TSTP Solution File: TOP004-2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : TOP004-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n021.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 : Thu Jul 21 21:31:40 EDT 2022
% Result : Unsatisfiable 0.19s 0.50s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 35
% Syntax : Number of formulae : 231 ( 111 unt; 13 typ; 0 def)
% Number of atoms : 1510 ( 381 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 3196 ( 394 ~; 530 |; 0 &;2272 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 4 con; 0-5 aty)
% Number of variables : 707 ( 0 ^ 707 !; 0 ?; 707 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_basis,type,
basis: $i > $i > $o ).
thf(tp_cx,type,
cx: $i ).
thf(tp_element_of_collection,type,
element_of_collection: $i > $i > $o ).
thf(tp_element_of_set,type,
element_of_set: $i > $i > $o ).
thf(tp_equal_sets,type,
equal_sets: $i > $i > $o ).
thf(tp_f,type,
f: $i ).
thf(tp_f10,type,
f10: $i > $i > $i > $i ).
thf(tp_f11,type,
f11: $i > $i > $i ).
thf(tp_f6,type,
f6: $i > $i > $i > $i > $i > $i ).
thf(tp_intersection_of_sets,type,
intersection_of_sets: $i > $i > $i ).
thf(tp_subset_sets,type,
subset_sets: $i > $i > $o ).
thf(tp_top_of_basis,type,
top_of_basis: $i > $i ).
thf(tp_union_of_members,type,
union_of_members: $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i] : ( equal_sets @ ( intersection_of_sets @ X @ Y ) @ ( intersection_of_sets @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_18) ).
thf(2,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( equal_sets @ X @ Y )
| ~ ( element_of_set @ Z @ X )
| ( element_of_set @ Z @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_17) ).
thf(3,axiom,
! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( subset_sets @ X @ Y )
| ~ ( subset_sets @ U @ V )
| ( subset_sets @ ( intersection_of_sets @ X @ U ) @ ( intersection_of_sets @ Y @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_16) ).
thf(4,axiom,
! [Z: $i,X: $i,Y: $i] :
( ( element_of_set @ Z @ ( intersection_of_sets @ X @ Y ) )
| ~ ( element_of_set @ Z @ X )
| ~ ( element_of_set @ Z @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_15) ).
thf(5,axiom,
! [Z: $i,X: $i,Y: $i] :
( ~ ( element_of_set @ Z @ ( intersection_of_sets @ X @ Y ) )
| ( element_of_set @ Z @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_14) ).
thf(6,axiom,
! [Z: $i,X: $i,Y: $i] :
( ~ ( element_of_set @ Z @ ( intersection_of_sets @ X @ Y ) )
| ( element_of_set @ Z @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_13) ).
thf(7,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( subset_sets @ X @ Y )
| ~ ( subset_sets @ Y @ Z )
| ( subset_sets @ X @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_12) ).
thf(8,axiom,
! [U: $i,Vf: $i,Uu11: $i] :
( ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ~ ( element_of_set @ ( f11 @ Vf @ U ) @ Uu11 )
| ~ ( element_of_collection @ Uu11 @ Vf )
| ~ ( subset_sets @ Uu11 @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topology_generated_41) ).
thf(9,axiom,
! [U: $i,Vf: $i] :
( ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ( element_of_set @ ( f11 @ Vf @ U ) @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topology_generated_40) ).
thf(10,axiom,
! [U: $i,Vf: $i,X: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ~ ( element_of_set @ X @ U )
| ( subset_sets @ ( f10 @ Vf @ U @ X ) @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topology_generated_39) ).
thf(11,axiom,
! [U: $i,Vf: $i,X: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ~ ( element_of_set @ X @ U )
| ( element_of_collection @ ( f10 @ Vf @ U @ X ) @ Vf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topology_generated_38) ).
thf(12,axiom,
! [U: $i,Vf: $i,X: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ~ ( element_of_set @ X @ U )
| ( element_of_set @ X @ ( f10 @ Vf @ U @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topology_generated_37) ).
thf(13,axiom,
! [X: $i,Vf: $i,Y: $i,Vb1: $i,Vb2: $i] :
( ~ ( basis @ X @ Vf )
| ~ ( element_of_set @ Y @ X )
| ~ ( element_of_collection @ Vb1 @ Vf )
| ~ ( element_of_collection @ Vb2 @ Vf )
| ~ ( element_of_set @ Y @ ( intersection_of_sets @ Vb1 @ Vb2 ) )
| ( subset_sets @ ( f6 @ X @ Vf @ Y @ Vb1 @ Vb2 ) @ ( intersection_of_sets @ Vb1 @ Vb2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_for_topology_31) ).
thf(14,axiom,
! [X: $i,Vf: $i,Y: $i,Vb1: $i,Vb2: $i] :
( ~ ( basis @ X @ Vf )
| ~ ( element_of_set @ Y @ X )
| ~ ( element_of_collection @ Vb1 @ Vf )
| ~ ( element_of_collection @ Vb2 @ Vf )
| ~ ( element_of_set @ Y @ ( intersection_of_sets @ Vb1 @ Vb2 ) )
| ( element_of_collection @ ( f6 @ X @ Vf @ Y @ Vb1 @ Vb2 ) @ Vf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_for_topology_30) ).
thf(15,axiom,
! [X: $i,Vf: $i,Y: $i,Vb1: $i,Vb2: $i] :
( ~ ( basis @ X @ Vf )
| ~ ( element_of_set @ Y @ X )
| ~ ( element_of_collection @ Vb1 @ Vf )
| ~ ( element_of_collection @ Vb2 @ Vf )
| ~ ( element_of_set @ Y @ ( intersection_of_sets @ Vb1 @ Vb2 ) )
| ( element_of_set @ Y @ ( f6 @ X @ Vf @ Y @ Vb1 @ Vb2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_for_topology_29) ).
thf(16,axiom,
! [X: $i,Vf: $i] :
( ~ ( basis @ X @ Vf )
| ( equal_sets @ ( union_of_members @ Vf ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_for_topology_28) ).
thf(17,axiom,
! [U: $i,Vf: $i,Uu1: $i] :
( ( element_of_set @ U @ ( union_of_members @ Vf ) )
| ~ ( element_of_set @ U @ Uu1 )
| ~ ( element_of_collection @ Uu1 @ Vf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_of_members_3) ).
thf(18,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(19,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[18]) ).
thf(20,negated_conjecture,
! [U: $i,V: $i] :
~ ( element_of_collection @ ( intersection_of_sets @ U @ V ) @ ( top_of_basis @ f ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1d_4) ).
thf(21,negated_conjecture,
! [V: $i] : ( element_of_collection @ V @ ( top_of_basis @ f ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1d_3) ).
thf(22,negated_conjecture,
! [U: $i] : ( element_of_collection @ U @ ( top_of_basis @ f ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1d_2) ).
thf(23,negated_conjecture,
basis @ cx @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1d_1) ).
thf(24,plain,
$false = $false,
inference(unfold_def,[status(thm)],[19]) ).
thf(25,plain,
( ( ! [X: $i,Y: $i] : ( equal_sets @ ( intersection_of_sets @ X @ Y ) @ ( intersection_of_sets @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(26,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equal_sets @ X @ Y )
| ~ ( element_of_set @ Z @ X )
| ( element_of_set @ Z @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ~ ( subset_sets @ X @ Y )
| ~ ( subset_sets @ U @ V )
| ( subset_sets @ ( intersection_of_sets @ X @ U ) @ ( intersection_of_sets @ Y @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(28,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ( element_of_set @ Z @ ( intersection_of_sets @ X @ Y ) )
| ~ ( element_of_set @ Z @ X )
| ~ ( element_of_set @ Z @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(29,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( element_of_set @ Z @ ( intersection_of_sets @ X @ Y ) )
| ( element_of_set @ Z @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(30,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( element_of_set @ Z @ ( intersection_of_sets @ X @ Y ) )
| ( element_of_set @ Z @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(31,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( subset_sets @ X @ Y )
| ~ ( subset_sets @ Y @ Z )
| ( subset_sets @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(32,plain,
( ( ! [U: $i,Vf: $i,Uu11: $i] :
( ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ~ ( element_of_set @ ( f11 @ Vf @ U ) @ Uu11 )
| ~ ( element_of_collection @ Uu11 @ Vf )
| ~ ( subset_sets @ Uu11 @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(33,plain,
( ( ! [U: $i,Vf: $i] :
( ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ( element_of_set @ ( f11 @ Vf @ U ) @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(34,plain,
( ( ! [U: $i,Vf: $i,X: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ~ ( element_of_set @ X @ U )
| ( subset_sets @ ( f10 @ Vf @ U @ X ) @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(35,plain,
( ( ! [U: $i,Vf: $i,X: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ~ ( element_of_set @ X @ U )
| ( element_of_collection @ ( f10 @ Vf @ U @ X ) @ Vf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(36,plain,
( ( ! [U: $i,Vf: $i,X: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ~ ( element_of_set @ X @ U )
| ( element_of_set @ X @ ( f10 @ Vf @ U @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(37,plain,
( ( ! [X: $i,Vf: $i,Y: $i,Vb1: $i,Vb2: $i] :
( ~ ( basis @ X @ Vf )
| ~ ( element_of_set @ Y @ X )
| ~ ( element_of_collection @ Vb1 @ Vf )
| ~ ( element_of_collection @ Vb2 @ Vf )
| ~ ( element_of_set @ Y @ ( intersection_of_sets @ Vb1 @ Vb2 ) )
| ( subset_sets @ ( f6 @ X @ Vf @ Y @ Vb1 @ Vb2 ) @ ( intersection_of_sets @ Vb1 @ Vb2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(38,plain,
( ( ! [X: $i,Vf: $i,Y: $i,Vb1: $i,Vb2: $i] :
( ~ ( basis @ X @ Vf )
| ~ ( element_of_set @ Y @ X )
| ~ ( element_of_collection @ Vb1 @ Vf )
| ~ ( element_of_collection @ Vb2 @ Vf )
| ~ ( element_of_set @ Y @ ( intersection_of_sets @ Vb1 @ Vb2 ) )
| ( element_of_collection @ ( f6 @ X @ Vf @ Y @ Vb1 @ Vb2 ) @ Vf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(39,plain,
( ( ! [X: $i,Vf: $i,Y: $i,Vb1: $i,Vb2: $i] :
( ~ ( basis @ X @ Vf )
| ~ ( element_of_set @ Y @ X )
| ~ ( element_of_collection @ Vb1 @ Vf )
| ~ ( element_of_collection @ Vb2 @ Vf )
| ~ ( element_of_set @ Y @ ( intersection_of_sets @ Vb1 @ Vb2 ) )
| ( element_of_set @ Y @ ( f6 @ X @ Vf @ Y @ Vb1 @ Vb2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(40,plain,
( ( ! [X: $i,Vf: $i] :
( ~ ( basis @ X @ Vf )
| ( equal_sets @ ( union_of_members @ Vf ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(41,plain,
( ( ! [U: $i,Vf: $i,Uu1: $i] :
( ( element_of_set @ U @ ( union_of_members @ Vf ) )
| ~ ( element_of_set @ U @ Uu1 )
| ~ ( element_of_collection @ Uu1 @ Vf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(42,plain,
( ( ! [U: $i,V: $i] :
~ ( element_of_collection @ ( intersection_of_sets @ U @ V ) @ ( top_of_basis @ f ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(43,plain,
( ( ! [V: $i] : ( element_of_collection @ V @ ( top_of_basis @ f ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(44,plain,
( ( ! [U: $i] : ( element_of_collection @ U @ ( top_of_basis @ f ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(45,plain,
( ( basis @ cx @ f )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(46,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[24]) ).
