%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT263-1 : 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 : n004.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 07:46:51 AM UTC 2026
% Result : Unsatisfiable 249.76s 70.81s
% Output : Refutation 246.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 304
% Syntax : Number of formulae : 950 ( 336 unt; 0 typ; 1 def)
% Number of atoms : 2260 ( 810 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 10398 (1189 ~;1037 |; 0 &;8172 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 80 ( 77 usr; 14 con; 0-5 aty)
% Number of variables : 2302 ( 0 ^;2300 !; 1 ?;2302 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(v_S_decl,type,
v_S: $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_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(c_Tarski_Oglb_decl,type,
c_Tarski_Oglb: $i > $i > $i > $i ).
thf(v_cl_decl,type,
v_cl: $i ).
thf(class_HOL_Ominus_decl,type,
class_HOL_Ominus: $i > $o ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_SetInterval_OatLeastLessThan_decl,type,
c_SetInterval_OatLeastLessThan: $i > $i > $i > $i ).
thf(c_less_decl,type,
c_less: $i > $i > $i > $o ).
thf(c_Orderings_Omax_decl,type,
c_Orderings_Omax: $i > $i > $i > $i ).
thf(c_Finite__Set_OFinites_decl,type,
c_Finite__Set_OFinites: $i ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(c_Orderings_Omin_decl,type,
c_Orderings_Omin: $i > $i > $i > $i ).
thf(c_Finite__Set_OMax_decl,type,
c_Finite__Set_OMax: $i > $i > $i ).
thf(c_Datatype__Universe_OScons_decl,type,
c_Datatype__Universe_OScons: $i > $i > $i > $i > $i ).
thf(tc_IntDef_Oint_decl,type,
tc_IntDef_Oint: $i ).
thf(c_minus_decl,type,
c_minus: $i > $i > $i > $i ).
thf(class_Nat_Opower_decl,type,
class_Nat_Opower: $i > $o ).
thf(class_Orderings_Oord_decl,type,
class_Orderings_Oord: $i > $o ).
thf(c_Tarski_OCompleteLattice_decl,type,
c_Tarski_OCompleteLattice: $i ).
thf(tc_Tarski_Opotype_Opotype__ext__type_decl,type,
tc_Tarski_Opotype_Opotype__ext__type: $i > $i > $i ).
thf(tc_Product__Type_Ounit_decl,type,
tc_Product__Type_Ounit: $i ).
thf(c_Relation_Otrans_decl,type,
c_Relation_Otrans: $i > $i > $o ).
thf(c_Tarski_Opotype_Oorder_decl,type,
c_Tarski_Opotype_Oorder: $i > $i > $i > $i ).
thf(c_SetInterval_OlessThan_decl,type,
c_SetInterval_OlessThan: $i > $i > $i ).
thf(c_SetInterval_OgreaterThanLessThan_decl,type,
c_SetInterval_OgreaterThanLessThan: $i > $i > $i > $i ).
thf(c_Main_Oempty__Union__conv__1_decl,type,
c_Main_Oempty__Union__conv__1: $i > $i > $i ).
thf(c_Union_decl,type,
c_Union: $i > $i > $i ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(c_Main_OUnion__empty__conv__1_decl,type,
c_Main_OUnion__empty__conv__1: $i > $i > $i ).
thf(c_Finite__Set_OMin_decl,type,
c_Finite__Set_OMin: $i > $i > $i ).
thf(c_union_decl,type,
c_union: $i > $i > $i > $i ).
thf(c_Pow_decl,type,
c_Pow: $i > $i > $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(c_UNIV_decl,type,
c_UNIV: $i ).
thf(c_Main_OUnionE__1_decl,type,
c_Main_OUnionE__1: $i > $i > $i > $i ).
thf(c_inter_decl,type,
c_inter: $i > $i > $i > $i ).
thf(c_SetInterval_OgreaterThanAtMost_decl,type,
c_SetInterval_OgreaterThanAtMost: $i > $i > $i > $i ).
thf(c_SetInterval_OatLeastAtMost_decl,type,
c_SetInterval_OatLeastAtMost: $i > $i > $i > $i ).
thf(c_Tarski_OPartialOrder_decl,type,
c_Tarski_OPartialOrder: $i ).
thf(c_Tarski_Opotype_Opset_decl,type,
c_Tarski_Opotype_Opset: $i > $i > $i > $i ).
thf(c_Tarski_Olub_decl,type,
c_Tarski_Olub: $i > $i > $i > $i ).
thf(c_uminus_decl,type,
c_uminus: $i > $i > $i ).
thf(c_Inter_decl,type,
c_Inter: $i > $i > $i ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(c_SetInterval_OatMost_decl,type,
c_SetInterval_OatMost: $i > $i > $i ).
thf(c_Main_OInter__UNIV__conv__1__1_decl,type,
c_Main_OInter__UNIV__conv__1__1: $i > $i > $i ).
thf(c_Main_OMax__le__iff__1_decl,type,
c_Main_OMax__le__iff__1: $i > $i > $i > $i ).
thf(c_SetInterval_OgreaterThan_decl,type,
c_SetInterval_OgreaterThan: $i > $i > $i ).
thf(c_SetInterval_OatLeast_decl,type,
c_SetInterval_OatLeast: $i > $i > $i ).
thf(c_Relation_Oantisym_decl,type,
c_Relation_Oantisym: $i > $i > $o ).
thf(c_Datatype__Universe_Ouprod_decl,type,
c_Datatype__Universe_Ouprod: $i > $i > $i > $i > $i ).
thf(tc_Datatype__Universe_Onode_decl,type,
tc_Datatype__Universe_Onode: $i > $i > $i ).
thf(c_Main_OuprodE__1_decl,type,
c_Main_OuprodE__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_OuprodE__2_decl,type,
c_Main_OuprodE__2: $i > $i > $i > $i > $i > $i ).
thf(c_Main_Ofinite__Union__1_decl,type,
c_Main_Ofinite__Union__1: $i > $i > $i ).
thf(c_Main_OMax__less__iff__1_decl,type,
c_Main_OMax__less__iff__1: $i > $i > $i > $i ).
thf(c_Main_OMin__gr__iff__1_decl,type,
c_Main_OMin__gr__iff__1: $i > $i > $i > $i ).
thf(c_Relation_Orefl_decl,type,
c_Relation_Orefl: $i > $i > $i > $o ).
thf(c_Tarski_Odual_decl,type,
c_Tarski_Odual: $i > $i > $i ).
thf(c_Main_OInter__UNIV__conv__2__1_decl,type,
c_Main_OInter__UNIV__conv__2__1: $i > $i > $i ).
thf(class_Finite__Set_Ofinite_decl,type,
class_Finite__Set_Ofinite: $i > $o ).
thf(c_Main_OUnion__iff__1_decl,type,
c_Main_OUnion__iff__1: $i > $i > $i > $i ).
thf(c_Main_OInter__iff__1_decl,type,
c_Main_OInter__iff__1: $i > $i > $i > $i ).
thf(c_Main_OInterI__1_decl,type,
c_Main_OInterI__1: $i > $i > $i > $i ).
thf(c_Main_OMin__ge__iff__1_decl,type,
c_Main_OMin__ge__iff__1: $i > $i > $i > $i ).
thf(c_Set_Ocontents_decl,type,
c_Set_Ocontents: $i > $i > $i ).
thf(c_Main_OsubsetI__1_decl,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_Infinite__Set_Oatmost__one_decl,type,
c_Infinite__Set_Oatmost__one: $i > $i > $o ).
thf(c_Main_Oall__not__in__conv__1_decl,type,
c_Main_Oall__not__in__conv__1: $i > $i > $i ).
thf(c_List_Olistset_decl,type,
c_List_Olistset: $i > $i > $i ).
thf(c_List_Oset__Cons_decl,type,
c_List_Oset__Cons: $i > $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i > $i > $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( B @ A ) ) ) )
= C ) ) ) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_SetInterval_OgreaterThanAtMost ) ) )
= c_emptyset )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__empty_0) ).
thf(645,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_SetInterval_OgreaterThanAtMost ) ) )
= c_emptyset )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(147,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_insert ) ) @ c_Finite__Set_OMin ) )
= ( A @ ( A @ ( B @ c_Finite__Set_OMin ) @ ( C @ c_Orderings_Omin ) ) ) )
| ( B = c_emptyset )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__insert_0) ).
thf(629,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_insert ) ) @ c_Finite__Set_OMin ) )
= ( A @ ( A @ ( B @ c_Finite__Set_OMin ) @ ( C @ c_Orderings_Omin ) ) ) )
| ( B = c_emptyset )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(219,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).
thf(804,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(226,axiom,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
thf(820,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(821,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[820]) ).
thf(2266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[804,821]) ).
thf(2267,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[2266]) ).
thf(2286,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != D )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_emptyset )
| ( A != C ) ),
inference(simp,[status(thm)],[2267]) ).
thf(2295,plain,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_emptyset ),
inference(simp,[status(thm)],[2286]) ).
thf(236,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_inter ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__absorb_0) ).
thf(845,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_inter ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(846,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_inter ) ) )
= A ),
inference(lifteq,[status(thm)],[845]) ).
thf(59,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
thf(419,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(2,negated_conjecture,
~ ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(305,plain,
~ ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(306,plain,
~ ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[305]) ).
thf(1884,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[419,306]) ).
thf(1885,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[1884]) ).
thf(1899,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= t_a )
| ( c_Finite__Set_OFinites != v_A )
| ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) )
!= ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) ) ) ),
inference(simp,[status(thm)],[1885]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInter__iff__1 ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_1) ).
thf(893,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInter__iff__1 ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(102,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_minus ) ) )
= ( C @ tc_set @ ( B @ ( D @ c_minus ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff1_0) ).
thf(518,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_minus ) ) )
= ( C @ tc_set @ ( B @ ( D @ c_minus ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(294,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( c_UNIV @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__UNIV_0) ).
thf(962,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( c_UNIV @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(283,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( D @ tc_set @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_1) ).
thf(941,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( D @ tc_set @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(207,axiom,
! [B: $i,A: $i] :
( ( c_emptyset
= ( B @ ( A @ c_Union ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Oempty__Union__conv__1 ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_1) ).
thf(777,plain,
! [B: $i,A: $i] :
( ( c_emptyset
= ( B @ ( A @ c_Union ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Oempty__Union__conv__1 ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(86,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( A @ c_minus ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).
thf(478,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( A @ c_minus ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(479,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( A @ c_minus ) ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[478]) ).
thf(6,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
thf(312,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(54,axiom,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__infinite_0) ).
thf(408,plain,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(409,plain,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[408]) ).
thf(1099,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[312,409]) ).
thf(1100,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[1099]) ).
thf(1103,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[1100]) ).
thf(1105,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[1103]) ).
thf(268,axiom,
! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_0) ).
thf(909,plain,
! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Omin ) ) @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_1) ).
thf(332,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Omin ) ) @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(333,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Omin ) ) @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[332]) ).
thf(87,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Inter ) )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__empty_0) ).
thf(480,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Inter ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(481,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Inter ) )
= c_UNIV ),
inference(lifteq,[status(thm)],[480]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ( c_emptyset
= ( B @ ( A @ c_Union ) ) )
| ( ( B @ ( A @ c_Main_Oempty__Union__conv__1 ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_2) ).
thf(352,plain,
! [B: $i,A: $i] :
( ( c_emptyset
= ( B @ ( A @ c_Union ) ) )
| ( ( B @ ( A @ c_Main_Oempty__Union__conv__1 ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(169,axiom,
! [A: $i] :
( ( A @ ( c_UNIV @ c_Union ) )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__UNIV_0) ).
thf(682,plain,
! [A: $i] :
( ( A @ ( c_UNIV @ c_Union ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(683,plain,
! [A: $i] :
( ( A @ ( c_UNIV @ c_Union ) )
= c_UNIV ),
inference(lifteq,[status(thm)],[682]) ).
thf(203,axiom,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
thf(770,plain,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(1278,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[770,409]) ).
thf(1279,plain,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[1278]) ).
thf(1286,plain,
! [B: $i,A: $i] :
( ( B
!= ( tc_nat @ tc_set ) )
| ( c_UNIV != c_Finite__Set_OFinites )
| ( A != c_UNIV ) ),
inference(simp,[status(thm)],[1279]) ).
thf(1290,plain,
c_UNIV != c_Finite__Set_OFinites,
inference(simp,[status(thm)],[1286]) ).
thf(4,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ ( D @ c_SetInterval_OatLeastLessThan ) ) @ ( A @ ( B @ ( E @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_3) ).
thf(308,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ ( D @ c_SetInterval_OatLeastLessThan ) ) @ ( A @ ( B @ ( E @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(192,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).
thf(741,plain,
c_UNIV != c_emptyset,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
thf(379,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(167,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_emptyset @ ( A @ c_minus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__empty_0) ).
thf(677,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_emptyset @ ( A @ c_minus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(133,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( A @ ( C @ ( A @ ( B @ c_Finite__Set_OMax ) @ c_less ) ) )
| ~ ( A @ ( C @ ( A @ ( C @ ( B @ c_Main_OMax__less__iff__1 ) ) @ c_less ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_2) ).
thf(597,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( A @ ( C @ ( A @ ( B @ c_Finite__Set_OMax ) @ c_less ) ) )
| ~ ( A @ ( C @ ( A @ ( C @ ( B @ c_Main_OMax__less__iff__1 ) ) @ c_less ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(244,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_0) ).
thf(861,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(303,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_2) ).
thf(977,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(104,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_union ) ) )
= ( D @ ( D @ ( C @ ( A @ c_union ) ) @ ( B @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).
thf(523,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_union ) ) )
= ( D @ ( D @ ( C @ ( A @ c_union ) ) @ ( B @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(127,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).
thf(582,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(251,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_1) ).
thf(873,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(73,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onot__Cons__self_0) ).
thf(447,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(448,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(polarity_switch,[status(thm)],[447]) ).
thf(449,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) )
!= A ),
inference(lifteq,[status(thm)],[448]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
= ( C @ ( B @ ( C @ ( A @ ( D @ c_insert ) ) @ c_inter ) ) ) )
| ( C @ ( B @ ( D @ c_in ) ) )
| ( c_emptyset
!= ( C @ ( B @ ( A @ c_inter ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_2) ).
thf(440,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
= ( C @ ( B @ ( C @ ( A @ ( D @ c_insert ) ) @ c_inter ) ) ) )
| ( C @ ( B @ ( D @ c_in ) ) )
| ( c_emptyset
!= ( C @ ( B @ ( A @ c_inter ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(158,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = c_emptyset )
| ( A @ ( A @ ( C @ c_Finite__Set_OMax ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__ge_0) ).
thf(655,plain,
! [C: $i,B: $i,A: $i] :
( ( C = c_emptyset )
| ( A @ ( A @ ( C @ c_Finite__Set_OMax ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(36,axiom,
tc_IntDef_Oint @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
thf(373,plain,
tc_IntDef_Oint @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(218,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl_0) ).
thf(802,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(803,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(cnf,[status(esa)],[802]) ).
thf(1492,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Orderings_Oorder )
!= ( A @ class_Orderings_Oorder ) )
| ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[373,803]) ).
