TSTP Solution File: SEU263+1 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU263+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:09:16 EDT 2022
% Result : Theorem 0.81s 1.00s
% Output : CNFRefutation 0.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 36
% Syntax : Number of formulae : 196 ( 140 unt; 16 typ; 0 def)
% Number of atoms : 770 ( 195 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1460 ( 165 ~; 154 |; 14 &;1095 @)
% ( 6 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 447 ( 0 ^ 441 !; 6 ?; 447 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_of2,type,
relation_of2: $i > $i > $i > $o ).
thf(tp_relation_of2_as_subset,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY39,type,
sK2_SY39: $i ).
thf(tp_sK3_SY42,type,
sK3_SY42: $i ).
thf(tp_sK4_SY44,type,
sK4_SY44: $i ).
thf(tp_sK5_C,type,
sK5_C: $i > $i > $i ).
thf(tp_sK6_B,type,
sK6_B: $i > $i ).
thf(tp_sK7_C,type,
sK7_C: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(2,axiom,
! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ( subset @ ( relation_dom @ C ) @ A )
& ( subset @ ( relation_rng @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_relset_1) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(6,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(8,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(9,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(10,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(12,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(13,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(14,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(15,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(16,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(17,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
<=> ( subset @ C @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relset_1) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(20,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ ( relation_rng @ D ) @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_relset_1) ).
thf(21,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ ( relation_rng @ D ) @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[20]) ).
thf(22,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( relation_of2_as_subset @ D @ C @ A )
=> ( ( subset @ ( relation_rng @ D ) @ B )
=> ( relation_of2_as_subset @ D @ C @ B ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[21]) ).
thf(23,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(24,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(25,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(26,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( ( subset @ ( relation_dom @ C ) @ A )
& ( subset @ ( relation_rng @ C ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(27,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(28,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(29,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(30,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(31,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(32,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(33,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(34,plain,
$true = $true,
inference(unfold_def,[status(thm)],[12]) ).
thf(35,plain,
$true = $true,
inference(unfold_def,[status(thm)],[13]) ).
thf(36,plain,
$true = $true,
inference(unfold_def,[status(thm)],[14]) ).
thf(37,plain,
$true = $true,
inference(unfold_def,[status(thm)],[15]) ).
thf(38,plain,
$true = $true,
inference(unfold_def,[status(thm)],[16]) ).
thf(39,plain,
$true = $true,
inference(unfold_def,[status(thm)],[17]) ).
thf(40,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
<=> ( subset @ C @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(41,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(42,plain,
( ( ! [SY39: $i,SY40: $i,SY41: $i] :
( ( relation_of2_as_subset @ SY41 @ SY40 @ sK1_A )
=> ( ( subset @ ( relation_rng @ SY41 ) @ SY39 )
=> ( relation_of2_as_subset @ SY41 @ SY40 @ SY39 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[22]) ).
thf(43,plain,
( ( ! [SY42: $i,SY43: $i] :
( ( relation_of2_as_subset @ SY43 @ SY42 @ sK1_A )
=> ( ( subset @ ( relation_rng @ SY43 ) @ sK2_SY39 )
=> ( relation_of2_as_subset @ SY43 @ SY42 @ sK2_SY39 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[42]) ).
thf(44,plain,
( ( ! [SY44: $i] :
( ( relation_of2_as_subset @ SY44 @ sK3_SY42 @ sK1_A )
=> ( ( subset @ ( relation_rng @ SY44 ) @ sK2_SY39 )
=> ( relation_of2_as_subset @ SY44 @ sK3_SY42 @ sK2_SY39 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[43]) ).
thf(45,plain,
( ( ( relation_of2_as_subset @ sK4_SY44 @ sK3_SY42 @ sK1_A )
=> ( ( subset @ ( relation_rng @ sK4_SY44 ) @ sK2_SY39 )
=> ( relation_of2_as_subset @ sK4_SY44 @ sK3_SY42 @ sK2_SY39 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(46,plain,
( ( relation_of2_as_subset @ sK4_SY44 @ sK3_SY42 @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[45]) ).
thf(47,plain,
( ( subset @ ( relation_rng @ sK4_SY44 ) @ sK2_SY39 )
= $true ),
inference(standard_cnf,[status(thm)],[45]) ).