thf(47,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equal_sets @ X @ Y )
| ! [Z: $i] :
( ~ ( element_of_set @ Z @ X )
| ( element_of_set @ Z @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(48,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( subset_sets @ X @ Y )
| ! [U: $i,V: $i] :
( ~ ( subset_sets @ U @ V )
| ( subset_sets @ ( intersection_of_sets @ X @ U ) @ ( intersection_of_sets @ Y @ V ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(49,plain,
( ( ! [Z: $i,X: $i] :
( ! [Y: $i] :
~ ( element_of_set @ Z @ ( intersection_of_sets @ X @ Y ) )
| ( element_of_set @ Z @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(50,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( subset_sets @ X @ Y )
| ! [Z: $i] :
( ~ ( subset_sets @ Y @ Z )
| ( subset_sets @ X @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(51,plain,
( ( ! [U: $i,Vf: $i] :
( ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ! [Uu11: $i] :
( ~ ( element_of_set @ ( f11 @ Vf @ U ) @ Uu11 )
| ~ ( element_of_collection @ Uu11 @ Vf )
| ~ ( subset_sets @ Uu11 @ U ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(52,plain,
( ( ! [U: $i,Vf: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ! [X: $i] :
( ~ ( element_of_set @ X @ U )
| ( subset_sets @ ( f10 @ Vf @ U @ X ) @ U ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(53,plain,
( ( ! [U: $i,Vf: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ! [X: $i] :
( ~ ( element_of_set @ X @ U )
| ( element_of_collection @ ( f10 @ Vf @ U @ X ) @ Vf ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(54,plain,
( ( ! [U: $i,Vf: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ! [X: $i] :
( ~ ( element_of_set @ X @ U )
| ( element_of_set @ X @ ( f10 @ Vf @ U @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(55,plain,
( ( ! [X: $i,Vf: $i,Y: $i] :
( ~ ( basis @ X @ Vf )
| ~ ( element_of_set @ Y @ X )
| ! [Vb1: $i] :
( ~ ( element_of_collection @ Vb1 @ Vf )
| ! [Vb2: $i] :
( ~ ( element_of_collection @ Vb2 @ Vf )
| ~ ( element_of_set @ Y @ ( intersection_of_sets @ Vb1 @ Vb2 ) )
| ( subset_sets @ ( f6 @ X @ Vf @ Y @ Vb1 @ Vb2 ) @ ( intersection_of_sets @ Vb1 @ Vb2 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(56,plain,
( ( ! [X: $i,Vf: $i,Y: $i] :
( ~ ( basis @ X @ Vf )
| ~ ( element_of_set @ Y @ X )
| ! [Vb1: $i] :
( ~ ( element_of_collection @ Vb1 @ Vf )
| ! [Vb2: $i] :
( ~ ( element_of_collection @ Vb2 @ Vf )
| ~ ( element_of_set @ Y @ ( intersection_of_sets @ Vb1 @ Vb2 ) )
| ( element_of_collection @ ( f6 @ X @ Vf @ Y @ Vb1 @ Vb2 ) @ Vf ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(57,plain,
( ( ! [X: $i,Vf: $i,Y: $i] :
( ~ ( basis @ X @ Vf )
| ~ ( element_of_set @ Y @ X )
| ! [Vb1: $i] :
( ~ ( element_of_collection @ Vb1 @ Vf )
| ! [Vb2: $i] :
( ~ ( element_of_collection @ Vb2 @ Vf )
| ~ ( element_of_set @ Y @ ( intersection_of_sets @ Vb1 @ Vb2 ) )
| ( element_of_set @ Y @ ( f6 @ X @ Vf @ Y @ Vb1 @ Vb2 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(58,plain,
( ( ! [U: $i,Vf: $i] :
( ( element_of_set @ U @ ( union_of_members @ Vf ) )
| ! [Uu1: $i] :
( ~ ( element_of_set @ U @ Uu1 )
| ~ ( element_of_collection @ Uu1 @ Vf ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(59,plain,
( ( basis @ cx @ f )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(60,plain,
( ( ! [U: $i] : ( element_of_collection @ U @ ( top_of_basis @ f ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(61,plain,
( ( ! [V: $i] : ( element_of_collection @ V @ ( top_of_basis @ f ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(62,plain,
( ( ! [U: $i,V: $i] :
~ ( element_of_collection @ ( intersection_of_sets @ U @ V ) @ ( top_of_basis @ f ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(63,plain,
( ( ! [U: $i,Vf: $i] :
( ( element_of_set @ U @ ( union_of_members @ Vf ) )
| ! [Uu1: $i] :
( ~ ( element_of_set @ U @ Uu1 )
| ~ ( element_of_collection @ Uu1 @ Vf ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(64,plain,
( ( ! [X: $i,Vf: $i] :
( ~ ( basis @ X @ Vf )
| ( equal_sets @ ( union_of_members @ Vf ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(65,plain,
( ( ! [X: $i,Vf: $i,Y: $i] :
( ~ ( basis @ X @ Vf )
| ~ ( element_of_set @ Y @ X )
| ! [Vb1: $i] :
( ~ ( element_of_collection @ Vb1 @ Vf )
| ! [Vb2: $i] :
( ~ ( element_of_collection @ Vb2 @ Vf )
| ~ ( element_of_set @ Y @ ( intersection_of_sets @ Vb1 @ Vb2 ) )
| ( element_of_set @ Y @ ( f6 @ X @ Vf @ Y @ Vb1 @ Vb2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(66,plain,
( ( ! [X: $i,Vf: $i,Y: $i] :
( ~ ( basis @ X @ Vf )
| ~ ( element_of_set @ Y @ X )
| ! [Vb1: $i] :
( ~ ( element_of_collection @ Vb1 @ Vf )
| ! [Vb2: $i] :
( ~ ( element_of_collection @ Vb2 @ Vf )
| ~ ( element_of_set @ Y @ ( intersection_of_sets @ Vb1 @ Vb2 ) )
| ( element_of_collection @ ( f6 @ X @ Vf @ Y @ Vb1 @ Vb2 ) @ Vf ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(67,plain,
( ( ! [X: $i,Vf: $i,Y: $i] :
( ~ ( basis @ X @ Vf )
| ~ ( element_of_set @ Y @ X )
| ! [Vb1: $i] :
( ~ ( element_of_collection @ Vb1 @ Vf )
| ! [Vb2: $i] :
( ~ ( element_of_collection @ Vb2 @ Vf )
| ~ ( element_of_set @ Y @ ( intersection_of_sets @ Vb1 @ Vb2 ) )
| ( subset_sets @ ( f6 @ X @ Vf @ Y @ Vb1 @ Vb2 ) @ ( intersection_of_sets @ Vb1 @ Vb2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(68,plain,
( ( ! [U: $i,Vf: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ! [X: $i] :
( ~ ( element_of_set @ X @ U )
| ( element_of_set @ X @ ( f10 @ Vf @ U @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(69,plain,
( ( ! [U: $i,Vf: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ! [X: $i] :
( ~ ( element_of_set @ X @ U )
| ( element_of_collection @ ( f10 @ Vf @ U @ X ) @ Vf ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(70,plain,
( ( ! [U: $i,Vf: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ! [X: $i] :
( ~ ( element_of_set @ X @ U )
| ( subset_sets @ ( f10 @ Vf @ U @ X ) @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(71,plain,
( ( ! [U: $i,Vf: $i] :
( ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ( element_of_set @ ( f11 @ Vf @ U ) @ U ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(72,plain,
( ( ! [U: $i,Vf: $i] :
( ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ! [Uu11: $i] :
( ~ ( element_of_set @ ( f11 @ Vf @ U ) @ Uu11 )
| ~ ( element_of_collection @ Uu11 @ Vf )
| ~ ( subset_sets @ Uu11 @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(73,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( subset_sets @ X @ Y )
| ! [Z: $i] :
( ~ ( subset_sets @ Y @ Z )
| ( subset_sets @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(74,plain,
( ( ! [Z: $i,X: $i] :
( ! [Y: $i] :
~ ( element_of_set @ Z @ ( intersection_of_sets @ X @ Y ) )
| ( element_of_set @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(75,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( element_of_set @ Z @ ( intersection_of_sets @ X @ Y ) )
| ( element_of_set @ Z @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(76,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ( element_of_set @ Z @ ( intersection_of_sets @ X @ Y ) )
| ~ ( element_of_set @ Z @ X )
| ~ ( element_of_set @ Z @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(77,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( subset_sets @ X @ Y )
| ! [U: $i,V: $i] :
( ~ ( subset_sets @ U @ V )
| ( subset_sets @ ( intersection_of_sets @ X @ U ) @ ( intersection_of_sets @ Y @ V ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(78,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equal_sets @ X @ Y )
