%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET862-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:42:23 AM UTC 2026
% Result : Unsatisfiable 85.86s 14.52s
% Output : CNFRefutation 85.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 16
% Syntax : Number of formulae : 137 ( 79 unt; 0 typ; 0 def)
% Number of atoms : 829 ( 219 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 3067 ( 207 ~; 290 |; 0 &;2570 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 7 con; 0-3 aty)
% Number of variables : 443 ( 0 ^; 443 !; 0 ?; 443 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Main_OsubsetI__1,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(tp_c_Zorn_Ochain,type,
c_Zorn_Ochain: $i > $i > $i ).
thf(tp_c_Zorn_Ochain__extend__1,type,
c_Zorn_Ochain__extend__1: $i > $i > $i > $i ).
thf(tp_c_Zorn_Omaxchain,type,
c_Zorn_Omaxchain: $i > $i > $i ).
thf(tp_c_Zorn_Omaxchain__super__lemma__1,type,
c_Zorn_Omaxchain__super__lemma__1: $i > $i > $i > $i ).
thf(tp_c_emptyset,type,
c_emptyset: $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_c_insert,type,
c_insert: $i > $i > $i > $i ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_c_union,type,
c_union: $i > $i > $i > $i ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_set,type,
tc_set: $i > $i ).
thf(tp_v_S,type,
v_S: $i ).
thf(tp_v_c,type,
v_c: $i ).
thf(tp_v_x,type,
v_x: $i > $i ).
thf(tp_v_y,type,
v_y: $i ).
thf(1,axiom,
! [V_z: $i,V_x: $i,T_a: $i,V_c: $i,V_S: $i,V_y: $i] :
( ~ ( c_in @ V_z @ V_x @ T_a )
| ~ ( c_in @ V_c @ ( c_Zorn_Omaxchain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ V_x @ c_emptyset @ ( tc_set @ T_a ) ) @ V_c @ ( tc_set @ T_a ) ) @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ V_c @ V_y @ T_a ) @ V_y @ ( tc_set @ T_a ) )
| ( c_in @ V_z @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_1) ).
thf(2,axiom,
! [V_z: $i,V_x: $i,T_a: $i,V_c: $i,V_S: $i,V_y: $i] :
( ~ ( c_in @ V_z @ V_x @ T_a )
| ~ ( c_in @ V_c @ ( c_Zorn_Omaxchain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ V_x @ c_emptyset @ ( tc_set @ T_a ) ) @ V_c @ ( tc_set @ T_a ) ) @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_in @ V_z @ V_y @ T_a )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ V_c @ V_y @ T_a ) @ V_c @ ( tc_set @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_0) ).
thf(3,axiom,
! [V_z: $i,V_S: $i,T_a: $i,V_c: $i] :
( ~ ( c_in @ V_z @ V_S @ ( tc_set @ T_a ) )
| ~ ( c_in @ V_c @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ V_c @ V_z @ T_a ) @ V_z @ ( tc_set @ T_a ) )
| ( c_in @ ( c_union @ ( c_insert @ V_z @ c_emptyset @ ( tc_set @ T_a ) ) @ V_c @ ( tc_set @ T_a ) ) @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_1) ).
thf(4,axiom,
! [V_z: $i,V_S: $i,T_a: $i,V_c: $i] :
( ~ ( c_in @ V_z @ V_S @ ( tc_set @ T_a ) )
| ~ ( c_in @ V_c @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_in @ ( c_Zorn_Ochain__extend__1 @ V_c @ V_z @ T_a ) @ V_c @ ( tc_set @ T_a ) )
| ( c_in @ ( c_union @ ( c_insert @ V_z @ c_emptyset @ ( tc_set @ T_a ) ) @ V_c @ ( tc_set @ T_a ) ) @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_0) ).
thf(5,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ V_A @ V_B @ T_a ) @ V_B @ T_a )
| ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(6,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ V_A @ V_B @ T_a ) @ V_A @ T_a )
| ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(7,axiom,
! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_in @ V_c @ V_B @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(8,axiom,
! [V_B: $i,V_A: $i,T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( V_A = V_B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(9,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(10,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[9]) ).
thf(11,negated_conjecture,
! [V_U: $i] :
( ( V_U
!= ( v_x @ V_U ) )
| ~ ( c_in @ V_U @ v_S @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(12,negated_conjecture,
! [V_U: $i] :
( ( c_lessequals @ V_U @ ( v_x @ V_U ) @ ( tc_set @ t_a ) )
| ~ ( c_in @ V_U @ v_S @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(13,negated_conjecture,
! [V_U: $i] :
( ( c_in @ ( v_x @ V_U ) @ v_S @ ( tc_set @ t_a ) )
| ~ ( c_in @ V_U @ v_S @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(14,negated_conjecture,
! [V_U: $i] :
( ( c_lessequals @ V_U @ v_y @ ( tc_set @ t_a ) )
| ~ ( c_in @ V_U @ v_c @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(15,negated_conjecture,
c_in @ v_y @ v_S @ ( tc_set @ t_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(16,negated_conjecture,
c_in @ v_c @ ( c_Zorn_Ochain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(17,negated_conjecture,
c_in @ v_c @ ( c_Zorn_Omaxchain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(18,plain,
$false = $false,
inference(unfold_def,[status(thm)],[10]) ).
thf(19,plain,
( ( ! [V_z: $i,V_x: $i,T_a: $i,V_c: $i,V_S: $i,V_y: $i] :
( ~ ( c_in @ V_z @ V_x @ T_a )
| ~ ( c_in @ V_c @ ( c_Zorn_Omaxchain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ V_x @ c_emptyset @ ( tc_set @ T_a ) ) @ V_c @ ( tc_set @ T_a ) ) @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ V_c @ V_y @ T_a ) @ V_y @ ( tc_set @ T_a ) )
| ( c_in @ V_z @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(20,plain,
( ( ! [V_z: $i,V_x: $i,T_a: $i,V_c: $i,V_S: $i,V_y: $i] :
( ~ ( c_in @ V_z @ V_x @ T_a )
| ~ ( c_in @ V_c @ ( c_Zorn_Omaxchain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ V_x @ c_emptyset @ ( tc_set @ T_a ) ) @ V_c @ ( tc_set @ T_a ) ) @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_in @ V_z @ V_y @ T_a )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ V_c @ V_y @ T_a ) @ V_c @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(21,plain,
