%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET991+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 10:42:42 AM UTC 2026
% Result : Theorem 0.10s 0.29s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 15
% Syntax : Number of formulae : 242 ( 106 unt; 0 typ; 0 def)
% Number of atoms : 2149 ( 807 equ; 0 cnn)
% Maximal formula atoms : 6 ( 8 avg)
% Number of connectives : 3807 (1078 ~; 680 |; 38 &;1968 @)
% ( 6 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 9 con; 0-3 aty)
% Number of variables : 496 ( 0 ^; 481 !; 15 ?; 496 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apply,type,
apply: $i > $i > $i ).
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_powerset,type,
powerset: $i > $i ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_sK10_SY42,type,
sK10_SY42: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY22,type,
sK2_SY22: $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_SY36,type,
sK7_SY36: $i > $i > $i ).
thf(tp_sK8_SY39,type,
sK8_SY39: $i > $i > $i > $i ).
thf(tp_sK9_SY42,type,
sK9_SY42: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(1,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(6,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(7,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(8,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(11,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(19,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(20,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(21,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(22,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(23,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(25,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(31,conjecture,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( in @ A @ ( relation_dom @ B ) )
=> ( in @ ( apply @ B @ A ) @ ( relation_rng @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_funct_1) ).
thf(32,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( in @ A @ ( relation_dom @ B ) )
=> ( in @ ( apply @ B @ A ) @ ( relation_rng @ B ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[31]) ).
thf(33,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( in @ A @ ( relation_dom @ B ) )
=> ( in @ ( apply @ B @ A ) @ ( relation_rng @ B ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[32]) ).
thf(34,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(35,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(36,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(37,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(38,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(39,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(40,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(42,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(43,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(44,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(45,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(46,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(47,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(48,plain,
( ( ! [SY22: $i] :
( ( ( relation @ SY22 )
& ( function @ SY22 ) )
=> ( ( in @ sK1_A @ ( relation_dom @ SY22 ) )
=> ( in @ ( apply @ SY22 @ sK1_A ) @ ( relation_rng @ SY22 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[33]) ).
thf(49,plain,
( ( ( ( relation @ sK2_SY22 )
& ( function @ sK2_SY22 ) )
=> ( ( in @ sK1_A @ ( relation_dom @ sK2_SY22 ) )
=> ( in @ ( apply @ sK2_SY22 @ sK1_A ) @ ( relation_rng @ sK2_SY22 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[48]) ).
thf(50,plain,
( ( relation @ sK2_SY22 )
= $true ),
inference(standard_cnf,[status(thm)],[49]) ).
thf(51,plain,
( ( function @ sK2_SY22 )
= $true ),
inference(standard_cnf,[status(thm)],[49]) ).
thf(52,plain,
( ( in @ sK1_A @ ( relation_dom @ sK2_SY22 ) )
= $true ),
inference(standard_cnf,[status(thm)],[49]) ).
thf(53,plain,
( ( in @ ( apply @ sK2_SY22 @ sK1_A ) @ ( relation_rng @ sK2_SY22 ) )
= $false ),
inference(standard_cnf,[status(thm)],[49]) ).
thf(54,plain,
( ( ~ ( in @ ( apply @ sK2_SY22 @ sK1_A ) @ ( relation_rng @ sK2_SY22 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[53]) ).
thf(55,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(56,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(57,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(58,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(59,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(60,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(61,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(62,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(63,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(64,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(65,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(66,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(68,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(69,plain,
( ( in @ sK1_A @ ( relation_dom @ sK2_SY22 ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(70,plain,
( ( function @ sK2_SY22 )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(71,plain,
( ( relation @ sK2_SY22 )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(72,plain,
( ( ~ ( in @ ( apply @ sK2_SY22 @ sK1_A ) @ ( relation_rng @ sK2_SY22 ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(73,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(74,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(75,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(76,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_dom @ SX0 ) )
| ~ ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(77,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(78,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_rng @ SX0 ) )
| ~ ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(79,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(80,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(81,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(82,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(83,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( relation_rng @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ ( relation_dom @ SX0 ) )
| ( SX2
!= ( apply @ SX0 @ SX3 ) ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ ( relation_dom @ SX0 ) )
| ( SX2
!= ( apply @ SX0 @ SX3 ) ) )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ ( relation_dom @ SX0 ) )
| ( SX2
!= ( apply @ SX0 @ SX3 ) ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ ( relation_dom @ SX0 ) )
| ( SX2
!= ( apply @ SX0 @ SX3 ) ) )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( relation_rng @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(84,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(85,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(86,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(87,plain,
( ( in @ ( apply @ sK2_SY22 @ sK1_A ) @ ( relation_rng @ sK2_SY22 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(88,plain,
! [SV1: $i] :
( ( ! [SY23: $i] :
( ~ ( in @ SV1 @ SY23 )
| ( element @ SV1 @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(89,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(90,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(91,plain,
! [SV2: $i] :
( ( ~ ( empty @ SV2 )
| ~ ( ~ ( empty @ ( relation_dom @ SV2 ) )
| ~ ( relation @ ( relation_dom @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(92,plain,
! [SV3: $i] :
( ( ! [SY24: $i] :
( ~ ( in @ SV3 @ SY24 )
| ~ ( in @ SY24 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(93,plain,
! [SV4: $i] :
( ( ~ ( empty @ SV4 )
| ~ ( ~ ( empty @ ( relation_rng @ SV4 ) )
| ~ ( relation @ ( relation_rng @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(94,plain,
! [SV5: $i] :
( ( ~ ( empty @ SV5 )
| ( relation @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(95,plain,
! [SV6: $i] :
( ( ~ ( empty @ SV6 )
| ( function @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(96,plain,
! [SV7: $i] :
( ( ! [SY25: $i] :
~ ~ ( ~ ( in @ SV7 @ SY25 )
| ~ ( empty @ SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(97,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(98,plain,
! [SV8: $i] :
( ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) )
| ! [SY26: $i] :
~ ( ~ ( ( SY26
!= ( relation_rng @ SV8 ) )
| ! [SY27: $i] :
~ ( ~ ( ~ ( in @ SY27 @ SY26 )
| ~ ! [SY28: $i] :
~ ~ ( ~ ( in @ SY28 @ ( relation_dom @ SV8 ) )
| ( SY27
!= ( apply @ SV8 @ SY28 ) ) ) )
| ~ ( ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( in @ SY29 @ ( relation_dom @ SV8 ) )
| ( SY27
!= ( apply @ SV8 @ SY29 ) ) )
| ( in @ SY27 @ SY26 ) ) ) )
| ~ ( ~ ! [SY30: $i] :
~ ( ~ ( ~ ( in @ SY30 @ SY26 )
| ~ ! [SY31: $i] :
~ ~ ( ~ ( in @ SY31 @ ( relation_dom @ SV8 ) )
| ( SY30
!= ( apply @ SV8 @ SY31 ) ) ) )
| ~ ( ~ ~ ! [SY32: $i] :
~ ~ ( ~ ( in @ SY32 @ ( relation_dom @ SV8 ) )
| ( SY30
!= ( apply @ SV8 @ SY32 ) ) )
| ( in @ SY30 @ SY26 ) ) )
| ( SY26
= ( relation_rng @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(99,plain,
! [SV9: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV9 )
| ~ ( relation @ SV9 ) )
| ~ ( empty @ ( relation_rng @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(100,plain,
! [SV10: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV10 )
| ~ ( relation @ SV10 ) )
| ~ ( empty @ ( relation_dom @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(101,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(102,plain,
! [SV11: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV11 )
| ( element @ SV1 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(103,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[89]) ).
