TSTP Solution File: SET863-2 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET863-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 03:05:49 EDT 2022
% Result : Unsatisfiable 0.40s 0.58s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 32
% Syntax : Number of formulae : 139 ( 72 unt; 17 typ; 0 def)
% Number of atoms : 758 ( 185 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 2961 ( 174 ~; 266 |; 0 &;2521 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 9 con; 0-3 aty)
% Number of variables : 417 ( 0 ^ 417 !; 0 ?; 417 :)
% 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 ).
thf(tp_v_xa,type,
v_xa: $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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(8,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(9,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,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/sandbox/benchmark/theBenchmark.p',cls_conjecture_7) ).
thf(11,negated_conjecture,
~ ( c_in @ v_xa @ v_y @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(12,negated_conjecture,
c_in @ v_xa @ v_x @ t_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(13,negated_conjecture,
c_lessequals @ v_y @ v_x @ ( tc_set @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(14,negated_conjecture,
c_in @ v_x @ v_S @ ( tc_set @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(15,negated_conjecture,
c_in @ v_c @ ( c_Zorn_Ochain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(16,negated_conjecture,
c_in @ v_c @ ( c_Zorn_Omaxchain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(17,plain,
$false = $false,
inference(unfold_def,[status(thm)],[9]) ).
thf(18,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(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_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(20,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(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_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(22,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(23,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(24,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(25,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)],[10]) ).
thf(26,plain,
( ( ~ ( c_in @ v_xa @ v_y @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(27,plain,
( ( c_in @ v_xa @ v_x @ t_a )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(28,plain,
( ( c_lessequals @ v_y @ v_x @ ( tc_set @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(29,plain,
( ( c_in @ v_x @ v_S @ ( tc_set @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(30,plain,
( ( c_in @ v_c @ ( c_Zorn_Ochain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(31,plain,
( ( c_in @ v_c @ ( c_Zorn_Omaxchain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(32,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[17]) ).
thf(33,plain,
( ( ! [V_z: $i,V_x: $i,T_a: $i,V_c: $i] :
( ~ ( c_in @ V_z @ V_x @ T_a )
| ! [V_S: $i] :
( ~ ( 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 ) ) )
| ! [V_y: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[18]) ).
thf(34,plain,
( ( ! [V_z: $i,V_x: $i,T_a: $i,V_c: $i] :
( ~ ( c_in @ V_z @ V_x @ T_a )
| ! [V_S: $i] :
( ~ ( 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 ) ) )
| ! [V_y: $i] :
( ( 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(extcnf_combined,[status(esa)],[19]) ).
thf(35,plain,
( ( ! [V_z: $i,V_S: $i,T_a: $i] :
( ~ ( c_in @ V_z @ V_S @ ( tc_set @ T_a ) )
| ! [V_c: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[20]) ).
thf(36,plain,
( ( ! [V_z: $i,V_S: $i,T_a: $i] :
( ~ ( c_in @ V_z @ V_S @ ( tc_set @ T_a ) )
| ! [V_c: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[21]) ).
thf(37,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ! [V_B: $i] :
( ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_in @ V_c @ V_B @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(38,plain,
( ( c_in @ v_c @ ( c_Zorn_Omaxchain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(39,plain,
( ( c_in @ v_c @ ( c_Zorn_Ochain @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(40,plain,
( ( c_in @ v_x @ v_S @ ( tc_set @ t_a ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(41,plain,
( ( c_lessequals @ v_y @ v_x @ ( tc_set @ t_a ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(42,plain,
( ( c_in @ v_xa @ v_x @ t_a )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(43,plain,
( ( ~ ( c_in @ v_xa @ v_y @ t_a ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(44,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)],[25]) ).
thf(45,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ! [V_B: $i] :
( ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_in @ V_c @ V_B @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(46,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)],[23]) ).
thf(47,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)],[22]) ).
thf(48,plain,
( ( ! [V_z: $i,V_S: $i,T_a: $i] :
( ~ ( c_in @ V_z @ V_S @ ( tc_set @ T_a ) )
| ! [V_c: $i] :
( ~ ( 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)],[36]) ).
thf(49,plain,
( ( ! [V_z: $i,V_S: $i,T_a: $i] :
( ~ ( c_in @ V_z @ V_S @ ( tc_set @ T_a ) )
| ! [V_c: $i] :
( ~ ( 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)],[35]) ).
thf(50,plain,
( ( ! [V_z: $i,V_x: $i,T_a: $i,V_c: $i] :
( ~ ( c_in @ V_z @ V_x @ T_a )
| ! [V_S: $i] :
( ~ ( 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 ) ) )
| ! [V_y: $i] :
( ( 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)],[34]) ).
thf(51,plain,
( ( ! [V_z: $i,V_x: $i,T_a: $i,V_c: $i] :
( ~ ( c_in @ V_z @ V_x @ T_a )
| ! [V_S: $i] :
( ~ ( 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 ) ) )
| ! [V_y: $i] :
( ~ ( 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)],[33]) ).
thf(52,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(53,plain,
( ( c_in @ v_xa @ v_y @ t_a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(54,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)],[44]) ).