thf(1493,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Orderings_Oorder )
!= ( A @ class_Orderings_Oorder ) )
| ~ ( A @ ( B @ ( B @ c_less ) ) ) ),
inference(simp,[status(thm)],[1492]) ).
thf(1494,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( A @ ( A @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[1493:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(1497,plain,
! [A: $i] :
~ ( tc_IntDef_Oint @ ( A @ ( A @ c_less ) ) ),
inference(simp,[status(thm)],[1494]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Omin ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0) ).
thf(384,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Omin ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(204,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).
thf(771,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(2023,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[771,306]) ).
thf(2024,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[2023]) ).
thf(2035,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set )
!= t_a )
| ( c_Finite__Set_OFinites != v_A )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) )
!= ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) ) ) ),
inference(simp,[status(thm)],[2024]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__not__empty_0) ).
thf(498,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(499,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_emptyset ),
inference(polarity_switch,[status(thm)],[498]) ).
thf(500,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_emptyset ),
inference(lifteq,[status(thm)],[499]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( c_emptyset @ c_minus ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Diff_0) ).
thf(471,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( c_emptyset @ c_minus ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(472,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( c_emptyset @ c_minus ) ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[471]) ).
thf(223,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Set_Ocontents ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).
thf(814,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Set_Ocontents ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(176,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_insert ) ) )
= ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_2) ).
thf(698,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_insert ) ) )
= ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(270,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olistset ) )
= ( C @ ( C @ ( B @ c_List_Olistset ) @ ( A @ c_List_Oset__Cons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__2_0) ).
thf(913,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Olistset ) )
= ( C @ ( C @ ( B @ c_List_Olistset ) @ ( A @ c_List_Oset__Cons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(285,axiom,
! [A: $i] : ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__empty_1) ).
thf(945,plain,
! [A: $i] : ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Omin ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1) ).
thf(339,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Omin ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(340,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Omin ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[339]) ).
thf(2025,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[771,409]) ).
thf(2026,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[2025]) ).
thf(2038,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[2026]) ).
thf(2042,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[2038]) ).
thf(110,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).
thf(538,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(164,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_2) ).
thf(670,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(23,axiom,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
thf(344,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1297,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[344,409]) ).
thf(1298,plain,
! [A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[1297]) ).
thf(1305,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( A @ c_SetInterval_OlessThan ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[1298]) ).
thf(1310,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_SetInterval_OlessThan ) )
!= c_UNIV ),
inference(simp,[status(thm)],[1305]) ).
thf(108,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
= ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_inter ) ) ) )
| ( C @ ( A @ ( D @ c_in ) ) )
| ( c_emptyset
!= ( C @ ( B @ ( A @ c_inter ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_2) ).
thf(533,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
= ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_inter ) ) ) )
| ( C @ ( A @ ( D @ c_in ) ) )
| ( c_emptyset
!= ( C @ ( B @ ( A @ c_inter ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_union ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
thf(403,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_union ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(404,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_union ) ) )
= A ),
inference(lifteq,[status(thm)],[403]) ).
thf(13,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_7) ).
thf(326,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1,negated_conjecture,
t_a @ tc_set @ ( v_A @ ( v_S @ c_lessequals ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(304,plain,
t_a @ tc_set @ ( v_A @ ( v_S @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(309,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ ( D @ c_SetInterval_OatLeastLessThan ) ) @ ( A @ ( B @ ( E @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[308]) ).
thf(982,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_A @ ( v_S @ c_lessequals ) ) )
!= ( A @ ( C @ ( B @ c_lessequals ) ) ) )
| ( A @ tc_set @ ( A @ ( C @ ( D @ c_SetInterval_OatLeastLessThan ) ) @ ( A @ ( B @ ( E @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( D @ c_lessequals ) ) )
| ~ $true
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(paramod_ordered,[status(thm)],[304,309]) ).
thf(983,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_A @ ( v_S @ c_lessequals ) ) )
!= ( A @ ( C @ ( B @ c_lessequals ) ) ) )
| ( A @ tc_set @ ( A @ ( C @ ( D @ c_SetInterval_OatLeastLessThan ) ) @ ( A @ ( B @ ( E @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( D @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(simp,[status(thm)],[982]) ).
thf(984,plain,
! [B: $i,A: $i] :
( ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( v_A @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( v_S @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ class_Orderings_Olinorder ) ),
inference(pattern_uni,[status(thm)],[983:[bind(A,$thf( t_a @ tc_set )),bind(B,$thf( v_S )),bind(C,$thf( v_A )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).
thf(1003,plain,
! [B: $i,A: $i] :
( ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( v_A @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( v_S @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ class_Orderings_Olinorder ) ),
inference(simp,[status(thm)],[984]) ).
thf(1269,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( v_A @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( v_S @ ( C @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ class_Orderings_Olinorder ) ),
inference(paramod_ordered,[status(thm)],[945,1003]) ).
thf(1270,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( v_A @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( v_S @ ( C @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ class_Orderings_Olinorder ) ),
inference(simp,[status(thm)],[1269]) ).
thf(1271,plain,
( ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( v_A @ ( c_emptyset @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( v_S @ ( c_emptyset @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ class_Orderings_Olinorder ) ),
inference(pattern_uni,[status(thm)],[1270:[bind(A,$thf( t_a )),bind(B,$thf( c_emptyset )),bind(C,$thf( c_emptyset ))]]) ).
thf(1382,plain,
( ( ( t_a @ tc_set @ class_Orderings_Olinorder )
!= ( tc_nat @ class_Orderings_Olinorder ) )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( v_A @ ( c_emptyset @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( v_S @ ( c_emptyset @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[326,1271]) ).
thf(1383,plain,
( ( ( t_a @ tc_set @ class_Orderings_Olinorder )
!= ( tc_nat @ class_Orderings_Olinorder ) )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( v_A @ ( c_emptyset @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( v_S @ ( c_emptyset @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1382]) ).
thf(1391,plain,
( ( ( t_a @ tc_set )
!= tc_nat )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( v_A @ ( c_emptyset @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( v_S @ ( c_emptyset @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1383]) ).
thf(209,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
thf(782,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(179,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( C @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_inter ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_0) ).
thf(709,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( C @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_inter ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OgreaterThan ) )
!= ( A @ ( C @ c_SetInterval_OgreaterThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff_0) ).
thf(565,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OgreaterThan ) )
!= ( A @ ( C @ c_SetInterval_OgreaterThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_1) ).
thf(436,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(63,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).
thf(425,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(2002,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[425,409]) ).
thf(2003,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[2002]) ).
thf(2015,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[2003]) ).
thf(2020,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[2015]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
thf(417,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_insert ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(269,axiom,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).
thf(910,plain,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(911,plain,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[910]) ).
thf(912,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) )
| ( A = c_emptyset ) ),
inference(lifteq,[status(thm)],[911]) ).
thf(296,axiom,
tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( t_a @ ( v_cl @ c_Tarski_Odual ) @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_APartialOrder_0) ).
thf(965,plain,
tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( t_a @ ( v_cl @ c_Tarski_Odual ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(1238,plain,
! [B: $i,A: $i] :
( ( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( t_a @ ( v_cl @ c_Tarski_Odual ) @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[965,821]) ).
thf(1239,plain,
! [B: $i,A: $i] :
( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( t_a @ ( v_cl @ c_Tarski_Odual ) @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1238]) ).
thf(1251,plain,
! [B: $i,A: $i] :
( ( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) )
!= B )
| ( c_Tarski_OPartialOrder != c_emptyset )
| ( ( t_a @ ( v_cl @ c_Tarski_Odual ) )
!= A ) ),
inference(simp,[status(thm)],[1239]) ).
thf(1253,plain,
c_Tarski_OPartialOrder != c_emptyset,
inference(simp,[status(thm)],[1251]) ).
thf(3621,plain,
! [B: $i,A: $i] :
( ( A != c_Tarski_OPartialOrder )
| ( c_emptyset != c_emptyset )
| ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[912,1253]) ).
thf(3622,plain,
! [B: $i,A: $i] :
( ( A != c_Tarski_OPartialOrder )
| ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[3621]) ).
thf(3623,plain,
! [A: $i] : ( A @ ( c_Tarski_OPartialOrder @ ( A @ ( c_Tarski_OPartialOrder @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[3622:[bind(A,$thf( c_Tarski_OPartialOrder ))]]) ).
thf(3976,plain,
! [A: $i] : ( A @ ( c_Tarski_OPartialOrder @ ( A @ ( c_Tarski_OPartialOrder @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ),
inference(simp,[status(thm)],[3623]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( B @ c_inter ) ) )
= c_emptyset )
| ( ( C @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_inter ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_1) ).
thf(587,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( B @ c_inter ) ) )
= c_emptyset )
| ( ( C @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_inter ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(33,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
thf(366,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(1812,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[366,306]) ).
thf(1813,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[1812]) ).
thf(1826,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= t_a )
| ( c_Finite__Set_OFinites != v_A )
| ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) )
!= ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) ) ) ),
inference(simp,[status(thm)],[1813]) ).
thf(272,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).
thf(917,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( C @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(196,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInter__iff__1 ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_2) ).
thf(751,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInter__iff__1 ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(279,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(934,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( B @ c_minus ) ) )
= A )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__cancel_0) ).
thf(357,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_minus ) ) @ ( B @ c_minus ) ) )
= A )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(112,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_UNIV )
| ( ( C @ ( B @ ( A @ c_inter ) ) )
!= c_UNIV ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_0) ).
thf(542,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_UNIV )
| ( ( C @ ( B @ ( A @ c_inter ) ) )
!= c_UNIV ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).
thf(460,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(60,axiom,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
thf(420,plain,
! [B: $i,A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(1908,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[420,306]) ).
thf(1909,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[1908]) ).
thf(1922,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= t_a )
| ( c_Finite__Set_OFinites != v_A )
| ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) )
!= ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) ) ) ),
inference(simp,[status(thm)],[1909]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( A @ ( A @ ( B @ c_Finite__Set_OMin ) @ ( C @ c_less ) ) )
| ( A @ ( B @ ( A @ ( C @ ( B @ c_Main_OMin__gr__iff__1 ) ) @ c_in ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_1) ).
thf(559,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( A @ ( A @ ( B @ c_Finite__Set_OMin ) @ ( C @ c_less ) ) )
| ( A @ ( B @ ( A @ ( C @ ( B @ c_Main_OMin__gr__iff__1 ) ) @ c_in ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(2169,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint != tc_nat )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[2042]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
thf(421,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(137,axiom,
! [B: $i,A: $i] :
( ( c_UNIV
= ( B @ ( A @ c_Inter ) ) )
| ( ( B @ ( A @ c_Main_OInter__UNIV__conv__2__1 ) )
!= c_UNIV ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_2) ).
thf(606,plain,
! [B: $i,A: $i] :
( ( c_UNIV
= ( B @ ( A @ c_Inter ) ) )
| ( ( B @ ( A @ c_Main_OInter__UNIV__conv__2__1 ) )
!= c_UNIV ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(255,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).
thf(881,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(12,axiom,
tc_IntDef_Oint @ class_Nat_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_62) ).
thf(325,plain,
tc_IntDef_Oint @ class_Nat_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(189,axiom,
! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
thf(735,plain,
! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(1222,plain,
! [A: $i] :
( ( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[735,306]) ).
thf(1223,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[1222]) ).
thf(1232,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= t_a )
| ( c_Finite__Set_OFinites != v_A )
| ( ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) )
!= c_emptyset ) ),
inference(simp,[status(thm)],[1223]) ).
thf(150,axiom,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).
thf(637,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(638,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[637]) ).
thf(240,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(853,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)],[240]) ).
thf(8,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_1) ).
thf(316,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(75,axiom,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
thf(452,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(1349,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[452,409]) ).
thf(1350,plain,
! [A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[1349]) ).
thf(1357,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[1350]) ).
thf(1362,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
!= c_UNIV ),
inference(simp,[status(thm)],[1357]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_SetInterval_OatLeastLessThan ) ) )
= c_emptyset )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
thf(475,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_SetInterval_OatLeastLessThan ) ) )
= c_emptyset )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(198,axiom,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_uminus ) )
= ( A @ ( B @ c_SetInterval_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__lessThan_0) ).
thf(756,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_uminus ) )
= ( A @ ( B @ c_SetInterval_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(71,axiom,
! [A: $i] :
( ( A @ ( c_UNIV @ c_Inter ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV_0) ).
thf(443,plain,
! [A: $i] :
( ( A @ ( c_UNIV @ c_Inter ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(38,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Union ) )
= c_emptyset )
| ( ( B @ ( A @ c_Main_OUnion__empty__conv__1 ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_2) ).
thf(376,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Union ) )
= c_emptyset )
| ( ( B @ ( A @ c_Main_OUnion__empty__conv__1 ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(144,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( A @ c_insert ) ) @ ( C @ ( B @ ( A @ c_insert ) ) @ c_inter ) ) )
= ( C @ ( C @ ( D @ ( B @ c_inter ) ) @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__inter__insert_0) ).
thf(623,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( A @ c_insert ) ) @ ( C @ ( B @ ( A @ c_insert ) ) @ c_inter ) ) )
= ( C @ ( C @ ( D @ ( B @ c_inter ) ) @ ( A @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(1814,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[366,409]) ).
thf(1815,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[1814]) ).
thf(1824,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[1815]) ).
thf(1828,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[1824]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( A @ ( B @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_0) ).
thf(937,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( A @ ( B @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OatLeastLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_1) ).
thf(330,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OatLeastLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(331,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OatLeastLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(cnf,[status(esa)],[330]) ).
thf(48,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(396,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(397,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[396]) ).
thf(1694,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ c_less ) ) )
!= ( tc_nat @ ( E @ ( E @ c_less ) ) ) )
| ~ $true
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OatLeastLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(paramod_ordered,[status(thm)],[331,397]) ).
thf(1695,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ c_less ) ) )
!= ( tc_nat @ ( E @ ( E @ c_less ) ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OatLeastLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(simp,[status(thm)],[1694]) ).
thf(1696,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( tc_nat @ class_Orderings_Oord ) ),
inference(pattern_uni,[status(thm)],[1695:[bind(A,$thf( tc_nat )),bind(B,$thf( D )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( D ))]]) ).
thf(1744,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( tc_nat @ class_Orderings_Oord ) ),
inference(simp,[status(thm)],[1696]) ).
thf(46,axiom,
tc_nat @ class_Orderings_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_2) ).
thf(393,plain,
tc_nat @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(2493,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ ( B @ c_in ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1744,393]) ).
thf(2494,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ ( B @ c_in ) ) ),
inference(simp,[status(thm)],[2493]) ).
thf(2513,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_SetInterval_OatLeastLessThan ) ) @ ( D @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[804,2494]) ).
thf(2514,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_SetInterval_OatLeastLessThan ) ) @ ( D @ c_in ) ) ) ),
inference(simp,[status(thm)],[2513]) ).
thf(2538,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != tc_nat )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( tc_nat @ ( D @ ( C @ c_SetInterval_OatLeastLessThan ) ) ) )
| ( A != D ) ),
inference(simp,[status(thm)],[2514]) ).