| ! [Z: $i] :
( ~ ( element_of_set @ Z @ X )
| ( element_of_set @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(79,plain,
( ( ! [X: $i,Y: $i] : ( equal_sets @ ( intersection_of_sets @ X @ Y ) @ ( intersection_of_sets @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(80,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(81,plain,
! [SV1: $i] :
( ( element_of_collection @ SV1 @ ( top_of_basis @ f ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(82,plain,
! [SV2: $i] :
( ( element_of_collection @ SV2 @ ( top_of_basis @ f ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(83,plain,
! [SV3: $i] :
( ( ! [SY59: $i] :
~ ( element_of_collection @ ( intersection_of_sets @ SV3 @ SY59 ) @ ( top_of_basis @ f ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(84,plain,
! [SV4: $i] :
( ( ! [SY60: $i] :
( ( element_of_set @ SV4 @ ( union_of_members @ SY60 ) )
| ! [SY61: $i] :
( ~ ( element_of_set @ SV4 @ SY61 )
| ~ ( element_of_collection @ SY61 @ SY60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(85,plain,
! [SV5: $i] :
( ( ! [SY62: $i] :
( ~ ( basis @ SV5 @ SY62 )
| ( equal_sets @ ( union_of_members @ SY62 ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(86,plain,
! [SV6: $i] :
( ( ! [SY63: $i,SY64: $i] :
( ~ ( basis @ SV6 @ SY63 )
| ~ ( element_of_set @ SY64 @ SV6 )
| ! [SY65: $i] :
( ~ ( element_of_collection @ SY65 @ SY63 )
| ! [SY66: $i] :
( ~ ( element_of_collection @ SY66 @ SY63 )
| ~ ( element_of_set @ SY64 @ ( intersection_of_sets @ SY65 @ SY66 ) )
| ( element_of_set @ SY64 @ ( f6 @ SV6 @ SY63 @ SY64 @ SY65 @ SY66 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(87,plain,
! [SV7: $i] :
( ( ! [SY67: $i,SY68: $i] :
( ~ ( basis @ SV7 @ SY67 )
| ~ ( element_of_set @ SY68 @ SV7 )
| ! [SY69: $i] :
( ~ ( element_of_collection @ SY69 @ SY67 )
| ! [SY70: $i] :
( ~ ( element_of_collection @ SY70 @ SY67 )
| ~ ( element_of_set @ SY68 @ ( intersection_of_sets @ SY69 @ SY70 ) )
| ( element_of_collection @ ( f6 @ SV7 @ SY67 @ SY68 @ SY69 @ SY70 ) @ SY67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(88,plain,
! [SV8: $i] :
( ( ! [SY71: $i,SY72: $i] :
( ~ ( basis @ SV8 @ SY71 )
| ~ ( element_of_set @ SY72 @ SV8 )
| ! [SY73: $i] :
( ~ ( element_of_collection @ SY73 @ SY71 )
| ! [SY74: $i] :
( ~ ( element_of_collection @ SY74 @ SY71 )
| ~ ( element_of_set @ SY72 @ ( intersection_of_sets @ SY73 @ SY74 ) )
| ( subset_sets @ ( f6 @ SV8 @ SY71 @ SY72 @ SY73 @ SY74 ) @ ( intersection_of_sets @ SY73 @ SY74 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(89,plain,
! [SV9: $i] :
( ( ! [SY75: $i] :
( ~ ( element_of_collection @ SV9 @ ( top_of_basis @ SY75 ) )
| ! [SY76: $i] :
( ~ ( element_of_set @ SY76 @ SV9 )
| ( element_of_set @ SY76 @ ( f10 @ SY75 @ SV9 @ SY76 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(90,plain,
! [SV10: $i] :
( ( ! [SY77: $i] :
( ~ ( element_of_collection @ SV10 @ ( top_of_basis @ SY77 ) )
| ! [SY78: $i] :
( ~ ( element_of_set @ SY78 @ SV10 )
| ( element_of_collection @ ( f10 @ SY77 @ SV10 @ SY78 ) @ SY77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(91,plain,
! [SV11: $i] :
( ( ! [SY79: $i] :
( ~ ( element_of_collection @ SV11 @ ( top_of_basis @ SY79 ) )
| ! [SY80: $i] :
( ~ ( element_of_set @ SY80 @ SV11 )
| ( subset_sets @ ( f10 @ SY79 @ SV11 @ SY80 ) @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(92,plain,
! [SV12: $i] :
( ( ! [SY81: $i] :
( ( element_of_collection @ SV12 @ ( top_of_basis @ SY81 ) )
| ( element_of_set @ ( f11 @ SY81 @ SV12 ) @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(93,plain,
! [SV13: $i] :
( ( ! [SY82: $i] :
( ( element_of_collection @ SV13 @ ( top_of_basis @ SY82 ) )
| ! [SY83: $i] :
( ~ ( element_of_set @ ( f11 @ SY82 @ SV13 ) @ SY83 )
| ~ ( element_of_collection @ SY83 @ SY82 )
| ~ ( subset_sets @ SY83 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(94,plain,
! [SV14: $i] :
( ( ! [SY84: $i] :
( ~ ( subset_sets @ SV14 @ SY84 )
| ! [SY85: $i] :
( ~ ( subset_sets @ SY84 @ SY85 )
| ( subset_sets @ SV14 @ SY85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(95,plain,
! [SV15: $i] :
( ( ! [SY86: $i] :
( ! [SY87: $i] :
~ ( element_of_set @ SV15 @ ( intersection_of_sets @ SY86 @ SY87 ) )
| ( element_of_set @ SV15 @ SY86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(96,plain,
! [SV16: $i] :
( ( ! [SY88: $i,SY89: $i] :
( ~ ( element_of_set @ SV16 @ ( intersection_of_sets @ SY88 @ SY89 ) )
| ( element_of_set @ SV16 @ SY89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(97,plain,
! [SV17: $i] :
( ( ! [SY90: $i,SY91: $i] :
( ( element_of_set @ SV17 @ ( intersection_of_sets @ SY90 @ SY91 ) )
| ~ ( element_of_set @ SV17 @ SY90 )
| ~ ( element_of_set @ SV17 @ SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(98,plain,
! [SV18: $i] :
( ( ! [SY92: $i] :
( ~ ( subset_sets @ SV18 @ SY92 )
| ! [SY93: $i,SY94: $i] :
( ~ ( subset_sets @ SY93 @ SY94 )
| ( subset_sets @ ( intersection_of_sets @ SV18 @ SY93 ) @ ( intersection_of_sets @ SY92 @ SY94 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(99,plain,
! [SV19: $i] :
( ( ! [SY95: $i] :
( ~ ( equal_sets @ SV19 @ SY95 )
| ! [SY96: $i] :
( ~ ( element_of_set @ SY96 @ SV19 )
| ( element_of_set @ SY96 @ SY95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(100,plain,
! [SV20: $i] :
( ( ! [SY97: $i] : ( equal_sets @ ( intersection_of_sets @ SV20 @ SY97 ) @ ( intersection_of_sets @ SY97 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(101,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(102,plain,
! [SV21: $i,SV3: $i] :
( ( ~ ( element_of_collection @ ( intersection_of_sets @ SV3 @ SV21 ) @ ( top_of_basis @ f ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(103,plain,
! [SV22: $i,SV4: $i] :
( ( ( element_of_set @ SV4 @ ( union_of_members @ SV22 ) )
| ! [SY98: $i] :
( ~ ( element_of_set @ SV4 @ SY98 )
| ~ ( element_of_collection @ SY98 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(104,plain,
! [SV23: $i,SV5: $i] :
( ( ~ ( basis @ SV5 @ SV23 )
| ( equal_sets @ ( union_of_members @ SV23 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(105,plain,
! [SV24: $i,SV6: $i] :
( ( ! [SY99: $i] :
( ~ ( basis @ SV6 @ SV24 )
| ~ ( element_of_set @ SY99 @ SV6 )
| ! [SY100: $i] :
( ~ ( element_of_collection @ SY100 @ SV24 )
| ! [SY101: $i] :
( ~ ( element_of_collection @ SY101 @ SV24 )
| ~ ( element_of_set @ SY99 @ ( intersection_of_sets @ SY100 @ SY101 ) )
| ( element_of_set @ SY99 @ ( f6 @ SV6 @ SV24 @ SY99 @ SY100 @ SY101 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(106,plain,
! [SV25: $i,SV7: $i] :
( ( ! [SY102: $i] :
( ~ ( basis @ SV7 @ SV25 )
| ~ ( element_of_set @ SY102 @ SV7 )
| ! [SY103: $i] :
( ~ ( element_of_collection @ SY103 @ SV25 )
| ! [SY104: $i] :
( ~ ( element_of_collection @ SY104 @ SV25 )
| ~ ( element_of_set @ SY102 @ ( intersection_of_sets @ SY103 @ SY104 ) )
| ( element_of_collection @ ( f6 @ SV7 @ SV25 @ SY102 @ SY103 @ SY104 ) @ SV25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(107,plain,
! [SV26: $i,SV8: $i] :
( ( ! [SY105: $i] :
( ~ ( basis @ SV8 @ SV26 )
| ~ ( element_of_set @ SY105 @ SV8 )
| ! [SY106: $i] :
( ~ ( element_of_collection @ SY106 @ SV26 )
| ! [SY107: $i] :
( ~ ( element_of_collection @ SY107 @ SV26 )
| ~ ( element_of_set @ SY105 @ ( intersection_of_sets @ SY106 @ SY107 ) )
| ( subset_sets @ ( f6 @ SV8 @ SV26 @ SY105 @ SY106 @ SY107 ) @ ( intersection_of_sets @ SY106 @ SY107 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(108,plain,
