SY36: $i] :
( ~ ( in @ SY36 @ SV12 )
| ( in @ SY36 @ SV18 ) ) )
| ~ ( ~ ! [SY37: $i] :
( ~ ( in @ SY37 @ SV12 )
| ( in @ SY37 @ SV18 ) )
| ( subset @ SV12 @ SV18 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(147,plain,
! [SV3: $i] :
( ( ( ~ ~ ( empty @ SV3 )
| ~ ( relation @ SV3 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(148,plain,
! [SV4: $i,SV14: $i] :
( ( ( relation @ SV14 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV4 @ ( relation_rng @ SV14 ) )
| ( ( relation_inverse_image @ SV14 @ ( singleton @ SV4 ) )
!= empty_set ) )
| ~ ( ~ ( ( ( relation_inverse_image @ SV14 @ ( singleton @ SV4 ) )
!= empty_set ) )
| ( in @ SV4 @ ( relation_rng @ SV14 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(149,plain,
( ( ~ ( relation @ sK3_SX0 )
| ~ ( relation_empty_yielding @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(150,plain,
! [SV15: $i,SV6: $i] :
( ( ( in @ SV6 @ SV15 )
= $false )
| ( ( element @ SV6 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(151,plain,
! [SV16: $i,SV8: $i] :
( ( ( in @ SV8 @ SV16 )
= $false )
| ( ( ~ ( in @ SV16 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(152,plain,
! [SV9: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV9 ) )
| ~ ( relation @ ( relation_rng @ SV9 ) ) )
= $false )
| ( ( empty @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(153,plain,
( ( ~ ( relation @ sK4_SX0 )
| ~ ( function @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(154,plain,
! [SV17: $i,SV10: $i] :
( ( ~ ( in @ SV10 @ SV17 )
| ~ ( empty @ SV17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(155,plain,
( ( ~ ~ ( empty @ sK5_SX0 )
| ~ ( relation @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(156,plain,
! [SV11: $i] :
( ( ( ~ ( in @ SV11 @ sK1_A ) )
= $true )
| ( ( ( relation_inverse_image @ sK2_SY25 @ ( singleton @ SV11 ) )
!= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(157,plain,
( ( ~ ( empty @ sK6_SX0 )
| ~ ( relation @ sK6_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(158,plain,
! [SV18: $i,SV12: $i] :
( ( ~ ( ~ ( subset @ SV12 @ SV18 )
| ! [SY36: $i] :
( ~ ( in @ SY36 @ SV12 )
| ( in @ SY36 @ SV18 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(159,plain,
! [SV18: $i,SV12: $i] :
( ( ~ ( ~ ! [SY37: $i] :
( ~ ( in @ SY37 @ SV12 )
| ( in @ SY37 @ SV18 ) )
| ( subset @ SV12 @ SV18 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(160,plain,
! [SV3: $i] :
( ( ( ~ ~ ( empty @ SV3 ) )
= $true )
| ( ( ~ ( relation @ SV3 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(161,plain,
! [SV14: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ SV4 @ ( relation_rng @ SV14 ) )
| ( ( relation_inverse_image @ SV14 @ ( singleton @ SV4 ) )
!= empty_set ) )
| ~ ( ~ ( ( ( relation_inverse_image @ SV14 @ ( singleton @ SV4 ) )
!= empty_set ) )
| ( in @ SV4 @ ( relation_rng @ SV14 ) ) ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(162,plain,
( ( ~ ( relation @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(163,plain,
( ( ~ ( relation_empty_yielding @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(164,plain,
! [SV8: $i,SV16: $i] :
( ( ( in @ SV16 @ SV8 )
= $false )
| ( ( in @ SV8 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(165,plain,
! [SV9: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV9 ) ) )
= $false )
| ( ( empty @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(166,plain,
! [SV9: $i] :
( ( ( ~ ( relation @ ( relation_rng @ SV9 ) ) )
= $false )
| ( ( empty @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(167,plain,
( ( ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(168,plain,
( ( ~ ( function @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(169,plain,
! [SV17: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV17 ) )
= $true )
| ( ( ~ ( empty @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(170,plain,
( ( ~ ~ ( empty @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(171,plain,
( ( ~ ( relation @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(172,plain,
! [SV11: $i] :
( ( ( in @ SV11 @ sK1_A )
= $false )
| ( ( ( relation_inverse_image @ sK2_SY25 @ ( singleton @ SV11 ) )
!= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(173,plain,
( ( ~ ( empty @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(174,plain,
( ( ~ ( relation @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(175,plain,
! [SV18: $i,SV12: $i] :
( ( ~ ( subset @ SV12 @ SV18 )
| ! [SY36: $i] :
( ~ ( in @ SY36 @ SV12 )
| ( in @ SY36 @ SV18 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(176,plain,
! [SV18: $i,SV12: $i] :
( ( ~ ! [SY37: $i] :