thf(55,plain,
! [SV2: $i] :
( ( ! [SY31: $i,SY32: $i] :
( ~ ( c_in @ SV2 @ SY31 @ SY32 )
| ! [SY33: $i] :
( ~ ( c_lessequals @ SY31 @ SY33 @ ( tc_set @ SY32 ) )
| ( c_in @ SV2 @ SY33 @ SY32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(56,plain,
! [SV3: $i] :
( ( ! [SY34: $i,SY35: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ SV3 @ SY34 @ SY35 ) @ SV3 @ SY35 )
| ( c_lessequals @ SV3 @ SY34 @ ( tc_set @ SY35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(57,plain,
! [SV4: $i] :
( ( ! [SY36: $i,SY37: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ SV4 @ SY36 @ SY37 ) @ SY36 @ SY37 )
| ( c_lessequals @ SV4 @ SY36 @ ( tc_set @ SY37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(58,plain,
! [SV5: $i] :
( ( ! [SY38: $i,SY39: $i] :
( ~ ( c_in @ SV5 @ SY38 @ ( tc_set @ SY39 ) )
| ! [SY40: $i] :
( ~ ( c_in @ SY40 @ ( c_Zorn_Ochain @ SY38 @ SY39 ) @ ( tc_set @ ( tc_set @ SY39 ) ) )
| ( c_in @ ( c_Zorn_Ochain__extend__1 @ SY40 @ SV5 @ SY39 ) @ SY40 @ ( tc_set @ SY39 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV5 @ c_emptyset @ ( tc_set @ SY39 ) ) @ SY40 @ ( tc_set @ SY39 ) ) @ ( c_Zorn_Ochain @ SY38 @ SY39 ) @ ( tc_set @ ( tc_set @ SY39 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(59,plain,
! [SV6: $i] :
( ( ! [SY41: $i,SY42: $i] :
( ~ ( c_in @ SV6 @ SY41 @ ( tc_set @ SY42 ) )
| ! [SY43: $i] :
( ~ ( c_in @ SY43 @ ( c_Zorn_Ochain @ SY41 @ SY42 ) @ ( tc_set @ ( tc_set @ SY42 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ SY43 @ SV6 @ SY42 ) @ SV6 @ ( tc_set @ SY42 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV6 @ c_emptyset @ ( tc_set @ SY42 ) ) @ SY43 @ ( tc_set @ SY42 ) ) @ ( c_Zorn_Ochain @ SY41 @ SY42 ) @ ( tc_set @ ( tc_set @ SY42 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(60,plain,
! [SV7: $i] :
( ( ! [SY44: $i,SY45: $i,SY46: $i] :
( ~ ( c_in @ SV7 @ SY44 @ SY45 )
| ! [SY47: $i] :
( ~ ( c_in @ SY46 @ ( c_Zorn_Omaxchain @ SY47 @ SY45 ) @ ( tc_set @ ( tc_set @ SY45 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SY44 @ c_emptyset @ ( tc_set @ SY45 ) ) @ SY46 @ ( tc_set @ SY45 ) ) @ ( c_Zorn_Ochain @ SY47 @ SY45 ) @ ( tc_set @ ( tc_set @ SY45 ) ) )
| ! [SY48: $i] :
( ( c_in @ SV7 @ SY48 @ SY45 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SY46 @ SY48 @ SY45 ) @ SY46 @ ( tc_set @ SY45 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(61,plain,
! [SV8: $i] :
( ( ! [SY49: $i,SY50: $i,SY51: $i] :
( ~ ( c_in @ SV8 @ SY49 @ SY50 )
| ! [SY52: $i] :
( ~ ( c_in @ SY51 @ ( c_Zorn_Omaxchain @ SY52 @ SY50 ) @ ( tc_set @ ( tc_set @ SY50 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SY49 @ c_emptyset @ ( tc_set @ SY50 ) ) @ SY51 @ ( tc_set @ SY50 ) ) @ ( c_Zorn_Ochain @ SY52 @ SY50 ) @ ( tc_set @ ( tc_set @ SY50 ) ) )
| ! [SY53: $i] :
( ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SY51 @ SY53 @ SY50 ) @ SY53 @ ( tc_set @ SY50 ) )
| ( c_in @ SV8 @ SY53 @ SY50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(62,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(63,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)],[54]) ).
thf(64,plain,
! [SV9: $i,SV2: $i] :
( ( ! [SY54: $i] :
( ~ ( c_in @ SV2 @ SV9 @ SY54 )
| ! [SY55: $i] :
( ~ ( c_lessequals @ SV9 @ SY55 @ ( tc_set @ SY54 ) )
| ( c_in @ SV2 @ SY55 @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(65,plain,
! [SV10: $i,SV3: $i] :
( ( ! [SY56: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ SV3 @ SV10 @ SY56 ) @ SV3 @ SY56 )
| ( c_lessequals @ SV3 @ SV10 @ ( tc_set @ SY56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(66,plain,
! [SV11: $i,SV4: $i] :
( ( ! [SY57: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ SV4 @ SV11 @ SY57 ) @ SV11 @ SY57 )
| ( c_lessequals @ SV4 @ SV11 @ ( tc_set @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(67,plain,
! [SV12: $i,SV5: $i] :
( ( ! [SY58: $i] :
( ~ ( c_in @ SV5 @ SV12 @ ( tc_set @ SY58 ) )
| ! [SY59: $i] :
( ~ ( c_in @ SY59 @ ( c_Zorn_Ochain @ SV12 @ SY58 ) @ ( tc_set @ ( tc_set @ SY58 ) ) )
| ( c_in @ ( c_Zorn_Ochain__extend__1 @ SY59 @ SV5 @ SY58 ) @ SY59 @ ( tc_set @ SY58 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV5 @ c_emptyset @ ( tc_set @ SY58 ) ) @ SY59 @ ( tc_set @ SY58 ) ) @ ( c_Zorn_Ochain @ SV12 @ SY58 ) @ ( tc_set @ ( tc_set @ SY58 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(68,plain,
! [SV13: $i,SV6: $i] :
( ( ! [SY60: $i] :
( ~ ( c_in @ SV6 @ SV13 @ ( tc_set @ SY60 ) )
| ! [SY61: $i] :
( ~ ( c_in @ SY61 @ ( c_Zorn_Ochain @ SV13 @ SY60 ) @ ( tc_set @ ( tc_set @ SY60 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ SY61 @ SV6 @ SY60 ) @ SV6 @ ( tc_set @ SY60 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV6 @ c_emptyset @ ( tc_set @ SY60 ) ) @ SY61 @ ( tc_set @ SY60 ) ) @ ( c_Zorn_Ochain @ SV13 @ SY60 ) @ ( tc_set @ ( tc_set @ SY60 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(69,plain,
! [SV14: $i,SV7: $i] :
( ( ! [SY62: $i,SY63: $i] :
( ~ ( c_in @ SV7 @ SV14 @ SY62 )
| ! [SY64: $i] :
( ~ ( c_in @ SY63 @ ( c_Zorn_Omaxchain @ SY64 @ SY62 ) @ ( tc_set @ ( tc_set @ SY62 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV14 @ c_emptyset @ ( tc_set @ SY62 ) ) @ SY63 @ ( tc_set @ SY62 ) ) @ ( c_Zorn_Ochain @ SY64 @ SY62 ) @ ( tc_set @ ( tc_set @ SY62 ) ) )
| ! [SY48: $i] :
( ( c_in @ SV7 @ SY48 @ SY62 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SY63 @ SY48 @ SY62 ) @ SY63 @ ( tc_set @ SY62 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(70,plain,
! [SV15: $i,SV8: $i] :
( ( ! [SY66: $i,SY67: $i] :
( ~ ( c_in @ SV8 @ SV15 @ SY66 )
| ! [SY68: $i] :
( ~ ( c_in @ SY67 @ ( c_Zorn_Omaxchain @ SY68 @ SY66 ) @ ( tc_set @ ( tc_set @ SY66 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV15 @ c_emptyset @ ( tc_set @ SY66 ) ) @ SY67 @ ( tc_set @ SY66 ) ) @ ( c_Zorn_Ochain @ SY68 @ SY66 ) @ ( tc_set @ ( tc_set @ SY66 ) ) )
| ! [SY53: $i] :
( ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SY67 @ SY53 @ SY66 ) @ SY53 @ ( tc_set @ SY66 ) )
| ( c_in @ SV8 @ SY53 @ SY66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(71,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)],[63]) ).