! [SV27: $i,SV9: $i] :
( ( ~ ( element_of_collection @ SV9 @ ( top_of_basis @ SV27 ) )
| ! [SY108: $i] :
( ~ ( element_of_set @ SY108 @ SV9 )
| ( element_of_set @ SY108 @ ( f10 @ SV27 @ SV9 @ SY108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(109,plain,
! [SV28: $i,SV10: $i] :
( ( ~ ( element_of_collection @ SV10 @ ( top_of_basis @ SV28 ) )
| ! [SY109: $i] :
( ~ ( element_of_set @ SY109 @ SV10 )
| ( element_of_collection @ ( f10 @ SV28 @ SV10 @ SY109 ) @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(110,plain,
! [SV29: $i,SV11: $i] :
( ( ~ ( element_of_collection @ SV11 @ ( top_of_basis @ SV29 ) )
| ! [SY110: $i] :
( ~ ( element_of_set @ SY110 @ SV11 )
| ( subset_sets @ ( f10 @ SV29 @ SV11 @ SY110 ) @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(111,plain,
! [SV30: $i,SV12: $i] :
( ( ( element_of_collection @ SV12 @ ( top_of_basis @ SV30 ) )
| ( element_of_set @ ( f11 @ SV30 @ SV12 ) @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(112,plain,
! [SV31: $i,SV13: $i] :
( ( ( element_of_collection @ SV13 @ ( top_of_basis @ SV31 ) )
| ! [SY111: $i] :
( ~ ( element_of_set @ ( f11 @ SV31 @ SV13 ) @ SY111 )
| ~ ( element_of_collection @ SY111 @ SV31 )
| ~ ( subset_sets @ SY111 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(113,plain,
! [SV32: $i,SV14: $i] :
( ( ~ ( subset_sets @ SV14 @ SV32 )
| ! [SY112: $i] :
( ~ ( subset_sets @ SV32 @ SY112 )
| ( subset_sets @ SV14 @ SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(114,plain,
! [SV33: $i,SV15: $i] :
( ( ! [SY113: $i] :
~ ( element_of_set @ SV15 @ ( intersection_of_sets @ SV33 @ SY113 ) )
| ( element_of_set @ SV15 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(115,plain,
! [SV34: $i,SV16: $i] :
( ( ! [SY114: $i] :
( ~ ( element_of_set @ SV16 @ ( intersection_of_sets @ SV34 @ SY114 ) )
| ( element_of_set @ SV16 @ SY114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(116,plain,
! [SV35: $i,SV17: $i] :
( ( ! [SY115: $i] :
( ( element_of_set @ SV17 @ ( intersection_of_sets @ SV35 @ SY115 ) )
| ~ ( element_of_set @ SV17 @ SV35 )
| ~ ( element_of_set @ SV17 @ SY115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(117,plain,
! [SV36: $i,SV18: $i] :
( ( ~ ( subset_sets @ SV18 @ SV36 )
| ! [SY116: $i,SY117: $i] :
( ~ ( subset_sets @ SY116 @ SY117 )
| ( subset_sets @ ( intersection_of_sets @ SV18 @ SY116 ) @ ( intersection_of_sets @ SV36 @ SY117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(118,plain,
! [SV37: $i,SV19: $i] :
( ( ~ ( equal_sets @ SV19 @ SV37 )
| ! [SY118: $i] :
( ~ ( element_of_set @ SY118 @ SV19 )
| ( element_of_set @ SY118 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(119,plain,
! [SV38: $i,SV20: $i] :
( ( equal_sets @ ( intersection_of_sets @ SV20 @ SV38 ) @ ( intersection_of_sets @ SV38 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(120,plain,
! [SV21: $i,SV3: $i] :
( ( element_of_collection @ ( intersection_of_sets @ SV3 @ SV21 ) @ ( top_of_basis @ f ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(121,plain,
! [SV22: $i,SV4: $i] :
( ( ( element_of_set @ SV4 @ ( union_of_members @ SV22 ) )
= $true )
| ( ( ! [SY98: $i] :
( ~ ( element_of_set @ SV4 @ SY98 )
| ~ ( element_of_collection @ SY98 @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(122,plain,
! [SV23: $i,SV5: $i] :
( ( ( ~ ( basis @ SV5 @ SV23 ) )
= $true )
| ( ( equal_sets @ ( union_of_members @ SV23 ) @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(123,plain,
! [SV39: $i,SV24: $i,SV6: $i] :
( ( ~ ( basis @ SV6 @ SV24 )
| ~ ( element_of_set @ SV39 @ SV6 )
| ! [SY119: $i] :
( ~ ( element_of_collection @ SY119 @ SV24 )
| ! [SY120: $i] :
( ~ ( element_of_collection @ SY120 @ SV24 )
| ~ ( element_of_set @ SV39 @ ( intersection_of_sets @ SY119 @ SY120 ) )
| ( element_of_set @ SV39 @ ( f6 @ SV6 @ SV24 @ SV39 @ SY119 @ SY120 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(124,plain,
! [SV40: $i,SV25: $i,SV7: $i] :
( ( ~ ( basis @ SV7 @ SV25 )
| ~ ( element_of_set @ SV40 @ SV7 )
| ! [SY121: $i] :
( ~ ( element_of_collection @ SY121 @ SV25 )
| ! [SY122: $i] :
( ~ ( element_of_collection @ SY122 @ SV25 )
| ~ ( element_of_set @ SV40 @ ( intersection_of_sets @ SY121 @ SY122 ) )
| ( element_of_collection @ ( f6 @ SV7 @ SV25 @ SV40 @ SY121 @ SY122 ) @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(125,plain,
! [SV41: $i,SV26: $i,SV8: $i] :
( ( ~ ( basis @ SV8 @ SV26 )
| ~ ( element_of_set @ SV41 @ SV8 )
| ! [SY123: $i] :
( ~ ( element_of_collection @ SY123 @ SV26 )
| ! [SY124: $i] :
( ~ ( element_of_collection @ SY124 @ SV26 )
| ~ ( element_of_set @ SV41 @ ( intersection_of_sets @ SY123 @ SY124 ) )
| ( subset_sets @ ( f6 @ SV8 @ SV26 @ SV41 @ SY123 @ SY124 ) @ ( intersection_of_sets @ SY123 @ SY124 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(126,plain,
! [SV27: $i,SV9: $i] :
( ( ( ~ ( element_of_collection @ SV9 @ ( top_of_basis @ SV27 ) ) )
= $true )
| ( ( ! [SY108: $i] :
( ~ ( element_of_set @ SY108 @ SV9 )
| ( element_of_set @ SY108 @ ( f10 @ SV27 @ SV9 @ SY108 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(127,plain,
! [SV28: $i,SV10: $i] :
( ( ( ~ ( element_of_collection @ SV10 @ ( top_of_basis @ SV28 ) ) )
= $true )
| ( ( ! [SY109: $i] :
( ~ ( element_of_set @ SY109 @ SV10 )
| ( element_of_collection @ ( f10 @ SV28 @ SV10 @ SY109 ) @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(128,plain,
! [SV29: $i,SV11: $i] :
( ( ( ~ ( element_of_collection @ SV11 @ ( top_of_basis @ SV29 ) ) )
= $true )
| ( ( ! [SY110: $i] :
( ~ ( element_of_set @ SY110 @ SV11 )
| ( subset_sets @ ( f10 @ SV29 @ SV11 @ SY110 ) @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(129,plain,
! [SV30: $i,SV12: $i] :
( ( ( element_of_collection @ SV12 @ ( top_of_basis @ SV30 ) )
= $true )
| ( ( element_of_set @ ( f11 @ SV30 @ SV12 ) @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(130,plain,
! [SV31: $i,SV13: $i] :
( ( ( element_of_collection @ SV13 @ ( top_of_basis @ SV31 ) )
= $true )
| ( ( ! [SY111: $i] :
( ~ ( element_of_set @ ( f11 @ SV31 @ SV13 ) @ SY111 )
| ~ ( element_of_collection @ SY111 @ SV31 )
| ~ ( subset_sets @ SY111 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(131,plain,
! [SV32: $i,SV14: $i] :
( ( ( ~ ( subset_sets @ SV14 @ SV32 ) )
= $true )
| ( ( ! [SY112: $i] :
( ~ ( subset_sets @ SV32 @ SY112 )
| ( subset_sets @ SV14 @ SY112 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(132,plain,
! [SV33: $i,SV15: $i] :
( ( ( ! [SY113: $i] :
~ ( element_of_set @ SV15 @ ( intersection_of_sets @ SV33 @ SY113 ) ) )
= $true )
| ( ( element_of_set @ SV15 @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(133,plain,
! [SV42: $i,SV34: $i,SV16: $i] :
( ( ~ ( element_of_set @ SV16 @ ( intersection_of_sets @ SV34 @ SV42 ) )
| ( element_of_set @ SV16 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(134,plain,
! [SV43: $i,SV35: $i,SV17: $i] :
( ( ( element_of_set @ SV17 @ ( intersection_of_sets @ SV35 @ SV43 ) )
| ~ ( element_of_set @ SV17 @ SV35 )
| ~ ( element_of_set @ SV17 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(135,plain,
! [SV36: $i,SV18: $i] :
( ( ( ~ ( subset_sets @ SV18 @ SV36 ) )
= $true )
| ( ( ! [SY116: $i,SY117: $i] :
( ~ ( subset_sets @ SY116 @ SY117 )
| ( subset_sets @ ( intersection_of_sets @ SV18 @ SY116 ) @ ( intersection_of_sets @ SV36 @ SY117 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(136,plain,
! [SV37: $i,SV19: $i] :
( ( ( ~ ( equal_sets @ SV19 @ SV37 ) )
= $true )
