%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT265-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n006.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 07:46:52 AM UTC 2026
% Result : Unsatisfiable 12.60s 9.60s
% Output : Refutation 13.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 350
% Syntax : Number of formulae : 701 ( 233 unt; 0 typ; 0 def)
% Number of atoms : 1487 ( 426 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 8084 ( 732 ~; 786 |; 0 &;6566 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 95 ( 93 usr; 16 con; 0-5 aty)
% Number of variables : 2026 ( 0 ^;2026 !; 0 ?;2026 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(v_S_decl,type,
v_S: $i ).
thf(c_Tarski_Opotype_Opset_decl,type,
c_Tarski_Opotype_Opset: $i > $i > $i > $i ).
thf(v_cl_decl,type,
v_cl: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(tc_Product__Type_Ounit_decl,type,
tc_Product__Type_Ounit: $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_x_decl,type,
v_x: $i ).
thf(c_Tarski_Odual_decl,type,
c_Tarski_Odual: $i > $i > $i ).
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(class_HOL_Ominus_decl,type,
class_HOL_Ominus: $i > $o ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_Relation_Oconverse_decl,type,
c_Relation_Oconverse: $i > $i > $i > $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_Relation_OImage_decl,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_Relation_Odiag_decl,type,
c_Relation_Odiag: $i > $i > $i ).
thf(c_inter_decl,type,
c_inter: $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_Wellfounded__Recursion_Owf_decl,type,
c_Wellfounded__Recursion_Owf: $i > $i > $o ).
thf(c_Wellfounded__Relations_Olex__prod_decl,type,
c_Wellfounded__Relations_Olex__prod: $i > $i > $i > $i > $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(class_Nat_Opower_decl,type,
class_Nat_Opower: $i > $o ).
thf(c_Relation_ORange_decl,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(c_Transitive__Closure_Otrancl_decl,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(c_Wellfounded__Recursion_Oacyclic_decl,type,
c_Wellfounded__Recursion_Oacyclic: $i > $i > $o ).
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(c_IntDef_Ointrel_decl,type,
c_IntDef_Ointrel: $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(c_Pair_decl,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(c_Relation_ODomain_decl,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(class_Orderings_Oord_decl,type,
class_Orderings_Oord: $i > $o ).
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_Finite__Set_OMin_decl,type,
c_Finite__Set_OMin: $i > $i > $i ).
thf(c_Main_OUnion__empty__conv__1_decl,type,
c_Main_OUnion__empty__conv__1: $i > $i > $i ).
thf(c_Tarski_Opotype_Opotype__ext_decl,type,
c_Tarski_Opotype_Opotype__ext: $i > $i > $i > $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_UNIV_decl,type,
c_UNIV: $i ).
thf(c_Main_OUnionE__1_decl,type,
c_Main_OUnionE__1: $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(class_Finite__Set_Ofinite_decl,type,
class_Finite__Set_Ofinite: $i > $o ).
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_Relation_Orel__comp_decl,type,
c_Relation_Orel__comp: $i > $i > $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_Tarski_Opotype_Oorder_decl,type,
c_Tarski_Opotype_Oorder: $i > $i > $i > $i ).
thf(c_SetInterval_OatLeast_decl,type,
c_SetInterval_OatLeast: $i > $i > $i ).
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_Main_OInter__UNIV__conv__2__1_decl,type,
c_Main_OInter__UNIV__conv__2__1: $i > $i > $i ).
thf(c_List_Ozip_decl,type,
c_List_Ozip: $i > $i > $i > $i > $i ).
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_Relation_Otrans_decl,type,
c_Relation_Otrans: $i > $i > $o ).
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(v_A_decl,type,
v_A: $i ).
thf(c_Relation_Oantisym_decl,type,
c_Relation_Oantisym: $i > $i > $o ).
thf(v_r_decl,type,
v_r: $i ).
thf(c_Infinite__Set_Oatmost__one_decl,type,
c_Infinite__Set_Oatmost__one: $i > $i > $o ).
thf(c_Relation_Orefl_decl,type,
c_Relation_Orefl: $i > $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(c_Tarski_Oglb_decl,type,
c_Tarski_Oglb: $i > $i > $i > $i ).
thf(c_Tarski_Olub_decl,type,
c_Tarski_Olub: $i > $i > $i > $i ).
thf(c_Tarski_OPartialOrder_decl,type,
c_Tarski_OPartialOrder: $i ).
thf(300,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/sandbox/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(1036,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)],[300]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( D @ ( C @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
thf(365,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( D @ ( C @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(182,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_0) ).
thf(760,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)],[182]) ).
thf(65,axiom,
tc_nat @ class_Orderings_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_2) ).
thf(479,plain,
tc_nat @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(85,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_0) ).
thf(518,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)],[85]) ).
thf(145,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_0) ).
thf(666,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)],[145]) ).
thf(2,negated_conjecture,
t_a @ ( v_S @ ( v_x @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(352,plain,
t_a @ ( v_S @ ( v_x @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(137,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_0) ).
thf(645,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(234,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/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_0) ).
thf(892,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)],[234]) ).
thf(242,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/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_1) ).
thf(909,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)],[242]) ).
thf(130,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/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).
thf(628,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)],[130]) ).
thf(265,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_1) ).
thf(962,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(60,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/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0) ).
thf(468,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)],[60]) ).
thf(33,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/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1) ).
thf(408,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)],[33]) ).
thf(151,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/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_0) ).
thf(683,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)],[151]) ).
thf(316,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_2) ).
thf(1068,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)],[316]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(994,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)],[279]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
thf(1073,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)],[319]) ).
thf(149,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff_0) ).
thf(677,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)],[149]) ).
thf(226,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__iff_1) ).
thf(873,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)],[226]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( c_emptyset @ ( A @ c_Relation_OImage ) ) ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__empty_0) ).
thf(449,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( c_emptyset @ ( A @ c_Relation_OImage ) ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(48,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).
thf(440,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( C @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__not__refl_0) ).
thf(655,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( C @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
thf(511,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(321,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(1078,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)],[321]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_Oconverse ) ) )
= ( B @ ( A @ c_Relation_Odiag ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__diag_0) ).