thf(72,plain,
! [SV16: $i,SV9: $i,SV2: $i] :
( ( ~ ( c_in @ SV2 @ SV9 @ SV16 )
| ! [SY70: $i] :
( ~ ( c_lessequals @ SV9 @ SY70 @ ( tc_set @ SV16 ) )
| ( c_in @ SV2 @ SY70 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(73,plain,
! [SV17: $i,SV10: $i,SV3: $i] :
( ( ( c_in @ ( c_Main_OsubsetI__1 @ SV3 @ SV10 @ SV17 ) @ SV3 @ SV17 )
| ( c_lessequals @ SV3 @ SV10 @ ( tc_set @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(74,plain,
! [SV18: $i,SV11: $i,SV4: $i] :
( ( ~ ( c_in @ ( c_Main_OsubsetI__1 @ SV4 @ SV11 @ SV18 ) @ SV11 @ SV18 )
| ( c_lessequals @ SV4 @ SV11 @ ( tc_set @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(75,plain,
! [SV19: $i,SV12: $i,SV5: $i] :
( ( ~ ( c_in @ SV5 @ SV12 @ ( tc_set @ SV19 ) )
| ! [SY71: $i] :
( ~ ( c_in @ SY71 @ ( c_Zorn_Ochain @ SV12 @ SV19 ) @ ( tc_set @ ( tc_set @ SV19 ) ) )
| ( c_in @ ( c_Zorn_Ochain__extend__1 @ SY71 @ SV5 @ SV19 ) @ SY71 @ ( tc_set @ SV19 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV5 @ c_emptyset @ ( tc_set @ SV19 ) ) @ SY71 @ ( tc_set @ SV19 ) ) @ ( c_Zorn_Ochain @ SV12 @ SV19 ) @ ( tc_set @ ( tc_set @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(76,plain,
! [SV20: $i,SV13: $i,SV6: $i] :
( ( ~ ( c_in @ SV6 @ SV13 @ ( tc_set @ SV20 ) )
| ! [SY72: $i] :
( ~ ( c_in @ SY72 @ ( c_Zorn_Ochain @ SV13 @ SV20 ) @ ( tc_set @ ( tc_set @ SV20 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ SY72 @ SV6 @ SV20 ) @ SV6 @ ( tc_set @ SV20 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV6 @ c_emptyset @ ( tc_set @ SV20 ) ) @ SY72 @ ( tc_set @ SV20 ) ) @ ( c_Zorn_Ochain @ SV13 @ SV20 ) @ ( tc_set @ ( tc_set @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(77,plain,
! [SV21: $i,SV14: $i,SV7: $i] :
( ( ! [SY73: $i] :
( ~ ( c_in @ SV7 @ SV14 @ SV21 )
| ! [SY74: $i] :
( ~ ( c_in @ SY73 @ ( c_Zorn_Omaxchain @ SY74 @ SV21 ) @ ( tc_set @ ( tc_set @ SV21 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV14 @ c_emptyset @ ( tc_set @ SV21 ) ) @ SY73 @ ( tc_set @ SV21 ) ) @ ( c_Zorn_Ochain @ SY74 @ SV21 ) @ ( tc_set @ ( tc_set @ SV21 ) ) )
| ! [SY75: $i] :
( ( c_in @ SV7 @ SY75 @ SV21 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SY73 @ SY75 @ SV21 ) @ SY73 @ ( tc_set @ SV21 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(78,plain,
! [SV22: $i,SV15: $i,SV8: $i] :
( ( ! [SY76: $i] :
( ~ ( c_in @ SV8 @ SV15 @ SV22 )
| ! [SY77: $i] :
( ~ ( c_in @ SY76 @ ( c_Zorn_Omaxchain @ SY77 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV15 @ c_emptyset @ ( tc_set @ SV22 ) ) @ SY76 @ ( tc_set @ SV22 ) ) @ ( c_Zorn_Ochain @ SY77 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) )
| ! [SY78: $i] :
( ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SY76 @ SY78 @ SV22 ) @ SY78 @ ( tc_set @ SV22 ) )
| ( c_in @ SV8 @ SY78 @ SV22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(79,plain,
! [SV16: $i,SV9: $i,SV2: $i] :
( ( ( ~ ( c_in @ SV2 @ SV9 @ SV16 ) )
= $true )
| ( ( ! [SY70: $i] :
( ~ ( c_lessequals @ SV9 @ SY70 @ ( tc_set @ SV16 ) )
| ( c_in @ SV2 @ SY70 @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(80,plain,
! [SV17: $i,SV10: $i,SV3: $i] :
( ( ( c_in @ ( c_Main_OsubsetI__1 @ SV3 @ SV10 @ SV17 ) @ SV3 @ SV17 )
= $true )
| ( ( c_lessequals @ SV3 @ SV10 @ ( tc_set @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(81,plain,
! [SV18: $i,SV11: $i,SV4: $i] :
( ( ( ~ ( c_in @ ( c_Main_OsubsetI__1 @ SV4 @ SV11 @ SV18 ) @ SV11 @ SV18 ) )
= $true )
| ( ( c_lessequals @ SV4 @ SV11 @ ( tc_set @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(82,plain,
! [SV19: $i,SV12: $i,SV5: $i] :
( ( ( ~ ( c_in @ SV5 @ SV12 @ ( tc_set @ SV19 ) ) )
= $true )
| ( ( ! [SY71: $i] :
( ~ ( c_in @ SY71 @ ( c_Zorn_Ochain @ SV12 @ SV19 ) @ ( tc_set @ ( tc_set @ SV19 ) ) )
| ( c_in @ ( c_Zorn_Ochain__extend__1 @ SY71 @ SV5 @ SV19 ) @ SY71 @ ( tc_set @ SV19 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV5 @ c_emptyset @ ( tc_set @ SV19 ) ) @ SY71 @ ( tc_set @ SV19 ) ) @ ( c_Zorn_Ochain @ SV12 @ SV19 ) @ ( tc_set @ ( tc_set @ SV19 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(83,plain,
! [SV20: $i,SV13: $i,SV6: $i] :
( ( ( ~ ( c_in @ SV6 @ SV13 @ ( tc_set @ SV20 ) ) )
= $true )
| ( ( ! [SY72: $i] :
