%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET854-2 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:42:14 AM UTC 2026
% Result : Unsatisfiable 234.67s 39.31s
% Output : CNFRefutation 234.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 19
% Syntax : Number of formulae : 164 ( 100 unt; 0 typ; 0 def)
% Number of atoms : 1045 ( 291 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 3891 ( 194 ~; 383 |; 0 &;3314 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 497 ( 0 ^; 497 !; 0 ?; 497 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Main_OsubsetI__1,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(tp_c_Union,type,
c_Union: $i > $i > $i ).
thf(tp_c_Zorn_OTFin,type,
c_Zorn_OTFin: $i > $i > $i ).
thf(tp_c_Zorn_OTFin__linear__lemma1__1,type,
c_Zorn_OTFin__linear__lemma1__1: $i > $i > $i > $i ).
thf(tp_c_Zorn_OUnion__lemma0__1,type,
c_Zorn_OUnion__lemma0__1: $i > $i > $i > $i > $i ).
thf(tp_c_Zorn_Osucc,type,
c_Zorn_Osucc: $i > $i > $i > $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
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_Y,type,
v_Y: $i ).
thf(tp_v_x,type,
v_x: $i ).
thf(1,axiom,
! [V_B: $i,V_A: $i,V_C: $i,T_a: $i] :
( ~ ( c_lessequals @ V_B @ ( c_Zorn_OUnion__lemma0__1 @ V_A @ V_B @ V_C @ T_a ) @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_B @ ( c_Union @ V_C @ T_a ) @ ( tc_set @ T_a ) )
| ( c_lessequals @ ( c_Union @ V_C @ T_a ) @ V_A @ ( tc_set @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_2) ).
thf(2,axiom,
! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ~ ( c_lessequals @ ( c_Zorn_OUnion__lemma0__1 @ V_A @ V_B @ V_C @ T_a ) @ V_A @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_B @ ( c_Union @ V_C @ T_a ) @ ( tc_set @ T_a ) )
| ( c_lessequals @ ( c_Union @ V_C @ T_a ) @ V_A @ ( tc_set @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_1) ).
thf(3,axiom,
! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_in @ ( c_Zorn_OUnion__lemma0__1 @ V_A @ V_B @ V_C @ T_a ) @ V_C @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_B @ ( c_Union @ V_C @ T_a ) @ ( tc_set @ T_a ) )
| ( c_lessequals @ ( c_Union @ V_C @ T_a ) @ V_A @ ( tc_set @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_0) ).
thf(4,axiom,
! [V_m: $i,V_S: $i,T_a: $i,V_n: $i] :
( ~ ( c_in @ V_m @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_in @ V_n @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Osucc @ V_S @ ( c_Zorn_OTFin__linear__lemma1__1 @ V_S @ V_m @ T_a ) @ T_a ) @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ V_n @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ V_S @ V_m @ T_a ) @ V_n @ ( tc_set @ ( tc_set @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_3) ).
thf(5,axiom,
! [V_m: $i,V_S: $i,T_a: $i,V_n: $i] :
( ~ ( c_in @ V_m @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_in @ V_n @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( ( c_Zorn_OTFin__linear__lemma1__1 @ V_S @ V_m @ T_a )
!= V_m )
| ( c_lessequals @ V_n @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ V_S @ V_m @ T_a ) @ V_n @ ( tc_set @ ( tc_set @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).
thf(6,axiom,
! [V_m: $i,V_S: $i,T_a: $i,V_n: $i] :
( ~ ( c_in @ V_m @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_in @ V_n @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ V_n @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ ( c_Zorn_OTFin__linear__lemma1__1 @ V_S @ V_m @ T_a ) @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ V_S @ V_m @ T_a ) @ V_n @ ( tc_set @ ( tc_set @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).
thf(7,axiom,
! [V_m: $i,V_S: $i,T_a: $i,V_n: $i] :
( ~ ( c_in @ V_m @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_in @ V_n @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_in @ ( c_Zorn_OTFin__linear__lemma1__1 @ V_S @ V_m @ T_a ) @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ V_n @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ V_S @ V_m @ T_a ) @ V_n @ ( tc_set @ ( tc_set @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).
thf(8,axiom,
! [V_x: $i,V_S: $i,T_a: $i] : ( c_lessequals @ V_x @ ( c_Zorn_Osucc @ V_S @ V_x @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
thf(9,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(10,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(11,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(12,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/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(13,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(14,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[13]) ).
thf(15,negated_conjecture,
! [V_V: $i,V_U: $i] :
( ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ V_V @ t_a ) @ V_U @ ( tc_set @ ( tc_set @ t_a ) ) )
| ( V_V = V_U )
| ~ ( c_lessequals @ V_V @ V_U @ ( tc_set @ ( tc_set @ t_a ) ) )
| ~ ( c_in @ V_V @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
| ~ ( c_in @ V_U @ v_Y @ ( tc_set @ ( tc_set @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(16,negated_conjecture,
~ ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ v_x @ t_a ) @ ( c_Union @ v_Y @ ( tc_set @ t_a ) ) @ ( tc_set @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(17,negated_conjecture,
( v_x
!= ( c_Union @ v_Y @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(18,negated_conjecture,
c_lessequals @ v_x @ ( c_Union @ v_Y @ ( tc_set @ t_a ) ) @ ( tc_set @ ( tc_set @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(19,negated_conjecture,
c_in @ v_x @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(20,negated_conjecture,
c_lessequals @ v_Y @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ ( tc_set @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(21,plain,
$false = $false,
inference(unfold_def,[status(thm)],[14]) ).
thf(22,plain,
( ( ! [V_B: $i,V_A: $i,V_C: $i,T_a: $i] :
( ~ ( c_lessequals @ V_B @ ( c_Zorn_OUnion__lemma0__1 @ V_A @ V_B @ V_C @ T_a ) @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_B @ ( c_Union @ V_C @ T_a ) @ ( tc_set @ T_a ) )
| ( c_lessequals @ ( c_Union @ V_C @ T_a ) @ V_A @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(23,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ~ ( c_lessequals @ ( c_Zorn_OUnion__lemma0__1 @ V_A @ V_B @ V_C @ T_a ) @ V_A @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_B @ ( c_Union @ V_C @ T_a ) @ ( tc_set @ T_a ) )
| ( c_lessequals @ ( c_Union @ V_C @ T_a ) @ V_A @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(24,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_in @ ( c_Zorn_OUnion__lemma0__1 @ V_A @ V_B @ V_C @ T_a ) @ V_C @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_B @ ( c_Union @ V_C @ T_a ) @ ( tc_set @ T_a ) )
| ( c_lessequals @ ( c_Union @ V_C @ T_a ) @ V_A @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(25,plain,
( ( ! [V_m: $i,V_S: $i,T_a: $i,V_n: $i] :
( ~ ( c_in @ V_m @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_in @ V_n @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Osucc @ V_S @ ( c_Zorn_OTFin__linear__lemma1__1 @ V_S @ V_m @ T_a ) @ T_a ) @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ V_n @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ V_S @ V_m @ T_a ) @ V_n @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(26,plain,
( ( ! [V_m: $i,V_S: $i,T_a: $i,V_n: $i] :
( ~ ( c_in @ V_m @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_in @ V_n @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( ( c_Zorn_OTFin__linear__lemma1__1 @ V_S @ V_m @ T_a )
!= V_m )
| ( c_lessequals @ V_n @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ V_S @ V_m @ T_a ) @ V_n @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(27,plain,
( ( ! [V_m: $i,V_S: $i,T_a: $i,V_n: $i] :
( ~ ( c_in @ V_m @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_in @ V_n @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ V_n @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ ( c_Zorn_OTFin__linear__lemma1__1 @ V_S @ V_m @ T_a ) @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ V_S @ V_m @ T_a ) @ V_n @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(28,plain,
( ( ! [V_m: $i,V_S: $i,T_a: $i,V_n: $i] :
( ~ ( c_in @ V_m @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_in @ V_n @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_in @ ( c_Zorn_OTFin__linear__lemma1__1 @ V_S @ V_m @ T_a ) @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ V_n @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ V_S @ V_m @ T_a ) @ V_n @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(29,plain,
( ( ! [V_x: $i,V_S: $i,T_a: $i] : ( c_lessequals @ V_x @ ( c_Zorn_Osucc @ V_S @ V_x @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(30,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)],[9]) ).
thf(31,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)],[10]) ).
thf(32,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)],[11]) ).
thf(33,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)],[12]) ).
thf(34,plain,
( ( ! [V_V: $i,V_U: $i] :
( ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ V_V @ t_a ) @ V_U @ ( tc_set @ ( tc_set @ t_a ) ) )
| ( V_V = V_U )
| ~ ( c_lessequals @ V_V @ V_U @ ( tc_set @ ( tc_set @ t_a ) ) )
| ~ ( c_in @ V_V @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
| ~ ( c_in @ V_U @ v_Y @ ( tc_set @ ( tc_set @ t_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(35,plain,
( ( ~ ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ v_x @ t_a ) @ ( c_Union @ v_Y @ ( tc_set @ t_a ) ) @ ( tc_set @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(36,plain,
( ( v_x
!= ( c_Union @ v_Y @ ( tc_set @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(37,plain,
( ( c_lessequals @ v_x @ ( c_Union @ v_Y @ ( tc_set @ t_a ) ) @ ( tc_set @ ( tc_set @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(38,plain,
( ( c_in @ v_x @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(39,plain,
( ( c_lessequals @ v_Y @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(40,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[21]) ).