thf(2555,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( c_emptyset @ ( B @ c_insert ) ) )
!= ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) ) ),
inference(simp,[status(thm)],[2538]) ).
thf(297,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(966,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(1095,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[312,821]) ).
thf(1096,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
!= ( D @ ( c_emptyset @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[1095]) ).
thf(1101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= D )
| ( c_emptyset != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
!= C ) ),
inference(simp,[status(thm)],[1096]) ).
thf(1104,plain,
c_emptyset != c_Finite__Set_OFinites,
inference(simp,[status(thm)],[1101]) ).
thf(2849,plain,
! [B: $i,A: $i] :
( ( c_emptyset != c_emptyset )
| ( A != c_Finite__Set_OFinites )
| ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[912,1104]) ).
thf(2850,plain,
! [B: $i,A: $i] :
( ( A != c_Finite__Set_OFinites )
| ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[2849:[]]) ).
thf(4102,plain,
! [A: $i] : ( A @ ( c_Finite__Set_OFinites @ ( A @ ( c_Finite__Set_OFinites @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ),
inference(simp,[status(thm)],[2850]) ).
thf(4265,plain,
! [A: $i] :
( ( ( A @ ( c_Finite__Set_OFinites @ ( A @ ( c_Finite__Set_OFinites @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4102,306]) ).
thf(4266,plain,
! [A: $i] :
( ( A @ ( c_Finite__Set_OFinites @ ( A @ ( c_Finite__Set_OFinites @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[4265]) ).
thf(4285,plain,
! [A: $i] :
( ( A != t_a )
| ( c_Finite__Set_OFinites != v_A )
| ( ( A @ ( c_Finite__Set_OFinites @ c_Main_Oall__not__in__conv__1 ) )
!= ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) ) ) ),
inference(simp,[status(thm)],[4266]) ).
thf(4297,plain,
( ( c_Finite__Set_OFinites != v_A )
| ( ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) )
!= ( t_a @ ( c_Finite__Set_OFinites @ c_Main_Oall__not__in__conv__1 ) ) ) ),
inference(simp,[status(thm)],[4285]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Omax ) ) @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_1) ).
thf(321,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Omax ) ) @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Orderings_Omax ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) ).
thf(346,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Orderings_Omax ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(347,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Orderings_Omax ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[346]) ).
thf(348,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Orderings_Olinorder )
| ( ( A @ ( B @ ( B @ c_Orderings_Omax ) ) )
= B ) ),
inference(lifteq,[status(thm)],[347]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_SetInterval_OatLeastAtMost ) ) )
= c_emptyset )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__empty_0) ).
thf(574,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ c_SetInterval_OatLeastAtMost ) ) )
= c_emptyset )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(266,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_1) ).
thf(905,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( B @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( C @ ( A @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
thf(602,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( C @ ( A @ c_inter ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(253,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OgreaterThanAtMost ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_1) ).
thf(877,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OgreaterThanAtMost ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff_0) ).
thf(453,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(206,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Inter ) )
= c_UNIV )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_OInter__UNIV__conv__1__1 ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_1) ).
thf(774,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Inter ) )
= c_UNIV )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_OInter__UNIV__conv__1__1 ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(65,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = c_emptyset )
| ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Finite__Set_OMin ) @ ( D @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_0) ).
thf(428,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = c_emptyset )
| ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_Finite__Set_OMin ) @ ( D @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(238,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_SetInterval_OatLeastAtMost ) ) @ ( B @ c_in ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_2) ).
thf(849,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_SetInterval_OatLeastAtMost ) ) @ ( B @ c_in ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(106,axiom,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OatLeast ) @ c_uminus ) )
= ( A @ ( B @ c_SetInterval_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atLeast_0) ).
thf(527,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OatLeast ) @ c_uminus ) )
= ( A @ ( B @ c_SetInterval_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(3,axiom,
tc_nat @ class_HOL_Ominus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_9) ).
thf(307,plain,
tc_nat @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(100,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).
thf(512,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( D @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__2 ) ) ) ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_Datatype__Universe_OScons ) ) ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(678,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_emptyset @ ( A @ c_minus ) ) )
= A ),
inference(lifteq,[status(thm)],[677]) ).
thf(1295,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[344,306]) ).
thf(1296,plain,
! [A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[1295]) ).
thf(1306,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set )
!= t_a )
| ( c_Finite__Set_OFinites != v_A )
| ( ( tc_nat @ ( A @ c_SetInterval_OlessThan ) )
!= ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) ) ) ),
inference(simp,[status(thm)],[1296]) ).
thf(200,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_0) ).
thf(761,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Orderings_Omin ) ) @ ( B @ c_Orderings_Omin ) ) )
= ( A @ ( C @ ( B @ c_Orderings_Omin ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0) ).
thf(381,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Orderings_Omin ) ) @ ( B @ c_Orderings_Omin ) ) )
= ( A @ ( C @ ( B @ c_Orderings_Omin ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(2270,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[804,306]) ).
thf(2271,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[2270]) ).
thf(2287,plain,
! [B: $i,A: $i] :
( ( B != t_a )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= v_A )
| ( A
!= ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) ) ) ),
inference(simp,[status(thm)],[2271]) ).
thf(2296,plain,
( ( t_a @ ( c_emptyset @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_insert ) ) )
!= v_A ),
inference(simp,[status(thm)],[2287]) ).
thf(181,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_SetInterval_OatLeastAtMost ) ) )
= ( A @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__singleton_0) ).
thf(714,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_SetInterval_OatLeastAtMost ) ) )
= ( A @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(216,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_insert ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__insert_0) ).
thf(798,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_insert ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
thf(654,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(2618,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[654,409]) ).
thf(2619,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[2618]) ).
thf(2637,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( tc_nat @ tc_set ) )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_Finite__Set_OFinites )
| ( A != c_UNIV ) ),
inference(simp,[status(thm)],[2619]) ).
thf(2646,plain,
! [A: $i] :
( ( tc_nat @ tc_set @ ( A @ ( c_UNIV @ c_insert ) ) )
!= c_Finite__Set_OFinites ),
inference(simp,[status(thm)],[2637]) ).
thf(276,axiom,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).
thf(925,plain,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(18,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( E @ ( D @ c_SetInterval_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_1) ).
thf(334,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( E @ ( D @ c_SetInterval_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10,axiom,
tc_IntDef_Oint @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
thf(323,plain,
tc_IntDef_Oint @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2401,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Orderings_Olinorder )
!= ( A @ class_Orderings_Olinorder ) )
| ~ $true
| ( ( A @ ( B @ ( B @ c_Orderings_Omax ) ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[323,348]) ).
thf(2402,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ class_Orderings_Olinorder )
!= ( A @ class_Orderings_Olinorder ) )
| ( ( A @ ( B @ ( B @ c_Orderings_Omax ) ) )
= B ) ),
inference(simp,[status(thm)],[2401]) ).
thf(2403,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( A @ c_Orderings_Omax ) ) )
= A ),
inference(pattern_uni,[status(thm)],[2402:[bind(A,$thf( tc_IntDef_Oint ))]]) ).
thf(2409,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( A @ c_Orderings_Omax ) ) )
= A ),
inference(simp,[status(thm)],[2403]) ).
thf(291,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_0) ).
thf(957,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(194,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ ( A @ c_insert ) ) @ c_Union ) )
= ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__insert_0) ).
thf(746,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ ( A @ c_insert ) ) @ c_Union ) )
= ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(228,axiom,
! [A: $i] :
( ( A @ ( c_UNIV @ c_Pow ) )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__UNIV_0) ).
thf(825,plain,
! [A: $i] :
( ( A @ ( c_UNIV @ c_Pow ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(289,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
thf(952,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( C @ tc_set @ ( B @ ( A @ c_less ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(317,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
inference(cnf,[status(esa)],[316]) ).
thf(318,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
inference(lifteq,[status(thm)],[317]) ).
thf(319,plain,
? [A: $i > $i > $i > $i > $i] :
! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_OScons ) ) ) @ ( E @ ( D @ ( B @ A ) ) ) )
= C ),
inference(detectInverse,[status(thm)],[318]) ).
thf(320,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( A @ sk1 ) ) ) )
= B ),
inference(cnf,[status(esa)],[319]) ).
thf(1255,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) @ ( D @ ( C @ ( A @ sk1 ) ) ) )
= B ),
inference(lifteq,[status(thm)],[320]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Orderings_Omax ) ) @ ( B @ c_Orderings_Omax ) ) )
= ( A @ ( C @ ( B @ c_Orderings_Omax ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0) ).
thf(349,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Orderings_Omax ) ) @ ( B @ c_Orderings_Omax ) ) )
= ( A @ ( C @ ( B @ c_Orderings_Omax ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(212,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( B @ c_insert ) ) @ c_Finite__Set_OMax ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__singleton_0) ).
thf(788,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( B @ c_insert ) ) @ c_Finite__Set_OMax ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(815,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Set_Ocontents ) )
= A ),
inference(lifteq,[status(thm)],[814]) ).
thf(302,axiom,
tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( v_cl @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Ocl_A_58_ACompleteLattice_A_61_61_ATrue_0) ).
thf(976,plain,
tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( v_cl @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(1073,plain,
! [B: $i,A: $i] :
( ( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( v_cl @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[976,821]) ).
thf(1074,plain,
! [B: $i,A: $i] :
( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( v_cl @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[1073]) ).
thf(1079,plain,
! [B: $i,A: $i] :
( ( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) )
!= B )
| ( c_Tarski_OCompleteLattice != c_emptyset )
| ( v_cl != A ) ),
inference(simp,[status(thm)],[1074]) ).
thf(1082,plain,
c_Tarski_OCompleteLattice != c_emptyset,
inference(simp,[status(thm)],[1079]) ).
thf(3025,plain,
! [B: $i,A: $i] :
( ( A != c_Tarski_OCompleteLattice )
| ( c_emptyset != c_emptyset )
| ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[912,1082]) ).
thf(3026,plain,
! [B: $i,A: $i] :
( ( A != c_Tarski_OCompleteLattice )
| ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[3025]) ).
thf(3027,plain,
! [A: $i] : ( A @ ( c_Tarski_OCompleteLattice @ ( A @ ( c_Tarski_OCompleteLattice @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[3026:[bind(A,$thf( c_Tarski_OCompleteLattice ))]]) ).
thf(4160,plain,
! [A: $i] : ( A @ ( c_Tarski_OCompleteLattice @ ( A @ ( c_Tarski_OCompleteLattice @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ),
inference(simp,[status(thm)],[3027]) ).
thf(53,axiom,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_1) ).
thf(407,plain,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(174,axiom,
! [B: $i,A: $i] :
( ( B = c_emptyset )
| ( A @ ( B @ ( A @ ( B @ c_Finite__Set_OMin ) @ c_in ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__in_0) ).
thf(693,plain,
! [B: $i,A: $i] :
( ( B = c_emptyset )
| ( A @ ( B @ ( A @ ( B @ c_Finite__Set_OMin ) @ c_in ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_0) ).
thf(625,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(254,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_0) ).
thf(879,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(15,axiom,
tc_IntDef_Oint @ class_Orderings_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
thf(329,plain,
tc_IntDef_Oint @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(161,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OgreaterThanAtMost ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_0) ).
thf(665,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OgreaterThanAtMost ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_1) ).
thf(493,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(116,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( A @ ( C @ ( A @ ( B @ c_Finite__Set_OMax ) @ c_less ) ) )
| ( A @ ( B @ ( A @ ( C @ ( B @ c_Main_OMax__less__iff__1 ) ) @ c_in ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_1) ).
thf(551,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( A @ ( C @ ( A @ ( B @ c_Finite__Set_OMax ) @ c_less ) ) )
| ( A @ ( B @ ( A @ ( C @ ( B @ c_Main_OMax__less__iff__1 ) ) @ c_in ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(1276,plain,
! [B: $i,A: $i] :
( ( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[770,306]) ).
thf(1277,plain,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[1276]) ).
thf(1287,plain,
! [B: $i,A: $i] :
( ( B != t_a )
| ( c_UNIV != v_A )
| ( A
!= ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) ) ) ),
inference(simp,[status(thm)],[1277]) ).
thf(1291,plain,
c_UNIV != v_A,
inference(simp,[status(thm)],[1287]) ).
thf(237,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ tc_set @ ( B @ tc_set @ ( C @ c_uminus ) @ ( B @ tc_set @ ( A @ c_uminus ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_0) ).
thf(847,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ tc_set @ ( B @ tc_set @ ( C @ c_uminus ) @ ( B @ tc_set @ ( A @ c_uminus ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(89,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Inter ) )
= c_UNIV )
| ( ( B @ ( A @ c_Main_OInter__UNIV__conv__1__1 ) )
!= c_UNIV ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_2) ).
thf(484,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Inter ) )
= c_UNIV )
| ( ( B @ ( A @ c_Main_OInter__UNIV__conv__1__1 ) )
!= c_UNIV ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_inter ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__empty__left_0) ).
thf(521,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_inter ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(522,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_inter ) ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[521]) ).
thf(230,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( A @ ( A @ ( B @ c_Finite__Set_OMin ) @ ( C @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( C @ ( B @ c_Main_OMin__ge__iff__1 ) ) @ c_in ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_1) ).
thf(830,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( A @ ( A @ ( B @ c_Finite__Set_OMin ) @ ( C @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( C @ ( B @ c_Main_OMin__ge__iff__1 ) ) @ c_in ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(11,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__le__self_0) ).
thf(324,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(301,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Inter ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_0) ).
thf(974,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Inter ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(141,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
= ( D @ ( C @ ( A @ c_inter ) ) ) )
| ( c_emptyset
!= ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_inter ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_1) ).
thf(615,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
= ( D @ ( C @ ( A @ c_inter ) ) ) )
| ( c_emptyset
!= ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_inter ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(985,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_A @ ( v_S @ c_lessequals ) ) )
!= ( A @ ( E @ ( D @ c_lessequals ) ) ) )
| ( A @ tc_set @ ( A @ ( C @ ( D @ c_SetInterval_OatLeastLessThan ) ) @ ( A @ ( B @ ( E @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ $true
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(paramod_ordered,[status(thm)],[304,309]) ).
thf(986,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_A @ ( v_S @ c_lessequals ) ) )
!= ( A @ ( E @ ( D @ c_lessequals ) ) ) )
| ( A @ tc_set @ ( A @ ( C @ ( D @ c_SetInterval_OatLeastLessThan ) ) @ ( A @ ( B @ ( E @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(simp,[status(thm)],[985]) ).
thf(987,plain,
! [B: $i,A: $i] :
( ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( B @ ( v_S @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( A @ ( v_A @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ class_Orderings_Olinorder ) ),
inference(pattern_uni,[status(thm)],[986:[bind(A,$thf( t_a @ tc_set )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( v_S )),bind(E,$thf( v_A ))]]) ).
thf(1004,plain,
! [B: $i,A: $i] :
( ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( B @ ( v_S @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( A @ ( v_A @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ class_Orderings_Olinorder ) ),
inference(simp,[status(thm)],[987]) ).
thf(1260,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( C @ ( v_S @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( B @ ( v_A @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ class_Orderings_Olinorder ) ),
inference(paramod_ordered,[status(thm)],[945,1004]) ).