( ( ! [V_z: $i,V_S: $i,T_a: $i,V_c: $i] :
( ~ ( c_in @ V_z @ V_S @ ( tc_set @ T_a ) )
| ~ ( c_in @ V_c @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ V_c @ V_z @ T_a ) @ V_z @ ( tc_set @ T_a ) )
| ( c_in @ ( c_union @ ( c_insert @ V_z @ c_emptyset @ ( tc_set @ T_a ) ) @ V_c @ ( tc_set @ T_a ) ) @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(22,plain,
( ( ! [V_z: $i,V_S: $i,T_a: $i,V_c: $i] :
( ~ ( c_in @ V_z @ V_S @ ( tc_set @ T_a ) )
| ~ ( c_in @ V_c @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_in @ ( c_Zorn_Ochain__extend__1 @ V_c @ V_z @ T_a ) @ V_c @ ( tc_set @ T_a ) )
| ( c_in @ ( c_union @ ( c_insert @ V_z @ c_emptyset @ ( tc_set @ T_a ) ) @ V_c @ ( tc_set @ T_a ) ) @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(23,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ V_A @ V_B @ T_a ) @ V_B @ T_a )
| ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(24,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ V_A @ V_B @ T_a ) @ V_A @ T_a )
| ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(25,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_in @ V_c @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(26,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( V_A = V_B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(27,plain,
( ( ! [V_U: $i] :
( ( V_U
!= ( v_x @ V_U ) )
| ~ ( c_in @ V_U @ v_S @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(28,plain,
( ( ! [V_U: $i] :
( ( c_lessequals @ V_U @ ( v_x @ V_U ) @ ( tc_set @ t_a ) )
| ~ ( c_in @ V_U @ v_S @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(29,plain,
( ( ! [V_U: $i] :
( ( c_in @ ( v_x @ V_U ) @ v_S @ ( tc_set @ t_a ) )
| ~ ( c_in @ V_U @ v_S @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(30,plain,
( ( ! [V_U: $i] :
( ( c_lessequals @ V_U @ v_y @ ( tc_set @ t_a ) )
| ~ ( c_in @ V_U @ v_c @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(31,plain,
( ( c_in @ v_y @ v_S @ ( tc_set @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(32,plain,
( ( c_in @ v_c @ ( c_Zorn_Ochain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(33,plain,
( ( c_in @ v_c @ ( c_Zorn_Omaxchain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(34,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(35,plain,
( ( c_in @ v_c @ ( c_Zorn_Omaxchain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(36,plain,
( ( c_in @ v_c @ ( c_Zorn_Ochain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(37,plain,
( ( c_in @ v_y @ v_S @ ( tc_set @ t_a ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(38,plain,
( ( ! [V_U: $i] :
( ( c_lessequals @ V_U @ v_y @ ( tc_set @ t_a ) )
| ~ ( c_in @ V_U @ v_c @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(39,plain,
( ( ! [V_U: $i] :
( ( c_in @ ( v_x @ V_U ) @ v_S @ ( tc_set @ t_a ) )
| ~ ( c_in @ V_U @ v_S @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(40,plain,
( ( ! [V_U: $i] :
( ( c_lessequals @ V_U @ ( v_x @ V_U ) @ ( tc_set @ t_a ) )
| ~ ( c_in @ V_U @ v_S @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(41,plain,
( ( ! [V_U: $i] :
( ( V_U
!= ( v_x @ V_U ) )
| ~ ( c_in @ V_U @ v_S @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(42,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_A @ ( tc_set @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( V_A = V_B ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(43,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_in @ V_c @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(44,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ V_A @ V_B @ T_a ) @ V_A @ T_a )
| ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(45,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ V_A @ V_B @ T_a ) @ V_B @ T_a )
| ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(46,plain,
( ( ! [V_z: $i,V_S: $i,T_a: $i,V_c: $i] :
( ~ ( c_in @ V_z @ V_S @ ( tc_set @ T_a ) )
| ~ ( c_in @ V_c @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_in @ ( c_Zorn_Ochain__extend__1 @ V_c @ V_z @ T_a ) @ V_c @ ( tc_set @ T_a ) )
| ( c_in @ ( c_union @ ( c_insert @ V_z @ c_emptyset @ ( tc_set @ T_a ) ) @ V_c @ ( tc_set @ T_a ) ) @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(47,plain,
( ( ! [V_z: $i,V_S: $i,T_a: $i,V_c: $i] :
( ~ ( c_in @ V_z @ V_S @ ( tc_set @ T_a ) )
| ~ ( c_in @ V_c @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ V_c @ V_z @ T_a ) @ V_z @ ( tc_set @ T_a ) )
| ( c_in @ ( c_union @ ( c_insert @ V_z @ c_emptyset @ ( tc_set @ T_a ) ) @ V_c @ ( tc_set @ T_a ) ) @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(48,plain,
( ( ! [V_z: $i,V_x: $i,T_a: $i,V_c: $i,V_S: $i,V_y: $i] :
( ~ ( c_in @ V_z @ V_x @ T_a )
| ~ ( c_in @ V_c @ ( c_Zorn_Omaxchain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ V_x @ c_emptyset @ ( tc_set @ T_a ) ) @ V_c @ ( tc_set @ T_a ) ) @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_in @ V_z @ V_y @ T_a )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ V_c @ V_y @ T_a ) @ V_c @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(49,plain,
( ( ! [V_z: $i,V_x: $i,T_a: $i,V_c: $i,V_S: $i,V_y: $i] :
( ~ ( c_in @ V_z @ V_x @ T_a )
| ~ ( c_in @ V_c @ ( c_Zorn_Omaxchain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ V_x @ c_emptyset @ ( tc_set @ T_a ) ) @ V_c @ ( tc_set @ T_a ) ) @ ( c_Zorn_Ochain @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ V_c @ V_y @ T_a ) @ V_y @ ( tc_set @ T_a ) )
| ( c_in @ V_z @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(50,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[34]) ).
thf(51,plain,
( ( ! [SX0: $i] :
( ( SX0
!= ( v_x @ SX0 ) )
| ~ ( c_in @ SX0 @ v_S @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(52,plain,