thf(41,plain,
( ( c_lessequals @ v_Y @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(42,plain,
( ( c_in @ v_x @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(43,plain,
( ( c_lessequals @ v_x @ ( c_Union @ v_Y @ ( tc_set @ t_a ) ) @ ( tc_set @ ( tc_set @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(44,plain,
( ( v_x
!= ( c_Union @ v_Y @ ( tc_set @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(45,plain,
( ( ~ ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ v_x @ t_a ) @ ( c_Union @ v_Y @ ( tc_set @ t_a ) ) @ ( tc_set @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(46,plain,
( ( ! [V_V: $i,V_U: $i] :
( ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ V_V @ t_a ) @ V_U @ ( tc_set @ ( tc_set @ t_a ) ) )
| ( V_V = V_U )
| ~ ( c_lessequals @ V_V @ V_U @ ( tc_set @ ( tc_set @ t_a ) ) )
| ~ ( c_in @ V_V @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
| ~ ( c_in @ V_U @ v_Y @ ( tc_set @ ( tc_set @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(47,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)],[33]) ).
thf(48,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)],[32]) ).
thf(49,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)],[31]) ).
thf(50,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)],[30]) ).
thf(51,plain,
( ( ! [V_x: $i,V_S: $i,T_a: $i] : ( c_lessequals @ V_x @ ( c_Zorn_Osucc @ V_S @ V_x @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(52,plain,
( ( ! [V_m: $i,V_S: $i,T_a: $i,V_n: $i] :
( ~ ( c_in @ V_m @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_in @ V_n @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_in @ ( c_Zorn_OTFin__linear__lemma1__1 @ V_S @ V_m @ T_a ) @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ V_n @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ V_S @ V_m @ T_a ) @ V_n @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(53,plain,
( ( ! [V_m: $i,V_S: $i,T_a: $i,V_n: $i] :
( ~ ( c_in @ V_m @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_in @ V_n @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ V_n @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ ( c_Zorn_OTFin__linear__lemma1__1 @ V_S @ V_m @ T_a ) @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ V_S @ V_m @ T_a ) @ V_n @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(54,plain,
( ( ! [V_m: $i,V_S: $i,T_a: $i,V_n: $i] :
( ~ ( c_in @ V_m @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_in @ V_n @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( ( c_Zorn_OTFin__linear__lemma1__1 @ V_S @ V_m @ T_a )
!= V_m )
| ( c_lessequals @ V_n @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ V_S @ V_m @ T_a ) @ V_n @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(55,plain,
( ( ! [V_m: $i,V_S: $i,T_a: $i,V_n: $i] :
( ~ ( c_in @ V_m @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_in @ V_n @ ( c_Zorn_OTFin @ V_S @ T_a ) @ ( tc_set @ ( tc_set @ T_a ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Osucc @ V_S @ ( c_Zorn_OTFin__linear__lemma1__1 @ V_S @ V_m @ T_a ) @ T_a ) @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ V_n @ V_m @ ( tc_set @ ( tc_set @ T_a ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ V_S @ V_m @ T_a ) @ V_n @ ( tc_set @ ( tc_set @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(56,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_in @ ( c_Zorn_OUnion__lemma0__1 @ V_A @ V_B @ V_C @ T_a ) @ V_C @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_B @ ( c_Union @ V_C @ T_a ) @ ( tc_set @ T_a ) )
| ( c_lessequals @ ( c_Union @ V_C @ T_a ) @ V_A @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(57,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ~ ( c_lessequals @ ( c_Zorn_OUnion__lemma0__1 @ V_A @ V_B @ V_C @ T_a ) @ V_A @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_B @ ( c_Union @ V_C @ T_a ) @ ( tc_set @ T_a ) )
| ( c_lessequals @ ( c_Union @ V_C @ T_a ) @ V_A @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(58,plain,
( ( ! [V_B: $i,V_A: $i,V_C: $i,T_a: $i] :
( ~ ( c_lessequals @ V_B @ ( c_Zorn_OUnion__lemma0__1 @ V_A @ V_B @ V_C @ T_a ) @ ( tc_set @ T_a ) )
| ( c_lessequals @ V_B @ ( c_Union @ V_C @ T_a ) @ ( tc_set @ T_a ) )
| ( c_lessequals @ ( c_Union @ V_C @ T_a ) @ V_A @ ( tc_set @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(59,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[40]) ).
thf(60,plain,
( ( v_x
!= ( c_Union @ v_Y @ ( tc_set @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(61,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( c_in @ SX0 @ ( c_Zorn_OTFin @ SX1 @ SX2 ) @ ( tc_set @ ( tc_set @ SX2 ) ) )
| ~ ( c_in @ SX3 @ ( c_Zorn_OTFin @ SX1 @ SX2 ) @ ( tc_set @ ( tc_set @ SX2 ) ) )
| ( ( c_Zorn_OTFin__linear__lemma1__1 @ SX1 @ SX0 @ SX2 )
!= SX0 )
| ( c_lessequals @ SX3 @ SX0 @ ( tc_set @ ( tc_set @ SX2 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SX1 @ SX0 @ SX2 ) @ SX3 @ ( tc_set @ ( tc_set @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(62,plain,
( ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ v_x @ t_a ) @ ( c_Union @ v_Y @ ( tc_set @ t_a ) ) @ ( tc_set @ ( tc_set @ t_a ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(63,plain,
! [SV1: $i] :
( ( ! [SY46: $i] :
( ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ SV1 @ t_a ) @ SY46 @ ( tc_set @ ( tc_set @ t_a ) ) )
| ( SV1 = SY46 )
| ~ ( c_lessequals @ SV1 @ SY46 @ ( tc_set @ ( tc_set @ t_a ) ) )
| ~ ( c_in @ SV1 @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
| ~ ( c_in @ SY46 @ v_Y @ ( tc_set @ ( tc_set @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(64,plain,
! [SV2: $i] :
( ( ! [SY47: $i,SY48: $i] :
( ~ ( c_lessequals @ SV2 @ SY47 @ ( tc_set @ SY48 ) )
| ~ ( c_lessequals @ SY47 @ SV2 @ ( tc_set @ SY48 ) )
| ( SY47 = SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(65,plain,
! [SV3: $i] :
( ( ! [SY49: $i,SY50: $i,SY51: $i] :
( ~ ( c_in @ SV3 @ SY49 @ SY50 )
| ~ ( c_lessequals @ SY49 @ SY51 @ ( tc_set @ SY50 ) )
| ( c_in @ SV3 @ SY51 @ SY50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(66,plain,
! [SV4: $i] :
( ( ! [SY52: $i,SY53: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ SV4 @ SY52 @ SY53 ) @ SV4 @ SY53 )
| ( c_lessequals @ SV4 @ SY52 @ ( tc_set @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(67,plain,
! [SV5: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ SV5 @ SY54 @ SY55 ) @ SY54 @ SY55 )
| ( c_lessequals @ SV5 @ SY54 @ ( tc_set @ SY55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(68,plain,
! [SV6: $i] :
( ( ! [SY56: $i,SY57: $i] : ( c_lessequals @ SV6 @ ( c_Zorn_Osucc @ SY56 @ SV6 @ SY57 ) @ ( tc_set @ ( tc_set @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(69,plain,
! [SV7: $i] :
( ( ! [SY58: $i,SY59: $i,SY60: $i] :
( ~ ( c_in @ SV7 @ ( c_Zorn_OTFin @ SY58 @ SY59 ) @ ( tc_set @ ( tc_set @ SY59 ) ) )
| ~ ( c_in @ SY60 @ ( c_Zorn_OTFin @ SY58 @ SY59 ) @ ( tc_set @ ( tc_set @ SY59 ) ) )