thf(104,plain,
( ( ~ ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( relation_empty_yielding @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[90]) ).
thf(105,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV2 ) )
| ~ ( relation @ ( relation_dom @ SV2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(106,plain,
! [SV12: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ SV12 )
| ~ ( in @ SV12 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(107,plain,
! [SV4: $i] :
( ( ( ~ ( empty @ SV4 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV4 ) )
| ~ ( relation @ ( relation_rng @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(108,plain,
! [SV5: $i] :
( ( ( ~ ( empty @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(109,plain,
! [SV6: $i] :
( ( ( ~ ( empty @ SV6 ) )
= $true )
| ( ( function @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(110,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ~ ( ~ ( in @ SV7 @ SV13 )
| ~ ( empty @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(111,plain,
( ( ~ ~ ( ~ ( empty @ sK5_SX0 )
| ~ ( relation @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[97]) ).
thf(112,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) ) )
= $true )
| ( ( ! [SY26: $i] :
~ ( ~ ( ( SY26
!= ( relation_rng @ SV8 ) )
| ! [SY27: $i] :
~ ( ~ ( ~ ( in @ SY27 @ SY26 )
| ~ ! [SY28: $i] :
~ ~ ( ~ ( in @ SY28 @ ( relation_dom @ SV8 ) )
| ( SY27
!= ( apply @ SV8 @ SY28 ) ) ) )
| ~ ( ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( in @ SY29 @ ( relation_dom @ SV8 ) )
| ( SY27
!= ( apply @ SV8 @ SY29 ) ) )
| ( in @ SY27 @ SY26 ) ) ) )
| ~ ( ~ ! [SY30: $i] :
~ ( ~ ( ~ ( in @ SY30 @ SY26 )
| ~ ! [SY31: $i] :
~ ~ ( ~ ( in @ SY31 @ ( relation_dom @ SV8 ) )
| ( SY30
!= ( apply @ SV8 @ SY31 ) ) ) )
| ~ ( ~ ~ ! [SY32: $i] :
~ ~ ( ~ ( in @ SY32 @ ( relation_dom @ SV8 ) )
| ( SY30
!= ( apply @ SV8 @ SY32 ) ) )
| ( in @ SY30 @ SY26 ) ) )
| ( SY26
= ( relation_rng @ SV8 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(113,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV9 )
| ~ ( relation @ SV9 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(114,plain,
! [SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV10 )
| ~ ( relation @ SV10 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(115,plain,
( ( ~ ~ ( ~ ( relation @ sK6_SX0 )
| ~ ( function @ sK6_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[101]) ).
thf(116,plain,
! [SV11: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV11 ) )
= $true )
| ( ( element @ SV1 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(117,plain,
( ( ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(118,plain,
( ( ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( relation_empty_yielding @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(119,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV2 ) )
| ~ ( relation @ ( relation_dom @ SV2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(120,plain,
! [SV12: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV12 ) )
= $true )
| ( ( ~ ( in @ SV12 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(121,plain,
! [SV4: $i] :
( ( ( empty @ SV4 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV4 ) )
| ~ ( relation @ ( relation_rng @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(122,plain,
! [SV5: $i] :
( ( ( empty @ SV5 )
= $false )
| ( ( relation @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(123,plain,
! [SV6: $i] :
( ( ( empty @ SV6 )
= $false )
| ( ( function @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(124,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( ~ ( in @ SV7 @ SV13 )
| ~ ( empty @ SV13 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(125,plain,
( ( ~ ( ~ ( empty @ sK5_SX0 )
| ~ ( relation @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[111]) ).
thf(126,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) ) )
= $false )
| ( ( ! [SY26: $i] :
~ ( ~ ( ( SY26
!= ( relation_rng @ SV8 ) )
| ! [SY27: $i] :
~ ( ~ ( ~ ( in @ SY27 @ SY26 )
| ~ ! [SY28: $i] :
~ ~ ( ~ ( in @ SY28 @ ( relation_dom @ SV8 ) )
| ( SY27
!= ( apply @ SV8 @ SY28 ) ) ) )
| ~ ( ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( in @ SY29 @ ( relation_dom @ SV8 ) )
| ( SY27
!= ( apply @ SV8 @ SY29 ) ) )
| ( in @ SY27 @ SY26 ) ) ) )
| ~ ( ~ ! [SY30: $i] :
~ ( ~ ( ~ ( in @ SY30 @ SY26 )
| ~ ! [SY31: $i] :
~ ~ ( ~ ( in @ SY31 @ ( relation_dom @ SV8 ) )
| ( SY30
!= ( apply @ SV8 @ SY31 ) ) ) )
| ~ ( ~ ~ ! [SY32: $i] :
~ ~ ( ~ ( in @ SY32 @ ( relation_dom @ SV8 ) )
| ( SY30
!= ( apply @ SV8 @ SY32 ) ) )
| ( in @ SY30 @ SY26 ) ) )
| ( SY26
= ( relation_rng @ SV8 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(127,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV9 )
| ~ ( relation @ SV9 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_rng @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(128,plain,
! [SV10: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV10 )
| ~ ( relation @ SV10 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_dom @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(129,plain,
( ( ~ ( ~ ( relation @ sK6_SX0 )
