%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PUZ064-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n005.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 08:21:16 AM UTC 2026
% Result : Unsatisfiable 198.88s 54.73s
% Output : Refutation 195.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 29
% Syntax : Number of formulae : 930 ( 373 unt; 0 typ; 0 def)
% Number of atoms : 2185 (1140 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 15227 (1184 ~;1007 |; 0 &;13036 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 9 con; 0-4 aty)
% Number of variables : 2131 ( 0 ^;2131 !; 0 ?;2131 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_a_decl,type,
v_a: $i ).
thf(v_A_decl,type,
v_A: $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(c_inter_decl,type,
c_inter: $i > $i > $i > $i ).
thf(v_t_decl,type,
v_t: $i ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(v_u_decl,type,
v_u: $i ).
thf(c_Mutil_Otiling_decl,type,
c_Mutil_Otiling: $i > $i > $i ).
thf(c_union_decl,type,
c_union: $i > $i > $i > $i ).
thf(c_Relation_OImage_decl,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_Relation_Odiag_decl,type,
c_Relation_Odiag: $i > $i > $i ).
thf(c_UNIV_decl,type,
c_UNIV: $i ).
thf(c_minus_decl,type,
c_minus: $i > $i > $i > $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_uminus_decl,type,
c_uminus: $i > $i > $i ).
thf(c_Main_OsubsetI__1_decl,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_UNIV @ c_union ) ) )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__left_0) ).
thf(68,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_UNIV @ c_union ) ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_UNIV @ c_union ) ) )
= c_UNIV ),
inference(lifteq,[status(thm)],[68]) ).
thf(4,negated_conjecture,
( ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_inter ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(35,plain,
( ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_inter ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(37,plain,
( ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_inter ) ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[35]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_union ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_union ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_union ) ) )
= A ),
inference(lifteq,[status(thm)],[41]) ).
thf(6,negated_conjecture,
( ~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( v_u @ c_in ) ) )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset )
| ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(32,plain,
( ~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( v_u @ c_in ) ) )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset )
| ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(39,plain,
( ~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( v_u @ c_in ) ) )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset )
| ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[32]) ).
thf(40,plain,
( ~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( v_u @ c_in ) ) )
| ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ c_in ) ) )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(3,negated_conjecture,
t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( v_u @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(34,plain,
t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( v_u @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(107,plain,
( ~ $true
| ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ c_in ) ) )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(rewrite,[status(thm)],[40,34]) ).
thf(108,plain,
( ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ c_in ) ) )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[107]) ).
thf(5,negated_conjecture,
~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_union ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(30,plain,
~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_union ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(38,plain,
~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_union ) ) @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[30]) ).
thf(111,plain,
( ( ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_union ) ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ c_in ) ) ) )
| ~ $true
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[108,38]) ).
thf(112,plain,
( ( ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_union ) ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ c_in ) ) ) )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[111]) ).
thf(118,plain,
( ( ( t_a @ tc_set )
!= ( t_a @ tc_set ) )
| ( ( t_a @ ( v_A @ c_Mutil_Otiling ) )
!= ( t_a @ ( v_A @ c_Mutil_Otiling ) ) )
| ( ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_union ) ) )
!= ( t_a @ ( v_u @ ( v_t @ c_union ) ) ) )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[112]) ).
thf(122,plain,
( ( ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_union ) ) )
!= ( t_a @ ( v_u @ ( v_t @ c_union ) ) ) )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[118]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_union ) ) )
= ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__assoc_0) ).
thf(76,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_union ) ) )
= ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(77,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_union ) ) )
= ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_union ) ) ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(3981,plain,
( ( ( t_a @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ ( v_a @ c_union ) ) )
!= ( t_a @ ( v_u @ ( v_t @ c_union ) ) ) )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(rewrite,[status(thm)],[122,77]) ).
thf(3990,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_union ) ) )
!= ( t_a @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ ( v_a @ c_union ) ) ) )
| ( A
!= ( t_a @ ( v_u @ ( v_t @ c_union ) ) ) )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[42,3981]) ).
thf(4070,plain,
! [A: $i] :
( ( A != t_a )
| ( ( t_a @ ( v_u @ ( v_t @ c_union ) ) )
!= ( t_a @ ( v_u @ ( v_t @ c_union ) ) ) )
| ( ( t_a @ ( v_u @ ( v_t @ c_union ) ) )
!= v_a )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[3990]) ).
thf(4193,plain,
( ( ( t_a @ ( v_u @ ( v_t @ c_union ) ) )
!= v_a )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[4070]) ).
thf(9899,plain,
( ( ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_inter ) ) )
!= ( t_a @ ( v_u @ ( v_t @ c_inter ) ) ) )
| ( ( t_a @ ( v_u @ ( v_t @ c_union ) ) )
!= v_a )
| ( c_emptyset != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[37,4193]) ).
thf(9900,plain,
( ( ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_inter ) ) )
!= ( t_a @ ( v_u @ ( v_t @ c_inter ) ) ) )
| ( ( t_a @ ( v_u @ ( v_t @ c_union ) ) )
!= v_a ) ),
inference(simp,[status(thm)],[9899]) ).
thf(9953,plain,
( ( t_a != t_a )
| ( v_u != v_u )
| ( ( t_a @ ( v_t @ ( v_a @ c_union ) ) )
!= v_t )
| ( ( t_a @ ( v_u @ ( v_t @ c_union ) ) )
!= v_a ) ),
inference(simp,[status(thm)],[9900]) ).
thf(9982,plain,
( ( ( t_a @ ( v_t @ ( v_a @ c_union ) ) )
!= v_t )
| ( ( t_a @ ( v_u @ ( v_t @ c_union ) ) )
!= v_a ) ),
inference(simp,[status(thm)],[9953]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ tc_set @ ( c_UNIV @ c_uminus ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).
thf(78,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_UNIV @ c_uminus ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(79,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_UNIV @ c_uminus ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[78]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( B @ tc_set @ ( A @ c_uminus ) @ c_uminus ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( B @ tc_set @ ( A @ c_uminus ) @ c_uminus ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( B @ tc_set @ ( A @ c_uminus ) @ c_uminus ) )
= A ),
inference(lifteq,[status(thm)],[56]) ).
thf(311,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_UNIV @ c_uminus ) )
!= ( C @ tc_set @ ( B @ c_uminus ) ) )
| ( ( C @ tc_set @ ( c_emptyset @ c_uminus ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[79,57]) ).
thf(312,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
= c_UNIV ),
inference(pattern_uni,[status(thm)],[311:[bind(A,$thf( A )),bind(B,$thf( c_UNIV )),bind(C,$thf( A ))]]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_minus ) ) )
= ( C @ ( B @ ( A @ c_inter ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__Compl_0) ).
thf(85,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_minus ) ) )
= ( C @ ( B @ ( A @ c_inter ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_minus ) ) )
= ( C @ ( B @ ( A @ c_inter ) ) ) ),
inference(lifteq,[status(thm)],[85]) ).
thf(387,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
!= ( D @ tc_set @ ( C @ c_uminus ) ) )
| ( ( D @ tc_set @ ( c_UNIV @ ( B @ c_minus ) ) )
= ( D @ ( C @ ( B @ c_inter ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[312,86]) ).
thf(388,plain,
! [B: $i,A: $i] :
( ( A @ tc_set @ ( c_UNIV @ ( B @ c_minus ) ) )
= ( A @ ( c_emptyset @ ( B @ c_inter ) ) ) ),
inference(pattern_uni,[status(thm)],[387:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( c_emptyset )),bind(D,$thf( A ))]]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_union ) ) )
= ( C @ ( B @ ( A @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel2_0) ).
thf(52,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_union ) ) )
= ( C @ ( B @ ( A @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_union ) ) )
= ( C @ ( B @ ( A @ c_union ) ) ) ),
inference(lifteq,[status(thm)],[52]) ).
thf(452,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_UNIV @ ( B @ c_minus ) ) )
!= ( E @ tc_set @ ( D @ ( C @ c_minus ) ) ) )
| ( ( E @ ( D @ ( A @ ( c_emptyset @ ( B @ c_inter ) ) @ c_union ) ) )
= ( E @ ( D @ ( C @ c_union ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[388,53]) ).
thf(453,plain,
! [B: $i,A: $i] :
( ( A @ ( c_UNIV @ ( A @ ( c_emptyset @ ( B @ c_inter ) ) @ c_union ) ) )
= ( A @ ( c_UNIV @ ( B @ c_union ) ) ) ),
inference(pattern_uni,[status(thm)],[452:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( c_UNIV )),bind(E,$thf( A ))]]) ).
thf(573,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( c_UNIV @ ( A @ ( c_emptyset @ ( B @ c_inter ) ) @ c_union ) ) )
!= ( D @ ( C @ ( C @ c_union ) ) ) )
| ( ( A @ ( c_UNIV @ ( B @ c_union ) ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[453,42]) ).
thf(603,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != D )
| ( c_UNIV != C )
| ( ( A @ ( c_emptyset @ ( B @ c_inter ) ) )
!= C )
| ( ( A @ ( c_UNIV @ ( B @ c_union ) ) )
= C ) ),
inference(simp,[status(thm)],[573]) ).
thf(629,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_emptyset @ ( A @ c_inter ) ) )
!= c_UNIV )
| ( ( B @ ( c_UNIV @ ( A @ c_union ) ) )
= ( B @ ( c_emptyset @ ( A @ c_inter ) ) ) ) ),
inference(simp,[status(thm)],[603]) ).
thf(391,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_UNIV @ c_uminus ) )
!= ( D @ tc_set @ ( C @ c_uminus ) ) )
| ( ( D @ tc_set @ ( c_emptyset @ ( B @ c_minus ) ) )
= ( D @ ( C @ ( B @ c_inter ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[79,86]) ).
thf(392,plain,
! [B: $i,A: $i] :
( ( A @ tc_set @ ( c_emptyset @ ( B @ c_minus ) ) )
= ( A @ ( c_UNIV @ ( B @ c_inter ) ) ) ),
inference(pattern_uni,[status(thm)],[391:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( c_UNIV )),bind(D,$thf( A ))]]) ).
thf(465,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_minus ) ) )
!= ( D @ tc_set @ ( c_emptyset @ ( E @ c_minus ) ) ) )
| ( ( C @ ( B @ ( A @ c_inter ) ) )
= ( D @ ( c_UNIV @ ( E @ c_inter ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[86,392]) ).
thf(468,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set )
!= ( D @ tc_set ) )
| ( ( C @ tc_set @ ( B @ c_uminus ) )
!= c_emptyset )
| ( A != E )
| ( ( C @ ( B @ ( A @ c_inter ) ) )
= ( D @ ( c_UNIV @ ( E @ c_inter ) ) ) ) ),
inference(simp,[status(thm)],[465]) ).
thf(472,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set )
!= ( C @ tc_set ) )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= c_emptyset )
| ( ( B @ ( A @ ( D @ c_inter ) ) )
= ( C @ ( c_UNIV @ ( D @ c_inter ) ) ) ) ),
inference(simp,[status(thm)],[468]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
= A ),
inference(lifteq,[status(thm)],[83]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( A @ ( B @ c_minus ) ) @ ( A @ c_union ) ) )
= ( C @ ( B @ ( A @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( A @ ( B @ c_minus ) ) @ ( A @ c_union ) ) )
= ( C @ ( B @ ( A @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( A @ ( B @ c_minus ) ) @ ( A @ c_union ) ) )
= ( C @ ( B @ ( A @ c_union ) ) ) ),
inference(lifteq,[status(thm)],[72]) ).
thf(389,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( B @ tc_set @ ( A @ c_uminus ) @ c_uminus ) )
!= ( E @ tc_set @ ( D @ c_uminus ) ) )
| ( ( E @ tc_set @ ( A @ ( C @ c_minus ) ) )
= ( E @ ( D @ ( C @ c_inter ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[57,86]) ).
thf(390,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
= ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_inter ) ) ) ),
inference(pattern_uni,[status(thm)],[389:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ tc_set @ ( F @ c_uminus ) )),bind(E,$thf( H ))]]) ).
thf(393,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
= ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_inter ) ) ) ),
inference(simp,[status(thm)],[390]) ).
thf(1362,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ tc_set @ ( A @ c_uminus ) @ ( B @ c_inter ) ) @ ( A @ c_union ) ) )
= ( C @ ( B @ ( A @ c_union ) ) ) ),
inference(rewrite,[status(thm)],[73,393]) ).
thf(1388,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
!= ( E @ ( E @ ( E @ tc_set @ ( C @ c_uminus ) @ ( D @ c_inter ) ) @ ( C @ c_union ) ) ) )
| ( A
= ( E @ ( D @ ( C @ c_union ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[84,1362]) ).
thf(1389,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_emptyset @ c_union ) ) )
= ( A @ ( A @ tc_set @ ( c_emptyset @ c_uminus ) @ ( B @ c_inter ) ) ) ),
inference(pattern_uni,[status(thm)],[1388:[bind(A,$thf( B @ ( B @ tc_set @ ( c_emptyset @ c_uminus ) @ ( F @ c_inter ) ) )),bind(B,$thf( B )),bind(C,$thf( c_emptyset )),bind(D,$thf( F )),bind(E,$thf( B ))]]) ).
thf(1486,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_emptyset @ c_union ) ) )
= ( A @ ( A @ tc_set @ ( c_emptyset @ c_uminus ) @ ( B @ c_inter ) ) ) ),
inference(simp,[status(thm)],[1389]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
= A ),
inference(lifteq,[status(thm)],[45]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_uminus ) )
= ( C @ ( B @ ( C @ tc_set @ ( A @ c_uminus ) @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Diff__eq_0) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_uminus ) )
= ( C @ ( B @ ( C @ tc_set @ ( A @ c_uminus ) @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_uminus ) )
= ( C @ ( B @ ( C @ tc_set @ ( A @ c_uminus ) @ c_union ) ) ) ),
inference(lifteq,[status(thm)],[58]) ).
thf(715,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ tc_set @ ( A @ c_uminus ) @ c_union ) ) )
= ( C @ tc_set @ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_inter ) ) @ c_uminus ) ) ),
inference(rewrite,[status(thm)],[59,393]) ).
thf(728,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
!= ( E @ ( D @ ( E @ tc_set @ ( C @ c_uminus ) @ c_union ) ) ) )
| ( A
= ( E @ tc_set @ ( E @ ( E @ tc_set @ ( D @ c_uminus ) @ ( C @ c_inter ) ) @ c_uminus ) ) ) ),
inference(paramod_ordered,[status(thm)],[46,715]) ).
thf(729,plain,
! [B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( A @ tc_set @ ( c_emptyset @ c_uminus ) @ ( B @ c_inter ) ) @ c_uminus ) )
= ( A @ tc_set @ ( B @ c_uminus ) ) ),
inference(pattern_uni,[status(thm)],[728:[bind(A,$thf( B @ tc_set @ ( F @ c_uminus ) )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( c_emptyset )),bind(E,$thf( B ))]]) ).
thf(770,plain,
! [B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( A @ tc_set @ ( c_emptyset @ c_uminus ) @ ( B @ c_inter ) ) @ c_uminus ) )
= ( A @ tc_set @ ( B @ c_uminus ) ) ),
inference(simp,[status(thm)],[729]) ).
thf(827,plain,
! [B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( c_UNIV @ ( B @ c_inter ) ) @ c_uminus ) )
= ( A @ tc_set @ ( B @ c_uminus ) ) ),
inference(rewrite,[status(thm)],[770,312]) ).
thf(737,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
!= ( D @ tc_set @ ( B @ c_uminus ) ) )
| ( ( D @ ( C @ ( c_UNIV @ c_union ) ) )
= ( D @ tc_set @ ( D @ ( D @ tc_set @ ( C @ c_uminus ) @ ( B @ c_inter ) ) @ c_uminus ) ) ) ),
inference(paramod_ordered,[status(thm)],[312,715]) ).
thf(738,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_UNIV @ c_union ) ) )
= ( A @ tc_set @ ( A @ ( A @ tc_set @ ( B @ c_uminus ) @ ( c_emptyset @ c_inter ) ) @ c_uminus ) ) ),
inference(pattern_uni,[status(thm)],[737:[bind(A,$thf( A )),bind(B,$thf( c_emptyset )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(772,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_UNIV @ c_union ) ) )
= ( A @ tc_set @ ( A @ ( A @ tc_set @ ( B @ c_uminus ) @ ( c_emptyset @ c_inter ) ) @ c_uminus ) ) ),
inference(simp,[status(thm)],[738]) ).
thf(910,plain,
! [B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( A @ tc_set @ ( B @ c_uminus ) @ ( c_emptyset @ c_inter ) ) @ c_uminus ) )
= c_UNIV ),
inference(rewrite,[status(thm)],[772,69]) ).
thf(931,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ ( c_UNIV @ ( B @ c_inter ) ) @ c_uminus ) )
!= ( C @ tc_set @ ( D @ c_uminus ) ) )
| ( ( C @ tc_set @ ( C @ ( A @ tc_set @ ( B @ c_uminus ) @ ( c_emptyset @ c_inter ) ) @ c_uminus ) )
= c_UNIV ) ),
inference(paramod_ordered,[status(thm)],[827,910]) ).
thf(932,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( B @ tc_set @ ( A @ c_uminus ) @ ( c_emptyset @ c_inter ) ) @ c_uminus ) )
= c_UNIV ),
inference(pattern_uni,[status(thm)],[931:[bind(A,$thf( G )),bind(B,$thf( E )),bind(C,$thf( G )),bind(D,$thf( G @ ( c_UNIV @ ( E @ c_inter ) ) ))]]) ).
thf(952,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( B @ tc_set @ ( A @ c_uminus ) @ ( c_emptyset @ c_inter ) ) @ c_uminus ) )
= c_UNIV ),
inference(simp,[status(thm)],[932]) ).
thf(918,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( B @ tc_set @ ( A @ c_uminus ) @ c_uminus ) )
!= ( C @ tc_set @ ( D @ c_uminus ) ) )
| ( ( C @ tc_set @ ( C @ ( A @ ( c_emptyset @ c_inter ) ) @ c_uminus ) )
= c_UNIV ) ),
inference(paramod_ordered,[status(thm)],[57,910]) ).
thf(919,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( A @ ( c_emptyset @ c_inter ) ) @ c_uminus ) )
= c_UNIV ),
inference(pattern_uni,[status(thm)],[918:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( G @ tc_set @ ( E @ c_uminus ) ))]]) ).
thf(960,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( A @ ( c_emptyset @ c_inter ) ) @ c_uminus ) )
= c_UNIV ),
inference(simp,[status(thm)],[919]) ).
thf(1088,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( B @ ( A @ ( c_emptyset @ c_inter ) ) @ c_uminus ) )
!= ( D @ tc_set @ ( C @ c_uminus ) ) )
| ( ( D @ tc_set @ ( c_UNIV @ c_uminus ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[960,57]) ).
thf(1089,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_inter ) ) )
= ( B @ tc_set @ ( c_UNIV @ c_uminus ) ) ),
inference(pattern_uni,[status(thm)],[1088:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G @ ( F @ ( c_emptyset @ c_inter ) ) )),bind(D,$thf( G ))]]) ).
thf(1115,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_inter ) ) )
= ( B @ tc_set @ ( c_UNIV @ c_uminus ) ) ),
inference(simp,[status(thm)],[1089]) ).
thf(1122,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_inter ) ) )
= c_emptyset ),
inference(rewrite,[status(thm)],[1115,79]) ).
thf(1494,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
= c_UNIV ),
inference(rewrite,[status(thm)],[952,1122]) ).
thf(3462,plain,
! [B: $i,A: $i] :
( ( A @ ( c_UNIV @ ( B @ c_inter ) ) )
= B ),
inference(rewrite,[status(thm)],[1486,84,1494]) ).
thf(25943,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set )
!= ( C @ tc_set ) )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= c_emptyset )
| ( ( B @ ( A @ ( D @ c_inter ) ) )
= D ) ),
inference(rewrite,[status(thm)],[472,3462]) ).
thf(16,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(60,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
thf(66,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(67,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[66]) ).
thf(1053,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( E @ tc_set @ ( F @ ( E @ ( D @ ( C @ c_union ) ) @ c_lessequals ) ) ) )
| ( E @ tc_set @ ( F @ ( D @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[60,67]) ).
thf(1054,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( E @ tc_set @ ( F @ ( E @ ( D @ ( C @ c_union ) ) @ c_lessequals ) ) ) )
| ( E @ tc_set @ ( F @ ( D @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1053]) ).
thf(1055,plain,
! [C: $i,B: $i,A: $i] : ( A @ tc_set @ ( A @ ( C @ ( B @ c_union ) ) @ ( C @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[1054:[bind(A,$thf( B @ ( K @ ( J @ c_union ) ) )),bind(B,$thf( B )),bind(C,$thf( J )),bind(D,$thf( K )),bind(E,$thf( B )),bind(F,$thf( B @ ( K @ ( J @ c_union ) ) ))]]) ).
thf(1079,plain,
! [C: $i,B: $i,A: $i] : ( A @ tc_set @ ( A @ ( C @ ( B @ c_union ) ) @ ( C @ c_lessequals ) ) ),
inference(simp,[status(thm)],[1055]) ).
thf(1173,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ ( C @ ( B @ c_union ) ) @ ( C @ c_lessequals ) ) )
!= ( F @ tc_set @ ( G @ ( F @ ( E @ ( D @ c_union ) ) @ c_lessequals ) ) ) )
| ( F @ tc_set @ ( G @ ( E @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1079,67]) ).
thf(1174,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ ( C @ ( B @ c_union ) ) @ ( C @ c_lessequals ) ) )
!= ( F @ tc_set @ ( G @ ( F @ ( E @ ( D @ c_union ) ) @ c_lessequals ) ) ) )
| ( F @ tc_set @ ( G @ ( E @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1173]) ).
thf(1175,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ tc_set @ ( B @ ( B @ ( D @ ( C @ c_union ) ) @ ( A @ c_union ) ) @ ( D @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[1174:[bind(A,$thf( M )),bind(B,$thf( K )),bind(C,$thf( M @ ( O @ ( N @ c_union ) ) )),bind(D,$thf( N )),bind(E,$thf( O )),bind(F,$thf( M )),bind(G,$thf( M @ ( M @ ( O @ ( N @ c_union ) ) @ ( K @ c_union ) ) ))]]) ).
thf(1183,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ tc_set @ ( B @ ( B @ ( D @ ( C @ c_union ) ) @ ( A @ c_union ) ) @ ( D @ c_lessequals ) ) ),
inference(simp,[status(thm)],[1175]) ).
thf(4765,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( c_UNIV @ c_union ) ) )
!= ( D @ ( F @ ( E @ c_union ) ) ) )
| ( D @ tc_set @ ( D @ ( c_UNIV @ ( C @ c_union ) ) @ ( F @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[69,1183]) ).
thf(4766,plain,
! [C: $i,B: $i,A: $i] : ( B @ tc_set @ ( B @ ( c_UNIV @ ( C @ c_union ) ) @ ( A @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[4765:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( c_UNIV )),bind(F,$thf( A ))]]) ).
thf(4881,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ tc_set @ ( A @ c_uminus ) @ c_union ) ) )
!= ( E @ ( c_UNIV @ ( F @ c_union ) ) ) )
| ( E @ tc_set @ ( C @ tc_set @ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_inter ) ) @ c_uminus ) @ ( D @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[715,4766]) ).
thf(4882,plain,
! [C: $i,B: $i,A: $i] : ( C @ tc_set @ ( C @ tc_set @ ( C @ ( C @ tc_set @ ( c_UNIV @ c_uminus ) @ ( B @ c_inter ) ) @ c_uminus ) @ ( A @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[4881:[bind(A,$thf( G )),bind(B,$thf( c_UNIV )),bind(C,$thf( I )),bind(D,$thf( D )),bind(E,$thf( I )),bind(F,$thf( I @ tc_set @ ( G @ c_uminus ) ))]]) ).
thf(4934,plain,
! [C: $i,B: $i,A: $i] : ( C @ tc_set @ ( C @ tc_set @ ( C @ ( C @ tc_set @ ( c_UNIV @ c_uminus ) @ ( B @ c_inter ) ) @ c_uminus ) @ ( A @ c_lessequals ) ) ),
inference(simp,[status(thm)],[4882]) ).
thf(11313,plain,
! [C: $i,B: $i,A: $i] : ( C @ tc_set @ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_inter ) ) @ c_uminus ) @ ( A @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[4934,79]) ).
thf(4787,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( c_UNIV @ ( A @ ( c_emptyset @ ( B @ c_inter ) ) @ c_union ) ) )
!= ( D @ ( F @ ( E @ c_union ) ) ) )
| ( D @ tc_set @ ( D @ ( A @ ( c_UNIV @ ( B @ c_union ) ) @ ( C @ c_union ) ) @ ( F @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[453,1183]) ).
thf(4788,plain,
! [C: $i,B: $i,A: $i] : ( C @ tc_set @ ( C @ ( C @ ( c_UNIV @ ( B @ c_union ) ) @ ( A @ c_union ) ) @ ( c_UNIV @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[4787:[bind(A,$thf( I )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( I )),bind(E,$thf( I @ ( c_emptyset @ ( G @ c_inter ) ) )),bind(F,$thf( c_UNIV ))]]) ).
