%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU031+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 10:42:47 AM UTC 2026
% Result : Theorem 2.34s 0.59s
% Output : CNFRefutation 2.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 26
% Syntax : Number of formulae : 405 ( 212 unt; 0 typ; 0 def)
% Number of atoms : 3145 (1062 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 4800 (1392 ~; 903 |; 145 &;2282 @)
% ( 0 <=>; 78 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 11 con; 0-2 aty)
% Number of variables : 483 ( 0 ^; 465 !; 18 ?; 483 :)
% 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_function_inverse,type,
function_inverse: $i > $i ).
thf(tp_identity_relation,type,
identity_relation: $i > $i ).
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_composition,type,
relation_composition: $i > $i > $i ).
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_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SX0,type,
sK5_SX0: $i ).
thf(tp_sK6_SX0,type,
sK6_SX0: $i ).
thf(tp_sK7_SX0,type,
sK7_SX0: $i ).
thf(tp_sK8_SX0,type,
sK8_SX0: $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(4,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( ( relation_composition @ A @ ( function_inverse @ A ) )
= ( identity_relation @ ( relation_dom @ A ) ) )
& ( ( relation_composition @ ( function_inverse @ A ) @ A )
= ( identity_relation @ ( relation_rng @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_funct_1) ).
thf(6,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( function_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( function_inverse @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
thf(12,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(13,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(16,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(17,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(20,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(21,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ! [D: $i] :
( ( ( relation @ D )
& ( function @ D ) )
=> ( ( ( ( relation_rng @ B )
= A )
& ( ( relation_composition @ B @ C )
= ( identity_relation @ ( relation_dom @ D ) ) )
& ( ( relation_composition @ C @ D )
= ( identity_relation @ A ) ) )
=> ( D = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l72_funct_1) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ A @ B ) )
& ( relation @ ( relation_composition @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(24,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(25,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(26,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(27,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(28,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(29,axiom,
! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_composition @ A @ B ) )
& ( function @ ( relation_composition @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(33,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ B @ A ) )
& ( relation @ ( relation_composition @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(36,axiom,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(38,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( function_inverse @ A ) )
& ( function @ ( function_inverse @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(39,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(40,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(41,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(43,conjecture,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( one_to_one @ A )
& ( ( relation_rng @ B )
= ( relation_dom @ A ) )
& ( ( relation_composition @ B @ A )
= ( identity_relation @ ( relation_rng @ A ) ) ) )
=> ( B
= ( function_inverse @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_funct_1) ).
thf(44,negated_conjecture,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( one_to_one @ A )
& ( ( relation_rng @ B )
= ( relation_dom @ A ) )
& ( ( relation_composition @ B @ A )
= ( identity_relation @ ( relation_rng @ A ) ) ) )
=> ( B
= ( function_inverse @ A ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[43]) ).
thf(45,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( one_to_one @ A )
& ( ( relation_rng @ B )
= ( relation_dom @ A ) )
& ( ( relation_composition @ B @ A )
= ( identity_relation @ ( relation_rng @ A ) ) ) )
=> ( B
= ( function_inverse @ A ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[44]) ).
thf(46,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( ( relation_composition @ A @ ( function_inverse @ A ) )
= ( identity_relation @ ( relation_dom @ A ) ) )
& ( ( relation_composition @ ( function_inverse @ A ) @ A )
= ( identity_relation @ ( relation_rng @ A ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(47,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( function_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( function_inverse @ A ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(48,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(49,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(50,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(51,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(52,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(53,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(54,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ! [D: $i] :
( ( ( relation @ D )
& ( function @ D ) )
=> ( ( ( ( relation_rng @ B )
= A )
& ( ( relation_composition @ B @ C )
= ( identity_relation @ ( relation_dom @ D ) ) )
& ( ( relation_composition @ C @ D )
= ( identity_relation @ A ) ) )
=> ( D = B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(55,plain,
( ( ! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ A @ B ) )
& ( relation @ ( relation_composition @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(56,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(57,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(58,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(59,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(60,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(61,plain,
( ( ! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(62,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_composition @ A @ B ) )
& ( function @ ( relation_composition @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(63,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(64,plain,
( ( ! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ B @ A ) )
& ( relation @ ( relation_composition @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(65,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(66,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(67,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( function_inverse @ A ) )
& ( function @ ( function_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(68,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(69,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(70,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(71,plain,
( ( ( ( relation @ sK1_A )
& ( function @ sK1_A ) )
=> ! [SY32: $i] :
( ( ( relation @ SY32 )
& ( function @ SY32 ) )
=> ( ( ( one_to_one @ sK1_A )
& ( ( relation_rng @ SY32 )
= ( relation_dom @ sK1_A ) )
& ( ( relation_composition @ SY32 @ sK1_A )
= ( identity_relation @ ( relation_rng @ sK1_A ) ) ) )
=> ( SY32
= ( function_inverse @ sK1_A ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[45]) ).
thf(72,plain,
( ( relation @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[71]) ).
thf(73,plain,
( ( function @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[71]) ).
thf(74,plain,
( ( ! [SY32: $i] :
( ( ( relation @ SY32 )
& ( function @ SY32 ) )
=> ( ( ( one_to_one @ sK1_A )
& ( ( relation_rng @ SY32 )
= ( relation_dom @ sK1_A ) )
& ( ( relation_composition @ SY32 @ sK1_A )
= ( identity_relation @ ( relation_rng @ sK1_A ) ) ) )
=> ( SY32
= ( function_inverse @ sK1_A ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[71]) ).
thf(75,plain,
( ( ~ ! [SY32: $i] :
( ( ( relation @ SY32 )
& ( function @ SY32 ) )
=> ( ( ( one_to_one @ sK1_A )
& ( ( relation_rng @ SY32 )
= ( relation_dom @ sK1_A ) )
& ( ( relation_composition @ SY32 @ sK1_A )
= ( identity_relation @ ( relation_rng @ sK1_A ) ) ) )
=> ( SY32
= ( function_inverse @ sK1_A ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[74]) ).
thf(76,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(77,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(78,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(79,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( function_inverse @ A ) )
& ( function @ ( function_inverse @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(80,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(81,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(82,plain,
( ( ! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ B @ A ) )
& ( relation @ ( relation_composition @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(83,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(84,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_composition @ A @ B ) )
& ( function @ ( relation_composition @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(85,plain,
( ( ! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(86,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(87,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(88,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(89,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(90,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(91,plain,
( ( ! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ A @ B ) )
& ( relation @ ( relation_composition @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(92,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ! [D: $i] :
( ( ( relation @ D )
& ( function @ D ) )
=> ( ( ( ( relation_rng @ B )
= A )
& ( ( relation_composition @ B @ C )
= ( identity_relation @ ( relation_dom @ D ) ) )
& ( ( relation_composition @ C @ D )
= ( identity_relation @ A ) ) )
=> ( D = B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(93,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(94,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(95,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(96,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(97,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(98,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(99,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( function_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( function_inverse @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(100,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( ( relation_composition @ A @ ( function_inverse @ A ) )
= ( identity_relation @ ( relation_dom @ A ) ) )
& ( ( relation_composition @ ( function_inverse @ A ) @ A )
= ( identity_relation @ ( relation_rng @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(101,plain,
( ( function @ sK1_A )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(102,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(103,plain,
( ( ~ ! [SY32: $i] :
( ( ( relation @ SY32 )
& ( function @ SY32 ) )
=> ( ( ( one_to_one @ sK1_A )
& ( ( relation_rng @ SY32 )
= ( relation_dom @ sK1_A ) )
& ( ( relation_composition @ SY32 @ sK1_A )
= ( identity_relation @ ( relation_rng @ sK1_A ) ) ) )
=> ( SY32
= ( function_inverse @ sK1_A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(104,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(105,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(106,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(107,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX1 )
| ~ ( function @ SX1 ) )
| ! [SX2: $i] :
( ~ ~ ( ~ ( relation @ SX2 )
| ~ ( function @ SX2 ) )
| ! [SX3: $i] :
( ~ ~ ( ~ ( relation @ SX3 )
| ~ ( function @ SX3 ) )
| ~ ~ ( ~ ~ ( ( ( relation_rng @ SX1 )
!= SX0 )
| ( ( relation_composition @ SX1 @ SX2 )
!= ( identity_relation @ ( relation_dom @ SX3 ) ) ) )