thf(385,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_Oconverse ) ) )
= ( B @ ( A @ c_Relation_Odiag ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(91,axiom,
! [A: $i] :
( ( A @ ( c_UNIV @ c_Inter ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV_0) ).
thf(533,plain,
! [A: $i] :
( ( A @ ( c_UNIV @ c_Inter ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(75,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
thf(500,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)],[75]) ).
thf(197,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_emptyset @ ( A @ c_minus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__empty_0) ).
thf(797,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_emptyset @ ( A @ c_minus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(258,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_2) ).
thf(945,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)],[258]) ).
thf(329,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/sandbox/benchmark/theBenchmark.p',cls_Tarski_Oglb__dual__lub_0) ).
thf(1095,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)],[329]) ).
thf(236,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/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_2) ).
thf(898,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)],[236]) ).
thf(283,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/sandbox/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0) ).
thf(1001,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)],[283]) ).
thf(161,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_2) ).
thf(709,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)],[161]) ).
thf(305,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/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff_0) ).
thf(1046,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)],[305]) ).
thf(22,axiom,
tc_IntDef_Oint @ class_Nat_Opower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_62) ).
thf(389,plain,
tc_IntDef_Oint @ class_Nat_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(106,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ tc_set @ ( A @ c_uminus ) @ ( A @ c_inter ) ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint_0) ).
thf(570,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)],[106]) ).
thf(165,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_1) ).
thf(719,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)],[165]) ).
thf(14,axiom,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
thf(372,plain,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(199,axiom,
! [A: $i] :
( ( A @ ( c_UNIV @ c_Union ) )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__UNIV_0) ).
thf(802,plain,
! [A: $i] :
( ( A @ ( c_UNIV @ c_Union ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(349,axiom,
tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( v_cl @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Ocl_A_58_ACompleteLattice_A_61_61_ATrue_0) ).
thf(1132,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)],[349]) ).
thf(95,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( G @ tc_prod ) @ ( G @ ( D @ ( C @ ( H @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( G @ tc_prod ) @ ( H @ ( C @ ( G @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).
thf(542,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( G @ tc_prod ) @ ( G @ ( D @ ( C @ ( H @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( G @ ( B @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( G @ tc_prod ) @ ( H @ ( C @ ( G @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(245,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).
thf(917,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)],[245]) ).
thf(158,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_0) ).
thf(702,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)],[158]) ).
thf(178,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_2) ).
thf(751,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)],[178]) ).
thf(238,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/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__Compl_0) ).
thf(902,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)],[238]) ).
thf(217,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/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff__single_0) ).
thf(853,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)],[217]) ).
thf(325,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/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__iff_1) ).
thf(1087,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)],[325]) ).
thf(51,axiom,
tc_IntDef_Oint @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
thf(448,plain,
tc_IntDef_Oint @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(332,axiom,
! [A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ( A @ tc_set @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_3) ).
thf(1100,plain,
! [A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ( A @ tc_set @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(39,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_ODomain ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomain__diag_0) ).
thf(421,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_ODomain ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(225,axiom,
c_UNIV != c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).
thf(870,plain,
c_UNIV != c_emptyset,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(268,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_1) ).
thf(969,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)],[268]) ).
thf(121,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Union ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__empty_0) ).
thf(606,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Union ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(248,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/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__insert0_0) ).
thf(924,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)],[248]) ).
thf(180,axiom,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).
thf(756,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(115,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_0) ).
thf(591,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)],[115]) ).
thf(211,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/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__Diff__eq_0) ).
thf(834,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)],[211]) ).
thf(254,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl_0) ).
thf(937,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(201,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( A @ ( B @ c_minus ) ) @ ( A @ c_inter ) ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__disjoint_0) ).
thf(806,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)],[201]) ).
thf(66,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/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_0) ).
thf(480,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)],[66]) ).
thf(302,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_1) ).
thf(1040,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)],[302]) ).
thf(336,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_0) ).
thf(1109,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)],[336]) ).
thf(293,axiom,
( v_r
= ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Oorder ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
thf(1020,plain,
( v_r
= ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Oorder ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_UNIV @ c_union ) ) )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__left_0) ).
thf(574,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_UNIV @ c_union ) ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(3,negated_conjecture,
~ ( 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/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(353,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)],[3]) ).
thf(267,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff_0) ).
thf(966,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)],[267]) ).
thf(26,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_7) ).
thf(397,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Transitive__Closure_Otrancl ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__empty_0) ).
thf(453,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Transitive__Closure_Otrancl ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(342,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/sandbox/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_APartialOrder_0) ).
thf(1119,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)],[342]) ).
thf(281,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_0) ).
thf(998,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)],[281]) ).
thf(276,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/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).
thf(988,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)],[276]) ).
thf(42,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/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_2) ).
thf(428,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)],[42]) ).
thf(334,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/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
thf(1104,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)],[334]) ).
thf(78,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
thf(507,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)],[78]) ).
thf(119,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_0) ).
thf(602,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(184,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__empty_0) ).
thf(766,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)],[184]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).
thf(877,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).
thf(692,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)],[154]) ).
thf(143,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
thf(661,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)],[143]) ).
thf(203,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Oivl__diff_0) ).
thf(810,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)],[203]) ).
thf(163,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
thf(714,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)],[163]) ).
thf(311,axiom,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).
thf(1057,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)],[311]) ).
thf(257,axiom,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( C @ ( B @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).
thf(942,plain,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( C @ ( B @ ( A @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(47,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
thf(439,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)],[47]) ).
thf(263,axiom,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
thf(957,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(303,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/sandbox/benchmark/theBenchmark.p',cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0) ).
thf(1042,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)],[303]) ).
thf(221,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).
thf(862,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)],[221]) ).
thf(207,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/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_2) ).
thf(820,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)],[207]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).
thf(561,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)],[103]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ tc_prod ) @ ( c_IntDef_Ointrel @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_IntDef_Ointrel @ c_Relation_OImage ) ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( B @ c_insert ) ) @ ( c_IntDef_Ointrel @ c_Relation_OImage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oequiv__intrel__iff_0) ).