! [SV1: $i] :
( ( ( c_lessequals @ SV1 @ v_y @ ( tc_set @ t_a ) )
| ~ ( c_in @ SV1 @ v_c @ ( tc_set @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(53,plain,
! [SV2: $i] :
( ( ( c_in @ ( v_x @ SV2 ) @ v_S @ ( tc_set @ t_a ) )
| ~ ( c_in @ SV2 @ v_S @ ( tc_set @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(54,plain,
! [SV3: $i] :
( ( ( c_lessequals @ SV3 @ ( v_x @ SV3 ) @ ( tc_set @ t_a ) )
| ~ ( c_in @ SV3 @ v_S @ ( tc_set @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(55,plain,
! [SV4: $i] :
( ( ! [SY37: $i,SY38: $i] :
( ~ ( c_lessequals @ SV4 @ SY37 @ ( tc_set @ SY38 ) )
| ~ ( c_lessequals @ SY37 @ SV4 @ ( tc_set @ SY38 ) )
| ( SY37 = SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(56,plain,
! [SV5: $i] :
( ( ! [SY39: $i,SY40: $i,SY41: $i] :
( ~ ( c_in @ SV5 @ SY39 @ SY40 )
| ~ ( c_lessequals @ SY39 @ SY41 @ ( tc_set @ SY40 ) )
| ( c_in @ SV5 @ SY41 @ SY40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(57,plain,
! [SV6: $i] :
( ( ! [SY42: $i,SY43: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ SV6 @ SY42 @ SY43 ) @ SV6 @ SY43 )
| ( c_lessequals @ SV6 @ SY42 @ ( tc_set @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(58,plain,
! [SV7: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ SV7 @ SY44 @ SY45 ) @ SY44 @ SY45 )
| ( c_lessequals @ SV7 @ SY44 @ ( tc_set @ SY45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(59,plain,
! [SV8: $i] :
( ( ! [SY46: $i,SY47: $i,SY48: $i] :
( ~ ( c_in @ SV8 @ SY46 @ ( tc_set @ SY47 ) )
| ~ ( c_in @ SY48 @ ( c_Zorn_Ochain @ SY46 @ SY47 ) @ ( tc_set @ ( tc_set @ SY47 ) ) )
| ( c_in @ ( c_Zorn_Ochain__extend__1 @ SY48 @ SV8 @ SY47 ) @ SY48 @ ( tc_set @ SY47 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV8 @ c_emptyset @ ( tc_set @ SY47 ) ) @ SY48 @ ( tc_set @ SY47 ) ) @ ( c_Zorn_Ochain @ SY46 @ SY47 ) @ ( tc_set @ ( tc_set @ SY47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(60,plain,
! [SV9: $i] :
( ( ! [SY49: $i,SY50: $i,SY51: $i] :
( ~ ( c_in @ SV9 @ SY49 @ ( tc_set @ SY50 ) )
| ~ ( c_in @ SY51 @ ( c_Zorn_Ochain @ SY49 @ SY50 ) @ ( tc_set @ ( tc_set @ SY50 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ SY51 @ SV9 @ SY50 ) @ SV9 @ ( tc_set @ SY50 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV9 @ c_emptyset @ ( tc_set @ SY50 ) ) @ SY51 @ ( tc_set @ SY50 ) ) @ ( c_Zorn_Ochain @ SY49 @ SY50 ) @ ( tc_set @ ( tc_set @ SY50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(61,plain,
! [SV10: $i] :
( ( ! [SY52: $i,SY53: $i,SY54: $i,SY55: $i,SY56: $i] :
( ~ ( c_in @ SV10 @ SY52 @ SY53 )
| ~ ( c_in @ SY54 @ ( c_Zorn_Omaxchain @ SY55 @ SY53 ) @ ( tc_set @ ( tc_set @ SY53 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SY52 @ c_emptyset @ ( tc_set @ SY53 ) ) @ SY54 @ ( tc_set @ SY53 ) ) @ ( c_Zorn_Ochain @ SY55 @ SY53 ) @ ( tc_set @ ( tc_set @ SY53 ) ) )
| ( c_in @ SV10 @ SY56 @ SY53 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SY54 @ SY56 @ SY53 ) @ SY54 @ ( tc_set @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(62,plain,
! [SV11: $i] :
( ( ! [SY57: $i,SY58: $i,SY59: $i,SY60: $i,SY61: $i] :
( ~ ( c_in @ SV11 @ SY57 @ SY58 )
| ~ ( c_in @ SY59 @ ( c_Zorn_Omaxchain @ SY60 @ SY58 ) @ ( tc_set @ ( tc_set @ SY58 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SY57 @ c_emptyset @ ( tc_set @ SY58 ) ) @ SY59 @ ( tc_set @ SY58 ) ) @ ( c_Zorn_Ochain @ SY60 @ SY58 ) @ ( tc_set @ ( tc_set @ SY58 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SY59 @ SY61 @ SY58 ) @ SY61 @ ( tc_set @ SY58 ) )
| ( c_in @ SV11 @ SY61 @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(63,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(64,plain,
! [SV12: $i] :
( ( ( SV12
!= ( v_x @ SV12 ) )
| ~ ( c_in @ SV12 @ v_S @ ( tc_set @ t_a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(65,plain,
! [SV1: $i] :
( ( ( c_lessequals @ SV1 @ v_y @ ( tc_set @ t_a ) )
= $true )
| ( ( ~ ( c_in @ SV1 @ v_c @ ( tc_set @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(66,plain,
! [SV2: $i] :
( ( ( c_in @ ( v_x @ SV2 ) @ v_S @ ( tc_set @ t_a ) )
= $true )
| ( ( ~ ( c_in @ SV2 @ v_S @ ( tc_set @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(67,plain,
! [SV3: $i] :
( ( ( c_lessequals @ SV3 @ ( v_x @ SV3 ) @ ( tc_set @ t_a ) )
= $true )
| ( ( ~ ( c_in @ SV3 @ v_S @ ( tc_set @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(68,plain,
! [SV13: $i,SV4: $i] :
( ( ! [SY62: $i] :
( ~ ( c_lessequals @ SV4 @ SV13 @ ( tc_set @ SY62 ) )
| ~ ( c_lessequals @ SV13 @ SV4 @ ( tc_set @ SY62 ) )
| ( SV13 = SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(69,plain,
! [SV14: $i,SV5: $i] :
( ( ! [SY63: $i,SY64: $i] :
( ~ ( c_in @ SV5 @ SV14 @ SY63 )
| ~ ( c_lessequals @ SV14 @ SY64 @ ( tc_set @ SY63 ) )
| ( c_in @ SV5 @ SY64 @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(70,plain,
! [SV15: $i,SV6: $i] :
( ( ! [SY65: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ SV6 @ SV15 @ SY65 ) @ SV6 @ SY65 )
| ( c_lessequals @ SV6 @ SV15 @ ( tc_set @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(71,plain,
! [SV16: $i,SV7: $i] :
( ( ! [SY66: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ SV7 @ SV16 @ SY66 ) @ SV16 @ SY66 )
| ( c_lessequals @ SV7 @ SV16 @ ( tc_set @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(72,plain,
! [SV17: $i,SV8: $i] :
( ( ! [SY67: $i,SY68: $i] :
( ~ ( c_in @ SV8 @ SV17 @ ( tc_set @ SY67 ) )
| ~ ( c_in @ SY68 @ ( c_Zorn_Ochain @ SV17 @ SY67 ) @ ( tc_set @ ( tc_set @ SY67 ) ) )
| ( c_in @ ( c_Zorn_Ochain__extend__1 @ SY68 @ SV8 @ SY67 ) @ SY68 @ ( tc_set @ SY67 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV8 @ c_emptyset @ ( tc_set @ SY67 ) ) @ SY68 @ ( tc_set @ SY67 ) ) @ ( c_Zorn_Ochain @ SV17 @ SY67 ) @ ( tc_set @ ( tc_set @ SY67 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(73,plain,