| ( ( relation_composition @ SX2 @ SX3 )
!= ( identity_relation @ SX0 ) ) )
| ( SX3 = SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(108,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(109,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(110,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 )
| ~ ( ( ( relation_rng @ SX0 )
!= ( relation_dom @ ( function_inverse @ SX0 ) ) )
| ( ( relation_dom @ SX0 )
!= ( relation_rng @ ( function_inverse @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(111,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(112,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 ) )
| ~ ( ~ ( empty @ ( relation_composition @ SX0 @ SX1 ) )
| ~ ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(113,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( relation @ SX1 ) )
| ~ ( function @ SX1 ) )
| ~ ( ~ ( relation @ ( relation_composition @ SX0 @ SX1 ) )
| ~ ( function @ ( relation_composition @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(114,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(115,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_rng @ SX0 ) )
| ~ ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(116,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(117,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 )
| ~ ( ( ( relation_composition @ SX0 @ ( function_inverse @ SX0 ) )
!= ( identity_relation @ ( relation_dom @ SX0 ) ) )
| ( ( relation_composition @ ( function_inverse @ SX0 ) @ SX0 )
!= ( identity_relation @ ( relation_rng @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(118,plain,
( ( ! [SX0: $i] :
~ ( ~ ( relation @ ( identity_relation @ SX0 ) )
| ~ ( function @ ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(119,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(120,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(121,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(122,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) )
| ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(123,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(124,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( ~ ( relation @ ( function_inverse @ SX0 ) )
| ~ ( function @ ( function_inverse @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(125,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_dom @ SX0 ) )
| ~ ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(126,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX1 ) )
| ~ ( ~ ( empty @ ( relation_composition @ SX1 @ SX0 ) )
| ~ ( relation @ ( relation_composition @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(127,plain,
( ( ~ ! [SX0: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ( one_to_one @ sK1_A )
| ( ( relation_rng @ SX0 )
!= ( relation_dom @ sK1_A ) ) )
| ( ( relation_composition @ SX0 @ sK1_A )
!= ( identity_relation @ ( relation_rng @ sK1_A ) ) ) )
| ( SX0
= ( function_inverse @ sK1_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(128,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(129,plain,
! [SV1: $i] :
( ( relation @ ( identity_relation @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(130,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(131,plain,
! [SV2: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV2 )
| ~ ( relation @ SV2 ) )
| ~ ( empty @ ( relation_rng @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(132,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(133,plain,
! [SV3: $i] :
( ( ! [SY33: $i] :
( ~ ~ ( ~ ( relation @ SY33 )
| ~ ( function @ SY33 ) )
| ! [SY34: $i] :
( ~ ~ ( ~ ( relation @ SY34 )
| ~ ( function @ SY34 ) )
| ! [SY35: $i] :
( ~ ~ ( ~ ( relation @ SY35 )
| ~ ( function @ SY35 ) )
| ~ ~ ( ~ ~ ( ( ( relation_rng @ SY33 )
!= SV3 )
| ( ( relation_composition @ SY33 @ SY34 )
!= ( identity_relation @ ( relation_dom @ SY35 ) ) ) )
| ( ( relation_composition @ SY34 @ SY35 )
!= ( identity_relation @ SV3 ) ) )
| ( SY35 = SY33 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(134,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(135,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(136,plain,
! [SV4: $i] :
( ( ~ ~ ( ~ ( relation @ SV4 )
| ~ ( function @ SV4 ) )
| ~ ( one_to_one @ SV4 )
| ~ ( ( ( relation_rng @ SV4 )
!= ( relation_dom @ ( function_inverse @ SV4 ) ) )
| ( ( relation_dom @ SV4 )
!= ( relation_rng @ ( function_inverse @ SV4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(137,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(138,plain,
! [SV5: $i] :
( ( ! [SY36: $i] :
( ~ ~ ( ~ ( empty @ SV5 )
| ~ ( relation @ SY36 ) )
| ~ ( ~ ( empty @ ( relation_composition @ SV5 @ SY36 ) )
| ~ ( relation @ ( relation_composition @ SV5 @ SY36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(139,plain,
! [SV6: $i] :
( ( ! [SY37: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ SV6 )
| ~ ( function @ SV6 ) )
| ~ ( relation @ SY37 ) )
| ~ ( function @ SY37 ) )
| ~ ( ~ ( relation @ ( relation_composition @ SV6 @ SY37 ) )
| ~ ( function @ ( relation_composition @ SV6 @ SY37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(140,plain,
! [SV7: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV7 )
| ~ ( relation @ SV7 ) )
| ~ ( empty @ ( relation_dom @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(141,plain,
! [SV8: $i] :
( ( ~ ( empty @ SV8 )
| ~ ( ~ ( empty @ ( relation_rng @ SV8 ) )
| ~ ( relation @ ( relation_rng @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(142,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(143,plain,
! [SV9: $i] :
( ( ~ ~ ( ~ ( relation @ SV9 )
| ~ ( function @ SV9 ) )
| ~ ( one_to_one @ SV9 )
| ~ ( ( ( relation_composition @ SV9 @ ( function_inverse @ SV9 ) )
!= ( identity_relation @ ( relation_dom @ SV9 ) ) )
| ( ( relation_composition @ ( function_inverse @ SV9 ) @ SV9 )
!= ( identity_relation @ ( relation_rng @ SV9 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(144,plain,
! [SV10: $i] :
( ( ~ ( ~ ( relation @ ( identity_relation @ SV10 ) )
| ~ ( function @ ( identity_relation @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(145,plain,
! [SV11: $i] :
( ( ~ ( empty @ SV11 )
| ( function @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(146,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(147,plain,
! [SV12: $i] :
( ( ~ ( empty @ SV12 )
| ( relation @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(148,plain,
! [SV13: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV13 )
| ~ ( empty @ SV13 ) )
| ~ ( function @ SV13 ) )
| ~ ( ~ ~ ( ~ ( relation @ SV13 )
| ~ ( function @ SV13 ) )
| ~ ( one_to_one @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(149,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(150,plain,
! [SV14: $i] :
( ( ~ ~ ( ~ ( relation @ SV14 )
| ~ ( function @ SV14 ) )
| ~ ( ~ ( relation @ ( function_inverse @ SV14 ) )
| ~ ( function @ ( function_inverse @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(151,plain,
! [SV15: $i] :
( ( ~ ( empty @ SV15 )
| ~ ( ~ ( empty @ ( relation_dom @ SV15 ) )
| ~ ( relation @ ( relation_dom @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(152,plain,
! [SV16: $i] :
( ( ! [SY38: $i] :
( ~ ~ ( ~ ( empty @ SV16 )
| ~ ( relation @ SY38 ) )
| ~ ( ~ ( empty @ ( relation_composition @ SY38 @ SV16 ) )
| ~ ( relation @ ( relation_composition @ SY38 @ SV16 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(153,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ( one_to_one @ sK1_A )
| ( ( relation_rng @ SX0 )
!= ( relation_dom @ sK1_A ) ) )
| ( ( relation_composition @ SX0 @ sK1_A )
!= ( identity_relation @ ( relation_rng @ sK1_A ) ) ) )
| ( SX0
= ( function_inverse @ sK1_A ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(154,plain,
! [SV17: $i] :
( ( ! [SY39: $i] :
( ~ ~ ( ~ ( relation @ SV17 )
| ~ ( relation @ SY39 ) )
| ( relation @ ( relation_composition @ SV17 @ SY39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(155,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(156,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[130]) ).
thf(157,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV2 )
| ~ ( relation @ SV2 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(158,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(159,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[132]) ).
thf(160,plain,
! [SV3: $i,SV18: $i] :
( ( ~ ~ ( ~ ( relation @ SV18 )
| ~ ( function @ SV18 ) )
| ! [SY40: $i] :
( ~ ~ ( ~ ( relation @ SY40 )
| ~ ( function @ SY40 ) )
| ! [SY41: $i] :
( ~ ~ ( ~ ( relation @ SY41 )
| ~ ( function @ SY41 ) )
| ~ ~ ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SY40 )
!= ( identity_relation @ ( relation_dom @ SY41 ) ) ) )
| ( ( relation_composition @ SY40 @ SY41 )
!= ( identity_relation @ SV3 ) ) )
| ( SY41 = SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(161,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK2_SX0 )
| ~ ( empty @ sK2_SX0 ) )
| ~ ( function @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[134]) ).
thf(162,plain,
( ( ~ ~ ( ~ ( relation @ sK3_SX0 )
| ~ ( function @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[135]) ).
thf(163,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV4 )
| ~ ( function @ SV4 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV4 )
| ~ ( ( ( relation_rng @ SV4 )
!= ( relation_dom @ ( function_inverse @ SV4 ) ) )
| ( ( relation_dom @ SV4 )
!= ( relation_rng @ ( function_inverse @ SV4 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(164,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( function @ sK4_SX0 ) )
| ~ ( one_to_one @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[137]) ).
thf(165,plain,
! [SV19: $i,SV5: $i] :
( ( ~ ~ ( ~ ( empty @ SV5 )
| ~ ( relation @ SV19 ) )
| ~ ( ~ ( empty @ ( relation_composition @ SV5 @ SV19 ) )
| ~ ( relation @ ( relation_composition @ SV5 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(166,plain,
! [SV20: $i,SV6: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ SV6 )
| ~ ( function @ SV6 ) )
| ~ ( relation @ SV20 ) )
| ~ ( function @ SV20 ) )
| ~ ( ~ ( relation @ ( relation_composition @ SV6 @ SV20 ) )
| ~ ( function @ ( relation_composition @ SV6 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(167,plain,
! [SV7: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV7 )
| ~ ( relation @ SV7 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(168,plain,
! [SV8: $i] :
( ( ( ~ ( empty @ SV8 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV8 ) )
| ~ ( relation @ ( relation_rng @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(169,plain,
( ( ~ ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( relation_empty_yielding @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[142]) ).
thf(170,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV9 )
| ~ ( function @ SV9 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV9 )
| ~ ( ( ( relation_composition @ SV9 @ ( function_inverse @ SV9 ) )
!= ( identity_relation @ ( relation_dom @ SV9 ) ) )
| ( ( relation_composition @ ( function_inverse @ SV9 ) @ SV9 )
!= ( identity_relation @ ( relation_rng @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(171,plain,
! [SV10: $i] :
( ( ~ ( relation @ ( identity_relation @ SV10 ) )
| ~ ( function @ ( identity_relation @ SV10 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(172,plain,
! [SV11: $i] :
( ( ( ~ ( empty @ SV11 ) )
= $true )
| ( ( function @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(173,plain,
( ( ~ ~ ( ~ ( empty @ sK6_SX0 )
| ~ ( relation @ sK6_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[146]) ).
thf(174,plain,
! [SV12: $i] :
( ( ( ~ ( empty @ SV12 ) )
= $true )
| ( ( relation @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(175,plain,
! [SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV13 )
| ~ ( empty @ SV13 ) )
| ~ ( function @ SV13 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV13 )
| ~ ( function @ SV13 ) )
| ~ ( one_to_one @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(176,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK7_SX0 )
| ~ ( relation @ sK7_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[149]) ).