thf(392,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ tc_prod ) @ ( c_IntDef_Ointrel @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_IntDef_Ointrel @ c_Relation_OImage ) ) ) )
!= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( B @ c_insert ) ) @ ( c_IntDef_Ointrel @ c_Relation_OImage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(193,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( B @ tc_set @ ( A @ c_uminus ) @ c_uminus ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
thf(788,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)],[193]) ).
thf(205,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__in_0) ).
thf(815,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)],[205]) ).
thf(170,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/sandbox/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_1) ).
thf(729,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)],[170]) ).
thf(176,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/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__insert_0) ).
thf(746,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)],[176]) ).
thf(327,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_1) ).
thf(1091,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)],[327]) ).
thf(32,axiom,
tc_IntDef_Oint @ class_HOL_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).
thf(407,plain,
tc_IntDef_Oint @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(131,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atLeast_0) ).
thf(630,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)],[131]) ).
thf(68,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/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) ).
thf(484,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)],[68]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__iff_0) ).
thf(1032,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(45,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_0) ).
thf(435,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)],[45]) ).
thf(112,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/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__Int__eq_0) ).
thf(583,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)],[112]) ).
thf(57,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/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
thf(461,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)],[57]) ).
thf(71,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_union ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
thf(493,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_union ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(296,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__iff_0) ).
thf(1027,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)],[296]) ).
thf(214,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/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_1) ).
thf(842,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)],[214]) ).
thf(289,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/sandbox/benchmark/theBenchmark.p',cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Aantisym_A_Iorder_Acl1_J_A_61_61_ATrue_0) ).
thf(1012,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)],[289]) ).
thf(98,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_0) ).
thf(551,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ c_Wellfounded__Recursion_Owf ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(347,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).
thf(1128,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)],[347]) ).
thf(125,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).
thf(615,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)],[125]) ).
thf(314,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_1) ).
thf(1064,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)],[314]) ).
thf(337,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_0) ).
thf(1111,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)],[337]) ).
thf(168,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_0) ).
thf(725,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( D @ ( c_emptyset @ ( C @ c_insert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(30,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/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_1) ).
thf(403,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)],[30]) ).
thf(286,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_0) ).
thf(1006,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)],[286]) ).
thf(21,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__le__self_0) ).
thf(388,plain,
! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_minus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oconverse ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__converse_0) ).
thf(356,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oconverse ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(156,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/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_1) ).
thf(697,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)],[156]) ).
thf(326,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_0) ).
thf(1089,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)],[326]) ).
thf(138,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_0) ).
thf(650,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)],[138]) ).
thf(259,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ tc_set @ ( A @ c_uminus ) )
!= ( B @ tc_set @ ( C @ c_uminus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff_0) ).
thf(948,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)],[259]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_Relation_ORange ) ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORange__empty_0) ).
thf(471,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_Relation_ORange ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(231,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/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_0) ).
thf(884,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)],[231]) ).
thf(252,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
thf(933,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(100,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff_0) ).
thf(554,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)],[100]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onot__Cons__self_0) ).
thf(537,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(146,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
thf(669,plain,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(88,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_1) ).
thf(526,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)],[88]) ).
thf(291,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_1) ).
thf(1016,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)],[291]) ).
thf(160,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( B @ c_insert ) ) @ c_Finite__Set_OMin ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__singleton_0) ).
thf(706,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)],[160]) ).
thf(237,axiom,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
thf(901,plain,
! [B: $i,A: $i] : ( B @ ( c_UNIV @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(152,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__empty_0) ).
thf(686,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)],[152]) ).
thf(320,axiom,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).
thf(1075,plain,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Orderings_Omin ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) ).
thf(476,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Orderings_Omin ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(339,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Tarski_Opotype_Opotype__ext ) ) ) ) @ c_Tarski_Opotype_Opset ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oselect__convs__1_0) ).
thf(1114,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Tarski_Opotype_Opotype__ext ) ) ) ) @ c_Tarski_Opotype_Opset ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(83,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).
thf(515,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)],[83]) ).
thf(274,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/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_0) ).
thf(984,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)],[274]) ).
thf(166,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_UNIV @ ( A @ c_minus ) ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__UNIV_0) ).
thf(721,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( c_UNIV @ ( A @ c_minus ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(284,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/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__iff_0) ).
thf(1002,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)],[284]) ).
thf(190,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/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).
thf(779,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)],[190]) ).
thf(312,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/sandbox/benchmark/theBenchmark.p',cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Atrans_A_Iorder_Acl1_J_A_61_61_ATrue_0) ).
thf(1060,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)],[312]) ).
thf(307,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/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff_1) ).
thf(1050,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)],[307]) ).
thf(195,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_inter ) ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__empty__right_0) ).
thf(792,plain,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_inter ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(324,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(1086,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(247,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( c_emptyset @ ( B @ c_insert ) ) @ c_Finite__Set_OMax ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__singleton_0) ).
thf(921,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)],[247]) ).
thf(141,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).
thf(657,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)],[141]) ).
thf(309,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
thf(1054,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)],[309]) ).
thf(27,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/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
thf(398,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)],[27]) ).
thf(148,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0) ).
thf(674,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)],[148]) ).
thf(90,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/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_2) ).
thf(530,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)],[90]) ).
thf(261,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_0) ).
thf(953,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)],[261]) ).
thf(132,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/sandbox/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_1) ).
thf(633,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)],[132]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_OImage ) ) ) )
= ( B @ ( C @ ( A @ c_inter ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__diag_0) ).
thf(360,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_OImage ) ) ) )
= ( B @ ( C @ ( A @ c_inter ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(102,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/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_1) ).
thf(558,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)],[102]) ).
thf(318,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_1) ).
thf(1071,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)],[318]) ).
thf(187,axiom,
! [A: $i] :
( ( A @ tc_set @ ( c_UNIV @ c_uminus ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).
thf(773,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_UNIV @ c_uminus ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(196,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/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_1) ).
thf(794,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)],[196]) ).
thf(240,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).
thf(906,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)],[240]) ).
thf(126,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_1) ).
thf(618,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)],[126]) ).
thf(153,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/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_1) ).
thf(689,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)],[153]) ).
thf(16,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0) ).
thf(375,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)],[16]) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_2) ).
thf(513,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)],[82]) ).
thf(43,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/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__cancel_0) ).