| ( c_in @ ( c_Zorn_OTFin__linear__lemma1__1 @ SY58 @ SV7 @ SY59 ) @ ( c_Zorn_OTFin @ SY58 @ SY59 ) @ ( tc_set @ ( tc_set @ SY59 ) ) )
| ( c_lessequals @ SY60 @ SV7 @ ( tc_set @ ( tc_set @ SY59 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SY58 @ SV7 @ SY59 ) @ SY60 @ ( tc_set @ ( tc_set @ SY59 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(70,plain,
! [SV8: $i] :
( ( ! [SY61: $i,SY62: $i,SY63: $i] :
( ~ ( c_in @ SV8 @ ( c_Zorn_OTFin @ SY61 @ SY62 ) @ ( tc_set @ ( tc_set @ SY62 ) ) )
| ~ ( c_in @ SY63 @ ( c_Zorn_OTFin @ SY61 @ SY62 ) @ ( tc_set @ ( tc_set @ SY62 ) ) )
| ( c_lessequals @ SY63 @ SV8 @ ( tc_set @ ( tc_set @ SY62 ) ) )
| ( c_lessequals @ ( c_Zorn_OTFin__linear__lemma1__1 @ SY61 @ SV8 @ SY62 ) @ SV8 @ ( tc_set @ ( tc_set @ SY62 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SY61 @ SV8 @ SY62 ) @ SY63 @ ( tc_set @ ( tc_set @ SY62 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(71,plain,
! [SV9: $i] :
( ( ! [SY64: $i,SY65: $i,SY66: $i] :
( ~ ( c_in @ SV9 @ ( c_Zorn_OTFin @ SY64 @ SY65 ) @ ( tc_set @ ( tc_set @ SY65 ) ) )
| ~ ( c_in @ SY66 @ ( c_Zorn_OTFin @ SY64 @ SY65 ) @ ( tc_set @ ( tc_set @ SY65 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Osucc @ SY64 @ ( c_Zorn_OTFin__linear__lemma1__1 @ SY64 @ SV9 @ SY65 ) @ SY65 ) @ SV9 @ ( tc_set @ ( tc_set @ SY65 ) ) )
| ( c_lessequals @ SY66 @ SV9 @ ( tc_set @ ( tc_set @ SY65 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SY64 @ SV9 @ SY65 ) @ SY66 @ ( tc_set @ ( tc_set @ SY65 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(72,plain,
! [SV10: $i] :
( ( ! [SY67: $i,SY68: $i,SY69: $i] :
( ( c_in @ ( c_Zorn_OUnion__lemma0__1 @ SV10 @ SY67 @ SY68 @ SY69 ) @ SY68 @ ( tc_set @ SY69 ) )
| ( c_lessequals @ SY67 @ ( c_Union @ SY68 @ SY69 ) @ ( tc_set @ SY69 ) )
| ( c_lessequals @ ( c_Union @ SY68 @ SY69 ) @ SV10 @ ( tc_set @ SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(73,plain,
! [SV11: $i] :
( ( ! [SY70: $i,SY71: $i,SY72: $i] :
( ~ ( c_lessequals @ ( c_Zorn_OUnion__lemma0__1 @ SV11 @ SY70 @ SY71 @ SY72 ) @ SV11 @ ( tc_set @ SY72 ) )
| ( c_lessequals @ SY70 @ ( c_Union @ SY71 @ SY72 ) @ ( tc_set @ SY72 ) )
| ( c_lessequals @ ( c_Union @ SY71 @ SY72 ) @ SV11 @ ( tc_set @ SY72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(74,plain,
! [SV12: $i] :
( ( ! [SY73: $i,SY74: $i,SY75: $i] :
( ~ ( c_lessequals @ SV12 @ ( c_Zorn_OUnion__lemma0__1 @ SY73 @ SV12 @ SY74 @ SY75 ) @ ( tc_set @ SY75 ) )
| ( c_lessequals @ SV12 @ ( c_Union @ SY74 @ SY75 ) @ ( tc_set @ SY75 ) )
| ( c_lessequals @ ( c_Union @ SY74 @ SY75 ) @ SY73 @ ( tc_set @ SY75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(75,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(76,plain,
( ( v_x
= ( c_Union @ v_Y @ ( tc_set @ t_a ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(77,plain,
! [SV13: $i] :
( ( ! [SY76: $i,SY77: $i,SY78: $i] :
( ~ ( c_in @ SV13 @ ( c_Zorn_OTFin @ SY76 @ SY77 ) @ ( tc_set @ ( tc_set @ SY77 ) ) )
| ~ ( c_in @ SY78 @ ( c_Zorn_OTFin @ SY76 @ SY77 ) @ ( tc_set @ ( tc_set @ SY77 ) ) )
| ( ( c_Zorn_OTFin__linear__lemma1__1 @ SY76 @ SV13 @ SY77 )
!= SV13 )
| ( c_lessequals @ SY78 @ SV13 @ ( tc_set @ ( tc_set @ SY77 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SY76 @ SV13 @ SY77 ) @ SY78 @ ( tc_set @ ( tc_set @ SY77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(78,plain,
! [SV14: $i,SV1: $i] :
( ( ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ SV1 @ t_a ) @ SV14 @ ( tc_set @ ( tc_set @ t_a ) ) )
| ( SV1 = SV14 )
| ~ ( c_lessequals @ SV1 @ SV14 @ ( tc_set @ ( tc_set @ t_a ) ) )
| ~ ( c_in @ SV1 @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
| ~ ( c_in @ SV14 @ v_Y @ ( tc_set @ ( tc_set @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(79,plain,
! [SV15: $i,SV2: $i] :
( ( ! [SY79: $i] :
( ~ ( c_lessequals @ SV2 @ SV15 @ ( tc_set @ SY79 ) )
| ~ ( c_lessequals @ SV15 @ SV2 @ ( tc_set @ SY79 ) )
| ( SV15 = SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(80,plain,
! [SV16: $i,SV3: $i] :
( ( ! [SY80: $i,SY81: $i] :
( ~ ( c_in @ SV3 @ SV16 @ SY80 )
| ~ ( c_lessequals @ SV16 @ SY81 @ ( tc_set @ SY80 ) )
| ( c_in @ SV3 @ SY81 @ SY80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(81,plain,
! [SV17: $i,SV4: $i] :
( ( ! [SY82: $i] :
( ( c_in @ ( c_Main_OsubsetI__1 @ SV4 @ SV17 @ SY82 ) @ SV4 @ SY82 )
| ( c_lessequals @ SV4 @ SV17 @ ( tc_set @ SY82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(82,plain,
! [SV18: $i,SV5: $i] :
( ( ! [SY83: $i] :
( ~ ( c_in @ ( c_Main_OsubsetI__1 @ SV5 @ SV18 @ SY83 ) @ SV18 @ SY83 )
| ( c_lessequals @ SV5 @ SV18 @ ( tc_set @ SY83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(83,plain,
! [SV19: $i,SV6: $i] :
( ( ! [SY84: $i] : ( c_lessequals @ SV6 @ ( c_Zorn_Osucc @ SV19 @ SV6 @ SY84 ) @ ( tc_set @ ( tc_set @ SY84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(84,plain,
! [SV20: $i,SV7: $i] :
( ( ! [SY85: $i,SY86: $i] :
( ~ ( c_in @ SV7 @ ( c_Zorn_OTFin @ SV20 @ SY85 ) @ ( tc_set @ ( tc_set @ SY85 ) ) )
| ~ ( c_in @ SY86 @ ( c_Zorn_OTFin @ SV20 @ SY85 ) @ ( tc_set @ ( tc_set @ SY85 ) ) )
| ( c_in @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV20 @ SV7 @ SY85 ) @ ( c_Zorn_OTFin @ SV20 @ SY85 ) @ ( tc_set @ ( tc_set @ SY85 ) ) )
| ( c_lessequals @ SY86 @ SV7 @ ( tc_set @ ( tc_set @ SY85 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV20 @ SV7 @ SY85 ) @ SY86 @ ( tc_set @ ( tc_set @ SY85 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(85,plain,
! [SV21: $i,SV8: $i] :
( ( ! [SY87: $i,SY88: $i] :
( ~ ( c_in @ SV8 @ ( c_Zorn_OTFin @ SV21 @ SY87 ) @ ( tc_set @ ( tc_set @ SY87 ) ) )
| ~ ( c_in @ SY88 @ ( c_Zorn_OTFin @ SV21 @ SY87 ) @ ( tc_set @ ( tc_set @ SY87 ) ) )
| ( c_lessequals @ SY88 @ SV8 @ ( tc_set @ ( tc_set @ SY87 ) ) )
| ( c_lessequals @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV21 @ SV8 @ SY87 ) @ SV8 @ ( tc_set @ ( tc_set @ SY87 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV21 @ SV8 @ SY87 ) @ SY88 @ ( tc_set @ ( tc_set @ SY87 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(86,plain,
! [SV22: $i,SV9: $i] :
( ( ! [SY89: $i,SY90: $i] :
( ~ ( c_in @ SV9 @ ( c_Zorn_OTFin @ SV22 @ SY89 ) @ ( tc_set @ ( tc_set @ SY89 ) ) )
| ~ ( c_in @ SY90 @ ( c_Zorn_OTFin @ SV22 @ SY89 ) @ ( tc_set @ ( tc_set @ SY89 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Osucc @ SV22 @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV22 @ SV9 @ SY89 ) @ SY89 ) @ SV9 @ ( tc_set @ ( tc_set @ SY89 ) ) )
| ( c_lessequals @ SY90 @ SV9 @ ( tc_set @ ( tc_set @ SY89 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV22 @ SV9 @ SY89 ) @ SY90 @ ( tc_set @ ( tc_set @ SY89 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(87,plain,
! [SV23: $i,SV10: $i] :
( ( ! [SY91: $i,SY92: $i] :
( ( c_in @ ( c_Zorn_OUnion__lemma0__1 @ SV10 @ SV23 @ SY91 @ SY92 ) @ SY91 @ ( tc_set @ SY92 ) )
| ( c_lessequals @ SV23 @ ( c_Union @ SY91 @ SY92 ) @ ( tc_set @ SY92 ) )
| ( c_lessequals @ ( c_Union @ SY91 @ SY92 ) @ SV10 @ ( tc_set @ SY92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(88,plain,
! [SV24: $i,SV11: $i] :