| ( ( ! [SY118: $i] :
( ~ ( element_of_set @ SY118 @ SV19 )
| ( element_of_set @ SY118 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(137,plain,
! [SV22: $i,SV44: $i,SV4: $i] :
( ( ( ~ ( element_of_set @ SV4 @ SV44 )
| ~ ( element_of_collection @ SV44 @ SV22 ) )
= $true )
| ( ( element_of_set @ SV4 @ ( union_of_members @ SV22 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(138,plain,
! [SV23: $i,SV5: $i] :
( ( ( basis @ SV5 @ SV23 )
= $false )
| ( ( equal_sets @ ( union_of_members @ SV23 ) @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(139,plain,
! [SV39: $i,SV24: $i,SV6: $i] :
( ( ( ~ ( basis @ SV6 @ SV24 ) )
= $true )
| ( ( ~ ( element_of_set @ SV39 @ SV6 )
| ! [SY119: $i] :
( ~ ( element_of_collection @ SY119 @ SV24 )
| ! [SY120: $i] :
( ~ ( element_of_collection @ SY120 @ SV24 )
| ~ ( element_of_set @ SV39 @ ( intersection_of_sets @ SY119 @ SY120 ) )
| ( element_of_set @ SV39 @ ( f6 @ SV6 @ SV24 @ SV39 @ SY119 @ SY120 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(140,plain,
! [SV40: $i,SV25: $i,SV7: $i] :
( ( ( ~ ( basis @ SV7 @ SV25 ) )
= $true )
| ( ( ~ ( element_of_set @ SV40 @ SV7 )
| ! [SY121: $i] :
( ~ ( element_of_collection @ SY121 @ SV25 )
| ! [SY122: $i] :
( ~ ( element_of_collection @ SY122 @ SV25 )
| ~ ( element_of_set @ SV40 @ ( intersection_of_sets @ SY121 @ SY122 ) )
| ( element_of_collection @ ( f6 @ SV7 @ SV25 @ SV40 @ SY121 @ SY122 ) @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(141,plain,
! [SV41: $i,SV26: $i,SV8: $i] :
( ( ( ~ ( basis @ SV8 @ SV26 ) )
= $true )
| ( ( ~ ( element_of_set @ SV41 @ SV8 )
| ! [SY123: $i] :
( ~ ( element_of_collection @ SY123 @ SV26 )
| ! [SY124: $i] :
( ~ ( element_of_collection @ SY124 @ SV26 )
| ~ ( element_of_set @ SV41 @ ( intersection_of_sets @ SY123 @ SY124 ) )
| ( subset_sets @ ( f6 @ SV8 @ SV26 @ SV41 @ SY123 @ SY124 ) @ ( intersection_of_sets @ SY123 @ SY124 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(142,plain,
! [SV27: $i,SV9: $i] :
( ( ( element_of_collection @ SV9 @ ( top_of_basis @ SV27 ) )
= $false )
| ( ( ! [SY108: $i] :
( ~ ( element_of_set @ SY108 @ SV9 )
| ( element_of_set @ SY108 @ ( f10 @ SV27 @ SV9 @ SY108 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(143,plain,
! [SV28: $i,SV10: $i] :
( ( ( element_of_collection @ SV10 @ ( top_of_basis @ SV28 ) )
= $false )
| ( ( ! [SY109: $i] :
( ~ ( element_of_set @ SY109 @ SV10 )
| ( element_of_collection @ ( f10 @ SV28 @ SV10 @ SY109 ) @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(144,plain,
! [SV29: $i,SV11: $i] :
( ( ( element_of_collection @ SV11 @ ( top_of_basis @ SV29 ) )
= $false )
| ( ( ! [SY110: $i] :
( ~ ( element_of_set @ SY110 @ SV11 )
| ( subset_sets @ ( f10 @ SV29 @ SV11 @ SY110 ) @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(145,plain,
! [SV45: $i,SV13: $i,SV31: $i] :
( ( ( ~ ( element_of_set @ ( f11 @ SV31 @ SV13 ) @ SV45 )
| ~ ( element_of_collection @ SV45 @ SV31 )
| ~ ( subset_sets @ SV45 @ SV13 ) )
= $true )
| ( ( element_of_collection @ SV13 @ ( top_of_basis @ SV31 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(146,plain,
! [SV32: $i,SV14: $i] :
( ( ( subset_sets @ SV14 @ SV32 )
= $false )
| ( ( ! [SY112: $i] :
( ~ ( subset_sets @ SV32 @ SY112 )
| ( subset_sets @ SV14 @ SY112 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(147,plain,
! [SV46: $i,SV33: $i,SV15: $i] :
( ( ( ~ ( element_of_set @ SV15 @ ( intersection_of_sets @ SV33 @ SV46 ) ) )
= $true )
| ( ( element_of_set @ SV15 @ SV33 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(148,plain,
! [SV42: $i,SV34: $i,SV16: $i] :
( ( ( ~ ( element_of_set @ SV16 @ ( intersection_of_sets @ SV34 @ SV42 ) ) )
= $true )
| ( ( element_of_set @ SV16 @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(149,plain,
! [SV43: $i,SV35: $i,SV17: $i] :
( ( ( element_of_set @ SV17 @ ( intersection_of_sets @ SV35 @ SV43 ) )
= $true )
| ( ( ~ ( element_of_set @ SV17 @ SV35 )
| ~ ( element_of_set @ SV17 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(150,plain,
! [SV36: $i,SV18: $i] :
( ( ( subset_sets @ SV18 @ SV36 )
= $false )
| ( ( ! [SY116: $i,SY117: $i] :
( ~ ( subset_sets @ SY116 @ SY117 )
| ( subset_sets @ ( intersection_of_sets @ SV18 @ SY116 ) @ ( intersection_of_sets @ SV36 @ SY117 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(151,plain,
! [SV37: $i,SV19: $i] :
( ( ( equal_sets @ SV19 @ SV37 )
= $false )
| ( ( ! [SY118: $i] :
( ~ ( element_of_set @ SY118 @ SV19 )
| ( element_of_set @ SY118 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(152,plain,
! [SV22: $i,SV44: $i,SV4: $i] :
( ( ( ~ ( element_of_set @ SV4 @ SV44 ) )
= $true )
| ( ( ~ ( element_of_collection @ SV44 @ SV22 ) )
= $true )
| ( ( element_of_set @ SV4 @ ( union_of_members @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(153,plain,
! [SV39: $i,SV24: $i,SV6: $i] :
( ( ( basis @ SV6 @ SV24 )
= $false )
| ( ( ~ ( element_of_set @ SV39 @ SV6 )
| ! [SY119: $i] :
( ~ ( element_of_collection @ SY119 @ SV24 )
| ! [SY120: $i] :
( ~ ( element_of_collection @ SY120 @ SV24 )
| ~ ( element_of_set @ SV39 @ ( intersection_of_sets @ SY119 @ SY120 ) )
| ( element_of_set @ SV39 @ ( f6 @ SV6 @ SV24 @ SV39 @ SY119 @ SY120 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(154,plain,
! [SV40: $i,SV25: $i,SV7: $i] :
( ( ( basis @ SV7 @ SV25 )
= $false )
| ( ( ~ ( element_of_set @ SV40 @ SV7 )
| ! [SY121: $i] :
( ~ ( element_of_collection @ SY121 @ SV25 )
| ! [SY122: $i] :
( ~ ( element_of_collection @ SY122 @ SV25 )
| ~ ( element_of_set @ SV40 @ ( intersection_of_sets @ SY121 @ SY122 ) )
| ( element_of_collection @ ( f6 @ SV7 @ SV25 @ SV40 @ SY121 @ SY122 ) @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(155,plain,
! [SV41: $i,SV26: $i,SV8: $i] :
( ( ( basis @ SV8 @ SV26 )
= $false )
| ( ( ~ ( element_of_set @ SV41 @ SV8 )
| ! [SY123: $i] :
( ~ ( element_of_collection @ SY123 @ SV26 )
| ! [SY124: $i] :
( ~ ( element_of_collection @ SY124 @ SV26 )
| ~ ( element_of_set @ SV41 @ ( intersection_of_sets @ SY123 @ SY124 ) )
| ( subset_sets @ ( f6 @ SV8 @ SV26 @ SV41 @ SY123 @ SY124 ) @ ( intersection_of_sets @ SY123 @ SY124 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(156,plain,
! [SV27: $i,SV9: $i,SV47: $i] :
( ( ( ~ ( element_of_set @ SV47 @ SV9 )
| ( element_of_set @ SV47 @ ( f10 @ SV27 @ SV9 @ SV47 ) ) )
= $true )
| ( ( element_of_collection @ SV9 @ ( top_of_basis @ SV27 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(157,plain,
! [SV28: $i,SV10: $i,SV48: $i] :
( ( ( ~ ( element_of_set @ SV48 @ SV10 )
| ( element_of_collection @ ( f10 @ SV28 @ SV10 @ SV48 ) @ SV28 ) )
= $true )
| ( ( element_of_collection @ SV10 @ ( top_of_basis @ SV28 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(158,plain,
! [SV29: $i,SV11: $i,SV49: $i] :
( ( ( ~ ( element_of_set @ SV49 @ SV11 )
| ( subset_sets @ ( f10 @ SV29 @ SV11 @ SV49 ) @ SV11 ) )
= $true )
| ( ( element_of_collection @ SV11 @ ( top_of_basis @ SV29 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(159,plain,
! [SV45: $i,SV13: $i,SV31: $i] :
( ( ( ~ ( element_of_set @ ( f11 @ SV31 @ SV13 ) @ SV45 ) )
= $true )
| ( ( ~ ( element_of_collection @ SV45 @ SV31 )
| ~ ( subset_sets @ SV45 @ SV13 ) )
= $true )
| ( ( element_of_collection @ SV13 @ ( top_of_basis @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(160,plain,
! [SV14: $i,SV50: $i,SV32: $i] :
( ( ( ~ ( subset_sets @ SV32 @ SV50 )
| ( subset_sets @ SV14 @ SV50 ) )
= $true )
| ( ( subset_sets @ SV14 @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(161,plain,