| ~ ( function @ sK6_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(130,plain,
! [SV11: $i,SV1: $i] :
( ( ( in @ SV1 @ SV11 )
= $false )
| ( ( element @ SV1 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(131,plain,
( ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(132,plain,
( ( ~ ( relation @ sK4_SX0 )
| ~ ( relation_empty_yielding @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(133,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV2 ) )
| ~ ( relation @ ( relation_dom @ SV2 ) ) )
= $false )
| ( ( empty @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(134,plain,
! [SV12: $i,SV3: $i] :
( ( ( in @ SV3 @ SV12 )
= $false )
| ( ( ~ ( in @ SV12 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(135,plain,
! [SV4: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV4 ) )
| ~ ( relation @ ( relation_rng @ SV4 ) ) )
= $false )
| ( ( empty @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(136,plain,
! [SV13: $i,SV7: $i] :
( ( ~ ( in @ SV7 @ SV13 )
| ~ ( empty @ SV13 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(137,plain,
( ( ~ ( empty @ sK5_SX0 )
| ~ ( relation @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(138,plain,
! [SV8: $i] :
( ( ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) )
= $true )
| ( ( ! [SY26: $i] :
~ ( ~ ( ( SY26
!= ( relation_rng @ SV8 ) )
| ! [SY27: $i] :
~ ( ~ ( ~ ( in @ SY27 @ SY26 )
| ~ ! [SY28: $i] :
~ ~ ( ~ ( in @ SY28 @ ( relation_dom @ SV8 ) )
| ( SY27
!= ( apply @ SV8 @ SY28 ) ) ) )
| ~ ( ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( in @ SY29 @ ( relation_dom @ SV8 ) )
| ( SY27
!= ( apply @ SV8 @ SY29 ) ) )
| ( in @ SY27 @ SY26 ) ) ) )
| ~ ( ~ ! [SY30: $i] :
~ ( ~ ( ~ ( in @ SY30 @ SY26 )
| ~ ! [SY31: $i] :
~ ~ ( ~ ( in @ SY31 @ ( relation_dom @ SV8 ) )
| ( SY30
!= ( apply @ SV8 @ SY31 ) ) ) )
| ~ ( ~ ~ ! [SY32: $i] :
~ ~ ( ~ ( in @ SY32 @ ( relation_dom @ SV8 ) )
| ( SY30
!= ( apply @ SV8 @ SY32 ) ) )
| ( in @ SY30 @ SY26 ) ) )
| ( SY26
= ( relation_rng @ SV8 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(139,plain,
! [SV9: $i] :
( ( ( ~ ~ ( empty @ SV9 )
| ~ ( relation @ SV9 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(140,plain,
! [SV10: $i] :
( ( ( ~ ~ ( empty @ SV10 )
| ~ ( relation @ SV10 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(141,plain,
( ( ~ ( relation @ sK6_SX0 )
| ~ ( function @ sK6_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(142,plain,
( ( ~ ~ ( empty @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(143,plain,
( ( ~ ( relation @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(144,plain,
( ( ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(145,plain,
( ( ~ ( relation_empty_yielding @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(146,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV2 ) ) )
= $false )
| ( ( empty @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(147,plain,
! [SV2: $i] :
( ( ( ~ ( relation @ ( relation_dom @ SV2 ) ) )
= $false )
| ( ( empty @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(148,plain,
! [SV3: $i,SV12: $i] :
( ( ( in @ SV12 @ SV3 )
= $false )
| ( ( in @ SV3 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(149,plain,
! [SV4: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV4 ) ) )
= $false )
| ( ( empty @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(150,plain,
! [SV4: $i] :
( ( ( ~ ( relation @ ( relation_rng @ SV4 ) ) )
= $false )
| ( ( empty @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(151,plain,
! [SV13: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV13 ) )
= $true )
| ( ( ~ ( empty @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(152,plain,
( ( ~ ( empty @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(153,plain,
( ( ~ ( relation @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(154,plain,
! [SV8: $i] :
( ( ( ~ ( relation @ SV8 ) )
= $true )
| ( ( ~ ( function @ SV8 ) )
= $true )
| ( ( ! [SY26: $i] :
~ ( ~ ( ( SY26
!= ( relation_rng @ SV8 ) )
| ! [SY27: $i] :
~ ( ~ ( ~ ( in @ SY27 @ SY26 )
| ~ ! [SY28: $i] :
~ ~ ( ~ ( in @ SY28 @ ( relation_dom @ SV8 ) )
| ( SY27
!= ( apply @ SV8 @ SY28 ) ) ) )
| ~ ( ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( in @ SY29 @ ( relation_dom @ SV8 ) )
| ( SY27
!= ( apply @ SV8 @ SY29 ) ) )
| ( in @ SY27 @ SY26 ) ) ) )
| ~ ( ~ ! [SY30: $i] :
~ ( ~ ( ~ ( in @ SY30 @ SY26 )
| ~ ! [SY31: $i] :
~ ~ ( ~ ( in @ SY31 @ ( relation_dom @ SV8 ) )
| ( SY30
!= ( apply @ SV8 @ SY31 ) ) ) )
| ~ ( ~ ~ ! [SY32: $i] :
~ ~ ( ~ ( in @ SY32 @ ( relation_dom @ SV8 ) )
| ( SY30
!= ( apply @ SV8 @ SY32 ) ) )
| ( in @ SY30 @ SY26 ) ) )
| ( SY26
= ( relation_rng @ SV8 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(155,plain,
! [SV9: $i] :
( ( ( ~ ~ ( empty @ SV9 ) )
= $true )
| ( ( ~ ( relation @ SV9 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(156,plain,
! [SV10: $i] :
( ( ( ~ ~ ( empty @ SV10 ) )
= $true )
| ( ( ~ ( relation @ SV10 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(157,plain,
( ( ~ ( relation @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(158,plain,
( ( ~ ( function @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(159,plain,