( ~ ( c_in @ SY72 @ ( c_Zorn_Ochain @ SV13 @ SV20 ) @ ( tc_set @ ( tc_set @ SV20 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ SY72 @ SV6 @ SV20 ) @ SV6 @ ( tc_set @ SV20 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV6 @ c_emptyset @ ( tc_set @ SV20 ) ) @ SY72 @ ( tc_set @ SV20 ) ) @ ( c_Zorn_Ochain @ SV13 @ SV20 ) @ ( tc_set @ ( tc_set @ SV20 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(84,plain,
! [SV23: $i,SV21: $i,SV14: $i,SV7: $i] :
( ( ~ ( c_in @ SV7 @ SV14 @ SV21 )
| ! [SY79: $i] :
( ~ ( c_in @ SV23 @ ( c_Zorn_Omaxchain @ SY79 @ SV21 ) @ ( tc_set @ ( tc_set @ SV21 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV14 @ c_emptyset @ ( tc_set @ SV21 ) ) @ SV23 @ ( tc_set @ SV21 ) ) @ ( c_Zorn_Ochain @ SY79 @ SV21 ) @ ( tc_set @ ( tc_set @ SV21 ) ) )
| ! [SY80: $i] :
( ( c_in @ SV7 @ SY80 @ SV21 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV23 @ SY80 @ SV21 ) @ SV23 @ ( tc_set @ SV21 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(85,plain,
! [SV24: $i,SV22: $i,SV15: $i,SV8: $i] :
( ( ~ ( c_in @ SV8 @ SV15 @ SV22 )
| ! [SY81: $i] :
( ~ ( c_in @ SV24 @ ( c_Zorn_Omaxchain @ SY81 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV15 @ c_emptyset @ ( tc_set @ SV22 ) ) @ SV24 @ ( tc_set @ SV22 ) ) @ ( c_Zorn_Ochain @ SY81 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) )
| ! [SY82: $i] :
( ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV24 @ SY82 @ SV22 ) @ SY82 @ ( tc_set @ SV22 ) )
| ( c_in @ SV8 @ SY82 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(86,plain,
! [SV16: $i,SV9: $i,SV2: $i] :
( ( ( c_in @ SV2 @ SV9 @ SV16 )
= $false )
| ( ( ! [SY70: $i] :
( ~ ( c_lessequals @ SV9 @ SY70 @ ( tc_set @ SV16 ) )
| ( c_in @ SV2 @ SY70 @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(87,plain,
! [SV18: $i,SV11: $i,SV4: $i] :
( ( ( c_in @ ( c_Main_OsubsetI__1 @ SV4 @ SV11 @ SV18 ) @ SV11 @ SV18 )
= $false )
| ( ( c_lessequals @ SV4 @ SV11 @ ( tc_set @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(88,plain,
! [SV19: $i,SV12: $i,SV5: $i] :
( ( ( c_in @ SV5 @ SV12 @ ( tc_set @ SV19 ) )
= $false )
| ( ( ! [SY71: $i] :
( ~ ( c_in @ SY71 @ ( c_Zorn_Ochain @ SV12 @ SV19 ) @ ( tc_set @ ( tc_set @ SV19 ) ) )
| ( c_in @ ( c_Zorn_Ochain__extend__1 @ SY71 @ SV5 @ SV19 ) @ SY71 @ ( tc_set @ SV19 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV5 @ c_emptyset @ ( tc_set @ SV19 ) ) @ SY71 @ ( tc_set @ SV19 ) ) @ ( c_Zorn_Ochain @ SV12 @ SV19 ) @ ( tc_set @ ( tc_set @ SV19 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(89,plain,
! [SV20: $i,SV13: $i,SV6: $i] :
( ( ( c_in @ SV6 @ SV13 @ ( tc_set @ SV20 ) )
= $false )
| ( ( ! [SY72: $i] :
( ~ ( c_in @ SY72 @ ( c_Zorn_Ochain @ SV13 @ SV20 ) @ ( tc_set @ ( tc_set @ SV20 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ SY72 @ SV6 @ SV20 ) @ SV6 @ ( tc_set @ SV20 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV6 @ c_emptyset @ ( tc_set @ SV20 ) ) @ SY72 @ ( tc_set @ SV20 ) ) @ ( c_Zorn_Ochain @ SV13 @ SV20 ) @ ( tc_set @ ( tc_set @ SV20 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(90,plain,
! [SV23: $i,SV21: $i,SV14: $i,SV7: $i] :
( ( ( ~ ( c_in @ SV7 @ SV14 @ SV21 ) )
= $true )
| ( ( ! [SY79: $i] :
( ~ ( c_in @ SV23 @ ( c_Zorn_Omaxchain @ SY79 @ SV21 ) @ ( tc_set @ ( tc_set @ SV21 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV14 @ c_emptyset @ ( tc_set @ SV21 ) ) @ SV23 @ ( tc_set @ SV21 ) ) @ ( c_Zorn_Ochain @ SY79 @ SV21 ) @ ( tc_set @ ( tc_set @ SV21 ) ) )
| ! [SY80: $i] :
( ( c_in @ SV7 @ SY80 @ SV21 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV23 @ SY80 @ SV21 ) @ SV23 @ ( tc_set @ SV21 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(91,plain,
! [SV24: $i,SV22: $i,SV15: $i,SV8: $i] :
( ( ( ~ ( c_in @ SV8 @ SV15 @ SV22 ) )
= $true )
| ( ( ! [SY81: $i] :
( ~ ( c_in @ SV24 @ ( c_Zorn_Omaxchain @ SY81 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV15 @ c_emptyset @ ( tc_set @ SV22 ) ) @ SV24 @ ( tc_set @ SV22 ) ) @ ( c_Zorn_Ochain @ SY81 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) )
| ! [SY82: $i] :
( ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV24 @ SY82 @ SV22 ) @ SY82 @ ( tc_set @ SV22 ) )
| ( c_in @ SV8 @ SY82 @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(92,plain,
! [SV2: $i,SV16: $i,SV25: $i,SV9: $i] :
( ( ( ~ ( c_lessequals @ SV9 @ SV25 @ ( tc_set @ SV16 ) )