thf(4852,plain,
! [C: $i,B: $i,A: $i] : ( C @ tc_set @ ( C @ ( C @ ( c_UNIV @ ( B @ c_union ) ) @ ( A @ c_union ) ) @ ( c_UNIV @ c_lessequals ) ) ),
inference(simp,[status(thm)],[4788]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
thf(70,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(71,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(1251,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( E @ tc_set @ ( F @ ( E @ ( D @ ( C @ c_union ) ) @ c_lessequals ) ) ) )
| ( E @ tc_set @ ( F @ ( C @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[60,71]) ).
thf(1252,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( E @ tc_set @ ( F @ ( E @ ( D @ ( C @ c_union ) ) @ c_lessequals ) ) ) )
| ( E @ tc_set @ ( F @ ( C @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1251]) ).
thf(1253,plain,
! [C: $i,B: $i,A: $i] : ( A @ tc_set @ ( A @ ( C @ ( B @ c_union ) ) @ ( B @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[1252:[bind(A,$thf( B @ ( K @ ( J @ c_union ) ) )),bind(B,$thf( B )),bind(C,$thf( J )),bind(D,$thf( K )),bind(E,$thf( B )),bind(F,$thf( B @ ( K @ ( J @ c_union ) ) ))]]) ).
thf(1279,plain,
! [C: $i,B: $i,A: $i] : ( A @ tc_set @ ( A @ ( C @ ( B @ c_union ) ) @ ( B @ c_lessequals ) ) ),
inference(simp,[status(thm)],[1253]) ).
thf(1303,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ ( C @ ( B @ c_union ) ) @ ( B @ c_lessequals ) ) )
!= ( F @ tc_set @ ( G @ ( F @ ( E @ ( D @ c_union ) ) @ c_lessequals ) ) ) )
| ( F @ tc_set @ ( G @ ( E @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1279,67]) ).
thf(1304,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ ( C @ ( B @ c_union ) ) @ ( B @ c_lessequals ) ) )
!= ( F @ tc_set @ ( G @ ( F @ ( E @ ( D @ c_union ) ) @ c_lessequals ) ) ) )
| ( F @ tc_set @ ( G @ ( E @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1303]) ).
thf(1305,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ tc_set @ ( B @ ( A @ ( B @ ( D @ ( C @ c_union ) ) @ c_union ) ) @ ( D @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[1304:[bind(A,$thf( M )),bind(B,$thf( M @ ( O @ ( N @ c_union ) ) )),bind(C,$thf( L )),bind(D,$thf( N )),bind(E,$thf( O )),bind(F,$thf( M )),bind(G,$thf( M @ ( L @ ( M @ ( O @ ( N @ c_union ) ) @ c_union ) ) ))]]) ).
thf(1315,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ tc_set @ ( B @ ( A @ ( B @ ( D @ ( C @ c_union ) ) @ c_union ) ) @ ( D @ c_lessequals ) ) ),
inference(simp,[status(thm)],[1305]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Mutil_Otiling_OUn_0) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(48,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(49,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(lifteq,[status(thm)],[48]) ).
thf(326,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
!= ( G @ tc_set @ ( F @ ( E @ c_in ) ) ) )
| ( G @ tc_set @ ( G @ ( F @ c_Mutil_Otiling ) @ ( G @ ( H @ ( E @ c_union ) ) @ c_in ) ) )
| ~ ( G @ tc_set @ ( G @ ( F @ c_Mutil_Otiling ) @ ( H @ c_in ) ) )
| ~ $true
| ( ( G @ ( H @ ( E @ c_inter ) ) )
!= c_emptyset )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[49,49]) ).
thf(327,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
!= ( G @ tc_set @ ( F @ ( E @ c_in ) ) ) )
| ( G @ tc_set @ ( G @ ( F @ c_Mutil_Otiling ) @ ( G @ ( H @ ( E @ c_union ) ) @ c_in ) ) )
| ~ ( G @ tc_set @ ( G @ ( F @ c_Mutil_Otiling ) @ ( H @ c_in ) ) )
| ( ( G @ ( H @ ( E @ c_inter ) ) )
!= c_emptyset )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[326]) ).
thf(328,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ tc_set @ ( E @ ( E @ ( D @ c_Mutil_Otiling ) @ c_Mutil_Otiling ) @ ( E @ ( A @ ( E @ ( C @ ( B @ c_union ) ) @ c_union ) ) @ c_in ) ) )
| ~ ( E @ tc_set @ ( E @ ( E @ ( D @ c_Mutil_Otiling ) @ c_Mutil_Otiling ) @ ( A @ c_in ) ) )
| ( ( E @ ( A @ ( E @ ( C @ ( B @ c_union ) ) @ c_inter ) ) )
!= c_emptyset )
| ~ ( E @ tc_set @ ( E @ ( D @ c_Mutil_Otiling ) @ ( C @ c_in ) ) )
| ~ ( E @ tc_set @ ( D @ ( B @ c_in ) ) )
| ( ( E @ ( C @ ( B @ c_inter ) ) )
!= c_emptyset ) ),
inference(pattern_uni,[status(thm)],[327:[bind(A,$thf( I )),bind(B,$thf( L )),bind(C,$thf( M )),bind(D,$thf( J )),bind(E,$thf( M @ ( J @ ( I @ c_union ) ) )),bind(F,$thf( M @ ( L @ c_Mutil_Otiling ) )),bind(G,$thf( M )),bind(H,$thf( H ))]]) ).
thf(365,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ tc_set @ ( E @ ( E @ ( D @ c_Mutil_Otiling ) @ c_Mutil_Otiling ) @ ( E @ ( A @ ( E @ ( C @ ( B @ c_union ) ) @ c_union ) ) @ c_in ) ) )
| ~ ( E @ tc_set @ ( E @ ( E @ ( D @ c_Mutil_Otiling ) @ c_Mutil_Otiling ) @ ( A @ c_in ) ) )
| ( ( E @ ( A @ ( E @ ( C @ ( B @ c_union ) ) @ c_inter ) ) )
!= c_emptyset )
| ~ ( E @ tc_set @ ( E @ ( D @ c_Mutil_Otiling ) @ ( C @ c_in ) ) )
| ~ ( E @ tc_set @ ( D @ ( B @ c_in ) ) )
| ( ( E @ ( C @ ( B @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[328]) ).
thf(1,negated_conjecture,
t_a @ tc_set @ ( v_A @ ( v_a @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(31,plain,
t_a @ tc_set @ ( v_A @ ( v_a @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(352,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_union ) ) @ c_in ) ) ) )
| ~ $true
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[49,38]) ).
thf(353,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_union ) ) @ c_in ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[352]) ).
thf(354,plain,
( ~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( v_u @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_A @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_in ) ) )
| ( ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_inter ) ) )
!= c_emptyset ) ),
inference(pattern_uni,[status(thm)],[353:[bind(A,$thf( t_a @ ( v_t @ ( v_a @ c_union ) ) )),bind(B,$thf( v_A )),bind(C,$thf( t_a )),bind(D,$thf( v_u ))]]) ).
thf(9125,plain,
( ~ $true
| ~ ( t_a @ tc_set @ ( v_A @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_in ) ) )
| ( c_emptyset != c_emptyset ) ),
inference(rewrite,[status(thm)],[354,34,37]) ).
thf(9126,plain,
~ ( t_a @ tc_set @ ( v_A @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_in ) ) ),
inference(simp,[status(thm)],[9125]) ).
thf(9148,plain,
( ( ( t_a @ tc_set @ ( v_A @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_A @ ( v_a @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[31,9126]) ).
thf(9149,plain,
( ( t_a @ tc_set @ ( v_A @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( v_A @ ( v_a @ c_in ) ) ) ),
inference(simp,[status(thm)],[9148]) ).
thf(9189,plain,
( ( ( t_a @ tc_set )
!= ( t_a @ tc_set ) )
| ( v_A != v_A )
| ( ( t_a @ ( v_t @ ( v_a @ c_union ) ) )
!= v_a ) ),
inference(simp,[status(thm)],[9149]) ).
thf(9220,plain,
( ( t_a @ ( v_t @ ( v_a @ c_union ) ) )
!= v_a ),
inference(simp,[status(thm)],[9189]) ).
thf(9230,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( c_UNIV @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( c_UNIV != v_a ) ),
inference(paramod_ordered,[status(thm)],[69,9220]) ).
thf(9256,plain,
! [B: $i,A: $i] :
( ( B != t_a )
| ( A != v_t )
| ( c_UNIV != v_a )
| ( c_UNIV != v_a ) ),
inference(simp,[status(thm)],[9230]) ).
thf(9273,plain,
c_UNIV != v_a,
inference(simp,[status(thm)],[9256]) ).
thf(415,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_minus ) ) )
!= ( F @ tc_set @ ( E @ ( D @ c_minus ) ) ) )
| ( ( F @ ( E @ ( C @ ( B @ ( A @ c_inter ) ) @ c_union ) ) )
= ( F @ ( E @ ( D @ c_union ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[86,53]) ).
thf(416,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( C @ ( B @ ( A @ c_inter ) ) @ c_union ) ) )
= ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_union ) ) ) ),
inference(pattern_uni,[status(thm)],[415:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( I )),bind(D,$thf( A )),bind(E,$thf( I @ tc_set @ ( G @ c_uminus ) )),bind(F,$thf( I ))]]) ).
thf(433,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( C @ ( B @ ( A @ c_inter ) ) @ c_union ) ) )
= ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_union ) ) ) ),
inference(simp,[status(thm)],[416]) ).
thf(15814,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_inter ) ) )
!= ( C @ ( B @ ( A @ c_inter ) ) ) )
| ( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( c_emptyset @ c_union ) ) )
= ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_union ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[37,433]) ).
thf(15815,plain,
( ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_union ) ) )
= ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( c_emptyset @ c_union ) ) ) ),
inference(pattern_uni,[status(thm)],[15814:[bind(A,$thf( t_a @ ( v_t @ ( v_a @ c_union ) ) )),bind(B,$thf( v_u )),bind(C,$thf( t_a ))]]) ).
thf(17997,plain,
( ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ ( v_a @ c_union ) ) )
= ( t_a @ tc_set @ ( v_u @ c_uminus ) ) ),
inference(rewrite,[status(thm)],[15815,84,77]) ).
thf(18074,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ ( v_a @ c_union ) ) )
!= ( B @ ( D @ ( C @ c_union ) ) ) )
| ( B @ tc_set @ ( B @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( A @ c_union ) ) @ ( D @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[17997,1183]) ).
thf(18075,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( A @ c_union ) ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[18074:[bind(A,$thf( A )),bind(B,$thf( t_a )),bind(C,$thf( v_a )),bind(D,$thf( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) ))]]) ).
thf(26292,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( A @ c_union ) ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ c_lessequals ) ) )
!= ( D @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_union ) ) @ c_lessequals ) ) ) )
| ( D @ tc_set @ ( E @ ( B @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18075,71]) ).
thf(26293,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( A @ c_union ) ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ c_lessequals ) ) )
!= ( D @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_union ) ) @ c_lessequals ) ) ) )
| ( D @ tc_set @ ( E @ ( B @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[26292]) ).
thf(26294,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( A @ c_union ) ) @ ( v_t @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[26293:[bind(A,$thf( I )),bind(B,$thf( v_t )),bind(C,$thf( t_a @ tc_set @ ( v_u @ c_uminus ) )),bind(D,$thf( t_a )),bind(E,$thf( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( I @ c_union ) ) ))]]) ).
thf(26466,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( A @ c_union ) ) @ ( v_t @ c_lessequals ) ) ),
inference(simp,[status(thm)],[26294]) ).
thf(99,plain,
( ( ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_union ) ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( v_u @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,38]) ).
thf(100,plain,
( ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_union ) ) @ c_in ) ) )
!= ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( v_u @ c_in ) ) ) ),
inference(simp,[status(thm)],[99]) ).
thf(103,plain,
( ( ( t_a @ tc_set )
!= ( t_a @ tc_set ) )
| ( ( t_a @ ( v_A @ c_Mutil_Otiling ) )
!= ( t_a @ ( v_A @ c_Mutil_Otiling ) ) )
| ( ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_union ) ) )
!= v_u ) ),
inference(simp,[status(thm)],[100]) ).
thf(105,plain,
( ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_union ) ) )
!= v_u ),
inference(simp,[status(thm)],[103]) ).
thf(257,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
!= ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_union ) ) ) )
| ( A != v_u ) ),
inference(paramod_ordered,[status(thm)],[84,105]) ).
thf(263,plain,
! [A: $i] :
( ( A != t_a )
| ( v_u != v_u )
| ( ( t_a @ ( v_t @ ( v_a @ c_union ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[257]) ).
thf(276,plain,
( ( t_a @ ( v_t @ ( v_a @ c_union ) ) )
!= c_emptyset ),
inference(simp,[status(thm)],[263]) ).
thf(1719,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_union ) ) )
!= ( E @ ( D @ ( C @ c_union ) ) ) )
| ( ( E @ ( F @ ( A @ c_union ) ) )
= ( E @ ( E @ ( F @ ( D @ c_union ) ) @ ( C @ c_union ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[42,77]) ).
thf(1720,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( A @ c_union ) ) @ ( A @ c_union ) ) )
= ( B @ ( C @ ( A @ c_union ) ) ) ),
inference(pattern_uni,[status(thm)],[1719:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(1813,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( A @ c_union ) ) @ ( A @ c_union ) ) )
= ( B @ ( C @ ( A @ c_union ) ) ) ),
inference(simp,[status(thm)],[1720]) ).
thf(7704,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_union ) ) )
!= ( F @ ( E @ ( F @ ( H @ ( G @ c_union ) ) @ c_union ) ) ) )
| ( F @ tc_set @ ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_union ) ) @ ( H @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,1315]) ).
thf(7705,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ tc_set @ ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_union ) ) @ ( B @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[7704:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( D )),bind(F,$thf( C )),bind(G,$thf( A )),bind(H,$thf( B ))]]) ).
thf(12068,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ ( A @ c_union ) ) @ ( A @ c_union ) ) )
!= ( F @ ( G @ ( E @ c_union ) ) ) )
| ( F @ tc_set @ ( F @ ( B @ ( C @ ( A @ c_union ) ) @ ( D @ c_union ) ) @ ( E @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[1813,7705]) ).
thf(12069,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ tc_set @ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_union ) ) @ ( B @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[12068:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( I )),bind(D,$thf( D )),bind(E,$thf( H )),bind(F,$thf( J )),bind(G,$thf( J @ ( I @ ( H @ c_union ) ) ))]]) ).
thf(12172,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ tc_set @ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_union ) ) @ ( B @ c_lessequals ) ) ),
inference(simp,[status(thm)],[12069]) ).
thf(412,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( ( t_a @ ( v_u @ ( C @ ( B @ ( A @ c_union ) ) @ c_union ) ) )
!= v_u ) ),
inference(paramod_ordered,[status(thm)],[53,105]) ).
thf(420,plain,
! [C: $i,B: $i,A: $i] :
( ( C != t_a )
| ( B != v_t )
| ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
!= v_a )
| ( ( t_a @ ( v_u @ ( C @ ( B @ ( A @ c_union ) ) @ c_union ) ) )
!= v_u ) ),
inference(simp,[status(thm)],[412]) ).
thf(436,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ ( v_t @ ( A @ c_minus ) ) )
!= v_a )
| ( ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( A @ c_union ) ) @ c_union ) ) )
!= v_u ) ),
inference(simp,[status(thm)],[420]) ).
thf(17641,plain,
! [A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( A @ c_inter ) ) )
!= v_a )
| ( ( t_a @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ ( A @ c_union ) ) )
!= v_u ) ),
inference(rewrite,[status(thm)],[436,393,77]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_UNIV @ c_inter ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__left_0) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_UNIV @ c_inter ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_UNIV @ c_inter ) ) )
= A ),
inference(lifteq,[status(thm)],[50]) ).
thf(358,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( c_UNIV @ c_inter ) ) )
!= ( E @ ( F @ ( C @ c_inter ) ) ) )
| ( E @ tc_set @ ( E @ ( D @ c_Mutil_Otiling ) @ ( E @ ( F @ ( C @ c_union ) ) @ c_in ) ) )
| ~ ( E @ tc_set @ ( E @ ( D @ c_Mutil_Otiling ) @ ( F @ c_in ) ) )
| ~ ( E @ tc_set @ ( D @ ( C @ c_in ) ) )
| ( A != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[51,49]) ).
thf(359,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( C @ c_Mutil_Otiling ) @ ( B @ ( A @ ( c_UNIV @ c_union ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( B @ ( C @ c_Mutil_Otiling ) @ ( A @ c_in ) ) )
| ~ ( B @ tc_set @ ( C @ ( c_UNIV @ c_in ) ) )
| ( A != c_emptyset ) ),
inference(pattern_uni,[status(thm)],[358:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( c_UNIV )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(364,plain,
! [B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_Mutil_Otiling ) @ ( A @ ( c_emptyset @ ( c_UNIV @ c_union ) ) @ c_in ) ) )
| ~ ( A @ tc_set @ ( A @ ( B @ c_Mutil_Otiling ) @ ( c_emptyset @ c_in ) ) )
| ~ ( A @ tc_set @ ( B @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[359]) ).
thf(9998,plain,
! [B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_Mutil_Otiling ) @ ( c_UNIV @ c_in ) ) )
| ~ ( A @ tc_set @ ( A @ ( B @ c_Mutil_Otiling ) @ ( c_emptyset @ c_in ) ) )
| ~ ( A @ tc_set @ ( B @ ( c_UNIV @ c_in ) ) ) ),
inference(rewrite,[status(thm)],[364,69]) ).
thf(410,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( C @ ( B @ ( A @ c_union ) ) @ c_union ) ) @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,38]) ).
thf(424,plain,
! [C: $i,B: $i,A: $i] :
( ( C != t_a )
| ( B != v_t )
| ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
!= v_a )
| ~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( C @ ( B @ ( A @ c_union ) ) @ c_union ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[410]) ).
thf(440,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ ( v_t @ ( A @ c_minus ) ) )
!= v_a )
| ~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( A @ c_union ) ) @ c_union ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[424]) ).
thf(19391,plain,
! [A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( A @ c_inter ) ) )
!= v_a )
| ~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(rewrite,[status(thm)],[440,393,77]) ).
thf(7699,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( c_UNIV @ ( A @ ( c_emptyset @ ( B @ c_inter ) ) @ c_union ) ) )
!= ( D @ ( F @ ( E @ c_union ) ) ) )
| ( D @ tc_set @ ( D @ ( C @ ( A @ ( c_UNIV @ ( B @ c_union ) ) @ c_union ) ) @ ( F @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[453,1315]) ).
thf(7700,plain,
! [C: $i,B: $i,A: $i] : ( C @ tc_set @ ( C @ ( A @ ( C @ ( c_UNIV @ ( B @ c_union ) ) @ c_union ) ) @ ( c_UNIV @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[7699:[bind(A,$thf( I )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( I )),bind(E,$thf( I @ ( c_emptyset @ ( G @ c_inter ) ) )),bind(F,$thf( c_UNIV ))]]) ).
thf(7757,plain,
! [C: $i,B: $i,A: $i] : ( C @ tc_set @ ( C @ ( A @ ( C @ ( c_UNIV @ ( B @ c_union ) ) @ c_union ) ) @ ( c_UNIV @ c_lessequals ) ) ),
inference(simp,[status(thm)],[7700]) ).
thf(7791,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( C @ tc_set @ ( A @ c_uminus ) @ ( B @ c_inter ) ) @ ( A @ c_union ) ) )
!= ( F @ ( D @ ( F @ ( c_UNIV @ ( E @ c_union ) ) @ c_union ) ) ) )
| ( F @ tc_set @ ( C @ ( B @ ( A @ c_union ) ) @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[1362,7757]) ).
thf(7792,plain,
! [C: $i,B: $i,A: $i] : ( B @ tc_set @ ( B @ ( A @ ( B @ ( c_UNIV @ ( C @ c_union ) ) @ c_union ) ) @ ( c_UNIV @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[7791:[bind(A,$thf( L @ ( c_UNIV @ ( O @ c_union ) ) )),bind(B,$thf( J )),bind(C,$thf( L )),bind(D,$thf( L @ ( L @ tc_set @ ( L @ ( c_UNIV @ ( O @ c_union ) ) @ c_uminus ) @ ( J @ c_inter ) ) )),bind(E,$thf( O )),bind(F,$thf( L ))]]) ).
thf(7886,plain,
! [C: $i,B: $i,A: $i] : ( B @ tc_set @ ( B @ ( A @ ( B @ ( c_UNIV @ ( C @ c_union ) ) @ c_union ) ) @ ( c_UNIV @ c_lessequals ) ) ),
inference(simp,[status(thm)],[7792]) ).
thf(748,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_UNIV @ c_uminus ) )
!= ( D @ tc_set @ ( B @ c_uminus ) ) )
| ( ( D @ ( C @ ( c_emptyset @ c_union ) ) )
= ( D @ tc_set @ ( D @ ( D @ tc_set @ ( C @ c_uminus ) @ ( B @ c_inter ) ) @ c_uminus ) ) ) ),
inference(paramod_ordered,[status(thm)],[79,715]) ).
thf(749,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_emptyset @ c_union ) ) )
= ( A @ tc_set @ ( A @ ( A @ tc_set @ ( B @ c_uminus ) @ ( c_UNIV @ c_inter ) ) @ c_uminus ) ) ),
inference(pattern_uni,[status(thm)],[748:[bind(A,$thf( A )),bind(B,$thf( c_UNIV )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(774,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_emptyset @ c_union ) ) )
= ( A @ tc_set @ ( A @ ( A @ tc_set @ ( B @ c_uminus ) @ ( c_UNIV @ c_inter ) ) @ c_uminus ) ) ),
inference(simp,[status(thm)],[749]) ).
thf(6340,plain,
! [B: $i,A: $i] :
( ( A @ tc_set @ ( A @ tc_set @ ( B @ c_uminus ) @ c_uminus ) )
= B ),
inference(rewrite,[status(thm)],[774,51,84]) ).
thf(2,negated_conjecture,
( ( t_a @ ( v_t @ ( v_a @ c_inter ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(33,plain,
( ( t_a @ ( v_t @ ( v_a @ c_inter ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(36,plain,
( ( t_a @ ( v_t @ ( v_a @ c_inter ) ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[33]) ).
thf(15933,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ ( v_t @ ( v_a @ c_inter ) ) )
!= ( C @ ( B @ ( A @ c_inter ) ) ) )
| ( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( c_emptyset @ c_union ) ) )
= ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_union ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,433]) ).
thf(15934,plain,
( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( c_emptyset @ c_union ) ) )
= ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) ) ),
inference(pattern_uni,[status(thm)],[15933:[bind(A,$thf( v_a )),bind(B,$thf( v_t )),bind(C,$thf( t_a ))]]) ).
thf(16183,plain,
( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) )
= ( t_a @ tc_set @ ( v_t @ c_uminus ) ) ),
inference(rewrite,[status(thm)],[15934,84]) ).
thf(16225,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( A @ ( C @ ( B @ c_union ) ) ) )
| ( A @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( B @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[16183,1279]) ).
thf(16226,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[16225:[bind(A,$thf( t_a )),bind(B,$thf( v_a )),bind(C,$thf( t_a @ tc_set @ ( v_t @ c_uminus ) ))]]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( A @ ( D @ c_union ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_2) ).
thf(54,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( A @ ( D @ c_union ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(55,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( A @ ( D @ c_union ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[54]) ).
thf(539,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( E @ tc_set @ ( D @ ( C @ c_lessequals ) ) ) )
| ( E @ tc_set @ ( D @ ( E @ ( C @ ( F @ c_union ) ) @ c_lessequals ) ) )
| ~ ( E @ tc_set @ ( D @ ( F @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[60,55]) ).
thf(540,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( E @ tc_set @ ( D @ ( C @ c_lessequals ) ) ) )
| ( E @ tc_set @ ( D @ ( E @ ( C @ ( F @ c_union ) ) @ c_lessequals ) ) )
| ~ ( E @ tc_set @ ( D @ ( F @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[539]) ).
thf(541,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( B @ ( A @ ( C @ c_union ) ) @ c_lessequals ) ) )
| ~ ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[540:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(568,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( B @ ( A @ ( C @ c_union ) ) @ c_lessequals ) ) )
| ~ ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[541]) ).
thf(34132,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ ( C @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16226,568]) ).
thf(34133,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ ( C @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[34132]) ).
thf(34134,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[34133:[bind(A,$thf( t_a @ tc_set @ ( v_t @ c_uminus ) )),bind(B,$thf( t_a )),bind(C,$thf( v_a ))]]) ).
thf(1497,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
!= ( D @ tc_set @ ( B @ c_uminus ) ) )
| ( ( D @ ( C @ ( c_UNIV @ c_union ) ) )
= ( D @ tc_set @ ( D @ ( D @ tc_set @ ( C @ c_uminus ) @ ( B @ c_inter ) ) @ c_uminus ) ) ) ),
inference(paramod_ordered,[status(thm)],[1494,715]) ).