thf(430,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)],[43]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ( c_emptyset
= ( B @ ( A @ c_Union ) ) )
| ( ( B @ ( A @ c_Main_Oempty__Union__conv__1 ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_2) ).
thf(423,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)],[40]) ).
thf(171,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_1) ).
thf(732,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)],[171]) ).
thf(110,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( A @ c_minus ) ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).
thf(579,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( A @ c_minus ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(345,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/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__iff_1) ).
thf(1124,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)],[345]) ).
thf(35,axiom,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OlessThan ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
thf(413,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)],[35]) ).
thf(239,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
thf(904,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(270,axiom,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_2) ).
thf(975,plain,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oorder ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(227,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__insert_0) ).
thf(875,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)],[227]) ).
thf(209,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/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).
thf(826,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)],[209]) ).
thf(135,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_1) ).
thf(641,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)],[135]) ).
thf(107,axiom,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( c_emptyset @ c_minus ) ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Diff_0) ).
thf(572,plain,
! [B: $i,A: $i] :
( ( B @ tc_set @ ( A @ ( c_emptyset @ c_minus ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(123,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_0) ).
thf(611,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)],[123]) ).
thf(74,axiom,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__infinite_0) ).
thf(498,plain,
~ ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( c_UNIV @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(335,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__iff_2) ).
thf(1107,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)],[335]) ).
thf(159,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_0) ).
thf(704,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)],[159]) ).
thf(94,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_inter ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__absorb_0) ).
thf(540,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_inter ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(246,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_1) ).
thf(919,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)],[246]) ).
thf(200,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Pow ) @ c_Union ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__Pow__eq_0) ).
thf(804,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Pow ) @ c_Union ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(210,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/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_0) ).
thf(831,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)],[210]) ).
thf(306,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/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_1) ).
thf(1048,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)],[306]) ).
thf(173,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/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__inter__insert_0) ).
thf(737,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)],[173]) ).
thf(344,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( tc_Product__Type_Ounit @ ( C @ ( D @ c_Tarski_Opotype_Oorder ) ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( tc_Product__Type_Ounit @ ( C @ ( C @ ( D @ c_Tarski_Odual ) @ c_Tarski_Opotype_Oorder ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0) ).
thf(1122,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( tc_Product__Type_Ounit @ ( C @ ( D @ c_Tarski_Opotype_Oorder ) ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( tc_Product__Type_Ounit @ ( C @ ( C @ ( D @ c_Tarski_Odual ) @ c_Tarski_Opotype_Oorder ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__not__empty_0) ).
thf(599,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(272,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/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_1) ).
thf(979,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)],[272]) ).
thf(120,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Tarski_Opotype_Opotype__ext ) ) ) ) @ c_Tarski_Opotype_Oorder ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oselect__convs__2_0) ).
thf(604,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Tarski_Opotype_Opotype__ext ) ) ) ) @ c_Tarski_Opotype_Oorder ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(191,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).
thf(784,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)],[191]) ).
thf(341,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
thf(1117,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)],[341]) ).
thf(277,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(990,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)],[277]) ).
thf(280,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
thf(996,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)],[280]) ).
thf(8,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/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_2) ).
thf(362,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)],[8]) ).
thf(53,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/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2) ).
thf(451,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)],[53]) ).
thf(105,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/sandbox/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_0) ).
thf(567,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)],[105]) ).
thf(79,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
thf(509,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)],[79]) ).
thf(229,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/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__iff_2) ).
thf(880,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)],[229]) ).
thf(233,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
thf(890,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(20,axiom,
tc_IntDef_Oint @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
thf(387,plain,
tc_IntDef_Oint @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(181,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_0) ).
thf(758,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(92,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_1) ).
thf(535,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)],[92]) ).
thf(116,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_1) ).
thf(594,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)],[116]) ).
thf(198,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/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_2) ).
thf(799,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)],[198]) ).
thf(127,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/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff1_0) ).
thf(621,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)],[127]) ).
thf(157,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_1) ).
thf(700,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( C @ ( c_emptyset @ ( A @ c_insert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(266,axiom,
! [A: $i] :
( ( A @ ( c_UNIV @ c_Pow ) )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__UNIV_0) ).
thf(964,plain,
! [A: $i] :
( ( A @ ( c_UNIV @ c_Pow ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(185,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_inter ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__right_0) ).
thf(769,plain,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_inter ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(294,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/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).
thf(1022,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)],[294]) ).
thf(219,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
thf(858,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(11,axiom,
tc_nat @ class_Nat_Opower,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_12) ).
thf(367,plain,
tc_nat @ class_Nat_Opower,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(297,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/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_0) ).
thf(1029,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)],[297]) ).
thf(235,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atMost_0) ).
thf(895,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)],[235]) ).
thf(129,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).
thf(626,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)],[129]) ).
thf(244,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
thf(915,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)],[244]) ).
thf(264,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_0) ).
thf(959,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)],[264]) ).
thf(315,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).
thf(1066,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)],[315]) ).
thf(55,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0) ).
thf(455,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)],[55]) ).
thf(122,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff_0) ).
thf(608,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)],[122]) ).
thf(275,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_2) ).
thf(986,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)],[275]) ).
thf(338,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
thf(1113,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( c_emptyset @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(282,axiom,
! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_4) ).
thf(1000,plain,
! [A: $i] : ( A @ tc_set @ class_Nat_Opower ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(333,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_0) ).
thf(1102,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)],[333]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_insert ) ) )
= ( C @ ( B @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).
thf(505,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)],[77]) ).
thf(243,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/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_1) ).
thf(912,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)],[243]) ).
thf(86,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Osingle__Diff__lessThan_0) ).
thf(521,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)],[86]) ).
thf(155,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
thf(695,plain,
! [A: $i] :
( ( A @ class_Orderings_Oord )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(133,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/sandbox/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_2) ).
thf(636,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)],[133]) ).
thf(304,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/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_0) ).
thf(1044,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)],[304]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_IntDef_Ointrel @ c_Relation_OImage ) ) ) )
= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( B @ c_insert ) ) @ ( c_IntDef_Ointrel @ c_Relation_OImage ) ) ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ tc_prod ) @ ( c_IntDef_Ointrel @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oequiv__intrel__iff_1) ).