( ( ~ ( empty @ sK3_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(160,plain,
( ( relation @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(161,plain,
( ( relation @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(162,plain,
( ( relation_empty_yielding @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(163,plain,
! [SV2: $i] :
( ( ( empty @ ( relation_dom @ SV2 ) )
= $true )
| ( ( empty @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(164,plain,
! [SV2: $i] :
( ( ( relation @ ( relation_dom @ SV2 ) )
= $true )
| ( ( empty @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(165,plain,
! [SV4: $i] :
( ( ( empty @ ( relation_rng @ SV4 ) )
= $true )
| ( ( empty @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(166,plain,
! [SV4: $i] :
( ( ( relation @ ( relation_rng @ SV4 ) )
= $true )
| ( ( empty @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(167,plain,
! [SV13: $i,SV7: $i] :
( ( ( in @ SV7 @ SV13 )
= $false )
| ( ( ~ ( empty @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(168,plain,
( ( empty @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(169,plain,
( ( relation @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(170,plain,
! [SV8: $i] :
( ( ( relation @ SV8 )
= $false )
| ( ( ~ ( function @ SV8 ) )
= $true )
| ( ( ! [SY26: $i] :
~ ( ~ ( ( SY26
!= ( relation_rng @ SV8 ) )
| ! [SY27: $i] :
~ ( ~ ( ~ ( in @ SY27 @ SY26 )
| ~ ! [SY28: $i] :
~ ~ ( ~ ( in @ SY28 @ ( relation_dom @ SV8 ) )
| ( SY27
!= ( apply @ SV8 @ SY28 ) ) ) )
| ~ ( ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( in @ SY29 @ ( relation_dom @ SV8 ) )
| ( SY27
!= ( apply @ SV8 @ SY29 ) ) )
| ( in @ SY27 @ SY26 ) ) ) )
| ~ ( ~ ! [SY30: $i] :
~ ( ~ ( ~ ( in @ SY30 @ SY26 )
| ~ ! [SY31: $i] :
~ ~ ( ~ ( in @ SY31 @ ( relation_dom @ SV8 ) )
| ( SY30
!= ( apply @ SV8 @ SY31 ) ) ) )
| ~ ( ~ ~ ! [SY32: $i] :
~ ~ ( ~ ( in @ SY32 @ ( relation_dom @ SV8 ) )
| ( SY30
!= ( apply @ SV8 @ SY32 ) ) )
| ( in @ SY30 @ SY26 ) ) )
| ( SY26
= ( relation_rng @ SV8 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(171,plain,
! [SV9: $i] :
( ( ( ~ ( empty @ SV9 ) )
= $false )
| ( ( ~ ( relation @ SV9 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(172,plain,
! [SV10: $i] :
( ( ( ~ ( empty @ SV10 ) )
= $false )
| ( ( ~ ( relation @ SV10 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(173,plain,
( ( relation @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(174,plain,
( ( function @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(175,plain,
( ( empty @ sK3_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(176,plain,
! [SV7: $i,SV13: $i] :
( ( ( empty @ SV13 )
= $false )
| ( ( in @ SV7 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(177,plain,
! [SV8: $i] :
( ( ( function @ SV8 )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( ! [SY26: $i] :
~ ( ~ ( ( SY26
!= ( relation_rng @ SV8 ) )
| ! [SY27: $i] :
~ ( ~ ( ~ ( in @ SY27 @ SY26 )
| ~ ! [SY28: $i] :
~ ~ ( ~ ( in @ SY28 @ ( relation_dom @ SV8 ) )
| ( SY27
!= ( apply @ SV8 @ SY28 ) ) ) )
| ~ ( ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( in @ SY29 @ ( relation_dom @ SV8 ) )
| ( SY27
!= ( apply @ SV8 @ SY29 ) ) )
| ( in @ SY27 @ SY26 ) ) ) )
| ~ ( ~ ! [SY30: $i] :
~ ( ~ ( ~ ( in @ SY30 @ SY26 )
| ~ ! [SY31: $i] :
~ ~ ( ~ ( in @ SY31 @ ( relation_dom @ SV8 ) )
| ( SY30
!= ( apply @ SV8 @ SY31 ) ) ) )
| ~ ( ~ ~ ! [SY32: $i] :
~ ~ ( ~ ( in @ SY32 @ ( relation_dom @ SV8 ) )
| ( SY30
!= ( apply @ SV8 @ SY32 ) ) )
| ( in @ SY30 @ SY26 ) ) )
| ( SY26
= ( relation_rng @ SV8 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(178,plain,
! [SV9: $i] :
( ( ( empty @ SV9 )
= $true )
| ( ( ~ ( relation @ SV9 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(179,plain,
! [SV10: $i] :
( ( ( empty @ SV10 )
= $true )
| ( ( ~ ( relation @ SV10 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(180,plain,
! [SV8: $i,SV14: $i] :
( ( ( ~ ( ~ ( ( SV14
!= ( relation_rng @ SV8 ) )
| ! [SY33: $i] :
~ ( ~ ( ~ ( in @ SY33 @ SV14 )
| ~ ! [SY28: $i] :
~ ~ ( ~ ( in @ SY28 @ ( relation_dom @ SV8 ) )
| ( SY33
!= ( apply @ SV8 @ SY28 ) ) ) )
| ~ ( ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( in @ SY29 @ ( relation_dom @ SV8 ) )
| ( SY33
!= ( apply @ SV8 @ SY29 ) ) )
| ( in @ SY33 @ SV14 ) ) ) )
| ~ ( ~ ! [SY36: $i] :
~ ( ~ ( ~ ( in @ SY36 @ SV14 )
| ~ ! [SY31: $i] :
~ ~ ( ~ ( in @ SY31 @ ( relation_dom @ SV8 ) )
| ( SY36
!= ( apply @ SV8 @ SY31 ) ) ) )
| ~ ( ~ ~ ! [SY32: $i] :
~ ~ ( ~ ( in @ SY32 @ ( relation_dom @ SV8 ) )
| ( SY36
!= ( apply @ SV8 @ SY32 ) ) )
| ( in @ SY36 @ SV14 ) ) )
| ( SV14
= ( relation_rng @ SV8 ) ) ) ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(181,plain,
! [SV9: $i] :
( ( ( relation @ SV9 )
= $false )
| ( ( empty @ SV9 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(182,plain,
! [SV10: $i] :
( ( ( relation @ SV10 )
= $false )
| ( ( empty @ SV10 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(183,plain,
! [SV8: $i,SV14: $i] :
( ( ( ~ ( ( SV14
!= ( relation_rng @ SV8 ) )
| ! [SY33: $i] :
~ ( ~ ( ~ ( in @ SY33 @ SV14 )
| ~ ! [SY28: $i] :
~ ~ ( ~ ( in @ SY28 @ ( relation_dom @ SV8 ) )
| ( SY33
!= ( apply @ SV8 @ SY28 ) ) ) )