thf(1498,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_UNIV @ c_union ) ) )
= ( A @ tc_set @ ( A @ ( A @ tc_set @ ( B @ c_uminus ) @ ( c_emptyset @ c_inter ) ) @ c_uminus ) ) ),
inference(pattern_uni,[status(thm)],[1497:[bind(A,$thf( A )),bind(B,$thf( c_emptyset )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(1520,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( c_UNIV @ c_union ) ) )
= ( A @ tc_set @ ( A @ ( A @ tc_set @ ( B @ c_uminus ) @ ( c_emptyset @ c_inter ) ) @ c_uminus ) ) ),
inference(simp,[status(thm)],[1498]) ).
thf(9070,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
= c_UNIV ),
inference(rewrite,[status(thm)],[1520,1122,69]) ).
thf(16263,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( C @ ( B @ ( A @ c_union ) ) ) )
| ( ( C @ ( D @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_union ) ) )
= ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_union ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[16183,77]) ).
thf(16264,plain,
! [A: $i] :
( ( t_a @ ( t_a @ ( A @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_union ) ) @ ( v_a @ c_union ) ) )
= ( t_a @ ( A @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_union ) ) ) ),
inference(pattern_uni,[status(thm)],[16263:[bind(A,$thf( v_a )),bind(B,$thf( t_a @ tc_set @ ( v_t @ c_uminus ) )),bind(C,$thf( t_a )),bind(D,$thf( D ))]]) ).
thf(16538,plain,
! [A: $i] :
( ( t_a @ ( t_a @ ( A @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_union ) ) @ ( v_a @ c_union ) ) )
= ( t_a @ ( A @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_union ) ) ) ),
inference(simp,[status(thm)],[16264]) ).
thf(28898,plain,
! [A: $i] :
( ( t_a @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_union ) ) )
= ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) ) ),
inference(rewrite,[status(thm)],[16538,715]) ).
thf(29148,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
!= ( t_a @ tc_set @ ( B @ c_uminus ) ) )
| ( ( t_a @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_union ) ) )
= ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( B @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) ) ) ),
inference(paramod_ordered,[status(thm)],[9070,28898]) ).
thf(29149,plain,
( ( t_a @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_union ) ) )
= ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( c_emptyset @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) ) ),
inference(pattern_uni,[status(thm)],[29148:[bind(A,$thf( t_a )),bind(B,$thf( c_emptyset ))]]) ).
thf(29516,plain,
( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) )
= ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) ) ),
inference(rewrite,[status(thm)],[29149,3462,9070]) ).
thf(34599,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[34134,29516]) ).
thf(542,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( E @ tc_set @ ( D @ ( F @ c_lessequals ) ) ) )
| ( E @ tc_set @ ( D @ ( E @ ( C @ ( F @ c_union ) ) @ c_lessequals ) ) )
| ~ $true
| ~ ( E @ tc_set @ ( D @ ( C @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[60,55]) ).
thf(543,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( E @ tc_set @ ( D @ ( F @ c_lessequals ) ) ) )
| ( E @ tc_set @ ( D @ ( E @ ( C @ ( F @ c_union ) ) @ c_lessequals ) ) )
| ~ ( E @ tc_set @ ( D @ ( C @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[542]) ).
thf(544,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) )
| ~ ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[543:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(34638,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34599,544]) ).
thf(34639,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[34638]) ).
thf(34640,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[34639:[bind(A,$thf( t_a @ tc_set @ ( v_t @ c_uminus ) )),bind(B,$thf( t_a )),bind(C,$thf( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) ))]]) ).
thf(41359,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[34640,715]) ).
thf(41390,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ tc_set @ ( B @ c_uminus ) @ c_uminus ) )
!= ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_uminus ) ) )
| ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( B @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[6340,41359]) ).
thf(41391,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[41390:[bind(A,$thf( t_a )),bind(B,$thf( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) ))]]) ).
thf(41674,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( v_t @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[41391,3462]) ).
thf(41720,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( v_t @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41674,544]) ).
thf(41721,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( v_t @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[41720]) ).
thf(41722,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( v_t @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[41721:[bind(A,$thf( t_a @ tc_set @ ( v_t @ c_uminus ) )),bind(B,$thf( t_a )),bind(C,$thf( t_a @ tc_set @ ( t_a @ ( v_t @ ( v_t @ c_inter ) ) @ c_uminus ) ))]]) ).
thf(43483,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( v_t @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[41722,715]) ).
thf(721,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ tc_set @ ( A @ c_uminus ) @ c_union ) ) )
!= ( E @ ( D @ ( D @ c_union ) ) ) )
| ( ( C @ tc_set @ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_inter ) ) @ c_uminus ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[715,42]) ).
thf(722,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( B @ tc_set @ ( B @ tc_set @ ( A @ c_uminus ) @ c_uminus ) @ ( A @ c_inter ) ) @ c_uminus ) )
= ( B @ tc_set @ ( A @ c_uminus ) ) ),
inference(pattern_uni,[status(thm)],[721:[bind(A,$thf( I )),bind(B,$thf( K @ tc_set @ ( I @ c_uminus ) )),bind(C,$thf( K )),bind(D,$thf( K @ tc_set @ ( I @ c_uminus ) )),bind(E,$thf( K ))]]) ).
thf(767,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( B @ tc_set @ ( B @ tc_set @ ( A @ c_uminus ) @ c_uminus ) @ ( A @ c_inter ) ) @ c_uminus ) )
= ( B @ tc_set @ ( A @ c_uminus ) ) ),
inference(simp,[status(thm)],[722]) ).
thf(63385,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( A @ ( A @ c_inter ) ) @ c_uminus ) )
= ( B @ tc_set @ ( A @ c_uminus ) ) ),
inference(rewrite,[status(thm)],[767,6340]) ).
thf(63387,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[43483,63385]) ).
thf(63955,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( v_t @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[63387,6340]) ).
thf(64004,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( v_t @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[63955,544]) ).
thf(64005,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( v_t @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[64004]) ).
thf(64006,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( v_t @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[64005:[bind(A,$thf( t_a @ tc_set @ ( v_t @ c_uminus ) )),bind(B,$thf( t_a )),bind(C,$thf( t_a @ tc_set @ ( t_a @ ( v_t @ ( v_t @ c_inter ) ) @ c_uminus ) ))]]) ).
thf(64164,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( v_t @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[64006,715]) ).
thf(397,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[53,276]) ).
thf(429,plain,
! [C: $i,B: $i,A: $i] :
( ( C != t_a )
| ( B != v_t )
| ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
!= v_a )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[397]) ).
thf(445,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ ( v_t @ ( A @ c_minus ) ) )
!= v_a )
| ( ( t_a @ ( v_t @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[429]) ).
thf(21766,plain,
! [A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( A @ c_inter ) ) )
!= v_a )
| ( ( t_a @ ( v_t @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(rewrite,[status(thm)],[445,393]) ).
thf(398,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_union ) ) )
!= ( E @ ( D @ ( c_emptyset @ c_union ) ) ) )
| ( ( C @ ( B @ ( A @ c_union ) ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[53,84]) ).
thf(419,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C != E )
| ( B != D )
| ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
!= c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
= D ) ),
inference(simp,[status(thm)],[398]) ).
thf(435,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
!= c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
= B ) ),
inference(simp,[status(thm)],[419]) ).
thf(17270,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_inter ) ) )
!= c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
= B ) ),
inference(rewrite,[status(thm)],[435,393]) ).
thf(1699,plain,
( ( t_a @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ ( v_a @ c_union ) ) )
!= v_u ),
inference(rewrite,[status(thm)],[105,77]) ).
thf(1824,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_union ) ) )
!= ( t_a @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ ( v_a @ c_union ) ) ) )
| ( A != v_u ) ),
inference(paramod_ordered,[status(thm)],[42,1699]) ).
thf(1835,plain,
! [A: $i] :
( ( A != t_a )
| ( ( t_a @ ( v_u @ ( v_t @ c_union ) ) )
!= v_u )
| ( v_u != v_a ) ),
inference(simp,[status(thm)],[1824]) ).
thf(1854,plain,
( ( ( t_a @ ( v_u @ ( v_t @ c_union ) ) )
!= v_u )
| ( v_u != v_a ) ),
inference(simp,[status(thm)],[1835]) ).
thf(17511,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_union ) ) )
!= ( t_a @ ( v_u @ ( v_t @ c_union ) ) ) )
| ( B != v_u )
| ( v_u != v_a )
| ( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[17270,1854]) ).
thf(17512,plain,
( ( v_u != v_u )
| ( v_u != v_a )
| ( ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(pattern_uni,[status(thm)],[17511:[bind(A,$thf( v_t )),bind(B,$thf( v_u )),bind(C,$thf( t_a ))]]) ).
thf(17577,plain,
( ( v_u != v_a )
| ( ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[17512]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( c_UNIV @ c_union ) ) )
!= ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_union ) ) ) )
| ~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( c_UNIV @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[69,38]) ).
thf(136,plain,
! [B: $i,A: $i] :
( ( B != t_a )
| ( A != v_u )
| ( ( t_a @ ( v_t @ ( v_a @ c_union ) ) )
!= c_UNIV )
| ~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[126]) ).
thf(142,plain,
( ( ( t_a @ ( v_t @ ( v_a @ c_union ) ) )
!= c_UNIV )
| ~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[136]) ).
thf(584,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( c_UNIV @ ( A @ ( c_emptyset @ ( B @ c_inter ) ) @ c_union ) ) )
!= ( E @ ( D @ ( E @ tc_set @ ( D @ ( C @ c_minus ) ) @ c_union ) ) ) )
| ( ( A @ ( c_UNIV @ ( B @ c_union ) ) )
= ( E @ ( D @ ( C @ c_union ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[453,53]) ).
thf(615,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A != E )
| ( c_UNIV != D )
| ( ( A @ ( c_emptyset @ ( B @ c_inter ) ) )
!= ( E @ tc_set @ ( D @ ( C @ c_minus ) ) ) )
| ( ( A @ ( c_UNIV @ ( B @ c_union ) ) )
= ( E @ ( D @ ( C @ c_union ) ) ) ) ),
inference(simp,[status(thm)],[584]) ).
thf(641,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_emptyset @ ( A @ c_inter ) ) )
!= ( C @ tc_set @ ( c_UNIV @ ( B @ c_minus ) ) ) )
| ( ( C @ ( c_UNIV @ ( A @ c_union ) ) )
= ( C @ ( c_UNIV @ ( B @ c_union ) ) ) ) ),
inference(simp,[status(thm)],[615]) ).
thf(49286,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_emptyset @ ( A @ c_inter ) ) )
!= ( C @ ( C @ tc_set @ ( c_UNIV @ c_uminus ) @ ( B @ c_inter ) ) ) )
| ( ( C @ ( c_UNIV @ ( A @ c_union ) ) )
= ( C @ ( c_UNIV @ ( B @ c_union ) ) ) ) ),
inference(rewrite,[status(thm)],[641,393]) ).
thf(18150,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ ( v_a @ c_union ) ) )
!= ( B @ ( C @ ( A @ c_union ) ) ) )
| ( ( B @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( A @ c_union ) ) )
= ( B @ ( C @ ( A @ c_union ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[17997,1813]) ).
thf(18151,plain,
( ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ ( v_a @ c_union ) ) )
= ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) ) ),
inference(pattern_uni,[status(thm)],[18150:[bind(A,$thf( v_a )),bind(B,$thf( t_a )),bind(C,$thf( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) ))]]) ).
thf(20205,plain,
( ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) )
= ( t_a @ tc_set @ ( v_u @ c_uminus ) ) ),
inference(rewrite,[status(thm)],[18151,17997]) ).
thf(20295,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( C @ ( B @ ( A @ c_union ) ) ) )
| ( ( C @ ( D @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_union ) ) )
= ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_union ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[20205,77]) ).
thf(20296,plain,
! [A: $i] :
( ( t_a @ ( t_a @ ( A @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_union ) ) @ ( v_a @ c_union ) ) )
= ( t_a @ ( A @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_union ) ) ) ),
inference(pattern_uni,[status(thm)],[20295:[bind(A,$thf( v_a )),bind(B,$thf( t_a @ tc_set @ ( v_u @ c_uminus ) )),bind(C,$thf( t_a )),bind(D,$thf( D ))]]) ).
thf(20556,plain,
! [A: $i] :
( ( t_a @ ( t_a @ ( A @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_union ) ) @ ( v_a @ c_union ) ) )
= ( t_a @ ( A @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_union ) ) ) ),
inference(simp,[status(thm)],[20296]) ).
thf(44635,plain,
! [A: $i] :
( ( t_a @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_union ) ) )
= ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) ) ),
inference(rewrite,[status(thm)],[20556,715]) ).
thf(44918,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
!= ( t_a @ tc_set @ ( B @ c_uminus ) ) )
| ( ( t_a @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_union ) ) )
= ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( B @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) ) ) ),
inference(paramod_ordered,[status(thm)],[9070,44635]) ).
thf(44919,plain,
( ( t_a @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_union ) ) )
= ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( c_emptyset @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) ) ),
inference(pattern_uni,[status(thm)],[44918:[bind(A,$thf( t_a )),bind(B,$thf( c_emptyset ))]]) ).
thf(45340,plain,
( ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) )
= ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_uminus ) ) ),
inference(rewrite,[status(thm)],[44919,3462,9070]) ).
thf(45350,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( B @ ( D @ ( C @ c_union ) ) ) )
| ( B @ tc_set @ ( B @ ( A @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_union ) ) @ ( D @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[45340,1315]) ).
thf(45351,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ ( A @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_union ) ) @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[45350:[bind(A,$thf( A )),bind(B,$thf( t_a )),bind(C,$thf( v_a )),bind(D,$thf( t_a @ tc_set @ ( v_u @ c_uminus ) ))]]) ).
thf(52204,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[45351,715]) ).
thf(29524,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( B @ ( D @ ( C @ c_union ) ) ) )
| ( B @ tc_set @ ( B @ ( A @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_union ) ) @ ( D @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[29516,1315]) ).
thf(29525,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ ( A @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_union ) ) @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[29524:[bind(A,$thf( A )),bind(B,$thf( t_a )),bind(C,$thf( v_a )),bind(D,$thf( t_a @ tc_set @ ( v_t @ c_uminus ) ))]]) ).
thf(37736,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[29525,715]) ).
thf(37768,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ tc_set @ ( B @ c_uminus ) @ c_uminus ) )
!= ( t_a @ tc_set @ ( C @ c_uminus ) ) )
| ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( B @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[6340,37736]) ).
thf(37769,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( A @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[37768:[bind(A,$thf( t_a )),bind(B,$thf( D )),bind(C,$thf( t_a @ tc_set @ ( D @ c_uminus ) ))]]) ).
thf(37982,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( A @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[37769]) ).
thf(39670,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( A @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[37982,3462]) ).
thf(1741,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_union ) ) )
!= ( E @ ( G @ ( F @ c_union ) ) ) )
| ( E @ tc_set @ ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_union ) ) @ ( G @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,1079]) ).
thf(1742,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ tc_set @ ( D @ ( D @ ( A @ ( C @ c_union ) ) @ ( B @ c_union ) ) @ ( A @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[1741:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( D )),bind(E,$thf( J )),bind(F,$thf( J @ ( I @ ( H @ c_union ) ) )),bind(G,$thf( D ))]]) ).
thf(1782,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ tc_set @ ( D @ ( D @ ( A @ ( C @ c_union ) ) @ ( B @ c_union ) ) @ ( A @ c_lessequals ) ) ),
inference(simp,[status(thm)],[1742]) ).
thf(18022,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ ( v_a @ c_union ) ) )
!= ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_union ) ) ) )
| ( D @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( B @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[17997,12172]) ).
thf(18023,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[18022:[bind(A,$thf( v_a )),bind(B,$thf( v_t )),bind(C,$thf( t_a @ tc_set @ ( v_u @ c_uminus ) )),bind(D,$thf( t_a ))]]) ).
thf(559,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( C @ ( A @ ( D @ c_union ) ) @ c_lessequals ) ) )
!= ( G @ tc_set @ ( F @ ( E @ c_lessequals ) ) ) )
| ( G @ tc_set @ ( F @ ( G @ ( E @ ( H @ c_union ) ) @ c_lessequals ) ) )
| ~ ( G @ tc_set @ ( F @ ( H @ c_lessequals ) ) )
| ~ $true
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[55,55]) ).
thf(560,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( C @ ( A @ ( D @ c_union ) ) @ c_lessequals ) ) )
!= ( G @ tc_set @ ( F @ ( E @ c_lessequals ) ) ) )
| ( G @ tc_set @ ( F @ ( G @ ( E @ ( H @ c_union ) ) @ c_lessequals ) ) )
| ~ ( G @ tc_set @ ( F @ ( H @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[559]) ).
thf(561,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ tc_set @ ( A @ ( E @ ( E @ ( D @ ( C @ c_union ) ) @ ( B @ c_union ) ) @ c_lessequals ) ) )
| ~ ( E @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( E @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( E @ tc_set @ ( A @ ( D @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[560:[bind(A,$thf( J )),bind(B,$thf( B )),bind(C,$thf( K )),bind(D,$thf( I )),bind(E,$thf( K @ ( J @ ( I @ c_union ) ) )),bind(F,$thf( B )),bind(G,$thf( K ))]]) ).
thf(565,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ tc_set @ ( A @ ( E @ ( E @ ( D @ ( C @ c_union ) ) @ ( B @ c_union ) ) @ c_lessequals ) ) )
| ~ ( E @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( E @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( E @ tc_set @ ( A @ ( D @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[561]) ).
thf(405,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_union ) ) )
!= ( E @ ( c_emptyset @ ( D @ c_union ) ) ) )
| ( ( C @ ( B @ ( A @ c_union ) ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[53,46]) ).
thf(406,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_emptyset @ ( A @ c_minus ) ) )
= ( B @ ( c_emptyset @ ( A @ c_union ) ) ) ),
inference(pattern_uni,[status(thm)],[405:[bind(A,$thf( F )),bind(B,$thf( c_emptyset )),bind(C,$thf( I )),bind(D,$thf( I @ tc_set @ ( c_emptyset @ ( F @ c_minus ) ) )),bind(E,$thf( I ))]]) ).
thf(449,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_emptyset @ ( A @ c_minus ) ) )
= ( B @ ( c_emptyset @ ( A @ c_union ) ) ) ),
inference(simp,[status(thm)],[406]) ).
thf(474,plain,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_inter ) ) )
= A ),
inference(rewrite,[status(thm)],[449,392,46]) ).
thf(477,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_inter ) ) )
!= ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_inter ) ) ) )
| ( A = c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[474,37]) ).
thf(490,plain,
! [B: $i,A: $i] :
( ( B != t_a )
| ( c_UNIV != v_u )
| ( A
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( A = c_emptyset ) ),
inference(simp,[status(thm)],[477]) ).
thf(497,plain,
( ( c_UNIV != v_u )
| ( ( t_a @ ( v_t @ ( v_a @ c_union ) ) )
= c_emptyset ) ),
inference(simp,[status(thm)],[490]) ).
thf(4948,plain,
c_UNIV != v_u,
inference(simplifyReflect,[status(thm)],[497,276]) ).
thf(18054,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ ( v_a @ c_union ) ) )
!= ( A @ ( C @ ( B @ c_union ) ) ) )
| ( A @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( B @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[17997,1279]) ).
thf(18055,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[18054:[bind(A,$thf( t_a )),bind(B,$thf( v_a )),bind(C,$thf( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) ))]]) ).
thf(34106,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ ( C @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18055,568]) ).
thf(34107,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ ( C @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[34106]) ).
thf(34108,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[34107:[bind(A,$thf( t_a @ tc_set @ ( v_u @ c_uminus ) )),bind(B,$thf( t_a )),bind(C,$thf( v_a ))]]) ).
thf(34341,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[34108,20205]) ).
thf(16207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( D @ ( C @ ( B @ c_union ) ) ) )
| ( D @ tc_set @ ( D @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( A @ c_union ) ) @ ( B @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[16183,12172]) ).
thf(16208,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( A @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[16207:[bind(A,$thf( A )),bind(B,$thf( v_a )),bind(C,$thf( t_a @ tc_set @ ( v_t @ c_uminus ) )),bind(D,$thf( t_a ))]]) ).
thf(17019,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ tc_set @ ( A @ c_uminus ) @ c_union ) ) )
!= ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( D @ c_union ) ) ) )
| ( t_a @ tc_set @ ( C @ tc_set @ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[715,16208]) ).
thf(17020,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_uminus ) @ ( A @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[17019:[bind(A,$thf( E )),bind(B,$thf( t_a @ tc_set @ ( v_t @ c_uminus ) )),bind(C,$thf( t_a )),bind(D,$thf( t_a @ tc_set @ ( E @ c_uminus ) ))]]) ).
thf(17138,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_uminus ) @ ( A @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(simp,[status(thm)],[17020]) ).
thf(22475,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( v_t @ ( A @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[17138,6340]) ).
thf(22480,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( c_emptyset @ c_inter ) ) )
!= ( t_a @ ( v_t @ ( C @ c_inter ) ) ) )
| ( t_a @ tc_set @ ( t_a @ tc_set @ ( c_emptyset @ c_uminus ) @ ( v_a @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[1122,22475]) ).
thf(22481,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( c_emptyset @ c_uminus ) @ ( v_a @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[22480:[bind(A,$thf( v_t )),bind(B,$thf( t_a )),bind(C,$thf( c_emptyset ))]]) ).
thf(22575,plain,
t_a @ tc_set @ ( c_UNIV @ ( v_a @ c_lessequals ) ),
inference(rewrite,[status(thm)],[22481,9070]) ).
thf(27,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/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(80,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)],[27]) ).
thf(81,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)],[80]) ).
thf(82,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)],[81]) ).
thf(22586,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( c_UNIV @ ( v_a @ c_lessequals ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ $true
| ( B = A ) ),
inference(paramod_ordered,[status(thm)],[22575,82]) ).
thf(22587,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( c_UNIV @ ( v_a @ c_lessequals ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ( B = A ) ),
inference(simp,[status(thm)],[22586]) ).
thf(22588,plain,
( ~ ( t_a @ tc_set @ ( v_a @ ( c_UNIV @ c_lessequals ) ) )
| ( c_UNIV = v_a ) ),
inference(pattern_uni,[status(thm)],[22587:[bind(A,$thf( v_a )),bind(B,$thf( c_UNIV )),bind(C,$thf( t_a ))]]) ).
thf(22621,plain,
~ ( t_a @ tc_set @ ( v_a @ ( c_UNIV @ c_lessequals ) ) ),
inference(simplifyReflect,[status(thm)],[22588,9273]) ).
thf(34351,plain,
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( v_a @ ( c_UNIV @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34341,22621]) ).
thf(34352,plain,
( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( v_a @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[34351]) ).
thf(34433,plain,
( ( ( t_a @ tc_set )
!= ( t_a @ tc_set ) )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= v_a )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[34352]) ).
thf(34442,plain,
( ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= v_a )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[34433]) ).
thf(347,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_inter ) ) )
!= ( C @ ( D @ ( A @ c_inter ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( c_emptyset != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[37,49]) ).
thf(348,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_inter ) ) )
!= ( C @ ( D @ ( A @ c_inter ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[347]) ).
thf(349,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( t_a @ ( A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_union ) ) @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( t_a @ ( A @ c_Mutil_Otiling ) @ ( v_u @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( A @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[348:[bind(A,$thf( t_a @ ( v_t @ ( v_a @ c_union ) ) )),bind(B,$thf( B )),bind(C,$thf( t_a )),bind(D,$thf( v_u ))]]) ).
thf(372,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( t_a @ ( A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_union ) ) @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( t_a @ ( A @ c_Mutil_Otiling ) @ ( v_u @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( A @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[349]) ).
thf(13611,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( t_a @ ( A @ c_Mutil_Otiling ) @ ( t_a @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ ( v_a @ c_union ) ) @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( t_a @ ( A @ c_Mutil_Otiling ) @ ( v_u @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( A @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_in ) ) ) ),
inference(rewrite,[status(thm)],[372,77]) ).
thf(200,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_union ) ) )
!= ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_union ) ) ) )
| ( A != v_u ) ),
inference(paramod_ordered,[status(thm)],[42,105]) ).
thf(217,plain,
! [A: $i] :
( ( A != t_a )
| ( v_u != v_u )
| ( ( t_a @ ( v_t @ ( v_a @ c_union ) ) )
!= v_u ) ),
inference(simp,[status(thm)],[200]) ).
thf(226,plain,
( ( t_a @ ( v_t @ ( v_a @ c_union ) ) )
!= v_u ),
inference(simp,[status(thm)],[217]) ).
thf(17464,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( B != v_u )
| ( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[17270,226]) ).
thf(17465,plain,
( ( v_u != v_t )
| ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_inter ) ) )
!= c_emptyset ) ),
inference(pattern_uni,[status(thm)],[17464:[bind(A,$thf( v_a )),bind(B,$thf( v_t )),bind(C,$thf( t_a ))]]) ).
thf(20168,plain,
( ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_inter ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_inter ) ) ) )
| ( v_u != v_t )
| ( c_emptyset != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[36,17465]) ).
thf(20169,plain,
( ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_inter ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_inter ) ) ) )
| ( v_u != v_t ) ),
inference(simp,[status(thm)],[20168]) ).
