%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET861-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n016.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 : Sun Sep 27 08:31:12 AM UTC 2026
% Result : Unsatisfiable 94.50s 24.68s
% Output : Refutation 90.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 15
% Syntax : Number of formulae : 261 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 997 ( 270 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 5199 ( 596 ~; 524 |; 0 &;4079 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 516 ( 0 ^; 516 !; 0 ?; 516 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_x_decl,type,
v_x: $i > $i ).
thf(v_S_decl,type,
v_S: $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(c_Zorn_Ochain_decl,type,
c_Zorn_Ochain: $i > $i > $i ).
thf(v_xa_decl,type,
v_xa: $i > $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Main_OsubsetI__1_decl,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_Zorn_Ochain__extend__1_decl,type,
c_Zorn_Ochain__extend__1: $i > $i > $i > $i ).
thf(c_union_decl,type,
c_union: $i > $i > $i > $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(c_Zorn_OHausdorff__1_decl,type,
c_Zorn_OHausdorff__1: $i > $i > $i ).
thf(c_Zorn_Omaxchain_decl,type,
c_Zorn_Omaxchain: $i > $i > $i ).
thf(c_Zorn_Omaxchain__super__lemma__1_decl,type,
c_Zorn_Omaxchain__super__lemma__1: $i > $i > $i > $i ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(3,negated_conjecture,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
| ( t_a @ tc_set @ ( A @ v_xa @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(19,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
| ( t_a @ tc_set @ ( A @ v_xa @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(26,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
| ( t_a @ tc_set @ ( A @ v_xa @ ( A @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[19]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(1400,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( A @ v_xa @ ( A @ c_lessequals ) ) )
!= ( D @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) )
| ~ ( D @ tc_set @ ( B @ ( C @ c_lessequals ) ) )
| ~ $true
| ( C = B )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,29]) ).
thf(1401,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( A @ v_xa @ ( A @ c_lessequals ) ) )
!= ( D @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) )
| ~ ( D @ tc_set @ ( B @ ( C @ c_lessequals ) ) )
| ( C = B )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1400]) ).
thf(1402,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( A @ ( A @ v_xa @ c_lessequals ) ) )
| ( ( A @ v_xa )
= A )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[1401:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ v_xa )),bind(D,$thf( t_a ))]]) ).
thf(1753,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( A @ ( A @ v_xa @ c_lessequals ) ) )
| ( ( A @ v_xa )
= A )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1402]) ).
thf(2,negated_conjecture,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
| ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(18,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
| ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
| ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ c_in ) ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(4,negated_conjecture,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
| ( A
!= ( A @ v_xa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(20,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
| ( A
!= ( A @ v_xa ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(21,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
| ( A
!= ( A @ v_xa ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(22,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
| ( ( A @ v_xa )
!= A ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ~ $true
| ( ( B @ v_xa )
!= B )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,22]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( ( B @ v_xa )
!= B )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(52,plain,
! [A: $i] :
( ( ( A @ v_xa @ v_xa )
!= ( A @ v_xa ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[51:[bind(A,$thf( C )),bind(B,$thf( C @ v_xa ))]]) ).
thf(59,plain,
! [A: $i] :
( ( ( A @ v_xa @ v_xa )
!= ( A @ v_xa ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( ( B @ v_xa @ v_xa )
!= ( B @ v_xa ) )
| ~ $true
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,59]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( ( B @ v_xa @ v_xa )
!= ( B @ v_xa ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(65,plain,
! [A: $i] :
( ( ( A @ v_xa @ v_xa @ v_xa )
!= ( A @ v_xa @ v_xa ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[64:[bind(A,$thf( C )),bind(B,$thf( C @ v_xa ))]]) ).
thf(71,plain,
! [A: $i] :
( ( ( A @ v_xa @ v_xa @ v_xa )
!= ( A @ v_xa @ v_xa ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[65]) ).
thf(3605,plain,
! [B: $i,A: $i] :
( ( ( A @ v_xa )
!= ( B @ v_xa ) )
| ( ( A @ v_xa @ v_xa )
!= ( B @ v_xa @ v_xa ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( A @ ( A @ v_xa @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[1753,71]) ).
thf(3606,plain,
! [A: $i] :
( ( ( A @ v_xa @ v_xa )
!= ( A @ v_xa @ v_xa ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( A @ ( A @ v_xa @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[3605:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(3832,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( A @ ( A @ v_xa @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[3606]) ).
thf(4007,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( D @ ( D @ v_xa @ c_lessequals ) ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ ( v_S @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,3832]) ).
thf(4008,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( D @ ( D @ v_xa @ c_lessequals ) ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[4007]) ).
thf(4009,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
| ~ ( t_a @ ( A @ ( t_a @ ( A @ ( A @ v_xa @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[4008:[bind(A,$thf( B @ v_xa )),bind(B,$thf( B )),bind(C,$thf( t_a )),bind(D,$thf( B ))]]) ).
thf(4057,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
| ~ ( t_a @ ( A @ ( t_a @ ( A @ ( A @ v_xa @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[4009]) ).
thf(5000,plain,
! [A: $i] :
( ~ $true
| ( ( t_a @ ( A @ ( t_a @ ( A @ ( A @ v_xa @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[4057]) ).
thf(5005,plain,
! [A: $i] :
( ( ( t_a @ tc_set )
!= t_a )
| ( A != v_S )
| ( ( t_a @ ( A @ ( A @ v_xa @ c_Main_OsubsetI__1 ) ) )
!= A )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[5000]) ).
thf(5027,plain,
( ( ( t_a @ tc_set )
!= t_a )
| ( ( t_a @ ( v_S @ ( v_S @ v_xa @ c_Main_OsubsetI__1 ) ) )
!= v_S )
| ~ ( t_a @ tc_set @ ( v_S @ ( v_S @ c_in ) ) ) ),
inference(simp,[status(thm)],[5005]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[32]) ).
thf(3999,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( D @ ( D @ v_xa @ c_lessequals ) ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ ( v_S @ ( D @ c_in ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,3832]) ).