| ~ ( ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( in @ SY29 @ ( relation_dom @ SV8 ) )
| ( SY33
!= ( apply @ SV8 @ SY29 ) ) )
| ( in @ SY33 @ SV14 ) ) ) )
| ~ ( ~ ! [SY36: $i] :
~ ( ~ ( ~ ( in @ SY36 @ SV14 )
| ~ ! [SY31: $i] :
~ ~ ( ~ ( in @ SY31 @ ( relation_dom @ SV8 ) )
| ( SY36
!= ( apply @ SV8 @ SY31 ) ) ) )
| ~ ( ~ ~ ! [SY32: $i] :
~ ~ ( ~ ( in @ SY32 @ ( relation_dom @ SV8 ) )
| ( SY36
!= ( apply @ SV8 @ SY32 ) ) )
| ( in @ SY36 @ SV14 ) ) )
| ( SV14
= ( relation_rng @ SV8 ) ) ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(184,plain,
! [SV9: $i] :
( ( ( empty @ ( relation_rng @ SV9 ) )
= $false )
| ( ( empty @ SV9 )
= $true )
| ( ( relation @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(185,plain,
! [SV10: $i] :
( ( ( empty @ ( relation_dom @ SV10 ) )
= $false )
| ( ( empty @ SV10 )
= $true )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(186,plain,
! [SV8: $i,SV14: $i] :
( ( ( ~ ( ( SV14
!= ( relation_rng @ SV8 ) )
| ! [SY33: $i] :
~ ( ~ ( ~ ( in @ SY33 @ SV14 )
| ~ ! [SY28: $i] :
~ ~ ( ~ ( in @ SY28 @ ( relation_dom @ SV8 ) )
| ( SY33
!= ( apply @ SV8 @ SY28 ) ) ) )
| ~ ( ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( in @ SY29 @ ( relation_dom @ SV8 ) )
| ( SY33
!= ( apply @ SV8 @ SY29 ) ) )
| ( in @ SY33 @ SV14 ) ) ) ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(187,plain,
! [SV8: $i,SV14: $i] :
( ( ( ~ ( ~ ! [SY36: $i] :
~ ( ~ ( ~ ( in @ SY36 @ SV14 )
| ~ ! [SY31: $i] :
~ ~ ( ~ ( in @ SY31 @ ( relation_dom @ SV8 ) )
| ( SY36
!= ( apply @ SV8 @ SY31 ) ) ) )
| ~ ( ~ ~ ! [SY32: $i] :
~ ~ ( ~ ( in @ SY32 @ ( relation_dom @ SV8 ) )
| ( SY36
!= ( apply @ SV8 @ SY32 ) ) )
| ( in @ SY36 @ SV14 ) ) )
| ( SV14
= ( relation_rng @ SV8 ) ) ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(188,plain,
! [SV8: $i,SV14: $i] :
( ( ( ( SV14
!= ( relation_rng @ SV8 ) )
| ! [SY33: $i] :
~ ( ~ ( ~ ( in @ SY33 @ SV14 )
| ~ ! [SY28: $i] :
~ ~ ( ~ ( in @ SY28 @ ( relation_dom @ SV8 ) )
| ( SY33
!= ( apply @ SV8 @ SY28 ) ) ) )
| ~ ( ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( in @ SY29 @ ( relation_dom @ SV8 ) )
| ( SY33
!= ( apply @ SV8 @ SY29 ) ) )
| ( in @ SY33 @ SV14 ) ) ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(189,plain,
! [SV8: $i,SV14: $i] :
( ( ( ~ ! [SY36: $i] :
~ ( ~ ( ~ ( in @ SY36 @ SV14 )
| ~ ! [SY31: $i] :
~ ~ ( ~ ( in @ SY31 @ ( relation_dom @ SV8 ) )
| ( SY36
!= ( apply @ SV8 @ SY31 ) ) ) )
| ~ ( ~ ~ ! [SY32: $i] :
~ ~ ( ~ ( in @ SY32 @ ( relation_dom @ SV8 ) )
| ( SY36
!= ( apply @ SV8 @ SY32 ) ) )
| ( in @ SY36 @ SV14 ) ) )
| ( SV14
= ( relation_rng @ SV8 ) ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(190,plain,
! [SV8: $i,SV14: $i] :
( ( ( SV14
!= ( relation_rng @ SV8 ) )
= $true )
| ( ( ! [SY33: $i] :
~ ( ~ ( ~ ( in @ SY33 @ SV14 )
| ~ ! [SY28: $i] :
~ ~ ( ~ ( in @ SY28 @ ( relation_dom @ SV8 ) )
| ( SY33
!= ( apply @ SV8 @ SY28 ) ) ) )
| ~ ( ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( in @ SY29 @ ( relation_dom @ SV8 ) )
| ( SY33
!= ( apply @ SV8 @ SY29 ) ) )
| ( in @ SY33 @ SV14 ) ) ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(191,plain,
! [SV8: $i,SV14: $i] :
( ( ( ~ ! [SY36: $i] :
~ ( ~ ( ~ ( in @ SY36 @ SV14 )
| ~ ! [SY31: $i] :
~ ~ ( ~ ( in @ SY31 @ ( relation_dom @ SV8 ) )
| ( SY36
!= ( apply @ SV8 @ SY31 ) ) ) )
| ~ ( ~ ~ ! [SY32: $i] :
~ ~ ( ~ ( in @ SY32 @ ( relation_dom @ SV8 ) )
| ( SY36
!= ( apply @ SV8 @ SY32 ) ) )
| ( in @ SY36 @ SV14 ) ) ) )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(192,plain,
! [SV8: $i,SV14: $i] :
( ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( ! [SY33: $i] :
~ ( ~ ( ~ ( in @ SY33 @ SV14 )
| ~ ! [SY28: $i] :
~ ~ ( ~ ( in @ SY28 @ ( relation_dom @ SV8 ) )
| ( SY33
!= ( apply @ SV8 @ SY28 ) ) ) )
| ~ ( ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( in @ SY29 @ ( relation_dom @ SV8 ) )
| ( SY33
!= ( apply @ SV8 @ SY29 ) ) )
| ( in @ SY33 @ SV14 ) ) ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(193,plain,
! [SV8: $i,SV14: $i] :
( ( ( ! [SY36: $i] :
~ ( ~ ( ~ ( in @ SY36 @ SV14 )
| ~ ! [SY31: $i] :
~ ~ ( ~ ( in @ SY31 @ ( relation_dom @ SV8 ) )
| ( SY36
!= ( apply @ SV8 @ SY31 ) ) ) )
| ~ ( ~ ~ ! [SY32: $i] :
~ ~ ( ~ ( in @ SY32 @ ( relation_dom @ SV8 ) )
| ( SY36
!= ( apply @ SV8 @ SY32 ) ) )
| ( in @ SY36 @ SV14 ) ) ) )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(194,plain,
! [SV8: $i,SV14: $i,SV15: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV15 @ SV14 )
| ~ ! [SY39: $i] :
~ ~ ( ~ ( in @ SY39 @ ( relation_dom @ SV8 ) )
| ( SV15
!= ( apply @ SV8 @ SY39 ) ) ) )
| ~ ( ~ ~ ! [SY40: $i] :
~ ~ ( ~ ( in @ SY40 @ ( relation_dom @ SV8 ) )
| ( SV15
!= ( apply @ SV8 @ SY40 ) ) )
| ( in @ SV15 @ SV14 ) ) ) )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(195,plain,
! [SV14: $i,SV8: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 )
| ~ ! [SY41: $i] :
~ ~ ( ~ ( in @ SY41 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY41 ) ) ) )
| ~ ( ~ ~ ! [SY42: $i] :
~ ~ ( ~ ( in @ SY42 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY42 ) ) )
| ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 ) ) ) )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[193]) ).