thf(48,plain,
( ( relation_of2_as_subset @ sK4_SY44 @ sK3_SY42 @ sK2_SY39 )
= $false ),
inference(standard_cnf,[status(thm)],[45]) ).
thf(49,plain,
( ( ~ ( relation_of2_as_subset @ sK4_SY44 @ sK3_SY42 @ sK2_SY39 ) )
= $true ),
inference(polarity_switch,[status(thm)],[48]) ).
thf(50,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(51,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(52,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(53,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( subset @ ( relation_dom @ C ) @ A ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( subset @ ( relation_rng @ C ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(54,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(55,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(56,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(57,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK5_C @ B @ A ) @ A @ B ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(58,plain,
( ( ! [A: $i] : ( element @ ( sK6_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(59,plain,
( ( ! [A: $i,B: $i] : ( relation_of2 @ ( sK7_C @ B @ A ) @ A @ B ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(60,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(61,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( subset @ C @ ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ C @ ( cartesian_product2 @ A @ B ) )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(62,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
| ( relation @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(63,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
| ( relation @ C ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(64,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( subset @ C @ ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ C @ ( cartesian_product2 @ A @ B ) )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(65,plain,
$true = $true,
inference(copy,[status(thm)],[39]) ).
thf(66,plain,
$true = $true,
inference(copy,[status(thm)],[38]) ).
thf(67,plain,
$true = $true,
inference(copy,[status(thm)],[37]) ).
thf(68,plain,
$true = $true,
inference(copy,[status(thm)],[36]) ).
thf(69,plain,
$true = $true,
inference(copy,[status(thm)],[35]) ).
thf(70,plain,
$true = $true,
inference(copy,[status(thm)],[34]) ).
thf(71,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(72,plain,
( ( ! [A: $i,B: $i] : ( relation_of2 @ ( sK7_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(73,plain,
( ( ! [A: $i] : ( element @ ( sK6_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(74,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK5_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(75,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(76,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(77,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(78,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( subset @ ( relation_dom @ C ) @ A ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( subset @ ( relation_rng @ C ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(79,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(80,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( subset @ A @ ( cartesian_product2 @ ( relation_dom @ A ) @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(81,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(82,plain,
( ( subset @ ( relation_rng @ sK4_SY44 ) @ sK2_SY39 )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(83,plain,
( ( relation_of2_as_subset @ sK4_SY44 @ sK3_SY42 @ sK1_A )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(84,plain,
( ( ~ ( relation_of2_as_subset @ sK4_SY44 @ sK3_SY42 @ sK2_SY39 ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(85,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( subset @ SX2 @ ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartesian_product2 @ SX0 @ SX1 ) )