( ~ ( in @ SY37 @ SV12 )
| ( in @ SY37 @ SV18 ) )
| ( subset @ SV12 @ SV18 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(177,plain,
! [SV3: $i] :
( ( ( ~ ( empty @ SV3 ) )
= $false )
| ( ( ~ ( relation @ SV3 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(178,plain,
! [SV14: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ SV4 @ ( relation_rng @ SV14 ) )
| ( ( relation_inverse_image @ SV14 @ ( singleton @ SV4 ) )
!= empty_set ) ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(179,plain,
! [SV4: $i,SV14: $i] :
( ( ( ~ ( ~ ( ( ( relation_inverse_image @ SV14 @ ( singleton @ SV4 ) )
!= empty_set ) )
| ( in @ SV4 @ ( relation_rng @ SV14 ) ) ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(180,plain,
( ( relation @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(181,plain,
( ( relation_empty_yielding @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(182,plain,
! [SV9: $i] :
( ( ( empty @ ( relation_rng @ SV9 ) )
= $true )
| ( ( empty @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(183,plain,
! [SV9: $i] :
( ( ( relation @ ( relation_rng @ SV9 ) )
= $true )
| ( ( empty @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(184,plain,
( ( relation @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(185,plain,
( ( function @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(186,plain,
! [SV17: $i,SV10: $i] :
( ( ( in @ SV10 @ SV17 )
= $false )
| ( ( ~ ( empty @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(187,plain,
( ( ~ ( empty @ sK5_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(188,plain,
( ( relation @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(189,plain,
! [SV11: $i] :
( ( ( ( relation_inverse_image @ sK2_SY25 @ ( singleton @ SV11 ) )
= empty_set )
= $false )
| ( ( in @ SV11 @ sK1_A )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(190,plain,
( ( empty @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(191,plain,
( ( relation @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(192,plain,
! [SV18: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV18 ) )
= $true )
| ( ( ! [SY36: $i] :
( ~ ( in @ SY36 @ SV12 )
| ( in @ SY36 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(193,plain,
! [SV18: $i,SV12: $i] :
( ( ( ~ ! [SY37: $i] :
( ~ ( in @ SY37 @ SV12 )
| ( in @ SY37 @ SV18 ) ) )
= $true )
| ( ( subset @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(194,plain,
! [SV3: $i] :
( ( ( empty @ SV3 )
= $true )
| ( ( ~ ( relation @ SV3 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(195,plain,
! [SV14: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ ( relation_rng @ SV14 ) )
| ( ( relation_inverse_image @ SV14 @ ( singleton @ SV4 ) )
!= empty_set ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(196,plain,
! [SV4: $i,SV14: $i] :
( ( ( ~ ( ( ( relation_inverse_image @ SV14 @ ( singleton @ SV4 ) )
!= empty_set ) )
| ( in @ SV4 @ ( relation_rng @ SV14 ) ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(197,plain,
! [SV10: $i,SV17: $i] :
( ( ( empty @ SV17 )
= $false )
| ( ( in @ SV10 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(198,plain,
( ( empty @ sK5_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(199,plain,
! [SV18: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV18 )
= $false )
| ( ( ! [SY36: $i] :
( ~ ( in @ SY36 @ SV12 )
| ( in @ SY36 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(200,plain,
! [SV18: $i,SV12: $i] :
( ( ( ! [SY37: $i] :
( ~ ( in @ SY37 @ SV12 )
| ( in @ SY37 @ SV18 ) ) )
= $false )
| ( ( subset @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(201,plain,
! [SV3: $i] :
( ( ( relation @ SV3 )
= $false )
| ( ( empty @ SV3 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(202,plain,
! [SV14: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ ( relation_rng @ SV14 ) ) )
= $true )
| ( ( ( relation_inverse_image @ SV14 @ ( singleton @ SV4 ) )
!= empty_set )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(203,plain,
! [SV4: $i,SV14: $i] :
( ( ( ~ ( ( ( relation_inverse_image @ SV14 @ ( singleton @ SV4 ) )
!= empty_set ) ) )
= $true )
| ( ( in @ SV4 @ ( relation_rng @ SV14 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(204,plain,
! [SV18: $i,SV12: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ SV12 )
| ( in @ SV19 @ SV18 ) )
= $true )
| ( ( subset @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(205,plain,
! [SV12: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK7_SY37 @ SV18 @ SV12 ) @ SV12 )
| ( in @ ( sK7_SY37 @ SV18 @ SV12 ) @ SV18 ) )
= $false )
| ( ( subset @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[200]) ).