! [SV18: $i,SV9: $i] :
( ( ! [SY69: $i,SY70: $i] :
( ~ ( c_in @ SV9 @ SV18 @ ( tc_set @ SY69 ) )
| ~ ( c_in @ SY70 @ ( c_Zorn_Ochain @ SV18 @ SY69 ) @ ( tc_set @ ( tc_set @ SY69 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ SY70 @ SV9 @ SY69 ) @ SV9 @ ( tc_set @ SY69 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV9 @ c_emptyset @ ( tc_set @ SY69 ) ) @ SY70 @ ( tc_set @ SY69 ) ) @ ( c_Zorn_Ochain @ SV18 @ SY69 ) @ ( tc_set @ ( tc_set @ SY69 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(74,plain,
! [SV19: $i,SV10: $i] :
( ( ! [SY71: $i,SY72: $i,SY73: $i,SY74: $i] :
( ~ ( c_in @ SV10 @ SV19 @ SY71 )
| ~ ( c_in @ SY72 @ ( c_Zorn_Omaxchain @ SY73 @ SY71 ) @ ( tc_set @ ( tc_set @ SY71 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV19 @ c_emptyset @ ( tc_set @ SY71 ) ) @ SY72 @ ( tc_set @ SY71 ) ) @ ( c_Zorn_Ochain @ SY73 @ SY71 ) @ ( tc_set @ ( tc_set @ SY71 ) ) )
| ( c_in @ SV10 @ SY74 @ SY71 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SY72 @ SY74 @ SY71 ) @ SY72 @ ( tc_set @ SY71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(75,plain,
! [SV20: $i,SV11: $i] :
( ( ! [SY75: $i,SY76: $i,SY77: $i,SY78: $i] :
( ~ ( c_in @ SV11 @ SV20 @ SY75 )
| ~ ( c_in @ SY76 @ ( c_Zorn_Omaxchain @ SY77 @ SY75 ) @ ( tc_set @ ( tc_set @ SY75 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV20 @ c_emptyset @ ( tc_set @ SY75 ) ) @ SY76 @ ( tc_set @ SY75 ) ) @ ( c_Zorn_Ochain @ SY77 @ SY75 ) @ ( tc_set @ ( tc_set @ SY75 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SY76 @ SY78 @ SY75 ) @ SY78 @ ( tc_set @ SY75 ) )
| ( c_in @ SV11 @ SY78 @ SY75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(76,plain,
! [SV12: $i] :
( ( ( SV12
!= ( v_x @ SV12 ) )
= $true )
| ( ( ~ ( c_in @ SV12 @ v_S @ ( tc_set @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(77,plain,
! [SV1: $i] :
( ( ( c_in @ SV1 @ v_c @ ( tc_set @ t_a ) )
= $false )
| ( ( c_lessequals @ SV1 @ v_y @ ( tc_set @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(78,plain,
! [SV2: $i] :
( ( ( c_in @ SV2 @ v_S @ ( tc_set @ t_a ) )
= $false )
| ( ( c_in @ ( v_x @ SV2 ) @ v_S @ ( tc_set @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(79,plain,
! [SV3: $i] :
( ( ( c_in @ SV3 @ v_S @ ( tc_set @ t_a ) )
= $false )
| ( ( c_lessequals @ SV3 @ ( v_x @ SV3 ) @ ( tc_set @ t_a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(80,plain,
! [SV21: $i,SV13: $i,SV4: $i] :
( ( ~ ( c_lessequals @ SV4 @ SV13 @ ( tc_set @ SV21 ) )
| ~ ( c_lessequals @ SV13 @ SV4 @ ( tc_set @ SV21 ) )
| ( SV13 = SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(81,plain,
! [SV22: $i,SV14: $i,SV5: $i] :
( ( ! [SY79: $i] :
( ~ ( c_in @ SV5 @ SV14 @ SV22 )
| ~ ( c_lessequals @ SV14 @ SY79 @ ( tc_set @ SV22 ) )
| ( c_in @ SV5 @ SY79 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(82,plain,
! [SV23: $i,SV15: $i,SV6: $i] :
( ( ( c_in @ ( c_Main_OsubsetI__1 @ SV6 @ SV15 @ SV23 ) @ SV6 @ SV23 )
| ( c_lessequals @ SV6 @ SV15 @ ( tc_set @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(83,plain,
! [SV24: $i,SV16: $i,SV7: $i] :
( ( ~ ( c_in @ ( c_Main_OsubsetI__1 @ SV7 @ SV16 @ SV24 ) @ SV16 @ SV24 )
| ( c_lessequals @ SV7 @ SV16 @ ( tc_set @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(84,plain,
! [SV25: $i,SV17: $i,SV8: $i] :
( ( ! [SY80: $i] :
( ~ ( c_in @ SV8 @ SV17 @ ( tc_set @ SV25 ) )
| ~ ( c_in @ SY80 @ ( c_Zorn_Ochain @ SV17 @ SV25 ) @ ( tc_set @ ( tc_set @ SV25 ) ) )
| ( c_in @ ( c_Zorn_Ochain__extend__1 @ SY80 @ SV8 @ SV25 ) @ SY80 @ ( tc_set @ SV25 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV8 @ c_emptyset @ ( tc_set @ SV25 ) ) @ SY80 @ ( tc_set @ SV25 ) ) @ ( c_Zorn_Ochain @ SV17 @ SV25 ) @ ( tc_set @ ( tc_set @ SV25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(85,plain,
! [SV26: $i,SV18: $i,SV9: $i] :
( ( ! [SY81: $i] :
( ~ ( c_in @ SV9 @ SV18 @ ( tc_set @ SV26 ) )
| ~ ( c_in @ SY81 @ ( c_Zorn_Ochain @ SV18 @ SV26 ) @ ( tc_set @ ( tc_set @ SV26 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ SY81 @ SV9 @ SV26 ) @ SV9 @ ( tc_set @ SV26 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV9 @ c_emptyset @ ( tc_set @ SV26 ) ) @ SY81 @ ( tc_set @ SV26 ) ) @ ( c_Zorn_Ochain @ SV18 @ SV26 ) @ ( tc_set @ ( tc_set @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(86,plain,
! [SV27: $i,SV19: $i,SV10: $i] :
( ( ! [SY82: $i,SY83: $i,SY84: $i] :
( ~ ( c_in @ SV10 @ SV19 @ SV27 )
| ~ ( c_in @ SY82 @ ( c_Zorn_Omaxchain @ SY83 @ SV27 ) @ ( tc_set @ ( tc_set @ SV27 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV19 @ c_emptyset @ ( tc_set @ SV27 ) ) @ SY82 @ ( tc_set @ SV27 ) ) @ ( c_Zorn_Ochain @ SY83 @ SV27 ) @ ( tc_set @ ( tc_set @ SV27 ) ) )
| ( c_in @ SV10 @ SY84 @ SV27 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SY82 @ SY84 @ SV27 ) @ SY82 @ ( tc_set @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(87,plain,
! [SV28: $i,SV20: $i,SV11: $i] :
( ( ! [SY85: $i,SY86: $i,SY87: $i] :
( ~ ( c_in @ SV11 @ SV20 @ SV28 )
| ~ ( c_in @ SY85 @ ( c_Zorn_Omaxchain @ SY86 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV20 @ c_emptyset @ ( tc_set @ SV28 ) ) @ SY85 @ ( tc_set @ SV28 ) ) @ ( c_Zorn_Ochain @ SY86 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SY85 @ SY87 @ SV28 ) @ SY87 @ ( tc_set @ SV28 ) )
| ( c_in @ SV11 @ SY87 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(88,plain,
! [SV12: $i] :
( ( ( SV12
= ( v_x @ SV12 ) )
= $false )
| ( ( ~ ( c_in @ SV12 @ v_S @ ( tc_set @ t_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(89,plain,
! [SV21: $i,SV13: $i,SV4: $i] :