| ( relation_of2 @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(86,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( relation_of2 @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(87,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(88,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( subset @ ( relation_dom @ SX2 ) @ SX0 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( subset @ ( relation_rng @ SX2 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(89,plain,
! [SV1: $i] :
( ( ! [SY45: $i,SY46: $i] :
( ~ ( element @ SY46 @ ( powerset @ ( cartesian_product2 @ SV1 @ SY45 ) ) )
| ( relation @ SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(90,plain,
! [SV2: $i] :
( ( ! [SY47: $i,SY48: $i] :
( ~ ( relation_of2_as_subset @ SY48 @ SV2 @ SY47 )
| ( element @ SY48 @ ( powerset @ ( cartesian_product2 @ SV2 @ SY47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(91,plain,
! [SV3: $i] :
( ( ! [SY49: $i] : ( relation_of2 @ ( sK7_C @ SY49 @ SV3 ) @ SV3 @ SY49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(92,plain,
! [SV4: $i] :
( ( element @ ( sK6_B @ SV4 ) @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(93,plain,
! [SV5: $i] :
( ( ! [SY50: $i] : ( relation_of2_as_subset @ ( sK5_C @ SY50 @ SV5 ) @ SV5 @ SY50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(94,plain,
! [SV6: $i] :
( ( subset @ SV6 @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(95,plain,
! [SV7: $i] :
( ( ! [SY51: $i,SY52: $i,SY53: $i] :
( ~ ( subset @ SV7 @ SY51 )
| ~ ( subset @ SY52 @ SY53 )
| ( subset @ ( cartesian_product2 @ SV7 @ SY52 ) @ ( cartesian_product2 @ SY51 @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(96,plain,
! [SV8: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ~ ( subset @ SV8 @ SY54 )
| ~ ( subset @ SY54 @ SY55 )
| ( subset @ SV8 @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(97,plain,
! [SV9: $i] :
( ( ~ ( relation @ SV9 )
| ( subset @ SV9 @ ( cartesian_product2 @ ( relation_dom @ SV9 ) @ ( relation_rng @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(98,plain,
( ( relation_of2_as_subset @ sK4_SY44 @ sK3_SY42 @ sK2_SY39 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(99,plain,
! [SV10: $i] :
( ( ~ ( ~ ! [SY56: $i,SY57: $i] :
( ~ ( relation_of2 @ SY57 @ SV10 @ SY56 )
| ( subset @ SY57 @ ( cartesian_product2 @ SV10 @ SY56 ) ) )
| ~ ! [SY58: $i,SY59: $i] :
( ~ ( subset @ SY59 @ ( cartesian_product2 @ SV10 @ SY58 ) )
| ( relation_of2 @ SY59 @ SV10 @ SY58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(100,plain,
! [SV11: $i] :
( ( ~ ( ~ ! [SY60: $i,SY61: $i] :
( ~ ( relation_of2 @ SY61 @ SV11 @ SY60 )
| ( relation_of2_as_subset @ SY61 @ SV11 @ SY60 ) )
| ~ ! [SY62: $i,SY63: $i] :
( ~ ( relation_of2_as_subset @ SY63 @ SV11 @ SY62 )
| ( relation_of2 @ SY63 @ SV11 @ SY62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(101,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(102,plain,
! [SV12: $i] :
( ( ~ ( ~ ! [SY64: $i,SY65: $i] :
( ~ ( relation_of2_as_subset @ SY65 @ SV12 @ SY64 )
| ( subset @ ( relation_dom @ SY65 ) @ SV12 ) )
| ~ ! [SY66: $i,SY67: $i] :
( ~ ( relation_of2_as_subset @ SY67 @ SV12 @ SY66 )
| ( subset @ ( relation_rng @ SY67 ) @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(103,plain,
! [SV13: $i,SV1: $i] :
( ( ! [SY68: $i] :
( ~ ( element @ SY68 @ ( powerset @ ( cartesian_product2 @ SV1 @ SV13 ) ) )
| ( relation @ SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(104,plain,
! [SV14: $i,SV2: $i] :
( ( ! [SY69: $i] :
( ~ ( relation_of2_as_subset @ SY69 @ SV2 @ SV14 )
| ( element @ SY69 @ ( powerset @ ( cartesian_product2 @ SV2 @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(105,plain,
! [SV3: $i,SV15: $i] :
( ( relation_of2 @ ( sK7_C @ SV15 @ SV3 ) @ SV3 @ SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(106,plain,
! [SV5: $i,SV16: $i] :
( ( relation_of2_as_subset @ ( sK5_C @ SV16 @ SV5 ) @ SV5 @ SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(107,plain,
! [SV17: $i,SV7: $i] :
( ( ! [SY70: $i,SY71: $i] :
( ~ ( subset @ SV7 @ SV17 )
| ~ ( subset @ SY70 @ SY71 )