thf(4000,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( D @ ( D @ v_xa @ c_lessequals ) ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( D @ c_in ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[3999]) ).
thf(4001,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
| ( t_a @ ( A @ v_xa @ ( t_a @ ( A @ ( A @ v_xa @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[4000:[bind(A,$thf( B @ v_xa )),bind(B,$thf( B )),bind(C,$thf( t_a )),bind(D,$thf( B ))]]) ).
thf(4053,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
| ( t_a @ ( A @ v_xa @ ( t_a @ ( A @ ( A @ v_xa @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[4001]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ~ $true
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,24]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[53]) ).
thf(55,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[54:[bind(A,$thf( C )),bind(B,$thf( C @ v_xa ))]]) ).
thf(60,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( ( B @ v_xa @ v_xa @ v_xa )
!= ( B @ v_xa @ v_xa ) )
| ~ $true
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[60,71]) ).
thf(127,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( ( B @ v_xa @ v_xa @ v_xa )
!= ( B @ v_xa @ v_xa ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[126]) ).
thf(128,plain,
! [A: $i] :
( ( ( A @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa )
!= ( A @ v_xa @ v_xa @ v_xa @ v_xa ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[127:[bind(A,$thf( D )),bind(B,$thf( D @ v_xa @ v_xa ))]]) ).
thf(141,plain,
! [A: $i] :
( ( ( A @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa )
!= ( A @ v_xa @ v_xa @ v_xa @ v_xa ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(13,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ tc_set @ tc_set @ ( B @ ( A @ c_Zorn_Ochain ) @ ( B @ ( A @ c_Zorn_Omaxchain ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__subset__chain_0) ).
thf(41,plain,
! [B: $i,A: $i] : ( B @ tc_set @ tc_set @ tc_set @ ( B @ ( A @ c_Zorn_Ochain ) @ ( B @ ( A @ c_Zorn_Omaxchain ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Ochain ) @ ( C @ tc_set @ ( D @ ( C @ tc_set @ ( c_emptyset @ ( A @ c_insert ) ) @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( A @ ( C @ ( A @ ( D @ c_Zorn_Ochain__extend__1 ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Ochain ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_1) ).
thf(38,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Ochain ) @ ( C @ tc_set @ ( D @ ( C @ tc_set @ ( c_emptyset @ ( A @ c_insert ) ) @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( A @ ( C @ ( A @ ( D @ c_Zorn_Ochain__extend__1 ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Ochain ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(39,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Ochain ) @ ( C @ tc_set @ ( D @ ( C @ tc_set @ ( c_emptyset @ ( A @ c_insert ) ) @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( A @ ( C @ ( A @ ( D @ c_Zorn_Ochain__extend__1 ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Ochain ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(12,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ tc_set @ ( B @ ( A @ c_Zorn_Omaxchain ) @ ( B @ ( A @ c_Zorn_OHausdorff__1 ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OHausdorff_0) ).
thf(40,plain,
! [B: $i,A: $i] : ( B @ tc_set @ tc_set @ ( B @ ( A @ c_Zorn_Omaxchain ) @ ( B @ ( A @ c_Zorn_OHausdorff__1 ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ tc_set @ ( B @ ( A @ c_Zorn_Omaxchain ) @ ( B @ ( A @ c_Zorn_OHausdorff__1 ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( C @ c_in ) ) ) )
| ( ( C @ v_xa @ v_xa @ v_xa )
!= ( C @ v_xa @ v_xa ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40,71]) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ tc_set @ ( B @ ( A @ c_Zorn_Omaxchain ) @ ( B @ ( A @ c_Zorn_OHausdorff__1 ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( C @ c_in ) ) ) )
| ( ( C @ v_xa @ v_xa @ v_xa )
!= ( C @ v_xa @ v_xa ) ) ),
inference(simp,[status(thm)],[78]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ tc_set @ ( B @ ( A @ c_Zorn_Omaxchain ) @ ( B @ ( A @ c_Zorn_OHausdorff__1 ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( C @ c_in ) ) ) )
| ( ( C @ v_xa @ v_xa )
!= ( C @ v_xa ) ) ),
inference(simp,[status(thm)],[79]) ).
thf(12810,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
| ( ( A @ v_xa @ v_xa )
!= ( A @ v_xa ) ) ),
inference(rewrite,[status(thm)],[80,40]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) )
| ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(17,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) )
| ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(23,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) )
| ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ c_in ) ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(114,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ~ $true
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[60,24]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(116,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( D )),bind(B,$thf( D @ v_xa @ v_xa ))]]) ).
thf(143,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(228,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,143]) ).
thf(229,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[228]) ).
thf(230,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[229:[bind(A,$thf( C )),bind(B,$thf( C @ v_x ))]]) ).
thf(235,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[230]) ).
thf(200,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ v_xa @ c_in ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[143,60]) ).
thf(201,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[200]) ).
thf(202,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[201:[bind(A,$thf( E )),bind(B,$thf( E @ v_xa @ v_xa @ v_xa ))]]) ).
thf(239,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[202]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ~ $true
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,24]) ).
thf(151,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[150]) ).
thf(152,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[151:[bind(A,$thf( C )),bind(B,$thf( C @ v_x ))]]) ).
thf(190,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(5,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( B @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( t_a @ tc_set @ ( B @ v_x @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(16,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( B @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( t_a @ tc_set @ ( B @ v_x @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( B @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( t_a @ tc_set @ ( B @ v_x @ ( A @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[16]) ).
thf(4014,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ~ ( t_a @ tc_set @ ( B @ ( B @ v_xa @ c_lessequals ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,3832]) ).
thf(4015,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ~ ( t_a @ tc_set @ ( B @ ( B @ v_xa @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[4014]) ).
thf(4016,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( A @ v_x @ ( A @ v_x @ v_xa @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[4015:[bind(A,$thf( C )),bind(B,$thf( C @ v_x ))]]) ).
thf(4060,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( A @ v_x @ ( A @ v_x @ v_xa @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[4016]) ).