thf(177,plain,
! [SV14: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV14 )
| ~ ( function @ SV14 ) ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV14 ) )
| ~ ( function @ ( function_inverse @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(178,plain,
! [SV15: $i] :
( ( ( ~ ( empty @ SV15 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV15 ) )
| ~ ( relation @ ( relation_dom @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(179,plain,
! [SV21: $i,SV16: $i] :
( ( ~ ~ ( ~ ( empty @ SV16 )
| ~ ( relation @ SV21 ) )
| ~ ( ~ ( empty @ ( relation_composition @ SV21 @ SV16 ) )
| ~ ( relation @ ( relation_composition @ SV21 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(180,plain,
( ( ~ ~ ( ~ ( relation @ sK8_SX0 )
| ~ ( function @ sK8_SX0 ) )
| ~ ~ ( ~ ~ ( ~ ( one_to_one @ sK1_A )
| ( ( relation_rng @ sK8_SX0 )
!= ( relation_dom @ sK1_A ) ) )
| ( ( relation_composition @ sK8_SX0 @ sK1_A )
!= ( identity_relation @ ( relation_rng @ sK1_A ) ) ) )
| ( sK8_SX0
= ( function_inverse @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[153]) ).
thf(181,plain,
! [SV22: $i,SV17: $i] :
( ( ~ ~ ( ~ ( relation @ SV17 )
| ~ ( relation @ SV22 ) )
| ( relation @ ( relation_composition @ SV17 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(182,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[155]) ).
thf(183,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(184,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV2 )
| ~ ( relation @ SV2 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_rng @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(185,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(186,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(187,plain,
! [SV3: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV18 )
| ~ ( function @ SV18 ) ) )
= $true )
| ( ( ! [SY40: $i] :
( ~ ~ ( ~ ( relation @ SY40 )
| ~ ( function @ SY40 ) )
| ! [SY41: $i] :
( ~ ~ ( ~ ( relation @ SY41 )
| ~ ( function @ SY41 ) )
| ~ ~ ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SY40 )
!= ( identity_relation @ ( relation_dom @ SY41 ) ) ) )
| ( ( relation_composition @ SY40 @ SY41 )
!= ( identity_relation @ SV3 ) ) )
| ( SY41 = SV18 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(188,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK2_SX0 )
| ~ ( empty @ sK2_SX0 ) )
| ~ ( function @ sK2_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(189,plain,
( ( ~ ( ~ ( relation @ sK3_SX0 )
| ~ ( function @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(190,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ( relation @ SV4 )
| ~ ( function @ SV4 ) ) )
= $false )
| ( ( ~ ( one_to_one @ SV4 )
| ~ ( ( ( relation_rng @ SV4 )
!= ( relation_dom @ ( function_inverse @ SV4 ) ) )
| ( ( relation_dom @ SV4 )
!= ( relation_rng @ ( function_inverse @ SV4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(191,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( function @ sK4_SX0 ) )
| ~ ( one_to_one @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(192,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( empty @ SV5 )
| ~ ( relation @ SV19 ) ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_composition @ SV5 @ SV19 ) )
| ~ ( relation @ ( relation_composition @ SV5 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(193,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ SV6 )
| ~ ( function @ SV6 ) )
| ~ ( relation @ SV20 ) )
| ~ ( function @ SV20 ) ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV6 @ SV20 ) )
| ~ ( function @ ( relation_composition @ SV6 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(194,plain,
! [SV7: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV7 )
| ~ ( relation @ SV7 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_dom @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(195,plain,
! [SV8: $i] :
( ( ( empty @ SV8 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV8 ) )
| ~ ( relation @ ( relation_rng @ SV8 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(196,plain,
( ( ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( relation_empty_yielding @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(197,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ( relation @ SV9 )
| ~ ( function @ SV9 ) ) )
= $false )
| ( ( ~ ( one_to_one @ SV9 )
| ~ ( ( ( relation_composition @ SV9 @ ( function_inverse @ SV9 ) )
!= ( identity_relation @ ( relation_dom @ SV9 ) ) )
| ( ( relation_composition @ ( function_inverse @ SV9 ) @ SV9 )
!= ( identity_relation @ ( relation_rng @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(198,plain,
! [SV10: $i] :
( ( ~ ( relation @ ( identity_relation @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(199,plain,
! [SV10: $i] :
( ( ~ ( function @ ( identity_relation @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(200,plain,
! [SV11: $i] :
( ( ( empty @ SV11 )
= $false )
| ( ( function @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(201,plain,
( ( ~ ( ~ ( empty @ sK6_SX0 )
| ~ ( relation @ sK6_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(202,plain,
! [SV12: $i] :
( ( ( empty @ SV12 )
= $false )
| ( ( relation @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(203,plain,
! [SV13: $i] :
( ( ( ~ ( ~ ~ ( ~ ( relation @ SV13 )
| ~ ( empty @ SV13 ) )
| ~ ( function @ SV13 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV13 )
| ~ ( function @ SV13 ) )
| ~ ( one_to_one @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(204,plain,
( ( ~ ( ~ ~ ( empty @ sK7_SX0 )
| ~ ( relation @ sK7_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(205,plain,
! [SV14: $i] :
( ( ( ~ ( ~ ( relation @ SV14 )
| ~ ( function @ SV14 ) ) )
= $false )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV14 ) )
| ~ ( function @ ( function_inverse @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(206,plain,
! [SV15: $i] :
( ( ( empty @ SV15 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV15 ) )
| ~ ( relation @ ( relation_dom @ SV15 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(207,plain,
! [SV21: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( empty @ SV16 )
| ~ ( relation @ SV21 ) ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_composition @ SV21 @ SV16 ) )
| ~ ( relation @ ( relation_composition @ SV21 @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(208,plain,
( ( ~ ~ ( ~ ( relation @ sK8_SX0 )
| ~ ( function @ sK8_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(209,plain,
( ( ~ ~ ( ~ ~ ( ~ ( one_to_one @ sK1_A )
| ( ( relation_rng @ sK8_SX0 )
!= ( relation_dom @ sK1_A ) ) )
| ( ( relation_composition @ sK8_SX0 @ sK1_A )
!= ( identity_relation @ ( relation_rng @ sK1_A ) ) ) )
| ( sK8_SX0
= ( function_inverse @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(210,plain,
! [SV22: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV17 )
| ~ ( relation @ SV22 ) ) )
= $true )
| ( ( relation @ ( relation_composition @ SV17 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(211,plain,
! [SV2: $i] :
( ( ( ~ ~ ( empty @ SV2 )
| ~ ( relation @ SV2 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(212,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(213,plain,
! [SV3: $i,SV18: $i] :
( ( ( ~ ( ~ ( relation @ SV18 )
| ~ ( function @ SV18 ) ) )
= $false )
| ( ( ! [SY40: $i] :
( ~ ~ ( ~ ( relation @ SY40 )
| ~ ( function @ SY40 ) )
| ! [SY41: $i] :
( ~ ~ ( ~ ( relation @ SY41 )
| ~ ( function @ SY41 ) )
| ~ ~ ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SY40 )
!= ( identity_relation @ ( relation_dom @ SY41 ) ) ) )
| ( ( relation_composition @ SY40 @ SY41 )
!= ( identity_relation @ SV3 ) ) )
| ( SY41 = SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(214,plain,
( ( ~ ~ ( ~ ( relation @ sK2_SX0 )
| ~ ( empty @ sK2_SX0 ) )
| ~ ( function @ sK2_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(215,plain,
( ( ~ ( relation @ sK3_SX0 )
| ~ ( function @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(216,plain,
! [SV4: $i] :
( ( ( ~ ( relation @ SV4 )
| ~ ( function @ SV4 ) )
= $true )
| ( ( ~ ( one_to_one @ SV4 )
| ~ ( ( ( relation_rng @ SV4 )
!= ( relation_dom @ ( function_inverse @ SV4 ) ) )
| ( ( relation_dom @ SV4 )
!= ( relation_rng @ ( function_inverse @ SV4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(217,plain,
( ( ~ ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( function @ sK4_SX0 ) )
| ~ ( one_to_one @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(218,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ( ~ ( empty @ SV5 )
| ~ ( relation @ SV19 ) ) )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_composition @ SV5 @ SV19 ) )
| ~ ( relation @ ( relation_composition @ SV5 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(219,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ SV6 )
| ~ ( function @ SV6 ) )
| ~ ( relation @ SV20 ) )
| ~ ( function @ SV20 ) ) )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV6 @ SV20 ) )
| ~ ( function @ ( relation_composition @ SV6 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(220,plain,
! [SV7: $i] :
( ( ( ~ ~ ( empty @ SV7 )
| ~ ( relation @ SV7 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(221,plain,
! [SV8: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV8 ) )
| ~ ( relation @ ( relation_rng @ SV8 ) ) )
= $false )
| ( ( empty @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(222,plain,
( ( ~ ( relation @ sK5_SX0 )
| ~ ( relation_empty_yielding @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(223,plain,
! [SV9: $i] :
( ( ( ~ ( relation @ SV9 )
| ~ ( function @ SV9 ) )
= $true )
| ( ( ~ ( one_to_one @ SV9 )
| ~ ( ( ( relation_composition @ SV9 @ ( function_inverse @ SV9 ) )
!= ( identity_relation @ ( relation_dom @ SV9 ) ) )
| ( ( relation_composition @ ( function_inverse @ SV9 ) @ SV9 )
!= ( identity_relation @ ( relation_rng @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(224,plain,
! [SV10: $i] :
( ( relation @ ( identity_relation @ SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(225,plain,
! [SV10: $i] :
( ( function @ ( identity_relation @ SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(226,plain,
( ( ~ ( empty @ sK6_SX0 )
| ~ ( relation @ sK6_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(227,plain,
! [SV13: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV13 )
| ~ ( empty @ SV13 ) )