( ( ! [SY93: $i,SY94: $i] :
( ~ ( c_lessequals @ ( c_Zorn_OUnion__lemma0__1 @ SV11 @ SV24 @ SY93 @ SY94 ) @ SV11 @ ( tc_set @ SY94 ) )
| ( c_lessequals @ SV24 @ ( c_Union @ SY93 @ SY94 ) @ ( tc_set @ SY94 ) )
| ( c_lessequals @ ( c_Union @ SY93 @ SY94 ) @ SV11 @ ( tc_set @ SY94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(89,plain,
! [SV25: $i,SV12: $i] :
( ( ! [SY95: $i,SY96: $i] :
( ~ ( c_lessequals @ SV12 @ ( c_Zorn_OUnion__lemma0__1 @ SV25 @ SV12 @ SY95 @ SY96 ) @ ( tc_set @ SY96 ) )
| ( c_lessequals @ SV12 @ ( c_Union @ SY95 @ SY96 ) @ ( tc_set @ SY96 ) )
| ( c_lessequals @ ( c_Union @ SY95 @ SY96 ) @ SV25 @ ( tc_set @ SY96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(90,plain,
! [SV26: $i,SV13: $i] :
( ( ! [SY97: $i,SY98: $i] :
( ~ ( c_in @ SV13 @ ( c_Zorn_OTFin @ SV26 @ SY97 ) @ ( tc_set @ ( tc_set @ SY97 ) ) )
| ~ ( c_in @ SY98 @ ( c_Zorn_OTFin @ SV26 @ SY97 ) @ ( tc_set @ ( tc_set @ SY97 ) ) )
| ( ( c_Zorn_OTFin__linear__lemma1__1 @ SV26 @ SV13 @ SY97 )
!= SV13 )
| ( c_lessequals @ SY98 @ SV13 @ ( tc_set @ ( tc_set @ SY97 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV26 @ SV13 @ SY97 ) @ SY98 @ ( tc_set @ ( tc_set @ SY97 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(91,plain,
! [SV14: $i,SV1: $i] :
( ( ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ SV1 @ t_a ) @ SV14 @ ( tc_set @ ( tc_set @ t_a ) ) )
= $true )
| ( ( ( SV1 = SV14 )
| ~ ( c_lessequals @ SV1 @ SV14 @ ( tc_set @ ( tc_set @ t_a ) ) )
| ~ ( c_in @ SV1 @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
| ~ ( c_in @ SV14 @ v_Y @ ( tc_set @ ( tc_set @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(92,plain,
! [SV27: $i,SV15: $i,SV2: $i] :
( ( ~ ( c_lessequals @ SV2 @ SV15 @ ( tc_set @ SV27 ) )
| ~ ( c_lessequals @ SV15 @ SV2 @ ( tc_set @ SV27 ) )
| ( SV15 = SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(93,plain,
! [SV28: $i,SV16: $i,SV3: $i] :
( ( ! [SY99: $i] :
( ~ ( c_in @ SV3 @ SV16 @ SV28 )
| ~ ( c_lessequals @ SV16 @ SY99 @ ( tc_set @ SV28 ) )
| ( c_in @ SV3 @ SY99 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(94,plain,
! [SV29: $i,SV17: $i,SV4: $i] :
( ( ( c_in @ ( c_Main_OsubsetI__1 @ SV4 @ SV17 @ SV29 ) @ SV4 @ SV29 )
| ( c_lessequals @ SV4 @ SV17 @ ( tc_set @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(95,plain,
! [SV30: $i,SV18: $i,SV5: $i] :
( ( ~ ( c_in @ ( c_Main_OsubsetI__1 @ SV5 @ SV18 @ SV30 ) @ SV18 @ SV30 )
| ( c_lessequals @ SV5 @ SV18 @ ( tc_set @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(96,plain,
! [SV31: $i,SV19: $i,SV6: $i] :
( ( c_lessequals @ SV6 @ ( c_Zorn_Osucc @ SV19 @ SV6 @ SV31 ) @ ( tc_set @ ( tc_set @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(97,plain,
! [SV32: $i,SV20: $i,SV7: $i] :
( ( ! [SY100: $i] :
( ~ ( c_in @ SV7 @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) )
| ~ ( c_in @ SY100 @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) )
| ( c_in @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV20 @ SV7 @ SV32 ) @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) )
| ( c_lessequals @ SY100 @ SV7 @ ( tc_set @ ( tc_set @ SV32 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV20 @ SV7 @ SV32 ) @ SY100 @ ( tc_set @ ( tc_set @ SV32 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(98,plain,
! [SV33: $i,SV21: $i,SV8: $i] :
( ( ! [SY101: $i] :
( ~ ( c_in @ SV8 @ ( c_Zorn_OTFin @ SV21 @ SV33 ) @ ( tc_set @ ( tc_set @ SV33 ) ) )
| ~ ( c_in @ SY101 @ ( c_Zorn_OTFin @ SV21 @ SV33 ) @ ( tc_set @ ( tc_set @ SV33 ) ) )
| ( c_lessequals @ SY101 @ SV8 @ ( tc_set @ ( tc_set @ SV33 ) ) )
| ( c_lessequals @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV21 @ SV8 @ SV33 ) @ SV8 @ ( tc_set @ ( tc_set @ SV33 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV21 @ SV8 @ SV33 ) @ SY101 @ ( tc_set @ ( tc_set @ SV33 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(99,plain,
! [SV34: $i,SV22: $i,SV9: $i] :
( ( ! [SY102: $i] :
( ~ ( c_in @ SV9 @ ( c_Zorn_OTFin @ SV22 @ SV34 ) @ ( tc_set @ ( tc_set @ SV34 ) ) )
| ~ ( c_in @ SY102 @ ( c_Zorn_OTFin @ SV22 @ SV34 ) @ ( tc_set @ ( tc_set @ SV34 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Osucc @ SV22 @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV22 @ SV9 @ SV34 ) @ SV34 ) @ SV9 @ ( tc_set @ ( tc_set @ SV34 ) ) )
| ( c_lessequals @ SY102 @ SV9 @ ( tc_set @ ( tc_set @ SV34 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV22 @ SV9 @ SV34 ) @ SY102 @ ( tc_set @ ( tc_set @ SV34 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(100,plain,
! [SV35: $i,SV23: $i,SV10: $i] :
( ( ! [SY103: $i] :
( ( c_in @ ( c_Zorn_OUnion__lemma0__1 @ SV10 @ SV23 @ SV35 @ SY103 ) @ SV35 @ ( tc_set @ SY103 ) )
| ( c_lessequals @ SV23 @ ( c_Union @ SV35 @ SY103 ) @ ( tc_set @ SY103 ) )
| ( c_lessequals @ ( c_Union @ SV35 @ SY103 ) @ SV10 @ ( tc_set @ SY103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(101,plain,
! [SV36: $i,SV24: $i,SV11: $i] :
( ( ! [SY104: $i] :
( ~ ( c_lessequals @ ( c_Zorn_OUnion__lemma0__1 @ SV11 @ SV24 @ SV36 @ SY104 ) @ SV11 @ ( tc_set @ SY104 ) )
| ( c_lessequals @ SV24 @ ( c_Union @ SV36 @ SY104 ) @ ( tc_set @ SY104 ) )
| ( c_lessequals @ ( c_Union @ SV36 @ SY104 ) @ SV11 @ ( tc_set @ SY104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(102,plain,
! [SV37: $i,SV25: $i,SV12: $i] :
( ( ! [SY105: $i] :
( ~ ( c_lessequals @ SV12 @ ( c_Zorn_OUnion__lemma0__1 @ SV25 @ SV12 @ SV37 @ SY105 ) @ ( tc_set @ SY105 ) )
| ( c_lessequals @ SV12 @ ( c_Union @ SV37 @ SY105 ) @ ( tc_set @ SY105 ) )
| ( c_lessequals @ ( c_Union @ SV37 @ SY105 ) @ SV25 @ ( tc_set @ SY105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(103,plain,
! [SV38: $i,SV26: $i,SV13: $i] :
( ( ! [SY106: $i] :
( ~ ( c_in @ SV13 @ ( c_Zorn_OTFin @ SV26 @ SV38 ) @ ( tc_set @ ( tc_set @ SV38 ) ) )
| ~ ( c_in @ SY106 @ ( c_Zorn_OTFin @ SV26 @ SV38 ) @ ( tc_set @ ( tc_set @ SV38 ) ) )
| ( ( c_Zorn_OTFin__linear__lemma1__1 @ SV26 @ SV13 @ SV38 )
!= SV13 )
| ( c_lessequals @ SY106 @ SV13 @ ( tc_set @ ( tc_set @ SV38 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV26 @ SV13 @ SV38 ) @ SY106 @ ( tc_set @ ( tc_set @ SV38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(104,plain,
! [SV14: $i,SV1: $i] :
( ( ( SV1 = SV14 )
= $true )
| ( ( ~ ( c_lessequals @ SV1 @ SV14 @ ( tc_set @ ( tc_set @ t_a ) ) )
| ~ ( c_in @ SV1 @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
| ~ ( c_in @ SV14 @ v_Y @ ( tc_set @ ( tc_set @ t_a ) ) ) )
= $true )
| ( ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ SV1 @ t_a ) @ SV14 @ ( tc_set @ ( tc_set @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(105,plain,
! [SV27: $i,SV15: $i,SV2: $i] :
( ( ( ~ ( c_lessequals @ SV2 @ SV15 @ ( tc_set @ SV27 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV15 @ SV2 @ ( tc_set @ SV27 ) )
| ( SV15 = SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(106,plain,
! [SV39: $i,SV28: $i,SV16: $i,SV3: $i] :
( ( ~ ( c_in @ SV3 @ SV16 @ SV28 )
| ~ ( c_lessequals @ SV16 @ SV39 @ ( tc_set @ SV28 ) )