( ( ( ~ ( c_lessequals @ SV4 @ SV13 @ ( tc_set @ SV21 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV13 @ SV4 @ ( tc_set @ SV21 ) )
| ( SV13 = SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(90,plain,
! [SV29: $i,SV22: $i,SV14: $i,SV5: $i] :
( ( ~ ( c_in @ SV5 @ SV14 @ SV22 )
| ~ ( c_lessequals @ SV14 @ SV29 @ ( tc_set @ SV22 ) )
| ( c_in @ SV5 @ SV29 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(91,plain,
! [SV23: $i,SV15: $i,SV6: $i] :
( ( ( c_in @ ( c_Main_OsubsetI__1 @ SV6 @ SV15 @ SV23 ) @ SV6 @ SV23 )
= $true )
| ( ( c_lessequals @ SV6 @ SV15 @ ( tc_set @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(92,plain,
! [SV24: $i,SV16: $i,SV7: $i] :
( ( ( ~ ( c_in @ ( c_Main_OsubsetI__1 @ SV7 @ SV16 @ SV24 ) @ SV16 @ SV24 ) )
= $true )
| ( ( c_lessequals @ SV7 @ SV16 @ ( tc_set @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(93,plain,
! [SV30: $i,SV25: $i,SV17: $i,SV8: $i] :
( ( ~ ( c_in @ SV8 @ SV17 @ ( tc_set @ SV25 ) )
| ~ ( c_in @ SV30 @ ( c_Zorn_Ochain @ SV17 @ SV25 ) @ ( tc_set @ ( tc_set @ SV25 ) ) )
| ( c_in @ ( c_Zorn_Ochain__extend__1 @ SV30 @ SV8 @ SV25 ) @ SV30 @ ( tc_set @ SV25 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV8 @ c_emptyset @ ( tc_set @ SV25 ) ) @ SV30 @ ( tc_set @ SV25 ) ) @ ( c_Zorn_Ochain @ SV17 @ SV25 ) @ ( tc_set @ ( tc_set @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(94,plain,
! [SV31: $i,SV26: $i,SV18: $i,SV9: $i] :
( ( ~ ( c_in @ SV9 @ SV18 @ ( tc_set @ SV26 ) )
| ~ ( c_in @ SV31 @ ( c_Zorn_Ochain @ SV18 @ SV26 ) @ ( tc_set @ ( tc_set @ SV26 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ SV31 @ SV9 @ SV26 ) @ SV9 @ ( tc_set @ SV26 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV9 @ c_emptyset @ ( tc_set @ SV26 ) ) @ SV31 @ ( tc_set @ SV26 ) ) @ ( c_Zorn_Ochain @ SV18 @ SV26 ) @ ( tc_set @ ( tc_set @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(95,plain,
! [SV32: $i,SV27: $i,SV19: $i,SV10: $i] :
( ( ! [SY88: $i,SY89: $i] :
( ~ ( c_in @ SV10 @ SV19 @ SV27 )
| ~ ( c_in @ SV32 @ ( c_Zorn_Omaxchain @ SY88 @ SV27 ) @ ( tc_set @ ( tc_set @ SV27 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV19 @ c_emptyset @ ( tc_set @ SV27 ) ) @ SV32 @ ( tc_set @ SV27 ) ) @ ( c_Zorn_Ochain @ SY88 @ SV27 ) @ ( tc_set @ ( tc_set @ SV27 ) ) )
| ( c_in @ SV10 @ SY89 @ SV27 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV32 @ SY89 @ SV27 ) @ SV32 @ ( tc_set @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(96,plain,
! [SV33: $i,SV28: $i,SV20: $i,SV11: $i] :
( ( ! [SY90: $i,SY91: $i] :
( ~ ( c_in @ SV11 @ SV20 @ SV28 )
| ~ ( c_in @ SV33 @ ( c_Zorn_Omaxchain @ SY90 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV20 @ c_emptyset @ ( tc_set @ SV28 ) ) @ SV33 @ ( tc_set @ SV28 ) ) @ ( c_Zorn_Ochain @ SY90 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV33 @ SY91 @ SV28 ) @ SY91 @ ( tc_set @ SV28 ) )
| ( c_in @ SV11 @ SY91 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(97,plain,
! [SV12: $i] :
( ( ( c_in @ SV12 @ v_S @ ( tc_set @ t_a ) )
= $false )
| ( ( SV12
= ( v_x @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(98,plain,
! [SV21: $i,SV13: $i,SV4: $i] :
( ( ( c_lessequals @ SV4 @ SV13 @ ( tc_set @ SV21 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV13 @ SV4 @ ( tc_set @ SV21 ) )
| ( SV13 = SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(99,plain,
! [SV29: $i,SV22: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( c_in @ SV5 @ SV14 @ SV22 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV14 @ SV29 @ ( tc_set @ SV22 ) )
| ( c_in @ SV5 @ SV29 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(100,plain,
! [SV24: $i,SV16: $i,SV7: $i] :
( ( ( c_in @ ( c_Main_OsubsetI__1 @ SV7 @ SV16 @ SV24 ) @ SV16 @ SV24 )
= $false )
| ( ( c_lessequals @ SV7 @ SV16 @ ( tc_set @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(101,plain,
! [SV30: $i,SV25: $i,SV17: $i,SV8: $i] :
( ( ( ~ ( c_in @ SV8 @ SV17 @ ( tc_set @ SV25 ) ) )
= $true )
| ( ( ~ ( c_in @ SV30 @ ( c_Zorn_Ochain @ SV17 @ SV25 ) @ ( tc_set @ ( tc_set @ SV25 ) ) )
| ( c_in @ ( c_Zorn_Ochain__extend__1 @ SV30 @ SV8 @ SV25 ) @ SV30 @ ( tc_set @ SV25 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV8 @ c_emptyset @ ( tc_set @ SV25 ) ) @ SV30 @ ( tc_set @ SV25 ) ) @ ( c_Zorn_Ochain @ SV17 @ SV25 ) @ ( tc_set @ ( tc_set @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(102,plain,
! [SV31: $i,SV26: $i,SV18: $i,SV9: $i] :
( ( ( ~ ( c_in @ SV9 @ SV18 @ ( tc_set @ SV26 ) ) )
= $true )
| ( ( ~ ( c_in @ SV31 @ ( c_Zorn_Ochain @ SV18 @ SV26 ) @ ( tc_set @ ( tc_set @ SV26 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ SV31 @ SV9 @ SV26 ) @ SV9 @ ( tc_set @ SV26 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV9 @ c_emptyset @ ( tc_set @ SV26 ) ) @ SV31 @ ( tc_set @ SV26 ) ) @ ( c_Zorn_Ochain @ SV18 @ SV26 ) @ ( tc_set @ ( tc_set @ SV26 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(103,plain,
! [SV34: $i,SV32: $i,SV27: $i,SV19: $i,SV10: $i] :
( ( ! [SY92: $i] :
( ~ ( c_in @ SV10 @ SV19 @ SV27 )
| ~ ( c_in @ SV32 @ ( c_Zorn_Omaxchain @ SV34 @ SV27 ) @ ( tc_set @ ( tc_set @ SV27 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV19 @ c_emptyset @ ( tc_set @ SV27 ) ) @ SV32 @ ( tc_set @ SV27 ) ) @ ( c_Zorn_Ochain @ SV34 @ SV27 ) @ ( tc_set @ ( tc_set @ SV27 ) ) )
| ( c_in @ SV10 @ SY92 @ SV27 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV32 @ SY92 @ SV27 ) @ SV32 @ ( tc_set @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(104,plain,
! [SV35: $i,SV33: $i,SV28: $i,SV20: $i,SV11: $i] :
( ( ! [SY93: $i] :
( ~ ( c_in @ SV11 @ SV20 @ SV28 )
| ~ ( c_in @ SV33 @ ( c_Zorn_Omaxchain @ SV35 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV20 @ c_emptyset @ ( tc_set @ SV28 ) ) @ SV33 @ ( tc_set @ SV28 ) ) @ ( c_Zorn_Ochain @ SV35 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV33 @ SY93 @ SV28 ) @ SY93 @ ( tc_set @ SV28 ) )