| ~ ( function @ SV13 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV13 )
| ~ ( function @ SV13 ) )
| ~ ( one_to_one @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(228,plain,
( ( ~ ~ ( empty @ sK7_SX0 )
| ~ ( relation @ sK7_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(229,plain,
! [SV14: $i] :
( ( ( ~ ( relation @ SV14 )
| ~ ( function @ SV14 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV14 ) )
| ~ ( function @ ( function_inverse @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(230,plain,
! [SV15: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV15 ) )
| ~ ( relation @ ( relation_dom @ SV15 ) ) )
= $false )
| ( ( empty @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(231,plain,
! [SV21: $i,SV16: $i] :
( ( ( ~ ( ~ ( empty @ SV16 )
| ~ ( relation @ SV21 ) ) )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_composition @ SV21 @ SV16 ) )
| ~ ( relation @ ( relation_composition @ SV21 @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(232,plain,
( ( ~ ( ~ ( relation @ sK8_SX0 )
| ~ ( function @ sK8_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(233,plain,
( ( ~ ~ ( ~ ~ ( ~ ( one_to_one @ sK1_A )
| ( ( relation_rng @ sK8_SX0 )
!= ( relation_dom @ sK1_A ) ) )
| ( ( relation_composition @ sK8_SX0 @ sK1_A )
!= ( identity_relation @ ( relation_rng @ sK1_A ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(234,plain,
( ( sK8_SX0
= ( function_inverse @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(235,plain,
! [SV22: $i,SV17: $i] :
( ( ( ~ ( ~ ( relation @ SV17 )
| ~ ( relation @ SV22 ) ) )
= $false )
| ( ( relation @ ( relation_composition @ SV17 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(236,plain,
! [SV2: $i] :
( ( ( ~ ~ ( empty @ SV2 ) )
= $true )
| ( ( ~ ( relation @ SV2 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(237,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(238,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(239,plain,
! [SV3: $i,SV18: $i] :
( ( ( ~ ( relation @ SV18 )
| ~ ( function @ SV18 ) )
= $true )
| ( ( ! [SY40: $i] :
( ~ ~ ( ~ ( relation @ SY40 )
| ~ ( function @ SY40 ) )
| ! [SY41: $i] :
( ~ ~ ( ~ ( relation @ SY41 )
| ~ ( function @ SY41 ) )
| ~ ~ ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SY40 )
!= ( identity_relation @ ( relation_dom @ SY41 ) ) ) )
| ( ( relation_composition @ SY40 @ SY41 )
!= ( identity_relation @ SV3 ) ) )
| ( SY41 = SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(240,plain,
( ( ~ ~ ( ~ ( relation @ sK2_SX0 )
| ~ ( empty @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(241,plain,
( ( ~ ( function @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(242,plain,
( ( ~ ( relation @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(243,plain,
( ( ~ ( function @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(244,plain,
! [SV4: $i] :
( ( ( ~ ( relation @ SV4 ) )
= $true )
| ( ( ~ ( function @ SV4 ) )
= $true )
| ( ( ~ ( one_to_one @ SV4 )
| ~ ( ( ( relation_rng @ SV4 )
!= ( relation_dom @ ( function_inverse @ SV4 ) ) )
| ( ( relation_dom @ SV4 )
!= ( relation_rng @ ( function_inverse @ SV4 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(245,plain,
( ( ~ ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( function @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(246,plain,
( ( ~ ( one_to_one @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(247,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ( empty @ SV5 )
| ~ ( relation @ SV19 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_composition @ SV5 @ SV19 ) )
| ~ ( relation @ ( relation_composition @ SV5 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(248,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV6 )
| ~ ( function @ SV6 ) )
| ~ ( relation @ SV20 ) )
| ~ ( function @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV6 @ SV20 ) )
| ~ ( function @ ( relation_composition @ SV6 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(249,plain,
! [SV7: $i] :
( ( ( ~ ~ ( empty @ SV7 ) )
= $true )
| ( ( ~ ( relation @ SV7 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(250,plain,
! [SV8: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV8 ) ) )
= $false )
| ( ( empty @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(251,plain,
! [SV8: $i] :
( ( ( ~ ( relation @ ( relation_rng @ SV8 ) ) )
= $false )
| ( ( empty @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(252,plain,
( ( ~ ( relation @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(253,plain,
( ( ~ ( relation_empty_yielding @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(254,plain,
! [SV9: $i] :
( ( ( ~ ( relation @ SV9 ) )
= $true )
| ( ( ~ ( function @ SV9 ) )
= $true )
| ( ( ~ ( one_to_one @ SV9 )
| ~ ( ( ( relation_composition @ SV9 @ ( function_inverse @ SV9 ) )
!= ( identity_relation @ ( relation_dom @ SV9 ) ) )
| ( ( relation_composition @ ( function_inverse @ SV9 ) @ SV9 )
!= ( identity_relation @ ( relation_rng @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(255,plain,
( ( ~ ( empty @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(256,plain,
( ( ~ ( relation @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(257,plain,
! [SV13: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV13 )
| ~ ( empty @ SV13 ) ) )
= $true )
| ( ( ~ ( function @ SV13 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV13 )
| ~ ( function @ SV13 ) )
| ~ ( one_to_one @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(258,plain,
( ( ~ ~ ( empty @ sK7_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[228]) ).
thf(259,plain,
( ( ~ ( relation @ sK7_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[228]) ).
thf(260,plain,
! [SV14: $i] :
( ( ( ~ ( relation @ SV14 ) )
= $true )
| ( ( ~ ( function @ SV14 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV14 ) )
| ~ ( function @ ( function_inverse @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(261,plain,
! [SV15: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV15 ) ) )
= $false )
| ( ( empty @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(262,plain,
! [SV15: $i] :
( ( ( ~ ( relation @ ( relation_dom @ SV15 ) ) )
= $false )
| ( ( empty @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(263,plain,
! [SV21: $i,SV16: $i] :
( ( ( ~ ( empty @ SV16 )
| ~ ( relation @ SV21 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_composition @ SV21 @ SV16 ) )
| ~ ( relation @ ( relation_composition @ SV21 @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(264,plain,
( ( ~ ( relation @ sK8_SX0 )
| ~ ( function @ sK8_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(265,plain,
( ( ~ ( ~ ~ ( ~ ( one_to_one @ sK1_A )
| ( ( relation_rng @ sK8_SX0 )
!= ( relation_dom @ sK1_A ) ) )
| ( ( relation_composition @ sK8_SX0 @ sK1_A )
!= ( identity_relation @ ( relation_rng @ sK1_A ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(266,plain,
! [SV22: $i,SV17: $i] :
( ( ( ~ ( relation @ SV17 )
| ~ ( relation @ SV22 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV17 @ SV22 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(267,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $false )
| ( ( ~ ( relation @ SV2 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(268,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(269,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(270,plain,
! [SV3: $i,SV18: $i] :
( ( ( ~ ( relation @ SV18 ) )
= $true )
| ( ( ~ ( function @ SV18 ) )
= $true )
| ( ( ! [SY40: $i] :
( ~ ~ ( ~ ( relation @ SY40 )
| ~ ( function @ SY40 ) )
| ! [SY41: $i] :
( ~ ~ ( ~ ( relation @ SY41 )
| ~ ( function @ SY41 ) )
| ~ ~ ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SY40 )
!= ( identity_relation @ ( relation_dom @ SY41 ) ) ) )
| ( ( relation_composition @ SY40 @ SY41 )
!= ( identity_relation @ SV3 ) ) )
| ( SY41 = SV18 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(271,plain,
( ( ~ ( ~ ( relation @ sK2_SX0 )
| ~ ( empty @ sK2_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(272,plain,
( ( function @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(273,plain,
( ( relation @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(274,plain,
( ( function @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(275,plain,
! [SV4: $i] :
( ( ( relation @ SV4 )
= $false )
| ( ( ~ ( function @ SV4 ) )
= $true )
| ( ( ~ ( one_to_one @ SV4 )
| ~ ( ( ( relation_rng @ SV4 )
!= ( relation_dom @ ( function_inverse @ SV4 ) ) )
| ( ( relation_dom @ SV4 )
!= ( relation_rng @ ( function_inverse @ SV4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(276,plain,
( ( ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( function @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(277,plain,
( ( one_to_one @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(278,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ( empty @ SV5 ) )
= $true )
| ( ( ~ ( relation @ SV19 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_composition @ SV5 @ SV19 ) )
| ~ ( relation @ ( relation_composition @ SV5 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(279,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV6 )
| ~ ( function @ SV6 ) )
| ~ ( relation @ SV20 ) ) )
= $true )
| ( ( ~ ( function @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV6 @ SV20 ) )
| ~ ( function @ ( relation_composition @ SV6 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(280,plain,
! [SV7: $i] :
( ( ( ~ ( empty @ SV7 ) )
= $false )
| ( ( ~ ( relation @ SV7 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(281,plain,
! [SV8: $i] :
( ( ( empty @ ( relation_rng @ SV8 ) )
= $true )
| ( ( empty @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(282,plain,
! [SV8: $i] :
( ( ( relation @ ( relation_rng @ SV8 ) )
= $true )
| ( ( empty @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(283,plain,
( ( relation @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(284,plain,
( ( relation_empty_yielding @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(285,plain,
! [SV9: $i] :
( ( ( relation @ SV9 )
= $false )
| ( ( ~ ( function @ SV9 ) )
= $true )
| ( ( ~ ( one_to_one @ SV9 )
| ~ ( ( ( relation_composition @ SV9 @ ( function_inverse @ SV9 ) )
!= ( identity_relation @ ( relation_dom @ SV9 ) ) )
| ( ( relation_composition @ ( function_inverse @ SV9 ) @ SV9 )
!= ( identity_relation @ ( relation_rng @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(286,plain,