thf(1261,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( C @ ( v_S @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( B @ ( v_A @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ class_Orderings_Olinorder ) ),
inference(simp,[status(thm)],[1260]) ).
thf(1262,plain,
( ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( c_emptyset @ ( v_S @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( c_emptyset @ ( v_A @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ class_Orderings_Olinorder ) ),
inference(pattern_uni,[status(thm)],[1261:[bind(A,$thf( t_a )),bind(B,$thf( c_emptyset )),bind(C,$thf( c_emptyset ))]]) ).
thf(1322,plain,
( ( ( t_a @ tc_set @ class_Orderings_Olinorder )
!= ( tc_IntDef_Oint @ class_Orderings_Olinorder ) )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( c_emptyset @ ( v_S @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( c_emptyset @ ( v_A @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[323,1262]) ).
thf(1323,plain,
( ( ( t_a @ tc_set @ class_Orderings_Olinorder )
!= ( tc_IntDef_Oint @ class_Orderings_Olinorder ) )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( c_emptyset @ ( v_S @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( c_emptyset @ ( v_A @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1322]) ).
thf(1328,plain,
( ( ( t_a @ tc_set )
!= tc_IntDef_Oint )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( c_emptyset @ ( v_S @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( c_emptyset @ ( v_A @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1323]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_Orderings_Omin ) ) @ ( B @ c_less ) ) )
| ~ ( A @ ( D @ ( B @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_2) ).
thf(355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_Orderings_Omin ) ) @ ( B @ c_less ) ) )
| ~ ( A @ ( D @ ( B @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(356,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_Orderings_Omin ) ) @ ( B @ c_less ) ) )
| ~ ( A @ ( D @ ( B @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[355]) ).
thf(249,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_0) ).
thf(869,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(242,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(857,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(155,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(650,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)],[155]) ).
thf(287,axiom,
! [A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ( A @ tc_set @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_3) ).
thf(948,plain,
! [A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ( A @ tc_set @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(42,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).
thf(386,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(1838,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[386,409]) ).
thf(1839,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[1838]) ).
thf(1851,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[1839]) ).
thf(1856,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[1851]) ).
thf(185,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = A )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_0) ).
thf(725,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = A )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(44,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( E @ ( D @ c_SetInterval_OatLeastLessThan ) ) @ ( A @ ( B @ ( C @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_2) ).
thf(388,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( E @ ( D @ c_SetInterval_OatLeastLessThan ) ) @ ( A @ ( B @ ( C @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(52,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Pow ) )
= ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__empty_0) ).
thf(405,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Pow ) )
= ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(406,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
= ( A @ ( c_emptyset @ c_Pow ) ) ),
inference(lifteq,[status(thm)],[405]) ).
thf(1876,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
!= ( D @ ( C @ ( B @ c_insert ) ) ) )
| ( ( A @ ( c_emptyset @ c_Pow ) )
!= c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[406,500]) ).
thf(1877,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Pow ) )
!= c_emptyset ),
inference(pattern_uni,[status(thm)],[1876:[bind(A,$thf( E )),bind(B,$thf( c_emptyset )),bind(C,$thf( c_emptyset )),bind(D,$thf( E @ tc_set ))]]) ).
thf(1878,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Pow ) )
!= c_emptyset ),
inference(simp,[status(thm)],[1877]) ).
thf(163,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(668,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)],[163]) ).
thf(669,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( B @ tc_set @ ( A @ c_uminus ) @ c_uminus ) )
= A ),
inference(lifteq,[status(thm)],[668]) ).
thf(152,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).
thf(642,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_0) ).
thf(590,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( A @ ( B @ c_SetInterval_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_SetInterval_OgreaterThanLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ ( B @ ( D @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_2) ).
thf(547,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_SetInterval_OgreaterThanLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ ( B @ ( D @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
thf(327,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(328,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[327]) ).
thf(4271,plain,
! [A: $i] :
( ( ( A @ ( c_Finite__Set_OFinites @ ( A @ ( c_Finite__Set_OFinites @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4102,409]) ).
thf(4272,plain,
! [A: $i] :
( ( A @ ( c_Finite__Set_OFinites @ ( A @ ( c_Finite__Set_OFinites @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[4271]) ).
thf(4288,plain,
! [A: $i] :
( ( A
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( A @ ( c_Finite__Set_OFinites @ c_Main_Oall__not__in__conv__1 ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[4272]) ).
thf(4291,plain,
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ c_Main_Oall__not__in__conv__1 ) )
!= c_UNIV ),
inference(simp,[status(thm)],[4288]) ).
thf(256,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_0) ).
thf(884,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OatLeast ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(1312,plain,
( ( ( t_a @ tc_set @ class_Orderings_Olinorder )
!= ( tc_nat @ class_Orderings_Olinorder ) )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( c_emptyset @ ( v_S @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( c_emptyset @ ( v_A @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[326,1262]) ).
thf(1313,plain,
( ( ( t_a @ tc_set @ class_Orderings_Olinorder )
!= ( tc_nat @ class_Orderings_Olinorder ) )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( c_emptyset @ ( v_S @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( c_emptyset @ ( v_A @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1312]) ).
thf(1329,plain,
( ( ( t_a @ tc_set )
!= tc_nat )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( c_emptyset @ ( v_S @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( c_emptyset @ ( v_A @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1313]) ).
thf(117,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = c_emptyset )
| ( A @ ( D @ ( B @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ c_Finite__Set_OMax ) @ c_less ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_0) ).
thf(554,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = c_emptyset )
| ( A @ ( D @ ( B @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ c_Finite__Set_OMax ) @ c_less ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(197,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( c_emptyset
!= ( C @ ( B @ c_Union ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_0) ).
thf(753,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( c_emptyset
!= ( C @ ( B @ c_Union ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( A @ c_uminus ) @ ( C @ tc_set @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_1) ).
thf(901,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ tc_set @ ( A @ c_uminus ) @ ( C @ tc_set @ ( B @ c_uminus ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( A @ ( B @ c_minus ) ) @ ( A @ c_inter ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__disjoint_0) ).
thf(686,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( A @ ( B @ c_minus ) ) @ ( A @ c_inter ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(168,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ ( A @ ( D @ c_insert ) ) @ c_inter ) ) )
= c_emptyset )
| ( C @ ( B @ ( D @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_2) ).
thf(679,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ ( A @ ( D @ c_insert ) ) @ c_inter ) ) )
= c_emptyset )
| ( C @ ( B @ ( D @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
thf(970,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(233,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( D @ ( A @ c_insert ) ) @ ( B @ c_inter ) ) )
!= c_emptyset )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_0) ).
thf(837,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( D @ ( A @ c_insert ) ) @ ( B @ c_inter ) ) )
!= c_emptyset )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(177,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = c_emptyset )
| ( A @ ( B @ ( A @ ( C @ c_Finite__Set_OMin ) @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__le_0) ).
thf(701,plain,
! [C: $i,B: $i,A: $i] :
( ( C = c_emptyset )
| ( A @ ( B @ ( A @ ( C @ c_Finite__Set_OMin ) @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(191,axiom,
! [B: $i,A: $i] :
( ( B = c_emptyset )
| ( A @ ( B @ ( A @ ( B @ c_Finite__Set_OMax ) @ c_in ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__in_0) ).
thf(738,plain,
! [B: $i,A: $i] :
( ( B = c_emptyset )
| ( A @ ( B @ ( A @ ( B @ c_Finite__Set_OMax ) @ c_in ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(78,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_1) ).
thf(457,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( D @ c_lessequals ) ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatLeast ) )
!= ( A @ ( C @ c_SetInterval_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff_0) ).
thf(503,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatLeast ) )
!= ( A @ ( C @ c_SetInterval_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(4338,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( c_Tarski_OCompleteLattice @ ( A @ ( c_Tarski_OCompleteLattice @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4160,2494]) ).
thf(4339,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_Tarski_OCompleteLattice @ ( A @ ( c_Tarski_OCompleteLattice @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[4338]) ).
thf(4350,plain,
! [C: $i,B: $i,A: $i] :
( ( A != tc_nat )
| ( ( tc_nat @ ( C @ ( B @ c_SetInterval_OatLeastLessThan ) ) )
!= c_Tarski_OCompleteLattice )
| ( ( A @ ( c_Tarski_OCompleteLattice @ c_Main_Oall__not__in__conv__1 ) )
!= C ) ),
inference(simp,[status(thm)],[4339]) ).
thf(4361,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Tarski_OCompleteLattice @ c_Main_Oall__not__in__conv__1 ) @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
!= c_Tarski_OCompleteLattice ),
inference(simp,[status(thm)],[4350]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( A @ ( C @ ( A @ ( B @ c_Finite__Set_OMax ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( C @ ( B @ c_Main_OMax__le__iff__1 ) ) @ c_in ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_1) ).
thf(515,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( A @ ( C @ ( A @ ( B @ c_Finite__Set_OMax ) @ c_lessequals ) ) )
| ( A @ ( B @ ( A @ ( C @ ( B @ c_Main_OMax__le__iff__1 ) ) @ c_in ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(1242,plain,
( ( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( t_a @ ( v_cl @ c_Tarski_Odual ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[965,409]) ).
thf(1243,plain,
( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( t_a @ ( v_cl @ c_Tarski_Odual ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[1242]) ).
thf(1249,plain,
( ( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) )
!= ( tc_nat @ tc_set ) )
| ( c_Tarski_OPartialOrder != c_Finite__Set_OFinites )
| ( ( t_a @ ( v_cl @ c_Tarski_Odual ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[1243]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff_0) ).
thf(341,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(342,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[341]) ).
thf(343,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_Orderings_Olinorder )
| ( B = C )
| ( ( A @ ( B @ c_SetInterval_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_OlessThan ) ) ) ),
inference(lifteq,[status(thm)],[342]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Omax ) ) @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_0) ).
thf(360,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Omax ) ) @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(220,axiom,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( C @ ( B @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).
thf(805,plain,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( C @ ( B @ ( A @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(98,axiom,
! [B: $i,A: $i] :
( ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Oantisym ) )
| ~ ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Aantisym_A_Iorder_Acl1_J_A_61_61_ATrue_0) ).
thf(508,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Oantisym ) )
| ~ ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Omax ) ) @ c_less ) ) )
| ~ ( A @ ( C @ ( D @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_2) ).
thf(310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Omax ) ) @ c_less ) ) )
| ~ ( A @ ( C @ ( D @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(311,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( B @ ( D @ c_Orderings_Omax ) ) @ c_less ) ) )
| ~ ( A @ ( C @ ( D @ c_less ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[310]) ).
thf(274,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_1) ).
thf(921,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Pow ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(246,axiom,
tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( t_a @ ( v_cl @ c_Tarski_Odual ) @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0) ).
thf(864,plain,
tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( t_a @ ( v_cl @ c_Tarski_Odual ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(1160,plain,
( ( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( t_a @ ( v_cl @ c_Tarski_Odual ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[864,409]) ).
thf(1161,plain,
( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( t_a @ ( v_cl @ c_Tarski_Odual ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[1160]) ).
thf(1170,plain,
( ( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) )
!= ( tc_nat @ tc_set ) )
| ( c_Tarski_OCompleteLattice != c_Finite__Set_OFinites )
| ( ( t_a @ ( v_cl @ c_Tarski_Odual ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[1161]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) ).
thf(398,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Omax ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(118,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(557,plain,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(558,plain,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
= A ),
inference(lifteq,[status(thm)],[557]) ).
thf(166,axiom,
! [B: $i,A: $i] :
( ( c_UNIV
= ( B @ ( A @ c_Inter ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_OInter__UNIV__conv__2__1 ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_1) ).
thf(674,plain,
! [B: $i,A: $i] :
( ( c_UNIV
= ( B @ ( A @ c_Inter ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_OInter__UNIV__conv__2__1 ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(1158,plain,
( ( ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) )
!= ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( t_a @ ( v_cl @ c_Tarski_Odual ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[864,306]) ).
thf(1159,plain,
( ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) )
!= ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( t_a @ ( v_cl @ c_Tarski_Odual ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[1158]) ).
thf(1167,plain,
( ( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) )
!= t_a )
| ( c_Tarski_OCompleteLattice != v_A )
| ( ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) )
!= ( t_a @ ( v_cl @ c_Tarski_Odual ) ) ) ),
inference(simp,[status(thm)],[1159]) ).
thf(107,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_inter ) ) )
= c_emptyset )
| ( ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_1) ).
thf(530,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_inter ) ) )
= c_emptyset )
| ( ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(258,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_UNIV )
| ( ( C @ ( B @ c_Inter ) )
!= c_UNIV )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_0) ).
thf(888,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_UNIV )
| ( ( C @ ( B @ c_Inter ) )
!= c_UNIV )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(205,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_union ) ) )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__right_0) ).
thf(772,plain,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_union ) ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(773,plain,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_union ) ) )
= c_UNIV ),
inference(lifteq,[status(thm)],[772]) ).
thf(214,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ ( A @ c_union ) ) @ c_Union ) )
= ( C @ ( C @ ( B @ c_Union ) @ ( C @ ( A @ c_Union ) @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Un__distrib_0) ).
thf(794,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ ( A @ c_union ) ) @ c_Union ) )
= ( C @ ( C @ ( B @ c_Union ) @ ( C @ ( A @ c_Union ) @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_inter ) ) )
!= c_emptyset )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_0) ).
thf(412,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_inter ) ) )
!= c_emptyset )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(142,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Union ) )
= c_emptyset )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_OUnion__empty__conv__1 ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_1) ).
thf(618,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Union ) )
= c_emptyset )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_OUnion__empty__conv__1 ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(4331,plain,
! [A: $i] :
( ( ( A @ ( c_Tarski_OCompleteLattice @ ( A @ ( c_Tarski_OCompleteLattice @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4160,409]) ).
thf(4332,plain,
! [A: $i] :
( ( A @ ( c_Tarski_OCompleteLattice @ ( A @ ( c_Tarski_OCompleteLattice @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[4331]) ).
thf(4348,plain,
! [A: $i] :
( ( A
!= ( tc_nat @ tc_set ) )
| ( c_Tarski_OCompleteLattice != c_Finite__Set_OFinites )
| ( ( A @ ( c_Tarski_OCompleteLattice @ c_Main_Oall__not__in__conv__1 ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[4332]) ).
thf(4359,plain,
( ( c_Tarski_OCompleteLattice != c_Finite__Set_OFinites )
| ( ( tc_nat @ tc_set @ ( c_Tarski_OCompleteLattice @ c_Main_Oall__not__in__conv__1 ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[4348]) ).
thf(444,plain,
! [A: $i] :
( ( A @ ( c_UNIV @ c_Inter ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[443]) ).
thf(188,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( F @ c_Datatype__Universe_Ouprod ) ) ) @ ( D @ ( C @ ( A @ ( E @ c_Datatype__Universe_OScons ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( F @ ( E @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).
thf(733,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( D @ ( C @ ( B @ ( F @ c_Datatype__Universe_Ouprod ) ) ) @ ( D @ ( C @ ( A @ ( E @ c_Datatype__Universe_OScons ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( F @ ( E @ c_in ) ) )
| ~ ( D @ ( C @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(195,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).