thf(20180,plain,
( ( t_a != t_a )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= v_t )
| ( v_a != v_a )
| ( v_u != v_t ) ),
inference(simp,[status(thm)],[20169]) ).
thf(20191,plain,
( ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= v_t )
| ( v_u != v_t ) ),
inference(simp,[status(thm)],[20180]) ).
thf(30172,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16226,544]) ).
thf(30173,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[30172]) ).
thf(30174,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ ( v_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[30173:[bind(A,$thf( t_a @ tc_set @ ( v_t @ c_uminus ) )),bind(B,$thf( t_a )),bind(C,$thf( v_a ))]]) ).
thf(30833,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_a @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[30174,715]) ).
thf(30854,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_a @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[30833,544]) ).
thf(30855,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_a @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[30854]) ).
thf(30856,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_a @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[30855:[bind(A,$thf( t_a @ tc_set @ ( v_t @ c_uminus ) )),bind(B,$thf( t_a )),bind(C,$thf( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_a @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) ))]]) ).
thf(60772,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_a @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[30856,715]) ).
thf(1300,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ ( C @ ( B @ c_union ) ) @ ( B @ c_lessequals ) ) )
!= ( F @ tc_set @ ( G @ ( F @ ( E @ ( D @ c_union ) ) @ c_lessequals ) ) ) )
| ( F @ tc_set @ ( G @ ( D @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1279,71]) ).
thf(1301,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ ( C @ ( B @ c_union ) ) @ ( B @ c_lessequals ) ) )
!= ( F @ tc_set @ ( G @ ( F @ ( E @ ( D @ c_union ) ) @ c_lessequals ) ) ) )
| ( F @ tc_set @ ( G @ ( D @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1300]) ).
thf(1302,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ tc_set @ ( B @ ( A @ ( B @ ( D @ ( C @ c_union ) ) @ c_union ) ) @ ( C @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[1301:[bind(A,$thf( M )),bind(B,$thf( M @ ( O @ ( N @ c_union ) ) )),bind(C,$thf( L )),bind(D,$thf( N )),bind(E,$thf( O )),bind(F,$thf( M )),bind(G,$thf( M @ ( L @ ( M @ ( O @ ( N @ c_union ) ) @ c_union ) ) ))]]) ).
thf(1313,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ tc_set @ ( B @ ( A @ ( B @ ( D @ ( C @ c_union ) ) @ c_union ) ) @ ( C @ c_lessequals ) ) ),
inference(simp,[status(thm)],[1302]) ).
thf(29563,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( B @ ( D @ ( C @ c_union ) ) ) )
| ( B @ tc_set @ ( B @ ( A @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_union ) ) @ ( C @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[29516,1313]) ).
thf(29564,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ ( A @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[29563:[bind(A,$thf( A )),bind(B,$thf( t_a )),bind(C,$thf( v_a )),bind(D,$thf( t_a @ tc_set @ ( v_t @ c_uminus ) ))]]) ).
thf(31913,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[29564,715]) ).
thf(588,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( c_UNIV @ ( A @ ( c_emptyset @ ( B @ c_inter ) ) @ c_union ) ) )
!= ( E @ ( F @ ( C @ c_union ) ) ) )
| ( E @ tc_set @ ( E @ ( D @ c_Mutil_Otiling ) @ ( A @ ( c_UNIV @ ( B @ c_union ) ) @ c_in ) ) )
| ~ ( E @ tc_set @ ( E @ ( D @ c_Mutil_Otiling ) @ ( F @ c_in ) ) )
| ~ ( E @ tc_set @ ( D @ ( C @ c_in ) ) )
| ( ( E @ ( F @ ( C @ c_inter ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[453,49]) ).
thf(589,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( A @ c_Mutil_Otiling ) @ ( C @ ( c_UNIV @ ( B @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( C @ ( A @ c_Mutil_Otiling ) @ ( c_UNIV @ c_in ) ) )
| ~ ( C @ tc_set @ ( A @ ( C @ ( c_emptyset @ ( B @ c_inter ) ) @ c_in ) ) )
| ( ( C @ ( c_UNIV @ ( C @ ( c_emptyset @ ( B @ c_inter ) ) @ c_inter ) ) )
!= c_emptyset ) ),
inference(pattern_uni,[status(thm)],[588:[bind(A,$thf( I )),bind(B,$thf( G )),bind(C,$thf( I @ ( c_emptyset @ ( G @ c_inter ) ) )),bind(D,$thf( D )),bind(E,$thf( I )),bind(F,$thf( c_UNIV ))]]) ).
thf(622,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( A @ c_Mutil_Otiling ) @ ( C @ ( c_UNIV @ ( B @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( C @ ( A @ c_Mutil_Otiling ) @ ( c_UNIV @ c_in ) ) )
| ~ ( C @ tc_set @ ( A @ ( C @ ( c_emptyset @ ( B @ c_inter ) ) @ c_in ) ) )
| ( ( C @ ( c_UNIV @ ( C @ ( c_emptyset @ ( B @ c_inter ) ) @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[589]) ).
thf(35774,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( A @ c_Mutil_Otiling ) @ ( C @ ( c_UNIV @ ( B @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( C @ ( A @ c_Mutil_Otiling ) @ ( c_UNIV @ c_in ) ) )
| ~ ( C @ tc_set @ ( A @ ( C @ ( c_emptyset @ ( B @ c_inter ) ) @ c_in ) ) )
| ( ( C @ ( c_emptyset @ ( B @ c_inter ) ) )
!= c_emptyset ) ),
inference(rewrite,[status(thm)],[622,3462]) ).
thf(41729,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( v_t @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ ( C @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41674,568]) ).
thf(41730,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( v_t @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ ( C @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[41729]) ).
thf(41731,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( v_t @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[41730:[bind(A,$thf( t_a @ tc_set @ ( v_t @ c_uminus ) )),bind(B,$thf( t_a )),bind(C,$thf( t_a @ tc_set @ ( t_a @ ( v_t @ ( v_t @ c_inter ) ) @ c_uminus ) ))]]) ).
thf(44060,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_uminus ) @ ( t_a @ ( v_t @ ( v_t @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[41731,715]) ).
thf(20250,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( B @ ( D @ ( C @ c_union ) ) ) )
| ( B @ tc_set @ ( B @ ( A @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_union ) ) @ ( C @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[20205,1313]) ).
thf(20251,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ ( A @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[20250:[bind(A,$thf( A )),bind(B,$thf( t_a )),bind(C,$thf( v_a )),bind(D,$thf( t_a @ tc_set @ ( v_u @ c_uminus ) ))]]) ).
thf(21092,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[20251,715]) ).
thf(404,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( ( t_a @ ( v_u @ ( C @ ( B @ ( A @ c_union ) ) @ c_inter ) ) )
= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[53,37]) ).
thf(427,plain,
! [C: $i,B: $i,A: $i] :
( ( C != t_a )
| ( B != v_t )
| ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
!= v_a )
| ( ( t_a @ ( v_u @ ( C @ ( B @ ( A @ c_union ) ) @ c_inter ) ) )
= c_emptyset ) ),
inference(simp,[status(thm)],[404]) ).
thf(443,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ ( v_t @ ( A @ c_minus ) ) )
!= v_a )
| ( ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( A @ c_union ) ) @ c_inter ) ) )
= c_emptyset ) ),
inference(simp,[status(thm)],[427]) ).
thf(21220,plain,
! [A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( A @ c_inter ) ) )
!= v_a )
| ( ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( A @ c_union ) ) @ c_inter ) ) )
= c_emptyset ) ),
inference(rewrite,[status(thm)],[443,393]) ).
thf(16192,plain,
( ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= v_t )
| ( ( t_a @ ( v_u @ ( v_t @ c_union ) ) )
!= v_a ) ),
inference(paramod_ordered,[status(thm)],[16183,9982]) ).
thf(16448,plain,
( ( t_a != t_a )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= v_t )
| ( v_a != v_a )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= v_t )
| ( ( t_a @ ( v_u @ ( v_t @ c_union ) ) )
!= v_a ) ),
inference(simp,[status(thm)],[16192]) ).
thf(16523,plain,
( ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= v_t )
| ( ( t_a @ ( v_u @ ( v_t @ c_union ) ) )
!= v_a ) ),
inference(simp,[status(thm)],[16448]) ).
thf(26732,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ tc_set @ ( A @ c_uminus ) @ c_union ) ) )
!= ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( D @ c_union ) ) ) )
| ( t_a @ tc_set @ ( C @ tc_set @ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_inter ) ) @ c_uminus ) @ ( v_t @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[715,26466]) ).
thf(26733,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_uminus ) @ ( A @ c_inter ) ) @ c_uminus ) @ ( v_t @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[26732:[bind(A,$thf( E )),bind(B,$thf( t_a @ tc_set @ ( v_u @ c_uminus ) )),bind(C,$thf( t_a )),bind(D,$thf( t_a @ tc_set @ ( E @ c_uminus ) ))]]) ).
thf(26870,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_uminus ) @ ( A @ c_inter ) ) @ c_uminus ) @ ( v_t @ c_lessequals ) ) ),
inference(simp,[status(thm)],[26733]) ).
thf(28298,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( v_u @ ( A @ c_inter ) ) @ c_uminus ) @ ( v_t @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[26870,6340]) ).
thf(18093,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ ( v_a @ c_union ) ) )
!= ( A @ ( C @ ( B @ c_union ) ) ) )
| ( A @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( C @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[17997,1079]) ).
thf(18094,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[18093:[bind(A,$thf( t_a )),bind(B,$thf( v_a )),bind(C,$thf( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) ))]]) ).
thf(17,axiom,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
thf(61,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(62,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[61]) ).
thf(87,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( v_u @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,62]) ).
thf(88,plain,
! [B: $i,A: $i] :
( ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( v_u @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set )
!= B )
| ( ( t_a @ ( v_A @ c_Mutil_Otiling ) )
!= c_emptyset )
| ( v_u != A ) ),
inference(simp,[status(thm)],[88]) ).
thf(93,plain,
( ( t_a @ ( v_A @ c_Mutil_Otiling ) )
!= c_emptyset ),
inference(simp,[status(thm)],[91]) ).
thf(323,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( v_u @ c_in ) ) )
!= ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
| ~ $true
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[34,49]) ).
thf(324,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( v_u @ c_in ) ) )
!= ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[323]) ).
thf(325,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( A @ c_union ) ) @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_A @ ( A @ c_in ) ) )
| ( ( t_a @ ( v_u @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(pattern_uni,[status(thm)],[324:[bind(A,$thf( A )),bind(B,$thf( v_A )),bind(C,$thf( t_a )),bind(D,$thf( v_u ))]]) ).
thf(20323,plain,
( ( ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= v_u ) ),
inference(paramod_ordered,[status(thm)],[20205,226]) ).
thf(20479,plain,
( ( t_a != t_a )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= v_t )
| ( v_a != v_a )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= v_u ) ),
inference(simp,[status(thm)],[20323]) ).
thf(20647,plain,
( ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= v_t )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= v_u ) ),
inference(simp,[status(thm)],[20479]) ).
thf(26750,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_union ) ) )
!= ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( E @ c_union ) ) ) )
| ( t_a @ tc_set @ ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_union ) ) @ ( v_t @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,26466]) ).
thf(26751,plain,
! [B: $i,A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( B @ c_union ) ) @ ( A @ c_union ) ) @ ( v_t @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[26750:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( t_a )),bind(D,$thf( t_a @ tc_set @ ( v_u @ c_uminus ) )),bind(E,$thf( t_a @ ( G @ ( F @ c_union ) ) ))]]) ).
thf(26871,plain,
! [B: $i,A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( B @ c_union ) ) @ ( A @ c_union ) ) @ ( v_t @ c_lessequals ) ) ),
inference(simp,[status(thm)],[26751]) ).
thf(1419,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( c_UNIV @ c_inter ) ) )
!= ( E @ ( E @ tc_set @ ( C @ c_uminus ) @ ( D @ c_inter ) ) ) )
| ( ( E @ ( A @ ( C @ c_union ) ) )
= ( E @ ( D @ ( C @ c_union ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[51,1362]) ).
thf(1420,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ tc_set @ ( B @ c_uminus ) @ ( B @ c_union ) ) )
= ( A @ ( c_UNIV @ ( B @ c_union ) ) ) ),
inference(pattern_uni,[status(thm)],[1419:[bind(A,$thf( B @ tc_set @ ( F @ c_uminus ) )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( c_UNIV )),bind(E,$thf( B ))]]) ).
thf(1452,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ tc_set @ ( B @ c_uminus ) @ ( B @ c_union ) ) )
= ( A @ ( c_UNIV @ ( B @ c_union ) ) ) ),
inference(simp,[status(thm)],[1420]) ).
thf(3782,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( B @ tc_set @ ( A @ c_uminus ) @ c_uminus ) )
!= ( C @ tc_set @ ( D @ c_uminus ) ) )
| ( ( C @ ( A @ ( D @ c_union ) ) )
= ( C @ ( c_UNIV @ ( D @ c_union ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[57,1452]) ).
thf(3783,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ tc_set @ ( A @ c_uminus ) @ c_union ) ) )
= ( B @ ( c_UNIV @ ( B @ tc_set @ ( A @ c_uminus ) @ c_union ) ) ) ),
inference(pattern_uni,[status(thm)],[3782:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( G @ tc_set @ ( E @ c_uminus ) ))]]) ).
thf(3887,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ tc_set @ ( A @ c_uminus ) @ c_union ) ) )
= ( B @ ( c_UNIV @ ( B @ tc_set @ ( A @ c_uminus ) @ c_union ) ) ) ),
inference(simp,[status(thm)],[3783]) ).
thf(592,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( c_UNIV @ ( A @ ( c_emptyset @ ( B @ c_inter ) ) @ c_union ) ) )
!= ( E @ ( C @ ( F @ c_union ) ) ) )
| ( E @ tc_set @ ( D @ ( A @ ( c_UNIV @ ( B @ c_union ) ) @ c_lessequals ) ) )
| ~ ( E @ tc_set @ ( D @ ( F @ c_lessequals ) ) )
| ~ ( E @ tc_set @ ( D @ ( C @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[453,55]) ).
thf(593,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( A @ ( C @ ( c_UNIV @ ( B @ c_union ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( A @ ( C @ ( c_emptyset @ ( B @ c_inter ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( A @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[592:[bind(A,$thf( I )),bind(B,$thf( G )),bind(C,$thf( c_UNIV )),bind(D,$thf( D )),bind(E,$thf( I )),bind(F,$thf( I @ ( c_emptyset @ ( G @ c_inter ) ) ))]]) ).
thf(623,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( A @ ( C @ ( c_UNIV @ ( B @ c_union ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( A @ ( C @ ( c_emptyset @ ( B @ c_inter ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( A @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[593]) ).
thf(571,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( c_UNIV @ c_union ) ) )
!= ( C @ ( c_UNIV @ ( C @ ( c_emptyset @ ( D @ c_inter ) ) @ c_union ) ) ) )
| ( ( C @ ( c_UNIV @ ( D @ c_union ) ) )
= c_UNIV ) ),
inference(paramod_ordered,[status(thm)],[69,453]) ).
thf(620,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != C )
| ( A != c_UNIV )
| ( ( C @ ( c_emptyset @ ( D @ c_inter ) ) )
!= c_UNIV )
| ( ( C @ ( c_UNIV @ ( D @ c_union ) ) )
= c_UNIV ) ),
inference(simp,[status(thm)],[571]) ).
thf(646,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c_emptyset @ ( B @ c_inter ) ) )
!= c_UNIV )
| ( ( A @ ( c_UNIV @ ( B @ c_union ) ) )
= c_UNIV ) ),
inference(simp,[status(thm)],[620]) ).
thf(417,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= v_u ) ),
inference(paramod_ordered,[status(thm)],[53,226]) ).
thf(428,plain,
! [C: $i,B: $i,A: $i] :
( ( C != t_a )
| ( B != v_t )
| ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
!= v_a )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= v_u ) ),
inference(simp,[status(thm)],[417]) ).
thf(444,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ ( v_t @ ( A @ c_minus ) ) )
!= v_a )
| ( ( t_a @ ( v_t @ ( A @ c_union ) ) )
!= v_u ) ),
inference(simp,[status(thm)],[428]) ).
thf(21626,plain,
! [A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( A @ c_inter ) ) )
!= v_a )
| ( ( t_a @ ( v_t @ ( A @ c_union ) ) )
!= v_u ) ),
inference(rewrite,[status(thm)],[444,393]) ).
thf(21632,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_union ) ) )
!= ( t_a @ ( v_t @ ( C @ c_union ) ) ) )
| ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( C @ c_inter ) ) )
!= v_a )
| ( A != v_u ) ),
inference(paramod_ordered,[status(thm)],[42,21626]) ).
thf(21633,plain,
( ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_t @ c_inter ) ) )
!= v_a )
| ( v_u != v_t ) ),
inference(pattern_uni,[status(thm)],[21632:[bind(A,$thf( v_t )),bind(B,$thf( t_a )),bind(C,$thf( v_t ))]]) ).
thf(20211,plain,
( ( ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= v_t )
| ( ( t_a @ ( v_u @ ( v_t @ c_union ) ) )
!= v_a ) ),
inference(paramod_ordered,[status(thm)],[20205,9982]) ).
thf(20470,plain,
( ( t_a != t_a )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= v_t )
| ( v_a != v_a )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= v_t )
| ( ( t_a @ ( v_u @ ( v_t @ c_union ) ) )
!= v_a ) ),
inference(simp,[status(thm)],[20211]) ).
thf(20636,plain,
( ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= v_t )
| ( ( t_a @ ( v_u @ ( v_t @ c_union ) ) )
!= v_a ) ),
inference(simp,[status(thm)],[20470]) ).
thf(109,plain,
( ( ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_inter ) ) )
!= ( t_a @ ( v_u @ ( v_t @ c_inter ) ) ) )
| ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ c_in ) ) )
| ( c_emptyset != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[37,108]) ).
thf(110,plain,
( ( ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_inter ) ) )
!= ( t_a @ ( v_u @ ( v_t @ c_inter ) ) ) )
| ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[109]) ).
thf(117,plain,
( ( t_a != t_a )
| ( v_u != v_u )
| ( ( t_a @ ( v_t @ ( v_a @ c_union ) ) )
!= v_t )
| ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[110]) ).
thf(121,plain,
( ( ( t_a @ ( v_t @ ( v_a @ c_union ) ) )
!= v_t )
| ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(16222,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( B @ ( D @ ( C @ c_union ) ) ) )
| ( B @ tc_set @ ( B @ ( A @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_union ) ) @ ( C @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[16183,1313]) ).
thf(16223,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ ( A @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[16222:[bind(A,$thf( A )),bind(B,$thf( t_a )),bind(C,$thf( v_a )),bind(D,$thf( t_a @ tc_set @ ( v_t @ c_uminus ) ))]]) ).
thf(17143,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[16223,715]) ).
thf(17148,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ tc_set @ ( B @ c_uminus ) @ c_uminus ) )
!= ( t_a @ tc_set @ ( C @ c_uminus ) ) )
| ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( B @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[6340,17143]) ).
thf(17149,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( A @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[17148:[bind(A,$thf( t_a )),bind(B,$thf( D )),bind(C,$thf( t_a @ tc_set @ ( D @ c_uminus ) ))]]) ).
thf(17266,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( A @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(simp,[status(thm)],[17149]) ).
thf(43515,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ tc_set @ ( B @ c_uminus ) @ c_uminus ) )
!= ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( v_t @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_uminus ) ) )
| ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( B @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[6340,43483]) ).
thf(43516,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ ( v_t @ ( v_t @ c_inter ) ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[43515:[bind(A,$thf( t_a )),bind(B,$thf( t_a @ ( v_t @ ( v_t @ c_inter ) ) ))]]) ).
thf(719,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ tc_set @ ( A @ c_uminus ) @ c_union ) ) )
!= ( F @ ( G @ ( D @ c_union ) ) ) )
| ( F @ tc_set @ ( F @ ( E @ c_Mutil_Otiling ) @ ( C @ tc_set @ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_inter ) ) @ c_uminus ) @ c_in ) ) )
| ~ ( F @ tc_set @ ( F @ ( E @ c_Mutil_Otiling ) @ ( G @ c_in ) ) )
| ~ ( F @ tc_set @ ( E @ ( D @ c_in ) ) )
| ( ( F @ ( G @ ( D @ c_inter ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[715,49]) ).
thf(720,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( D @ ( B @ c_Mutil_Otiling ) @ ( D @ tc_set @ ( D @ ( D @ tc_set @ ( A @ c_uminus ) @ ( C @ c_inter ) ) @ c_uminus ) @ c_in ) ) )
| ~ ( D @ tc_set @ ( D @ ( B @ c_Mutil_Otiling ) @ ( A @ c_in ) ) )
| ~ ( D @ tc_set @ ( B @ ( D @ tc_set @ ( C @ c_uminus ) @ c_in ) ) )
| ( ( D @ ( A @ ( D @ tc_set @ ( C @ c_uminus ) @ c_inter ) ) )
!= c_emptyset ) ),
inference(pattern_uni,[status(thm)],[719:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( J )),bind(D,$thf( J @ tc_set @ ( H @ c_uminus ) )),bind(E,$thf( E )),bind(F,$thf( J )),bind(G,$thf( B ))]]) ).
thf(766,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( D @ ( B @ c_Mutil_Otiling ) @ ( D @ tc_set @ ( D @ ( D @ tc_set @ ( A @ c_uminus ) @ ( C @ c_inter ) ) @ c_uminus ) @ c_in ) ) )
| ~ ( D @ tc_set @ ( D @ ( B @ c_Mutil_Otiling ) @ ( A @ c_in ) ) )
| ~ ( D @ tc_set @ ( B @ ( D @ tc_set @ ( C @ c_uminus ) @ c_in ) ) )
| ( ( D @ ( A @ ( D @ tc_set @ ( C @ c_uminus ) @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[720]) ).
thf(45393,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( B @ ( D @ ( C @ c_union ) ) ) )
| ( B @ tc_set @ ( B @ ( A @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_union ) ) @ ( C @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[45340,1313]) ).
thf(45394,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ ( A @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[45393:[bind(A,$thf( A )),bind(B,$thf( t_a )),bind(C,$thf( v_a )),bind(D,$thf( t_a @ tc_set @ ( v_u @ c_uminus ) ))]]) ).
thf(47231,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[45394,715]) ).
thf(47375,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
!= ( t_a @ tc_set @ ( B @ c_uminus ) ) )
| ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[9070,47231]) ).
thf(47376,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[47375:[bind(A,$thf( t_a )),bind(B,$thf( c_emptyset ))]]) ).
thf(47503,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ),
inference(rewrite,[status(thm)],[47376,3462]) ).
thf(28301,plain,
! [A: $i] :
( ( ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_inter ) ) )
!= ( t_a @ ( v_u @ ( A @ c_inter ) ) ) )
| ( t_a @ tc_set @ ( t_a @ tc_set @ ( c_emptyset @ c_uminus ) @ ( v_t @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[37,28298]) ).
thf(28302,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( c_emptyset @ c_uminus ) @ ( v_t @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[28301:[bind(A,$thf( t_a @ ( v_t @ ( v_a @ c_union ) ) ))]]) ).
thf(28426,plain,
t_a @ tc_set @ ( c_UNIV @ ( v_t @ c_lessequals ) ),
inference(rewrite,[status(thm)],[28302,9070]) ).
thf(20224,plain,
( ( ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[20205,276]) ).
thf(20453,plain,
( ( t_a != t_a )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= v_t )
| ( v_a != v_a )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[20224]) ).
thf(20619,plain,
( ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= v_t )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[20453]) ).
thf(44689,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( C @ ( E @ ( D @ c_union ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_union ) ) @ ( D @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[44635,1313]) ).
thf(44690,plain,
! [B: $i,A: $i] : ( t_a @ tc_set @ ( t_a @ ( A @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( B @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[44689:[bind(A,$thf( K )),bind(B,$thf( B )),bind(C,$thf( t_a )),bind(D,$thf( v_a )),bind(E,$thf( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( K @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) ))]]) ).
thf(45177,plain,
! [B: $i,A: $i] : ( t_a @ tc_set @ ( t_a @ ( A @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( B @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(simp,[status(thm)],[44690]) ).
thf(63087,plain,
! [B: $i,A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( B @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[45177,715]) ).
thf(60806,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ tc_set @ ( B @ c_uminus ) @ c_uminus ) )
!= ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_a @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_uminus ) ) )
| ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( B @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[6340,60772]) ).
thf(60807,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_a @ c_uminus ) @ ( v_t @ c_inter ) ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[60806:[bind(A,$thf( t_a )),bind(B,$thf( t_a @ ( t_a @ tc_set @ ( v_a @ c_uminus ) @ ( v_t @ c_inter ) ) ))]]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).
thf(74,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1826,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
!= ( t_a @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ ( v_a @ c_union ) ) ) )
| ( A != v_u ) ),
inference(paramod_ordered,[status(thm)],[46,1699]) ).
thf(1844,plain,
! [A: $i] :
( ( A != t_a )
| ( ( t_a @ ( v_u @ ( v_t @ c_union ) ) )
!= c_emptyset )
| ( v_u != v_a ) ),
inference(simp,[status(thm)],[1826]) ).