| ( c_in @ SV2 @ SV25 @ SV16 ) )
= $true )
| ( ( c_in @ SV2 @ SV9 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(93,plain,
! [SV5: $i,SV19: $i,SV12: $i,SV26: $i] :
( ( ( ~ ( c_in @ SV26 @ ( c_Zorn_Ochain @ SV12 @ SV19 ) @ ( tc_set @ ( tc_set @ SV19 ) ) )
| ( c_in @ ( c_Zorn_Ochain__extend__1 @ SV26 @ SV5 @ SV19 ) @ SV26 @ ( tc_set @ SV19 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV5 @ c_emptyset @ ( tc_set @ SV19 ) ) @ SV26 @ ( tc_set @ SV19 ) ) @ ( c_Zorn_Ochain @ SV12 @ SV19 ) @ ( tc_set @ ( tc_set @ SV19 ) ) ) )
= $true )
| ( ( c_in @ SV5 @ SV12 @ ( tc_set @ SV19 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(94,plain,
! [SV6: $i,SV20: $i,SV13: $i,SV27: $i] :
( ( ( ~ ( c_in @ SV27 @ ( c_Zorn_Ochain @ SV13 @ SV20 ) @ ( tc_set @ ( tc_set @ SV20 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ SV27 @ SV6 @ SV20 ) @ SV6 @ ( tc_set @ SV20 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV6 @ c_emptyset @ ( tc_set @ SV20 ) ) @ SV27 @ ( tc_set @ SV20 ) ) @ ( c_Zorn_Ochain @ SV13 @ SV20 ) @ ( tc_set @ ( tc_set @ SV20 ) ) ) )
= $true )
| ( ( c_in @ SV6 @ SV13 @ ( tc_set @ SV20 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(95,plain,
! [SV23: $i,SV21: $i,SV14: $i,SV7: $i] :
( ( ( c_in @ SV7 @ SV14 @ SV21 )
= $false )
| ( ( ! [SY79: $i] :
( ~ ( c_in @ SV23 @ ( c_Zorn_Omaxchain @ SY79 @ SV21 ) @ ( tc_set @ ( tc_set @ SV21 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV14 @ c_emptyset @ ( tc_set @ SV21 ) ) @ SV23 @ ( tc_set @ SV21 ) ) @ ( c_Zorn_Ochain @ SY79 @ SV21 ) @ ( tc_set @ ( tc_set @ SV21 ) ) )
| ! [SY80: $i] :
( ( c_in @ SV7 @ SY80 @ SV21 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV23 @ SY80 @ SV21 ) @ SV23 @ ( tc_set @ SV21 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(96,plain,
! [SV24: $i,SV22: $i,SV15: $i,SV8: $i] :
( ( ( c_in @ SV8 @ SV15 @ SV22 )
= $false )
| ( ( ! [SY81: $i] :
( ~ ( c_in @ SV24 @ ( c_Zorn_Omaxchain @ SY81 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV15 @ c_emptyset @ ( tc_set @ SV22 ) ) @ SV24 @ ( tc_set @ SV22 ) ) @ ( c_Zorn_Ochain @ SY81 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) )
| ! [SY82: $i] :
( ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV24 @ SY82 @ SV22 ) @ SY82 @ ( tc_set @ SV22 ) )
| ( c_in @ SV8 @ SY82 @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(97,plain,
! [SV2: $i,SV16: $i,SV25: $i,SV9: $i] :
( ( ( ~ ( c_lessequals @ SV9 @ SV25 @ ( tc_set @ SV16 ) ) )
= $true )
| ( ( c_in @ SV2 @ SV25 @ SV16 )
= $true )
| ( ( c_in @ SV2 @ SV9 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(98,plain,
! [SV5: $i,SV19: $i,SV12: $i,SV26: $i] :
( ( ( ~ ( c_in @ SV26 @ ( c_Zorn_Ochain @ SV12 @ SV19 ) @ ( tc_set @ ( tc_set @ SV19 ) ) ) )
= $true )
| ( ( ( c_in @ ( c_Zorn_Ochain__extend__1 @ SV26 @ SV5 @ SV19 ) @ SV26 @ ( tc_set @ SV19 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV5 @ c_emptyset @ ( tc_set @ SV19 ) ) @ SV26 @ ( tc_set @ SV19 ) ) @ ( c_Zorn_Ochain @ SV12 @ SV19 ) @ ( tc_set @ ( tc_set @ SV19 ) ) ) )
= $true )
| ( ( c_in @ SV5 @ SV12 @ ( tc_set @ SV19 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(99,plain,
! [SV6: $i,SV20: $i,SV13: $i,SV27: $i] :
( ( ( ~ ( c_in @ SV27 @ ( c_Zorn_Ochain @ SV13 @ SV20 ) @ ( tc_set @ ( tc_set @ SV20 ) ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ SV27 @ SV6 @ SV20 ) @ SV6 @ ( tc_set @ SV20 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV6 @ c_emptyset @ ( tc_set @ SV20 ) ) @ SV27 @ ( tc_set @ SV20 ) ) @ ( c_Zorn_Ochain @ SV13 @ SV20 ) @ ( tc_set @ ( tc_set @ SV20 ) ) ) )
= $true )
| ( ( c_in @ SV6 @ SV13 @ ( tc_set @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(100,plain,
! [SV7: $i,SV14: $i,SV21: $i,SV28: $i,SV23: $i] :
( ( ( ~ ( c_in @ SV23 @ ( c_Zorn_Omaxchain @ SV28 @ SV21 ) @ ( tc_set @ ( tc_set @ SV21 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV14 @ c_emptyset @ ( tc_set @ SV21 ) ) @ SV23 @ ( tc_set @ SV21 ) ) @ ( c_Zorn_Ochain @ SV28 @ SV21 ) @ ( tc_set @ ( tc_set @ SV21 ) ) )
| ! [SY80: $i] :
( ( c_in @ SV7 @ SY80 @ SV21 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV23 @ SY80 @ SV21 ) @ SV23 @ ( tc_set @ SV21 ) ) ) )
= $true )
| ( ( c_in @ SV7 @ SV14 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(101,plain,
! [SV8: $i,SV15: $i,SV22: $i,SV29: $i,SV24: $i] :