thf(748,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(749,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
inference(polarity_switch,[status(thm)],[748]) ).
thf(750,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
inference(lifteq,[status(thm)],[749]) ).
thf(120,axiom,
! [B: $i,A: $i] :
( ( B = c_emptyset )
| ( A @ ( A @ ( B @ c_Finite__Set_OMax ) @ ( A @ ( B @ c_Finite__Set_OMin ) @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0) ).
thf(562,plain,
! [B: $i,A: $i] :
( ( B = c_emptyset )
| ( A @ ( A @ ( B @ c_Finite__Set_OMax ) @ ( A @ ( B @ c_Finite__Set_OMin ) @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(24,axiom,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).
thf(345,plain,
! [B: $i,A: $i] : ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1649,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[345,409]) ).
thf(1650,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[1649]) ).
thf(1657,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[1650]) ).
thf(1662,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[1657]) ).
thf(1833,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint != tc_nat )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[1662]) ).
thf(62,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ ( B @ c_SetInterval_OgreaterThanAtMost ) ) @ ( C @ c_in ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_2) ).
thf(423,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( D @ ( B @ c_SetInterval_OgreaterThanAtMost ) ) @ ( C @ c_in ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(187,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ tc_set @ ( A @ c_uminus ) @ c_inter ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint2_0) ).
thf(731,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ tc_set @ ( A @ c_uminus ) @ c_inter ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(732,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ tc_set @ ( A @ c_uminus ) @ c_inter ) ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[731]) ).
thf(235,axiom,
! [A: $i] :
( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__empty__eq_0) ).
thf(843,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(742,plain,
c_UNIV != c_emptyset,
inference(polarity_switch,[status(thm)],[741]) ).
thf(743,plain,
c_UNIV != c_emptyset,
inference(lifteq,[status(thm)],[742]) ).
thf(126,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
= c_emptyset )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_1) ).
thf(579,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( A @ c_minus ) ) )
= c_emptyset )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).
thf(545,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ( B @ tc_set @ ( A @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(252,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(875,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)],[252]) ).
thf(826,plain,
! [A: $i] :
( ( A @ ( c_UNIV @ c_Pow ) )
= c_UNIV ),
inference(lifteq,[status(thm)],[825]) ).
thf(125,axiom,
! [B: $i,A: $i] :
( ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Opset ) ) @ c_Relation_Orefl ) ) )
| ~ ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Arefl_A_Ipset_Acl1_J_A_Iorder_Acl1_J_A_61_61_ATrue_0) ).
thf(577,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Opset ) ) @ c_Relation_Orefl ) ) )
| ~ ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(4221,plain,
! [A: $i] :
( ( ( A @ ( c_Tarski_OPartialOrder @ ( A @ ( c_Tarski_OPartialOrder @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3976,409]) ).
thf(4222,plain,
! [A: $i] :
( ( A @ ( c_Tarski_OPartialOrder @ ( A @ ( c_Tarski_OPartialOrder @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[4221]) ).
thf(4239,plain,
! [A: $i] :
( ( A
!= ( tc_nat @ tc_set ) )
| ( c_Tarski_OPartialOrder != c_Finite__Set_OFinites )
| ( ( A @ ( c_Tarski_OPartialOrder @ c_Main_Oall__not__in__conv__1 ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[4222]) ).
thf(4251,plain,
( ( c_Tarski_OPartialOrder != c_Finite__Set_OFinites )
| ( ( tc_nat @ tc_set @ ( c_Tarski_OPartialOrder @ c_Main_Oall__not__in__conv__1 ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[4239]) ).
thf(72,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_1) ).
thf(445,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(139,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_UNIV @ ( A @ c_minus ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__UNIV_0) ).
thf(611,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_UNIV @ ( A @ c_minus ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( C @ ( C @ ( D @ ( A @ c_insert ) ) @ ( B @ c_inter ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_0) ).
thf(466,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
!= ( C @ ( C @ ( D @ ( A @ c_insert ) ) @ ( B @ c_inter ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(335,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( E @ ( D @ c_SetInterval_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[334]) ).
thf(178,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).
thf(704,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_0) ).
thf(540,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_SetInterval_OlessThan ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(165,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_inter ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__empty__right_0) ).
thf(672,plain,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_inter ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_Finite__Set_OMax ) @ ( B @ c_Orderings_Omin ) ) )
= B )
| ( C = c_emptyset )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0) ).
thf(313,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_Finite__Set_OMax ) @ ( B @ c_Orderings_Omin ) ) )
= B )
| ( C = c_emptyset )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2268,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ( C @ ( A @ ( c_emptyset @ c_Pow ) @ ( B @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[406,804]) ).
thf(2269,plain,
! [A: $i] : ( A @ tc_set @ ( A @ ( c_emptyset @ c_Pow ) @ ( c_emptyset @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[2268:[bind(A,$thf( D )),bind(B,$thf( c_emptyset )),bind(C,$thf( D @ tc_set ))]]) ).
thf(2293,plain,
! [A: $i] : ( A @ tc_set @ ( A @ ( c_emptyset @ c_Pow ) @ ( c_emptyset @ c_in ) ) ),
inference(simp,[status(thm)],[2269]) ).
thf(273,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(919,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)],[273]) ).
thf(2612,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( E @ ( c_emptyset @ ( D @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[654,821]) ).
thf(2613,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( E @ ( c_emptyset @ ( D @ c_in ) ) ) ),
inference(simp,[status(thm)],[2612]) ).
thf(2633,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C != E )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_emptyset )
| ( A != D ) ),
inference(simp,[status(thm)],[2613]) ).
thf(2642,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ c_insert ) ) )
!= c_emptyset ),
inference(simp,[status(thm)],[2633]) ).
thf(210,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).
thf(784,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Union ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ c_Main_Ofinite__Union__1 ) @ c_in ) ) )
| ~ ( B @ tc_set @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(190,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(736,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(31,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( E @ ( D @ c_SetInterval_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_0) ).
thf(362,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( E @ ( D @ c_SetInterval_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(245,axiom,
! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_4) ).
thf(863,plain,
! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(201,axiom,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_uminus ) )
= ( A @ ( B @ c_SetInterval_OgreaterThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atMost_0) ).
thf(764,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_uminus ) )
= ( A @ ( B @ c_SetInterval_OgreaterThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(136,axiom,
! [B: $i,A: $i] :
( ( tc_Product__Type_Ounit @ ( B @ ( B @ ( A @ c_Tarski_Odual ) @ c_Tarski_Opotype_Opset ) ) )
= ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Opset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0) ).
thf(604,plain,
! [B: $i,A: $i] :
( ( tc_Product__Type_Ounit @ ( B @ ( B @ ( A @ c_Tarski_Odual ) @ c_Tarski_Opotype_Opset ) ) )
= ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Opset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(737,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
= A ),
inference(lifteq,[status(thm)],[736]) ).
thf(154,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_inter ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__right_0) ).
thf(648,plain,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_inter ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(649,plain,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_inter ) ) )
= A ),
inference(lifteq,[status(thm)],[648]) ).
thf(1006,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_A @ ( v_S @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( v_A @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( v_S @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ $true
| ~ ( t_a @ tc_set @ class_Orderings_Olinorder ) ),
inference(paramod_ordered,[status(thm)],[304,1003]) ).
thf(1007,plain,
! [B: $i,A: $i] :
( ( ( t_a @ tc_set @ ( v_A @ ( v_S @ c_lessequals ) ) )
!= ( t_a @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( v_A @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( v_S @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ class_Orderings_Olinorder ) ),
inference(simp,[status(thm)],[1006]) ).
thf(1008,plain,
( ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( v_A @ ( v_S @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( v_S @ ( v_A @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ class_Orderings_Olinorder ) ),
inference(pattern_uni,[status(thm)],[1007:[bind(A,$thf( v_S )),bind(B,$thf( v_A ))]]) ).
thf(1039,plain,
( ( ( t_a @ tc_set @ class_Orderings_Olinorder )
!= ( tc_IntDef_Oint @ class_Orderings_Olinorder ) )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( v_A @ ( v_S @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( v_S @ ( v_A @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[323,1008]) ).
thf(1040,plain,
( ( ( t_a @ tc_set @ class_Orderings_Olinorder )
!= ( tc_IntDef_Oint @ class_Orderings_Olinorder ) )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( v_A @ ( v_S @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( v_S @ ( v_A @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1039]) ).
thf(1043,plain,
( ( ( t_a @ tc_set )
!= tc_IntDef_Oint )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( v_A @ ( v_S @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( v_S @ ( v_A @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1040]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ ( A @ c_inter ) ) @ c_uminus ) )
= ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( C @ tc_set @ ( A @ c_uminus ) @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Int_0) ).
thf(434,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ ( A @ c_inter ) ) @ c_uminus ) )
= ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( C @ tc_set @ ( A @ c_uminus ) @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(1075,plain,
( ( ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) )
!= ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( v_cl @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[976,306]) ).
thf(1076,plain,
( ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) )
!= ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( v_cl @ c_in ) ) ) ),
inference(simp,[status(thm)],[1075]) ).
thf(1080,plain,
( ( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) )
!= t_a )
| ( c_Tarski_OCompleteLattice != v_A )
| ( ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) )
!= v_cl ) ),
inference(simp,[status(thm)],[1076]) ).
thf(224,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OgreaterThanLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_0) ).
thf(816,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OgreaterThanLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_1) ).
thf(609,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(132,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( B @ c_insert ) ) @ c_Finite__Set_OMin ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__singleton_0) ).
thf(594,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( B @ c_insert ) ) @ c_Finite__Set_OMin ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(143,axiom,
! [A: $i] :
( ( A @ ( c_UNIV @ ( c_UNIV @ c_inter ) ) )
= c_UNIV ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_2) ).
thf(621,plain,
! [A: $i] :
( ( A @ ( c_UNIV @ ( c_UNIV @ c_inter ) ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(2404,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_Orderings_Olinorder )
!= ( A @ class_Orderings_Olinorder ) )
| ~ $true
| ( ( A @ ( B @ ( B @ c_Orderings_Omax ) ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[326,348]) ).
thf(2405,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ class_Orderings_Olinorder )
!= ( A @ class_Orderings_Olinorder ) )
| ( ( A @ ( B @ ( B @ c_Orderings_Omax ) ) )
= B ) ),
inference(simp,[status(thm)],[2404]) ).
thf(2406,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_Orderings_Omax ) ) )
= A ),
inference(pattern_uni,[status(thm)],[2405:[bind(A,$thf( tc_nat ))]]) ).
thf(2410,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( A @ c_Orderings_Omax ) ) )
= A ),
inference(simp,[status(thm)],[2406]) ).
thf(261,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_1) ).
thf(895,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(271,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( A @ ( C @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_1) ).
thf(915,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( A @ ( C @ c_SetInterval_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(2272,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[804,409]) ).
thf(2273,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[2272]) ).
thf(2288,plain,
! [B: $i,A: $i] :
( ( B
!= ( tc_nat @ tc_set ) )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= c_Finite__Set_OFinites )
| ( A != c_UNIV ) ),
inference(simp,[status(thm)],[2273]) ).
thf(2289,plain,
( ( tc_nat @ tc_set @ ( c_emptyset @ ( c_UNIV @ c_insert ) ) )
!= c_Finite__Set_OFinites ),
inference(simp,[status(thm)],[2288]) ).
thf(284,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Tarski_Oglb ) ) )
= ( C @ ( C @ ( B @ c_Tarski_Odual ) @ ( A @ c_Tarski_Olub ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Oglb__dual__lub_0) ).
thf(943,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Tarski_Oglb ) ) )
= ( C @ ( C @ ( B @ c_Tarski_Odual ) @ ( A @ c_Tarski_Olub ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(222,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff_0) ).
thf(811,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(43,axiom,
tc_nat @ class_Nat_Opower,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_12) ).
thf(387,plain,
tc_nat @ class_Nat_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(34,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).
thf(367,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(292,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OatLeastAtMost ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_0) ).
thf(959,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OatLeastAtMost ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(229,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatMost ) )
!= ( A @ ( C @ c_SetInterval_OatMost ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff_0) ).
thf(827,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_OatMost ) )
!= ( A @ ( C @ c_SetInterval_OatMost ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(149,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(635,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_UNIV @ c_inter ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(636,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_UNIV @ c_inter ) ) )
= A ),
inference(lifteq,[status(thm)],[635]) ).
thf(248,axiom,
( v_A
= ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Opset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
thf(867,plain,
( v_A
= ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Opset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(868,plain,
( ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Opset ) ) )
= v_A ),
inference(lifteq,[status(thm)],[867]) ).
thf(208,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(780,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)],[208]) ).
thf(77,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_SetInterval_OatLeastLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_2) ).
thf(455,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_SetInterval_OatLeastLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Otrans ) )
| ~ ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Atrans_A_Iorder_Acl1_J_A_61_61_ATrue_0) ).
thf(337,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Otrans ) )
| ~ ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(338,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Otrans ) )
| ~ ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[337]) ).
thf(2099,plain,
! [B: $i,A: $i] :
( ( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( t_a @ ( v_cl @ c_Tarski_Odual ) @ c_in ) ) )
!= ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( A @ c_in ) ) ) )
| ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Otrans ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[864,338]) ).
thf(2100,plain,
! [B: $i,A: $i] :
( ( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( t_a @ ( v_cl @ c_Tarski_Odual ) @ c_in ) ) )
!= ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( A @ c_in ) ) ) )
| ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Otrans ) ) ),
inference(simp,[status(thm)],[2099]) ).
thf(2101,plain,
t_a @ ( tc_Product__Type_Ounit @ ( t_a @ ( t_a @ ( v_cl @ c_Tarski_Odual ) @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Otrans ),
inference(pattern_uni,[status(thm)],[2100:[bind(A,$thf( t_a @ ( v_cl @ c_Tarski_Odual ) )),bind(B,$thf( t_a ))]]) ).
thf(1240,plain,
( ( ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) )
!= ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( t_a @ ( v_cl @ c_Tarski_Odual ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[965,306]) ).
thf(1241,plain,
( ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) )
!= ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( t_a @ ( v_cl @ c_Tarski_Odual ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[1240]) ).
thf(1250,plain,
( ( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) )
!= t_a )
| ( c_Tarski_OPartialOrder != v_A )
| ( ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) )
!= ( t_a @ ( v_cl @ c_Tarski_Odual ) ) ) ),
inference(simp,[status(thm)],[1241]) ).
thf(232,axiom,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).
thf(836,plain,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(1489,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ class_Orderings_Oorder )
!= ( B @ class_Orderings_Oorder ) )
| ~ ( B @ ( C @ ( C @ c_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[836,803]) ).
thf(1490,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ class_Orderings_Oorder )
!= ( B @ class_Orderings_Oorder ) )
| ~ ( B @ ( C @ ( C @ c_less ) ) ) ),
inference(simp,[status(thm)],[1489]) ).
thf(1491,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( A @ ( A @ c_less ) ) ),
inference(pattern_uni,[status(thm)],[1490:[bind(A,$thf( D )),bind(B,$thf( D @ tc_set ))]]) ).
thf(1496,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( A @ ( A @ c_less ) ) ),
inference(simp,[status(thm)],[1491]) ).