thf(1863,plain,
( ( ( t_a @ ( v_u @ ( v_t @ c_union ) ) )
!= c_emptyset )
| ( v_u != v_a ) ),
inference(simp,[status(thm)],[1844]) ).
thf(376,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
!= ( C @ tc_set @ ( C @ tc_set @ ( B @ c_uminus ) @ c_uminus ) ) )
| ( c_UNIV = B ) ),
inference(paramod_ordered,[status(thm)],[312,57]) ).
thf(381,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set )
!= ( C @ tc_set ) )
| ( ( C @ tc_set @ ( B @ c_uminus ) )
!= c_emptyset )
| ( c_UNIV = B ) ),
inference(simp,[status(thm)],[376]) ).
thf(341,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_A @ ( v_a @ c_in ) ) )
!= ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
| ~ $true
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[31,49]) ).
thf(342,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_A @ ( v_a @ c_in ) ) )
!= ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[341]) ).
thf(360,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set )
!= ( C @ tc_set ) )
| ( ( C @ ( B @ c_Mutil_Otiling ) )
!= v_A )
| ( v_a != D )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset )
| ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[342]) ).
thf(366,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set )
!= ( C @ tc_set ) )
| ( ( C @ ( B @ c_Mutil_Otiling ) )
!= v_A )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( v_a @ ( A @ c_inter ) ) )
!= c_emptyset )
| ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( v_a @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[360]) ).
thf(332,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ c_in ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ $true
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[108,49]) ).
thf(333,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ c_in ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[332]) ).
thf(334,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( t_a @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ c_Mutil_Otiling ) @ ( t_a @ ( A @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ c_union ) ) @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( t_a @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ c_Mutil_Otiling ) @ ( A @ c_in ) ) )
| ( ( t_a @ ( A @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ c_inter ) ) )
!= c_emptyset )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(pattern_uni,[status(thm)],[333:[bind(A,$thf( t_a @ ( v_u @ ( v_t @ c_union ) ) )),bind(B,$thf( t_a @ ( v_A @ c_Mutil_Otiling ) )),bind(C,$thf( t_a )),bind(D,$thf( D ))]]) ).
thf(369,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( t_a @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ c_Mutil_Otiling ) @ ( t_a @ ( A @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ c_union ) ) @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( t_a @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ c_Mutil_Otiling ) @ ( A @ c_in ) ) )
| ( ( t_a @ ( A @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ c_inter ) ) )
!= c_emptyset )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[334]) ).
thf(12385,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( t_a @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ c_Mutil_Otiling ) @ ( t_a @ ( t_a @ ( A @ ( v_u @ c_union ) ) @ ( v_t @ c_union ) ) @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( t_a @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ c_Mutil_Otiling ) @ ( A @ c_in ) ) )
| ( ( t_a @ ( A @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ c_inter ) ) )
!= c_emptyset )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(rewrite,[status(thm)],[369,77]) ).
thf(152,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
!= ( t_a @ ( v_u @ ( v_t @ c_union ) ) ) )
| ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( A @ c_in ) ) )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[46,108]) ).
thf(153,plain,
! [B: $i,A: $i] :
( ( B != t_a )
| ( v_u != c_emptyset )
| ( A != v_t )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset )
| ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(160,plain,
( ( v_u != c_emptyset )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset )
| ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( v_t @ c_in ) ) ) ),
inference(simp,[status(thm)],[153]) ).
thf(177,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( c_UNIV @ c_inter ) ) )
!= ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_inter ) ) ) )
| ( A = c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[51,37]) ).
thf(186,plain,
! [B: $i,A: $i] :
( ( B != t_a )
| ( A != v_u )
| ( ( t_a @ ( v_t @ ( v_a @ c_union ) ) )
!= c_UNIV )
| ( A = c_emptyset ) ),
inference(simp,[status(thm)],[177]) ).
thf(192,plain,
( ( ( t_a @ ( v_t @ ( v_a @ c_union ) ) )
!= c_UNIV )
| ( v_u = c_emptyset ) ),
inference(simp,[status(thm)],[186]) ).
thf(6444,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ tc_set @ ( B @ c_uminus ) @ ( B @ c_union ) ) )
!= ( D @ ( F @ ( E @ c_union ) ) ) )
| ( D @ tc_set @ ( D @ ( C @ ( A @ ( c_UNIV @ ( B @ c_union ) ) @ c_union ) ) @ ( E @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[1452,1313]) ).
thf(6445,plain,
! [C: $i,B: $i,A: $i] : ( C @ tc_set @ ( C @ ( A @ ( C @ ( c_UNIV @ ( B @ c_union ) ) @ c_union ) ) @ ( B @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[6444:[bind(A,$thf( I )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( I )),bind(E,$thf( G )),bind(F,$thf( I @ tc_set @ ( G @ c_uminus ) ))]]) ).
thf(6496,plain,
! [C: $i,B: $i,A: $i] : ( C @ tc_set @ ( C @ ( A @ ( C @ ( c_UNIV @ ( B @ c_union ) ) @ c_union ) ) @ ( B @ c_lessequals ) ) ),
inference(simp,[status(thm)],[6445]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
!= ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_union ) ) ) )
| ~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( A @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[46,38]) ).
thf(158,plain,
! [B: $i,A: $i] :
( ( B != t_a )
| ( v_u != c_emptyset )
| ( A
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[148]) ).
thf(165,plain,
( ( v_u != c_emptyset )
| ~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(19,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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(64,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)],[19]) ).
thf(65,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)],[64]) ).
thf(1267,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ ( C @ ( B @ c_union ) ) @ ( C @ c_lessequals ) ) )
!= ( F @ tc_set @ ( G @ ( F @ ( E @ ( D @ c_union ) ) @ c_lessequals ) ) ) )
| ( F @ tc_set @ ( G @ ( D @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1079,71]) ).
thf(1268,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ ( C @ ( B @ c_union ) ) @ ( C @ c_lessequals ) ) )
!= ( F @ tc_set @ ( G @ ( F @ ( E @ ( D @ c_union ) ) @ c_lessequals ) ) ) )
| ( F @ tc_set @ ( G @ ( D @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1267]) ).
thf(1269,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ tc_set @ ( B @ ( B @ ( D @ ( C @ c_union ) ) @ ( A @ c_union ) ) @ ( C @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[1268:[bind(A,$thf( M )),bind(B,$thf( K )),bind(C,$thf( M @ ( O @ ( N @ c_union ) ) )),bind(D,$thf( N )),bind(E,$thf( O )),bind(F,$thf( M )),bind(G,$thf( M @ ( M @ ( O @ ( N @ c_union ) ) @ ( K @ c_union ) ) ))]]) ).
thf(1280,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ tc_set @ ( B @ ( B @ ( D @ ( C @ c_union ) ) @ ( A @ c_union ) ) @ ( C @ c_lessequals ) ) ),
inference(simp,[status(thm)],[1269]) ).
thf(5889,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( C @ tc_set @ ( A @ c_uminus ) @ ( B @ c_inter ) ) @ ( A @ c_union ) ) )
!= ( E @ ( G @ ( F @ c_union ) ) ) )
| ( E @ tc_set @ ( E @ ( C @ ( B @ ( A @ c_union ) ) @ ( D @ c_union ) ) @ ( F @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[1362,1280]) ).
thf(5890,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ tc_set @ ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_union ) ) @ ( D @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[5889:[bind(A,$thf( K )),bind(B,$thf( H )),bind(C,$thf( J )),bind(D,$thf( D )),bind(E,$thf( J )),bind(F,$thf( K )),bind(G,$thf( J @ ( J @ tc_set @ ( K @ c_uminus ) @ ( H @ c_inter ) ) ))]]) ).
thf(5936,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ tc_set @ ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_union ) ) @ ( D @ c_lessequals ) ) ),
inference(simp,[status(thm)],[5890]) ).
thf(16287,plain,
( ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= v_u ) ),
inference(paramod_ordered,[status(thm)],[16183,226]) ).
thf(16374,plain,
( ( t_a != t_a )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= v_t )
| ( v_a != v_a )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= v_u ) ),
inference(simp,[status(thm)],[16287]) ).
thf(16569,plain,
( ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= v_t )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= v_u ) ),
inference(simp,[status(thm)],[16374]) ).
thf(30070,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18023,544]) ).
thf(30071,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[30070]) ).
thf(30072,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( v_t @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[30071:[bind(A,$thf( t_a @ tc_set @ ( v_u @ c_uminus ) )),bind(B,$thf( t_a )),bind(C,$thf( v_t ))]]) ).
thf(30455,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[30072,715]) ).
thf(30476,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[30455,544]) ).
thf(30477,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[30476]) ).
thf(30478,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[30477:[bind(A,$thf( t_a @ tc_set @ ( v_u @ c_uminus ) )),bind(B,$thf( t_a )),bind(C,$thf( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) ))]]) ).
thf(58754,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[30478,715]) ).
thf(58787,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ tc_set @ ( B @ c_uminus ) @ c_uminus ) )
!= ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_uminus ) ) )
| ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( B @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[6340,58754]) ).
thf(58788,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_u @ c_inter ) ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[58787:[bind(A,$thf( t_a )),bind(B,$thf( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_u @ c_inter ) ) ))]]) ).
thf(44921,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_UNIV @ c_uminus ) )
!= ( t_a @ tc_set @ ( B @ c_uminus ) ) )
| ( ( t_a @ ( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_union ) ) )
= ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( B @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) ) ) ),
inference(paramod_ordered,[status(thm)],[79,44635]) ).
thf(44922,plain,
( ( t_a @ ( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_union ) ) )
= ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( c_UNIV @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) ) ),
inference(pattern_uni,[status(thm)],[44921:[bind(A,$thf( t_a )),bind(B,$thf( c_UNIV ))]]) ).
thf(48315,plain,
( ( t_a @ ( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_union ) ) )
= ( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_u @ c_inter ) ) @ c_uminus ) ) ),
inference(rewrite,[status(thm)],[44922,79]) ).
thf(48369,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( B @ ( D @ ( C @ c_union ) ) ) )
| ( B @ tc_set @ ( B @ ( A @ ( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_union ) ) @ ( C @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[48315,1313]) ).
thf(48370,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ ( A @ ( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[48369:[bind(A,$thf( A )),bind(B,$thf( t_a )),bind(C,$thf( v_a )),bind(D,$thf( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_u @ c_inter ) ) @ c_uminus ) ))]]) ).
thf(51528,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( t_a @ ( c_emptyset @ ( v_u @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[48370,715]) ).
thf(51672,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
!= ( t_a @ tc_set @ ( B @ c_uminus ) ) )
| ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( t_a @ ( c_emptyset @ ( v_u @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[9070,51528]) ).
thf(51673,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( t_a @ ( c_emptyset @ ( v_u @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[51672:[bind(A,$thf( t_a )),bind(B,$thf( c_emptyset ))]]) ).
thf(51792,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ),
inference(rewrite,[status(thm)],[51673,3462]) ).
thf(30095,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18094,544]) ).
thf(30096,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[30095]) ).
thf(30097,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[30096:[bind(A,$thf( t_a @ tc_set @ ( v_u @ c_uminus ) )),bind(B,$thf( t_a )),bind(C,$thf( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) ))]]) ).
thf(38240,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[30097,715]) ).
thf(28439,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( c_UNIV @ ( v_t @ c_lessequals ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ $true
| ( B = A ) ),
inference(paramod_ordered,[status(thm)],[28426,82]) ).
thf(28440,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( c_UNIV @ ( v_t @ c_lessequals ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ( B = A ) ),
inference(simp,[status(thm)],[28439]) ).
thf(28441,plain,
( ~ ( t_a @ tc_set @ ( v_t @ ( c_UNIV @ c_lessequals ) ) )
| ( c_UNIV = v_t ) ),
inference(pattern_uni,[status(thm)],[28440:[bind(A,$thf( v_t )),bind(B,$thf( c_UNIV )),bind(C,$thf( t_a ))]]) ).
thf(481,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_inter ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_inter ) ) ) )
| ( A = c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[474,36]) ).
thf(487,plain,
! [B: $i,A: $i] :
( ( B != t_a )
| ( c_UNIV != v_t )
| ( A != v_a )
| ( A = c_emptyset ) ),
inference(simp,[status(thm)],[481]) ).
thf(494,plain,
( ( c_UNIV != v_t )
| ( c_emptyset = v_a ) ),
inference(simp,[status(thm)],[487]) ).
thf(252,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( ( t_a @ ( v_u @ ( A @ c_inter ) ) )
= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[84,37]) ).
thf(265,plain,
! [B: $i,A: $i] :
( ( B != t_a )
| ( A != v_t )
| ( c_emptyset != v_a )
| ( ( t_a @ ( v_u @ ( A @ c_inter ) ) )
= c_emptyset ) ),
inference(simp,[status(thm)],[252]) ).
thf(278,plain,
( ( c_emptyset != v_a )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
= c_emptyset ) ),
inference(simp,[status(thm)],[265]) ).
thf(3998,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
!= ( t_a @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ ( v_a @ c_union ) ) ) )
| ( A
!= ( t_a @ ( v_u @ ( v_t @ c_union ) ) ) )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[84,3981]) ).
thf(4074,plain,
! [A: $i] :
( ( A != t_a )
| ( ( t_a @ ( v_u @ ( v_t @ c_union ) ) )
!= ( t_a @ ( v_u @ ( v_t @ c_union ) ) ) )
| ( c_emptyset != v_a )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[3998]) ).
thf(4197,plain,
( ( c_emptyset != v_a )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[4074]) ).
thf(5182,plain,
( ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= ( t_a @ ( v_u @ ( v_t @ c_inter ) ) ) )
| ( c_emptyset != v_a )
| ( c_emptyset != c_emptyset )
| ( c_emptyset != v_a ) ),
inference(paramod_ordered,[status(thm)],[278,4197]) ).
thf(5183,plain,
( ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= ( t_a @ ( v_u @ ( v_t @ c_inter ) ) ) )
| ( c_emptyset != v_a ) ),
inference(simp,[status(thm)],[5182]) ).
thf(5184,plain,
c_emptyset != v_a,
inference(pattern_uni,[status(thm)],[5183:[]]) ).
thf(5236,plain,
c_UNIV != v_t,
inference(simplifyReflect,[status(thm)],[494,5184]) ).
thf(28480,plain,
~ ( t_a @ tc_set @ ( v_t @ ( c_UNIV @ c_lessequals ) ) ),
inference(simplifyReflect,[status(thm)],[28441,5236]) ).
thf(30152,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18055,544]) ).
thf(30153,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[30152]) ).
thf(30154,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( v_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[30153:[bind(A,$thf( t_a @ tc_set @ ( v_u @ c_uminus ) )),bind(B,$thf( t_a )),bind(C,$thf( v_a ))]]) ).
thf(30644,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_a @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[30154,715]) ).
thf(5905,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ tc_set @ ( B @ c_uminus ) @ ( B @ c_union ) ) )
!= ( D @ ( F @ ( E @ c_union ) ) ) )
| ( D @ tc_set @ ( D @ ( A @ ( c_UNIV @ ( B @ c_union ) ) @ ( C @ c_union ) ) @ ( E @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[1452,1280]) ).
thf(5906,plain,
! [C: $i,B: $i,A: $i] : ( C @ tc_set @ ( C @ ( C @ ( c_UNIV @ ( B @ c_union ) ) @ ( A @ c_union ) ) @ ( B @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[5905:[bind(A,$thf( I )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( I )),bind(E,$thf( G )),bind(F,$thf( I @ tc_set @ ( G @ c_uminus ) ))]]) ).
thf(5941,plain,
! [C: $i,B: $i,A: $i] : ( C @ tc_set @ ( C @ ( C @ ( c_UNIV @ ( B @ c_union ) ) @ ( A @ c_union ) ) @ ( B @ c_lessequals ) ) ),
inference(simp,[status(thm)],[5906]) ).
thf(15036,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_UNIV @ c_uminus ) )
!= ( C @ tc_set @ ( B @ c_uminus ) ) )
| ( ( C @ ( c_UNIV @ ( C @ tc_set @ ( B @ c_uminus ) @ c_union ) ) )
= ( C @ ( B @ ( c_emptyset @ c_union ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[79,3887]) ).
thf(15037,plain,
! [A: $i] :
( ( A @ ( c_UNIV @ ( A @ tc_set @ ( c_UNIV @ c_uminus ) @ c_union ) ) )
= ( A @ ( c_UNIV @ ( c_emptyset @ c_union ) ) ) ),
inference(pattern_uni,[status(thm)],[15036:[bind(A,$thf( A )),bind(B,$thf( c_UNIV )),bind(C,$thf( A ))]]) ).
thf(24870,plain,
! [A: $i] :
( ( A @ ( c_UNIV @ ( c_emptyset @ c_union ) ) )
= c_UNIV ),
inference(rewrite,[status(thm)],[15037,84,79]) ).
thf(32037,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
!= ( t_a @ tc_set @ ( B @ c_uminus ) ) )
| ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[9070,31913]) ).
thf(32038,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[32037:[bind(A,$thf( t_a )),bind(B,$thf( c_emptyset ))]]) ).
thf(32153,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ),
inference(rewrite,[status(thm)],[32038,3462]) ).
thf(34126,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ ( C @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32153,568]) ).
thf(34127,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ ( C @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[34126]) ).
thf(34128,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[34127:[bind(A,$thf( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) )),bind(B,$thf( t_a )),bind(C,$thf( v_a ))]]) ).
thf(41124,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[34128,3462]) ).
thf(1163,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ tc_set @ ( A @ c_uminus ) @ c_union ) ) )
!= ( D @ ( F @ ( E @ c_union ) ) ) )
| ( D @ tc_set @ ( C @ tc_set @ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_inter ) ) @ c_uminus ) @ ( F @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[715,1079]) ).
thf(1164,plain,
! [C: $i,B: $i,A: $i] : ( C @ tc_set @ ( C @ tc_set @ ( C @ ( C @ tc_set @ ( A @ c_uminus ) @ ( B @ c_inter ) ) @ c_uminus ) @ ( A @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[1163:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( I )),bind(D,$thf( I )),bind(E,$thf( I @ tc_set @ ( G @ c_uminus ) )),bind(F,$thf( B ))]]) ).
thf(1185,plain,
! [C: $i,B: $i,A: $i] : ( C @ tc_set @ ( C @ tc_set @ ( C @ ( C @ tc_set @ ( A @ c_uminus ) @ ( B @ c_inter ) ) @ c_uminus ) @ ( A @ c_lessequals ) ) ),
inference(simp,[status(thm)],[1164]) ).
thf(14589,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( c_UNIV @ c_inter ) ) )
!= ( E @ ( E @ tc_set @ ( C @ c_uminus ) @ ( D @ c_inter ) ) ) )
| ( E @ tc_set @ ( E @ tc_set @ ( A @ c_uminus ) @ ( C @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[51,1185]) ).
thf(14590,plain,
! [B: $i,A: $i] : ( A @ tc_set @ ( A @ tc_set @ ( A @ tc_set @ ( B @ c_uminus ) @ c_uminus ) @ ( B @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[14589:[bind(A,$thf( B @ tc_set @ ( F @ c_uminus ) )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( c_UNIV )),bind(E,$thf( B ))]]) ).
thf(14628,plain,
! [B: $i,A: $i] : ( A @ tc_set @ ( A @ tc_set @ ( A @ tc_set @ ( B @ c_uminus ) @ c_uminus ) @ ( B @ c_lessequals ) ) ),
inference(simp,[status(thm)],[14590]) ).
thf(14671,plain,
! [B: $i,A: $i] : ( A @ tc_set @ ( B @ ( B @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[14628,6340]) ).
thf(30200,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( B @ ( B @ c_lessequals ) ) )
!= ( D @ tc_set @ ( C @ ( E @ c_lessequals ) ) ) )
| ( D @ tc_set @ ( C @ ( D @ ( E @ ( C @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14671,544]) ).
thf(30201,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( B @ ( B @ c_lessequals ) ) )
!= ( D @ tc_set @ ( C @ ( E @ c_lessequals ) ) ) )
| ( D @ tc_set @ ( C @ ( D @ ( E @ ( C @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[30200]) ).
thf(30202,plain,
! [B: $i,A: $i] : ( A @ tc_set @ ( B @ ( A @ ( B @ ( B @ c_union ) ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[30201:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(580,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( c_UNIV @ ( A @ ( c_emptyset @ ( B @ c_inter ) ) @ c_union ) ) )
!= ( D @ ( C @ ( c_emptyset @ c_union ) ) ) )
| ( ( A @ ( c_UNIV @ ( B @ c_union ) ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[453,84]) ).
thf(606,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != D )
| ( c_UNIV != C )
| ( ( A @ ( c_emptyset @ ( B @ c_inter ) ) )
!= c_emptyset )
| ( ( A @ ( c_UNIV @ ( B @ c_union ) ) )
= C ) ),
inference(simp,[status(thm)],[580]) ).
thf(632,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_emptyset @ ( A @ c_inter ) ) )
!= c_emptyset )
| ( ( B @ ( c_UNIV @ ( A @ c_union ) ) )
= c_UNIV ) ),
inference(simp,[status(thm)],[606]) ).
thf(40608,plain,
! [B: $i,A: $i] :
( ( ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_inter ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_inter ) ) ) )
| ( c_emptyset != c_emptyset )
| ( ( B @ ( c_UNIV @ ( A @ c_union ) ) )
= c_UNIV ) ),
inference(paramod_ordered,[status(thm)],[37,632]) ).
thf(40609,plain,
! [B: $i,A: $i] :
( ( ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_inter ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_inter ) ) ) )
| ( ( B @ ( c_UNIV @ ( A @ c_union ) ) )
= c_UNIV ) ),
inference(simp,[status(thm)],[40608]) ).
thf(40945,plain,
! [B: $i,A: $i] :
( ( t_a != B )
| ( v_u != c_emptyset )
| ( ( t_a @ ( v_t @ ( v_a @ c_union ) ) )
!= A )
| ( ( B @ ( c_UNIV @ ( A @ c_union ) ) )
= c_UNIV ) ),
inference(simp,[status(thm)],[40609]) ).
thf(41105,plain,
( ( v_u != c_emptyset )
| ( ( t_a @ ( c_UNIV @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_union ) ) )
= c_UNIV ) ),
inference(simp,[status(thm)],[40945]) ).
thf(45945,plain,
( ( v_u != c_emptyset )
| ( ( t_a @ ( t_a @ ( c_UNIV @ ( v_t @ c_union ) ) @ ( v_a @ c_union ) ) )
= c_UNIV ) ),
inference(rewrite,[status(thm)],[41105,77]) ).
thf(46019,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
!= ( t_a @ ( t_a @ ( c_UNIV @ ( v_t @ c_union ) ) @ ( v_a @ c_union ) ) ) )
| ( v_u != c_emptyset )
| ( A = c_UNIV ) ),
inference(paramod_ordered,[status(thm)],[46,45945]) ).
thf(46360,plain,
! [B: $i,A: $i] :
( ( B != t_a )
| ( ( t_a @ ( c_UNIV @ ( v_t @ c_union ) ) )
!= c_emptyset )
| ( A != v_a )
| ( v_u != c_emptyset )
| ( A = c_UNIV ) ),
inference(simp,[status(thm)],[46019]) ).
thf(46540,plain,
( ( ( t_a @ ( c_UNIV @ ( v_t @ c_union ) ) )
!= c_emptyset )
| ( v_u != c_emptyset )
| ( c_UNIV = v_a ) ),
inference(simp,[status(thm)],[46360]) ).
thf(55819,plain,
( ( ( t_a @ ( c_UNIV @ ( v_t @ c_union ) ) )
!= c_emptyset )
| ( v_u != c_emptyset ) ),
inference(simplifyReflect,[status(thm)],[46540,9273]) ).
thf(228,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( A != v_u ) ),
inference(paramod_ordered,[status(thm)],[42,226]) ).
thf(232,plain,
! [A: $i] :
( ( A != t_a )
| ( v_u != v_t )
| ( v_u != v_a ) ),
inference(simp,[status(thm)],[228]) ).
thf(237,plain,
( ( v_u != v_t )
| ( v_u != v_a ) ),
inference(simp,[status(thm)],[232]) ).
thf(581,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
!= ( C @ ( c_UNIV @ ( C @ ( c_emptyset @ ( D @ c_inter ) ) @ c_union ) ) ) )
| ( A
= ( C @ ( c_UNIV @ ( D @ c_union ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[84,453]) ).
thf(607,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != C )
| ( A != c_UNIV )
| ( ( C @ ( c_emptyset @ ( D @ c_inter ) ) )
!= c_emptyset )
| ( A
= ( C @ ( c_UNIV @ ( D @ c_union ) ) ) ) ),
inference(simp,[status(thm)],[581]) ).
thf(633,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c_emptyset @ ( B @ c_inter ) ) )
!= c_emptyset )
| ( ( A @ ( c_UNIV @ ( B @ c_union ) ) )
= c_UNIV ) ),
inference(simp,[status(thm)],[607]) ).
thf(45422,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( B @ ( D @ ( C @ c_union ) ) ) )
| ( B @ tc_set @ ( B @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( A @ c_union ) ) @ ( D @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[45340,1183]) ).