( ( ( ~ ( c_in @ SV24 @ ( c_Zorn_Omaxchain @ SV29 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) )
| ~ ( c_in @ ( c_union @ ( c_insert @ SV15 @ c_emptyset @ ( tc_set @ SV22 ) ) @ SV24 @ ( tc_set @ SV22 ) ) @ ( c_Zorn_Ochain @ SV29 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) )
| ! [SY82: $i] :
( ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV24 @ SY82 @ SV22 ) @ SY82 @ ( tc_set @ SV22 ) )
| ( c_in @ SV8 @ SY82 @ SV22 ) ) )
= $true )
| ( ( c_in @ SV8 @ SV15 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(102,plain,
! [SV2: $i,SV16: $i,SV25: $i,SV9: $i] :
( ( ( c_lessequals @ SV9 @ SV25 @ ( tc_set @ SV16 ) )
= $false )
| ( ( c_in @ SV2 @ SV25 @ SV16 )
= $true )
| ( ( c_in @ SV2 @ SV9 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(103,plain,
! [SV5: $i,SV19: $i,SV12: $i,SV26: $i] :
( ( ( c_in @ SV26 @ ( c_Zorn_Ochain @ SV12 @ SV19 ) @ ( tc_set @ ( tc_set @ SV19 ) ) )
= $false )
| ( ( ( c_in @ ( c_Zorn_Ochain__extend__1 @ SV26 @ SV5 @ SV19 ) @ SV26 @ ( tc_set @ SV19 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV5 @ c_emptyset @ ( tc_set @ SV19 ) ) @ SV26 @ ( tc_set @ SV19 ) ) @ ( c_Zorn_Ochain @ SV12 @ SV19 ) @ ( tc_set @ ( tc_set @ SV19 ) ) ) )
= $true )
| ( ( c_in @ SV5 @ SV12 @ ( tc_set @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(104,plain,
! [SV6: $i,SV20: $i,SV13: $i,SV27: $i] :
( ( ( c_in @ SV27 @ ( c_Zorn_Ochain @ SV13 @ SV20 ) @ ( tc_set @ ( tc_set @ SV20 ) ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ SV27 @ SV6 @ SV20 ) @ SV6 @ ( tc_set @ SV20 ) )
| ( c_in @ ( c_union @ ( c_insert @ SV6 @ c_emptyset @ ( tc_set @ SV20 ) ) @ SV27 @ ( tc_set @ SV20 ) ) @ ( c_Zorn_Ochain @ SV13 @ SV20 ) @ ( tc_set @ ( tc_set @ SV20 ) ) ) )
= $true )
| ( ( c_in @ SV6 @ SV13 @ ( tc_set @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(105,plain,
! [SV7: $i,SV14: $i,SV21: $i,SV28: $i,SV23: $i] :
( ( ( ~ ( c_in @ SV23 @ ( c_Zorn_Omaxchain @ SV28 @ SV21 ) @ ( tc_set @ ( tc_set @ SV21 ) ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_union @ ( c_insert @ SV14 @ c_emptyset @ ( tc_set @ SV21 ) ) @ SV23 @ ( tc_set @ SV21 ) ) @ ( c_Zorn_Ochain @ SV28 @ SV21 ) @ ( tc_set @ ( tc_set @ SV21 ) ) )
| ! [SY80: $i] :
( ( c_in @ SV7 @ SY80 @ SV21 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV23 @ SY80 @ SV21 ) @ SV23 @ ( tc_set @ SV21 ) ) ) )
= $true )
| ( ( c_in @ SV7 @ SV14 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(106,plain,
! [SV8: $i,SV15: $i,SV22: $i,SV29: $i,SV24: $i] :
( ( ( ~ ( c_in @ SV24 @ ( c_Zorn_Omaxchain @ SV29 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_union @ ( c_insert @ SV15 @ c_emptyset @ ( tc_set @ SV22 ) ) @ SV24 @ ( tc_set @ SV22 ) ) @ ( c_Zorn_Ochain @ SV29 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) )
| ! [SY82: $i] :
( ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV24 @ SY82 @ SV22 ) @ SY82 @ ( tc_set @ SV22 ) )
| ( c_in @ SV8 @ SY82 @ SV22 ) ) )
= $true )
| ( ( c_in @ SV8 @ SV15 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(107,plain,
! [SV12: $i,SV19: $i,SV5: $i,SV26: $i] :
( ( ( c_in @ ( c_Zorn_Ochain__extend__1 @ SV26 @ SV5 @ SV19 ) @ SV26 @ ( tc_set @ SV19 ) )
= $true )
| ( ( c_in @ ( c_union @ ( c_insert @ SV5 @ c_emptyset @ ( tc_set @ SV19 ) ) @ SV26 @ ( tc_set @ SV19 ) ) @ ( c_Zorn_Ochain @ SV12 @ SV19 ) @ ( tc_set @ ( tc_set @ SV19 ) ) )
= $true )
| ( ( c_in @ SV26 @ ( c_Zorn_Ochain @ SV12 @ SV19 ) @ ( tc_set @ ( tc_set @ SV19 ) ) )
= $false )
| ( ( c_in @ SV5 @ SV12 @ ( tc_set @ SV19 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(108,plain,
! [SV13: $i,SV20: $i,SV6: $i,SV27: $i] :
( ( ( ~ ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ SV27 @ SV6 @ SV20 ) @ SV6 @ ( tc_set @ SV20 ) ) )
= $true )
| ( ( c_in @ ( c_union @ ( c_insert @ SV6 @ c_emptyset @ ( tc_set @ SV20 ) ) @ SV27 @ ( tc_set @ SV20 ) ) @ ( c_Zorn_Ochain @ SV13 @ SV20 ) @ ( tc_set @ ( tc_set @ SV20 ) ) )
= $true )
| ( ( c_in @ SV27 @ ( c_Zorn_Ochain @ SV13 @ SV20 ) @ ( tc_set @ ( tc_set @ SV20 ) ) )
= $false )
| ( ( c_in @ SV6 @ SV13 @ ( tc_set @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(109,plain,
! [SV7: $i,SV14: $i,SV21: $i,SV28: $i,SV23: $i] :
( ( ( c_in @ SV23 @ ( c_Zorn_Omaxchain @ SV28 @ SV21 ) @ ( tc_set @ ( tc_set @ SV21 ) ) )