! [SV46: $i,SV33: $i,SV15: $i] :
( ( ( element_of_set @ SV15 @ ( intersection_of_sets @ SV33 @ SV46 ) )
= $false )
| ( ( element_of_set @ SV15 @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(162,plain,
! [SV42: $i,SV34: $i,SV16: $i] :
( ( ( element_of_set @ SV16 @ ( intersection_of_sets @ SV34 @ SV42 ) )
= $false )
| ( ( element_of_set @ SV16 @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(163,plain,
! [SV43: $i,SV35: $i,SV17: $i] :
( ( ( ~ ( element_of_set @ SV17 @ SV35 ) )
= $true )
| ( ( ~ ( element_of_set @ SV17 @ SV43 ) )
= $true )
| ( ( element_of_set @ SV17 @ ( intersection_of_sets @ SV35 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(164,plain,
! [SV36: $i,SV18: $i,SV51: $i] :
( ( ( ! [SY125: $i] :
( ~ ( subset_sets @ SV51 @ SY125 )
| ( subset_sets @ ( intersection_of_sets @ SV18 @ SV51 ) @ ( intersection_of_sets @ SV36 @ SY125 ) ) ) )
= $true )
| ( ( subset_sets @ SV18 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(165,plain,
! [SV37: $i,SV19: $i,SV52: $i] :
( ( ( ~ ( element_of_set @ SV52 @ SV19 )
| ( element_of_set @ SV52 @ SV37 ) )
= $true )
| ( ( equal_sets @ SV19 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(166,plain,
! [SV22: $i,SV44: $i,SV4: $i] :
( ( ( element_of_set @ SV4 @ SV44 )
= $false )
| ( ( ~ ( element_of_collection @ SV44 @ SV22 ) )
= $true )
| ( ( element_of_set @ SV4 @ ( union_of_members @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(167,plain,
! [SV24: $i,SV6: $i,SV39: $i] :
( ( ( ~ ( element_of_set @ SV39 @ SV6 ) )
= $true )
| ( ( ! [SY119: $i] :
( ~ ( element_of_collection @ SY119 @ SV24 )
| ! [SY120: $i] :
( ~ ( element_of_collection @ SY120 @ SV24 )
| ~ ( element_of_set @ SV39 @ ( intersection_of_sets @ SY119 @ SY120 ) )
| ( element_of_set @ SV39 @ ( f6 @ SV6 @ SV24 @ SV39 @ SY119 @ SY120 ) ) ) ) )
= $true )
| ( ( basis @ SV6 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(168,plain,
! [SV25: $i,SV7: $i,SV40: $i] :
( ( ( ~ ( element_of_set @ SV40 @ SV7 ) )
= $true )
| ( ( ! [SY121: $i] :
( ~ ( element_of_collection @ SY121 @ SV25 )
| ! [SY122: $i] :
( ~ ( element_of_collection @ SY122 @ SV25 )
| ~ ( element_of_set @ SV40 @ ( intersection_of_sets @ SY121 @ SY122 ) )
| ( element_of_collection @ ( f6 @ SV7 @ SV25 @ SV40 @ SY121 @ SY122 ) @ SV25 ) ) ) )
= $true )
| ( ( basis @ SV7 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(169,plain,
! [SV26: $i,SV8: $i,SV41: $i] :
( ( ( ~ ( element_of_set @ SV41 @ SV8 ) )
= $true )
| ( ( ! [SY123: $i] :
( ~ ( element_of_collection @ SY123 @ SV26 )
| ! [SY124: $i] :
( ~ ( element_of_collection @ SY124 @ SV26 )
| ~ ( element_of_set @ SV41 @ ( intersection_of_sets @ SY123 @ SY124 ) )
| ( subset_sets @ ( f6 @ SV8 @ SV26 @ SV41 @ SY123 @ SY124 ) @ ( intersection_of_sets @ SY123 @ SY124 ) ) ) ) )
= $true )
| ( ( basis @ SV8 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(170,plain,
! [SV27: $i,SV9: $i,SV47: $i] :
( ( ( ~ ( element_of_set @ SV47 @ SV9 ) )
= $true )
| ( ( element_of_set @ SV47 @ ( f10 @ SV27 @ SV9 @ SV47 ) )
= $true )
| ( ( element_of_collection @ SV9 @ ( top_of_basis @ SV27 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(171,plain,
! [SV28: $i,SV10: $i,SV48: $i] :
( ( ( ~ ( element_of_set @ SV48 @ SV10 ) )
= $true )
| ( ( element_of_collection @ ( f10 @ SV28 @ SV10 @ SV48 ) @ SV28 )
= $true )
| ( ( element_of_collection @ SV10 @ ( top_of_basis @ SV28 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(172,plain,
! [SV29: $i,SV11: $i,SV49: $i] :
( ( ( ~ ( element_of_set @ SV49 @ SV11 ) )
= $true )
| ( ( subset_sets @ ( f10 @ SV29 @ SV11 @ SV49 ) @ SV11 )
= $true )
| ( ( element_of_collection @ SV11 @ ( top_of_basis @ SV29 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(173,plain,
! [SV45: $i,SV13: $i,SV31: $i] :
( ( ( element_of_set @ ( f11 @ SV31 @ SV13 ) @ SV45 )
= $false )
| ( ( ~ ( element_of_collection @ SV45 @ SV31 )
| ~ ( subset_sets @ SV45 @ SV13 ) )
= $true )
| ( ( element_of_collection @ SV13 @ ( top_of_basis @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(174,plain,
! [SV14: $i,SV50: $i,SV32: $i] :
( ( ( ~ ( subset_sets @ SV32 @ SV50 ) )
= $true )
| ( ( subset_sets @ SV14 @ SV50 )
= $true )
| ( ( subset_sets @ SV14 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(175,plain,
! [SV43: $i,SV35: $i,SV17: $i] :
( ( ( element_of_set @ SV17 @ SV35 )
= $false )
| ( ( ~ ( element_of_set @ SV17 @ SV43 ) )
= $true )
| ( ( element_of_set @ SV17 @ ( intersection_of_sets @ SV35 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(176,plain,
! [SV36: $i,SV18: $i,SV53: $i,SV51: $i] :
( ( ( ~ ( subset_sets @ SV51 @ SV53 )
| ( subset_sets @ ( intersection_of_sets @ SV18 @ SV51 ) @ ( intersection_of_sets @ SV36 @ SV53 ) ) )
= $true )
| ( ( subset_sets @ SV18 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(177,plain,
! [SV37: $i,SV19: $i,SV52: $i] :
( ( ( ~ ( element_of_set @ SV52 @ SV19 ) )
= $true )
| ( ( element_of_set @ SV52 @ SV37 )
= $true )
| ( ( equal_sets @ SV19 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(178,plain,
! [SV4: $i,SV22: $i,SV44: $i] :
( ( ( element_of_collection @ SV44 @ SV22 )
= $false )
| ( ( element_of_set @ SV4 @ SV44 )
= $false )
| ( ( element_of_set @ SV4 @ ( union_of_members @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(179,plain,
! [SV24: $i,SV6: $i,SV39: $i] :
( ( ( element_of_set @ SV39 @ SV6 )
= $false )
| ( ( ! [SY119: $i] :
( ~ ( element_of_collection @ SY119 @ SV24 )
| ! [SY120: $i] :
( ~ ( element_of_collection @ SY120 @ SV24 )
| ~ ( element_of_set @ SV39 @ ( intersection_of_sets @ SY119 @ SY120 ) )
| ( element_of_set @ SV39 @ ( f6 @ SV6 @ SV24 @ SV39 @ SY119 @ SY120 ) ) ) ) )
= $true )
| ( ( basis @ SV6 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(180,plain,
! [SV25: $i,SV7: $i,SV40: $i] :
( ( ( element_of_set @ SV40 @ SV7 )
= $false )
| ( ( ! [SY121: $i] :
( ~ ( element_of_collection @ SY121 @ SV25 )
| ! [SY122: $i] :
( ~ ( element_of_collection @ SY122 @ SV25 )
| ~ ( element_of_set @ SV40 @ ( intersection_of_sets @ SY121 @ SY122 ) )
| ( element_of_collection @ ( f6 @ SV7 @ SV25 @ SV40 @ SY121 @ SY122 ) @ SV25 ) ) ) )
= $true )
| ( ( basis @ SV7 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(181,plain,
! [SV26: $i,SV8: $i,SV41: $i] :
( ( ( element_of_set @ SV41 @ SV8 )
= $false )
| ( ( ! [SY123: $i] :
( ~ ( element_of_collection @ SY123 @ SV26 )
| ! [SY124: $i] :
( ~ ( element_of_collection @ SY124 @ SV26 )
| ~ ( element_of_set @ SV41 @ ( intersection_of_sets @ SY123 @ SY124 ) )
| ( subset_sets @ ( f6 @ SV8 @ SV26 @ SV41 @ SY123 @ SY124 ) @ ( intersection_of_sets @ SY123 @ SY124 ) ) ) ) )
= $true )
| ( ( basis @ SV8 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(182,plain,
! [SV27: $i,SV9: $i,SV47: $i] :
( ( ( element_of_set @ SV47 @ SV9 )
= $false )
| ( ( element_of_set @ SV47 @ ( f10 @ SV27 @ SV9 @ SV47 ) )
= $true )
| ( ( element_of_collection @ SV9 @ ( top_of_basis @ SV27 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(183,plain,
! [SV28: $i,SV10: $i,SV48: $i] :
( ( ( element_of_set @ SV48 @ SV10 )
= $false )
| ( ( element_of_collection @ ( f10 @ SV28 @ SV10 @ SV48 ) @ SV28 )
= $true )
| ( ( element_of_collection @ SV10 @ ( top_of_basis @ SV28 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(184,plain,
! [SV29: $i,SV11: $i,SV49: $i] :
( ( ( element_of_set @ SV49 @ SV11 )
= $false )
| ( ( subset_sets @ ( f10 @ SV29 @ SV11 @ SV49 ) @ SV11 )
= $true )
| ( ( element_of_collection @ SV11 @ ( top_of_basis @ SV29 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(185,plain,