thf(196,plain,
! [SV8: $i,SV14: $i,SV15: $i] :
( ( ( ~ ( ~ ( in @ SV15 @ SV14 )
| ~ ! [SY39: $i] :
~ ~ ( ~ ( in @ SY39 @ ( relation_dom @ SV8 ) )
| ( SV15
!= ( apply @ SV8 @ SY39 ) ) ) )
| ~ ( ~ ~ ! [SY40: $i] :
~ ~ ( ~ ( in @ SY40 @ ( relation_dom @ SV8 ) )
| ( SV15
!= ( apply @ SV8 @ SY40 ) ) )
| ( in @ SV15 @ SV14 ) ) )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(197,plain,
! [SV14: $i,SV8: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 )
| ~ ! [SY41: $i] :
~ ~ ( ~ ( in @ SY41 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY41 ) ) ) )
| ~ ( ~ ~ ! [SY42: $i] :
~ ~ ( ~ ( in @ SY42 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY42 ) ) )
| ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(198,plain,
! [SV8: $i,SV14: $i,SV15: $i] :
( ( ( ~ ( ~ ( in @ SV15 @ SV14 )
| ~ ! [SY39: $i] :
~ ~ ( ~ ( in @ SY39 @ ( relation_dom @ SV8 ) )
| ( SV15
!= ( apply @ SV8 @ SY39 ) ) ) ) )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(199,plain,
! [SV14: $i,SV15: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ! [SY40: $i] :
~ ~ ( ~ ( in @ SY40 @ ( relation_dom @ SV8 ) )
| ( SV15
!= ( apply @ SV8 @ SY40 ) ) )
| ( in @ SV15 @ SV14 ) ) )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(200,plain,
! [SV14: $i,SV8: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 )
| ~ ! [SY41: $i] :
~ ~ ( ~ ( in @ SY41 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY41 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY42: $i] :
~ ~ ( ~ ( in @ SY42 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY42 ) ) )
| ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(201,plain,
! [SV8: $i,SV14: $i,SV15: $i] :
( ( ( ~ ( in @ SV15 @ SV14 )
| ~ ! [SY39: $i] :
~ ~ ( ~ ( in @ SY39 @ ( relation_dom @ SV8 ) )
| ( SV15
!= ( apply @ SV8 @ SY39 ) ) ) )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(202,plain,
! [SV14: $i,SV15: $i,SV8: $i] :
( ( ( ~ ~ ! [SY40: $i] :
~ ~ ( ~ ( in @ SY40 @ ( relation_dom @ SV8 ) )
| ( SV15
!= ( apply @ SV8 @ SY40 ) ) )
| ( in @ SV15 @ SV14 ) )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(203,plain,
! [SV14: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 )
| ~ ! [SY41: $i] :
~ ~ ( ~ ( in @ SY41 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY41 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY42: $i] :
~ ~ ( ~ ( in @ SY42 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY42 ) ) )
| ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(204,plain,
! [SV8: $i,SV14: $i,SV15: $i] :
( ( ( ~ ( in @ SV15 @ SV14 ) )
= $true )
| ( ( ~ ! [SY39: $i] :
~ ~ ( ~ ( in @ SY39 @ ( relation_dom @ SV8 ) )
| ( SV15
!= ( apply @ SV8 @ SY39 ) ) ) )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(205,plain,
! [SV14: $i,SV15: $i,SV8: $i] :
( ( ( ~ ~ ! [SY40: $i] :
~ ~ ( ~ ( in @ SY40 @ ( relation_dom @ SV8 ) )
| ( SV15
!= ( apply @ SV8 @ SY40 ) ) ) )
= $true )
| ( ( in @ SV15 @ SV14 )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(206,plain,
! [SV14: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY42: $i] :
~ ~ ( ~ ( in @ SY42 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY42 ) ) )
| ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(207,plain,
! [SV14: $i,SV8: $i] :
( ( ( ~ ! [SY41: $i] :
~ ~ ( ~ ( in @ SY41 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY41 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY42: $i] :
~ ~ ( ~ ( in @ SY42 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY42 ) ) )
| ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(208,plain,
! [SV8: $i,SV14: $i,SV15: $i] :
( ( ( in @ SV15 @ SV14 )
= $false )
| ( ( ~ ! [SY39: $i] :
~ ~ ( ~ ( in @ SY39 @ ( relation_dom @ SV8 ) )
| ( SV15
!= ( apply @ SV8 @ SY39 ) ) ) )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(209,plain,
! [SV14: $i,SV15: $i,SV8: $i] :
( ( ( ~ ! [SY40: $i] :
~ ~ ( ~ ( in @ SY40 @ ( relation_dom @ SV8 ) )
| ( SV15
!= ( apply @ SV8 @ SY40 ) ) ) )
= $false )
| ( ( in @ SV15 @ SV14 )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(210,plain,
! [SV14: $i,SV8: $i] :
( ( ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 )
= $true )
| ( ( ~ ( ~ ~ ! [SY42: $i] :
~ ~ ( ~ ( in @ SY42 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY42 ) ) )
| ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(211,plain,
! [SV14: $i,SV8: $i] :
( ( ( ! [SY41: $i] :
~ ~ ( ~ ( in @ SY41 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY41 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY42: $i] :
~ ~ ( ~ ( in @ SY42 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY42 ) ) )
| ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(212,plain,
! [SV14: $i,SV15: $i,SV8: $i] :
( ( ( ! [SY39: $i] :
~ ~ ( ~ ( in @ SY39 @ ( relation_dom @ SV8 ) )
| ( SV15
!= ( apply @ SV8 @ SY39 ) ) ) )
= $false )
| ( ( in @ SV15 @ SV14 )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(213,plain,
! [SV14: $i,SV15: $i,SV8: $i] :
( ( ( ! [SY40: $i] :
~ ~ ( ~ ( in @ SY40 @ ( relation_dom @ SV8 ) )
| ( SV15
!= ( apply @ SV8 @ SY40 ) ) ) )
= $true )
| ( ( in @ SV15 @ SV14 )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(214,plain,
! [SV14: $i,SV8: $i] :
( ( ( ~ ~ ! [SY42: $i] :
~ ~ ( ~ ( in @ SY42 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY42 ) ) )
| ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 ) )
= $false )
| ( ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(215,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( in @ SV16 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SV16 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY42: $i] :
~ ~ ( ~ ( in @ SY42 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY42 ) ) )
| ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(216,plain,
! [SV8: $i,SV15: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_SY39 @ SV14 @ SV15 @ SV8 ) @ ( relation_dom @ SV8 ) )
| ( SV15
!= ( apply @ SV8 @ ( sK8_SY39 @ SV14 @ SV15 @ SV8 ) ) ) ) )
= $false )
| ( ( in @ SV15 @ SV14 )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[212]) ).