| ( subset @ ( cartesian_product2 @ SV7 @ SY70 ) @ ( cartesian_product2 @ SV17 @ SY71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(108,plain,
! [SV18: $i,SV8: $i] :
( ( ! [SY72: $i] :
( ~ ( subset @ SV8 @ SV18 )
| ~ ( subset @ SV18 @ SY72 )
| ( subset @ SV8 @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(109,plain,
! [SV9: $i] :
( ( ( ~ ( relation @ SV9 ) )
= $true )
| ( ( subset @ SV9 @ ( cartesian_product2 @ ( relation_dom @ SV9 ) @ ( relation_rng @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(110,plain,
! [SV10: $i] :
( ( ~ ! [SY56: $i,SY57: $i] :
( ~ ( relation_of2 @ SY57 @ SV10 @ SY56 )
| ( subset @ SY57 @ ( cartesian_product2 @ SV10 @ SY56 ) ) )
| ~ ! [SY58: $i,SY59: $i] :
( ~ ( subset @ SY59 @ ( cartesian_product2 @ SV10 @ SY58 ) )
| ( relation_of2 @ SY59 @ SV10 @ SY58 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(111,plain,
! [SV11: $i] :
( ( ~ ! [SY60: $i,SY61: $i] :
( ~ ( relation_of2 @ SY61 @ SV11 @ SY60 )
| ( relation_of2_as_subset @ SY61 @ SV11 @ SY60 ) )
| ~ ! [SY62: $i,SY63: $i] :
( ~ ( relation_of2_as_subset @ SY63 @ SV11 @ SY62 )
| ( relation_of2 @ SY63 @ SV11 @ SY62 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(112,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(113,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(114,plain,
! [SV12: $i] :
( ( ~ ! [SY64: $i,SY65: $i] :
( ~ ( relation_of2_as_subset @ SY65 @ SV12 @ SY64 )
| ( subset @ ( relation_dom @ SY65 ) @ SV12 ) )
| ~ ! [SY66: $i,SY67: $i] :
( ~ ( relation_of2_as_subset @ SY67 @ SV12 @ SY66 )
| ( subset @ ( relation_rng @ SY67 ) @ SY66 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(115,plain,
! [SV13: $i,SV1: $i,SV19: $i] :
( ( ~ ( element @ SV19 @ ( powerset @ ( cartesian_product2 @ SV1 @ SV13 ) ) )
| ( relation @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(116,plain,
! [SV14: $i,SV2: $i,SV20: $i] :
( ( ~ ( relation_of2_as_subset @ SV20 @ SV2 @ SV14 )
| ( element @ SV20 @ ( powerset @ ( cartesian_product2 @ SV2 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(117,plain,
! [SV21: $i,SV17: $i,SV7: $i] :
( ( ! [SY73: $i] :
( ~ ( subset @ SV7 @ SV17 )
| ~ ( subset @ SV21 @ SY73 )
| ( subset @ ( cartesian_product2 @ SV7 @ SV21 ) @ ( cartesian_product2 @ SV17 @ SY73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(118,plain,
! [SV22: $i,SV18: $i,SV8: $i] :
( ( ~ ( subset @ SV8 @ SV18 )
| ~ ( subset @ SV18 @ SV22 )
| ( subset @ SV8 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(119,plain,
! [SV9: $i] :
( ( ( relation @ SV9 )
= $false )
| ( ( subset @ SV9 @ ( cartesian_product2 @ ( relation_dom @ SV9 ) @ ( relation_rng @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(120,plain,
! [SV10: $i] :
( ( ~ ! [SY56: $i,SY57: $i] :
( ~ ( relation_of2 @ SY57 @ SV10 @ SY56 )
| ( subset @ SY57 @ ( cartesian_product2 @ SV10 @ SY56 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(121,plain,
! [SV10: $i] :
( ( ~ ! [SY58: $i,SY59: $i] :
( ~ ( subset @ SY59 @ ( cartesian_product2 @ SV10 @ SY58 ) )
| ( relation_of2 @ SY59 @ SV10 @ SY58 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(122,plain,
! [SV11: $i] :
( ( ~ ! [SY60: $i,SY61: $i] :
( ~ ( relation_of2 @ SY61 @ SV11 @ SY60 )
| ( relation_of2_as_subset @ SY61 @ SV11 @ SY60 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(123,plain,
! [SV11: $i] :
( ( ~ ! [SY62: $i,SY63: $i] :
( ~ ( relation_of2_as_subset @ SY63 @ SV11 @ SY62 )
| ( relation_of2 @ SY63 @ SV11 @ SY62 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(124,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(125,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(126,plain,
! [SV12: $i] :
( ( ~ ! [SY64: $i,SY65: $i] :
( ~ ( relation_of2_as_subset @ SY65 @ SV12 @ SY64 )
| ( subset @ ( relation_dom @ SY65 ) @ SV12 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(127,plain,
! [SV12: $i] :
( ( ~ ! [SY66: $i,SY67: $i] :
( ~ ( relation_of2_as_subset @ SY67 @ SV12 @ SY66 )
| ( subset @ ( relation_rng @ SY67 ) @ SY66 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[114]) ).