thf(69,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ ( A @ c_union ) ) @ c_uminus ) )
= ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( C @ tc_set @ ( A @ c_uminus ) @ c_inter ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Un_0) ).
thf(438,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ ( A @ c_union ) ) @ c_uminus ) )
= ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( C @ tc_set @ ( A @ c_uminus ) @ c_inter ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OlessThan ) @ ( A @ ( c_emptyset @ ( B @ c_insert ) ) @ c_minus ) ) )
= ( A @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Osingle__Diff__lessThan_0) ).
thf(431,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OlessThan ) @ ( A @ ( c_emptyset @ ( B @ c_insert ) ) @ c_minus ) ) )
= ( A @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(156,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(652,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_UNIV @ c_uminus ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(653,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_UNIV @ c_uminus ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[652]) ).
thf(159,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).
thf(658,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(170,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Pow ) @ c_Union ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Pow__eq_0) ).
thf(684,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Pow ) @ c_Union ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(685,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Pow ) @ c_Union ) )
= A ),
inference(lifteq,[status(thm)],[684]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Omin ) ) @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_0) ).
thf(394,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_Orderings_Omin ) ) @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(239,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).
thf(851,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(1097,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[312,306]) ).
thf(1098,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[1097]) ).
thf(1102,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= t_a )
| ( c_Finite__Set_OFinites != v_A )
| ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
!= ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) ) ) ),
inference(simp,[status(thm)],[1098]) ).
thf(84,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(473,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_UNIV @ c_union ) ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ c_Union ) )
!= c_emptyset )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_0) ).
thf(490,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ c_Union ) )
!= c_emptyset )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(64,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Opset ) ) @ ( B @ ( A @ ( C @ c_Tarski_Olub ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Opset ) ) @ ( C @ c_lessequals ) ) )
| ~ ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( A @ c_in ) ) )
| ~ ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OCL_Olub__in__lattice_0) ).
thf(426,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Opset ) ) @ ( B @ ( A @ ( C @ c_Tarski_Olub ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Opset ) ) @ ( C @ c_lessequals ) ) )
| ~ ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( A @ c_in ) ) )
| ~ ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(160,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_union ) ) )
= ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).
thf(663,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_union ) ) )
= ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(1905,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint != tc_nat )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[1856]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_Orderings_Omin ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2) ).
thf(374,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( D @ c_Orderings_Omin ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(4277,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( c_Finite__Set_OFinites @ ( A @ ( c_Finite__Set_OFinites @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4102,2494]) ).
thf(4278,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_Finite__Set_OFinites @ ( A @ ( c_Finite__Set_OFinites @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[4277]) ).
thf(4289,plain,
! [C: $i,B: $i,A: $i] :
( ( A != tc_nat )
| ( ( tc_nat @ ( C @ ( B @ c_SetInterval_OatLeastLessThan ) ) )
!= c_Finite__Set_OFinites )
| ( ( A @ ( c_Finite__Set_OFinites @ c_Main_Oall__not__in__conv__1 ) )
!= C ) ),
inference(simp,[status(thm)],[4278]) ).
thf(4292,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Finite__Set_OFinites @ c_Main_Oall__not__in__conv__1 ) @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
!= c_Finite__Set_OFinites ),
inference(simp,[status(thm)],[4289]) ).
thf(1077,plain,
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
!= ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( v_cl @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[976,409]) ).
thf(1078,plain,
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) )
!= ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( v_cl @ c_in ) ) ) ),
inference(simp,[status(thm)],[1077]) ).
thf(1081,plain,
( ( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) )
!= ( tc_nat @ tc_set ) )
| ( c_Tarski_OCompleteLattice != c_Finite__Set_OFinites )
| ( c_UNIV != v_cl ) ),
inference(simp,[status(thm)],[1078]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_1) ).
thf(939,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OatMost ) @ ( A @ ( B @ c_SetInterval_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(298,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__iff_1) ).
thf(968,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( A @ ( C @ ( A @ ( B @ c_Finite__Set_OMax ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ ( C @ ( B @ c_Main_OMax__le__iff__1 ) ) @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_2) ).
thf(487,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( A @ ( C @ ( A @ ( B @ c_Finite__Set_OMax ) @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( A @ ( C @ ( B @ c_Main_OMax__le__iff__1 ) ) @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(105,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).
thf(525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(241,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_1) ).
thf(855,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ c_SetInterval_OatLeast ) @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(173,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ ( C @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ ( A @ ( D @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ c_minus ) ) )
= ( A @ ( D @ ( C @ c_SetInterval_OatLeastLessThan ) ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__diff_0) ).
thf(690,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ ( C @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ ( A @ ( D @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ c_minus ) ) )
= ( A @ ( D @ ( C @ c_SetInterval_OatLeastLessThan ) ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(180,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(712,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)],[180]) ).
thf(673,plain,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_inter ) ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[672]) ).
thf(213,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( C @ ( D @ ( A @ c_insert ) ) @ ( B @ c_minus ) ) )
= ( C @ tc_set @ ( D @ ( B @ c_minus ) ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__insert0_0) ).
thf(791,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( C @ ( D @ ( A @ c_insert ) ) @ ( B @ c_minus ) ) )
= ( C @ tc_set @ ( D @ ( B @ c_minus ) ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(128,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
thf(585,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(182,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).
thf(717,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(95,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Union ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty_0) ).
thf(501,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Union ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(502,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Union ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[501]) ).
thf(234,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_1) ).
thf(840,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( c_emptyset @ ( D @ c_insert ) ) @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
thf(463,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(267,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
thf(907,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(4335,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( c_Tarski_OCompleteLattice @ ( A @ ( c_Tarski_OCompleteLattice @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) )
!= ( tc_Product__Type_Ounit @ ( C @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( B @ c_in ) ) ) )
| ( C @ ( tc_Product__Type_Ounit @ ( C @ ( B @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Otrans ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4160,338]) ).
thf(4336,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( c_Tarski_OCompleteLattice @ ( A @ ( c_Tarski_OCompleteLattice @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) )
!= ( tc_Product__Type_Ounit @ ( C @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( B @ c_in ) ) ) )
| ( C @ ( tc_Product__Type_Ounit @ ( C @ ( B @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Otrans ) ) ),
inference(simp,[status(thm)],[4335]) ).
thf(4337,plain,
! [A: $i] : ( A @ ( tc_Product__Type_Ounit @ ( A @ ( tc_Product__Type_Ounit @ ( A @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ c_Main_Oall__not__in__conv__1 ) @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Otrans ) ),
inference(pattern_uni,[status(thm)],[4336:[bind(A,$thf( tc_Product__Type_Ounit @ ( F @ tc_Tarski_Opotype_Opotype__ext__type ) )),bind(B,$thf( tc_Product__Type_Ounit @ ( F @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ c_Main_Oall__not__in__conv__1 ) )),bind(C,$thf( F ))]]) ).
thf(4351,plain,
! [A: $i] : ( A @ ( tc_Product__Type_Ounit @ ( A @ ( tc_Product__Type_Ounit @ ( A @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ c_Main_Oall__not__in__conv__1 ) @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Otrans ) ),
inference(simp,[status(thm)],[4337]) ).
thf(82,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ tc_set @ ( A @ c_uminus ) @ ( A @ c_inter ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint_0) ).
thf(469,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ tc_set @ ( A @ c_uminus ) @ ( A @ c_inter ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(470,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ tc_set @ ( A @ c_uminus ) @ ( A @ c_inter ) ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[469]) ).
thf(1647,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[345,306]) ).
thf(1648,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[1647]) ).
thf(1658,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set )
!= t_a )
| ( c_Finite__Set_OFinites != v_A )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanLessThan ) ) )
!= ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) ) ) ),
inference(simp,[status(thm)],[1648]) ).
thf(4213,plain,
! [A: $i] :
( ( ( A @ ( c_Tarski_OPartialOrder @ ( A @ ( c_Tarski_OPartialOrder @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3976,306]) ).
thf(4214,plain,
! [A: $i] :
( ( A @ ( c_Tarski_OPartialOrder @ ( A @ ( c_Tarski_OPartialOrder @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[4213]) ).
thf(4240,plain,
! [A: $i] :
( ( A != t_a )
| ( c_Tarski_OPartialOrder != v_A )
| ( ( A @ ( c_Tarski_OPartialOrder @ c_Main_Oall__not__in__conv__1 ) )
!= ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) ) ) ),
inference(simp,[status(thm)],[4214]) ).
thf(4241,plain,
( ( c_Tarski_OPartialOrder != v_A )
| ( ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) )
!= ( t_a @ ( c_Tarski_OPartialOrder @ c_Main_Oall__not__in__conv__1 ) ) ) ),
inference(simp,[status(thm)],[4240]) ).
thf(221,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( A @ ( A @ ( B @ c_Finite__Set_OMin ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ ( B @ c_Main_OMin__ge__iff__1 ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_2) ).
thf(808,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( A @ ( A @ ( B @ c_Finite__Set_OMin ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( C @ ( B @ c_Main_OMin__ge__iff__1 ) ) @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(1347,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[452,306]) ).
thf(1348,plain,
! [A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[1347]) ).
thf(1358,plain,
! [A: $i] :
( ( ( tc_nat @ tc_set )
!= t_a )
| ( c_Finite__Set_OFinites != v_A )
| ( ( tc_nat @ ( A @ c_SetInterval_OatMost ) )
!= ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) ) ) ),
inference(simp,[status(thm)],[1348]) ).
thf(193,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Main_OUnion__iff__1 ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_1) ).
thf(744,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Main_OUnion__iff__1 ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(19,axiom,
tc_IntDef_Oint @ class_HOL_Ominus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).
thf(336,plain,
tc_IntDef_Oint @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1836,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[386,306]) ).
thf(1837,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[1836]) ).
thf(1849,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set )
!= t_a )
| ( c_Finite__Set_OFinites != v_A )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
!= ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) ) ) ),
inference(simp,[status(thm)],[1837]) ).
thf(140,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).
thf(613,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(134,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(600,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)],[134]) ).
thf(123,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_0) ).
thf(571,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(612,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_UNIV @ ( A @ c_minus ) ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[611]) ).
thf(243,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(859,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)],[243]) ).
thf(2000,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[425,306]) ).
thf(2001,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[2000]) ).
thf(2013,plain,
! [B: $i,A: $i] :
( ( ( tc_IntDef_Oint @ tc_set )
!= t_a )
| ( c_Finite__Set_OFinites != v_A )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) )
!= ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) ) ) ),
inference(simp,[status(thm)],[2001]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ ( A @ c_insert ) ) @ c_Inter ) )
= ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_inter ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__insert_0) ).
thf(627,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ ( A @ c_insert ) ) @ c_Inter ) )
= ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_inter ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_minus ) ) )
= ( C @ tc_set @ ( B @ ( A @ c_minus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__idemp_0) ).
thf(450,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_minus ) ) )
= ( C @ tc_set @ ( B @ ( A @ c_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(278,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_UNIV )
| ( c_UNIV
!= ( C @ ( B @ c_Inter ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_0) ).
thf(931,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_UNIV )
| ( c_UNIV
!= ( C @ ( B @ c_Inter ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_inter ) ) @ c_Pow ) )
= ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( C @ ( A @ c_Pow ) @ c_inter ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__Int__eq_0) ).
thf(482,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_inter ) ) @ c_Pow ) )
= ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( C @ ( A @ c_Pow ) @ c_inter ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(93,axiom,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ c_uminus ) )
= ( A @ ( B @ c_SetInterval_OatMost ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__greaterThan_0) ).
thf(495,plain,
! [B: $i,A: $i] :
( ( ( A @ tc_set @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ c_uminus ) )
= ( A @ ( B @ c_SetInterval_OatMost ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(199,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
thf(759,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(259,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__iff_0) ).
thf(891,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(1378,plain,
( ( ( t_a @ tc_set @ class_Orderings_Olinorder )
!= ( tc_IntDef_Oint @ class_Orderings_Olinorder ) )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( v_A @ ( c_emptyset @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( v_S @ ( c_emptyset @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[323,1271]) ).
thf(1379,plain,
( ( ( t_a @ tc_set @ class_Orderings_Olinorder )
!= ( tc_IntDef_Oint @ class_Orderings_Olinorder ) )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( v_A @ ( c_emptyset @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( v_S @ ( c_emptyset @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1378]) ).
thf(1390,plain,
( ( ( t_a @ tc_set )
!= tc_IntDef_Oint )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( v_A @ ( c_emptyset @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( v_S @ ( c_emptyset @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1379]) ).
thf(172,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).
thf(688,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(265,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_1) ).
thf(903,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(35,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_0) ).
thf(368,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Datatype__Universe_OScons ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Datatype__Universe_OScons ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(844,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
= c_UNIV ),
inference(lifteq,[status(thm)],[843]) ).
thf(2616,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[654,306]) ).
thf(2617,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[2616]) ).
thf(2634,plain,
! [C: $i,B: $i,A: $i] :
( ( C != t_a )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= v_A )
| ( A
!= ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) ) ) ),
inference(simp,[status(thm)],[2617]) ).
thf(2643,plain,
! [A: $i] :
( ( t_a @ ( A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_insert ) ) )
!= v_A ),
inference(simp,[status(thm)],[2634]) ).
thf(293,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(961,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(295,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
thf(963,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Orderings_Omin ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) ).
thf(390,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Orderings_Omin ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( A @ ( A @ ( B @ c_Finite__Set_OMin ) @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ ( B @ c_Main_OMin__gr__iff__1 ) ) @ ( C @ c_less ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_2) ).
thf(632,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( A @ ( A @ ( B @ c_Finite__Set_OMin ) @ ( C @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ ( B @ c_Main_OMin__gr__iff__1 ) ) @ ( C @ c_less ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(2523,plain,
! [B: $i,A: $i] :
( ( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( v_cl @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ ( B @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[976,2494]) ).
thf(2524,plain,
! [B: $i,A: $i] :
( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( v_cl @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) @ ( B @ c_in ) ) ) ),
inference(simp,[status(thm)],[2523]) ).
thf(2537,plain,
! [B: $i,A: $i] :
( ( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) )
!= tc_nat )
| ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
!= c_Tarski_OCompleteLattice )
| ( v_cl != B ) ),
inference(simp,[status(thm)],[2524]) ).
thf(2554,plain,
! [A: $i] :
( ( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) )
!= tc_nat )
| ( ( tc_nat @ ( v_cl @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
!= c_Tarski_OCompleteLattice ) ),
inference(simp,[status(thm)],[2537]) ).
thf(4227,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( c_Tarski_OPartialOrder @ ( A @ ( c_Tarski_OPartialOrder @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ ( C @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3976,2494]) ).
thf(4228,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( c_Tarski_OPartialOrder @ ( A @ ( c_Tarski_OPartialOrder @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) )
!= ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_SetInterval_OatLeastLessThan ) ) @ ( C @ c_in ) ) ) ),
inference(simp,[status(thm)],[4227]) ).