( ( empty @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(287,plain,
( ( relation @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(288,plain,
! [SV13: $i] :
( ( ( ~ ( ~ ( relation @ SV13 )
| ~ ( empty @ SV13 ) ) )
= $false )
| ( ( ~ ( function @ SV13 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV13 )
| ~ ( function @ SV13 ) )
| ~ ( one_to_one @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(289,plain,
( ( ~ ( empty @ sK7_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(290,plain,
( ( relation @ sK7_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(291,plain,
! [SV14: $i] :
( ( ( relation @ SV14 )
= $false )
| ( ( ~ ( function @ SV14 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV14 ) )
| ~ ( function @ ( function_inverse @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(292,plain,
! [SV15: $i] :
( ( ( empty @ ( relation_dom @ SV15 ) )
= $true )
| ( ( empty @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(293,plain,
! [SV15: $i] :
( ( ( relation @ ( relation_dom @ SV15 ) )
= $true )
| ( ( empty @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(294,plain,
! [SV21: $i,SV16: $i] :
( ( ( ~ ( empty @ SV16 ) )
= $true )
| ( ( ~ ( relation @ SV21 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_composition @ SV21 @ SV16 ) )
| ~ ( relation @ ( relation_composition @ SV21 @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(295,plain,
( ( ~ ( relation @ sK8_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(296,plain,
( ( ~ ( function @ sK8_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(297,plain,
( ( ~ ~ ( ~ ( one_to_one @ sK1_A )
| ( ( relation_rng @ sK8_SX0 )
!= ( relation_dom @ sK1_A ) ) )
| ( ( relation_composition @ sK8_SX0 @ sK1_A )
!= ( identity_relation @ ( relation_rng @ sK1_A ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(298,plain,
! [SV22: $i,SV17: $i] :
( ( ( ~ ( relation @ SV17 ) )
= $true )
| ( ( ~ ( relation @ SV22 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV17 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(299,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $true )
| ( ( ~ ( relation @ SV2 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(300,plain,
! [SV3: $i,SV18: $i] :
( ( ( relation @ SV18 )
= $false )
| ( ( ~ ( function @ SV18 ) )
= $true )
| ( ( ! [SY40: $i] :
( ~ ~ ( ~ ( relation @ SY40 )
| ~ ( function @ SY40 ) )
| ! [SY41: $i] :
( ~ ~ ( ~ ( relation @ SY41 )
| ~ ( function @ SY41 ) )
| ~ ~ ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SY40 )
!= ( identity_relation @ ( relation_dom @ SY41 ) ) ) )
| ( ( relation_composition @ SY40 @ SY41 )
!= ( identity_relation @ SV3 ) ) )
| ( SY41 = SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(301,plain,
( ( ~ ( relation @ sK2_SX0 )
| ~ ( empty @ sK2_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(302,plain,
! [SV4: $i] :
( ( ( function @ SV4 )
= $false )
| ( ( relation @ SV4 )
= $false )
| ( ( ~ ( one_to_one @ SV4 )
| ~ ( ( ( relation_rng @ SV4 )
!= ( relation_dom @ ( function_inverse @ SV4 ) ) )
| ( ( relation_dom @ SV4 )
!= ( relation_rng @ ( function_inverse @ SV4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(303,plain,
( ( ~ ( relation @ sK4_SX0 )
| ~ ( function @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(304,plain,
! [SV19: $i,SV5: $i] :
( ( ( empty @ SV5 )
= $false )
| ( ( ~ ( relation @ SV19 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_composition @ SV5 @ SV19 ) )
| ~ ( relation @ ( relation_composition @ SV5 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(305,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ( ~ ~ ( ~ ( relation @ SV6 )
| ~ ( function @ SV6 ) )
| ~ ( relation @ SV20 ) ) )
= $false )
| ( ( ~ ( function @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV6 @ SV20 ) )
| ~ ( function @ ( relation_composition @ SV6 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(306,plain,
! [SV7: $i] :
( ( ( empty @ SV7 )
= $true )
| ( ( ~ ( relation @ SV7 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(307,plain,
! [SV9: $i] :
( ( ( function @ SV9 )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( ~ ( one_to_one @ SV9 )
| ~ ( ( ( relation_composition @ SV9 @ ( function_inverse @ SV9 ) )
!= ( identity_relation @ ( relation_dom @ SV9 ) ) )
| ( ( relation_composition @ ( function_inverse @ SV9 ) @ SV9 )
!= ( identity_relation @ ( relation_rng @ SV9 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(308,plain,
! [SV13: $i] :
( ( ( ~ ( relation @ SV13 )
| ~ ( empty @ SV13 ) )
= $true )
| ( ( ~ ( function @ SV13 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV13 )
| ~ ( function @ SV13 ) )
| ~ ( one_to_one @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(309,plain,
( ( empty @ sK7_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(310,plain,
! [SV14: $i] :
( ( ( function @ SV14 )
= $false )
| ( ( relation @ SV14 )
= $false )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV14 ) )
| ~ ( function @ ( function_inverse @ SV14 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(311,plain,
! [SV21: $i,SV16: $i] :
( ( ( empty @ SV16 )
= $false )
| ( ( ~ ( relation @ SV21 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_composition @ SV21 @ SV16 ) )
| ~ ( relation @ ( relation_composition @ SV21 @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(312,plain,
( ( relation @ sK8_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(313,plain,
( ( function @ sK8_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(314,plain,
( ( ~ ~ ( ~ ( one_to_one @ sK1_A )
| ( ( relation_rng @ sK8_SX0 )
!= ( relation_dom @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(315,plain,
( ( ( relation_composition @ sK8_SX0 @ sK1_A )
!= ( identity_relation @ ( relation_rng @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[297]) ).
thf(316,plain,
! [SV22: $i,SV17: $i] :
( ( ( relation @ SV17 )
= $false )
| ( ( ~ ( relation @ SV22 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV17 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(317,plain,
! [SV2: $i] :
( ( ( relation @ SV2 )
= $false )
| ( ( empty @ SV2 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(318,plain,
! [SV3: $i,SV18: $i] :
( ( ( function @ SV18 )
= $false )
| ( ( relation @ SV18 )
= $false )
| ( ( ! [SY40: $i] :
( ~ ~ ( ~ ( relation @ SY40 )
| ~ ( function @ SY40 ) )
| ! [SY41: $i] :
( ~ ~ ( ~ ( relation @ SY41 )
| ~ ( function @ SY41 ) )
| ~ ~ ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SY40 )
!= ( identity_relation @ ( relation_dom @ SY41 ) ) ) )
| ( ( relation_composition @ SY40 @ SY41 )
!= ( identity_relation @ SV3 ) ) )
| ( SY41 = SV18 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(319,plain,
( ( ~ ( relation @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(320,plain,
( ( ~ ( empty @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(321,plain,
! [SV4: $i] :
( ( ( ~ ( one_to_one @ SV4 ) )
= $true )
| ( ( ~ ( ( ( relation_rng @ SV4 )
!= ( relation_dom @ ( function_inverse @ SV4 ) ) )
| ( ( relation_dom @ SV4 )
!= ( relation_rng @ ( function_inverse @ SV4 ) ) ) ) )
= $true )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(322,plain,
( ( ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(323,plain,
( ( ~ ( function @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(324,plain,
! [SV5: $i,SV19: $i] :
( ( ( relation @ SV19 )
= $false )
| ( ( empty @ SV5 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_composition @ SV5 @ SV19 ) )
| ~ ( relation @ ( relation_composition @ SV5 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(325,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV6 )
| ~ ( function @ SV6 ) )
| ~ ( relation @ SV20 ) )
= $true )
| ( ( ~ ( function @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV6 @ SV20 ) )
| ~ ( function @ ( relation_composition @ SV6 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(326,plain,
! [SV7: $i] :
( ( ( relation @ SV7 )
= $false )
| ( ( empty @ SV7 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(327,plain,
! [SV9: $i] :
( ( ( ~ ( one_to_one @ SV9 ) )
= $true )
| ( ( ~ ( ( ( relation_composition @ SV9 @ ( function_inverse @ SV9 ) )
!= ( identity_relation @ ( relation_dom @ SV9 ) ) )
| ( ( relation_composition @ ( function_inverse @ SV9 ) @ SV9 )
!= ( identity_relation @ ( relation_rng @ SV9 ) ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(328,plain,
! [SV13: $i] :
( ( ( ~ ( relation @ SV13 ) )
= $true )
| ( ( ~ ( empty @ SV13 ) )
= $true )
| ( ( ~ ( function @ SV13 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV13 )
| ~ ( function @ SV13 ) )
| ~ ( one_to_one @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(329,plain,
! [SV14: $i] :
( ( ( ~ ( relation @ ( function_inverse @ SV14 ) )
| ~ ( function @ ( function_inverse @ SV14 ) ) )
= $false )
| ( ( relation @ SV14 )
= $false )
| ( ( function @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(330,plain,
! [SV16: $i,SV21: $i] :
( ( ( relation @ SV21 )
= $false )
| ( ( empty @ SV16 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_composition @ SV21 @ SV16 ) )
| ~ ( relation @ ( relation_composition @ SV21 @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(331,plain,
( ( ~ ( ~ ( one_to_one @ sK1_A )
| ( ( relation_rng @ sK8_SX0 )
!= ( relation_dom @ sK1_A ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[314]) ).
thf(332,plain,
( ( ( relation_composition @ sK8_SX0 @ sK1_A )
= ( identity_relation @ ( relation_rng @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(333,plain,
! [SV17: $i,SV22: $i] :
( ( ( relation @ SV22 )
= $false )
| ( ( relation @ SV17 )
= $false )
| ( ( relation @ ( relation_composition @ SV17 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(334,plain,
! [SV2: $i] :
( ( ( empty @ ( relation_rng @ SV2 ) )
= $false )
| ( ( empty @ SV2 )
= $true )
| ( ( relation @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(335,plain,
! [SV3: $i,SV18: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV23 )
| ~ ( function @ SV23 ) )
| ! [SY42: $i] :
( ~ ~ ( ~ ( relation @ SY42 )
| ~ ( function @ SY42 ) )
| ~ ~ ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SV23 )
!= ( identity_relation @ ( relation_dom @ SY42 ) ) ) )
| ( ( relation_composition @ SV23 @ SY42 )
!= ( identity_relation @ SV3 ) ) )
| ( SY42 = SV18 ) ) )
= $true )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(336,plain,
( ( relation @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[319]) ).