thf(128,plain,
! [SV13: $i,SV1: $i,SV19: $i] :
( ( ( ~ ( element @ SV19 @ ( powerset @ ( cartesian_product2 @ SV1 @ SV13 ) ) ) )
= $true )
| ( ( relation @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(129,plain,
! [SV14: $i,SV2: $i,SV20: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV20 @ SV2 @ SV14 ) )
= $true )
| ( ( element @ SV20 @ ( powerset @ ( cartesian_product2 @ SV2 @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(130,plain,
! [SV23: $i,SV21: $i,SV17: $i,SV7: $i] :
( ( ~ ( subset @ SV7 @ SV17 )
| ~ ( subset @ SV21 @ SV23 )
| ( subset @ ( cartesian_product2 @ SV7 @ SV21 ) @ ( cartesian_product2 @ SV17 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(131,plain,
! [SV22: $i,SV18: $i,SV8: $i] :
( ( ( ~ ( subset @ SV8 @ SV18 )
| ~ ( subset @ SV18 @ SV22 ) )
= $true )
| ( ( subset @ SV8 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(132,plain,
! [SV10: $i] :
( ( ! [SY56: $i,SY57: $i] :
( ~ ( relation_of2 @ SY57 @ SV10 @ SY56 )
| ( subset @ SY57 @ ( cartesian_product2 @ SV10 @ SY56 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(133,plain,
! [SV10: $i] :
( ( ! [SY58: $i,SY59: $i] :
( ~ ( subset @ SY59 @ ( cartesian_product2 @ SV10 @ SY58 ) )
| ( relation_of2 @ SY59 @ SV10 @ SY58 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(134,plain,
! [SV11: $i] :
( ( ! [SY60: $i,SY61: $i] :
( ~ ( relation_of2 @ SY61 @ SV11 @ SY60 )
| ( relation_of2_as_subset @ SY61 @ SV11 @ SY60 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(135,plain,
! [SV11: $i] :
( ( ! [SY62: $i,SY63: $i] :
( ~ ( relation_of2_as_subset @ SY63 @ SV11 @ SY62 )
| ( relation_of2 @ SY63 @ SV11 @ SY62 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(136,plain,
! [SV24: $i] :
( ( ! [SY74: $i] :
( ~ ( element @ SV24 @ ( powerset @ SY74 ) )
| ( subset @ SV24 @ SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(137,plain,
! [SV25: $i] :
( ( ! [SY75: $i] :
( ~ ( subset @ SV25 @ SY75 )
| ( element @ SV25 @ ( powerset @ SY75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(138,plain,
! [SV12: $i] :
( ( ! [SY64: $i,SY65: $i] :
( ~ ( relation_of2_as_subset @ SY65 @ SV12 @ SY64 )
| ( subset @ ( relation_dom @ SY65 ) @ SV12 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(139,plain,
! [SV12: $i] :
( ( ! [SY66: $i,SY67: $i] :
( ~ ( relation_of2_as_subset @ SY67 @ SV12 @ SY66 )
| ( subset @ ( relation_rng @ SY67 ) @ SY66 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(140,plain,
! [SV13: $i,SV1: $i,SV19: $i] :
( ( ( element @ SV19 @ ( powerset @ ( cartesian_product2 @ SV1 @ SV13 ) ) )
= $false )
| ( ( relation @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(141,plain,
! [SV14: $i,SV2: $i,SV20: $i] :
( ( ( relation_of2_as_subset @ SV20 @ SV2 @ SV14 )
= $false )
| ( ( element @ SV20 @ ( powerset @ ( cartesian_product2 @ SV2 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(142,plain,
! [SV23: $i,SV21: $i,SV17: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV17 )
| ~ ( subset @ SV21 @ SV23 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV7 @ SV21 ) @ ( cartesian_product2 @ SV17 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(143,plain,
! [SV22: $i,SV18: $i,SV8: $i] :
( ( ( ~ ( subset @ SV8 @ SV18 ) )
= $true )
| ( ( ~ ( subset @ SV18 @ SV22 ) )
= $true )
| ( ( subset @ SV8 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(144,plain,
! [SV26: $i,SV10: $i] :
( ( ! [SY76: $i] :
( ~ ( relation_of2 @ SY76 @ SV10 @ SV26 )
| ( subset @ SY76 @ ( cartesian_product2 @ SV10 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(145,plain,
! [SV27: $i,SV10: $i] :
( ( ! [SY77: $i] :
( ~ ( subset @ SY77 @ ( cartesian_product2 @ SV10 @ SV27 ) )
| ( relation_of2 @ SY77 @ SV10 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(146,plain,
! [SV28: $i,SV11: $i] :
( ( ! [SY78: $i] :
( ~ ( relation_of2 @ SY78 @ SV11 @ SV28 )