thf(9415,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( B @ v_x @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( C @ v_x @ ( C @ v_x @ v_xa @ c_lessequals ) ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( C @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( B @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,4060]) ).
thf(9416,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( B @ v_x @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( C @ v_x @ ( C @ v_x @ v_xa @ c_lessequals ) ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( C @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( B @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[9415]) ).
thf(9417,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( A @ ( A @ v_x @ v_xa @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[9416:[bind(A,$thf( B @ v_x @ v_xa )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(9583,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( A @ ( A @ v_x @ v_xa @ c_in ) ) ) ),
inference(simp,[status(thm)],[9417]) ).
thf(9770,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( B @ ( B @ v_x @ v_xa @ c_in ) ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( B @ c_in ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[190,9583]) ).
thf(9771,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( B @ ( B @ v_x @ v_xa @ c_in ) ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( B @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[9770]) ).
thf(9772,plain,
( ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( v_S @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( v_S @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[9771:[bind(A,$thf( v_S )),bind(B,$thf( v_S ))]]) ).
thf(9823,plain,
~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( v_S @ c_in ) ) ),
inference(simp,[status(thm)],[9772]) ).
thf(9940,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
!= ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( v_S @ c_in ) ) ) )
| ~ $true
| ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,9823]) ).
thf(9941,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
!= ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( v_S @ c_in ) ) ) )
| ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[9940]) ).
thf(9974,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( t_a @ tc_set @ tc_set ) )
| ( A
!= ( t_a @ ( v_S @ c_Zorn_Ochain ) ) )
| ( ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) )
!= v_S )
| ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[9941]) ).
thf(10007,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ tc_set @ ( A @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ c_Main_OsubsetI__1 ) ) )
!= v_S )
| ( t_a @ tc_set @ tc_set @ tc_set @ ( A @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[9974]) ).
thf(92,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( D @ c_in ) ) ) )
| ~ $true
| ( ( D @ v_xa )
!= D )
| ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,22]) ).
thf(93,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( D @ c_in ) ) ) )
| ( ( D @ v_xa )
!= D )
| ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[92]) ).
thf(94,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ ( A @ ( v_S @ c_Main_OsubsetI__1 ) ) @ v_xa )
!= ( t_a @ tc_set @ ( A @ ( v_S @ c_Main_OsubsetI__1 ) ) ) )
| ( t_a @ tc_set @ tc_set @ ( A @ ( v_S @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( v_S )),bind(B,$thf( F )),bind(C,$thf( t_a @ tc_set )),bind(D,$thf( t_a @ tc_set @ ( F @ ( v_S @ c_Main_OsubsetI__1 ) ) ))]]) ).
thf(101,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ ( A @ ( v_S @ c_Main_OsubsetI__1 ) ) @ v_xa )
!= ( t_a @ tc_set @ ( A @ ( v_S @ c_Main_OsubsetI__1 ) ) ) )
| ( t_a @ tc_set @ tc_set @ ( A @ ( v_S @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(31,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[30]) ).
thf(2517,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( A @ v_xa @ ( A @ c_lessequals ) ) )
!= ( D @ tc_set @ ( E @ ( C @ c_lessequals ) ) ) )
| ( D @ ( E @ ( B @ c_in ) ) )
| ~ $true
| ~ ( D @ ( C @ ( B @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,31]) ).
thf(2518,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( A @ v_xa @ ( A @ c_lessequals ) ) )
!= ( D @ tc_set @ ( E @ ( C @ c_lessequals ) ) ) )
| ( D @ ( E @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ ( B @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[2517]) ).
thf(2519,plain,
! [B: $i,A: $i] :
( ( t_a @ ( B @ v_xa @ ( A @ c_in ) ) )
| ~ ( t_a @ ( B @ ( A @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[2518:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( t_a )),bind(E,$thf( F @ v_xa ))]]) ).
thf(2544,plain,
! [B: $i,A: $i] :
( ( t_a @ ( B @ v_xa @ ( A @ c_in ) ) )
| ~ ( t_a @ ( B @ ( A @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[2519]) ).
thf(9153,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) )
!= ( t_a @ ( B @ ( A @ c_in ) ) ) )
| ( t_a @ ( B @ v_xa @ ( A @ c_in ) ) )
| ~ ( t_a @ ( B @ ( A @ c_in ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[2544]) ).
thf(9218,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set )
!= t_a )
| ( v_S != B )
| ( B != A )
| ~ ( t_a @ ( B @ ( A @ c_in ) ) )
| ( t_a @ ( B @ v_xa @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[9153]) ).
thf(9241,plain,
( ( ( t_a @ tc_set )
!= t_a )
| ~ ( t_a @ ( v_S @ ( v_S @ c_in ) ) )
| ( t_a @ ( v_S @ v_xa @ ( v_S @ c_in ) ) ) ),
inference(simp,[status(thm)],[9218]) ).
thf(10146,plain,
! [A: $i] :
( ( ( t_a @ ( v_S @ v_xa @ ( v_S @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) )
| ( ( A @ v_xa @ v_xa )
!= ( A @ v_xa ) )
| ~ $true
| ( ( t_a @ tc_set )
!= t_a )
| ~ ( t_a @ ( v_S @ ( v_S @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[9241,59]) ).
thf(10147,plain,
! [A: $i] :
( ( ( t_a @ ( v_S @ v_xa @ ( v_S @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) )
| ( ( A @ v_xa @ v_xa )
!= ( A @ v_xa ) )
| ( ( t_a @ tc_set )
!= t_a )
| ~ ( t_a @ ( v_S @ ( v_S @ c_in ) ) ) ),
inference(simp,[status(thm)],[10146]) ).
thf(10277,plain,
! [A: $i] :
( ( ( t_a @ tc_set )
!= t_a )
| ( ( v_S @ v_xa )
!= v_S )
| ( v_S != A )
| ( ( A @ v_xa )
!= A )
| ( ( t_a @ tc_set )
!= t_a )
| ~ ( t_a @ ( v_S @ ( v_S @ c_in ) ) ) ),
inference(simp,[status(thm)],[10147]) ).