thf(4238,plain,
! [C: $i,B: $i,A: $i] :
( ( A != tc_nat )
| ( ( tc_nat @ ( C @ ( B @ c_SetInterval_OatLeastLessThan ) ) )
!= c_Tarski_OPartialOrder )
| ( ( A @ ( c_Tarski_OPartialOrder @ c_Main_Oall__not__in__conv__1 ) )
!= C ) ),
inference(simp,[status(thm)],[4228]) ).
thf(4250,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( c_Tarski_OPartialOrder @ c_Main_Oall__not__in__conv__1 ) @ ( A @ c_SetInterval_OatLeastLessThan ) ) )
!= c_Tarski_OPartialOrder ),
inference(simp,[status(thm)],[4238]) ).
thf(286,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OatLeastAtMost ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_1) ).
thf(946,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OatLeastAtMost ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(350,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Orderings_Omax ) ) @ ( B @ c_Orderings_Omax ) ) )
= ( A @ ( C @ ( B @ c_Orderings_Omax ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[349]) ).
thf(351,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ class_Orderings_Olinorder )
| ( ( A @ ( A @ ( C @ ( B @ c_Orderings_Omax ) ) @ ( B @ c_Orderings_Omax ) ) )
= ( A @ ( C @ ( B @ c_Orderings_Omax ) ) ) ) ),
inference(lifteq,[status(thm)],[350]) ).
thf(211,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_1) ).
thf(786,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_UNIV )
| ( ( C @ ( B @ ( A @ c_inter ) ) )
!= c_UNIV ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_1) ).
thf(568,plain,
! [C: $i,B: $i,A: $i] :
( ( B = c_UNIV )
| ( ( C @ ( B @ ( A @ c_inter ) ) )
!= c_UNIV ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_0) ).
thf(510,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(162,axiom,
tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
thf(667,plain,
tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(263,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_0) ).
thf(899,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( C @ ( B @ c_Pow ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(109,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OgreaterThanLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_1) ).
thf(536,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_less ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OgreaterThanLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(1031,plain,
( ( ( t_a @ tc_set @ class_Orderings_Olinorder )
!= ( tc_nat @ class_Orderings_Olinorder ) )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( v_A @ ( v_S @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( v_S @ ( v_A @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[326,1008]) ).
thf(1032,plain,
( ( ( t_a @ tc_set @ class_Orderings_Olinorder )
!= ( tc_nat @ class_Orderings_Olinorder ) )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( v_A @ ( v_S @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( v_S @ ( v_A @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1031]) ).
thf(1045,plain,
( ( ( t_a @ tc_set )
!= tc_nat )
| ( t_a @ tc_set @ tc_set @ ( t_a @ tc_set @ ( v_A @ ( v_S @ c_SetInterval_OatLeastLessThan ) ) @ ( t_a @ tc_set @ ( v_S @ ( v_A @ c_SetInterval_OatLeastLessThan ) ) @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[1032]) ).
thf(217,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
thf(800,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ c_Inter ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_Main_OInterI__1 ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(115,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(549,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)],[115]) ).
thf(314,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_Finite__Set_OMax ) @ ( B @ c_Orderings_Omin ) ) )
= B )
| ( C = c_emptyset )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[313]) ).
thf(315,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder )
| ( ( A @ ( A @ ( C @ c_Finite__Set_OMax ) @ ( B @ c_Orderings_Omin ) ) )
= B )
| ( C = c_emptyset ) ),
inference(lifteq,[status(thm)],[314]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_0) ).
thf(950,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( A @ ( C @ c_SetInterval_OgreaterThan ) @ ( A @ ( B @ c_SetInterval_OgreaterThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(225,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
thf(818,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(247,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_0) ).
thf(865,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(2300,plain,
! [A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
!= ( t_a @ ( c_emptyset @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_insert ) ) ) )
| ( ( A @ ( c_emptyset @ c_Pow ) )
!= v_A ) ),
inference(paramod_ordered,[status(thm)],[406,2296]) ).
thf(2301,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= t_a )
| ( c_emptyset != c_emptyset )
| ( ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) )
!= c_emptyset )
| ( ( A @ ( c_emptyset @ c_Pow ) )
!= v_A ) ),
inference(simp,[status(thm)],[2300]) ).
thf(2302,plain,
! [A: $i] :
( ( ( A @ tc_set )
!= t_a )
| ( ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) )
!= c_emptyset )
| ( ( A @ ( c_emptyset @ c_Pow ) )
!= v_A ) ),
inference(simp,[status(thm)],[2301]) ).
thf(231,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_inter ) ) )
= c_emptyset )
| ( C @ ( A @ ( D @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_2) ).
thf(833,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_inter ) ) )
= c_emptyset )
| ( C @ ( A @ ( D @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_inter ) ) )
!= c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
thf(410,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Main_OUnionE__1 ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_0) ).
thf(506,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( C @ ( A @ c_minus ) ) @ c_in ) ) )
| ~ ( D @ tc_set @ ( c_Finite__Set_OFinites @ ( D @ tc_set @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_minus ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_Finite__Set_OMin ) @ ( B @ c_Orderings_Omax ) ) )
= B )
| ( C = c_emptyset )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0) ).
thf(400,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ c_Finite__Set_OMin ) @ ( B @ c_Orderings_Omax ) ) )
= B )
| ( C = c_emptyset )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(175,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).
thf(696,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_insert ) ) @ c_Finite__Set_OMax ) )
= ( A @ ( A @ ( B @ c_Finite__Set_OMax ) @ ( C @ c_Orderings_Omax ) ) ) )
| ( B = c_emptyset )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__insert_0) ).
thf(720,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( C @ c_insert ) ) @ c_Finite__Set_OMax ) )
= ( A @ ( A @ ( B @ c_Finite__Set_OMax ) @ ( C @ c_Orderings_Omax ) ) ) )
| ( B = c_emptyset )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(290,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_2) ).
thf(955,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ c_Union ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(215,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_union ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_2) ).
thf(796,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( B @ ( A @ ( C @ c_union ) ) @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( B @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(262,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( D @ tc_set @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_0) ).
thf(897,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( D @ tc_set @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(474,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_UNIV @ c_union ) ) )
= c_UNIV ),
inference(lifteq,[status(thm)],[473]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
= ( C @ ( A @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_2) ).
thf(767,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( c_emptyset @ ( B @ c_insert ) ) )
= ( C @ ( A @ ( B @ c_insert ) ) ) )
| ~ ( C @ tc_set @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(257,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnion__iff__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_0) ).
thf(886,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( B @ ( A @ c_Main_OUnion__iff__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Union ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(277,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(928,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)],[277]) ).
thf(57,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_insert ) ) )
= ( C @ ( B @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).
thf(415,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_insert ) ) )
= ( C @ ( B @ ( A @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(186,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
= ( C @ ( D @ ( B @ c_inter ) ) ) )
| ( c_emptyset
!= ( C @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_inter ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_1) ).
thf(728,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_emptyset
= ( C @ ( D @ ( B @ c_inter ) ) ) )
| ( c_emptyset
!= ( C @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_inter ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(184,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( B @ c_minus ) ) @ ( A @ c_insert ) ) )
= ( C @ ( B @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff__single_0) ).
thf(723,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( B @ c_minus ) ) @ ( A @ c_insert ) ) )
= ( C @ ( B @ ( A @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(227,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = c_emptyset )
| ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ c_Finite__Set_OMax ) @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_0) ).
thf(822,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = c_emptyset )
| ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ c_Finite__Set_OMax ) @ c_lessequals ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(1910,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[420,409]) ).
thf(1911,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[1910]) ).
thf(1921,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[1911]) ).
thf(1925,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OatLeastAtMost ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[1921]) ).
thf(250,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_2) ).
thf(871,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(3301,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) )
| ~ $true
| ( A = c_emptyset ) ),
inference(paramod_ordered,[status(thm)],[912,306]) ).
thf(3302,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) )
!= ( t_a @ ( v_A @ ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) @ c_in ) ) ) )
| ( A = c_emptyset ) ),
inference(simp,[status(thm)],[3301]) ).
thf(3781,plain,
! [B: $i,A: $i] :
( ( B != t_a )
| ( A != v_A )
| ( ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) )
!= ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) ) )
| ( A = c_emptyset ) ),
inference(simp,[status(thm)],[3302]) ).
thf(4071,plain,
( ( ( t_a @ ( v_cl @ ( v_S @ c_Tarski_Oglb ) ) )
!= ( t_a @ ( v_A @ c_Main_Oall__not__in__conv__1 ) ) )
| ( c_emptyset = v_A ) ),
inference(simp,[status(thm)],[3781]) ).
thf(1886,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[419,409]) ).
thf(1887,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) @ c_in ) ) )
!= ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ) ),
inference(simp,[status(thm)],[1886]) ).
thf(1896,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ tc_set )
!= ( tc_nat @ tc_set ) )
| ( c_Finite__Set_OFinites != c_Finite__Set_OFinites )
| ( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[1887]) ).
thf(1902,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) )
!= c_UNIV ),
inference(simp,[status(thm)],[1896]) ).
thf(322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ c_less ) ) )
| ~ ( A @ ( D @ ( A @ ( C @ ( B @ c_Orderings_Omax ) ) @ c_less ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(cnf,[status(esa)],[321]) ).
thf(353,plain,
! [B: $i,A: $i] :
( ( c_emptyset
= ( B @ ( A @ c_Union ) ) )
| ( ( B @ ( A @ c_Main_Oempty__Union__conv__1 ) )
!= c_emptyset ) ),
inference(cnf,[status(esa)],[352]) ).
thf(354,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Union ) )
= c_emptyset )
| ( ( B @ ( A @ c_Main_Oempty__Union__conv__1 ) )
!= c_emptyset ) ),
inference(lifteq,[status(thm)],[353]) ).
thf(280,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ ( D @ c_minus ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_1) ).
thf(935,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ ( D @ c_minus ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(275,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
thf(923,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(2059,plain,
! [B: $i,A: $i] :
( ( tc_IntDef_Oint != tc_nat )
| ( ( tc_IntDef_Oint @ ( B @ ( A @ c_SetInterval_OgreaterThanAtMost ) ) )
!= c_UNIV ) ),
inference(simp,[status(thm)],[2020]) ).
thf(151,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = c_emptyset )
| ( A @ ( B @ ( D @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_Finite__Set_OMin ) @ ( D @ c_less ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_0) ).
thf(639,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = c_emptyset )
| ( A @ ( B @ ( D @ c_less ) ) )
| ~ ( A @ ( A @ ( C @ c_Finite__Set_OMin ) @ ( D @ c_less ) ) )
| ~ ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ c_in ) ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(2349,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ( ( C @ ( A @ ( c_emptyset @ c_Pow ) @ c_Set_Ocontents ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[406,815]) ).
thf(2350,plain,
! [A: $i] :
( ( A @ tc_set @ ( A @ ( c_emptyset @ c_Pow ) @ c_Set_Ocontents ) )
= c_emptyset ),
inference(pattern_uni,[status(thm)],[2349:[bind(A,$thf( D )),bind(B,$thf( c_emptyset )),bind(C,$thf( D @ tc_set ))]]) ).
thf(2351,plain,
! [A: $i] :
( ( A @ tc_set @ ( A @ ( c_emptyset @ c_Pow ) @ c_Set_Ocontents ) )
= c_emptyset ),
inference(simp,[status(thm)],[2350]) ).
thf(2104,plain,
! [B: $i,A: $i] :
( ( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( v_cl @ c_in ) ) )
!= ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( A @ c_in ) ) ) )
| ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Otrans ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[976,338]) ).
thf(2105,plain,
! [B: $i,A: $i] :
( ( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( v_cl @ c_in ) ) )
!= ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( A @ c_in ) ) ) )
| ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Otrans ) ) ),
inference(simp,[status(thm)],[2104]) ).
thf(2106,plain,
t_a @ ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Otrans ),
inference(pattern_uni,[status(thm)],[2105:[bind(A,$thf( v_cl )),bind(B,$thf( t_a ))]]) ).
thf(131,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_0) ).
thf(592,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_union ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OatLeastLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_0) ).
thf(364,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( A @ ( D @ ( C @ c_SetInterval_OatLeastLessThan ) ) @ ( B @ c_in ) ) )
| ~ ( A @ class_Orderings_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(300,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).
thf(972,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_OuprodE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_Datatype__Universe_Onode ) @ tc_set @ ( E @ ( D @ ( C @ ( B @ c_Datatype__Universe_Ouprod ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(86956,plain,
$false,
inference(e,[status(thm)],[645,629,2295,846,1899,893,518,962,941,777,479,1105,909,333,481,352,683,1290,308,741,379,677,597,861,408,977,523,582,873,449,440,655,1497,384,2035,500,472,814,698,913,945,340,2042,538,670,1310,533,404,1391,782,709,565,436,2020,417,3976,587,1826,917,751,802,344,934,357,542,460,1922,559,2169,421,606,770,881,325,1232,638,853,316,1362,475,756,443,376,623,1828,937,2555,966,821,4297,321,348,574,905,480,602,397,877,453,774,396,428,1104,849,527,312,307,452,512,678,1306,761,381,366,2296,714,798,2646,925,334,2409,910,957,746,825,952,1255,349,820,788,815,4160,407,693,625,879,329,665,493,682,551,1291,847,484,522,830,324,974,615,1328,403,356,869,420,857,650,948,1856,725,388,1878,1082,339,669,642,637,590,547,328,471,4291,884,1329,554,753,901,686,679,970,837,393,701,738,654,457,503,4361,515,1249,343,360,805,508,311,921,1170,398,558,674,1167,530,888,773,794,412,618,425,4359,444,733,965,750,562,1833,423,732,843,772,743,579,545,875,826,577,4251,445,1271,611,498,466,335,704,540,672,313,2293,919,804,406,2642,784,419,736,362,863,764,604,737,318,649,1043,434,1080,816,609,323,594,621,2410,895,915,2289,943,668,330,811,387,345,367,959,827,636,868,780,455,2101,1250,1496,438,431,653,658,912,685,521,394,306,851,1102,473,490,1662,426,663,1905,374,4292,1081,939,355,968,836,648,487,525,855,690,327,409,310,712,557,1003,673,791,331,585,717,502,840,1262,463,907,4351,338,470,1658,4241,808,1358,744,336,1849,613,600,864,386,1008,571,612,859,845,2013,627,450,931,482,495,759,891,4102,1390,771,976,688,903,368,844,2643,1253,961,963,748,390,632,2554,304,4250,946,652,351,731,786,568,510,667,478,899,684,346,536,1045,800,549,2494,315,950,818,405,867,865,373,735,2302,447,833,410,305,326,341,506,400,635,696,720,955,796,897,474,767,886,928,415,728,332,723,822,1925,1004,871,501,4071,1902,322,803,337,469,354,935,923,309,2059,639,2351,2106,592,364,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT263-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.23/0.48 % Computer : n004.cluster.edu
% 0.23/0.48 % Model : x86_64 x86_64
% 0.23/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.48 % Memory : 8046.5625MB
% 0.23/0.48 % OS : Linux 6.8.0-71-generic
% 0.23/0.48 % CPULimit : 300
% 0.23/0.48 % WCLimit : 300
% 0.23/0.48 % DateTime : Fri Sep 25 20:21:37 UTC 2026
% 0.23/0.48 % CPUTime :
% 0.23/0.49 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
% 1.21/1.15 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.77/1.68 % [INFO] Parsing done (526ms).