| ( relation_of2_as_subset @ SY78 @ SV11 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(147,plain,
! [SV29: $i,SV11: $i] :
( ( ! [SY79: $i] :
( ~ ( relation_of2_as_subset @ SY79 @ SV11 @ SV29 )
| ( relation_of2 @ SY79 @ SV11 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(148,plain,
! [SV30: $i,SV24: $i] :
( ( ~ ( element @ SV24 @ ( powerset @ SV30 ) )
| ( subset @ SV24 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(149,plain,
! [SV31: $i,SV25: $i] :
( ( ~ ( subset @ SV25 @ SV31 )
| ( element @ SV25 @ ( powerset @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(150,plain,
! [SV32: $i,SV12: $i] :
( ( ! [SY80: $i] :
( ~ ( relation_of2_as_subset @ SY80 @ SV12 @ SV32 )
| ( subset @ ( relation_dom @ SY80 ) @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(151,plain,
! [SV33: $i,SV12: $i] :
( ( ! [SY81: $i] :
( ~ ( relation_of2_as_subset @ SY81 @ SV12 @ SV33 )
| ( subset @ ( relation_rng @ SY81 ) @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(152,plain,
! [SV23: $i,SV21: $i,SV17: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV17 ) )
= $true )
| ( ( ~ ( subset @ SV21 @ SV23 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV7 @ SV21 ) @ ( cartesian_product2 @ SV17 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(153,plain,
! [SV22: $i,SV18: $i,SV8: $i] :
( ( ( subset @ SV8 @ SV18 )
= $false )
| ( ( ~ ( subset @ SV18 @ SV22 ) )
= $true )
| ( ( subset @ SV8 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(154,plain,
! [SV26: $i,SV10: $i,SV34: $i] :
( ( ~ ( relation_of2 @ SV34 @ SV10 @ SV26 )
| ( subset @ SV34 @ ( cartesian_product2 @ SV10 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(155,plain,
! [SV27: $i,SV10: $i,SV35: $i] :
( ( ~ ( subset @ SV35 @ ( cartesian_product2 @ SV10 @ SV27 ) )
| ( relation_of2 @ SV35 @ SV10 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(156,plain,
! [SV28: $i,SV11: $i,SV36: $i] :
( ( ~ ( relation_of2 @ SV36 @ SV11 @ SV28 )
| ( relation_of2_as_subset @ SV36 @ SV11 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(157,plain,
! [SV29: $i,SV11: $i,SV37: $i] :
( ( ~ ( relation_of2_as_subset @ SV37 @ SV11 @ SV29 )
| ( relation_of2 @ SV37 @ SV11 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(158,plain,
! [SV30: $i,SV24: $i] :
( ( ( ~ ( element @ SV24 @ ( powerset @ SV30 ) ) )
= $true )
| ( ( subset @ SV24 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(159,plain,
! [SV31: $i,SV25: $i] :
( ( ( ~ ( subset @ SV25 @ SV31 ) )
= $true )
| ( ( element @ SV25 @ ( powerset @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(160,plain,
! [SV32: $i,SV12: $i,SV38: $i] :
( ( ~ ( relation_of2_as_subset @ SV38 @ SV12 @ SV32 )
| ( subset @ ( relation_dom @ SV38 ) @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(161,plain,
! [SV33: $i,SV12: $i,SV39: $i] :
( ( ~ ( relation_of2_as_subset @ SV39 @ SV12 @ SV33 )
| ( subset @ ( relation_rng @ SV39 ) @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(162,plain,
! [SV23: $i,SV21: $i,SV17: $i,SV7: $i] :
( ( ( subset @ SV7 @ SV17 )
= $false )
| ( ( ~ ( subset @ SV21 @ SV23 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV7 @ SV21 ) @ ( cartesian_product2 @ SV17 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(163,plain,
! [SV8: $i,SV22: $i,SV18: $i] :
( ( ( subset @ SV18 @ SV22 )
= $false )
| ( ( subset @ SV8 @ SV18 )
= $false )
| ( ( subset @ SV8 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(164,plain,
! [SV26: $i,SV10: $i,SV34: $i] :
( ( ( ~ ( relation_of2 @ SV34 @ SV10 @ SV26 ) )
= $true )
| ( ( subset @ SV34 @ ( cartesian_product2 @ SV10 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(165,plain,
! [SV27: $i,SV10: $i,SV35: $i] :
( ( ( ~ ( subset @ SV35 @ ( cartesian_product2 @ SV10 @ SV27 ) ) )
= $true )
| ( ( relation_of2 @ SV35 @ SV10 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(166,plain,
! [SV28: $i,SV11: $i,SV36: $i] :
( ( ( ~ ( relation_of2 @ SV36 @ SV11 @ SV28 ) )
= $true )