! [SV13: $i,SV31: $i,SV45: $i] :
( ( ( ~ ( element_of_collection @ SV45 @ SV31 ) )
= $true )
| ( ( ~ ( subset_sets @ SV45 @ SV13 ) )
= $true )
| ( ( element_of_set @ ( f11 @ SV31 @ SV13 ) @ SV45 )
= $false )
| ( ( element_of_collection @ SV13 @ ( top_of_basis @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(186,plain,
! [SV14: $i,SV50: $i,SV32: $i] :
( ( ( subset_sets @ SV32 @ SV50 )
= $false )
| ( ( subset_sets @ SV14 @ SV50 )
= $true )
| ( ( subset_sets @ SV14 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(187,plain,
! [SV35: $i,SV43: $i,SV17: $i] :
( ( ( element_of_set @ SV17 @ SV43 )
= $false )
| ( ( element_of_set @ SV17 @ SV35 )
= $false )
| ( ( element_of_set @ SV17 @ ( intersection_of_sets @ SV35 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(188,plain,
! [SV36: $i,SV18: $i,SV53: $i,SV51: $i] :
( ( ( ~ ( subset_sets @ SV51 @ SV53 ) )
= $true )
| ( ( subset_sets @ ( intersection_of_sets @ SV18 @ SV51 ) @ ( intersection_of_sets @ SV36 @ SV53 ) )
= $true )
| ( ( subset_sets @ SV18 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(189,plain,
! [SV37: $i,SV19: $i,SV52: $i] :
( ( ( element_of_set @ SV52 @ SV19 )
= $false )
| ( ( element_of_set @ SV52 @ SV37 )
= $true )
| ( ( equal_sets @ SV19 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(190,plain,
! [SV6: $i,SV39: $i,SV24: $i,SV54: $i] :
( ( ( ~ ( element_of_collection @ SV54 @ SV24 )
| ! [SY126: $i] :
( ~ ( element_of_collection @ SY126 @ SV24 )
| ~ ( element_of_set @ SV39 @ ( intersection_of_sets @ SV54 @ SY126 ) )
| ( element_of_set @ SV39 @ ( f6 @ SV6 @ SV24 @ SV39 @ SV54 @ SY126 ) ) ) )
= $true )
| ( ( element_of_set @ SV39 @ SV6 )
= $false )
| ( ( basis @ SV6 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(191,plain,
! [SV7: $i,SV40: $i,SV25: $i,SV55: $i] :
( ( ( ~ ( element_of_collection @ SV55 @ SV25 )
| ! [SY127: $i] :
( ~ ( element_of_collection @ SY127 @ SV25 )
| ~ ( element_of_set @ SV40 @ ( intersection_of_sets @ SV55 @ SY127 ) )
| ( element_of_collection @ ( f6 @ SV7 @ SV25 @ SV40 @ SV55 @ SY127 ) @ SV25 ) ) )
= $true )
| ( ( element_of_set @ SV40 @ SV7 )
= $false )
| ( ( basis @ SV7 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(192,plain,
! [SV8: $i,SV41: $i,SV26: $i,SV56: $i] :
( ( ( ~ ( element_of_collection @ SV56 @ SV26 )
| ! [SY128: $i] :
( ~ ( element_of_collection @ SY128 @ SV26 )
| ~ ( element_of_set @ SV41 @ ( intersection_of_sets @ SV56 @ SY128 ) )
| ( subset_sets @ ( f6 @ SV8 @ SV26 @ SV41 @ SV56 @ SY128 ) @ ( intersection_of_sets @ SV56 @ SY128 ) ) ) )
= $true )
| ( ( element_of_set @ SV41 @ SV8 )
= $false )
| ( ( basis @ SV8 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(193,plain,
! [SV13: $i,SV31: $i,SV45: $i] :
( ( ( element_of_collection @ SV45 @ SV31 )
= $false )
| ( ( ~ ( subset_sets @ SV45 @ SV13 ) )
= $true )
| ( ( element_of_set @ ( f11 @ SV31 @ SV13 ) @ SV45 )
= $false )
| ( ( element_of_collection @ SV13 @ ( top_of_basis @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(194,plain,
! [SV36: $i,SV18: $i,SV53: $i,SV51: $i] :
( ( ( subset_sets @ SV51 @ SV53 )
= $false )
| ( ( subset_sets @ ( intersection_of_sets @ SV18 @ SV51 ) @ ( intersection_of_sets @ SV36 @ SV53 ) )
= $true )
| ( ( subset_sets @ SV18 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(195,plain,
! [SV6: $i,SV39: $i,SV24: $i,SV54: $i] :
( ( ( ~ ( element_of_collection @ SV54 @ SV24 ) )
= $true )
| ( ( ! [SY126: $i] :
( ~ ( element_of_collection @ SY126 @ SV24 )
| ~ ( element_of_set @ SV39 @ ( intersection_of_sets @ SV54 @ SY126 ) )
| ( element_of_set @ SV39 @ ( f6 @ SV6 @ SV24 @ SV39 @ SV54 @ SY126 ) ) ) )
= $true )
| ( ( element_of_set @ SV39 @ SV6 )
= $false )
| ( ( basis @ SV6 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(196,plain,
! [SV7: $i,SV40: $i,SV25: $i,SV55: $i] :
( ( ( ~ ( element_of_collection @ SV55 @ SV25 ) )
= $true )
| ( ( ! [SY127: $i] :
( ~ ( element_of_collection @ SY127 @ SV25 )
| ~ ( element_of_set @ SV40 @ ( intersection_of_sets @ SV55 @ SY127 ) )
| ( element_of_collection @ ( f6 @ SV7 @ SV25 @ SV40 @ SV55 @ SY127 ) @ SV25 ) ) )
= $true )
| ( ( element_of_set @ SV40 @ SV7 )
= $false )
| ( ( basis @ SV7 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(197,plain,
! [SV8: $i,SV41: $i,SV26: $i,SV56: $i] :
( ( ( ~ ( element_of_collection @ SV56 @ SV26 ) )
= $true )
| ( ( ! [SY128: $i] :
( ~ ( element_of_collection @ SY128 @ SV26 )
| ~ ( element_of_set @ SV41 @ ( intersection_of_sets @ SV56 @ SY128 ) )
| ( subset_sets @ ( f6 @ SV8 @ SV26 @ SV41 @ SV56 @ SY128 ) @ ( intersection_of_sets @ SV56 @ SY128 ) ) ) )
= $true )
| ( ( element_of_set @ SV41 @ SV8 )
= $false )
| ( ( basis @ SV8 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(198,plain,
! [SV31: $i,SV13: $i,SV45: $i] :
( ( ( subset_sets @ SV45 @ SV13 )
= $false )
| ( ( element_of_collection @ SV45 @ SV31 )
= $false )
| ( ( element_of_set @ ( f11 @ SV31 @ SV13 ) @ SV45 )
= $false )
| ( ( element_of_collection @ SV13 @ ( top_of_basis @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(199,plain,
! [SV6: $i,SV39: $i,SV24: $i,SV54: $i] :
( ( ( element_of_collection @ SV54 @ SV24 )
= $false )
| ( ( ! [SY126: $i] :
( ~ ( element_of_collection @ SY126 @ SV24 )
| ~ ( element_of_set @ SV39 @ ( intersection_of_sets @ SV54 @ SY126 ) )
| ( element_of_set @ SV39 @ ( f6 @ SV6 @ SV24 @ SV39 @ SV54 @ SY126 ) ) ) )
= $true )
| ( ( element_of_set @ SV39 @ SV6 )
= $false )
| ( ( basis @ SV6 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(200,plain,
! [SV7: $i,SV40: $i,SV25: $i,SV55: $i] :
( ( ( element_of_collection @ SV55 @ SV25 )
= $false )
| ( ( ! [SY127: $i] :
( ~ ( element_of_collection @ SY127 @ SV25 )
| ~ ( element_of_set @ SV40 @ ( intersection_of_sets @ SV55 @ SY127 ) )
| ( element_of_collection @ ( f6 @ SV7 @ SV25 @ SV40 @ SV55 @ SY127 ) @ SV25 ) ) )
= $true )
| ( ( element_of_set @ SV40 @ SV7 )
= $false )
| ( ( basis @ SV7 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(201,plain,
! [SV8: $i,SV41: $i,SV26: $i,SV56: $i] :
( ( ( element_of_collection @ SV56 @ SV26 )
= $false )
| ( ( ! [SY128: $i] :
( ~ ( element_of_collection @ SY128 @ SV26 )
| ~ ( element_of_set @ SV41 @ ( intersection_of_sets @ SV56 @ SY128 ) )
| ( subset_sets @ ( f6 @ SV8 @ SV26 @ SV41 @ SV56 @ SY128 ) @ ( intersection_of_sets @ SV56 @ SY128 ) ) ) )
= $true )
| ( ( element_of_set @ SV41 @ SV8 )
= $false )
| ( ( basis @ SV8 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(202,plain,
! [SV6: $i,SV54: $i,SV39: $i,SV24: $i,SV57: $i] :
( ( ( ~ ( element_of_collection @ SV57 @ SV24 )
| ~ ( element_of_set @ SV39 @ ( intersection_of_sets @ SV54 @ SV57 ) )
| ( element_of_set @ SV39 @ ( f6 @ SV6 @ SV24 @ SV39 @ SV54 @ SV57 ) ) )
= $true )
| ( ( element_of_collection @ SV54 @ SV24 )
= $false )
| ( ( element_of_set @ SV39 @ SV6 )
= $false )
| ( ( basis @ SV6 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(203,plain,
! [SV7: $i,SV55: $i,SV40: $i,SV25: $i,SV58: $i] :
( ( ( ~ ( element_of_collection @ SV58 @ SV25 )
| ~ ( element_of_set @ SV40 @ ( intersection_of_sets @ SV55 @ SV58 ) )
| ( element_of_collection @ ( f6 @ SV7 @ SV25 @ SV40 @ SV55 @ SV58 ) @ SV25 ) )
= $true )
| ( ( element_of_collection @ SV55 @ SV25 )
= $false )
| ( ( element_of_set @ SV40 @ SV7 )
= $false )
| ( ( basis @ SV7 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(204,plain,
! [SV8: $i,SV56: $i,SV41: $i,SV26: $i,SV59: $i] :
( ( ( ~ ( element_of_collection @ SV59 @ SV26 )