thf(473,plain,
! [B: $i,A: $i] :
( ( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( A @ c_insert ) ) @ ( c_IntDef_Ointrel @ c_Relation_OImage ) ) ) )
= ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( B @ c_insert ) ) @ ( c_IntDef_Ointrel @ c_Relation_OImage ) ) ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ tc_prod ) @ ( c_IntDef_Ointrel @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(299,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/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__iff_1) ).
thf(1034,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)],[299]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Relation_Odiag ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Odiag__empty_0) ).
thf(426,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Relation_Odiag ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(150,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_UNIV )
| ( ( C @ ( B @ ( A @ c_inter ) ) )
!= c_UNIV ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_1) ).
thf(680,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)],[150]) ).
thf(144,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_1) ).
thf(663,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)],[144]) ).
thf(249,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__Un__distrib_0) ).
thf(927,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)],[249]) ).
thf(322,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/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_0) ).
thf(1081,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)],[322]) ).
thf(84,axiom,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite )
| ( B @ ( A @ tc_prod ) @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_prod_0) ).
thf(516,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite )
| ( B @ ( A @ tc_prod ) @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(255,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).
thf(939,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(292,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/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_0) ).
thf(1018,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)],[292]) ).
thf(4,axiom,
tc_nat @ class_HOL_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_9) ).
thf(355,plain,
tc_nat @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(179,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_UNIV @ c_inter ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__left_0) ).
thf(754,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_UNIV @ c_inter ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(99,axiom,
! [A: $i] : ( tc_nat @ tc_set @ ( c_Finite__Set_OFinites @ ( tc_nat @ ( A @ c_SetInterval_OatMost ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
thf(553,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)],[99]) ).
thf(212,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_SetInterval_OatLeastAtMost ) ) )
= ( A @ ( c_emptyset @ ( B @ c_insert ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__singleton_0) ).
thf(836,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)],[212]) ).
thf(56,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Union ) )
= c_emptyset )
| ( ( B @ ( A @ c_Main_OUnion__empty__conv__1 ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_2) ).
thf(458,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)],[56]) ).
thf(208,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__le_0) ).
thf(823,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)],[208]) ).
thf(189,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__ge_0) ).
thf(776,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)],[189]) ).
thf(162,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/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).
thf(712,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)],[162]) ).
thf(218,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/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_0) ).
thf(855,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)],[218]) ).
thf(295,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_0) ).
thf(1025,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)],[295]) ).
thf(317,axiom,
tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
thf(1070,plain,
tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(232,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__lessThan_0) ).
thf(887,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)],[232]) ).
thf(36,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).
thf(414,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)],[36]) ).
thf(174,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = G )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Tarski_Opotype_Opotype__ext ) ) ) ) )
!= ( E @ ( D @ ( H @ ( G @ ( F @ c_Tarski_Opotype_Opotype__ext ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oext__inject_1) ).
thf(739,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = G )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Tarski_Opotype_Opotype__ext ) ) ) ) )
!= ( E @ ( D @ ( H @ ( G @ ( F @ c_Tarski_Opotype_Opotype__ext ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(331,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_1) ).
thf(1098,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)],[331]) ).
thf(49,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_0) ).
thf(441,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)],[49]) ).
thf(76,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/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_0) ).
thf(502,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)],[76]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_ORange ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORange__diag_0) ).
thf(463,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_ORange ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(348,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( tc_Product__Type_Ounit @ ( C @ ( D @ c_Tarski_Opotype_Oorder ) ) @ ( C @ ( C @ ( C @ ( D @ ( B @ c_Tarski_Olub ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( tc_Product__Type_Ounit @ ( C @ ( D @ c_Tarski_Opotype_Opset ) ) @ ( B @ c_lessequals ) ) )
| ~ ( tc_Product__Type_Ounit @ ( C @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( D @ c_in ) ) )
| ~ ( tc_Product__Type_Ounit @ ( C @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OCL_Olub__upper_0) ).
thf(1130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( tc_Product__Type_Ounit @ ( C @ ( D @ c_Tarski_Opotype_Oorder ) ) @ ( C @ ( C @ ( C @ ( D @ ( B @ c_Tarski_Olub ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( tc_Product__Type_Ounit @ ( C @ ( D @ c_Tarski_Opotype_Opset ) ) @ ( B @ c_lessequals ) ) )
| ~ ( tc_Product__Type_Ounit @ ( C @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( D @ c_in ) ) )
| ~ ( tc_Product__Type_Ounit @ ( C @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OCompleteLattice @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(136,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/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).
thf(643,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)],[136]) ).
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/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__iff_0) ).
thf(1038,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(113,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/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_2) ).
thf(585,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)],[113]) ).
thf(13,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_2) ).
thf(370,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)],[13]) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).
thf(470,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)],[61]) ).
thf(109,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
thf(576,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)],[109]) ).
thf(260,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Set_Ocontents ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).
thf(951,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Set_Ocontents ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(202,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).
thf(808,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)],[202]) ).
thf(96,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = F )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Tarski_Opotype_Opotype__ext ) ) ) ) )
!= ( E @ ( D @ ( H @ ( G @ ( F @ c_Tarski_Opotype_Opotype__ext ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oext__inject_0) ).
thf(544,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = F )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Tarski_Opotype_Opotype__ext ) ) ) ) )
!= ( E @ ( D @ ( H @ ( G @ ( F @ c_Tarski_Opotype_Opotype__ext ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(241,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_union ) ) )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__right_0) ).
thf(907,plain,
! [B: $i,A: $i] :
( ( B @ ( c_UNIV @ ( A @ c_union ) ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(175,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_0) ).
thf(744,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)],[175]) ).
thf(124,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/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__iff_0) ).
thf(613,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)],[124]) ).
thf(308,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_1) ).
thf(1052,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)],[308]) ).
thf(222,axiom,
! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
thf(864,plain,
! [A: $i] : ( A @ tc_set @ ( c_Finite__Set_OFinites @ ( c_emptyset @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(169,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).
thf(727,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)],[169]) ).
thf(287,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/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_2) ).
thf(1008,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)],[287]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ODomain ) ) )
= ( B @ ( B @ ( A @ c_Relation_ODomain ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__domain_0) ).