thf(10340,plain,
( ( ( v_S @ v_xa )
!= v_S )
| ( ( v_S @ v_xa )
!= v_S )
| ( ( t_a @ tc_set )
!= t_a )
| ~ ( t_a @ ( v_S @ ( v_S @ c_in ) ) ) ),
inference(simp,[status(thm)],[10277]) ).
thf(11242,plain,
( ( ( v_S @ v_xa )
!= v_S )
| ( ( t_a @ tc_set )
!= t_a )
| ~ ( t_a @ ( v_S @ ( v_S @ c_in ) ) ) ),
inference(simp,[status(thm)],[10340]) ).
thf(11257,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ c_in ) ) )
!= ( t_a @ ( v_S @ ( v_S @ c_in ) ) ) )
| ( ( v_S @ v_xa )
!= v_S )
| ( ( t_a @ tc_set )
!= t_a )
| ~ $true
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,11242]) ).
thf(11258,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ c_in ) ) )
!= ( t_a @ ( v_S @ ( v_S @ c_in ) ) ) )
| ( ( v_S @ v_xa )
!= v_S )
| ( ( t_a @ tc_set )
!= t_a )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[11257]) ).
thf(11356,plain,
! [A: $i] :
( ( ( t_a @ tc_set )
!= t_a )
| ( v_S != v_S )
| ( ( A @ v_xa )
!= v_S )
| ( ( v_S @ v_xa )
!= v_S )
| ( ( t_a @ tc_set )
!= t_a )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[11258]) ).
thf(11394,plain,
! [A: $i] :
( ( ( A @ v_xa )
!= v_S )
| ( ( v_S @ v_xa )
!= v_S )
| ( ( t_a @ tc_set )
!= t_a )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[11356]) ).
thf(120,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ v_xa @ c_in ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[60,60]) ).
thf(121,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(122,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[121:[bind(A,$thf( D )),bind(B,$thf( D @ v_xa @ v_xa ))]]) ).
thf(146,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[122]) ).
thf(657,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[239,146]) ).
thf(658,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[657]) ).
thf(659,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[658:[bind(A,$thf( G )),bind(B,$thf( G @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa ))]]) ).
thf(677,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[659]) ).
thf(86,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( D @ c_in ) ) ) )
| ~ $true
| ( t_a @ tc_set @ ( v_S @ ( D @ v_xa @ c_in ) ) )
| ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,24]) ).
thf(87,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( D @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( D @ v_xa @ c_in ) ) )
| ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[86]) ).
thf(88,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( t_a @ tc_set @ ( A @ ( v_S @ c_Main_OsubsetI__1 ) ) @ v_xa @ c_in ) ) )
| ( t_a @ tc_set @ tc_set @ ( A @ ( v_S @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[87:[bind(A,$thf( v_S )),bind(B,$thf( F )),bind(C,$thf( t_a @ tc_set )),bind(D,$thf( t_a @ tc_set @ ( F @ ( v_S @ c_Main_OsubsetI__1 ) ) ))]]) ).
thf(99,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( t_a @ tc_set @ ( A @ ( v_S @ c_Main_OsubsetI__1 ) ) @ v_xa @ c_in ) ) )
| ( t_a @ tc_set @ tc_set @ ( A @ ( v_S @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[88]) ).
thf(375,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( t_a @ tc_set @ ( A @ ( v_S @ c_Main_OsubsetI__1 ) ) @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ $true
| ( t_a @ tc_set @ tc_set @ ( A @ ( v_S @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[99,146]) ).
thf(376,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( t_a @ tc_set @ ( A @ ( v_S @ c_Main_OsubsetI__1 ) ) @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ( t_a @ tc_set @ tc_set @ ( A @ ( v_S @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[375]) ).
thf(377,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( t_a @ tc_set @ ( A @ ( v_S @ c_Main_OsubsetI__1 ) ) @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ( t_a @ tc_set @ tc_set @ ( A @ ( v_S @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[376:[bind(A,$thf( E )),bind(B,$thf( t_a @ tc_set @ ( E @ ( v_S @ c_Main_OsubsetI__1 ) ) @ v_xa ))]]) ).
thf(404,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( t_a @ tc_set @ ( A @ ( v_S @ c_Main_OsubsetI__1 ) ) @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ( t_a @ tc_set @ tc_set @ ( A @ ( v_S @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[377]) ).
thf(14,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( C @ ( F @ ( D @ c_Zorn_Omaxchain__super__lemma__1 ) ) @ c_in ) ) )
| ( C @ ( F @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( E @ c_Zorn_Ochain ) @ ( C @ tc_set @ ( D @ ( C @ tc_set @ ( c_emptyset @ ( B @ c_insert ) ) @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( E @ c_Zorn_Omaxchain ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_0) ).
thf(42,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( C @ ( F @ ( D @ c_Zorn_Omaxchain__super__lemma__1 ) ) @ c_in ) ) )
| ( C @ ( F @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( E @ c_Zorn_Ochain ) @ ( C @ tc_set @ ( D @ ( C @ tc_set @ ( c_emptyset @ ( B @ c_insert ) ) @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( E @ c_Zorn_Omaxchain ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Ochain ) @ ( C @ tc_set @ ( D @ ( C @ tc_set @ ( c_emptyset @ ( A @ c_insert ) ) @ c_union ) ) @ c_in ) ) )
| ( C @ tc_set @ ( D @ ( C @ ( A @ ( D @ c_Zorn_Ochain__extend__1 ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Ochain ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_0) ).
thf(36,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Ochain ) @ ( C @ tc_set @ ( D @ ( C @ tc_set @ ( c_emptyset @ ( A @ c_insert ) ) @ c_union ) ) @ c_in ) ) )
| ( C @ tc_set @ ( D @ ( C @ ( A @ ( D @ c_Zorn_Ochain__extend__1 ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Ochain ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(37,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Ochain ) @ ( C @ tc_set @ ( D @ ( C @ tc_set @ ( c_emptyset @ ( A @ c_insert ) ) @ c_union ) ) @ c_in ) ) )
| ( C @ tc_set @ ( D @ ( C @ ( A @ ( D @ c_Zorn_Ochain__extend__1 ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Ochain ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[36]) ).