| ( c_in @ SV11 @ SY93 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(105,plain,
! [SV21: $i,SV4: $i,SV13: $i] :
( ( ( ~ ( c_lessequals @ SV13 @ SV4 @ ( tc_set @ SV21 ) ) )
= $true )
| ( ( SV13 = SV4 )
= $true )
| ( ( c_lessequals @ SV4 @ SV13 @ ( tc_set @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(106,plain,
! [SV29: $i,SV22: $i,SV14: $i,SV5: $i] :
( ( ( c_in @ SV5 @ SV14 @ SV22 )
= $false )
| ( ( ~ ( c_lessequals @ SV14 @ SV29 @ ( tc_set @ SV22 ) )
| ( c_in @ SV5 @ SV29 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(107,plain,
! [SV30: $i,SV25: $i,SV17: $i,SV8: $i] :
( ( ( c_in @ SV8 @ SV17 @ ( tc_set @ SV25 ) )
= $false )
| ( ( ~ ( c_in @ SV30 @ ( c_Zorn_Ochain @ SV17 @ SV25 ) @ ( tc_set @ ( tc_set @ SV25 ) ) )
| ( c_in @ ( c_Zorn_Ochain__extend__1 @ SV30 @ SV8 @ SV25 ) @ SV30 @ ( tc_set @ SV25 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV8 @ c_emptyset @ ( tc_set @ SV25 ) ) @ SV30 @ ( tc_set @ SV25 ) ) @ ( c_Zorn_Ochain @ SV17 @ SV25 ) @ ( tc_set @ ( tc_set @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(108,plain,
! [SV31: $i,SV26: $i,SV18: $i,SV9: $i] :
( ( ( c_in @ SV9 @ SV18 @ ( tc_set @ SV26 ) )
= $false )
| ( ( ~ ( c_in @ SV31 @ ( c_Zorn_Ochain @ SV18 @ SV26 ) @ ( tc_set @ ( tc_set @ SV26 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ SV31 @ SV9 @ SV26 ) @ SV9 @ ( tc_set @ SV26 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV9 @ c_emptyset @ ( tc_set @ SV26 ) ) @ SV31 @ ( tc_set @ SV26 ) ) @ ( c_Zorn_Ochain @ SV18 @ SV26 ) @ ( tc_set @ ( tc_set @ SV26 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(109,plain,
! [SV36: $i,SV34: $i,SV32: $i,SV27: $i,SV19: $i,SV10: $i] :
( ( ~ ( c_in @ SV10 @ SV19 @ SV27 )
| ~ ( c_in @ SV32 @ ( c_Zorn_Omaxchain @ SV34 @ SV27 ) @ ( tc_set @ ( tc_set @ SV27 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV19 @ c_emptyset @ ( tc_set @ SV27 ) ) @ SV32 @ ( tc_set @ SV27 ) ) @ ( c_Zorn_Ochain @ SV34 @ SV27 ) @ ( tc_set @ ( tc_set @ SV27 ) ) )
| ( c_in @ SV10 @ SV36 @ SV27 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV32 @ SV36 @ SV27 ) @ SV32 @ ( tc_set @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(110,plain,
! [SV37: $i,SV35: $i,SV33: $i,SV28: $i,SV20: $i,SV11: $i] :
( ( ~ ( c_in @ SV11 @ SV20 @ SV28 )
| ~ ( c_in @ SV33 @ ( c_Zorn_Omaxchain @ SV35 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV20 @ c_emptyset @ ( tc_set @ SV28 ) ) @ SV33 @ ( tc_set @ SV28 ) ) @ ( c_Zorn_Ochain @ SV35 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV33 @ SV37 @ SV28 ) @ SV37 @ ( tc_set @ SV28 ) )
| ( c_in @ SV11 @ SV37 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(111,plain,
! [SV21: $i,SV4: $i,SV13: $i] :
( ( ( c_lessequals @ SV13 @ SV4 @ ( tc_set @ SV21 ) )
= $false )
| ( ( SV13 = SV4 )
= $true )
| ( ( c_lessequals @ SV4 @ SV13 @ ( tc_set @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(112,plain,
! [SV5: $i,SV22: $i,SV29: $i,SV14: $i] :
( ( ( ~ ( c_lessequals @ SV14 @ SV29 @ ( tc_set @ SV22 ) ) )
= $true )
| ( ( c_in @ SV5 @ SV29 @ SV22 )
= $true )
| ( ( c_in @ SV5 @ SV14 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(113,plain,
! [SV8: $i,SV25: $i,SV17: $i,SV30: $i] :
( ( ( ~ ( c_in @ SV30 @ ( c_Zorn_Ochain @ SV17 @ SV25 ) @ ( tc_set @ ( tc_set @ SV25 ) ) ) )
= $true )
| ( ( ( c_in @ ( c_Zorn_Ochain__extend__1 @ SV30 @ SV8 @ SV25 ) @ SV30 @ ( tc_set @ SV25 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV8 @ c_emptyset @ ( tc_set @ SV25 ) ) @ SV30 @ ( tc_set @ SV25 ) ) @ ( c_Zorn_Ochain @ SV17 @ SV25 ) @ ( tc_set @ ( tc_set @ SV25 ) ) ) )
= $true )
| ( ( c_in @ SV8 @ SV17 @ ( tc_set @ SV25 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(114,plain,
! [SV9: $i,SV26: $i,SV18: $i,SV31: $i] :
( ( ( ~ ( c_in @ SV31 @ ( c_Zorn_Ochain @ SV18 @ SV26 ) @ ( tc_set @ ( tc_set @ SV26 ) ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ SV31 @ SV9 @ SV26 ) @ SV9 @ ( tc_set @ SV26 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV9 @ c_emptyset @ ( tc_set @ SV26 ) ) @ SV31 @ ( tc_set @ SV26 ) ) @ ( c_Zorn_Ochain @ SV18 @ SV26 ) @ ( tc_set @ ( tc_set @ SV26 ) ) ) )
= $true )
| ( ( c_in @ SV9 @ SV18 @ ( tc_set @ SV26 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(115,plain,
! [SV36: $i,SV34: $i,SV32: $i,SV27: $i,SV19: $i,SV10: $i] :
( ( ( ~ ( c_in @ SV10 @ SV19 @ SV27 ) )
= $true )
| ( ( ~ ( c_in @ SV32 @ ( c_Zorn_Omaxchain @ SV34 @ SV27 ) @ ( tc_set @ ( tc_set @ SV27 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV19 @ c_emptyset @ ( tc_set @ SV27 ) ) @ SV32 @ ( tc_set @ SV27 ) ) @ ( c_Zorn_Ochain @ SV34 @ SV27 ) @ ( tc_set @ ( tc_set @ SV27 ) ) )
| ( c_in @ SV10 @ SV36 @ SV27 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV32 @ SV36 @ SV27 ) @ SV32 @ ( tc_set @ SV27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(116,plain,
! [SV37: $i,SV35: $i,SV33: $i,SV28: $i,SV20: $i,SV11: $i] :
( ( ( ~ ( c_in @ SV11 @ SV20 @ SV28 ) )
= $true )
| ( ( ~ ( c_in @ SV33 @ ( c_Zorn_Omaxchain @ SV35 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV20 @ c_emptyset @ ( tc_set @ SV28 ) ) @ SV33 @ ( tc_set @ SV28 ) ) @ ( c_Zorn_Ochain @ SV35 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV33 @ SV37 @ SV28 ) @ SV37 @ ( tc_set @ SV28 ) )
| ( c_in @ SV11 @ SV37 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(117,plain,
! [SV5: $i,SV22: $i,SV29: $i,SV14: $i] :
( ( ( c_lessequals @ SV14 @ SV29 @ ( tc_set @ SV22 ) )
= $false )
| ( ( c_in @ SV5 @ SV29 @ SV22 )
= $true )
| ( ( c_in @ SV5 @ SV14 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(118,plain,
! [SV8: $i,SV25: $i,SV17: $i,SV30: $i] :