thf(337,plain,
( ( empty @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(338,plain,
! [SV4: $i] :
( ( ( one_to_one @ SV4 )
= $false )
| ( ( ~ ( ( ( relation_rng @ SV4 )
!= ( relation_dom @ ( function_inverse @ SV4 ) ) )
| ( ( relation_dom @ SV4 )
!= ( relation_rng @ ( function_inverse @ SV4 ) ) ) ) )
= $true )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(339,plain,
( ( relation @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[322]) ).
thf(340,plain,
( ( function @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(341,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ( empty @ ( relation_composition @ SV5 @ SV19 ) )
| ~ ( relation @ ( relation_composition @ SV5 @ SV19 ) ) )
= $false )
| ( ( empty @ SV5 )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(342,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV6 )
| ~ ( function @ SV6 ) ) )
= $true )
| ( ( ~ ( relation @ SV20 ) )
= $true )
| ( ( ~ ( function @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV6 @ SV20 ) )
| ~ ( function @ ( relation_composition @ SV6 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(343,plain,
! [SV7: $i] :
( ( ( empty @ ( relation_dom @ SV7 ) )
= $false )
| ( ( empty @ SV7 )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(344,plain,
! [SV9: $i] :
( ( ( one_to_one @ SV9 )
= $false )
| ( ( ~ ( ( ( relation_composition @ SV9 @ ( function_inverse @ SV9 ) )
!= ( identity_relation @ ( relation_dom @ SV9 ) ) )
| ( ( relation_composition @ ( function_inverse @ SV9 ) @ SV9 )
!= ( identity_relation @ ( relation_rng @ SV9 ) ) ) ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(345,plain,
! [SV13: $i] :
( ( ( relation @ SV13 )
= $false )
| ( ( ~ ( empty @ SV13 ) )
= $true )
| ( ( ~ ( function @ SV13 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV13 )
| ~ ( function @ SV13 ) )
| ~ ( one_to_one @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(346,plain,
! [SV14: $i] :
( ( ( ~ ( relation @ ( function_inverse @ SV14 ) ) )
= $false )
| ( ( relation @ SV14 )
= $false )
| ( ( function @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[329]) ).
thf(347,plain,
! [SV14: $i] :
( ( ( ~ ( function @ ( function_inverse @ SV14 ) ) )
= $false )
| ( ( relation @ SV14 )
= $false )
| ( ( function @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[329]) ).
thf(348,plain,
! [SV16: $i,SV21: $i] :
( ( ( ~ ( empty @ ( relation_composition @ SV21 @ SV16 ) )
| ~ ( relation @ ( relation_composition @ SV21 @ SV16 ) ) )
= $false )
| ( ( empty @ SV16 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(349,plain,
( ( ~ ( one_to_one @ sK1_A )
| ( ( relation_rng @ sK8_SX0 )
!= ( relation_dom @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(350,plain,
! [SV3: $i,SV18: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV23 )
| ~ ( function @ SV23 ) ) )
= $true )
| ( ( ! [SY42: $i] :
( ~ ~ ( ~ ( relation @ SY42 )
| ~ ( function @ SY42 ) )
| ~ ~ ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SV23 )
!= ( identity_relation @ ( relation_dom @ SY42 ) ) ) )
| ( ( relation_composition @ SV23 @ SY42 )
!= ( identity_relation @ SV3 ) ) )
| ( SY42 = SV18 ) ) )
= $true )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(351,plain,
! [SV4: $i] :
( ( ( ( ( relation_rng @ SV4 )
!= ( relation_dom @ ( function_inverse @ SV4 ) ) )
| ( ( relation_dom @ SV4 )
!= ( relation_rng @ ( function_inverse @ SV4 ) ) ) )
= $false )
| ( ( one_to_one @ SV4 )
= $false )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(352,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ( empty @ ( relation_composition @ SV5 @ SV19 ) ) )
= $false )
| ( ( empty @ SV5 )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(353,plain,
! [SV19: $i,SV5: $i] :
( ( ( ~ ( relation @ ( relation_composition @ SV5 @ SV19 ) ) )
= $false )
| ( ( empty @ SV5 )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(354,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ( ~ ( relation @ SV6 )
| ~ ( function @ SV6 ) ) )
= $false )
| ( ( ~ ( relation @ SV20 ) )
= $true )
| ( ( ~ ( function @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV6 @ SV20 ) )
| ~ ( function @ ( relation_composition @ SV6 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(355,plain,
! [SV9: $i] :
( ( ( ( ( relation_composition @ SV9 @ ( function_inverse @ SV9 ) )
!= ( identity_relation @ ( relation_dom @ SV9 ) ) )
| ( ( relation_composition @ ( function_inverse @ SV9 ) @ SV9 )
!= ( identity_relation @ ( relation_rng @ SV9 ) ) ) )
= $false )
| ( ( one_to_one @ SV9 )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(356,plain,
! [SV13: $i] :
( ( ( empty @ SV13 )
= $false )
| ( ( relation @ SV13 )
= $false )
| ( ( ~ ( function @ SV13 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV13 )
| ~ ( function @ SV13 ) )
| ~ ( one_to_one @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(357,plain,
! [SV14: $i] :
( ( ( relation @ ( function_inverse @ SV14 ) )
= $true )
| ( ( relation @ SV14 )
= $false )
| ( ( function @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(358,plain,
! [SV14: $i] :
( ( ( function @ ( function_inverse @ SV14 ) )
= $true )
| ( ( relation @ SV14 )
= $false )
| ( ( function @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[347]) ).
thf(359,plain,
! [SV16: $i,SV21: $i] :
( ( ( ~ ( empty @ ( relation_composition @ SV21 @ SV16 ) ) )
= $false )
| ( ( empty @ SV16 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[348]) ).
thf(360,plain,
! [SV16: $i,SV21: $i] :
( ( ( ~ ( relation @ ( relation_composition @ SV21 @ SV16 ) ) )
= $false )
| ( ( empty @ SV16 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[348]) ).
thf(361,plain,
( ( ~ ( one_to_one @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[349]) ).
thf(362,plain,
( ( ( relation_rng @ sK8_SX0 )
!= ( relation_dom @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[349]) ).
thf(363,plain,
! [SV3: $i,SV18: $i,SV23: $i] :
( ( ( ~ ( ~ ( relation @ SV23 )
| ~ ( function @ SV23 ) ) )
= $false )
| ( ( ! [SY42: $i] :
( ~ ~ ( ~ ( relation @ SY42 )
| ~ ( function @ SY42 ) )
| ~ ~ ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SV23 )
!= ( identity_relation @ ( relation_dom @ SY42 ) ) ) )
| ( ( relation_composition @ SV23 @ SY42 )
!= ( identity_relation @ SV3 ) ) )
| ( SY42 = SV18 ) ) )
= $true )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(364,plain,
! [SV4: $i] :
( ( ( ( relation_rng @ SV4 )
!= ( relation_dom @ ( function_inverse @ SV4 ) ) )
= $false )
| ( ( one_to_one @ SV4 )
= $false )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[351]) ).
thf(365,plain,
! [SV4: $i] :
( ( ( ( relation_dom @ SV4 )
!= ( relation_rng @ ( function_inverse @ SV4 ) ) )
= $false )
| ( ( one_to_one @ SV4 )
= $false )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[351]) ).
thf(366,plain,
! [SV19: $i,SV5: $i] :
( ( ( empty @ ( relation_composition @ SV5 @ SV19 ) )
= $true )
| ( ( empty @ SV5 )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(367,plain,
! [SV19: $i,SV5: $i] :
( ( ( relation @ ( relation_composition @ SV5 @ SV19 ) )
= $true )
| ( ( empty @ SV5 )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(368,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ( relation @ SV6 )
| ~ ( function @ SV6 ) )
= $true )
| ( ( ~ ( relation @ SV20 ) )
= $true )
| ( ( ~ ( function @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV6 @ SV20 ) )
| ~ ( function @ ( relation_composition @ SV6 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(369,plain,
! [SV9: $i] :
( ( ( ( relation_composition @ SV9 @ ( function_inverse @ SV9 ) )
!= ( identity_relation @ ( relation_dom @ SV9 ) ) )
= $false )
| ( ( one_to_one @ SV9 )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(370,plain,
! [SV9: $i] :
( ( ( ( relation_composition @ ( function_inverse @ SV9 ) @ SV9 )
!= ( identity_relation @ ( relation_rng @ SV9 ) ) )
= $false )
| ( ( one_to_one @ SV9 )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(371,plain,
! [SV13: $i] :
( ( ( function @ SV13 )
= $false )
| ( ( relation @ SV13 )
= $false )
| ( ( empty @ SV13 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV13 )
| ~ ( function @ SV13 ) )
| ~ ( one_to_one @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(372,plain,
! [SV16: $i,SV21: $i] :
( ( ( empty @ ( relation_composition @ SV21 @ SV16 ) )
= $true )
| ( ( empty @ SV16 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(373,plain,
! [SV16: $i,SV21: $i] :
( ( ( relation @ ( relation_composition @ SV21 @ SV16 ) )
= $true )
| ( ( empty @ SV16 )
= $false )
| ( ( relation @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(374,plain,
( ( one_to_one @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[361]) ).
thf(375,plain,
( ( ( relation_rng @ sK8_SX0 )
= ( relation_dom @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[362]) ).
thf(376,plain,
! [SV3: $i,SV18: $i,SV23: $i] :
( ( ( ~ ( relation @ SV23 )
| ~ ( function @ SV23 ) )
= $true )
| ( ( ! [SY42: $i] :
( ~ ~ ( ~ ( relation @ SY42 )
| ~ ( function @ SY42 ) )
| ~ ~ ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SV23 )
!= ( identity_relation @ ( relation_dom @ SY42 ) ) ) )
| ( ( relation_composition @ SV23 @ SY42 )
!= ( identity_relation @ SV3 ) ) )
| ( SY42 = SV18 ) ) )
= $true )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[363]) ).