thf(217,plain,
! [SV14: $i,SV15: $i,SV8: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( in @ SV17 @ ( relation_dom @ SV8 ) )
| ( SV15
!= ( apply @ SV8 @ SV17 ) ) ) )
= $true )
| ( ( in @ SV15 @ SV14 )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(218,plain,
! [SV14: $i,SV8: $i] :
( ( ( ~ ~ ! [SY42: $i] :
~ ~ ( ~ ( in @ SY42 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY42 ) ) ) )
= $false )
| ( ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(219,plain,
! [SV14: $i,SV8: $i] :
( ( ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 )
= $false )
| ( ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(220,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( ~ ( in @ SV16 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SV16 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY42: $i] :
~ ~ ( ~ ( in @ SY42 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY42 ) ) )
| ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(221,plain,
! [SV8: $i,SV15: $i,SV14: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY39 @ SV14 @ SV15 @ SV8 ) @ ( relation_dom @ SV8 ) )
| ( SV15
!= ( apply @ SV8 @ ( sK8_SY39 @ SV14 @ SV15 @ SV8 ) ) ) ) )
= $true )
| ( ( in @ SV15 @ SV14 )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(222,plain,
! [SV14: $i,SV15: $i,SV8: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ SV17 @ ( relation_dom @ SV8 ) )
| ( SV15
!= ( apply @ SV8 @ SV17 ) ) ) )
= $false )
| ( ( in @ SV15 @ SV14 )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(223,plain,
! [SV14: $i,SV8: $i] :
( ( ( ~ ! [SY42: $i] :
~ ~ ( ~ ( in @ SY42 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY42 ) ) ) )
= $true )
| ( ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(224,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SV16 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY42: $i] :
~ ~ ( ~ ( in @ SY42 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY42 ) ) )
| ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(225,plain,
! [SV8: $i,SV15: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK8_SY39 @ SV14 @ SV15 @ SV8 ) @ ( relation_dom @ SV8 ) )
| ( SV15
!= ( apply @ SV8 @ ( sK8_SY39 @ SV14 @ SV15 @ SV8 ) ) ) )
= $false )
| ( ( in @ SV15 @ SV14 )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(226,plain,
! [SV14: $i,SV15: $i,SV8: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ ( relation_dom @ SV8 ) )
| ( SV15
!= ( apply @ SV8 @ SV17 ) ) )
= $true )
| ( ( in @ SV15 @ SV14 )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(227,plain,
! [SV14: $i,SV8: $i] :
( ( ( ! [SY42: $i] :
~ ~ ( ~ ( in @ SY42 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY42 ) ) ) )
= $false )
| ( ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(228,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ ( relation_dom @ SV8 ) ) )
= $true )
| ( ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SV16 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY42: $i] :
~ ~ ( ~ ( in @ SY42 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY42 ) ) )
| ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(229,plain,
! [SV8: $i,SV15: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK8_SY39 @ SV14 @ SV15 @ SV8 ) @ ( relation_dom @ SV8 ) ) )
= $false )
| ( ( in @ SV15 @ SV14 )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(230,plain,
! [SV14: $i,SV8: $i,SV15: $i] :
( ( ( SV15
!= ( apply @ SV8 @ ( sK8_SY39 @ SV14 @ SV15 @ SV8 ) ) )
= $false )
| ( ( in @ SV15 @ SV14 )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(231,plain,
! [SV14: $i,SV15: $i,SV8: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ ( relation_dom @ SV8 ) ) )
= $true )
| ( ( SV15
!= ( apply @ SV8 @ SV17 ) )
= $true )
| ( ( in @ SV15 @ SV14 )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(232,plain,
! [SV8: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK9_SY42 @ SV14 @ SV8 ) @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ ( sK9_SY42 @ SV14 @ SV8 ) ) ) ) )
= $false )
| ( ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[227]) ).
thf(233,plain,
! [SV14: $i,SV8: $i,SV16: $i] :
( ( ( in @ SV16 @ ( relation_dom @ SV8 ) )
= $false )
| ( ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SV16 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY42: $i] :
~ ~ ( ~ ( in @ SY42 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY42 ) ) )
| ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(234,plain,
! [SV8: $i,SV15: $i,SV14: $i] :
( ( ( in @ ( sK8_SY39 @ SV14 @ SV15 @ SV8 ) @ ( relation_dom @ SV8 ) )
= $true )
| ( ( in @ SV15 @ SV14 )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(235,plain,
! [SV14: $i,SV8: $i,SV15: $i] :
( ( ( SV15
= ( apply @ SV8 @ ( sK8_SY39 @ SV14 @ SV15 @ SV8 ) ) )
= $true )
| ( ( in @ SV15 @ SV14 )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(236,plain,
! [SV14: $i,SV15: $i,SV8: $i,SV17: $i] :
( ( ( in @ SV17 @ ( relation_dom @ SV8 ) )
= $false )
| ( ( SV15
!= ( apply @ SV8 @ SV17 ) )
= $true )
| ( ( in @ SV15 @ SV14 )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(237,plain,
! [SV8: $i,SV14: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_SY42 @ SV14 @ SV8 ) @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ ( sK9_SY42 @ SV14 @ SV8 ) ) ) ) )
= $true )
| ( ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(238,plain,
! [SV16: $i,SV14: $i,SV8: $i] :
( ( ( ( sK7_SY36 @ SV8 @ SV14 )
= ( apply @ SV8 @ SV16 ) )
= $false )
| ( ( in @ SV16 @ ( relation_dom @ SV8 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY42: $i] :
~ ~ ( ~ ( in @ SY42 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY42 ) ) )
| ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 ) ) )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(239,plain,
! [SV14: $i,SV17: $i,SV8: $i,SV15: $i] :
( ( ( SV15
= ( apply @ SV8 @ SV17 ) )
= $false )
| ( ( in @ SV17 @ ( relation_dom @ SV8 ) )
= $false )
| ( ( in @ SV15 @ SV14 )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(240,plain,
! [SV8: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK9_SY42 @ SV14 @ SV8 ) @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ ( sK9_SY42 @ SV14 @ SV8 ) ) ) )
= $false )
| ( ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(241,plain,
! [SV16: $i,SV14: $i,SV8: $i] :