thf(45423,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( A @ c_union ) ) @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[45422:[bind(A,$thf( A )),bind(B,$thf( t_a )),bind(C,$thf( v_a )),bind(D,$thf( t_a @ tc_set @ ( v_u @ c_uminus ) ))]]) ).
thf(54962,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( A @ c_union ) ) @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[45423,3462]) ).
thf(29606,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( A @ ( C @ ( B @ c_union ) ) ) )
| ( A @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( C @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[29516,1079]) ).
thf(29607,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[29606:[bind(A,$thf( t_a )),bind(B,$thf( v_a )),bind(C,$thf( t_a @ tc_set @ ( v_t @ c_uminus ) ))]]) ).
thf(30349,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[29607,3462]) ).
thf(30350,plain,
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( v_t @ ( c_UNIV @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[30349,28480]) ).
thf(30351,plain,
( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( v_t @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[30350]) ).
thf(30421,plain,
( ( ( t_a @ tc_set )
!= ( t_a @ tc_set ) )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= v_t )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[30351]) ).
thf(30438,plain,
( ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= v_t )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[30421]) ).
thf(16227,plain,
! [B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_union ) ) ) )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[16183,46]) ).
thf(16388,plain,
! [B: $i,A: $i] :
( ( t_a != B )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= c_emptyset )
| ( v_a != A )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
= A ) ),
inference(simp,[status(thm)],[16227]) ).
thf(16464,plain,
( ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= c_emptyset )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
= v_a ) ),
inference(simp,[status(thm)],[16388]) ).
thf(1698,plain,
~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ ( v_a @ c_union ) ) @ c_in ) ) ),
inference(rewrite,[status(thm)],[38,77]) ).
thf(411,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_union ) ) )
!= ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_union ) ) ) )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= v_u ) ),
inference(paramod_ordered,[status(thm)],[53,105]) ).
thf(431,plain,
! [C: $i,B: $i,A: $i] :
( ( C != t_a )
| ( B != v_u )
| ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= v_u ) ),
inference(simp,[status(thm)],[411]) ).
thf(447,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ ( v_u @ ( A @ c_minus ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( ( t_a @ ( v_u @ ( A @ c_union ) ) )
!= v_u ) ),
inference(simp,[status(thm)],[431]) ).
thf(22040,plain,
! [A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( A @ c_inter ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( ( t_a @ ( v_u @ ( A @ c_union ) ) )
!= v_u ) ),
inference(rewrite,[status(thm)],[447,393]) ).
thf(22047,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_union ) ) )
!= ( t_a @ ( v_u @ ( C @ c_union ) ) ) )
| ( ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( C @ c_inter ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( A != v_u ) ),
inference(paramod_ordered,[status(thm)],[42,22040]) ).
thf(22048,plain,
( ( ( t_a @ ( v_t @ ( v_a @ c_union ) ) )
!= ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_u @ c_inter ) ) ) )
| ( v_u != v_u ) ),
inference(pattern_uni,[status(thm)],[22047:[bind(A,$thf( v_u )),bind(B,$thf( t_a )),bind(C,$thf( v_u ))]]) ).
thf(22218,plain,
( ( t_a @ ( v_t @ ( v_a @ c_union ) ) )
!= ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_u @ c_inter ) ) ) ),
inference(simp,[status(thm)],[22048]) ).
thf(4891,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_union ) ) )
!= ( F @ ( c_UNIV @ ( G @ c_union ) ) ) )
| ( F @ tc_set @ ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_union ) ) @ ( E @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,4766]) ).
thf(4892,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ tc_set @ ( D @ ( D @ ( c_UNIV @ ( C @ c_union ) ) @ ( B @ c_union ) ) @ ( A @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[4891:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( c_UNIV )),bind(E,$thf( E )),bind(F,$thf( J )),bind(G,$thf( J @ ( I @ ( H @ c_union ) ) ))]]) ).
thf(4943,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ tc_set @ ( D @ ( D @ ( c_UNIV @ ( C @ c_union ) ) @ ( B @ c_union ) ) @ ( A @ c_lessequals ) ) ),
inference(simp,[status(thm)],[4892]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_OImage ) ) ) )
= ( B @ ( C @ ( A @ c_inter ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__diag_0) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_OImage ) ) ) )
= ( B @ ( C @ ( A @ c_inter ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_OImage ) ) ) )
= ( B @ ( C @ ( A @ c_inter ) ) ) ),
inference(lifteq,[status(thm)],[43]) ).
thf(29151,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_UNIV @ c_uminus ) )
!= ( t_a @ tc_set @ ( B @ c_uminus ) ) )
| ( ( t_a @ ( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_union ) ) )
= ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( B @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) ) ) ),
inference(paramod_ordered,[status(thm)],[79,28898]) ).
thf(29152,plain,
( ( t_a @ ( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_union ) ) )
= ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( c_UNIV @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) ) ),
inference(pattern_uni,[status(thm)],[29151:[bind(A,$thf( t_a )),bind(B,$thf( c_UNIV ))]]) ).
thf(33382,plain,
( ( t_a @ ( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_union ) ) )
= ( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_t @ c_inter ) ) @ c_uminus ) ) ),
inference(rewrite,[status(thm)],[29152,79]) ).
thf(33404,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( D @ ( C @ ( B @ c_union ) ) ) )
| ( D @ tc_set @ ( D @ ( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( A @ c_union ) ) @ ( B @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[33382,12172]) ).
thf(33405,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( A @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[33404:[bind(A,$thf( A )),bind(B,$thf( v_a )),bind(C,$thf( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_t @ c_inter ) ) @ c_uminus ) )),bind(D,$thf( t_a ))]]) ).
thf(35558,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_union ) ) )
!= ( t_a @ ( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( E @ c_union ) ) ) )
| ( t_a @ tc_set @ ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_union ) ) @ ( v_a @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,33405]) ).
thf(35559,plain,
! [B: $i,A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( B @ c_union ) ) @ ( A @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[35558:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( t_a )),bind(D,$thf( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_t @ c_inter ) ) @ c_uminus ) )),bind(E,$thf( t_a @ ( G @ ( F @ c_union ) ) ))]]) ).
thf(35750,plain,
! [B: $i,A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( B @ c_union ) ) @ ( A @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(simp,[status(thm)],[35559]) ).
thf(316,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( c_UNIV @ c_union ) ) )
!= ( E @ ( F @ ( C @ c_union ) ) ) )
| ( E @ tc_set @ ( E @ ( D @ c_Mutil_Otiling ) @ ( c_UNIV @ c_in ) ) )
| ~ ( E @ tc_set @ ( E @ ( D @ c_Mutil_Otiling ) @ ( F @ c_in ) ) )
| ~ ( E @ tc_set @ ( D @ ( C @ c_in ) ) )
| ( ( E @ ( F @ ( C @ c_inter ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[69,49]) ).
thf(317,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( C @ c_Mutil_Otiling ) @ ( c_UNIV @ c_in ) ) )
| ~ ( B @ tc_set @ ( B @ ( C @ c_Mutil_Otiling ) @ ( A @ c_in ) ) )
| ~ ( B @ tc_set @ ( C @ ( c_UNIV @ c_in ) ) )
| ( ( B @ ( A @ ( c_UNIV @ c_inter ) ) )
!= c_emptyset ) ),
inference(pattern_uni,[status(thm)],[316:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( c_UNIV )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(371,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( C @ c_Mutil_Otiling ) @ ( c_UNIV @ c_in ) ) )
| ~ ( B @ tc_set @ ( B @ ( C @ c_Mutil_Otiling ) @ ( A @ c_in ) ) )
| ~ ( B @ tc_set @ ( C @ ( c_UNIV @ c_in ) ) )
| ( ( B @ ( A @ ( c_UNIV @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[317]) ).
thf(13157,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( C @ c_Mutil_Otiling ) @ ( c_UNIV @ c_in ) ) )
| ~ ( B @ tc_set @ ( B @ ( C @ c_Mutil_Otiling ) @ ( A @ c_in ) ) )
| ~ ( B @ tc_set @ ( C @ ( c_UNIV @ c_in ) ) )
| ( A != c_emptyset ) ),
inference(rewrite,[status(thm)],[371,51]) ).
thf(44093,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ tc_set @ ( B @ c_uminus ) @ c_uminus ) )
!= ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_uminus ) ) )
| ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( B @ ( t_a @ ( v_t @ ( v_t @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[6340,44060]) ).
thf(44094,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( v_t @ ( t_a @ ( v_t @ ( v_t @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[44093:[bind(A,$thf( t_a )),bind(B,$thf( v_t ))]]) ).
thf(30125,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( D @ tc_set @ ( C @ ( E @ c_lessequals ) ) ) )
| ( D @ tc_set @ ( C @ ( D @ ( E @ ( C @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[60,544]) ).
thf(30126,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) )
!= ( D @ tc_set @ ( C @ ( E @ c_lessequals ) ) ) )
| ( D @ tc_set @ ( C @ ( D @ ( E @ ( C @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[30125]) ).
thf(30127,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( B @ ( A @ ( A @ c_union ) ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[30126:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B )),bind(E,$thf( A ))]]) ).
thf(18024,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ ( v_a @ c_union ) ) )
!= ( D @ ( C @ ( B @ c_union ) ) ) )
| ( D @ tc_set @ ( D @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( A @ c_union ) ) @ ( B @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[17997,12172]) ).
thf(18025,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( A @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[18024:[bind(A,$thf( A )),bind(B,$thf( v_a )),bind(C,$thf( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) )),bind(D,$thf( t_a ))]]) ).
thf(18757,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_union ) ) )
!= ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( E @ c_union ) ) ) )
| ( t_a @ tc_set @ ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_union ) ) @ ( v_a @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,18025]) ).
thf(18758,plain,
! [B: $i,A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( B @ c_union ) ) @ ( A @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[18757:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( t_a )),bind(D,$thf( t_a @ tc_set @ ( v_u @ c_uminus ) )),bind(E,$thf( t_a @ ( G @ ( F @ c_union ) ) ))]]) ).
thf(18839,plain,
! [B: $i,A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( B @ c_union ) ) @ ( A @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(simp,[status(thm)],[18758]) ).
thf(403,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_union ) ) )
!= ( E @ ( D @ ( E @ tc_set @ ( D @ ( C @ c_minus ) ) @ c_union ) ) ) )
| ( A
= ( E @ ( D @ ( C @ c_union ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[42,53]) ).
thf(418,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B != E )
| ( A != D )
| ( A
!= ( E @ tc_set @ ( D @ ( C @ c_minus ) ) ) )
| ( A
= ( E @ ( D @ ( C @ c_union ) ) ) ) ),
inference(simp,[status(thm)],[403]) ).
thf(434,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
!= B )
| ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
= ( C @ ( B @ ( A @ c_union ) ) ) ) ),
inference(simp,[status(thm)],[418]) ).
thf(16649,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_inter ) ) )
!= B )
| ( ( C @ ( B @ ( A @ c_union ) ) )
= ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_inter ) ) ) ) ),
inference(rewrite,[status(thm)],[434,393]) ).
thf(52361,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
!= ( t_a @ tc_set @ ( B @ c_uminus ) ) )
| ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[9070,52204]) ).
thf(52362,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[52361:[bind(A,$thf( t_a )),bind(B,$thf( c_emptyset ))]]) ).
thf(52500,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[52362,3462]) ).
thf(16882,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_union ) ) )
!= ( t_a @ ( v_u @ ( v_t @ c_union ) ) ) )
| ( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_inter ) ) )
!= v_u )
| ( v_u != v_a )
| ( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_inter ) ) )
!= B ) ),
inference(paramod_ordered,[status(thm)],[16649,1854]) ).
thf(16883,plain,
( ( ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_inter ) ) )
!= v_u )
| ( v_u != v_a )
| ( ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_inter ) ) )
!= v_u ) ),
inference(pattern_uni,[status(thm)],[16882:[bind(A,$thf( v_t )),bind(B,$thf( v_u )),bind(C,$thf( t_a ))]]) ).
thf(17009,plain,
( ( v_u != v_a )
| ( ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_inter ) ) )
!= v_u ) ),
inference(simp,[status(thm)],[16883]) ).
thf(243,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( c_UNIV @ c_union ) ) )
!= ( D @ ( C @ ( c_emptyset @ c_union ) ) ) )
| ( c_UNIV = C ) ),
inference(paramod_ordered,[status(thm)],[69,84]) ).
thf(264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != D )
| ( A != C )
| ( c_UNIV != c_emptyset )
| ( c_UNIV = C ) ),
inference(simp,[status(thm)],[243]) ).
thf(277,plain,
! [A: $i] :
( ( c_UNIV != c_emptyset )
| ( c_UNIV = A ) ),
inference(simp,[status(thm)],[264]) ).
thf(6989,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( c_UNIV != c_emptyset )
| ( c_UNIV != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[277,276]) ).
thf(6990,plain,
! [A: $i] :
( ( A
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( c_UNIV != c_emptyset ) ),
inference(simp,[status(thm)],[6989]) ).
thf(6991,plain,
c_UNIV != c_emptyset,
inference(pattern_uni,[status(thm)],[6990:[bind(A,$thf( t_a @ ( v_t @ ( v_a @ c_union ) ) ))]]) ).
thf(41189,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41124,544]) ).
thf(41190,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[41189]) ).
thf(41191,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[41190:[bind(A,$thf( t_a @ tc_set @ ( v_t @ c_uminus ) )),bind(B,$thf( t_a )),bind(C,$thf( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) ))]]) ).
thf(42779,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[41191,715]) ).
thf(5561,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ tc_set @ ( D @ ( D @ ( c_UNIV @ ( C @ c_union ) ) @ ( B @ c_union ) ) @ ( A @ c_lessequals ) ) )
!= ( G @ tc_set @ ( H @ ( G @ ( F @ ( E @ c_union ) ) @ c_lessequals ) ) ) )
| ( G @ tc_set @ ( H @ ( E @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4943,71]) ).
thf(5562,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ tc_set @ ( D @ ( D @ ( c_UNIV @ ( C @ c_union ) ) @ ( B @ c_union ) ) @ ( A @ c_lessequals ) ) )
!= ( G @ tc_set @ ( H @ ( G @ ( F @ ( E @ c_union ) ) @ c_lessequals ) ) ) )
| ( G @ tc_set @ ( H @ ( E @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[5561]) ).
thf(5563,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ tc_set @ ( C @ ( C @ ( c_UNIV @ ( D @ c_union ) ) @ ( B @ c_union ) ) @ ( A @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[5562:[bind(A,$thf( N @ ( J @ ( I @ c_union ) ) )),bind(B,$thf( L )),bind(C,$thf( O )),bind(D,$thf( N )),bind(E,$thf( I )),bind(F,$thf( J )),bind(G,$thf( N )),bind(H,$thf( N @ ( N @ ( c_UNIV @ ( O @ c_union ) ) @ ( L @ c_union ) ) ))]]) ).
thf(5634,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ tc_set @ ( C @ ( C @ ( c_UNIV @ ( D @ c_union ) ) @ ( B @ c_union ) ) @ ( A @ c_lessequals ) ) ),
inference(simp,[status(thm)],[5563]) ).
thf(28946,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( C @ ( E @ ( D @ c_union ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_union ) ) @ ( D @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[28898,1313]) ).
thf(28947,plain,
! [B: $i,A: $i] : ( t_a @ tc_set @ ( t_a @ ( A @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( B @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[28946:[bind(A,$thf( K )),bind(B,$thf( B )),bind(C,$thf( t_a )),bind(D,$thf( v_a )),bind(E,$thf( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( K @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) ))]]) ).
thf(29453,plain,
! [B: $i,A: $i] : ( t_a @ tc_set @ ( t_a @ ( A @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( B @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(simp,[status(thm)],[28947]) ).
thf(58247,plain,
! [B: $i,A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( B @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[29453,715]) ).
thf(377,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( B @ tc_set @ ( A @ c_uminus ) @ c_uminus ) )
!= ( C @ tc_set @ ( c_emptyset @ c_uminus ) ) )
| ( A = c_UNIV ) ),
inference(paramod_ordered,[status(thm)],[57,312]) ).
thf(382,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set )
!= ( C @ tc_set ) )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= c_emptyset )
| ( A = c_UNIV ) ),
inference(simp,[status(thm)],[377]) ).
thf(45991,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_union ) ) )
!= ( t_a @ ( t_a @ ( c_UNIV @ ( v_t @ c_union ) ) @ ( v_a @ c_union ) ) ) )
| ( v_u != c_emptyset )
| ( A = c_UNIV ) ),
inference(paramod_ordered,[status(thm)],[42,45945]) ).
thf(46379,plain,
! [B: $i,A: $i] :
( ( B != t_a )
| ( A
!= ( t_a @ ( c_UNIV @ ( v_t @ c_union ) ) ) )
| ( A != v_a )
| ( v_u != c_emptyset )
| ( A = c_UNIV ) ),
inference(simp,[status(thm)],[45991]) ).
thf(46559,plain,
( ( ( t_a @ ( c_UNIV @ ( v_t @ c_union ) ) )
!= v_a )
| ( v_u != c_emptyset )
| ( c_UNIV = v_a ) ),
inference(simp,[status(thm)],[46379]) ).
thf(57795,plain,
( ( ( t_a @ ( c_UNIV @ ( v_t @ c_union ) ) )
!= v_a )
| ( v_u != c_emptyset ) ),
inference(simplifyReflect,[status(thm)],[46559,9273]) ).
thf(681,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_inter ) ) @ c_union ) ) )
= ( C @ ( B @ ( A @ c_union ) ) ) ),
inference(rewrite,[status(thm)],[53,393]) ).
thf(28527,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( v_t @ ( c_UNIV @ c_lessequals ) ) ) )
| ~ $true
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[65,28480]) ).
thf(28528,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( v_t @ ( c_UNIV @ c_lessequals ) ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[28527]) ).
thf(28529,plain,
t_a @ ( c_UNIV @ ( t_a @ ( v_t @ ( c_UNIV @ c_Main_OsubsetI__1 ) ) @ c_in ) ),
inference(pattern_uni,[status(thm)],[28528:[bind(A,$thf( c_UNIV )),bind(B,$thf( v_t )),bind(C,$thf( t_a ))]]) ).
thf(47559,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ ( C @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47503,568]) ).
thf(47560,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ ( C @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[47559]) ).
thf(47561,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[47560:[bind(A,$thf( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_uminus ) )),bind(B,$thf( t_a )),bind(C,$thf( v_a ))]]) ).
thf(55537,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[47561,3462]) ).
thf(55620,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ ( C @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[55537,568]) ).
thf(55621,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ ( C @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[55620]) ).
thf(55622,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[55621:[bind(A,$thf( t_a @ tc_set @ ( v_u @ c_uminus ) )),bind(B,$thf( t_a )),bind(C,$thf( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) ))]]) ).
thf(56998,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_union ) ) @ ( v_a @ c_union ) ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[55622,77]) ).
thf(320,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( v_u @ c_in ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ $true
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[34,49]) ).
thf(321,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( v_u @ c_in ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[320]) ).
thf(322,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( t_a @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ c_Mutil_Otiling ) @ ( t_a @ ( A @ ( v_u @ c_union ) ) @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( t_a @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ c_Mutil_Otiling ) @ ( A @ c_in ) ) )
| ( ( t_a @ ( A @ ( v_u @ c_inter ) ) )
!= c_emptyset ) ),
inference(pattern_uni,[status(thm)],[321:[bind(A,$thf( v_u )),bind(B,$thf( t_a @ ( v_A @ c_Mutil_Otiling ) )),bind(C,$thf( t_a )),bind(D,$thf( D ))]]) ).
thf(362,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( t_a @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ c_Mutil_Otiling ) @ ( t_a @ ( A @ ( v_u @ c_union ) ) @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( t_a @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ c_Mutil_Otiling ) @ ( A @ c_in ) ) )
| ( ( t_a @ ( A @ ( v_u @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[322]) ).
thf(6424,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( C @ tc_set @ ( A @ c_uminus ) @ ( B @ c_inter ) ) @ ( A @ c_union ) ) )
!= ( E @ ( G @ ( F @ c_union ) ) ) )
| ( E @ tc_set @ ( E @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_union ) ) @ ( F @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[1362,1313]) ).
thf(6425,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ tc_set @ ( C @ ( A @ ( C @ ( B @ ( D @ c_union ) ) @ c_union ) ) @ ( D @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[6424:[bind(A,$thf( K )),bind(B,$thf( H )),bind(C,$thf( J )),bind(D,$thf( D )),bind(E,$thf( J )),bind(F,$thf( K )),bind(G,$thf( J @ ( J @ tc_set @ ( K @ c_uminus ) @ ( H @ c_inter ) ) ))]]) ).
thf(6490,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ tc_set @ ( C @ ( A @ ( C @ ( B @ ( D @ c_union ) ) @ c_union ) ) @ ( D @ c_lessequals ) ) ),
inference(simp,[status(thm)],[6425]) ).
thf(12102,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( C @ ( A @ c_union ) ) @ ( A @ c_union ) ) )
!= ( F @ ( E @ ( G @ c_union ) ) ) )
| ( F @ tc_set @ ( F @ ( D @ ( B @ ( C @ ( A @ c_union ) ) @ c_union ) ) @ ( G @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[1813,6490]) ).
thf(12103,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ tc_set @ ( D @ ( A @ ( D @ ( C @ ( B @ c_union ) ) @ c_union ) ) @ ( B @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[12102:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( I )),bind(D,$thf( D )),bind(E,$thf( J @ ( I @ ( H @ c_union ) ) )),bind(F,$thf( J )),bind(G,$thf( H ))]]) ).
thf(12182,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ tc_set @ ( D @ ( A @ ( D @ ( C @ ( B @ c_union ) ) @ c_union ) ) @ ( B @ c_lessequals ) ) ),
inference(simp,[status(thm)],[12103]) ).
thf(562,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( C @ ( A @ ( D @ c_union ) ) @ c_lessequals ) ) )
!= ( G @ tc_set @ ( F @ ( H @ c_lessequals ) ) ) )
| ( G @ tc_set @ ( F @ ( G @ ( E @ ( H @ c_union ) ) @ c_lessequals ) ) )
| ~ $true
| ~ ( G @ tc_set @ ( F @ ( E @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[55,55]) ).
thf(563,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( C @ ( A @ ( D @ c_union ) ) @ c_lessequals ) ) )
!= ( G @ tc_set @ ( F @ ( H @ c_lessequals ) ) ) )
| ( G @ tc_set @ ( F @ ( G @ ( E @ ( H @ c_union ) ) @ c_lessequals ) ) )
| ~ ( G @ tc_set @ ( F @ ( E @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[562]) ).
thf(564,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ tc_set @ ( A @ ( E @ ( B @ ( E @ ( D @ ( C @ c_union ) ) @ c_union ) ) @ c_lessequals ) ) )
| ~ ( E @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( E @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( E @ tc_set @ ( A @ ( D @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[563:[bind(A,$thf( J )),bind(B,$thf( B )),bind(C,$thf( K )),bind(D,$thf( I )),bind(E,$thf( E )),bind(F,$thf( B )),bind(G,$thf( K )),bind(H,$thf( K @ ( J @ ( I @ c_union ) ) ))]]) ).
thf(567,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ tc_set @ ( A @ ( E @ ( B @ ( E @ ( D @ ( C @ c_union ) ) @ c_union ) ) @ c_lessequals ) ) )
| ~ ( E @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( E @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( E @ tc_set @ ( A @ ( D @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[564]) ).
thf(343,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
!= ( F @ ( c_emptyset @ ( E @ c_in ) ) ) )
| ~ $true
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[49,62]) ).
thf(344,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
!= ( F @ ( c_emptyset @ ( E @ c_in ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[343]) ).
thf(361,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set )
!= F )
| ( ( C @ ( B @ c_Mutil_Otiling ) )
!= c_emptyset )
| ( ( C @ ( D @ ( A @ c_union ) ) )
!= E )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[344]) ).
thf(367,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ c_Mutil_Otiling ) )
!= c_emptyset )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[361]) ).
thf(16300,plain,
( ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= v_a ) ),
inference(paramod_ordered,[status(thm)],[16183,9220]) ).
thf(16375,plain,
( ( t_a != t_a )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= v_t )
| ( v_a != v_a )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= v_a ) ),
inference(simp,[status(thm)],[16300]) ).
thf(16570,plain,
( ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= v_t )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= v_a ) ),
inference(simp,[status(thm)],[16375]) ).
thf(9232,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( A != v_a ) ),
inference(paramod_ordered,[status(thm)],[42,9220]) ).
thf(9258,plain,
! [A: $i] :
( ( A != t_a )
| ( v_t != v_a )
| ( v_a != v_a ) ),
inference(simp,[status(thm)],[9232]) ).
thf(9275,plain,
v_t != v_a,
inference(simp,[status(thm)],[9258]) ).
thf(7800,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_union ) ) )
!= ( G @ ( E @ ( G @ ( c_UNIV @ ( F @ c_union ) ) @ c_union ) ) ) )
| ( G @ tc_set @ ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_union ) ) @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,7757]) ).