thf(446,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ODomain ) ) )
= ( B @ ( B @ ( A @ c_Relation_ODomain ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(73,axiom,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_1) ).
thf(497,plain,
! [A: $i] : ( A @ tc_set @ class_Orderings_Oord ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(215,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_1) ).
thf(845,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(59,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/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0) ).
thf(465,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)],[59]) ).
thf(323,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( tc_Product__Type_Ounit @ ( C @ ( C @ ( D @ c_Tarski_Odual ) @ c_Tarski_Opotype_Oorder ) ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( tc_Product__Type_Ounit @ ( C @ ( D @ c_Tarski_Opotype_Oorder ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_1) ).
thf(1084,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( tc_Product__Type_Ounit @ ( C @ ( C @ ( D @ c_Tarski_Odual ) @ c_Tarski_Opotype_Oorder ) ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( tc_Product__Type_Ounit @ ( C @ ( D @ c_Tarski_Opotype_Oorder ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(101,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_2) ).
thf(556,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)],[101]) ).
thf(251,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__insert_0) ).
thf(931,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)],[251]) ).
thf(67,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(482,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(147,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_1) ).
thf(671,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)],[147]) ).
thf(271,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/sandbox/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_0) ).
thf(976,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)],[271]) ).
thf(72,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Pow ) )
= ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_insert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__empty_0) ).
thf(495,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)],[72]) ).
thf(346,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/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
thf(1126,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)],[346]) ).
thf(288,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/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_1) ).
thf(1010,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)],[288]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ORange ) ) )
= ( B @ ( B @ ( A @ c_Relation_ORange ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__range_0) ).
thf(368,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ORange ) ) )
= ( B @ ( B @ ( A @ c_Relation_ORange ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(186,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel2_0) ).
thf(771,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)],[186]) ).
thf(87,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/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__Int_0) ).
thf(524,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)],[87]) ).
thf(111,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Inter ) )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__empty_0) ).
thf(581,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Inter ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(114,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_2) ).
thf(588,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)],[114]) ).
thf(204,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( C @ ( F @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Ozip ) ) ) )
= ( F @ ( C @ tc_prod ) @ ( F @ ( C @ ( E @ ( B @ c_List_Ozip ) ) ) @ ( F @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ozip__Cons__Cons_0) ).
thf(813,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( C @ ( F @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_List_Ozip ) ) ) )
= ( F @ ( C @ tc_prod ) @ ( F @ ( C @ ( E @ ( B @ c_List_Ozip ) ) ) @ ( F @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(177,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__insert_0) ).
thf(748,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)],[177]) ).
thf(313,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/sandbox/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__2_0) ).
thf(1062,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)],[313]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_1) ).
thf(390,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(29,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_1) ).
thf(401,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)],[29]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_UNIV )
| ( ( C @ ( B @ ( A @ c_inter ) ) )
!= c_UNIV ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_0) ).
thf(652,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)],[139]) ).
thf(1,negated_conjecture,
t_a @ tc_set @ ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Opset ) ) @ ( v_S @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(351,plain,
t_a @ tc_set @ ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Opset ) ) @ ( v_S @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(38,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/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0) ).
thf(418,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)],[38]) ).
thf(192,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_0) ).
thf(786,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)],[192]) ).
thf(17,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/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_1) ).
thf(378,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)],[17]) ).
thf(250,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_2) ).
thf(929,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)],[250]) ).
thf(183,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/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).
thf(763,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)],[183]) ).
thf(18,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/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_1) ).
thf(383,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)],[18]) ).
thf(97,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/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__idemp_0) ).
thf(549,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)],[97]) ).
thf(164,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/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_2) ).
thf(716,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)],[164]) ).
thf(44,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/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_0) ).
thf(433,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)],[44]) ).
thf(80,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
thf(510,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)],[80]) ).
thf(340,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( c_UNIV @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__UNIV_0) ).
thf(1116,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( c_UNIV @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(350,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/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__iff_2) ).
thf(1133,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)],[350]) ).
thf(34,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff_0) ).
thf(410,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)],[34]) ).
thf(330,axiom,
! [A: $i] : ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__empty_1) ).
thf(1097,plain,
! [A: $i] : ( A @ tc_set @ ( c_emptyset @ ( c_emptyset @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(206,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).
thf(818,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)],[206]) ).
thf(31,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_1) ).
thf(405,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)],[31]) ).
thf(194,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty_2) ).
thf(790,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(224,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__in_0) ).
thf(867,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)],[224]) ).
thf(223,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
thf(865,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_0) ).
thf(373,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(172,axiom,
! [A: $i] :
( ( A @ ( c_UNIV @ ( c_UNIV @ c_inter ) ) )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_2) ).
thf(735,plain,
! [A: $i] :
( ( A @ ( c_UNIV @ ( c_UNIV @ c_inter ) ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(104,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
thf(564,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)],[104]) ).
thf(6,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_3) ).
thf(358,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)],[6]) ).
thf(46,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_0) ).
thf(437,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)],[46]) ).
thf(310,axiom,
! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_0) ).
thf(1056,plain,
! [A: $i] : ( A @ tc_set @ class_HOL_Ominus ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(28,axiom,
tc_IntDef_Oint @ class_Orderings_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
thf(400,plain,
tc_IntDef_Oint @ class_Orderings_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(262,axiom,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
thf(955,plain,
! [A: $i] :
( ( A @ class_Orderings_Oorder )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Orderings_Omax ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) ).
thf(415,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Orderings_Omax ) ) )
= B )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(220,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ tc_set @ ( A @ c_uminus ) @ c_inter ) ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint2_0) ).
thf(860,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)],[220]) ).
thf(117,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__greaterThan_0) ).
thf(596,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)],[117]) ).
thf(89,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/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__Un_0) ).
thf(528,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)],[89]) ).
thf(278,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_1) ).
thf(992,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)],[278]) ).
thf(167,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
thf(723,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(216,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/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__insert_0) ).
thf(850,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)],[216]) ).
thf(343,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(1120,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)],[343]) ).
thf(328,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/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_1) ).
thf(1093,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)],[328]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_Relation_ODomain ) ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomain__empty_0) ).