| ( c_in @ SV3 @ SV39 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(107,plain,
! [SV29: $i,SV17: $i,SV4: $i] :
( ( ( c_in @ ( c_Main_OsubsetI__1 @ SV4 @ SV17 @ SV29 ) @ SV4 @ SV29 )
= $true )
| ( ( c_lessequals @ SV4 @ SV17 @ ( tc_set @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(108,plain,
! [SV30: $i,SV18: $i,SV5: $i] :
( ( ( ~ ( c_in @ ( c_Main_OsubsetI__1 @ SV5 @ SV18 @ SV30 ) @ SV18 @ SV30 ) )
= $true )
| ( ( c_lessequals @ SV5 @ SV18 @ ( tc_set @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(109,plain,
! [SV40: $i,SV32: $i,SV20: $i,SV7: $i] :
( ( ~ ( c_in @ SV7 @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) )
| ~ ( c_in @ SV40 @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) )
| ( c_in @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV20 @ SV7 @ SV32 ) @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) )
| ( c_lessequals @ SV40 @ SV7 @ ( tc_set @ ( tc_set @ SV32 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV20 @ SV7 @ SV32 ) @ SV40 @ ( tc_set @ ( tc_set @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(110,plain,
! [SV41: $i,SV33: $i,SV21: $i,SV8: $i] :
( ( ~ ( c_in @ SV8 @ ( c_Zorn_OTFin @ SV21 @ SV33 ) @ ( tc_set @ ( tc_set @ SV33 ) ) )
| ~ ( c_in @ SV41 @ ( c_Zorn_OTFin @ SV21 @ SV33 ) @ ( tc_set @ ( tc_set @ SV33 ) ) )
| ( c_lessequals @ SV41 @ SV8 @ ( tc_set @ ( tc_set @ SV33 ) ) )
| ( c_lessequals @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV21 @ SV8 @ SV33 ) @ SV8 @ ( tc_set @ ( tc_set @ SV33 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV21 @ SV8 @ SV33 ) @ SV41 @ ( tc_set @ ( tc_set @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(111,plain,
! [SV42: $i,SV34: $i,SV22: $i,SV9: $i] :
( ( ~ ( c_in @ SV9 @ ( c_Zorn_OTFin @ SV22 @ SV34 ) @ ( tc_set @ ( tc_set @ SV34 ) ) )
| ~ ( c_in @ SV42 @ ( c_Zorn_OTFin @ SV22 @ SV34 ) @ ( tc_set @ ( tc_set @ SV34 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Osucc @ SV22 @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV22 @ SV9 @ SV34 ) @ SV34 ) @ SV9 @ ( tc_set @ ( tc_set @ SV34 ) ) )
| ( c_lessequals @ SV42 @ SV9 @ ( tc_set @ ( tc_set @ SV34 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV22 @ SV9 @ SV34 ) @ SV42 @ ( tc_set @ ( tc_set @ SV34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(112,plain,
! [SV43: $i,SV35: $i,SV23: $i,SV10: $i] :
( ( ( c_in @ ( c_Zorn_OUnion__lemma0__1 @ SV10 @ SV23 @ SV35 @ SV43 ) @ SV35 @ ( tc_set @ SV43 ) )
| ( c_lessequals @ SV23 @ ( c_Union @ SV35 @ SV43 ) @ ( tc_set @ SV43 ) )
| ( c_lessequals @ ( c_Union @ SV35 @ SV43 ) @ SV10 @ ( tc_set @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(113,plain,
! [SV44: $i,SV36: $i,SV24: $i,SV11: $i] :
( ( ~ ( c_lessequals @ ( c_Zorn_OUnion__lemma0__1 @ SV11 @ SV24 @ SV36 @ SV44 ) @ SV11 @ ( tc_set @ SV44 ) )
| ( c_lessequals @ SV24 @ ( c_Union @ SV36 @ SV44 ) @ ( tc_set @ SV44 ) )
| ( c_lessequals @ ( c_Union @ SV36 @ SV44 ) @ SV11 @ ( tc_set @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(114,plain,
! [SV45: $i,SV37: $i,SV25: $i,SV12: $i] :
( ( ~ ( c_lessequals @ SV12 @ ( c_Zorn_OUnion__lemma0__1 @ SV25 @ SV12 @ SV37 @ SV45 ) @ ( tc_set @ SV45 ) )
| ( c_lessequals @ SV12 @ ( c_Union @ SV37 @ SV45 ) @ ( tc_set @ SV45 ) )
| ( c_lessequals @ ( c_Union @ SV37 @ SV45 ) @ SV25 @ ( tc_set @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(115,plain,
! [SV46: $i,SV38: $i,SV26: $i,SV13: $i] :
( ( ~ ( c_in @ SV13 @ ( c_Zorn_OTFin @ SV26 @ SV38 ) @ ( tc_set @ ( tc_set @ SV38 ) ) )
| ~ ( c_in @ SV46 @ ( c_Zorn_OTFin @ SV26 @ SV38 ) @ ( tc_set @ ( tc_set @ SV38 ) ) )
| ( ( c_Zorn_OTFin__linear__lemma1__1 @ SV26 @ SV13 @ SV38 )
!= SV13 )
| ( c_lessequals @ SV46 @ SV13 @ ( tc_set @ ( tc_set @ SV38 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV26 @ SV13 @ SV38 ) @ SV46 @ ( tc_set @ ( tc_set @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(116,plain,
! [SV14: $i,SV1: $i] :
( ( ( ~ ( c_lessequals @ SV1 @ SV14 @ ( tc_set @ ( tc_set @ t_a ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV1 @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
| ~ ( c_in @ SV14 @ v_Y @ ( tc_set @ ( tc_set @ t_a ) ) ) )
= $true )
| ( ( SV1 = SV14 )
= $true )
| ( ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ SV1 @ t_a ) @ SV14 @ ( tc_set @ ( tc_set @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(117,plain,
! [SV27: $i,SV15: $i,SV2: $i] :
( ( ( c_lessequals @ SV2 @ SV15 @ ( tc_set @ SV27 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV15 @ SV2 @ ( tc_set @ SV27 ) )
| ( SV15 = SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(118,plain,
! [SV39: $i,SV28: $i,SV16: $i,SV3: $i] :
( ( ( ~ ( c_in @ SV3 @ SV16 @ SV28 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV16 @ SV39 @ ( tc_set @ SV28 ) )
| ( c_in @ SV3 @ SV39 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(119,plain,
! [SV30: $i,SV18: $i,SV5: $i] :
( ( ( c_in @ ( c_Main_OsubsetI__1 @ SV5 @ SV18 @ SV30 ) @ SV18 @ SV30 )
= $false )
| ( ( c_lessequals @ SV5 @ SV18 @ ( tc_set @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(120,plain,
! [SV40: $i,SV32: $i,SV20: $i,SV7: $i] :
( ( ( ~ ( c_in @ SV7 @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV40 @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) )
| ( c_in @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV20 @ SV7 @ SV32 ) @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) )
| ( c_lessequals @ SV40 @ SV7 @ ( tc_set @ ( tc_set @ SV32 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV20 @ SV7 @ SV32 ) @ SV40 @ ( tc_set @ ( tc_set @ SV32 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(121,plain,
! [SV41: $i,SV33: $i,SV21: $i,SV8: $i] :
( ( ( ~ ( c_in @ SV8 @ ( c_Zorn_OTFin @ SV21 @ SV33 ) @ ( tc_set @ ( tc_set @ SV33 ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV41 @ ( c_Zorn_OTFin @ SV21 @ SV33 ) @ ( tc_set @ ( tc_set @ SV33 ) ) )
| ( c_lessequals @ SV41 @ SV8 @ ( tc_set @ ( tc_set @ SV33 ) ) )
| ( c_lessequals @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV21 @ SV8 @ SV33 ) @ SV8 @ ( tc_set @ ( tc_set @ SV33 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV21 @ SV8 @ SV33 ) @ SV41 @ ( tc_set @ ( tc_set @ SV33 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(122,plain,
! [SV42: $i,SV34: $i,SV22: $i,SV9: $i] :
( ( ( ~ ( c_in @ SV9 @ ( c_Zorn_OTFin @ SV22 @ SV34 ) @ ( tc_set @ ( tc_set @ SV34 ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV42 @ ( c_Zorn_OTFin @ SV22 @ SV34 ) @ ( tc_set @ ( tc_set @ SV34 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Osucc @ SV22 @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV22 @ SV9 @ SV34 ) @ SV34 ) @ SV9 @ ( tc_set @ ( tc_set @ SV34 ) ) )
| ( c_lessequals @ SV42 @ SV9 @ ( tc_set @ ( tc_set @ SV34 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV22 @ SV9 @ SV34 ) @ SV42 @ ( tc_set @ ( tc_set @ SV34 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(123,plain,
! [SV43: $i,SV35: $i,SV23: $i,SV10: $i] :