thf(377,plain,
! [SV4: $i] :
( ( ( ( relation_rng @ SV4 )
= ( relation_dom @ ( function_inverse @ SV4 ) ) )
= $true )
| ( ( one_to_one @ SV4 )
= $false )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[364]) ).
thf(378,plain,
! [SV4: $i] :
( ( ( ( relation_dom @ SV4 )
= ( relation_rng @ ( function_inverse @ SV4 ) ) )
= $true )
| ( ( one_to_one @ SV4 )
= $false )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[365]) ).
thf(379,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ( relation @ SV6 ) )
= $true )
| ( ( ~ ( function @ SV6 ) )
= $true )
| ( ( ~ ( relation @ SV20 ) )
= $true )
| ( ( ~ ( function @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV6 @ SV20 ) )
| ~ ( function @ ( relation_composition @ SV6 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(380,plain,
! [SV9: $i] :
( ( ( ( relation_composition @ SV9 @ ( function_inverse @ SV9 ) )
= ( identity_relation @ ( relation_dom @ SV9 ) ) )
= $true )
| ( ( one_to_one @ SV9 )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(381,plain,
! [SV9: $i] :
( ( ( ( relation_composition @ ( function_inverse @ SV9 ) @ SV9 )
= ( identity_relation @ ( relation_rng @ SV9 ) ) )
= $true )
| ( ( one_to_one @ SV9 )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[370]) ).
thf(382,plain,
! [SV13: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV13 )
| ~ ( function @ SV13 ) )
| ~ ( one_to_one @ SV13 ) )
= $false )
| ( ( empty @ SV13 )
= $false )
| ( ( relation @ SV13 )
= $false )
| ( ( function @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(383,plain,
! [SV3: $i,SV18: $i,SV23: $i] :
( ( ( ~ ( relation @ SV23 ) )
= $true )
| ( ( ~ ( function @ SV23 ) )
= $true )
| ( ( ! [SY42: $i] :
( ~ ~ ( ~ ( relation @ SY42 )
| ~ ( function @ SY42 ) )
| ~ ~ ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SV23 )
!= ( identity_relation @ ( relation_dom @ SY42 ) ) ) )
| ( ( relation_composition @ SV23 @ SY42 )
!= ( identity_relation @ SV3 ) ) )
| ( SY42 = SV18 ) ) )
= $true )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[376]) ).
thf(384,plain,
! [SV20: $i,SV6: $i] :
( ( ( relation @ SV6 )
= $false )
| ( ( ~ ( function @ SV6 ) )
= $true )
| ( ( ~ ( relation @ SV20 ) )
= $true )
| ( ( ~ ( function @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV6 @ SV20 ) )
| ~ ( function @ ( relation_composition @ SV6 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(385,plain,
! [SV13: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV13 )
| ~ ( function @ SV13 ) ) )
= $false )
| ( ( empty @ SV13 )
= $false )
| ( ( relation @ SV13 )
= $false )
| ( ( function @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[382]) ).
thf(386,plain,
! [SV13: $i] :
( ( ( ~ ( one_to_one @ SV13 ) )
= $false )
| ( ( empty @ SV13 )
= $false )
| ( ( relation @ SV13 )
= $false )
| ( ( function @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[382]) ).
thf(387,plain,
! [SV3: $i,SV18: $i,SV23: $i] :
( ( ( relation @ SV23 )
= $false )
| ( ( ~ ( function @ SV23 ) )
= $true )
| ( ( ! [SY42: $i] :
( ~ ~ ( ~ ( relation @ SY42 )
| ~ ( function @ SY42 ) )
| ~ ~ ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SV23 )
!= ( identity_relation @ ( relation_dom @ SY42 ) ) ) )
| ( ( relation_composition @ SV23 @ SY42 )
!= ( identity_relation @ SV3 ) ) )
| ( SY42 = SV18 ) ) )
= $true )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(388,plain,
! [SV20: $i,SV6: $i] :
( ( ( function @ SV6 )
= $false )
| ( ( relation @ SV6 )
= $false )
| ( ( ~ ( relation @ SV20 ) )
= $true )
| ( ( ~ ( function @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV6 @ SV20 ) )
| ~ ( function @ ( relation_composition @ SV6 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(389,plain,
! [SV13: $i] :
( ( ( ~ ( ~ ( relation @ SV13 )
| ~ ( function @ SV13 ) ) )
= $true )
| ( ( empty @ SV13 )
= $false )
| ( ( relation @ SV13 )
= $false )
| ( ( function @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[385]) ).
thf(390,plain,
! [SV13: $i] :
( ( ( one_to_one @ SV13 )
= $true )
| ( ( empty @ SV13 )
= $false )
| ( ( relation @ SV13 )
= $false )
| ( ( function @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[386]) ).
thf(391,plain,
! [SV3: $i,SV18: $i,SV23: $i] :
( ( ( function @ SV23 )
= $false )
| ( ( relation @ SV23 )
= $false )
| ( ( ! [SY42: $i] :
( ~ ~ ( ~ ( relation @ SY42 )
| ~ ( function @ SY42 ) )
| ~ ~ ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SV23 )
!= ( identity_relation @ ( relation_dom @ SY42 ) ) ) )
| ( ( relation_composition @ SV23 @ SY42 )
!= ( identity_relation @ SV3 ) ) )
| ( SY42 = SV18 ) ) )
= $true )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(392,plain,
! [SV6: $i,SV20: $i] :
( ( ( relation @ SV20 )
= $false )
| ( ( relation @ SV6 )
= $false )
| ( ( function @ SV6 )
= $false )
| ( ( ~ ( function @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV6 @ SV20 ) )
| ~ ( function @ ( relation_composition @ SV6 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(393,plain,
! [SV13: $i] :
( ( ( ~ ( relation @ SV13 )
| ~ ( function @ SV13 ) )
= $false )
| ( ( empty @ SV13 )
= $false )
| ( ( relation @ SV13 )
= $false )
| ( ( function @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(394,plain,
! [SV23: $i,SV3: $i,SV18: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV24 )
| ~ ( function @ SV24 ) )
| ~ ~ ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SV23 )
!= ( identity_relation @ ( relation_dom @ SV24 ) ) ) )
| ( ( relation_composition @ SV23 @ SV24 )
!= ( identity_relation @ SV3 ) ) )
| ( SV24 = SV18 ) )
= $true )
| ( ( relation @ SV23 )
= $false )
| ( ( function @ SV23 )
= $false )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(395,plain,
! [SV6: $i,SV20: $i] :
( ( ( function @ SV20 )
= $false )
| ( ( function @ SV6 )
= $false )
| ( ( relation @ SV6 )
= $false )
| ( ( relation @ SV20 )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV6 @ SV20 ) )
| ~ ( function @ ( relation_composition @ SV6 @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(396,plain,
! [SV13: $i] :
( ( ( ~ ( relation @ SV13 ) )
= $false )
| ( ( empty @ SV13 )
= $false )
| ( ( relation @ SV13 )
= $false )
| ( ( function @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[393]) ).
thf(397,plain,
! [SV13: $i] :
( ( ( ~ ( function @ SV13 ) )
= $false )
| ( ( empty @ SV13 )
= $false )
| ( ( relation @ SV13 )
= $false )
| ( ( function @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[393]) ).
thf(398,plain,
! [SV23: $i,SV3: $i,SV18: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV24 )
| ~ ( function @ SV24 ) ) )
= $true )
| ( ( ~ ~ ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SV23 )
!= ( identity_relation @ ( relation_dom @ SV24 ) ) ) )
| ( ( relation_composition @ SV23 @ SV24 )
!= ( identity_relation @ SV3 ) ) )
| ( SV24 = SV18 ) )
= $true )
| ( ( relation @ SV23 )
= $false )
| ( ( function @ SV23 )
= $false )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(399,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ( relation @ ( relation_composition @ SV6 @ SV20 ) )
| ~ ( function @ ( relation_composition @ SV6 @ SV20 ) ) )
= $false )
| ( ( relation @ SV20 )
= $false )
| ( ( relation @ SV6 )
= $false )
| ( ( function @ SV6 )
= $false )
| ( ( function @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(400,plain,
! [SV13: $i] :
( ( ( relation @ SV13 )
= $true )
| ( ( empty @ SV13 )
= $false )
| ( ( relation @ SV13 )
= $false )
| ( ( function @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[396]) ).
thf(401,plain,
! [SV13: $i] :
( ( ( function @ SV13 )
= $true )
| ( ( empty @ SV13 )
= $false )
| ( ( relation @ SV13 )
= $false )
| ( ( function @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[397]) ).
thf(402,plain,
! [SV23: $i,SV3: $i,SV18: $i,SV24: $i] :
( ( ( ~ ( ~ ( relation @ SV24 )
| ~ ( function @ SV24 ) ) )
= $false )
| ( ( ~ ~ ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SV23 )
!= ( identity_relation @ ( relation_dom @ SV24 ) ) ) )
| ( ( relation_composition @ SV23 @ SV24 )
!= ( identity_relation @ SV3 ) ) )
| ( SV24 = SV18 ) )
= $true )
| ( ( relation @ SV23 )
= $false )
| ( ( function @ SV23 )
= $false )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(403,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ( relation @ ( relation_composition @ SV6 @ SV20 ) ) )
= $false )
| ( ( relation @ SV20 )
= $false )
| ( ( relation @ SV6 )
= $false )
| ( ( function @ SV6 )
= $false )
| ( ( function @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[399]) ).
thf(404,plain,
! [SV20: $i,SV6: $i] :
( ( ( ~ ( function @ ( relation_composition @ SV6 @ SV20 ) ) )
= $false )
| ( ( relation @ SV20 )
= $false )
| ( ( relation @ SV6 )
= $false )
| ( ( function @ SV6 )
= $false )
| ( ( function @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[399]) ).