% 3.18/1.70 % [INFO] Running in sequential loop mode.
% 3.92/2.10 % [INFO] eprover registered as external prover.
% 3.92/2.11 % [INFO] Scanning for conjecture ...
% 4.67/2.39 % [INFO] Found a conjecture (or negated_conjecture) and 2746 axioms. Running axiom selection ...
% 5.93/2.64 % [INFO] Axiom selection finished. Selected 301 axioms (removed 2445 axioms).
% 6.42/2.81 % [INFO] Problem is propositional (TPTP CNF).
% 6.42/2.83 % [INFO] Type checking passed.
% 6.42/2.83 % [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 ...
% 249.76/70.80 % External prover 'e' found a proof!
% 249.76/70.80 % [INFO] Killing All external provers ...
% 249.76/70.80 % Time passed: 70114ms (effective reasoning time: 69098ms)
% 249.76/70.81 % Axioms used in derivation (301): cls_Set_OPow__UNIV_0, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0, cls_Set_OPow__iff_1, cls_Set_Oempty__Union__conv_1, cls_SetInterval_OgreaterThanLessThan__iff_0, cls_Set_Oinsert__disjoint__1_1, cls_Datatype__Universe_OuprodI_0, cls_Finite__Set_Ofinite__Union_0, cls_Set_OCompl__subset__Compl__iff_1, cls_Finite__Set_OMin__gr__iff_2, cls_SetInterval_OgreaterThanAtMost__iff_2, cls_Set_Osingleton__insert__inj__eq_0, cls_Finite__Set_OMin__insert_0, cls_Set_OInt__iff_2, cls_Set_OUNIV__not__empty_0, cls_Set_OsubsetI_1, cls_Set_ODiff__cancel_0, clsarity_nat_7, cls_Set_Osubset__UNIV_0, cls_Finite__Set_OMin__singleton_0, cls_Set_Oinsert__Diff1_0, cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2, cls_Finite__Set_OFinites_OemptyI_0, cls_Finite__Set_OMax__less__iff_2, cls_Set_OInt__UNIV__left_0, cls_Datatype__Universe_OScons__Scons__eq_1, clsrel_Orderings_Olinorder_4, cls_SetInterval_OCompl__atLeast_0, cls_SetInterval_OgreaterThan__subset__iff_1, cls_Orderings_Oorder__less__irrefl_0, cls_SetInterval_OatLeast__iff_1, cls_Set_Oinsert__disjoint__2_2, cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0, cls_Set_Osingleton__inject__dest_0, cls_Set_OInt__subset__iff_0, cls_Set_OUnionE_1, cls_Set_OCompl__iff_1, cls_List_Olist_Oinject_1, cls_Finite__Set_OFinites_OinsertI_0, cls_Set_OUn__subset__iff_2, cls_Nat_Oless__irrefl_0, clsarity_set_2, clsarity_nat_3, cls_Set_OInt__UNIV_2, cls_Set_OUn__UNIV__left_0, cls_Set_ODiff__idemp_0, cls_Nat_Odiff__le__self_0, cls_SetInterval_Ofinite__atLeastLessThan__int_0, cls_SetInterval_OlessThan__subset__iff_1, cls_Set_OPow__iff_0, cls_SetInterval_OatMost__iff_1, cls_Set_Osingleton__insert__inj__eq_H_0, cls_Set_Odisjoint__insert__2_1, cls_Finite__Set_Ofinite__Int_0, cls_Set_OInter__UNIV_0, cls_Set_ODiff__UNIV_0, clsarity_IntDef__Oint_0, cls_Set_OInter__iff_0, cls_Set_Osubset__refl_0, cls_SetInterval_Oivl__subset_1, cls_Finite__Set_Ofinite__Pow__iff_1, cls_Set_OCompl__eq__Compl__iff_0, cls_Finite__Set_Ofinite__Un_2, cls_Set_OpsubsetI_0, cls_Set_ODiff__iff_2, cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0, cls_Set_OInterI_1, cls_Finite__Set_Ofinite__Diff__insert_1, cls_SetInterval_OatLeastLessThan__iff_2, cls_Finite__Set_Ofinite__Un_0, cls_SetInterval_Ofinite__greaterThanAtMost_0, clsarity_IntDef__Oint_35, cls_Set_OUnion__insert_0, cls_SetInterval_Ofinite__greaterThanAtMost__int_0, cls_Set_OUn__Diff__cancel2_0, cls_Set_Odisjoint__insert__1_1, cls_Orderings_Omax__less__iff__conj_0, cls_SetInterval_OatLeastAtMost__iff_2, cls_Set_Osubset__empty_0, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2, cls_SetInterval_OatLeastAtMost__empty_0, cls_Set_ODiff__insert0_0, cls_Set_OsubsetI_0, cls_Set_OUNIV__I_0, cls_SetInterval_OatLeastAtMost__singleton_0, cls_Finite__Set_OMin__ge__iff_2, cls_Infinite__Set_Onat__infinite_0, cls_Finite__Set_OMax__le__iff_2, cls_SetInterval_OgreaterThan__subset__iff_0, cls_Set_Oinsert__subset_2, cls_Set_OUn__UNIV__right_0, cls_Set_OUnion__empty__conv_1, cls_Set_OUn__iff_0, cls_Set_OUnion__iff_1, cls_Set_Osingleton__insert__inj__eq_H_1, cls_Tarski_OA_A_61_61_Apset_Acl_0, cls_Set_OUn__empty_1, cls_Tarski_OCL_Olub__in__lattice_0, cls_Set_OInter__UNIV__conv__1_0, cls_Set_Oinsert__disjoint__2_1, cls_Orderings_Omin__less__iff__conj_2, cls_Finite__Set_OMin__gr__iff_1, cls_SetInterval_OatLeast__subset__iff_0, cls_Finite__Set_Ofinite__insert_0, cls_Set_Oinsert__iff_2, cls_SetInterval_OlessThan__subset__iff_0, cls_Set_OCompl__Un_0, cls_Set_OCompl__subset__Compl__iff_0, clsarity_set_3, cls_SetInterval_Ofinite__atLeastAtMost_0, cls_SetInterval_Osingle__Diff__lessThan_0, cls_SetInterval_Ofinite__atLeastLessThan_0, cls_Set_Oinsert__not__empty_0, cls_SetInterval_OgreaterThan__iff_0, cls_Set_OsingletonD__dest_0, cls_Finite__Set_OMax__less__iff_1, cls_SetInterval_OlessThan__iff_0, cls_SetInterval_OCompl__greaterThan_0, cls_Set_OInter__UNIV__conv__2_2, cls_Finite__Set_Ofinite__Int_1, clsarity_IntDef__Oint_31, cls_Tarski_Ocl_A_58_ACompleteLattice_A_61_61_ATrue_0, cls_SetInterval_OCompl__lessThan_0, cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0, cls_SetInterval_Ofinite__lessThan_0, cls_List_Olist_Oinject_0, cls_Set_Oempty__iff_0, cls_Set_Oempty__subsetI_0, cls_Set_OInt__UNIV__right_0, cls_Set_OUnion__iff_0, cls_Set_OUn__subset__iff_0, cls_SetInterval_Ofinite__atLeastAtMost__int_0, cls_Finite__Set_OMin__le_0, cls_Set_OsubsetD_0, cls_Set_OUnion__empty__conv_2, cls_Set_Oempty__Diff_0, cls_SetInterval_OatLeastLessThan__iff_1, cls_Set_Odisjoint__insert__2_2, cls_Set_OUnion__empty__conv_0, cls_Set_OsingletonI_0, cls_SetInterval_OCompl__atMost_0, cls_Set_OCompl__empty__eq_0, cls_Set_ODiff__iff_1, cls_Finite__Set_OMax__ge_0, cls_Set_Osubset__antisym_0, cls_Set_OInt__empty__left_0, cls_SetInterval_OatLeastLessThan__iff_0, cls_Finite__Set_Ofinite__Diff__insert_0, cls_SetInterval_OatMost__iff_0, cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1, cls_SetInterval_Ofinite__greaterThanLessThan__int_0, cls_Set_OUnion__Un__distrib_0, cls_Tarski_Odual_Acl_A_58_APartialOrder_0, cls_Set_OCompl__iff_0, cls_Datatype__Universe_OuprodE_2, clsrel_Orderings_Oorder_0, cls_Set_Oall__not__in__conv_0, cls_Set_Oinsert__iff_1, cls_Finite__Set_Ofinite__Un_1, cls_Set_Osubset__empty_1, cls_Set_Osingleton__insert__inj__eq_1, cls_Datatype__Universe_OuprodE_0, cls_Set_OCompl__Diff__eq_0, cls_Finite__Set_OMax__singleton_0, cls_SetInterval_OgreaterThanLessThan__iff_2, cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0, cls_Finite__Set_Ofinite__Pow__iff_0, cls_Set_Oinsert__disjoint__1_0, cls_Set_Oempty__Union__conv_0, cls_SetInterval_Oivl__subset_0, cls_Set_Odisjoint__insert__1_2, cls_Infinite__Set_Oatmost__one__unique_0, cls_SetInterval_OatLeastAtMost__iff_1, cls_Set_Oinsert__subset_1, cls_Finite__Set_OMin__ge__iff_1, cls_SetInterval_OatLeastLessThan__empty_0, cls_Set_Oinsert__Diff__single_0, cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0, clsarity_set_1, cls_SetInterval_OgreaterThanAtMost__iff_0, cls_Set_OInt__UNIV_0, cls_Set_Oinsert__disjoint__2_0, cls_SetInterval_OatLeast__eq__iff_0, cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0, cls_Set_OCompl__UNIV__eq_0, cls_Set_OInter__UNIV__conv__1_1, cls_Finite__Set_Ofinite__Union_1, cls_Set_OUn__insert__left_0, cls_Set_OInt__empty__right_0, cls_Finite__Set_OMin__ge__iff_0, cls_Orderings_Omax__less__iff__conj_1, cls_Set_Osingleton__insert__inj__eq_H_2, cls_Set_OUn__insert__right_0, cls_SetInterval_OatLeast__subset__iff_1, cls_NatArith_Odiff__diff__cancel_0, cls_Set_OInter__iff_2, cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Aantisym_A_Iorder_Acl1_J_A_61_61_ATrue_0, cls_Set_OCompl__Int_0, cls_Finite__Set_OMax__less__iff_0, cls_Set_OUnion__iff_2, cls_SetInterval_Ofinite__greaterThanLessThan_0, cls_SetInterval_Oivl__diff_0, cls_Finite__Set_OMax__le__iff_0, cls_Set_OInter__UNIV__conv__2_1, cls_Finite__Set_OMin__gr__iff_0, clsarity_nat_12, cls_List_Onot__Cons__self_0, clsarity_IntDef__Oint_62, cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0, cls_Set_OUn__iff_1, cls_Finite__Set_OMax__le__iff_1, clsarity_IntDef__Oint_5, cls_SetInterval_OlessThan__iff_1, cls_Set_OUnion__empty_0, cls_Set_ODiff__Compl_0, cls_SetInterval_Oivl__subset_3, cls_Datatype__Universe_OuprodE_1, cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0, cls_Set_ODiff__eq__empty__iff_0, cls_Set_Oempty__not__insert_0, cls_Set_OpsubsetE_0, cls_SetInterval_OgreaterThan__iff_1, cls_Orderings_Omin__less__iff__conj_0, cls_Set_ODiff__eq__empty__iff_1, cls_Set_OInt__subset__iff_2, cls_Set_OInt__iff_0, cls_Set_ODiff__empty_0, cls_SetInterval_OatMost__eq__iff_0, cls_Finite__Set_OMax__in_0, clsarity_nat_9, cls_Set_Oempty__Union__conv_2, cls_Set_Oinsert__disjoint__1_2, cls_Set_OInter__UNIV__conv__1_2, cls_SetInterval_OatLeast__iff_0, cls_Set_OUn__empty__right_0, cls_SetInterval_OgreaterThanLessThan__iff_1, cls_Tarski_Oglb__dual__lub_0, cls_Set_OInt__iff_1, cls_Set_OInt__UNIV_1, cls_Set_OUn__empty__left_0, cls_Set_OInterI_0, cls_Set_OUn__Diff__cancel_0, cls_Set_Ocontents__eq_0, cls_Set_OPow__Int__eq_0, cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Arefl_A_Ipset_Acl1_J_A_Iorder_Acl1_J_A_61_61_ATrue_0, cls_SetInterval_OgreaterThanAtMost__iff_1, cls_Set_OInter__insert_0, cls_Orderings_Oorder__class_Oaxioms__1_0, cls_Finite__Set_OMin__in_0, cls_Set_ODiff__disjoint_0, clsrel_Orderings_Olinorder_3, cls_Finite__Set_Ofinite__Diff_0, cls_SetInterval_OatMost__subset__iff_0, cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0, cls_Set_ODiff__iff_0, clsarity_Product____Type__Ounit_0, cls_SetInterval_OgreaterThan__eq__iff_0, cls_Set_OUnionE_0, cls_Set_OCompl__disjoint_0, cls_Set_OInter__empty_0, clsarity_set_0, cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0, cls_Set_OInt__absorb_0, cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Atrans_A_Iorder_Acl1_J_A_61_61_ATrue_0, cls_Set_OUn__empty_0, cls_Set_Oinsert__iff_0, cls_List_Olistset_Osimps__2_0, cls_Set_Oinsert__absorb2_0, cls_SetInterval_OlessThan__eq__iff_0, cls_Set_OUn__subset__iff_1, cls_Set_OUnion__Pow__eq_0, cls_Set_Onot__psubset__empty_0, cls_SetInterval_OgreaterThanAtMost__empty_0, cls_Set_Odisjoint__insert__2_0, cls_Set_OUn__empty_2, cls_Finite__Set_OMax__insert_0, clsarity_nat_2, cls_Set_OUn__iff_2, cls_Set_OpsubsetE_1, cls_Orderings_Omax__less__iff__conj_2, cls_Set_OPow__empty_0, cls_Set_Osingleton__insert__inj__eq_2, cls_Set_Oinsert__inter__insert_0, cls_SetInterval_OatMost__subset__iff_1, cls_SetInterval_Ofinite__atMost_0, cls_Set_OInter__UNIV__conv__2_0, cls_SetInterval_Oivl__subset_2, clsarity_set_4, cls_Set_Odisjoint__insert__1_0, cls_Set_OUnion__UNIV_0, cls_Set_OInter__iff_1, cls_SetInterval_OatLeastAtMost__iff_0, cls_Set_Odouble__complement_0, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1, cls_Datatype__Universe_OScons__Scons__eq_0, cls_Set_Oinsert__subset_0, cls_Set_OUn__absorb_0, cls_Orderings_Omin__less__iff__conj_1, cls_Set_OInt__subset__iff_1, cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0, cls_Set_OCompl__disjoint2_0
% 249.76/70.81 % No. of inferences in proof: 949
% 249.76/70.81 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 70114 ms resp. 69098 ms w/o parsing
% 246.55/71.06 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 246.55/71.07 % [INFO] Killing All external provers ...
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