( ( ( c_in @ ( c_Zorn_OUnion__lemma0__1 @ SV10 @ SV23 @ SV35 @ SV43 ) @ SV35 @ ( tc_set @ SV43 ) )
= $true )
| ( ( ( c_lessequals @ SV23 @ ( c_Union @ SV35 @ SV43 ) @ ( tc_set @ SV43 ) )
| ( c_lessequals @ ( c_Union @ SV35 @ SV43 ) @ SV10 @ ( tc_set @ SV43 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(124,plain,
! [SV44: $i,SV36: $i,SV24: $i,SV11: $i] :
( ( ( ~ ( c_lessequals @ ( c_Zorn_OUnion__lemma0__1 @ SV11 @ SV24 @ SV36 @ SV44 ) @ SV11 @ ( tc_set @ SV44 ) ) )
= $true )
| ( ( ( c_lessequals @ SV24 @ ( c_Union @ SV36 @ SV44 ) @ ( tc_set @ SV44 ) )
| ( c_lessequals @ ( c_Union @ SV36 @ SV44 ) @ SV11 @ ( tc_set @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(125,plain,
! [SV45: $i,SV37: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( c_lessequals @ SV12 @ ( c_Zorn_OUnion__lemma0__1 @ SV25 @ SV12 @ SV37 @ SV45 ) @ ( tc_set @ SV45 ) ) )
= $true )
| ( ( ( c_lessequals @ SV12 @ ( c_Union @ SV37 @ SV45 ) @ ( tc_set @ SV45 ) )
| ( c_lessequals @ ( c_Union @ SV37 @ SV45 ) @ SV25 @ ( tc_set @ SV45 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(126,plain,
! [SV46: $i,SV38: $i,SV26: $i,SV13: $i] :
( ( ( ~ ( c_in @ SV13 @ ( c_Zorn_OTFin @ SV26 @ SV38 ) @ ( tc_set @ ( tc_set @ SV38 ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV46 @ ( c_Zorn_OTFin @ SV26 @ SV38 ) @ ( tc_set @ ( tc_set @ SV38 ) ) )
| ( ( c_Zorn_OTFin__linear__lemma1__1 @ SV26 @ SV13 @ SV38 )
!= SV13 )
| ( c_lessequals @ SV46 @ SV13 @ ( tc_set @ ( tc_set @ SV38 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV26 @ SV13 @ SV38 ) @ SV46 @ ( tc_set @ ( tc_set @ SV38 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(127,plain,
! [SV14: $i,SV1: $i] :
( ( ( c_lessequals @ SV1 @ SV14 @ ( tc_set @ ( tc_set @ t_a ) ) )
= $false )
| ( ( ~ ( c_in @ SV1 @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
| ~ ( c_in @ SV14 @ v_Y @ ( tc_set @ ( tc_set @ t_a ) ) ) )
= $true )
| ( ( SV1 = SV14 )
= $true )
| ( ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ SV1 @ t_a ) @ SV14 @ ( tc_set @ ( tc_set @ t_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(128,plain,
! [SV27: $i,SV2: $i,SV15: $i] :
( ( ( ~ ( c_lessequals @ SV15 @ SV2 @ ( tc_set @ SV27 ) ) )
= $true )
| ( ( SV15 = SV2 )
= $true )
| ( ( c_lessequals @ SV2 @ SV15 @ ( tc_set @ SV27 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(129,plain,
! [SV39: $i,SV28: $i,SV16: $i,SV3: $i] :
( ( ( c_in @ SV3 @ SV16 @ SV28 )
= $false )
| ( ( ~ ( c_lessequals @ SV16 @ SV39 @ ( tc_set @ SV28 ) )
| ( c_in @ SV3 @ SV39 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(130,plain,
! [SV40: $i,SV32: $i,SV20: $i,SV7: $i] :
( ( ( c_in @ SV7 @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) )
= $false )
| ( ( ~ ( c_in @ SV40 @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) )
| ( c_in @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV20 @ SV7 @ SV32 ) @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) )
| ( c_lessequals @ SV40 @ SV7 @ ( tc_set @ ( tc_set @ SV32 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV20 @ SV7 @ SV32 ) @ SV40 @ ( tc_set @ ( tc_set @ SV32 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(131,plain,
! [SV41: $i,SV33: $i,SV21: $i,SV8: $i] :
( ( ( c_in @ SV8 @ ( c_Zorn_OTFin @ SV21 @ SV33 ) @ ( tc_set @ ( tc_set @ SV33 ) ) )
= $false )
| ( ( ~ ( c_in @ SV41 @ ( c_Zorn_OTFin @ SV21 @ SV33 ) @ ( tc_set @ ( tc_set @ SV33 ) ) )
| ( c_lessequals @ SV41 @ SV8 @ ( tc_set @ ( tc_set @ SV33 ) ) )
| ( c_lessequals @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV21 @ SV8 @ SV33 ) @ SV8 @ ( tc_set @ ( tc_set @ SV33 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV21 @ SV8 @ SV33 ) @ SV41 @ ( tc_set @ ( tc_set @ SV33 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(132,plain,
! [SV42: $i,SV34: $i,SV22: $i,SV9: $i] :
( ( ( c_in @ SV9 @ ( c_Zorn_OTFin @ SV22 @ SV34 ) @ ( tc_set @ ( tc_set @ SV34 ) ) )
= $false )
| ( ( ~ ( c_in @ SV42 @ ( c_Zorn_OTFin @ SV22 @ SV34 ) @ ( tc_set @ ( tc_set @ SV34 ) ) )
| ~ ( c_lessequals @ ( c_Zorn_Osucc @ SV22 @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV22 @ SV9 @ SV34 ) @ SV34 ) @ SV9 @ ( tc_set @ ( tc_set @ SV34 ) ) )
| ( c_lessequals @ SV42 @ SV9 @ ( tc_set @ ( tc_set @ SV34 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV22 @ SV9 @ SV34 ) @ SV42 @ ( tc_set @ ( tc_set @ SV34 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(133,plain,
! [SV10: $i,SV43: $i,SV35: $i,SV23: $i] :
( ( ( c_lessequals @ SV23 @ ( c_Union @ SV35 @ SV43 ) @ ( tc_set @ SV43 ) )
= $true )
| ( ( c_lessequals @ ( c_Union @ SV35 @ SV43 ) @ SV10 @ ( tc_set @ SV43 ) )
= $true )
| ( ( c_in @ ( c_Zorn_OUnion__lemma0__1 @ SV10 @ SV23 @ SV35 @ SV43 ) @ SV35 @ ( tc_set @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(134,plain,
! [SV44: $i,SV36: $i,SV24: $i,SV11: $i] :
( ( ( c_lessequals @ ( c_Zorn_OUnion__lemma0__1 @ SV11 @ SV24 @ SV36 @ SV44 ) @ SV11 @ ( tc_set @ SV44 ) )
= $false )
| ( ( ( c_lessequals @ SV24 @ ( c_Union @ SV36 @ SV44 ) @ ( tc_set @ SV44 ) )
| ( c_lessequals @ ( c_Union @ SV36 @ SV44 ) @ SV11 @ ( tc_set @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(135,plain,
! [SV45: $i,SV37: $i,SV25: $i,SV12: $i] :
( ( ( c_lessequals @ SV12 @ ( c_Zorn_OUnion__lemma0__1 @ SV25 @ SV12 @ SV37 @ SV45 ) @ ( tc_set @ SV45 ) )
= $false )
| ( ( ( c_lessequals @ SV12 @ ( c_Union @ SV37 @ SV45 ) @ ( tc_set @ SV45 ) )
| ( c_lessequals @ ( c_Union @ SV37 @ SV45 ) @ SV25 @ ( tc_set @ SV45 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(136,plain,
! [SV46: $i,SV38: $i,SV26: $i,SV13: $i] :
( ( ( c_in @ SV13 @ ( c_Zorn_OTFin @ SV26 @ SV38 ) @ ( tc_set @ ( tc_set @ SV38 ) ) )
= $false )
| ( ( ~ ( c_in @ SV46 @ ( c_Zorn_OTFin @ SV26 @ SV38 ) @ ( tc_set @ ( tc_set @ SV38 ) ) )
| ( ( c_Zorn_OTFin__linear__lemma1__1 @ SV26 @ SV13 @ SV38 )
!= SV13 )
| ( c_lessequals @ SV46 @ SV13 @ ( tc_set @ ( tc_set @ SV38 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV26 @ SV13 @ SV38 ) @ SV46 @ ( tc_set @ ( tc_set @ SV38 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(137,plain,
! [SV14: $i,SV1: $i] :
( ( ( ~ ( c_in @ SV1 @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) ) )
= $true )
| ( ( ~ ( c_in @ SV14 @ v_Y @ ( tc_set @ ( tc_set @ t_a ) ) ) )
= $true )
| ( ( c_lessequals @ SV1 @ SV14 @ ( tc_set @ ( tc_set @ t_a ) ) )
= $false )
| ( ( SV1 = SV14 )
= $true )
| ( ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ SV1 @ t_a ) @ SV14 @ ( tc_set @ ( tc_set @ t_a ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(138,plain,
! [SV27: $i,SV2: $i,SV15: $i] :
( ( ( c_lessequals @ SV15 @ SV2 @ ( tc_set @ SV27 ) )
= $false )
| ( ( SV15 = SV2 )
= $true )
| ( ( c_lessequals @ SV2 @ SV15 @ ( tc_set @ SV27 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(139,plain,
! [SV3: $i,SV28: $i,SV39: $i,SV16: $i] :
( ( ( ~ ( c_lessequals @ SV16 @ SV39 @ ( tc_set @ SV28 ) ) )
= $true )
| ( ( c_in @ SV3 @ SV39 @ SV28 )
= $true )
| ( ( c_in @ SV3 @ SV16 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(140,plain,
! [SV7: $i,SV32: $i,SV20: $i,SV40: $i] :