thf(3509,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
!= ( F @ ( E @ ( F @ ( E @ ( D @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) )
| ( F @ tc_set @ ( E @ ( D @ c_lessequals ) ) )
| ~ $true
| ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,35]) ).
thf(3510,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
!= ( F @ ( E @ ( F @ ( E @ ( D @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) )
| ( F @ tc_set @ ( E @ ( D @ c_lessequals ) ) )
| ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[3509]) ).
thf(3511,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
| ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[3510:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( A )),bind(F,$thf( C ))]]) ).
thf(3557,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
inference(simp,[status(thm)],[3511]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ~ $true
| ( t_a @ tc_set @ ( B @ v_xa @ ( B @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[60,26]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( B @ v_xa @ ( B @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[137]) ).
thf(139,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( A @ v_xa @ v_xa @ v_xa @ ( A @ v_xa @ v_xa @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[138:[bind(A,$thf( D )),bind(B,$thf( D @ v_xa @ v_xa ))]]) ).
thf(147,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( A @ v_xa @ v_xa @ v_xa @ ( A @ v_xa @ v_xa @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[139]) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ tc_set @ ( B @ ( A @ c_Zorn_Omaxchain ) @ ( B @ ( A @ c_Zorn_OHausdorff__1 ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( C @ c_in ) ) ) )
| ~ $true
| ( t_a @ tc_set @ ( v_S @ ( C @ v_xa @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[40,24]) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ tc_set @ ( B @ ( A @ c_Zorn_Omaxchain ) @ ( B @ ( A @ c_Zorn_OHausdorff__1 ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( C @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( C @ v_xa @ c_in ) ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ tc_set )
!= ( t_a @ tc_set ) )
| ( ( B @ ( A @ c_Zorn_Omaxchain ) )
!= v_S )
| ( ( B @ ( A @ c_Zorn_OHausdorff__1 ) )
!= C )
| ( t_a @ tc_set @ ( v_S @ ( C @ v_xa @ c_in ) ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set @ tc_set )
!= ( t_a @ tc_set ) )
| ( ( B @ ( A @ c_Zorn_Omaxchain ) )
!= v_S )
| ( t_a @ tc_set @ ( v_S @ ( B @ ( A @ c_Zorn_OHausdorff__1 ) @ v_xa @ c_in ) ) ) ),
inference(simp,[status(thm)],[58]) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[143,143]) ).
thf(213,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[212]) ).
thf(214,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[213:[bind(A,$thf( E )),bind(B,$thf( E @ v_xa @ v_xa @ v_xa ))]]) ).
thf(243,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[214]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( ( B @ v_xa @ v_xa @ v_xa )
!= ( B @ v_xa @ v_xa ) )
| ~ $true
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,71]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( ( B @ v_xa @ v_xa @ v_xa )
!= ( B @ v_xa @ v_xa ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[75]) ).
thf(77,plain,
! [A: $i] :
( ( ( A @ v_xa @ v_xa @ v_xa @ v_xa )
!= ( A @ v_xa @ v_xa @ v_xa ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[76:[bind(A,$thf( C )),bind(B,$thf( C @ v_xa ))]]) ).
thf(85,plain,
! [A: $i] :
( ( ( A @ v_xa @ v_xa @ v_xa @ v_xa )
!= ( A @ v_xa @ v_xa @ v_xa ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(5578,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( v_S @ c_in ) ) ) )
| ( ( t_a @ tc_set )
!= t_a )
| ( ( t_a @ ( v_S @ ( v_S @ v_xa @ c_Main_OsubsetI__1 ) ) )
!= v_S )
| ~ $true
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[143,5027]) ).
thf(5579,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( v_S @ c_in ) ) ) )
| ( ( t_a @ tc_set )
!= t_a )
| ( ( t_a @ ( v_S @ ( v_S @ v_xa @ c_Main_OsubsetI__1 ) ) )
!= v_S )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[5578]) ).
thf(5591,plain,
! [A: $i] :
( ( ( t_a @ tc_set )
!= ( t_a @ tc_set ) )
| ( v_S != v_S )
| ( ( A @ v_xa @ v_xa @ v_xa )
!= v_S )
| ( ( t_a @ tc_set )
!= t_a )
| ( ( t_a @ ( v_S @ ( v_S @ v_xa @ c_Main_OsubsetI__1 ) ) )
!= v_S )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[5579]) ).
thf(5611,plain,
! [A: $i] :
( ( ( A @ v_xa @ v_xa @ v_xa )
!= v_S )
| ( ( t_a @ tc_set )
!= t_a )
| ( ( t_a @ ( v_S @ ( v_S @ v_xa @ c_Main_OsubsetI__1 ) ) )
!= v_S )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[5591]) ).
thf(264,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[146,143]) ).
thf(265,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[264]) ).
thf(266,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[265:[bind(A,$thf( F )),bind(B,$thf( F @ v_xa @ v_xa @ v_xa @ v_xa ))]]) ).
thf(297,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[266]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( ( B @ v_xa @ v_xa )
!= ( B @ v_xa ) )
| ~ $true
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,59]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( ( B @ v_xa @ v_xa )
!= ( B @ v_xa ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[169]) ).
thf(171,plain,
! [A: $i] :
( ( ( A @ v_x @ v_xa @ v_xa )
!= ( A @ v_x @ v_xa ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[170:[bind(A,$thf( C )),bind(B,$thf( C @ v_x ))]]) ).
thf(192,plain,
! [A: $i] :
( ( ( A @ v_x @ v_xa @ v_xa )
!= ( A @ v_x @ v_xa ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[171]) ).
thf(3990,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ~ ( t_a @ tc_set @ ( B @ ( B @ v_xa @ c_lessequals ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[60,3832]) ).
thf(3991,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ~ ( t_a @ tc_set @ ( B @ ( B @ v_xa @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[3990]) ).