| ~ ( element_of_set @ SV41 @ ( intersection_of_sets @ SV56 @ SV59 ) )
| ( subset_sets @ ( f6 @ SV8 @ SV26 @ SV41 @ SV56 @ SV59 ) @ ( intersection_of_sets @ SV56 @ SV59 ) ) )
= $true )
| ( ( element_of_collection @ SV56 @ SV26 )
= $false )
| ( ( element_of_set @ SV41 @ SV8 )
= $false )
| ( ( basis @ SV8 @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(205,plain,
! [SV6: $i,SV54: $i,SV39: $i,SV24: $i,SV57: $i] :
( ( ( ~ ( element_of_collection @ SV57 @ SV24 ) )
= $true )
| ( ( ~ ( element_of_set @ SV39 @ ( intersection_of_sets @ SV54 @ SV57 ) )
| ( element_of_set @ SV39 @ ( f6 @ SV6 @ SV24 @ SV39 @ SV54 @ SV57 ) ) )
= $true )
| ( ( element_of_collection @ SV54 @ SV24 )
= $false )
| ( ( element_of_set @ SV39 @ SV6 )
= $false )
| ( ( basis @ SV6 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(206,plain,
! [SV7: $i,SV55: $i,SV40: $i,SV25: $i,SV58: $i] :
( ( ( ~ ( element_of_collection @ SV58 @ SV25 ) )
= $true )
| ( ( ~ ( element_of_set @ SV40 @ ( intersection_of_sets @ SV55 @ SV58 ) )
| ( element_of_collection @ ( f6 @ SV7 @ SV25 @ SV40 @ SV55 @ SV58 ) @ SV25 ) )
= $true )
| ( ( element_of_collection @ SV55 @ SV25 )
= $false )
| ( ( element_of_set @ SV40 @ SV7 )
= $false )
| ( ( basis @ SV7 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(207,plain,
! [SV8: $i,SV56: $i,SV41: $i,SV26: $i,SV59: $i] :
( ( ( ~ ( element_of_collection @ SV59 @ SV26 ) )
= $true )
| ( ( ~ ( element_of_set @ SV41 @ ( intersection_of_sets @ SV56 @ SV59 ) )
| ( subset_sets @ ( f6 @ SV8 @ SV26 @ SV41 @ SV56 @ SV59 ) @ ( intersection_of_sets @ SV56 @ SV59 ) ) )
= $true )
| ( ( element_of_collection @ SV56 @ SV26 )
= $false )
| ( ( element_of_set @ SV41 @ SV8 )
= $false )
| ( ( basis @ SV8 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(208,plain,
! [SV6: $i,SV54: $i,SV39: $i,SV24: $i,SV57: $i] :
( ( ( element_of_collection @ SV57 @ SV24 )
= $false )
| ( ( ~ ( element_of_set @ SV39 @ ( intersection_of_sets @ SV54 @ SV57 ) )
| ( element_of_set @ SV39 @ ( f6 @ SV6 @ SV24 @ SV39 @ SV54 @ SV57 ) ) )
= $true )
| ( ( element_of_collection @ SV54 @ SV24 )
= $false )
| ( ( element_of_set @ SV39 @ SV6 )
= $false )
| ( ( basis @ SV6 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(209,plain,
! [SV7: $i,SV55: $i,SV40: $i,SV25: $i,SV58: $i] :
( ( ( element_of_collection @ SV58 @ SV25 )
= $false )
| ( ( ~ ( element_of_set @ SV40 @ ( intersection_of_sets @ SV55 @ SV58 ) )
| ( element_of_collection @ ( f6 @ SV7 @ SV25 @ SV40 @ SV55 @ SV58 ) @ SV25 ) )
= $true )
| ( ( element_of_collection @ SV55 @ SV25 )
= $false )
| ( ( element_of_set @ SV40 @ SV7 )
= $false )
| ( ( basis @ SV7 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(210,plain,
! [SV8: $i,SV56: $i,SV41: $i,SV26: $i,SV59: $i] :
( ( ( element_of_collection @ SV59 @ SV26 )
= $false )
| ( ( ~ ( element_of_set @ SV41 @ ( intersection_of_sets @ SV56 @ SV59 ) )
| ( subset_sets @ ( f6 @ SV8 @ SV26 @ SV41 @ SV56 @ SV59 ) @ ( intersection_of_sets @ SV56 @ SV59 ) ) )
= $true )
| ( ( element_of_collection @ SV56 @ SV26 )
= $false )
| ( ( element_of_set @ SV41 @ SV8 )
= $false )
| ( ( basis @ SV8 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(211,plain,
! [SV24: $i,SV6: $i,SV57: $i,SV54: $i,SV39: $i] :
( ( ( ~ ( element_of_set @ SV39 @ ( intersection_of_sets @ SV54 @ SV57 ) ) )
= $true )
| ( ( element_of_set @ SV39 @ ( f6 @ SV6 @ SV24 @ SV39 @ SV54 @ SV57 ) )
= $true )
| ( ( element_of_collection @ SV57 @ SV24 )
= $false )
| ( ( element_of_collection @ SV54 @ SV24 )
= $false )
| ( ( element_of_set @ SV39 @ SV6 )
= $false )
| ( ( basis @ SV6 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(212,plain,
! [SV25: $i,SV7: $i,SV58: $i,SV55: $i,SV40: $i] :
( ( ( ~ ( element_of_set @ SV40 @ ( intersection_of_sets @ SV55 @ SV58 ) ) )
= $true )
| ( ( element_of_collection @ ( f6 @ SV7 @ SV25 @ SV40 @ SV55 @ SV58 ) @ SV25 )
= $true )
| ( ( element_of_collection @ SV58 @ SV25 )
= $false )
| ( ( element_of_collection @ SV55 @ SV25 )
= $false )
| ( ( element_of_set @ SV40 @ SV7 )
= $false )
| ( ( basis @ SV7 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(213,plain,
! [SV26: $i,SV8: $i,SV59: $i,SV56: $i,SV41: $i] :
( ( ( ~ ( element_of_set @ SV41 @ ( intersection_of_sets @ SV56 @ SV59 ) ) )
= $true )
| ( ( subset_sets @ ( f6 @ SV8 @ SV26 @ SV41 @ SV56 @ SV59 ) @ ( intersection_of_sets @ SV56 @ SV59 ) )
= $true )
| ( ( element_of_collection @ SV59 @ SV26 )
= $false )
| ( ( element_of_collection @ SV56 @ SV26 )
= $false )
| ( ( element_of_set @ SV41 @ SV8 )
= $false )
| ( ( basis @ SV8 @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(214,plain,
! [SV24: $i,SV6: $i,SV57: $i,SV54: $i,SV39: $i] :
( ( ( element_of_set @ SV39 @ ( intersection_of_sets @ SV54 @ SV57 ) )
= $false )
| ( ( element_of_set @ SV39 @ ( f6 @ SV6 @ SV24 @ SV39 @ SV54 @ SV57 ) )
= $true )
| ( ( element_of_collection @ SV57 @ SV24 )
= $false )
| ( ( element_of_collection @ SV54 @ SV24 )
= $false )
| ( ( element_of_set @ SV39 @ SV6 )
= $false )
| ( ( basis @ SV6 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(215,plain,
! [SV25: $i,SV7: $i,SV58: $i,SV55: $i,SV40: $i] :
( ( ( element_of_set @ SV40 @ ( intersection_of_sets @ SV55 @ SV58 ) )
= $false )
| ( ( element_of_collection @ ( f6 @ SV7 @ SV25 @ SV40 @ SV55 @ SV58 ) @ SV25 )
= $true )
| ( ( element_of_collection @ SV58 @ SV25 )
= $false )
| ( ( element_of_collection @ SV55 @ SV25 )
= $false )
| ( ( element_of_set @ SV40 @ SV7 )
= $false )
| ( ( basis @ SV7 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(216,plain,
! [SV26: $i,SV8: $i,SV59: $i,SV56: $i,SV41: $i] :
( ( ( element_of_set @ SV41 @ ( intersection_of_sets @ SV56 @ SV59 ) )
= $false )
| ( ( subset_sets @ ( f6 @ SV8 @ SV26 @ SV41 @ SV56 @ SV59 ) @ ( intersection_of_sets @ SV56 @ SV59 ) )
= $true )
| ( ( element_of_collection @ SV59 @ SV26 )
= $false )
| ( ( element_of_collection @ SV56 @ SV26 )
= $false )
| ( ( element_of_set @ SV41 @ SV8 )
= $false )
| ( ( basis @ SV8 @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(217,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[59,216,215,214,198,194,189,187,186,184,183,182,178,162,161,138,129,120,119,101,82,81]) ).
thf(218,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[217]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : TOP004-2 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n021.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 May 29 09:50:27 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 21
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.38 .
% 0.13/0.38 (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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:23,loop_count:0,foatp_calls:0,translation:fof_full)............
% 0.19/0.50
% 0.19/0.50 ********************************
% 0.19/0.50 * All subproblems solved! *
% 0.19/0.50 ********************************
% 0.19/0.50 % SZS status Unsatisfiable 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:217,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.52
% 0.19/0.52 %**** Beginning of derivation protocol ****
% 0.19/0.52 % SZS output start CNFRefutation
% See solution above
% 0.19/0.52
% 0.19/0.52 %**** End of derivation protocol ****
% 0.19/0.52 %**** no. of clauses in derivation: 218 ****
% 0.19/0.52 %**** clause counter: 217 ****
% 0.19/0.52
% 0.19/0.52 % SZS status Unsatisfiable 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:217,loop_count:0,foatp_calls:1,translation:fof_full)
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