( ( ( ~ ( c_in @ SV40 @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) ) )
= $true )
| ( ( ( c_in @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV20 @ SV7 @ SV32 ) @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) )
| ( c_lessequals @ SV40 @ SV7 @ ( tc_set @ ( tc_set @ SV32 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV20 @ SV7 @ SV32 ) @ SV40 @ ( tc_set @ ( tc_set @ SV32 ) ) ) )
= $true )
| ( ( c_in @ SV7 @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(141,plain,
! [SV8: $i,SV33: $i,SV21: $i,SV41: $i] :
( ( ( ~ ( c_in @ SV41 @ ( c_Zorn_OTFin @ SV21 @ SV33 ) @ ( tc_set @ ( tc_set @ SV33 ) ) ) )
= $true )
| ( ( ( c_lessequals @ SV41 @ SV8 @ ( tc_set @ ( tc_set @ SV33 ) ) )
| ( c_lessequals @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV21 @ SV8 @ SV33 ) @ SV8 @ ( tc_set @ ( tc_set @ SV33 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV21 @ SV8 @ SV33 ) @ SV41 @ ( tc_set @ ( tc_set @ SV33 ) ) ) )
= $true )
| ( ( c_in @ SV8 @ ( c_Zorn_OTFin @ SV21 @ SV33 ) @ ( tc_set @ ( tc_set @ SV33 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(142,plain,
! [SV9: $i,SV34: $i,SV22: $i,SV42: $i] :
( ( ( ~ ( c_in @ SV42 @ ( c_Zorn_OTFin @ SV22 @ SV34 ) @ ( tc_set @ ( tc_set @ SV34 ) ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Zorn_Osucc @ SV22 @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV22 @ SV9 @ SV34 ) @ SV34 ) @ SV9 @ ( tc_set @ ( tc_set @ SV34 ) ) )
| ( c_lessequals @ SV42 @ SV9 @ ( tc_set @ ( tc_set @ SV34 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV22 @ SV9 @ SV34 ) @ SV42 @ ( tc_set @ ( tc_set @ SV34 ) ) ) )
= $true )
| ( ( c_in @ SV9 @ ( c_Zorn_OTFin @ SV22 @ SV34 ) @ ( tc_set @ ( tc_set @ SV34 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(143,plain,
! [SV11: $i,SV44: $i,SV36: $i,SV24: $i] :
( ( ( c_lessequals @ SV24 @ ( c_Union @ SV36 @ SV44 ) @ ( tc_set @ SV44 ) )
= $true )
| ( ( c_lessequals @ ( c_Union @ SV36 @ SV44 ) @ SV11 @ ( tc_set @ SV44 ) )
= $true )
| ( ( c_lessequals @ ( c_Zorn_OUnion__lemma0__1 @ SV11 @ SV24 @ SV36 @ SV44 ) @ SV11 @ ( tc_set @ SV44 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(144,plain,
! [SV25: $i,SV45: $i,SV37: $i,SV12: $i] :
( ( ( c_lessequals @ SV12 @ ( c_Union @ SV37 @ SV45 ) @ ( tc_set @ SV45 ) )
= $true )
| ( ( c_lessequals @ ( c_Union @ SV37 @ SV45 ) @ SV25 @ ( tc_set @ SV45 ) )
= $true )
| ( ( c_lessequals @ SV12 @ ( c_Zorn_OUnion__lemma0__1 @ SV25 @ SV12 @ SV37 @ SV45 ) @ ( tc_set @ SV45 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(145,plain,
! [SV13: $i,SV38: $i,SV26: $i,SV46: $i] :
( ( ( ~ ( c_in @ SV46 @ ( c_Zorn_OTFin @ SV26 @ SV38 ) @ ( tc_set @ ( tc_set @ SV38 ) ) ) )
= $true )
| ( ( ( ( c_Zorn_OTFin__linear__lemma1__1 @ SV26 @ SV13 @ SV38 )
!= SV13 )
| ( c_lessequals @ SV46 @ SV13 @ ( tc_set @ ( tc_set @ SV38 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV26 @ SV13 @ SV38 ) @ SV46 @ ( tc_set @ ( tc_set @ SV38 ) ) ) )
= $true )
| ( ( c_in @ SV13 @ ( c_Zorn_OTFin @ SV26 @ SV38 ) @ ( tc_set @ ( tc_set @ SV38 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(146,plain,
! [SV14: $i,SV1: $i] :
( ( ( c_in @ SV1 @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
= $false )
| ( ( ~ ( c_in @ SV14 @ v_Y @ ( tc_set @ ( tc_set @ t_a ) ) ) )
= $true )
| ( ( c_lessequals @ SV1 @ SV14 @ ( tc_set @ ( tc_set @ t_a ) ) )
= $false )
| ( ( SV1 = SV14 )
= $true )
| ( ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ SV1 @ t_a ) @ SV14 @ ( tc_set @ ( tc_set @ t_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(147,plain,
! [SV3: $i,SV28: $i,SV39: $i,SV16: $i] :
( ( ( c_lessequals @ SV16 @ SV39 @ ( tc_set @ SV28 ) )
= $false )
| ( ( c_in @ SV3 @ SV39 @ SV28 )
= $true )
| ( ( c_in @ SV3 @ SV16 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(148,plain,
! [SV7: $i,SV32: $i,SV20: $i,SV40: $i] :
( ( ( c_in @ SV40 @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) )
= $false )
| ( ( ( c_in @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV20 @ SV7 @ SV32 ) @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) )
| ( c_lessequals @ SV40 @ SV7 @ ( tc_set @ ( tc_set @ SV32 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV20 @ SV7 @ SV32 ) @ SV40 @ ( tc_set @ ( tc_set @ SV32 ) ) ) )
= $true )
| ( ( c_in @ SV7 @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(149,plain,
! [SV8: $i,SV33: $i,SV21: $i,SV41: $i] :
( ( ( c_in @ SV41 @ ( c_Zorn_OTFin @ SV21 @ SV33 ) @ ( tc_set @ ( tc_set @ SV33 ) ) )
= $false )
| ( ( ( c_lessequals @ SV41 @ SV8 @ ( tc_set @ ( tc_set @ SV33 ) ) )
| ( c_lessequals @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV21 @ SV8 @ SV33 ) @ SV8 @ ( tc_set @ ( tc_set @ SV33 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV21 @ SV8 @ SV33 ) @ SV41 @ ( tc_set @ ( tc_set @ SV33 ) ) ) )
= $true )
| ( ( c_in @ SV8 @ ( c_Zorn_OTFin @ SV21 @ SV33 ) @ ( tc_set @ ( tc_set @ SV33 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(150,plain,
! [SV9: $i,SV34: $i,SV22: $i,SV42: $i] :
( ( ( c_in @ SV42 @ ( c_Zorn_OTFin @ SV22 @ SV34 ) @ ( tc_set @ ( tc_set @ SV34 ) ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Zorn_Osucc @ SV22 @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV22 @ SV9 @ SV34 ) @ SV34 ) @ SV9 @ ( tc_set @ ( tc_set @ SV34 ) ) )
| ( c_lessequals @ SV42 @ SV9 @ ( tc_set @ ( tc_set @ SV34 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV22 @ SV9 @ SV34 ) @ SV42 @ ( tc_set @ ( tc_set @ SV34 ) ) ) )
= $true )
| ( ( c_in @ SV9 @ ( c_Zorn_OTFin @ SV22 @ SV34 ) @ ( tc_set @ ( tc_set @ SV34 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(151,plain,
! [SV13: $i,SV38: $i,SV26: $i,SV46: $i] :
( ( ( c_in @ SV46 @ ( c_Zorn_OTFin @ SV26 @ SV38 ) @ ( tc_set @ ( tc_set @ SV38 ) ) )
= $false )
| ( ( ( ( c_Zorn_OTFin__linear__lemma1__1 @ SV26 @ SV13 @ SV38 )
!= SV13 )
| ( c_lessequals @ SV46 @ SV13 @ ( tc_set @ ( tc_set @ SV38 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV26 @ SV13 @ SV38 ) @ SV46 @ ( tc_set @ ( tc_set @ SV38 ) ) ) )
= $true )
| ( ( c_in @ SV13 @ ( c_Zorn_OTFin @ SV26 @ SV38 ) @ ( tc_set @ ( tc_set @ SV38 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(152,plain,
! [SV1: $i,SV14: $i] :
( ( ( c_in @ SV14 @ v_Y @ ( tc_set @ ( tc_set @ t_a ) ) )
= $false )
| ( ( c_in @ SV1 @ ( c_Zorn_OTFin @ v_S @ t_a ) @ ( tc_set @ ( tc_set @ t_a ) ) )
= $false )
| ( ( c_lessequals @ SV1 @ SV14 @ ( tc_set @ ( tc_set @ t_a ) ) )
= $false )
| ( ( SV1 = SV14 )
= $true )
| ( ( c_lessequals @ ( c_Zorn_Osucc @ v_S @ SV1 @ t_a ) @ SV14 @ ( tc_set @ ( tc_set @ t_a ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(153,plain,
! [SV40: $i,SV32: $i,SV7: $i,SV20: $i] :
( ( ( c_in @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV20 @ SV7 @ SV32 ) @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) )
= $true )
| ( ( ( c_lessequals @ SV40 @ SV7 @ ( tc_set @ ( tc_set @ SV32 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV20 @ SV7 @ SV32 ) @ SV40 @ ( tc_set @ ( tc_set @ SV32 ) ) ) )
= $true )
| ( ( c_in @ SV40 @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) )