thf(7801,plain,
! [C: $i,B: $i,A: $i] : ( B @ tc_set @ ( B @ ( B @ ( C @ ( c_UNIV @ c_union ) ) @ ( A @ c_union ) ) @ ( c_UNIV @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[7800:[bind(A,$thf( A )),bind(B,$thf( c_UNIV )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( D )),bind(F,$thf( A )),bind(G,$thf( C ))]]) ).
thf(7889,plain,
! [C: $i,B: $i,A: $i] : ( B @ tc_set @ ( B @ ( B @ ( C @ ( c_UNIV @ c_union ) ) @ ( A @ c_union ) ) @ ( c_UNIV @ c_lessequals ) ) ),
inference(simp,[status(thm)],[7801]) ).
thf(8052,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( B @ ( c_UNIV @ ( A @ c_union ) ) @ ( c_UNIV @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[7889,69]) ).
thf(47550,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47503,544]) ).
thf(47551,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[47550]) ).
thf(47552,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( t_a @ ( v_a @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[47551:[bind(A,$thf( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_uminus ) )),bind(B,$thf( t_a )),bind(C,$thf( v_a ))]]) ).
thf(55242,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_a @ c_uminus ) @ ( t_a @ ( c_UNIV @ ( v_u @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[47552,3462,715]) ).
thf(570,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( c_UNIV @ ( A @ ( c_emptyset @ ( B @ c_inter ) ) @ c_union ) ) )
!= ( D @ ( C @ ( c_UNIV @ c_union ) ) ) )
| ( ( A @ ( c_UNIV @ ( B @ c_union ) ) )
= c_UNIV ) ),
inference(paramod_ordered,[status(thm)],[453,69]) ).
thf(610,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != D )
| ( c_UNIV != C )
| ( ( A @ ( c_emptyset @ ( B @ c_inter ) ) )
!= c_UNIV )
| ( ( A @ ( c_UNIV @ ( B @ c_union ) ) )
= c_UNIV ) ),
inference(simp,[status(thm)],[570]) ).
thf(636,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_emptyset @ ( A @ c_inter ) ) )
!= c_UNIV )
| ( ( B @ ( c_UNIV @ ( A @ c_union ) ) )
= c_UNIV ) ),
inference(simp,[status(thm)],[610]) ).
thf(15025,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
!= ( C @ tc_set @ ( B @ c_uminus ) ) )
| ( ( C @ ( c_UNIV @ ( C @ tc_set @ ( B @ c_uminus ) @ c_union ) ) )
= ( C @ ( B @ ( c_UNIV @ c_union ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[9070,3887]) ).
thf(15026,plain,
! [A: $i] :
( ( A @ ( c_UNIV @ ( A @ tc_set @ ( c_emptyset @ c_uminus ) @ c_union ) ) )
= ( A @ ( c_emptyset @ ( c_UNIV @ c_union ) ) ) ),
inference(pattern_uni,[status(thm)],[15025:[bind(A,$thf( A )),bind(B,$thf( c_emptyset )),bind(C,$thf( A ))]]) ).
thf(15432,plain,
! [A: $i] :
( ( A @ ( c_UNIV @ ( c_UNIV @ c_union ) ) )
= c_UNIV ),
inference(rewrite,[status(thm)],[15026,69,9070]) ).
thf(20336,plain,
( ( ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= v_a ) ),
inference(paramod_ordered,[status(thm)],[20205,9220]) ).
thf(20497,plain,
( ( t_a != t_a )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= v_t )
| ( v_a != v_a )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= v_a ) ),
inference(simp,[status(thm)],[20336]) ).
thf(20536,plain,
( ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= v_t )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= v_a ) ),
inference(simp,[status(thm)],[20497]) ).
thf(16205,plain,
( ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[16183,276]) ).
thf(16391,plain,
( ( t_a != t_a )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= v_t )
| ( v_a != v_a )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[16205]) ).
thf(16467,plain,
( ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= v_t )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[16391]) ).
thf(3812,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ tc_set @ ( B @ c_uminus ) @ ( B @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( ( A @ ( c_UNIV @ ( B @ c_union ) ) )
!= v_u ) ),
inference(paramod_ordered,[status(thm)],[1452,226]) ).
thf(3860,plain,
! [B: $i,A: $i] :
( ( A != t_a )
| ( ( A @ tc_set @ ( B @ c_uminus ) )
!= v_t )
| ( B != v_a )
| ( ( A @ ( c_UNIV @ ( B @ c_union ) ) )
!= v_u ) ),
inference(simp,[status(thm)],[3812]) ).
thf(3881,plain,
( ( ( t_a @ tc_set @ ( v_a @ c_uminus ) )
!= v_t )
| ( ( t_a @ ( c_UNIV @ ( v_a @ c_union ) ) )
!= v_u ) ),
inference(simp,[status(thm)],[3860]) ).
thf(20257,plain,
! [B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_union ) ) ) )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[20205,46]) ).
thf(20488,plain,
! [B: $i,A: $i] :
( ( t_a != B )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= c_emptyset )
| ( v_a != A )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
= A ) ),
inference(simp,[status(thm)],[20257]) ).
thf(20526,plain,
( ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= c_emptyset )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
= v_a ) ),
inference(simp,[status(thm)],[20488]) ).
thf(32182,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32153,544]) ).
thf(32183,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[32182]) ).
thf(32184,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( t_a @ ( v_a @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[32183:[bind(A,$thf( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) )),bind(B,$thf( t_a )),bind(C,$thf( v_a ))]]) ).
thf(38810,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_a @ c_uminus ) @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[32184,3462,715]) ).
thf(44659,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( E @ ( D @ ( C @ c_union ) ) ) )
| ( E @ tc_set @ ( E @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( B @ c_union ) ) @ ( C @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[44635,12172]) ).
thf(44660,plain,
! [B: $i,A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( B @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( A @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[44659:[bind(A,$thf( K )),bind(B,$thf( B )),bind(C,$thf( v_a )),bind(D,$thf( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( K @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) )),bind(E,$thf( t_a ))]]) ).
thf(45174,plain,
! [B: $i,A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( B @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( A @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(simp,[status(thm)],[44660]) ).
thf(61929,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ tc_set @ ( B @ c_uminus ) @ c_uminus ) )
!= ( t_a @ tc_set @ ( D @ c_uminus ) ) )
| ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( B @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( C @ c_union ) ) @ ( v_a @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[6340,45174]) ).
thf(61930,plain,
! [B: $i,A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( B @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( A @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[61929:[bind(A,$thf( t_a )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( t_a @ tc_set @ ( E @ c_uminus ) ))]]) ).
thf(62213,plain,
! [B: $i,A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( B @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( A @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(simp,[status(thm)],[61930]) ).
thf(29589,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( B @ ( D @ ( C @ c_union ) ) ) )
| ( B @ tc_set @ ( B @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( A @ c_union ) ) @ ( D @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[29516,1183]) ).
thf(29590,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( A @ c_union ) ) @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[29589:[bind(A,$thf( A )),bind(B,$thf( t_a )),bind(C,$thf( v_a )),bind(D,$thf( t_a @ tc_set @ ( v_t @ c_uminus ) ))]]) ).
thf(38582,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( A @ c_union ) ) @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[29590,3462]) ).
thf(17032,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_union ) ) )
!= ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( E @ c_union ) ) ) )
| ( t_a @ tc_set @ ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_union ) ) @ ( v_a @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,16208]) ).
thf(17033,plain,
! [B: $i,A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( B @ c_union ) ) @ ( A @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[17032:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( t_a )),bind(D,$thf( t_a @ tc_set @ ( v_t @ c_uminus ) )),bind(E,$thf( t_a @ ( G @ ( F @ c_union ) ) ))]]) ).
thf(17112,plain,
! [B: $i,A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( B @ c_union ) ) @ ( A @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(simp,[status(thm)],[17033]) ).
thf(9238,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ tc_set @ ( B @ c_uminus ) @ ( B @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( ( A @ ( c_UNIV @ ( B @ c_union ) ) )
!= v_a ) ),
inference(paramod_ordered,[status(thm)],[1452,9220]) ).
thf(9259,plain,
! [B: $i,A: $i] :
( ( A != t_a )
| ( ( A @ tc_set @ ( B @ c_uminus ) )
!= v_t )
| ( B != v_a )
| ( ( A @ ( c_UNIV @ ( B @ c_union ) ) )
!= v_a ) ),
inference(simp,[status(thm)],[9238]) ).
thf(9276,plain,
( ( ( t_a @ tc_set @ ( v_a @ c_uminus ) )
!= v_t )
| ( ( t_a @ ( c_UNIV @ ( v_a @ c_union ) ) )
!= v_a ) ),
inference(simp,[status(thm)],[9259]) ).
thf(454,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_UNIV @ ( B @ c_minus ) ) )
!= ( E @ tc_set @ ( E @ tc_set @ ( D @ c_uminus ) @ ( C @ c_minus ) ) ) )
| ( ( A @ ( c_emptyset @ ( B @ c_inter ) ) )
= ( E @ ( D @ ( C @ c_inter ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[388,86]) ).
thf(456,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set )
!= ( E @ tc_set ) )
| ( ( E @ tc_set @ ( D @ c_uminus ) )
!= c_UNIV )
| ( B != C )
| ( ( A @ ( c_emptyset @ ( B @ c_inter ) ) )
= ( E @ ( D @ ( C @ c_inter ) ) ) ) ),
inference(simp,[status(thm)],[454]) ).
thf(458,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set )
!= ( D @ tc_set ) )
| ( ( D @ tc_set @ ( C @ c_uminus ) )
!= c_UNIV )
| ( ( A @ ( c_emptyset @ ( B @ c_inter ) ) )
= ( D @ ( C @ ( B @ c_inter ) ) ) ) ),
inference(simp,[status(thm)],[456]) ).
thf(3762,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ tc_set @ ( B @ c_uminus ) @ ( B @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( ( A @ ( c_UNIV @ ( B @ c_union ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[1452,276]) ).
thf(3834,plain,
! [B: $i,A: $i] :
( ( A != t_a )
| ( ( A @ tc_set @ ( B @ c_uminus ) )
!= v_t )
| ( B != v_a )
| ( ( A @ ( c_UNIV @ ( B @ c_union ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[3762]) ).
thf(3904,plain,
( ( ( t_a @ tc_set @ ( v_a @ c_uminus ) )
!= v_t )
| ( ( t_a @ ( c_UNIV @ ( v_a @ c_union ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[3834]) ).
thf(55609,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[55537,544]) ).
thf(55610,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[55609]) ).
thf(55611,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[55610:[bind(A,$thf( t_a @ tc_set @ ( v_u @ c_uminus ) )),bind(B,$thf( t_a )),bind(C,$thf( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) ))]]) ).
thf(56604,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_a @ c_union ) ) @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[55611,715]) ).
thf(557,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_union ) ) )
!= ( F @ ( D @ ( G @ c_union ) ) ) )
| ( F @ tc_set @ ( E @ ( C @ ( B @ ( A @ c_union ) ) @ c_lessequals ) ) )
| ~ ( F @ tc_set @ ( E @ ( G @ c_lessequals ) ) )
| ~ ( F @ tc_set @ ( E @ ( D @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,55]) ).
thf(558,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( A @ ( D @ ( C @ ( B @ c_union ) ) @ c_lessequals ) ) )
| ~ ( D @ tc_set @ ( A @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ c_lessequals ) ) )
| ~ ( D @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) ),
inference(pattern_uni,[status(thm)],[557:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( I )),bind(E,$thf( E )),bind(F,$thf( K )),bind(G,$thf( K @ tc_set @ ( I @ ( H @ c_minus ) ) ))]]) ).
thf(569,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( A @ ( D @ ( C @ ( B @ c_union ) ) @ c_lessequals ) ) )
| ~ ( D @ tc_set @ ( A @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ c_lessequals ) ) )
| ~ ( D @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[558]) ).
thf(34792,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( A @ ( D @ ( C @ ( B @ c_union ) ) @ c_lessequals ) ) )
| ~ ( D @ tc_set @ ( A @ ( D @ ( D @ tc_set @ ( C @ c_uminus ) @ ( B @ c_inter ) ) @ c_lessequals ) ) )
| ~ ( D @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) ),
inference(rewrite,[status(thm)],[569,393]) ).
thf(34041,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ ( C @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18094,568]) ).
thf(34042,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ ( C @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[34041]) ).
thf(34043,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[34042:[bind(A,$thf( t_a @ tc_set @ ( v_u @ c_uminus ) )),bind(B,$thf( t_a )),bind(C,$thf( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) ))]]) ).
thf(40204,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_union ) ) @ ( v_t @ c_union ) ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[34043,77]) ).
thf(18,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
thf(63,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(395,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_union ) ) )
!= ( E @ ( D @ ( c_UNIV @ c_union ) ) ) )
| ( ( C @ ( B @ ( A @ c_union ) ) )
= c_UNIV ) ),
inference(paramod_ordered,[status(thm)],[53,69]) ).
thf(426,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C != E )
| ( B != D )
| ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
!= c_UNIV )
| ( ( C @ ( B @ ( A @ c_union ) ) )
= c_UNIV ) ),
inference(simp,[status(thm)],[395]) ).
thf(442,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
!= c_UNIV )
| ( ( C @ ( B @ ( A @ c_union ) ) )
= c_UNIV ) ),
inference(simp,[status(thm)],[426]) ).
thf(20685,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_inter ) ) )
!= c_UNIV )
| ( ( C @ ( B @ ( A @ c_union ) ) )
= c_UNIV ) ),
inference(rewrite,[status(thm)],[442,393]) ).
thf(20822,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( c_UNIV != c_UNIV )
| ( v_u = c_emptyset )
| ( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_inter ) ) )
!= c_UNIV ) ),
inference(paramod_ordered,[status(thm)],[20685,192]) ).
thf(20823,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( v_u = c_emptyset )
| ( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_inter ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[20822]) ).
thf(20824,plain,
( ( v_u = c_emptyset )
| ( ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_inter ) ) )
!= c_UNIV ) ),
inference(pattern_uni,[status(thm)],[20823:[bind(A,$thf( v_a )),bind(B,$thf( v_t )),bind(C,$thf( t_a ))]]) ).
thf(18743,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ tc_set @ ( A @ c_uminus ) @ c_union ) ) )
!= ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( D @ c_union ) ) ) )
| ( t_a @ tc_set @ ( C @ tc_set @ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[715,18025]) ).
thf(18744,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_uminus ) @ ( A @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[18743:[bind(A,$thf( E )),bind(B,$thf( t_a @ tc_set @ ( v_u @ c_uminus ) )),bind(C,$thf( t_a )),bind(D,$thf( t_a @ tc_set @ ( E @ c_uminus ) ))]]) ).
thf(18866,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_uminus ) @ ( A @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(simp,[status(thm)],[18744]) ).
thf(27791,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( v_u @ ( A @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[18866,6340]) ).
thf(9233,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ( A != v_a ) ),
inference(paramod_ordered,[status(thm)],[46,9220]) ).
thf(9264,plain,
! [A: $i] :
( ( A != t_a )
| ( c_emptyset != v_t )
| ( v_a != v_a ) ),
inference(simp,[status(thm)],[9233]) ).
thf(9281,plain,
c_emptyset != v_t,
inference(simp,[status(thm)],[9264]) ).
thf(413,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_union ) ) )
!= ( F @ ( G @ ( D @ c_union ) ) ) )
| ( F @ tc_set @ ( F @ ( E @ c_Mutil_Otiling ) @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) )
| ~ ( F @ tc_set @ ( F @ ( E @ c_Mutil_Otiling ) @ ( G @ c_in ) ) )
| ~ ( F @ tc_set @ ( E @ ( D @ c_in ) ) )
| ( ( F @ ( G @ ( D @ c_inter ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[53,49]) ).
thf(414,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( D @ ( A @ c_Mutil_Otiling ) @ ( D @ ( C @ ( B @ c_union ) ) @ c_in ) ) )
| ~ ( D @ tc_set @ ( D @ ( A @ c_Mutil_Otiling ) @ ( C @ c_in ) ) )
| ~ ( D @ tc_set @ ( A @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ c_in ) ) )
| ( ( D @ ( C @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ c_inter ) ) )
!= c_emptyset ) ),
inference(pattern_uni,[status(thm)],[413:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( K @ tc_set @ ( I @ ( H @ c_minus ) ) )),bind(E,$thf( E )),bind(F,$thf( K )),bind(G,$thf( I ))]]) ).
thf(451,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( D @ ( A @ c_Mutil_Otiling ) @ ( D @ ( C @ ( B @ c_union ) ) @ c_in ) ) )
| ~ ( D @ tc_set @ ( D @ ( A @ c_Mutil_Otiling ) @ ( C @ c_in ) ) )
| ~ ( D @ tc_set @ ( A @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ c_in ) ) )
| ( ( D @ ( C @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[414]) ).
thf(23544,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( D @ ( A @ c_Mutil_Otiling ) @ ( D @ ( C @ ( B @ c_union ) ) @ c_in ) ) )
| ~ ( D @ tc_set @ ( D @ ( A @ c_Mutil_Otiling ) @ ( C @ c_in ) ) )
| ~ ( D @ tc_set @ ( A @ ( D @ ( D @ tc_set @ ( C @ c_uminus ) @ ( B @ c_inter ) ) @ c_in ) ) )
| ( ( D @ ( C @ ( D @ ( D @ tc_set @ ( C @ c_uminus ) @ ( B @ c_inter ) ) @ c_inter ) ) )
!= c_emptyset ) ),
inference(rewrite,[status(thm)],[451,393]) ).
thf(338,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_A @ ( v_a @ c_in ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ $true
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[31,49]) ).
thf(339,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_A @ ( v_a @ c_in ) ) )
!= ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[338]) ).
thf(340,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( A @ ( v_a @ c_union ) ) @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( A @ c_in ) ) )
| ( ( t_a @ ( A @ ( v_a @ c_inter ) ) )
!= c_emptyset ) ),
inference(pattern_uni,[status(thm)],[339:[bind(A,$thf( v_a )),bind(B,$thf( v_A )),bind(C,$thf( t_a ))]]) ).
thf(370,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( A @ ( v_a @ c_union ) ) @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( A @ c_in ) ) )
| ( ( t_a @ ( A @ ( v_a @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[340]) ).
thf(33433,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( B @ ( D @ ( C @ c_union ) ) ) )
| ( B @ tc_set @ ( B @ ( A @ ( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_union ) ) @ ( C @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[33382,1313]) ).
thf(33434,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ ( A @ ( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[33433:[bind(A,$thf( A )),bind(B,$thf( t_a )),bind(C,$thf( v_a )),bind(D,$thf( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_t @ c_inter ) ) @ c_uminus ) ))]]) ).
thf(36301,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( t_a @ ( c_emptyset @ ( v_t @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[33434,715]) ).
thf(36441,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
!= ( t_a @ tc_set @ ( B @ c_uminus ) ) )
| ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( t_a @ ( c_emptyset @ ( v_t @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[9070,36301]) ).
thf(36442,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( t_a @ ( c_emptyset @ ( v_t @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[36441:[bind(A,$thf( t_a )),bind(B,$thf( c_emptyset ))]]) ).
thf(36557,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_emptyset @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ),
inference(rewrite,[status(thm)],[36442,3462]) ).
thf(34647,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ ( C @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34599,568]) ).
thf(34648,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ ( C @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[34647]) ).
thf(34649,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[34648:[bind(A,$thf( t_a @ tc_set @ ( v_t @ c_uminus ) )),bind(B,$thf( t_a )),bind(C,$thf( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_uminus ) ))]]) ).
thf(42461,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_uminus ) @ ( t_a @ ( c_UNIV @ ( v_t @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[34649,715]) ).
thf(30352,plain,
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( v_a @ ( c_UNIV @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[30349,22621]) ).
thf(30353,plain,
( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( v_a @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[30352]) ).
thf(30419,plain,
( ( ( t_a @ tc_set )
!= ( t_a @ tc_set ) )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= v_a )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[30353]) ).
thf(30437,plain,
( ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= v_a )
| ( ( t_a @ tc_set @ ( v_t @ c_uminus ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[30419]) ).
thf(310,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( B @ tc_set @ ( A @ c_uminus ) @ c_uminus ) )
!= ( C @ tc_set @ ( c_UNIV @ c_uminus ) ) )
| ( A = c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[57,79]) ).
thf(314,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set )
!= ( C @ tc_set ) )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= c_UNIV )
| ( A = c_emptyset ) ),
inference(simp,[status(thm)],[310]) ).
thf(355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( v_t @ ( v_a @ c_inter ) ) )
!= ( C @ ( D @ ( A @ c_inter ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( c_emptyset != c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[36,49]) ).
thf(356,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( v_t @ ( v_a @ c_inter ) ) )
!= ( C @ ( D @ ( A @ c_inter ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[355]) ).
thf(357,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( t_a @ ( A @ c_Mutil_Otiling ) @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( t_a @ ( A @ c_Mutil_Otiling ) @ ( v_t @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( A @ ( v_a @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[356:[bind(A,$thf( v_a )),bind(B,$thf( B )),bind(C,$thf( t_a )),bind(D,$thf( v_t ))]]) ).
thf(363,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( t_a @ ( A @ c_Mutil_Otiling ) @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( t_a @ ( A @ c_Mutil_Otiling ) @ ( v_t @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( A @ ( v_a @ c_in ) ) ) ),
inference(simp,[status(thm)],[357]) ).
thf(6635,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( C @ tc_set @ ( A @ c_uminus ) @ ( B @ c_inter ) ) @ ( A @ c_union ) ) )
!= ( F @ ( D @ ( F @ ( c_UNIV @ ( E @ c_union ) ) @ c_union ) ) ) )
| ( F @ tc_set @ ( C @ ( B @ ( A @ c_union ) ) @ ( E @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[1362,6496]) ).
thf(6636,plain,
! [C: $i,B: $i,A: $i] : ( B @ tc_set @ ( B @ ( A @ ( B @ ( c_UNIV @ ( C @ c_union ) ) @ c_union ) ) @ ( C @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[6635:[bind(A,$thf( L @ ( c_UNIV @ ( O @ c_union ) ) )),bind(B,$thf( J )),bind(C,$thf( L )),bind(D,$thf( L @ ( L @ tc_set @ ( L @ ( c_UNIV @ ( O @ c_union ) ) @ c_uminus ) @ ( J @ c_inter ) ) )),bind(E,$thf( O )),bind(F,$thf( L ))]]) ).
thf(6721,plain,
! [C: $i,B: $i,A: $i] : ( B @ tc_set @ ( B @ ( A @ ( B @ ( c_UNIV @ ( C @ c_union ) ) @ c_union ) ) @ ( C @ c_lessequals ) ) ),
inference(simp,[status(thm)],[6636]) ).
thf(202,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_union ) ) )
!= ( t_a @ ( v_u @ ( v_t @ c_union ) ) ) )
| ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( A @ c_in ) ) )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[42,108]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( B != t_a )
| ( A != v_u )
| ( A != v_t )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset )
| ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[202]) ).
thf(218,plain,
( ( v_u != v_t )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset )
| ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( v_t @ c_in ) ) ) ),
inference(simp,[status(thm)],[209]) ).
thf(329,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
!= ( G @ tc_set @ ( G @ ( F @ c_Mutil_Otiling ) @ ( H @ c_in ) ) ) )
| ( G @ tc_set @ ( G @ ( F @ c_Mutil_Otiling ) @ ( G @ ( H @ ( E @ c_union ) ) @ c_in ) ) )
| ~ $true
| ~ ( G @ tc_set @ ( F @ ( E @ c_in ) ) )
| ( ( G @ ( H @ ( E @ c_inter ) ) )
!= c_emptyset )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[49,49]) ).
thf(330,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
!= ( G @ tc_set @ ( G @ ( F @ c_Mutil_Otiling ) @ ( H @ c_in ) ) ) )
| ( G @ tc_set @ ( G @ ( F @ c_Mutil_Otiling ) @ ( G @ ( H @ ( E @ c_union ) ) @ c_in ) ) )
| ~ ( G @ tc_set @ ( F @ ( E @ c_in ) ) )
| ( ( G @ ( H @ ( E @ c_inter ) ) )
!= c_emptyset )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[329]) ).
thf(331,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ tc_set @ ( E @ ( A @ c_Mutil_Otiling ) @ ( E @ ( E @ ( D @ ( C @ c_union ) ) @ ( B @ c_union ) ) @ c_in ) ) )
| ~ ( E @ tc_set @ ( A @ ( B @ c_in ) ) )
| ( ( E @ ( E @ ( D @ ( C @ c_union ) ) @ ( B @ c_inter ) ) )
!= c_emptyset )
| ~ ( E @ tc_set @ ( E @ ( A @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ ( E @ tc_set @ ( A @ ( C @ c_in ) ) )
| ( ( E @ ( D @ ( C @ c_inter ) ) )
!= c_emptyset ) ),
inference(pattern_uni,[status(thm)],[330:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( K )),bind(D,$thf( J )),bind(E,$thf( E )),bind(F,$thf( B )),bind(G,$thf( K )),bind(H,$thf( K @ ( J @ ( I @ c_union ) ) ))]]) ).