thf(405,plain,
! [SV23: $i,SV3: $i,SV18: $i,SV24: $i] :
( ( ( ~ ( relation @ SV24 )
| ~ ( function @ SV24 ) )
= $true )
| ( ( ~ ~ ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SV23 )
!= ( identity_relation @ ( relation_dom @ SV24 ) ) ) )
| ( ( relation_composition @ SV23 @ SV24 )
!= ( identity_relation @ SV3 ) ) )
| ( SV24 = SV18 ) )
= $true )
| ( ( relation @ SV23 )
= $false )
| ( ( function @ SV23 )
= $false )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[402]) ).
thf(406,plain,
! [SV20: $i,SV6: $i] :
( ( ( relation @ ( relation_composition @ SV6 @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false )
| ( ( relation @ SV6 )
= $false )
| ( ( function @ SV6 )
= $false )
| ( ( function @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[403]) ).
thf(407,plain,
! [SV20: $i,SV6: $i] :
( ( ( function @ ( relation_composition @ SV6 @ SV20 ) )
= $true )
| ( ( relation @ SV20 )
= $false )
| ( ( relation @ SV6 )
= $false )
| ( ( function @ SV6 )
= $false )
| ( ( function @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[404]) ).
thf(408,plain,
! [SV23: $i,SV3: $i,SV18: $i,SV24: $i] :
( ( ( ~ ( relation @ SV24 ) )
= $true )
| ( ( ~ ( function @ SV24 ) )
= $true )
| ( ( ~ ~ ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SV23 )
!= ( identity_relation @ ( relation_dom @ SV24 ) ) ) )
| ( ( relation_composition @ SV23 @ SV24 )
!= ( identity_relation @ SV3 ) ) )
| ( SV24 = SV18 ) )
= $true )
| ( ( relation @ SV23 )
= $false )
| ( ( function @ SV23 )
= $false )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(409,plain,
! [SV23: $i,SV3: $i,SV18: $i,SV24: $i] :
( ( ( relation @ SV24 )
= $false )
| ( ( ~ ( function @ SV24 ) )
= $true )
| ( ( ~ ~ ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SV23 )
!= ( identity_relation @ ( relation_dom @ SV24 ) ) ) )
| ( ( relation_composition @ SV23 @ SV24 )
!= ( identity_relation @ SV3 ) ) )
| ( SV24 = SV18 ) )
= $true )
| ( ( relation @ SV23 )
= $false )
| ( ( function @ SV23 )
= $false )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(410,plain,
! [SV23: $i,SV3: $i,SV18: $i,SV24: $i] :
( ( ( function @ SV24 )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( ~ ~ ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SV23 )
!= ( identity_relation @ ( relation_dom @ SV24 ) ) ) )
| ( ( relation_composition @ SV23 @ SV24 )
!= ( identity_relation @ SV3 ) ) )
| ( SV24 = SV18 ) )
= $true )
| ( ( relation @ SV23 )
= $false )
| ( ( function @ SV23 )
= $false )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(411,plain,
! [SV24: $i,SV23: $i,SV3: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SV23 )
!= ( identity_relation @ ( relation_dom @ SV24 ) ) ) )
| ( ( relation_composition @ SV23 @ SV24 )
!= ( identity_relation @ SV3 ) ) ) )
= $true )
| ( ( SV24 = SV18 )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false )
| ( ( relation @ SV23 )
= $false )
| ( ( function @ SV23 )
= $false )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(412,plain,
! [SV24: $i,SV23: $i,SV3: $i,SV18: $i] :
( ( ( ~ ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SV23 )
!= ( identity_relation @ ( relation_dom @ SV24 ) ) ) )
| ( ( relation_composition @ SV23 @ SV24 )
!= ( identity_relation @ SV3 ) ) ) )
= $false )
| ( ( SV24 = SV18 )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false )
| ( ( relation @ SV23 )
= $false )
| ( ( function @ SV23 )
= $false )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(413,plain,
! [SV24: $i,SV23: $i,SV3: $i,SV18: $i] :
( ( ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SV23 )
!= ( identity_relation @ ( relation_dom @ SV24 ) ) ) )
| ( ( relation_composition @ SV23 @ SV24 )
!= ( identity_relation @ SV3 ) ) )
= $true )
| ( ( SV24 = SV18 )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false )
| ( ( relation @ SV23 )
= $false )
| ( ( function @ SV23 )
= $false )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[412]) ).
thf(414,plain,
! [SV24: $i,SV23: $i,SV3: $i,SV18: $i] :
( ( ( ~ ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SV23 )
!= ( identity_relation @ ( relation_dom @ SV24 ) ) ) ) )
= $true )
| ( ( ( relation_composition @ SV23 @ SV24 )
!= ( identity_relation @ SV3 ) )
= $true )
| ( ( SV24 = SV18 )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false )
| ( ( relation @ SV23 )
= $false )
| ( ( function @ SV23 )
= $false )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(415,plain,
! [SV24: $i,SV23: $i,SV3: $i,SV18: $i] :
( ( ( ~ ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SV23 )
!= ( identity_relation @ ( relation_dom @ SV24 ) ) ) ) )
= $false )
| ( ( ( relation_composition @ SV23 @ SV24 )
!= ( identity_relation @ SV3 ) )
= $true )
| ( ( SV24 = SV18 )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false )
| ( ( relation @ SV23 )
= $false )
| ( ( function @ SV23 )
= $false )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(416,plain,
! [SV24: $i,SV23: $i,SV3: $i,SV18: $i] :
( ( ( ( ( relation_rng @ SV18 )
!= SV3 )
| ( ( relation_composition @ SV18 @ SV23 )
!= ( identity_relation @ ( relation_dom @ SV24 ) ) ) )
= $true )
| ( ( ( relation_composition @ SV23 @ SV24 )
!= ( identity_relation @ SV3 ) )
= $true )
| ( ( SV24 = SV18 )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false )
| ( ( relation @ SV23 )
= $false )
| ( ( function @ SV23 )
= $false )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[415]) ).
thf(417,plain,
! [SV24: $i,SV23: $i,SV3: $i,SV18: $i] :
( ( ( ( relation_rng @ SV18 )
!= SV3 )
= $true )
| ( ( ( relation_composition @ SV18 @ SV23 )
!= ( identity_relation @ ( relation_dom @ SV24 ) ) )
= $true )
| ( ( ( relation_composition @ SV23 @ SV24 )
!= ( identity_relation @ SV3 ) )
= $true )
| ( ( SV24 = SV18 )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false )
| ( ( relation @ SV23 )
= $false )
| ( ( function @ SV23 )
= $false )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(418,plain,
! [SV24: $i,SV23: $i,SV3: $i,SV18: $i] :
( ( ( ( relation_rng @ SV18 )
= SV3 )
= $false )
| ( ( ( relation_composition @ SV18 @ SV23 )
!= ( identity_relation @ ( relation_dom @ SV24 ) ) )
= $true )
| ( ( ( relation_composition @ SV23 @ SV24 )
!= ( identity_relation @ SV3 ) )
= $true )
| ( ( SV24 = SV18 )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false )
| ( ( relation @ SV23 )
= $false )
| ( ( function @ SV23 )
= $false )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(419,plain,
! [SV3: $i,SV24: $i,SV23: $i,SV18: $i] :
( ( ( ( relation_composition @ SV18 @ SV23 )
= ( identity_relation @ ( relation_dom @ SV24 ) ) )
= $false )
| ( ( ( relation_rng @ SV18 )
= SV3 )
= $false )
| ( ( ( relation_composition @ SV23 @ SV24 )
!= ( identity_relation @ SV3 ) )
= $true )
| ( ( SV24 = SV18 )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false )
| ( ( relation @ SV23 )
= $false )
| ( ( function @ SV23 )
= $false )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(420,plain,
! [SV18: $i,SV3: $i,SV24: $i,SV23: $i] :
( ( ( ( relation_composition @ SV23 @ SV24 )
= ( identity_relation @ SV3 ) )
= $false )
| ( ( ( relation_rng @ SV18 )
= SV3 )
= $false )
| ( ( ( relation_composition @ SV18 @ SV23 )
= ( identity_relation @ ( relation_dom @ SV24 ) ) )
= $false )
| ( ( SV24 = SV18 )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false )
| ( ( relation @ SV23 )
= $false )
| ( ( function @ SV23 )
= $false )
| ( ( relation @ SV18 )
= $false )
| ( ( function @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(421,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[101,420,407,406,401,400,390,381,380,378,377,375,374,373,372,367,366,358,357,343,340,339,337,336,334,333,332,313,312,309,293,292,290,287,286,284,283,282,281,277,274,273,272,269,268,234,225,224,202,200,186,183,182,129,102]) ).
thf(422,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[421]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU031+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.15 % Computer : n019.cluster.edu
% 0.09/0.15 % Model : x86_64 x86_64
% 0.09/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.15 % Memory : 8046.5625MB
% 0.09/0.15 % OS : Linux 6.8.0-71-generic
% 0.09/0.15 % CPULimit : 300
% 0.09/0.15 % WCLimit : 300
% 0.09/0.15 % DateTime : Tue Oct 6 14:58:46 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.34/0.59
% 2.34/0.59 No.of.Axioms: 25
% 2.34/0.59
% 2.34/0.59 Length.of.Defs: 0
% 2.34/0.59
% 2.34/0.59 Contains.Choice.Funs: false
% 2.34/0.59 ..........
% 2.34/0.59
% 2.34/0.59 ********************************
% 2.34/0.59 * All subproblems solved! *
% 2.34/0.59 ********************************
% 2.34/0.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:27,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:421,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.34/0.59
% 2.34/0.59 %**** Beginning of derivation protocol ****
% 2.34/0.59 % SZS output start CNFRefutation
% See solution above
% 2.34/0.59
% 2.34/0.59 %**** End of derivation protocol ****
% 2.34/0.59 %**** no. of clauses in derivation: 405 ****
% 2.34/0.59 %**** clause counter: 421 ****
% 2.34/0.59
% 2.34/0.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:27,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:421,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------