= $false )
| ( ( c_in @ SV7 @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(154,plain,
! [SV21: $i,SV33: $i,SV8: $i,SV41: $i] :
( ( ( c_lessequals @ SV41 @ SV8 @ ( tc_set @ ( tc_set @ SV33 ) ) )
= $true )
| ( ( ( c_lessequals @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV21 @ SV8 @ SV33 ) @ SV8 @ ( tc_set @ ( tc_set @ SV33 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV21 @ SV8 @ SV33 ) @ SV41 @ ( tc_set @ ( tc_set @ SV33 ) ) ) )
= $true )
| ( ( c_in @ SV41 @ ( c_Zorn_OTFin @ SV21 @ SV33 ) @ ( tc_set @ ( tc_set @ SV33 ) ) )
= $false )
| ( ( c_in @ SV8 @ ( c_Zorn_OTFin @ SV21 @ SV33 ) @ ( tc_set @ ( tc_set @ SV33 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(155,plain,
! [SV42: $i,SV34: $i,SV9: $i,SV22: $i] :
( ( ( ~ ( c_lessequals @ ( c_Zorn_Osucc @ SV22 @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV22 @ SV9 @ SV34 ) @ SV34 ) @ SV9 @ ( tc_set @ ( tc_set @ SV34 ) ) ) )
= $true )
| ( ( ( c_lessequals @ SV42 @ SV9 @ ( tc_set @ ( tc_set @ SV34 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV22 @ SV9 @ SV34 ) @ SV42 @ ( tc_set @ ( tc_set @ SV34 ) ) ) )
= $true )
| ( ( c_in @ SV42 @ ( c_Zorn_OTFin @ SV22 @ SV34 ) @ ( tc_set @ ( tc_set @ SV34 ) ) )
= $false )
| ( ( c_in @ SV9 @ ( c_Zorn_OTFin @ SV22 @ SV34 ) @ ( tc_set @ ( tc_set @ SV34 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(156,plain,
! [SV46: $i,SV38: $i,SV13: $i,SV26: $i] :
( ( ( ( c_Zorn_OTFin__linear__lemma1__1 @ SV26 @ SV13 @ SV38 )
!= SV13 )
= $true )
| ( ( ( c_lessequals @ SV46 @ SV13 @ ( tc_set @ ( tc_set @ SV38 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV26 @ SV13 @ SV38 ) @ SV46 @ ( tc_set @ ( tc_set @ SV38 ) ) ) )
= $true )
| ( ( c_in @ SV46 @ ( c_Zorn_OTFin @ SV26 @ SV38 ) @ ( tc_set @ ( tc_set @ SV38 ) ) )
= $false )
| ( ( c_in @ SV13 @ ( c_Zorn_OTFin @ SV26 @ SV38 ) @ ( tc_set @ ( tc_set @ SV38 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(157,plain,
! [SV20: $i,SV32: $i,SV7: $i,SV40: $i] :
( ( ( c_lessequals @ SV40 @ SV7 @ ( tc_set @ ( tc_set @ SV32 ) ) )
= $true )
| ( ( c_lessequals @ ( c_Zorn_Osucc @ SV20 @ SV7 @ SV32 ) @ SV40 @ ( tc_set @ ( tc_set @ SV32 ) ) )
= $true )
| ( ( c_in @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV20 @ SV7 @ SV32 ) @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) )
= $true )
| ( ( c_in @ SV40 @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) )
= $false )
| ( ( c_in @ SV7 @ ( c_Zorn_OTFin @ SV20 @ SV32 ) @ ( tc_set @ ( tc_set @ SV32 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(158,plain,
! [SV41: $i,SV33: $i,SV8: $i,SV21: $i] :
( ( ( c_lessequals @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV21 @ SV8 @ SV33 ) @ SV8 @ ( tc_set @ ( tc_set @ SV33 ) ) )
= $true )
| ( ( c_lessequals @ ( c_Zorn_Osucc @ SV21 @ SV8 @ SV33 ) @ SV41 @ ( tc_set @ ( tc_set @ SV33 ) ) )
= $true )
| ( ( c_lessequals @ SV41 @ SV8 @ ( tc_set @ ( tc_set @ SV33 ) ) )
= $true )
| ( ( c_in @ SV41 @ ( c_Zorn_OTFin @ SV21 @ SV33 ) @ ( tc_set @ ( tc_set @ SV33 ) ) )
= $false )
| ( ( c_in @ SV8 @ ( c_Zorn_OTFin @ SV21 @ SV33 ) @ ( tc_set @ ( tc_set @ SV33 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(159,plain,
! [SV42: $i,SV34: $i,SV9: $i,SV22: $i] :
( ( ( c_lessequals @ ( c_Zorn_Osucc @ SV22 @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV22 @ SV9 @ SV34 ) @ SV34 ) @ SV9 @ ( tc_set @ ( tc_set @ SV34 ) ) )
= $false )
| ( ( ( c_lessequals @ SV42 @ SV9 @ ( tc_set @ ( tc_set @ SV34 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV22 @ SV9 @ SV34 ) @ SV42 @ ( tc_set @ ( tc_set @ SV34 ) ) ) )
= $true )
| ( ( c_in @ SV42 @ ( c_Zorn_OTFin @ SV22 @ SV34 ) @ ( tc_set @ ( tc_set @ SV34 ) ) )
= $false )
| ( ( c_in @ SV9 @ ( c_Zorn_OTFin @ SV22 @ SV34 ) @ ( tc_set @ ( tc_set @ SV34 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(160,plain,
! [SV46: $i,SV38: $i,SV13: $i,SV26: $i] :
( ( ( ( c_Zorn_OTFin__linear__lemma1__1 @ SV26 @ SV13 @ SV38 )
= SV13 )
= $false )
| ( ( ( c_lessequals @ SV46 @ SV13 @ ( tc_set @ ( tc_set @ SV38 ) ) )
| ( c_lessequals @ ( c_Zorn_Osucc @ SV26 @ SV13 @ SV38 ) @ SV46 @ ( tc_set @ ( tc_set @ SV38 ) ) ) )
= $true )
| ( ( c_in @ SV46 @ ( c_Zorn_OTFin @ SV26 @ SV38 ) @ ( tc_set @ ( tc_set @ SV38 ) ) )
= $false )
| ( ( c_in @ SV13 @ ( c_Zorn_OTFin @ SV26 @ SV38 ) @ ( tc_set @ ( tc_set @ SV38 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(161,plain,
! [SV22: $i,SV34: $i,SV9: $i,SV42: $i] :
( ( ( c_lessequals @ SV42 @ SV9 @ ( tc_set @ ( tc_set @ SV34 ) ) )
= $true )
| ( ( c_lessequals @ ( c_Zorn_Osucc @ SV22 @ SV9 @ SV34 ) @ SV42 @ ( tc_set @ ( tc_set @ SV34 ) ) )
= $true )
| ( ( c_lessequals @ ( c_Zorn_Osucc @ SV22 @ ( c_Zorn_OTFin__linear__lemma1__1 @ SV22 @ SV9 @ SV34 ) @ SV34 ) @ SV9 @ ( tc_set @ ( tc_set @ SV34 ) ) )
= $false )
| ( ( c_in @ SV42 @ ( c_Zorn_OTFin @ SV22 @ SV34 ) @ ( tc_set @ ( tc_set @ SV34 ) ) )
= $false )
| ( ( c_in @ SV9 @ ( c_Zorn_OTFin @ SV22 @ SV34 ) @ ( tc_set @ ( tc_set @ SV34 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(162,plain,
! [SV26: $i,SV38: $i,SV13: $i,SV46: $i] :
( ( ( c_lessequals @ SV46 @ SV13 @ ( tc_set @ ( tc_set @ SV38 ) ) )
= $true )
| ( ( c_lessequals @ ( c_Zorn_Osucc @ SV26 @ SV13 @ SV38 ) @ SV46 @ ( tc_set @ ( tc_set @ SV38 ) ) )
= $true )
| ( ( ( c_Zorn_OTFin__linear__lemma1__1 @ SV26 @ SV13 @ SV38 )
= SV13 )
= $false )
| ( ( c_in @ SV46 @ ( c_Zorn_OTFin @ SV26 @ SV38 ) @ ( tc_set @ ( tc_set @ SV38 ) ) )
= $false )
| ( ( c_in @ SV13 @ ( c_Zorn_OTFin @ SV26 @ SV38 ) @ ( tc_set @ ( tc_set @ SV38 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(163,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[41,162,161,158,157,152,147,144,143,138,133,119,107,96,76,75,62,43,42]) ).
thf(164,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET854-2 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n019.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 14:54:16 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 234.67/39.31
% 234.67/39.31 No.of.Axioms: 18
% 234.67/39.31
% 234.67/39.31 Length.of.Defs: 0
% 234.67/39.31
% 234.67/39.31 Contains.Choice.Funs: false
% 234.67/39.31 .....
% 234.67/39.31
% 234.67/39.31 ********************************
% 234.67/39.31 * All subproblems solved! *
% 234.67/39.31 ********************************
% 234.67/39.31 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:18,ps:3,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:163,loop_count:0,foatp_calls:1,translation:fof_full)
% 234.67/39.31
% 234.67/39.31 %**** Beginning of derivation protocol ****
% 234.67/39.31 % SZS output start CNFRefutation
% See solution above
% 234.67/39.31
% 234.67/39.31 %**** End of derivation protocol ****
% 234.67/39.31 %**** no. of clauses in derivation: 164 ****
% 234.67/39.31 %**** clause counter: 163 ****
% 234.67/39.31
% 234.67/39.31 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:18,ps:3,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:163,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------