thf(206,plain,
! [SV3: $i] :
( ( ( empty @ ( relation_rng @ SV3 ) )
= $false )
| ( ( empty @ SV3 )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(207,plain,
! [SV14: $i,SV4: $i] :
( ( ( in @ SV4 @ ( relation_rng @ SV14 ) )
= $false )
| ( ( ( relation_inverse_image @ SV14 @ ( singleton @ SV4 ) )
!= empty_set )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(208,plain,
! [SV4: $i,SV14: $i] :
( ( ( ( relation_inverse_image @ SV14 @ ( singleton @ SV4 ) )
!= empty_set )
= $false )
| ( ( in @ SV4 @ ( relation_rng @ SV14 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(209,plain,
! [SV18: $i,SV12: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ SV12 ) )
= $true )
| ( ( in @ SV19 @ SV18 )
= $true )
| ( ( subset @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(210,plain,
! [SV12: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK7_SY37 @ SV18 @ SV12 ) @ SV12 ) )
= $false )
| ( ( subset @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(211,plain,
! [SV12: $i,SV18: $i] :
( ( ( in @ ( sK7_SY37 @ SV18 @ SV12 ) @ SV18 )
= $false )
| ( ( subset @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(212,plain,
! [SV4: $i,SV14: $i] :
( ( ( ( relation_inverse_image @ SV14 @ ( singleton @ SV4 ) )
= empty_set )
= $false )
| ( ( in @ SV4 @ ( relation_rng @ SV14 ) )
= $false )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(213,plain,
! [SV4: $i,SV14: $i] :
( ( ( ( relation_inverse_image @ SV14 @ ( singleton @ SV4 ) )
= empty_set )
= $true )
| ( ( in @ SV4 @ ( relation_rng @ SV14 ) )
= $true )
| ( ( relation @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(214,plain,
! [SV18: $i,SV12: $i,SV19: $i] :
( ( ( in @ SV19 @ SV12 )
= $false )
| ( ( in @ SV19 @ SV18 )
= $true )
| ( ( subset @ SV12 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(215,plain,
! [SV12: $i,SV18: $i] :
( ( ( in @ ( sK7_SY37 @ SV18 @ SV12 ) @ SV12 )
= $true )
| ( ( subset @ SV12 @ SV18 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(216,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[63,215,214,213,212,211,206,198,197,191,190,189,188,185,184,183,182,181,180,164,150,138,136,134,133,114,113,97,78]) ).
thf(217,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[216]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU062+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
% 0.09/0.18 % Computer : n004.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 14:59:09 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.29
% 0.09/0.29 No.of.Axioms: 17
% 0.09/0.29
% 0.09/0.29 Length.of.Defs: 0
% 0.09/0.29
% 0.09/0.29 Contains.Choice.Funs: false
% 0.09/0.29 ....
% 0.09/0.29
% 0.09/0.29 ********************************
% 0.09/0.29 * All subproblems solved! *
% 0.09/0.29 ********************************
% 0.09/0.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:19,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:216,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.29
% 0.09/0.29 %**** Beginning of derivation protocol ****
% 0.09/0.29 % SZS output start CNFRefutation
% See solution above
% 0.09/0.29
% 0.09/0.29 %**** End of derivation protocol ****
% 0.09/0.29 %**** no. of clauses in derivation: 201 ****
% 0.09/0.29 %**** clause counter: 216 ****
% 0.09/0.29
% 0.09/0.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:19,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:216,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------