thf(395,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_Relation_ODomain ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(128,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_inter ) ) )
= c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__empty__left_0) ).
thf(624,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_inter ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(213,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).
thf(839,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)],[213]) ).
thf(273,axiom,
! [A: $i] :
( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
= c_UNIV ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__empty__eq_0) ).
thf(982,plain,
! [A: $i] :
( ( A @ tc_set @ ( c_emptyset @ c_uminus ) )
= c_UNIV ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(285,axiom,
( v_A
= ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Opset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
thf(1004,plain,
( v_A
= ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Opset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(69,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = H )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Tarski_Opotype_Opotype__ext ) ) ) ) )
!= ( E @ ( D @ ( H @ ( G @ ( F @ c_Tarski_Opotype_Opotype__ext ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oext__inject_2) ).
thf(486,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C = H )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Tarski_Opotype_Opotype__ext ) ) ) ) )
!= ( E @ ( D @ ( H @ ( G @ ( F @ c_Tarski_Opotype_Opotype__ext ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(256,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( F @ c_Relation_OImage ) ) ) @ ( D @ c_in ) ) )
| ~ ( E @ ( C @ tc_prod ) @ ( F @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).
thf(940,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( F @ c_Relation_OImage ) ) ) @ ( D @ c_in ) ) )
| ~ ( E @ ( C @ tc_prod ) @ ( F @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(253,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/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
thf(935,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)],[253]) ).
thf(142,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_2) ).
thf(659,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)],[142]) ).
thf(188,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
thf(775,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
| ~ ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse_1) ).
thf(639,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
| ~ ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse_0) ).
thf(491,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( A @ c_in ) ) )
| ~ ( B @ ( C @ tc_prod ) @ tc_set @ ( c_Finite__Set_OFinites @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(9,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/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
thf(364,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)],[9]) ).
thf(230,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Relation_Otrans ) )
| ~ ( D @ ( C @ c_Relation_Otrans ) )
| ~ ( B @ ( A @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).
thf(882,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ tc_prod ) @ ( B @ ( D @ ( A @ ( C @ c_Wellfounded__Relations_Olex__prod ) ) ) @ c_Relation_Otrans ) )
| ~ ( D @ ( C @ c_Relation_Otrans ) )
| ~ ( B @ ( A @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(290,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/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
thf(1014,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)],[290]) ).
thf(269,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/sandbox/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_2) ).
thf(972,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)],[269]) ).
thf(1138,plain,
$false,
inference(e,[status(thm)],[1036,365,760,479,518,666,352,645,892,909,628,962,468,408,683,1068,994,1073,677,873,449,440,655,511,1078,385,533,500,797,945,1095,898,1001,709,1046,389,570,719,372,802,1132,542,917,702,751,902,853,1087,448,1100,421,870,969,606,924,756,591,834,937,806,480,1040,1109,1020,574,353,966,397,453,1119,998,988,428,1104,507,602,766,877,692,661,810,714,1057,942,439,957,1042,862,820,561,392,788,815,729,746,1091,407,630,484,1032,435,583,461,493,1027,842,1012,551,1128,615,1064,1111,725,403,1006,388,356,697,1089,650,948,471,884,933,554,537,669,526,1016,706,901,686,1075,476,1114,515,984,721,1002,779,1060,1050,792,1086,921,657,1054,398,674,530,953,633,360,558,1071,773,794,906,618,689,375,513,430,423,732,579,1124,413,904,975,875,826,641,572,611,498,1107,704,540,919,804,831,1048,737,1122,599,979,604,784,1117,990,996,362,451,567,509,880,890,387,758,535,594,799,621,700,964,769,1022,858,367,1029,895,626,915,959,1066,455,608,986,1113,1000,1102,505,912,521,695,636,1044,473,1034,426,680,663,927,1081,516,939,1018,355,754,553,836,458,823,776,712,855,1025,1070,887,414,739,1098,441,502,463,1130,643,1038,585,370,470,576,951,808,544,907,744,613,1052,864,727,1008,446,497,845,465,1084,556,931,482,671,976,495,1126,1010,368,771,524,581,588,813,748,1062,390,401,652,351,418,786,378,929,763,383,549,716,433,510,1116,1133,410,1097,818,405,790,867,865,373,735,564,358,437,1056,400,955,415,860,596,528,992,723,850,1120,1093,395,624,839,982,1004,486,940,935,659,775,639,491,364,882,1014,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT265-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/5.41 % Computer : n006.cluster.edu
% 0.14/5.41 % Model : x86_64 x86_64
% 0.14/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.41 % Memory : 8046.5625MB
% 0.14/5.41 % OS : Linux 6.8.0-71-generic
% 0.14/5.41 % CPULimit : 300
% 0.14/5.41 % WCLimit : 300
% 0.14/5.41 % DateTime : Fri Sep 25 20:21:36 UTC 2026
% 0.14/5.41 % CPUTime :
% 0.14/5.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.18/6.02 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.72/6.83 % [INFO] Parsing done (802ms).
% 2.72/6.85 % [INFO] Running in sequential loop mode.
% 3.30/7.17 % [INFO] eprover registered as external prover.
% 3.30/7.17 % [INFO] Scanning for conjecture ...
% 4.44/7.41 % [INFO] Found a conjecture (or negated_conjecture) and 2749 axioms. Running axiom selection ...
% 5.73/7.70 % [INFO] Axiom selection finished. Selected 347 axioms (removed 2402 axioms).
% 5.98/7.89 % [INFO] Problem is propositional (TPTP CNF).
% 6.25/7.91 % [INFO] Type checking passed.
% 6.25/7.91 % [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 ...
% 12.11/9.59 % External prover 'e' found a proof!
% 12.11/9.59 % [INFO] Killing All external provers ...