( ( ( c_in @ SV30 @ ( c_Zorn_Ochain @ SV17 @ SV25 ) @ ( tc_set @ ( tc_set @ SV25 ) ) )
= $false )
| ( ( ( c_in @ ( c_Zorn_Ochain__extend__1 @ SV30 @ SV8 @ SV25 ) @ SV30 @ ( tc_set @ SV25 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV8 @ c_emptyset @ ( tc_set @ SV25 ) ) @ SV30 @ ( tc_set @ SV25 ) ) @ ( c_Zorn_Ochain @ SV17 @ SV25 ) @ ( tc_set @ ( tc_set @ SV25 ) ) ) )
= $true )
| ( ( c_in @ SV8 @ SV17 @ ( tc_set @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(119,plain,
! [SV9: $i,SV26: $i,SV18: $i,SV31: $i] :
( ( ( c_in @ SV31 @ ( c_Zorn_Ochain @ SV18 @ SV26 ) @ ( tc_set @ ( tc_set @ SV26 ) ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ SV31 @ SV9 @ SV26 ) @ SV9 @ ( tc_set @ SV26 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV9 @ c_emptyset @ ( tc_set @ SV26 ) ) @ SV31 @ ( tc_set @ SV26 ) ) @ ( c_Zorn_Ochain @ SV18 @ SV26 ) @ ( tc_set @ ( tc_set @ SV26 ) ) ) )
= $true )
| ( ( c_in @ SV9 @ SV18 @ ( tc_set @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(120,plain,
! [SV36: $i,SV34: $i,SV32: $i,SV27: $i,SV19: $i,SV10: $i] :
( ( ( c_in @ SV10 @ SV19 @ SV27 )
= $false )
| ( ( ~ ( c_in @ SV32 @ ( c_Zorn_Omaxchain @ SV34 @ SV27 ) @ ( tc_set @ ( tc_set @ SV27 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV19 @ c_emptyset @ ( tc_set @ SV27 ) ) @ SV32 @ ( tc_set @ SV27 ) ) @ ( c_Zorn_Ochain @ SV34 @ SV27 ) @ ( tc_set @ ( tc_set @ SV27 ) ) )
| ( c_in @ SV10 @ SV36 @ SV27 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV32 @ SV36 @ SV27 ) @ SV32 @ ( tc_set @ SV27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(121,plain,
! [SV37: $i,SV35: $i,SV33: $i,SV28: $i,SV20: $i,SV11: $i] :
( ( ( c_in @ SV11 @ SV20 @ SV28 )
= $false )
| ( ( ~ ( c_in @ SV33 @ ( c_Zorn_Omaxchain @ SV35 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV20 @ c_emptyset @ ( tc_set @ SV28 ) ) @ SV33 @ ( tc_set @ SV28 ) ) @ ( c_Zorn_Ochain @ SV35 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV33 @ SV37 @ SV28 ) @ SV37 @ ( tc_set @ SV28 ) )
| ( c_in @ SV11 @ SV37 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(122,plain,
! [SV17: $i,SV25: $i,SV8: $i,SV30: $i] :
( ( ( c_in @ ( c_Zorn_Ochain__extend__1 @ SV30 @ SV8 @ SV25 ) @ SV30 @ ( tc_set @ SV25 ) )
= $true )
| ( ( c_in @ ( c_union @ ( c_insert @ SV8 @ c_emptyset @ ( tc_set @ SV25 ) ) @ SV30 @ ( tc_set @ SV25 ) ) @ ( c_Zorn_Ochain @ SV17 @ SV25 ) @ ( tc_set @ ( tc_set @ SV25 ) ) )
= $true )
| ( ( c_in @ SV30 @ ( c_Zorn_Ochain @ SV17 @ SV25 ) @ ( tc_set @ ( tc_set @ SV25 ) ) )
= $false )
| ( ( c_in @ SV8 @ SV17 @ ( tc_set @ SV25 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(123,plain,
! [SV18: $i,SV26: $i,SV9: $i,SV31: $i] :
( ( ( ~ ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ SV31 @ SV9 @ SV26 ) @ SV9 @ ( tc_set @ SV26 ) ) )
= $true )
| ( ( c_in @ ( c_union @ ( c_insert @ SV9 @ c_emptyset @ ( tc_set @ SV26 ) ) @ SV31 @ ( tc_set @ SV26 ) ) @ ( c_Zorn_Ochain @ SV18 @ SV26 ) @ ( tc_set @ ( tc_set @ SV26 ) ) )
= $true )
| ( ( c_in @ SV31 @ ( c_Zorn_Ochain @ SV18 @ SV26 ) @ ( tc_set @ ( tc_set @ SV26 ) ) )
= $false )
| ( ( c_in @ SV9 @ SV18 @ ( tc_set @ SV26 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(124,plain,
! [SV36: $i,SV10: $i,SV19: $i,SV27: $i,SV34: $i,SV32: $i] :
( ( ( ~ ( c_in @ SV32 @ ( c_Zorn_Omaxchain @ SV34 @ SV27 ) @ ( tc_set @ ( tc_set @ SV27 ) ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_union @ ( c_insert @ SV19 @ c_emptyset @ ( tc_set @ SV27 ) ) @ SV32 @ ( tc_set @ SV27 ) ) @ ( c_Zorn_Ochain @ SV34 @ SV27 ) @ ( tc_set @ ( tc_set @ SV27 ) ) )
| ( c_in @ SV10 @ SV36 @ SV27 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV32 @ SV36 @ SV27 ) @ SV32 @ ( tc_set @ SV27 ) ) )
= $true )
| ( ( c_in @ SV10 @ SV19 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(125,plain,
! [SV11: $i,SV37: $i,SV20: $i,SV28: $i,SV35: $i,SV33: $i] :
( ( ( ~ ( c_in @ SV33 @ ( c_Zorn_Omaxchain @ SV35 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_union @ ( c_insert @ SV20 @ c_emptyset @ ( tc_set @ SV28 ) ) @ SV33 @ ( tc_set @ SV28 ) ) @ ( c_Zorn_Ochain @ SV35 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV33 @ SV37 @ SV28 ) @ SV37 @ ( tc_set @ SV28 ) )
| ( c_in @ SV11 @ SV37 @ SV28 ) )
= $true )
| ( ( c_in @ SV11 @ SV20 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(126,plain,
! [SV18: $i,SV26: $i,SV9: $i,SV31: $i] :
( ( ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ SV31 @ SV9 @ SV26 ) @ SV9 @ ( tc_set @ SV26 ) )
= $false )
| ( ( c_in @ ( c_union @ ( c_insert @ SV9 @ c_emptyset @ ( tc_set @ SV26 ) ) @ SV31 @ ( tc_set @ SV26 ) ) @ ( c_Zorn_Ochain @ SV18 @ SV26 ) @ ( tc_set @ ( tc_set @ SV26 ) ) )
= $true )
| ( ( c_in @ SV31 @ ( c_Zorn_Ochain @ SV18 @ SV26 ) @ ( tc_set @ ( tc_set @ SV26 ) ) )
= $false )
| ( ( c_in @ SV9 @ SV18 @ ( tc_set @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(127,plain,
! [SV36: $i,SV10: $i,SV19: $i,SV27: $i,SV34: $i,SV32: $i] :
( ( ( c_in @ SV32 @ ( c_Zorn_Omaxchain @ SV34 @ SV27 ) @ ( tc_set @ ( tc_set @ SV27 ) ) )
= $false )
| ( ( ~ ( c_in @ ( c_union @ ( c_insert @ SV19 @ c_emptyset @ ( tc_set @ SV27 ) ) @ SV32 @ ( tc_set @ SV27 ) ) @ ( c_Zorn_Ochain @ SV34 @ SV27 ) @ ( tc_set @ ( tc_set @ SV27 ) ) )
| ( c_in @ SV10 @ SV36 @ SV27 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV32 @ SV36 @ SV27 ) @ SV32 @ ( tc_set @ SV27 ) ) )
= $true )
| ( ( c_in @ SV10 @ SV19 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(128,plain,
! [SV11: $i,SV37: $i,SV20: $i,SV28: $i,SV35: $i,SV33: $i] :
( ( ( c_in @ SV33 @ ( c_Zorn_Omaxchain @ SV35 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) )
= $false )
| ( ( ~ ( c_in @ ( c_union @ ( c_insert @ SV20 @ c_emptyset @ ( tc_set @ SV28 ) ) @ SV33 @ ( tc_set @ SV28 ) ) @ ( c_Zorn_Ochain @ SV35 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV33 @ SV37 @ SV28 ) @ SV37 @ ( tc_set @ SV28 ) )