= $false )
| ( ( ~ ( c_in @ ( c_union @ ( c_insert @ SV14 @ c_emptyset @ ( tc_set @ SV21 ) ) @ SV23 @ ( tc_set @ SV21 ) ) @ ( c_Zorn_Ochain @ SV28 @ SV21 ) @ ( tc_set @ ( tc_set @ SV21 ) ) )
| ! [SY80: $i] :
( ( c_in @ SV7 @ SY80 @ SV21 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV23 @ SY80 @ SV21 ) @ SV23 @ ( tc_set @ SV21 ) ) ) )
= $true )
| ( ( c_in @ SV7 @ SV14 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(110,plain,
! [SV8: $i,SV15: $i,SV22: $i,SV29: $i,SV24: $i] :
( ( ( c_in @ SV24 @ ( c_Zorn_Omaxchain @ SV29 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) )
= $false )
| ( ( ~ ( c_in @ ( c_union @ ( c_insert @ SV15 @ c_emptyset @ ( tc_set @ SV22 ) ) @ SV24 @ ( tc_set @ SV22 ) ) @ ( c_Zorn_Ochain @ SV29 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) )
| ! [SY82: $i] :
( ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV24 @ SY82 @ SV22 ) @ SY82 @ ( tc_set @ SV22 ) )
| ( c_in @ SV8 @ SY82 @ SV22 ) ) )
= $true )
| ( ( c_in @ SV8 @ SV15 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(111,plain,
! [SV13: $i,SV20: $i,SV6: $i,SV27: $i] :
( ( ( c_lessequals @ ( c_Zorn_Ochain__extend__1 @ SV27 @ SV6 @ SV20 ) @ SV6 @ ( tc_set @ SV20 ) )
= $false )
| ( ( c_in @ ( c_union @ ( c_insert @ SV6 @ c_emptyset @ ( tc_set @ SV20 ) ) @ SV27 @ ( tc_set @ SV20 ) ) @ ( c_Zorn_Ochain @ SV13 @ SV20 ) @ ( tc_set @ ( tc_set @ SV20 ) ) )
= $true )
| ( ( c_in @ SV27 @ ( c_Zorn_Ochain @ SV13 @ SV20 ) @ ( tc_set @ ( tc_set @ SV20 ) ) )
= $false )
| ( ( c_in @ SV6 @ SV13 @ ( tc_set @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(112,plain,
! [SV7: $i,SV28: $i,SV23: $i,SV21: $i,SV14: $i] :
( ( ( ~ ( c_in @ ( c_union @ ( c_insert @ SV14 @ c_emptyset @ ( tc_set @ SV21 ) ) @ SV23 @ ( tc_set @ SV21 ) ) @ ( c_Zorn_Ochain @ SV28 @ SV21 ) @ ( tc_set @ ( tc_set @ SV21 ) ) ) )
= $true )
| ( ( ! [SY80: $i] :
( ( c_in @ SV7 @ SY80 @ SV21 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV23 @ SY80 @ SV21 ) @ SV23 @ ( tc_set @ SV21 ) ) ) )
= $true )
| ( ( c_in @ SV23 @ ( c_Zorn_Omaxchain @ SV28 @ SV21 ) @ ( tc_set @ ( tc_set @ SV21 ) ) )
= $false )
| ( ( c_in @ SV7 @ SV14 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(113,plain,
! [SV8: $i,SV29: $i,SV24: $i,SV22: $i,SV15: $i] :
( ( ( ~ ( c_in @ ( c_union @ ( c_insert @ SV15 @ c_emptyset @ ( tc_set @ SV22 ) ) @ SV24 @ ( tc_set @ SV22 ) ) @ ( c_Zorn_Ochain @ SV29 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) ) )
= $true )
| ( ( ! [SY82: $i] :
( ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV24 @ SY82 @ SV22 ) @ SY82 @ ( tc_set @ SV22 ) )
| ( c_in @ SV8 @ SY82 @ SV22 ) ) )
= $true )
| ( ( c_in @ SV24 @ ( c_Zorn_Omaxchain @ SV29 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) )
= $false )
| ( ( c_in @ SV8 @ SV15 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(114,plain,
! [SV7: $i,SV28: $i,SV23: $i,SV21: $i,SV14: $i] :
( ( ( c_in @ ( c_union @ ( c_insert @ SV14 @ c_emptyset @ ( tc_set @ SV21 ) ) @ SV23 @ ( tc_set @ SV21 ) ) @ ( c_Zorn_Ochain @ SV28 @ SV21 ) @ ( tc_set @ ( tc_set @ SV21 ) ) )
= $false )
| ( ( ! [SY80: $i] :
( ( c_in @ SV7 @ SY80 @ SV21 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV23 @ SY80 @ SV21 ) @ SV23 @ ( tc_set @ SV21 ) ) ) )
= $true )
| ( ( c_in @ SV23 @ ( c_Zorn_Omaxchain @ SV28 @ SV21 ) @ ( tc_set @ ( tc_set @ SV21 ) ) )
= $false )
| ( ( c_in @ SV7 @ SV14 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(115,plain,
! [SV8: $i,SV29: $i,SV24: $i,SV22: $i,SV15: $i] :
( ( ( c_in @ ( c_union @ ( c_insert @ SV15 @ c_emptyset @ ( tc_set @ SV22 ) ) @ SV24 @ ( tc_set @ SV22 ) ) @ ( c_Zorn_Ochain @ SV29 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) )
= $false )
| ( ( ! [SY82: $i] :
( ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV24 @ SY82 @ SV22 ) @ SY82 @ ( tc_set @ SV22 ) )
| ( c_in @ SV8 @ SY82 @ SV22 ) ) )
= $true )
| ( ( c_in @ SV24 @ ( c_Zorn_Omaxchain @ SV29 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) )
= $false )
| ( ( c_in @ SV8 @ SV15 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(116,plain,
! [SV28: $i,SV14: $i,SV23: $i,SV21: $i,SV30: $i,SV7: $i] :
( ( ( ( c_in @ SV7 @ SV30 @ SV21 )
| ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV23 @ SV30 @ SV21 ) @ SV23 @ ( tc_set @ SV21 ) ) )
= $true )