% 12.11/9.59 % Time passed: 4036ms (effective reasoning time: 2727ms)
% 12.60/9.60 % Axioms used in derivation (347): cls_Set_OPow__UNIV_0, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0, cls_Relation_ODomain__empty_0, cls_Set_OPow__iff_1, cls_Set_Oempty__Union__conv_1, cls_Set_Oinsert__disjoint__1_1, cls_Datatype__Universe_OuprodI_0, cls_Tarski_Opotype_Oselect__convs__2_0, cls_Finite__Set_Ofinite__Union_0, cls_Set_OCompl__subset__Compl__iff_1, cls_SetInterval_OgreaterThanLessThan__iff_0, cls_Transitive__Closure_Otrancl__range_0, cls_Finite__Set_OMin__gr__iff_2, cls_SetInterval_OgreaterThanAtMost__iff_2, cls_Set_Osingleton__insert__inj__eq_0, cls_Tarski_Opotype_Oext__inject_1, cls_Finite__Set_OMin__insert_0, cls_Relation_OImageI_0, cls_Set_OInt__iff_2, cls_Relation_ODomain__diag_0, cls_Set_OUNIV__not__empty_0, clsarity_prod_0, cls_Relation_ORange__diag_0, cls_Set_OsubsetI_1, cls_Set_ODiff__cancel_0, cls_Wellfounded__Recursion_Owf__insert_0, clsarity_nat_7, cls_Set_Osubset__UNIV_0, cls_Finite__Set_OMin__singleton_0, cls_Set_Oinsert__Diff1_0, cls_Transitive__Closure_Otrancl_Or__into__trancl_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_Set_OUn__subset__iff_2, cls_Nat_Oless__irrefl_0, clsarity_set_2, clsarity_nat_3, cls_Tarski_OCL_Olub__upper_0, cls_List_Olist_Oinject_1, cls_Finite__Set_OFinites_OinsertI_0, cls_Wellfounded__Relations_Owf__lex__prod_0, 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_Relation_Oconverse__converse_0, cls_Finite__Set_Ofinite__Int_0, cls_Set_OInter__UNIV_0, cls_Set_ODiff__UNIV_0, clsarity_IntDef__Oint_0, cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_1, 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_Wellfounded__Recursion_Oacyclic__converse_1, cls_Set_OUn__Diff__cancel2_0, cls_Set_Odisjoint__insert__1_1, cls_Orderings_Omax__less__iff__conj_0, cls_Set_Osubset__empty_0, cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2, cls_SetInterval_OatLeastAtMost__empty_0, cls_Relation_OdiagI_0, cls_SetInterval_OatLeastAtMost__iff_2, cls_Set_ODiff__insert0_0, cls_Set_OsubsetI_0, cls_Finite__Set_Ofinite__converse_1, 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_Set_Oinsert__subset_2, cls_Set_OUn__UNIV__right_0, cls_Set_OUnion__empty__conv_1, cls_Tarski_Opotype_Oext__inject_2, cls_Set_OUn__iff_0, cls_Set_OUnion__iff_1, cls_SetInterval_OgreaterThan__subset__iff_0, cls_Relation_ODomainI_0, cls_Set_Osingleton__insert__inj__eq_H_1, cls_Tarski_OA_A_61_61_Apset_Acl_0, cls_Set_OUn__empty_1, 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_Set_Oinsert__not__empty_0, cls_SetInterval_OgreaterThan__iff_0, cls_Set_OsingletonD__dest_0, cls_SetInterval_Ofinite__atLeastLessThan_0, cls_Relation_OImage__singleton__iff_1, cls_Finite__Set_OMax__less__iff_1, cls_SetInterval_OlessThan__iff_0, cls_Wellfounded__Recursion_Owf__not__refl_0, 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_Transitive__Closure_Otrancl__empty_0, cls_SetInterval_OCompl__greaterThan_0, cls_Set_Oempty__subsetI_0, cls_Set_OInt__UNIV__right_0, cls_Relation_Oconverse__iff_1, cls_Set_OInter__UNIV__conv__2_2, 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_Relation_ORange__empty_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_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0, cls_Relation_OImage__empty_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_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_Set_Osubset__empty_1, cls_Finite__Set_Ofinite__converse_0, 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_Relation_ORangeI_0, 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_Relation_Oconverse__diag_0, 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_Tarski_Or_A_61_61_Aorder_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_Finite__Set_OMin__ge__iff_0, cls_Set_OInt__empty__right_0, cls_Wellfounded__Recursion_Oacyclic__converse_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_IntDef_Oequiv__intrel__iff_0, cls_Product__Type_OPair__eq_1, 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_Wellfounded__Recursion_Owf__empty_0, cls_Finite__Set_OMax__less__iff_0, cls_Set_OUnion__iff_2, cls_SetInterval_Ofinite__greaterThanLessThan_0, cls_SetInterval_Oivl__diff_0, cls_Relation_Oconverse__iff_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_Relation_OImage__singleton__iff_0, 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_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_Relation_Orel__compI_0, cls_Set_ODiff__eq__empty__iff_0, cls_Set_OInt__iff_0, cls_Transitive__Closure_Otrancl__domain_0, cls_Set_ODiff__empty_0, cls_SetInterval_OatMost__eq__iff_0, cls_Finite__Set_OMax__in_0, clsarity_nat_9, cls_Wellfounded__Relations_Otrans__lex__prod_0, cls_Set_Oempty__Union__conv_2, cls_Set_Oinsert__disjoint__1_2, cls_Set_OInter__UNIV__conv__1_2, cls_Relation_Odiag__empty_0, 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_Set_ODiff__iff_0, clsarity_Product____Type__Ounit_0, cls_SetInterval_OgreaterThan__eq__iff_0, cls_Set_OUnionE_0, cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0, cls_IntDef_Oequiv__intrel__iff_1, cls_Set_OCompl__disjoint_0, cls_Set_OInter__empty_0, cls_Product__Type_OPair__eq_0, clsarity_set_0, cls_List_Ozip__Cons__Cons_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_List_Olistset_Osimps__2_0, cls_Set_Oinsert__absorb2_0, cls_SetInterval_OlessThan__eq__iff_0, cls_Set_OUn__subset__iff_1, cls_Set_Oinsert__iff_0, cls_Wellfounded__Recursion_Oacyclic__insert_0, 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_Tarski_Opotype_Oselect__convs__1_0, 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_Relation_OImage__diag_0, cls_Tarski_Opotype_Oext__inject_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
% 12.60/9.60 % No. of inferences in proof: 701
% 12.60/9.60 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 4036 ms resp. 2727 ms w/o parsing
% 13.22/9.84 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.22/9.85 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------