thf(3992,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( A @ v_xa @ v_xa @ ( A @ v_xa @ v_xa @ v_xa @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[3991:[bind(A,$thf( D )),bind(B,$thf( D @ v_xa @ v_xa ))]]) ).
thf(4049,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( A @ v_xa @ v_xa @ ( A @ v_xa @ v_xa @ v_xa @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[3992]) ).
thf(155,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ v_xa @ c_in ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,60]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[155]) ).
thf(157,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[156:[bind(A,$thf( C )),bind(B,$thf( C @ v_x ))]]) ).
thf(193,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(15,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( F @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( F @ ( C @ ( F @ ( D @ c_Zorn_Omaxchain__super__lemma__1 ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( E @ c_Zorn_Ochain ) @ ( C @ tc_set @ ( D @ ( C @ tc_set @ ( c_emptyset @ ( B @ c_insert ) ) @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( E @ c_Zorn_Omaxchain ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_1) ).
thf(44,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( F @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( F @ ( C @ ( F @ ( D @ c_Zorn_Omaxchain__super__lemma__1 ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( E @ c_Zorn_Ochain ) @ ( C @ tc_set @ ( D @ ( C @ tc_set @ ( c_emptyset @ ( B @ c_insert ) ) @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( E @ c_Zorn_Omaxchain ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(45,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( F @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( F @ ( C @ ( F @ ( D @ c_Zorn_Omaxchain__super__lemma__1 ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( E @ c_Zorn_Ochain ) @ ( C @ tc_set @ ( D @ ( C @ tc_set @ ( c_emptyset @ ( B @ c_insert ) ) @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( E @ c_Zorn_Omaxchain ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[44]) ).
thf(123,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( D @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( D @ v_xa @ v_xa @ c_in ) ) )
| ~ $true
| ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,60]) ).
thf(124,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( D @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( D @ v_xa @ v_xa @ c_in ) ) )
| ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[123]) ).
thf(125,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( t_a @ tc_set @ ( A @ ( v_S @ c_Main_OsubsetI__1 ) ) @ v_xa @ v_xa @ c_in ) ) )
| ( t_a @ tc_set @ tc_set @ ( A @ ( v_S @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[124:[bind(A,$thf( v_S )),bind(B,$thf( F )),bind(C,$thf( t_a @ tc_set )),bind(D,$thf( t_a @ tc_set @ ( F @ ( v_S @ c_Main_OsubsetI__1 ) ) ))]]) ).
thf(149,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( t_a @ tc_set @ ( A @ ( v_S @ c_Main_OsubsetI__1 ) ) @ v_xa @ v_xa @ c_in ) ) )
| ( t_a @ tc_set @ tc_set @ ( A @ ( v_S @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[125]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ~ $true
| ( ( B @ v_xa )
!= B )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,22]) ).
thf(167,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( ( B @ v_xa )
!= B )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[166]) ).
thf(168,plain,
! [A: $i] :
( ( ( A @ v_x @ v_xa )
!= ( A @ v_x ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[167:[bind(A,$thf( C )),bind(B,$thf( C @ v_x ))]]) ).
thf(191,plain,
! [A: $i] :
( ( ( A @ v_x @ v_xa )
!= ( A @ v_x ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[168]) ).
thf(286,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,146]) ).
thf(287,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[286]) ).
thf(288,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[287:[bind(A,$thf( C )),bind(B,$thf( C @ v_x ))]]) ).
thf(291,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[288]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ tc_set @ ( B @ ( A @ c_Zorn_Omaxchain ) @ ( B @ ( A @ c_Zorn_OHausdorff__1 ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( C @ c_in ) ) ) )
| ~ $true
| ( ( C @ v_xa )
!= C ) ),
inference(paramod_ordered,[status(thm)],[40,22]) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ tc_set @ ( B @ ( A @ c_Zorn_Omaxchain ) @ ( B @ ( A @ c_Zorn_OHausdorff__1 ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( C @ c_in ) ) ) )
| ( ( C @ v_xa )
!= C ) ),
inference(simp,[status(thm)],[46]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ tc_set )
!= ( t_a @ tc_set ) )
| ( ( B @ ( A @ c_Zorn_Omaxchain ) )
!= v_S )
| ( ( B @ ( A @ c_Zorn_OHausdorff__1 ) )
!= C )
| ( ( C @ v_xa )
!= C ) ),
inference(simp,[status(thm)],[47]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set @ tc_set )
!= ( t_a @ tc_set ) )
| ( ( B @ ( A @ c_Zorn_Omaxchain ) )
!= v_S )
| ( ( B @ ( A @ c_Zorn_OHausdorff__1 ) @ v_xa )
!= ( B @ ( A @ c_Zorn_OHausdorff__1 ) ) ) ),
inference(simp,[status(thm)],[48]) ).
thf(270,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[146,146]) ).
thf(271,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[270]) ).
thf(272,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[271:[bind(A,$thf( F )),bind(B,$thf( F @ v_xa @ v_xa @ v_xa @ v_xa ))]]) ).
thf(299,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[272]) ).
thf(206,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( D @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( D @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ $true
| ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,143]) ).
thf(207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( D @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( D @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[206]) ).
thf(208,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( t_a @ tc_set @ ( A @ ( v_S @ c_Main_OsubsetI__1 ) ) @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ( t_a @ tc_set @ tc_set @ ( A @ ( v_S @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( v_S )),bind(B,$thf( F )),bind(C,$thf( t_a @ tc_set )),bind(D,$thf( t_a @ tc_set @ ( F @ ( v_S @ c_Main_OsubsetI__1 ) ) ))]]) ).
thf(241,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( t_a @ tc_set @ ( A @ ( v_S @ c_Main_OsubsetI__1 ) ) @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ( t_a @ tc_set @ tc_set @ ( A @ ( v_S @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[208]) ).
thf(5518,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( v_S @ c_in ) ) ) )
| ( ( t_a @ tc_set )
!= t_a )
| ( ( t_a @ ( v_S @ ( v_S @ v_xa @ c_Main_OsubsetI__1 ) ) )
!= v_S )
| ~ $true
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,5027]) ).