( ( ( ~ ~ ! [SY42: $i] :
~ ~ ( ~ ( in @ SY42 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY42 ) ) )
| ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 ) )
= $false )
| ( ( in @ SV16 @ ( relation_dom @ SV8 ) )
= $false )
| ( ( ( sK7_SY36 @ SV8 @ SV14 )
= ( apply @ SV8 @ SV16 ) )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(242,plain,
! [SV8: $i,SV14: $i] :
( ( ( ~ ( in @ ( sK9_SY42 @ SV14 @ SV8 ) @ ( relation_dom @ SV8 ) ) )
= $false )
| ( ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(243,plain,
! [SV14: $i,SV8: $i] :
( ( ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ ( sK9_SY42 @ SV14 @ SV8 ) ) )
= $false )
| ( ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(244,plain,
! [SV16: $i,SV14: $i,SV8: $i] :
( ( ( ~ ~ ! [SY42: $i] :
~ ~ ( ~ ( in @ SY42 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY42 ) ) ) )
= $false )
| ( ( in @ SV16 @ ( relation_dom @ SV8 ) )
= $false )
| ( ( ( sK7_SY36 @ SV8 @ SV14 )
= ( apply @ SV8 @ SV16 ) )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(245,plain,
! [SV16: $i,SV14: $i,SV8: $i] :
( ( ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 )
= $false )
| ( ( in @ SV16 @ ( relation_dom @ SV8 ) )
= $false )
| ( ( ( sK7_SY36 @ SV8 @ SV14 )
= ( apply @ SV8 @ SV16 ) )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(246,plain,
! [SV8: $i,SV14: $i] :
( ( ( in @ ( sK9_SY42 @ SV14 @ SV8 ) @ ( relation_dom @ SV8 ) )
= $true )
| ( ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(247,plain,
! [SV14: $i,SV8: $i] :
( ( ( ( sK7_SY36 @ SV8 @ SV14 )
= ( apply @ SV8 @ ( sK9_SY42 @ SV14 @ SV8 ) ) )
= $true )
| ( ( in @ ( sK7_SY36 @ SV8 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(248,plain,
! [SV16: $i,SV14: $i,SV8: $i] :
( ( ( ~ ! [SY42: $i] :
~ ~ ( ~ ( in @ SY42 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY42 ) ) ) )
= $true )
| ( ( in @ SV16 @ ( relation_dom @ SV8 ) )
= $false )
| ( ( ( sK7_SY36 @ SV8 @ SV14 )
= ( apply @ SV8 @ SV16 ) )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(249,plain,
! [SV16: $i,SV14: $i,SV8: $i] :
( ( ( ! [SY42: $i] :
~ ~ ( ~ ( in @ SY42 @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ SY42 ) ) ) )
= $false )
| ( ( in @ SV16 @ ( relation_dom @ SV8 ) )
= $false )
| ( ( ( sK7_SY36 @ SV8 @ SV14 )
= ( apply @ SV8 @ SV16 ) )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(250,plain,
! [SV8: $i,SV14: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_SY42 @ SV16 @ SV14 @ SV8 ) @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ ( sK10_SY42 @ SV16 @ SV14 @ SV8 ) ) ) ) )
= $false )
| ( ( in @ SV16 @ ( relation_dom @ SV8 ) )
= $false )
| ( ( ( sK7_SY36 @ SV8 @ SV14 )
= ( apply @ SV8 @ SV16 ) )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[249]) ).
thf(251,plain,
! [SV8: $i,SV14: $i,SV16: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY42 @ SV16 @ SV14 @ SV8 ) @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ ( sK10_SY42 @ SV16 @ SV14 @ SV8 ) ) ) ) )
= $true )
| ( ( in @ SV16 @ ( relation_dom @ SV8 ) )
= $false )
| ( ( ( sK7_SY36 @ SV8 @ SV14 )
= ( apply @ SV8 @ SV16 ) )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(252,plain,
! [SV8: $i,SV14: $i,SV16: $i] :
( ( ( ~ ( in @ ( sK10_SY42 @ SV16 @ SV14 @ SV8 ) @ ( relation_dom @ SV8 ) )
| ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ ( sK10_SY42 @ SV16 @ SV14 @ SV8 ) ) ) )
= $false )
| ( ( in @ SV16 @ ( relation_dom @ SV8 ) )
= $false )
| ( ( ( sK7_SY36 @ SV8 @ SV14 )
= ( apply @ SV8 @ SV16 ) )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(253,plain,
! [SV8: $i,SV14: $i,SV16: $i] :
( ( ( ~ ( in @ ( sK10_SY42 @ SV16 @ SV14 @ SV8 ) @ ( relation_dom @ SV8 ) ) )
= $false )
| ( ( in @ SV16 @ ( relation_dom @ SV8 ) )
= $false )
| ( ( ( sK7_SY36 @ SV8 @ SV14 )
= ( apply @ SV8 @ SV16 ) )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(254,plain,
! [SV16: $i,SV14: $i,SV8: $i] :
( ( ( ( sK7_SY36 @ SV8 @ SV14 )
!= ( apply @ SV8 @ ( sK10_SY42 @ SV16 @ SV14 @ SV8 ) ) )
= $false )
| ( ( in @ SV16 @ ( relation_dom @ SV8 ) )
= $false )
| ( ( ( sK7_SY36 @ SV8 @ SV14 )
= ( apply @ SV8 @ SV16 ) )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(255,plain,
! [SV8: $i,SV14: $i,SV16: $i] :
( ( ( in @ ( sK10_SY42 @ SV16 @ SV14 @ SV8 ) @ ( relation_dom @ SV8 ) )
= $true )
| ( ( in @ SV16 @ ( relation_dom @ SV8 ) )
= $false )
| ( ( ( sK7_SY36 @ SV8 @ SV14 )
= ( apply @ SV8 @ SV16 ) )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(256,plain,
! [SV16: $i,SV14: $i,SV8: $i] :
( ( ( ( sK7_SY36 @ SV8 @ SV14 )
= ( apply @ SV8 @ ( sK10_SY42 @ SV16 @ SV14 @ SV8 ) ) )
= $true )
| ( ( in @ SV16 @ ( relation_dom @ SV8 ) )
= $false )
| ( ( ( sK7_SY36 @ SV8 @ SV14 )
= ( apply @ SV8 @ SV16 ) )
= $false )
| ( ( SV14
= ( relation_rng @ SV8 ) )
= $true )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(257,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[69,256,255,247,246,245,239,235,234,219,185,184,176,175,174,173,169,168,166,165,164,163,162,161,160,148,130,123,122,87,71,70]) ).
thf(258,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[257]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET991+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
% 0.10/0.18 % Computer : n019.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Oct 6 14:58:01 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.29
% 0.10/0.29 No.of.Axioms: 14
% 0.10/0.29
% 0.10/0.29 Length.of.Defs: 0
% 0.10/0.29
% 0.10/0.29 Contains.Choice.Funs: false
% 0.10/0.29 ......
% 0.10/0.29
% 0.10/0.29 ********************************
% 0.10/0.29 * All subproblems solved! *
% 0.10/0.29 ********************************
% 0.10/0.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:17,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:257,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.29
% 0.10/0.29 %**** Beginning of derivation protocol ****
% 0.10/0.29 % SZS output start CNFRefutation
% See solution above
% 0.10/0.30
% 0.10/0.30 %**** End of derivation protocol ****
% 0.10/0.30 %**** no. of clauses in derivation: 242 ****
% 0.10/0.30 %**** clause counter: 257 ****
% 0.10/0.30
% 0.10/0.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:17,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:257,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------