| ( c_in @ SV11 @ SV37 @ SV28 ) )
= $true )
| ( ( c_in @ SV11 @ SV20 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(129,plain,
! [SV36: $i,SV10: $i,SV34: $i,SV32: $i,SV27: $i,SV19: $i] :
( ( ( ~ ( c_in @ ( c_union @ ( c_insert @ SV19 @ c_emptyset @ ( tc_set @ SV27 ) ) @ SV32 @ ( tc_set @ SV27 ) ) @ ( c_Zorn_Ochain @ SV34 @ SV27 ) @ ( tc_set @ ( tc_set @ SV27 ) ) ) )
= $true )
| ( ( ( c_in @ SV10 @ SV36 @ SV27 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV32 @ SV36 @ SV27 ) @ SV32 @ ( tc_set @ SV27 ) ) )
= $true )
| ( ( c_in @ SV32 @ ( c_Zorn_Omaxchain @ SV34 @ SV27 ) @ ( tc_set @ ( tc_set @ SV27 ) ) )
= $false )
| ( ( c_in @ SV10 @ SV19 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(130,plain,
! [SV11: $i,SV37: $i,SV35: $i,SV33: $i,SV28: $i,SV20: $i] :
( ( ( ~ ( c_in @ ( c_union @ ( c_insert @ SV20 @ c_emptyset @ ( tc_set @ SV28 ) ) @ SV33 @ ( tc_set @ SV28 ) ) @ ( c_Zorn_Ochain @ SV35 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV33 @ SV37 @ SV28 ) @ SV37 @ ( tc_set @ SV28 ) )
| ( c_in @ SV11 @ SV37 @ SV28 ) )
= $true )
| ( ( c_in @ SV33 @ ( c_Zorn_Omaxchain @ SV35 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) )
= $false )
| ( ( c_in @ SV11 @ SV20 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(131,plain,
! [SV36: $i,SV10: $i,SV34: $i,SV32: $i,SV27: $i,SV19: $i] :
( ( ( c_in @ ( c_union @ ( c_insert @ SV19 @ c_emptyset @ ( tc_set @ SV27 ) ) @ SV32 @ ( tc_set @ SV27 ) ) @ ( c_Zorn_Ochain @ SV34 @ SV27 ) @ ( tc_set @ ( tc_set @ SV27 ) ) )
= $false )
| ( ( ( c_in @ SV10 @ SV36 @ SV27 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV32 @ SV36 @ SV27 ) @ SV32 @ ( tc_set @ SV27 ) ) )
= $true )
| ( ( c_in @ SV32 @ ( c_Zorn_Omaxchain @ SV34 @ SV27 ) @ ( tc_set @ ( tc_set @ SV27 ) ) )
= $false )
| ( ( c_in @ SV10 @ SV19 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(132,plain,
! [SV11: $i,SV37: $i,SV35: $i,SV33: $i,SV28: $i,SV20: $i] :
( ( ( c_in @ ( c_union @ ( c_insert @ SV20 @ c_emptyset @ ( tc_set @ SV28 ) ) @ SV33 @ ( tc_set @ SV28 ) ) @ ( c_Zorn_Ochain @ SV35 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV33 @ SV37 @ SV28 ) @ SV37 @ ( tc_set @ SV28 ) )
| ( c_in @ SV11 @ SV37 @ SV28 ) )
= $true )
| ( ( c_in @ SV33 @ ( c_Zorn_Omaxchain @ SV35 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) )
= $false )
| ( ( c_in @ SV11 @ SV20 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(133,plain,
! [SV34: $i,SV19: $i,SV32: $i,SV27: $i,SV36: $i,SV10: $i] :
( ( ( c_in @ SV10 @ SV36 @ SV27 )
= $true )
| ( ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV32 @ SV36 @ SV27 ) @ SV32 @ ( tc_set @ SV27 ) )
= $true )
| ( ( c_in @ ( c_union @ ( c_insert @ SV19 @ c_emptyset @ ( tc_set @ SV27 ) ) @ SV32 @ ( tc_set @ SV27 ) ) @ ( c_Zorn_Ochain @ SV34 @ SV27 ) @ ( tc_set @ ( tc_set @ SV27 ) ) )
= $false )
| ( ( c_in @ SV32 @ ( c_Zorn_Omaxchain @ SV34 @ SV27 ) @ ( tc_set @ ( tc_set @ SV27 ) ) )
= $false )
| ( ( c_in @ SV10 @ SV19 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(134,plain,
! [SV35: $i,SV20: $i,SV11: $i,SV28: $i,SV37: $i,SV33: $i] :
( ( ( ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV33 @ SV37 @ SV28 ) @ SV37 @ ( tc_set @ SV28 ) ) )
= $true )
| ( ( c_in @ SV11 @ SV37 @ SV28 )
= $true )
| ( ( c_in @ ( c_union @ ( c_insert @ SV20 @ c_emptyset @ ( tc_set @ SV28 ) ) @ SV33 @ ( tc_set @ SV28 ) ) @ ( c_Zorn_Ochain @ SV35 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) )
= $false )
| ( ( c_in @ SV33 @ ( c_Zorn_Omaxchain @ SV35 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) )
= $false )
| ( ( c_in @ SV11 @ SV20 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(135,plain,
! [SV35: $i,SV20: $i,SV11: $i,SV28: $i,SV37: $i,SV33: $i] :
( ( ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV33 @ SV37 @ SV28 ) @ SV37 @ ( tc_set @ SV28 ) )
= $false )
| ( ( c_in @ SV11 @ SV37 @ SV28 )
= $true )
| ( ( c_in @ ( c_union @ ( c_insert @ SV20 @ c_emptyset @ ( tc_set @ SV28 ) ) @ SV33 @ ( tc_set @ SV28 ) ) @ ( c_Zorn_Ochain @ SV35 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) )
= $false )
| ( ( c_in @ SV33 @ ( c_Zorn_Omaxchain @ SV35 @ SV28 ) @ ( tc_set @ ( tc_set @ SV28 ) ) )
= $false )
| ( ( c_in @ SV11 @ SV20 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(136,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[35,135,133,126,122,117,111,100,97,91,79,78,77,63,37,36]) ).
thf(137,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET862-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n015.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 14:58:45 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 85.86/14.52
% 85.86/14.52 No.of.Axioms: 15
% 85.86/14.52
% 85.86/14.52 Length.of.Defs: 0
% 85.86/14.52
% 85.86/14.52 Contains.Choice.Funs: false
% 85.86/14.52 ....
% 85.86/14.52
% 85.86/14.52 ********************************
% 85.86/14.52 * All subproblems solved! *
% 85.86/14.52 ********************************
% 85.86/14.52 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:15,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:136,loop_count:0,foatp_calls:1,translation:fof_full)
% 85.86/14.52
% 85.86/14.52 %**** Beginning of derivation protocol ****
% 85.86/14.52 % SZS output start CNFRefutation
% See solution above
% 85.86/14.52
% 85.86/14.52 %**** End of derivation protocol ****
% 85.86/14.52 %**** no. of clauses in derivation: 137 ****
% 85.86/14.52 %**** clause counter: 136 ****
% 85.86/14.52
% 85.86/14.52 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:15,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:136,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------