thf(368,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ tc_set @ ( E @ ( A @ c_Mutil_Otiling ) @ ( E @ ( E @ ( D @ ( C @ c_union ) ) @ ( B @ c_union ) ) @ c_in ) ) )
| ~ ( E @ tc_set @ ( A @ ( B @ c_in ) ) )
| ( ( E @ ( E @ ( D @ ( C @ c_union ) ) @ ( B @ c_inter ) ) )
!= c_emptyset )
| ~ ( E @ tc_set @ ( E @ ( A @ c_Mutil_Otiling ) @ ( D @ c_in ) ) )
| ~ ( E @ tc_set @ ( A @ ( C @ c_in ) ) )
| ( ( E @ ( D @ ( C @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[331]) ).
thf(18011,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ ( v_a @ c_union ) ) )
!= ( B @ ( D @ ( C @ c_union ) ) ) )
| ( B @ tc_set @ ( B @ ( A @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_union ) ) @ ( D @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[17997,1315]) ).
thf(18012,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ ( A @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_union ) ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[18011:[bind(A,$thf( A )),bind(B,$thf( t_a )),bind(C,$thf( v_a )),bind(D,$thf( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) ))]]) ).
thf(23308,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[18012,715]) ).
thf(23328,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ c_lessequals ) ) )
!= ( D @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_union ) ) @ c_lessequals ) ) ) )
| ( D @ tc_set @ ( E @ ( B @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23308,71]) ).
thf(23329,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ c_lessequals ) ) )
!= ( D @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_union ) ) @ c_lessequals ) ) ) )
| ( D @ tc_set @ ( E @ ( B @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[23328]) ).
thf(23330,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_t @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[23329:[bind(A,$thf( N )),bind(B,$thf( v_t )),bind(C,$thf( t_a @ tc_set @ ( v_u @ c_uminus ) )),bind(D,$thf( t_a )),bind(E,$thf( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( N @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) ))]]) ).
thf(23490,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_t @ c_lessequals ) ) ),
inference(simp,[status(thm)],[23330]) ).
thf(24064,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ tc_set @ ( B @ c_uminus ) @ c_uminus ) )
!= ( t_a @ tc_set @ ( C @ c_uminus ) ) )
| ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( B @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_t @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[6340,23490]) ).
thf(24065,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( A @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_t @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[24064:[bind(A,$thf( t_a )),bind(B,$thf( D )),bind(C,$thf( t_a @ tc_set @ ( D @ c_uminus ) ))]]) ).
thf(24150,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( A @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_t @ c_lessequals ) ) ),
inference(simp,[status(thm)],[24065]) ).
thf(23334,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ tc_set @ ( B @ c_uminus ) @ c_uminus ) )
!= ( t_a @ tc_set @ ( C @ c_uminus ) ) )
| ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( B @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[6340,23308]) ).
thf(23335,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( A @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[23334:[bind(A,$thf( t_a )),bind(B,$thf( D )),bind(C,$thf( t_a @ tc_set @ ( D @ c_uminus ) ))]]) ).
thf(23495,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( A @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[23335]) ).
thf(36327,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ tc_set @ ( B @ c_uminus ) @ c_uminus ) )
!= ( t_a @ tc_set @ ( C @ c_uminus ) ) )
| ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( B @ ( t_a @ ( c_emptyset @ ( v_t @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[6340,36301]) ).
thf(36328,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( A @ ( t_a @ ( c_emptyset @ ( v_t @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[36327:[bind(A,$thf( t_a )),bind(B,$thf( D )),bind(C,$thf( t_a @ tc_set @ ( D @ c_uminus ) ))]]) ).
thf(36528,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( A @ ( t_a @ ( c_emptyset @ ( v_t @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(simp,[status(thm)],[36328]) ).
thf(400,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_union ) ) )
!= ( t_a @ ( v_u @ ( v_t @ c_union ) ) ) )
| ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[53,108]) ).
thf(425,plain,
! [C: $i,B: $i,A: $i] :
( ( C != t_a )
| ( B != v_u )
| ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
!= v_t )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset )
| ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[400]) ).
thf(441,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ ( v_u @ ( A @ c_minus ) ) )
!= v_t )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset )
| ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[425]) ).
thf(19697,plain,
! [A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( A @ c_inter ) ) )
!= v_t )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset )
| ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(rewrite,[status(thm)],[441,393]) ).
thf(30665,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_a @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[30644,544]) ).
thf(30666,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_a @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( C @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[30665]) ).
thf(30667,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_a @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[30666:[bind(A,$thf( t_a @ tc_set @ ( v_u @ c_uminus ) )),bind(B,$thf( t_a )),bind(C,$thf( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_a @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) ))]]) ).
thf(60136,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_a @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[30667,715]) ).
thf(75,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[74]) ).
thf(41200,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ ( C @ c_union ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41124,568]) ).
thf(41201,plain,
! [C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) @ c_lessequals ) ) )
!= ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ ( C @ c_union ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[41200]) ).
thf(41202,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) @ c_union ) ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[41201:[bind(A,$thf( t_a @ tc_set @ ( v_t @ c_uminus ) )),bind(B,$thf( t_a )),bind(C,$thf( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( v_a @ c_union ) ) ))]]) ).
thf(43127,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ ( t_a @ tc_set @ ( v_t @ c_uminus ) @ c_union ) ) @ ( v_a @ c_union ) ) @ c_lessequals ) ),
inference(rewrite,[status(thm)],[41202,77]) ).
thf(27958,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( A @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ c_lessequals ) ) )
!= ( D @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_union ) ) @ c_lessequals ) ) ) )
| ( D @ tc_set @ ( E @ ( C @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23495,67]) ).
thf(27959,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( A @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ c_lessequals ) ) )
!= ( D @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_union ) ) @ c_lessequals ) ) ) )
| ( D @ tc_set @ ( E @ ( C @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[27958]) ).
thf(27960,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( A @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[27959:[bind(A,$thf( L )),bind(B,$thf( v_t )),bind(C,$thf( t_a @ tc_set @ ( v_u @ c_uminus ) )),bind(D,$thf( t_a )),bind(E,$thf( t_a @ tc_set @ ( t_a @ ( L @ ( v_u @ c_inter ) ) @ c_uminus ) ))]]) ).
thf(28117,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( A @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_lessequals ) ) ),
inference(simp,[status(thm)],[27960]) ).
thf(51558,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ tc_set @ ( B @ c_uminus ) @ c_uminus ) )
!= ( t_a @ tc_set @ ( C @ c_uminus ) ) )
| ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( B @ ( t_a @ ( c_emptyset @ ( v_u @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[6340,51528]) ).
thf(51559,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( A @ ( t_a @ ( c_emptyset @ ( v_u @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[51558:[bind(A,$thf( t_a )),bind(B,$thf( D )),bind(C,$thf( t_a @ tc_set @ ( D @ c_uminus ) ))]]) ).
thf(51761,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( A @ ( t_a @ ( c_emptyset @ ( v_u @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(simp,[status(thm)],[51559]) ).
thf(22658,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( v_a @ ( c_UNIV @ c_lessequals ) ) ) )
| ~ $true
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[65,22621]) ).
thf(22659,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( v_a @ ( c_UNIV @ c_lessequals ) ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[22658]) ).
thf(22660,plain,
t_a @ ( c_UNIV @ ( t_a @ ( v_a @ ( c_UNIV @ c_Main_OsubsetI__1 ) ) @ c_in ) ),
inference(pattern_uni,[status(thm)],[22659:[bind(A,$thf( c_UNIV )),bind(B,$thf( v_a )),bind(C,$thf( t_a ))]]) ).
thf(464,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ ( B @ c_minus ) ) )
!= ( E @ tc_set @ ( E @ tc_set @ ( D @ c_uminus ) @ ( C @ c_minus ) ) ) )
| ( ( A @ ( c_UNIV @ ( B @ c_inter ) ) )
= ( E @ ( D @ ( C @ c_inter ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[392,86]) ).
thf(469,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set )
!= ( E @ tc_set ) )
| ( ( E @ tc_set @ ( D @ c_uminus ) )
!= c_emptyset )
| ( B != C )
| ( ( A @ ( c_UNIV @ ( B @ c_inter ) ) )
= ( E @ ( D @ ( C @ c_inter ) ) ) ) ),
inference(simp,[status(thm)],[464]) ).
thf(473,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set )
!= ( D @ tc_set ) )
| ( ( D @ tc_set @ ( C @ c_uminus ) )
!= c_emptyset )
| ( ( A @ ( c_UNIV @ ( B @ c_inter ) ) )
= ( D @ ( C @ ( B @ c_inter ) ) ) ) ),
inference(simp,[status(thm)],[469]) ).
thf(26501,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set )
!= ( D @ tc_set ) )
| ( ( D @ tc_set @ ( C @ c_uminus ) )
!= c_emptyset )
| ( ( D @ ( C @ ( B @ c_inter ) ) )
= B ) ),
inference(rewrite,[status(thm)],[473,3462]) ).
thf(313,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_UNIV @ c_uminus ) )
!= ( C @ tc_set @ ( C @ tc_set @ ( B @ c_uminus ) @ c_uminus ) ) )
| ( c_emptyset = B ) ),
inference(paramod_ordered,[status(thm)],[79,57]) ).
thf(315,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set )
!= ( C @ tc_set ) )
| ( ( C @ tc_set @ ( B @ c_uminus ) )
!= c_UNIV )
| ( c_emptyset = B ) ),
inference(simp,[status(thm)],[313]) ).
thf(350,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
!= ( E @ ( F @ ( C @ c_union ) ) ) )
| ( E @ tc_set @ ( E @ ( D @ c_Mutil_Otiling ) @ ( A @ c_in ) ) )
| ~ ( E @ tc_set @ ( E @ ( D @ c_Mutil_Otiling ) @ ( F @ c_in ) ) )
| ~ ( E @ tc_set @ ( D @ ( C @ c_in ) ) )
| ( ( E @ ( F @ ( C @ c_inter ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[46,49]) ).
thf(351,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( C @ c_Mutil_Otiling ) @ ( A @ c_in ) ) )
| ~ ( B @ tc_set @ ( B @ ( C @ c_Mutil_Otiling ) @ ( c_emptyset @ c_in ) ) )
| ~ ( B @ tc_set @ ( C @ ( A @ c_in ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(pattern_uni,[status(thm)],[350:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( c_emptyset ))]]) ).
thf(373,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( C @ c_Mutil_Otiling ) @ ( A @ c_in ) ) )
| ~ ( B @ tc_set @ ( B @ ( C @ c_Mutil_Otiling ) @ ( c_emptyset @ c_in ) ) )
| ~ ( B @ tc_set @ ( C @ ( A @ c_in ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[351]) ).
thf(34353,plain,
( ( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( v_t @ ( c_UNIV @ c_lessequals ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34341,28480]) ).
thf(34354,plain,
( ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( v_t @ ( c_UNIV @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[34353]) ).
thf(34436,plain,
( ( ( t_a @ tc_set )
!= ( t_a @ tc_set ) )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= v_t )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[34354]) ).
thf(34444,plain,
( ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= v_t )
| ( ( t_a @ tc_set @ ( v_u @ c_uminus ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[34436]) ).
thf(60166,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ tc_set @ ( B @ c_uminus ) @ c_uminus ) )
!= ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( v_a @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_uminus ) ) )
| ( t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( B @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[6340,60136]) ).
thf(60167,plain,
t_a @ tc_set @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( t_a @ tc_set @ ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_a @ c_uminus ) @ ( v_u @ c_inter ) ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ c_lessequals ) ),
inference(pattern_uni,[status(thm)],[60166:[bind(A,$thf( t_a )),bind(B,$thf( t_a @ ( t_a @ tc_set @ ( v_a @ c_uminus ) @ ( v_u @ c_inter ) ) ))]]) ).
thf(28920,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_union ) ) )
!= ( E @ ( D @ ( C @ c_union ) ) ) )
| ( E @ tc_set @ ( E @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( B @ c_union ) ) @ ( C @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[28898,12172]) ).
thf(28921,plain,
! [B: $i,A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( B @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( A @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[28920:[bind(A,$thf( K )),bind(B,$thf( B )),bind(C,$thf( v_a )),bind(D,$thf( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( K @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) )),bind(E,$thf( t_a ))]]) ).
thf(29451,plain,
! [B: $i,A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( B @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( A @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(simp,[status(thm)],[28921]) ).
thf(57500,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ tc_set @ ( B @ c_uminus ) @ c_uminus ) )
!= ( t_a @ tc_set @ ( D @ c_uminus ) ) )
| ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( B @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( C @ c_union ) ) @ ( v_a @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[6340,29451]) ).
thf(57501,plain,
! [B: $i,A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( B @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( A @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[57500:[bind(A,$thf( t_a )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( t_a @ tc_set @ ( E @ c_uminus ) ))]]) ).
thf(57753,plain,
! [B: $i,A: $i] : ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( t_a @ ( B @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( A @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(simp,[status(thm)],[57501]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_A @ ( v_a @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[31,62]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ( t_a @ tc_set @ ( v_A @ ( v_a @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(92,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set )
!= B )
| ( c_emptyset != v_A )
| ( v_a != A ) ),
inference(simp,[status(thm)],[90]) ).
thf(94,plain,
c_emptyset != v_A,
inference(simp,[status(thm)],[92]) ).
thf(58400,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
!= ( t_a @ tc_set @ ( B @ c_uminus ) ) )
| ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( t_a @ ( t_a @ tc_set @ ( C @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[9070,58247]) ).
thf(58401,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[58400:[bind(A,$thf( t_a )),bind(B,$thf( c_emptyset ))]]) ).
thf(58469,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( c_UNIV @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(simp,[status(thm)],[58401]) ).
thf(58542,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( v_t @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[58469,3462]) ).
thf(455,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_minus ) ) )
!= ( D @ tc_set @ ( c_UNIV @ ( E @ c_minus ) ) ) )
| ( ( C @ ( B @ ( A @ c_inter ) ) )
= ( D @ ( c_emptyset @ ( E @ c_inter ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[86,388]) ).
thf(457,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set )
!= ( D @ tc_set ) )
| ( ( C @ tc_set @ ( B @ c_uminus ) )
!= c_UNIV )
| ( A != E )
| ( ( C @ ( B @ ( A @ c_inter ) ) )
= ( D @ ( c_emptyset @ ( E @ c_inter ) ) ) ) ),
inference(simp,[status(thm)],[455]) ).
thf(459,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ tc_set )
!= ( C @ tc_set ) )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= c_UNIV )
| ( ( B @ ( A @ ( D @ c_inter ) ) )
= ( C @ ( c_emptyset @ ( D @ c_inter ) ) ) ) ),
inference(simp,[status(thm)],[457]) ).
thf(585,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_union ) ) )
!= ( D @ ( c_UNIV @ ( D @ ( c_emptyset @ ( E @ c_inter ) ) @ c_union ) ) ) )
| ( ( C @ ( B @ ( A @ c_union ) ) )
= ( D @ ( c_UNIV @ ( E @ c_union ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,453]) ).
thf(618,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C != D )
| ( B != c_UNIV )
| ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
!= ( D @ ( c_emptyset @ ( E @ c_inter ) ) ) )
| ( ( C @ ( B @ ( A @ c_union ) ) )
= ( D @ ( c_UNIV @ ( E @ c_union ) ) ) ) ),
inference(simp,[status(thm)],[585]) ).
thf(644,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ tc_set @ ( c_UNIV @ ( A @ c_minus ) ) )
!= ( B @ ( c_emptyset @ ( C @ c_inter ) ) ) )
| ( ( B @ ( c_UNIV @ ( A @ c_union ) ) )
= ( B @ ( c_UNIV @ ( C @ c_union ) ) ) ) ),
inference(simp,[status(thm)],[618]) ).
thf(52710,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ tc_set @ ( c_UNIV @ c_uminus ) @ ( A @ c_inter ) ) )
!= ( B @ ( c_emptyset @ ( C @ c_inter ) ) ) )
| ( ( B @ ( c_UNIV @ ( A @ c_union ) ) )
= ( B @ ( c_UNIV @ ( C @ c_union ) ) ) ) ),
inference(rewrite,[status(thm)],[644,393]) ).
thf(11360,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( c_UNIV @ c_inter ) ) )
!= ( E @ ( c_emptyset @ ( D @ c_inter ) ) ) )
| ( E @ tc_set @ ( E @ tc_set @ ( A @ c_uminus ) @ ( C @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[51,11313]) ).
thf(11361,plain,
! [B: $i,A: $i] : ( A @ tc_set @ ( A @ tc_set @ ( c_emptyset @ c_uminus ) @ ( B @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[11360:[bind(A,$thf( c_emptyset )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( c_UNIV )),bind(E,$thf( B ))]]) ).
thf(11384,plain,
! [B: $i,A: $i] : ( A @ tc_set @ ( A @ tc_set @ ( c_emptyset @ c_uminus ) @ ( B @ c_lessequals ) ) ),
inference(simp,[status(thm)],[11361]) ).
thf(11479,plain,
! [B: $i,A: $i] : ( A @ tc_set @ ( c_UNIV @ ( B @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[11384,9070]) ).
thf(335,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ c_in ) ) )
!= ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
| ~ $true
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[108,49]) ).
thf(336,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ c_in ) ) )
!= ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( D @ c_in ) ) ) )
| ( C @ tc_set @ ( C @ ( B @ c_Mutil_Otiling ) @ ( C @ ( D @ ( A @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( D @ ( A @ c_inter ) ) )
!= c_emptyset )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[335]) ).
thf(337,plain,
! [A: $i] :
( ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ ( A @ c_union ) ) @ c_in ) ) )
| ~ ( t_a @ tc_set @ ( v_A @ ( A @ c_in ) ) )
| ( ( t_a @ ( t_a @ ( v_u @ ( v_t @ c_union ) ) @ ( A @ c_inter ) ) )
!= c_emptyset )
| ( ( t_a @ ( v_u @ ( v_t @ c_inter ) ) )
!= c_emptyset ) ),
inference(pattern_uni,[status(thm)],[336:[bind(A,$thf( A )),bind(B,$thf( v_A )),bind(C,$thf( t_a )),bind(D,$thf( t_a @ ( v_u @ ( v_t @ c_union ) ) ))]]) ).
thf(18051,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) @ ( v_a @ c_union ) ) )
!= ( B @ ( D @ ( C @ c_union ) ) ) )
| ( B @ tc_set @ ( B @ ( A @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_union ) ) @ ( C @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[17997,1313]) ).
thf(18052,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ ( A @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ c_union ) ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[18051:[bind(A,$thf( A )),bind(B,$thf( t_a )),bind(C,$thf( v_a )),bind(D,$thf( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( v_t @ c_union ) ) ))]]) ).
thf(18968,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( t_a @ tc_set @ ( A @ c_uminus ) @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(rewrite,[status(thm)],[18052,715]) ).
thf(18973,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ tc_set @ ( B @ c_uminus ) @ c_uminus ) )
!= ( t_a @ tc_set @ ( C @ c_uminus ) ) )
| ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( B @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[6340,18968]) ).
thf(18974,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( A @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[18973:[bind(A,$thf( t_a )),bind(B,$thf( D )),bind(C,$thf( t_a @ tc_set @ ( D @ c_uminus ) ))]]) ).
thf(19072,plain,
! [A: $i] : ( t_a @ tc_set @ ( t_a @ tc_set @ ( t_a @ ( A @ ( v_u @ c_inter ) ) @ c_uminus ) @ ( v_a @ c_lessequals ) ) ),
inference(simp,[status(thm)],[18974]) ).
thf(574,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ c_union ) ) )
!= ( C @ ( c_UNIV @ ( C @ ( c_emptyset @ ( D @ c_inter ) ) @ c_union ) ) ) )
| ( A
= ( C @ ( c_UNIV @ ( D @ c_union ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[42,453]) ).
thf(613,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != C )
| ( A != c_UNIV )
| ( A
!= ( C @ ( c_emptyset @ ( D @ c_inter ) ) ) )
| ( A
= ( C @ ( c_UNIV @ ( D @ c_union ) ) ) ) ),
inference(simp,[status(thm)],[574]) ).
thf(639,plain,
! [B: $i,A: $i] :
( ( ( A @ ( c_emptyset @ ( B @ c_inter ) ) )
!= c_UNIV )
| ( ( A @ ( c_UNIV @ ( B @ c_union ) ) )
= ( A @ ( c_emptyset @ ( B @ c_inter ) ) ) ) ),
inference(simp,[status(thm)],[613]) ).
thf(409,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_union ) ) )
!= ( t_a @ ( v_u @ ( t_a @ ( v_t @ ( v_a @ c_union ) ) @ c_union ) ) ) )
| ~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,38]) ).
thf(432,plain,
! [C: $i,B: $i,A: $i] :
( ( C != t_a )
| ( B != v_u )
| ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[409]) ).
thf(448,plain,
! [A: $i] :
( ( ( t_a @ tc_set @ ( v_u @ ( A @ c_minus ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[432]) ).
thf(22809,plain,
! [A: $i] :
( ( ( t_a @ ( t_a @ tc_set @ ( v_u @ c_uminus ) @ ( A @ c_inter ) ) )
!= ( t_a @ ( v_t @ ( v_a @ c_union ) ) ) )
| ~ ( t_a @ tc_set @ ( t_a @ ( v_A @ c_Mutil_Otiling ) @ ( t_a @ ( v_u @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(rewrite,[status(thm)],[448,393]) ).
thf(79872,plain,
$false,
inference(e,[status(thm)],[69,9982,629,25943,11313,4852,1315,365,9273,26466,276,12172,17641,9998,19391,7886,64164,56,715,21766,17577,142,49286,52204,39670,1782,42,18023,565,4948,34442,13611,37,20191,22621,60772,31913,17270,35774,44060,4766,16208,52,21092,1313,1279,21220,16523,28298,18094,46,93,325,34341,1362,78,20647,26871,3887,18075,623,646,21633,20636,121,17266,43516,84,1183,766,47503,28426,61,20619,63087,453,60807,74,1863,60,85,381,366,44635,12385,7757,160,63385,70,33,192,9126,6496,165,65,1079,29516,5936,16569,58788,51792,38240,28480,30644,5941,24870,45340,77,41124,30455,18055,393,41,30202,30833,55819,63955,237,633,54962,37736,1185,30438,16464,1698,45,64,22218,32,34,4943,44,35750,13157,44094,30127,18839,16649,52500,17009,47231,32153,6991,49,42779,5634,71,58247,382,54,57795,681,16226,33382,34599,28529,1122,56998,362,12182,6340,76,567,367,66,108,16570,9275,8052,1699,55242,636,15432,45945,20536,80,35,226,16467,22040,3881,20526,38810,3981,62213,38582,17112,9276,458,3904,3462,56604,34792,40204,63,7705,48315,20824,50,67,27791,9281,23544,370,14671,36557,1813,1452,20685,9220,42461,544,31,22475,17997,30437,72,314,43,55537,363,6721,218,368,5184,24150,23495,36528,19697,30349,55,632,1854,60136,75,568,58,433,43127,28117,51761,82,22660,41359,36,30,51,26501,6490,315,1280,17465,9070,373,34444,79,18025,60167,57753,28898,4193,58754,94,58542,459,52710,5236,68,62,47,11479,337,21626,83,19072,639,22809,22575]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ064-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.41 % Computer : n005.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 05:11:31 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.84/1.02 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/1.22 % [INFO] Parsing done (197ms).
% 1.31/1.23 % [INFO] Running in sequential loop mode.
% 2.01/1.64 % [INFO] eprover registered as external prover.
% 2.01/1.64 % [INFO] Scanning for conjecture ...
% 2.25/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 23 axioms. Running axiom selection ...
% 2.40/1.83 % [INFO] Axiom selection finished. Selected 23 axioms (removed 0 axioms).
% 2.40/1.86 % [INFO] Problem is propositional (TPTP CNF).
% 2.40/1.87 % [INFO] Type checking passed.
% 2.40/1.87 % [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 ...
% 198.88/54.72 % External prover 'e' found a proof!
% 198.88/54.73 % [INFO] Killing All external provers ...
% 198.88/54.73 % Time passed: 54157ms (effective reasoning time: 53489ms)
% 198.88/54.73 % Axioms used in derivation (23): cls_Set_OInt__UNIV__left_0, cls_Set_Osubset__refl_0, cls_Set_OUn__Diff__cancel2_0, cls_Set_OsubsetI_0, cls_Set_Osubset__antisym_0, cls_Set_OCompl__Diff__eq_0, cls_Set_OCompl__UNIV__eq_0, cls_Set_ODiff__Compl_0, cls_Set_OUn__Diff__cancel_0, cls_Mutil_Otiling_OUn_0, cls_Set_OUn__subset__iff_1, cls_Set_Odouble__complement_0, cls_Set_OUn__subset__iff_2, cls_Set_OUn__UNIV__left_0, cls_Set_Oempty__subsetI_0, cls_Set_OUn__subset__iff_0, cls_Set_Oempty__iff_0, cls_Set_OInt__iff_1, cls_Set_OUn__empty__left_0, cls_Set_OUn__empty__right_0, cls_Set_OUn__assoc_0, cls_Set_OUn__absorb_0, cls_Relation_OImage__diag_0
% 198.88/54.73 % No. of inferences in proof: 930
% 198.88/54.73 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 54157 ms resp. 53489 ms w/o parsing
% 195.69/54.98 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 195.69/54.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------