| ( ( c_in @ ( c_union @ ( c_insert @ SV14 @ c_emptyset @ ( tc_set @ SV21 ) ) @ SV23 @ ( tc_set @ SV21 ) ) @ ( c_Zorn_Ochain @ SV28 @ SV21 ) @ ( tc_set @ ( tc_set @ SV21 ) ) )
= $false )
| ( ( c_in @ SV23 @ ( c_Zorn_Omaxchain @ SV28 @ SV21 ) @ ( tc_set @ ( tc_set @ SV21 ) ) )
= $false )
| ( ( c_in @ SV7 @ SV14 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(117,plain,
! [SV29: $i,SV15: $i,SV8: $i,SV22: $i,SV31: $i,SV24: $i] :
( ( ( ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV24 @ SV31 @ SV22 ) @ SV31 @ ( tc_set @ SV22 ) )
| ( c_in @ SV8 @ SV31 @ SV22 ) )
= $true )
| ( ( c_in @ ( c_union @ ( c_insert @ SV15 @ c_emptyset @ ( tc_set @ SV22 ) ) @ SV24 @ ( tc_set @ SV22 ) ) @ ( c_Zorn_Ochain @ SV29 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) )
= $false )
| ( ( c_in @ SV24 @ ( c_Zorn_Omaxchain @ SV29 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) )
= $false )
| ( ( c_in @ SV8 @ SV15 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(118,plain,
! [SV28: $i,SV14: $i,SV23: $i,SV21: $i,SV30: $i,SV7: $i] :
( ( ( c_in @ SV7 @ SV30 @ SV21 )
= $true )
| ( ( c_in @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV23 @ SV30 @ SV21 ) @ SV23 @ ( tc_set @ SV21 ) )
= $true )
| ( ( c_in @ ( c_union @ ( c_insert @ SV14 @ c_emptyset @ ( tc_set @ SV21 ) ) @ SV23 @ ( tc_set @ SV21 ) ) @ ( c_Zorn_Ochain @ SV28 @ SV21 ) @ ( tc_set @ ( tc_set @ SV21 ) ) )
= $false )
| ( ( c_in @ SV23 @ ( c_Zorn_Omaxchain @ SV28 @ SV21 ) @ ( tc_set @ ( tc_set @ SV21 ) ) )
= $false )
| ( ( c_in @ SV7 @ SV14 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(119,plain,
! [SV29: $i,SV15: $i,SV8: $i,SV22: $i,SV31: $i,SV24: $i] :
( ( ( ~ ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV24 @ SV31 @ SV22 ) @ SV31 @ ( tc_set @ SV22 ) ) )
= $true )
| ( ( c_in @ SV8 @ SV31 @ SV22 )
= $true )
| ( ( c_in @ ( c_union @ ( c_insert @ SV15 @ c_emptyset @ ( tc_set @ SV22 ) ) @ SV24 @ ( tc_set @ SV22 ) ) @ ( c_Zorn_Ochain @ SV29 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) )
= $false )
| ( ( c_in @ SV24 @ ( c_Zorn_Omaxchain @ SV29 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) )
= $false )
| ( ( c_in @ SV8 @ SV15 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(120,plain,
! [SV29: $i,SV15: $i,SV8: $i,SV22: $i,SV31: $i,SV24: $i] :
( ( ( c_lessequals @ ( c_Zorn_Omaxchain__super__lemma__1 @ SV24 @ SV31 @ SV22 ) @ SV31 @ ( tc_set @ SV22 ) )
= $false )
| ( ( c_in @ SV8 @ SV31 @ SV22 )
= $true )
| ( ( c_in @ ( c_union @ ( c_insert @ SV15 @ c_emptyset @ ( tc_set @ SV22 ) ) @ SV24 @ ( tc_set @ SV22 ) ) @ ( c_Zorn_Ochain @ SV29 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) )
= $false )
| ( ( c_in @ SV24 @ ( c_Zorn_Omaxchain @ SV29 @ SV22 ) @ ( tc_set @ ( tc_set @ SV22 ) ) )
= $false )
| ( ( c_in @ SV8 @ SV15 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(121,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[38,120,118,111,107,102,87,80,71,62,53,42,41,40,39]) ).
thf(122,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET863-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n026.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 : Mon Jul 11 07:35:27 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.37
% 0.19/0.37 No.of.Axioms: 14
% 0.19/0.37
% 0.19/0.37 Length.of.Defs: 0
% 0.19/0.37
% 0.19/0.37 Contains.Choice.Funs: false
% 0.19/0.39 (rf:0,axioms:14,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:16,loop_count:0,foatp_calls:0,translation:fof_full)........
% 0.40/0.58
% 0.40/0.58 ********************************
% 0.40/0.58 * All subproblems solved! *
% 0.40/0.58 ********************************
% 0.40/0.58 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:14,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:121,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.40/0.58
% 0.40/0.58 %**** Beginning of derivation protocol ****
% 0.40/0.58 % SZS output start CNFRefutation
% See solution above
% 0.40/0.58
% 0.40/0.58 %**** End of derivation protocol ****
% 0.40/0.58 %**** no. of clauses in derivation: 122 ****
% 0.40/0.58 %**** clause counter: 121 ****
% 0.40/0.58
% 0.40/0.58 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:14,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:121,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------