thf(5519,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( v_S @ c_in ) ) ) )
| ( ( t_a @ tc_set )
!= t_a )
| ( ( t_a @ ( v_S @ ( v_S @ v_xa @ c_Main_OsubsetI__1 ) ) )
!= v_S )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[5518]) ).
thf(5600,plain,
! [A: $i] :
( ( ( t_a @ tc_set )
!= ( t_a @ tc_set ) )
| ( v_S != v_S )
| ( ( A @ v_xa )
!= v_S )
| ( ( t_a @ tc_set )
!= t_a )
| ( ( t_a @ ( v_S @ ( v_S @ v_xa @ c_Main_OsubsetI__1 ) ) )
!= v_S )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[5519]) ).
thf(5624,plain,
! [A: $i] :
( ( ( A @ v_xa )
!= v_S )
| ( ( t_a @ tc_set )
!= t_a )
| ( ( t_a @ ( v_S @ ( v_S @ v_xa @ c_Main_OsubsetI__1 ) ) )
!= v_S )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[5600]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ tc_set @ ( B @ ( A @ c_Zorn_Omaxchain ) @ ( B @ ( A @ c_Zorn_OHausdorff__1 ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( C @ c_in ) ) ) )
| ( ( C @ v_xa @ v_xa )
!= ( C @ v_xa ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40,59]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ tc_set @ ( B @ ( A @ c_Zorn_Omaxchain ) @ ( B @ ( A @ c_Zorn_OHausdorff__1 ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( C @ c_in ) ) ) )
| ( ( C @ v_xa @ v_xa )
!= ( C @ v_xa ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(68,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ tc_set @ ( B @ ( A @ c_Zorn_Omaxchain ) @ ( B @ ( A @ c_Zorn_OHausdorff__1 ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( C @ c_in ) ) ) )
| ( ( C @ v_xa )
!= C ) ),
inference(simp,[status(thm)],[67]) ).
thf(11770,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) )
| ( ( A @ v_xa )
!= A ) ),
inference(rewrite,[status(thm)],[68,40]) ).
thf(258,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( D @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( D @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ $true
| ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,146]) ).
thf(259,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( D @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( D @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[258]) ).
thf(260,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( t_a @ tc_set @ ( A @ ( v_S @ c_Main_OsubsetI__1 ) ) @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ( t_a @ tc_set @ tc_set @ ( A @ ( v_S @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[259:[bind(A,$thf( v_S )),bind(B,$thf( F )),bind(C,$thf( t_a @ tc_set )),bind(D,$thf( t_a @ tc_set @ ( F @ ( v_S @ c_Main_OsubsetI__1 ) ) ))]]) ).
thf(295,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( t_a @ tc_set @ ( A @ ( v_S @ c_Main_OsubsetI__1 ) ) @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ( t_a @ tc_set @ tc_set @ ( A @ ( v_S @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[260]) ).
thf(69,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ tc_set )
!= ( t_a @ tc_set ) )
| ( ( B @ ( A @ c_Zorn_Omaxchain ) )
!= v_S )
| ( ( B @ ( A @ c_Zorn_OHausdorff__1 ) )
!= C )
| ( ( C @ v_xa @ v_xa )
!= ( C @ v_xa ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( ( B @ tc_set @ tc_set )
!= ( t_a @ tc_set ) )
| ( ( B @ ( A @ c_Zorn_Omaxchain ) )
!= v_S )
| ( ( B @ ( A @ c_Zorn_OHausdorff__1 ) @ v_xa @ v_xa )
!= ( B @ ( A @ c_Zorn_OHausdorff__1 ) @ v_xa ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(43,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( C @ ( F @ ( D @ c_Zorn_Omaxchain__super__lemma__1 ) ) @ c_in ) ) )
| ( C @ ( F @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( E @ c_Zorn_Ochain ) @ ( C @ tc_set @ ( D @ ( C @ tc_set @ ( c_emptyset @ ( B @ c_insert ) ) @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( E @ c_Zorn_Omaxchain ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[42]) ).
thf(10199,plain,
( ( ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( v_S @ c_in ) ) )
!= ( t_a @ ( v_S @ v_xa @ ( v_S @ c_in ) ) ) )
| ~ $true
| ( ( t_a @ tc_set )
!= t_a )
| ~ ( t_a @ ( v_S @ ( v_S @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[9241,9823]) ).
thf(10200,plain,
( ( ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( v_S @ c_in ) ) )
!= ( t_a @ ( v_S @ v_xa @ ( v_S @ c_in ) ) ) )
| ( ( t_a @ tc_set )
!= t_a )
| ~ ( t_a @ ( v_S @ ( v_S @ c_in ) ) ) ),
inference(simp,[status(thm)],[10199]) ).
thf(10268,plain,
( ( ( t_a @ tc_set @ tc_set )
!= t_a )
| ( ( t_a @ ( v_S @ c_Zorn_Ochain ) )
!= ( v_S @ v_xa ) )
| ( v_S != v_S )
| ( ( t_a @ tc_set )
!= t_a )
| ~ ( t_a @ ( v_S @ ( v_S @ c_in ) ) ) ),
inference(simp,[status(thm)],[10200]) ).
thf(10332,plain,
( ( ( t_a @ tc_set @ tc_set )
!= t_a )
| ( ( t_a @ ( v_S @ c_Zorn_Ochain ) )
!= ( v_S @ v_xa ) )
| ( ( t_a @ tc_set )
!= t_a )
| ~ ( t_a @ ( v_S @ ( v_S @ c_in ) ) ) ),
inference(simp,[status(thm)],[10268]) ).
thf(557,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[190,146]) ).
thf(558,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( v_S @ ( B @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[557]) ).
thf(559,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[558:[bind(A,$thf( D )),bind(B,$thf( D @ v_x @ v_xa ))]]) ).
thf(581,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ v_xa @ v_xa @ v_xa @ v_xa @ v_xa @ c_in ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[559]) ).
thf(3953,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ~ ( t_a @ tc_set @ ( B @ ( B @ v_xa @ c_lessequals ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,3832]) ).