| ( ( relation_of2_as_subset @ SV36 @ SV11 @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(167,plain,
! [SV29: $i,SV11: $i,SV37: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV37 @ SV11 @ SV29 ) )
= $true )
| ( ( relation_of2 @ SV37 @ SV11 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(168,plain,
! [SV30: $i,SV24: $i] :
( ( ( element @ SV24 @ ( powerset @ SV30 ) )
= $false )
| ( ( subset @ SV24 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(169,plain,
! [SV31: $i,SV25: $i] :
( ( ( subset @ SV25 @ SV31 )
= $false )
| ( ( element @ SV25 @ ( powerset @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(170,plain,
! [SV32: $i,SV12: $i,SV38: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV38 @ SV12 @ SV32 ) )
= $true )
| ( ( subset @ ( relation_dom @ SV38 ) @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(171,plain,
! [SV33: $i,SV12: $i,SV39: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV39 @ SV12 @ SV33 ) )
= $true )
| ( ( subset @ ( relation_rng @ SV39 ) @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(172,plain,
! [SV17: $i,SV7: $i,SV23: $i,SV21: $i] :
( ( ( subset @ SV21 @ SV23 )
= $false )
| ( ( subset @ SV7 @ SV17 )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV7 @ SV21 ) @ ( cartesian_product2 @ SV17 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(173,plain,
! [SV26: $i,SV10: $i,SV34: $i] :
( ( ( relation_of2 @ SV34 @ SV10 @ SV26 )
= $false )
| ( ( subset @ SV34 @ ( cartesian_product2 @ SV10 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(174,plain,
! [SV27: $i,SV10: $i,SV35: $i] :
( ( ( subset @ SV35 @ ( cartesian_product2 @ SV10 @ SV27 ) )
= $false )
| ( ( relation_of2 @ SV35 @ SV10 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(175,plain,
! [SV28: $i,SV11: $i,SV36: $i] :
( ( ( relation_of2 @ SV36 @ SV11 @ SV28 )
= $false )
| ( ( relation_of2_as_subset @ SV36 @ SV11 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(176,plain,
! [SV29: $i,SV11: $i,SV37: $i] :
( ( ( relation_of2_as_subset @ SV37 @ SV11 @ SV29 )
= $false )
| ( ( relation_of2 @ SV37 @ SV11 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(177,plain,
! [SV32: $i,SV12: $i,SV38: $i] :
( ( ( relation_of2_as_subset @ SV38 @ SV12 @ SV32 )
= $false )
| ( ( subset @ ( relation_dom @ SV38 ) @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(178,plain,
! [SV33: $i,SV12: $i,SV39: $i] :
( ( ( relation_of2_as_subset @ SV39 @ SV12 @ SV33 )
= $false )
| ( ( subset @ ( relation_rng @ SV39 ) @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(179,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[65,178,177,176,175,174,173,172,169,168,163,141,140,119,106,105,98,94,92,83,82,70,69,68,67,66]) ).
thf(180,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU263+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 20:39:31 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 19
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.36 (rf:0,axioms:19,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:21,loop_count:0,foatp_calls:0,translation:fof_full).........
% 0.81/1.00
% 0.81/1.00 ********************************
% 0.81/1.00 * All subproblems solved! *
% 0.81/1.00 ********************************
% 0.81/1.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:21,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:179,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.81/1.00
% 0.81/1.00 %**** Beginning of derivation protocol ****
% 0.81/1.00 % SZS output start CNFRefutation
% See solution above
% 0.81/1.01
% 0.81/1.01 %**** End of derivation protocol ****
% 0.81/1.01 %**** no. of clauses in derivation: 180 ****
% 0.81/1.01 %**** clause counter: 179 ****
% 0.81/1.01
% 0.81/1.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:21,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:179,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------