thf(3954,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ~ ( t_a @ tc_set @ ( B @ ( B @ v_xa @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[3953]) ).
thf(3955,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( A @ v_xa @ ( A @ v_xa @ v_xa @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[3954:[bind(A,$thf( C )),bind(B,$thf( C @ v_xa ))]]) ).
thf(4061,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( A @ v_xa @ ( A @ v_xa @ v_xa @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[3955]) ).
thf(3959,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( C @ ( C @ v_xa @ c_lessequals ) ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ ( v_S @ ( C @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[3557,3832]) ).
thf(3960,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( C @ ( C @ v_xa @ c_lessequals ) ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[3959]) ).
thf(4034,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set )
!= ( t_a @ tc_set ) )
| ( A != C )
| ( A
!= ( C @ v_xa ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[3960]) ).
thf(4039,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set )
!= ( t_a @ tc_set ) )
| ( ( B @ v_xa )
!= B )
| ~ ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[4034]) ).
thf(174,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ~ $true
| ( t_a @ tc_set @ ( B @ v_xa @ ( B @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,26]) ).
thf(175,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_x @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( B @ v_xa @ ( B @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[174]) ).
thf(176,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( A @ v_x @ v_xa @ ( A @ v_x @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[175:[bind(A,$thf( C )),bind(B,$thf( C @ v_x ))]]) ).
thf(183,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( A @ v_x @ v_xa @ ( A @ v_x @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[176]) ).
thf(2505,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( A @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( E @ c_in ) ) ) )
| ~ $true
| ( ( E @ v_xa )
!= E )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,22]) ).
thf(2506,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( A @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( E @ c_in ) ) ) )
| ( ( E @ v_xa )
!= E )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[2505]) ).
thf(2507,plain,
! [B: $i,A: $i] :
( ( ( A @ v_xa )
!= A )
| ~ ( t_a @ tc_set @ tc_set @ ( v_S @ ( B @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[2506:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( t_a @ tc_set )),bind(D,$thf( v_S )),bind(E,$thf( A ))]]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ~ $true
| ( t_a @ tc_set @ ( B @ v_xa @ ( B @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,26]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( B @ c_in ) ) ) )
| ( t_a @ tc_set @ ( B @ v_xa @ ( B @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[102]) ).
thf(104,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( A @ v_xa @ v_xa @ ( A @ v_xa @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[103:[bind(A,$thf( C )),bind(B,$thf( C @ v_xa ))]]) ).
thf(111,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( A @ v_xa @ v_xa @ ( A @ v_xa @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(5568,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( v_S @ c_in ) ) ) )
| ( ( t_a @ tc_set )
!= t_a )
| ( ( t_a @ ( v_S @ ( v_S @ v_xa @ c_Main_OsubsetI__1 ) ) )
!= v_S )
| ~ $true
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[60,5027]) ).
thf(5569,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ ( v_S @ ( A @ v_xa @ v_xa @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_S @ ( v_S @ c_in ) ) ) )
| ( ( t_a @ tc_set )
!= t_a )
| ( ( t_a @ ( v_S @ ( v_S @ v_xa @ c_Main_OsubsetI__1 ) ) )
!= v_S )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[5568]) ).
thf(5596,plain,
! [A: $i] :
( ( ( t_a @ tc_set )
!= ( t_a @ tc_set ) )
| ( v_S != v_S )
| ( ( A @ v_xa @ v_xa )
!= v_S )
| ( ( t_a @ tc_set )
!= t_a )
| ( ( t_a @ ( v_S @ ( v_S @ v_xa @ c_Main_OsubsetI__1 ) ) )
!= v_S )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[5569]) ).
thf(5618,plain,
! [A: $i] :
( ( ( A @ v_xa @ v_xa )
!= v_S )
| ( ( t_a @ tc_set )
!= t_a )
| ( ( t_a @ ( v_S @ ( v_S @ v_xa @ c_Main_OsubsetI__1 ) ) )
!= v_S )
| ~ ( t_a @ tc_set @ ( v_S @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[5596]) ).
thf(39430,plain,
$false,
inference(e,[status(thm)],[5027,4053,141,41,39,12810,235,239,10007,101,2544,11394,9241,677,404,42,24,37,25,20,3557,29,147,11242,61,243,60,85,5611,38,297,192,33,4049,193,45,17,149,32,34,191,22,44,291,59,27,71,49,4060,3832,299,241,35,5624,11770,295,18,16,31,4057,72,143,43,10332,99,581,4061,40,26,23,4039,36,9823,146,30,190,183,19,9583,2507,111,5618]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET861-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.09 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.18/0.46 % Computer : n016.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Sat Sep 26 08:28:00 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.28/1.28 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.81/1.57 % [INFO] Parsing done (283ms).
% 1.81/1.59 % [INFO] Running in sequential loop mode.
% 3.14/2.20 % [INFO] eprover registered as external prover.
% 3.14/2.21 % [INFO] Scanning for conjecture ...
% 3.36/2.37 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 3.54/2.44 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 3.54/2.48 % [INFO] Problem is propositional (TPTP CNF).
% 3.54/2.49 % [INFO] Type checking passed.
% 3.75/2.50 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 94.50/24.68 % External prover 'e' found a proof!
% 94.50/24.68 % [INFO] Killing All external provers ...
% 94.50/24.68 % Time passed: 24014ms (effective reasoning time: 23080ms)
% 94.50/24.68 % Axioms used in derivation (10): cls_Set_OsubsetI_1, cls_Zorn_Ochain__extend_0, cls_Zorn_Omaxchain__super__lemma_0, cls_Set_OsubsetI_0, cls_Zorn_Ochain__extend_1, cls_Zorn_Omaxchain__subset__chain_0, cls_Set_OsubsetD_0, cls_Set_Osubset__antisym_0, cls_Zorn_OHausdorff_0, cls_Zorn_Omaxchain__super__lemma_1
% 94.50/24.68 % No. of inferences in proof: 261
% 94.50/24.68 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 24014 ms resp. 23080 ms w/o parsing
% 90.55/24.84 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 90.55/24.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------