%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT281-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n001.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 07:46:57 AM UTC 2026
% Result : Unsatisfiable 32.61s 7.86s
% Output : Refutation 29.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 167
% Syntax : Number of formulae : 384 ( 168 unt; 0 typ; 0 def)
% Number of atoms : 686 ( 251 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 5683 ( 319 ~; 278 |; 0 &;5086 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 82 ( 79 usr; 18 con; 0-6 aty)
% Number of variables : 1146 ( 0 ^;1146 !; 0 ?;1146 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(c_Pair_decl,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(v_a_decl,type,
v_a: $i ).
thf(v_b_decl,type,
v_b: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(v_r_decl,type,
v_r: $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(v_c_decl,type,
v_c: $i ).
thf(c_Relation_Oantisym_decl,type,
c_Relation_Oantisym: $i > $i > $o ).
thf(c_Tarski_Opotype_Oorder_decl,type,
c_Tarski_Opotype_Oorder: $i > $i > $i > $i ).
thf(tc_Product__Type_Ounit_decl,type,
tc_Product__Type_Ounit: $i ).
thf(c_Relation_Orefl_decl,type,
c_Relation_Orefl: $i > $i > $i > $o ).
thf(c_Tarski_Opotype_Opset_decl,type,
c_Tarski_Opotype_Opset: $i > $i > $i > $i ).
thf(c_Relation_Otrans_decl,type,
c_Relation_Otrans: $i > $i > $o ).
thf(c_Tarski_OPartialOrder_decl,type,
c_Tarski_OPartialOrder: $i ).
thf(tc_Tarski_Opotype_Opotype__ext__type_decl,type,
tc_Tarski_Opotype_Opotype__ext__type: $i > $i > $i ).
thf(c_List_Olist_OCons_decl,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(tc_List_Olist_decl,type,
tc_List_Olist: $i > $i ).
thf(c_List_Olistrel_decl,type,
c_List_Olistrel: $i > $i > $i ).
thf(c_Main_Olistrel__Cons2__1_decl,type,
c_Main_Olistrel__Cons2__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_Olistrel__Cons2__2_decl,type,
c_Main_Olistrel__Cons2__2: $i > $i > $i > $i > $i > $i ).
thf(c_Main_Olistrel__Cons1__1_decl,type,
c_Main_Olistrel__Cons1__1: $i > $i > $i > $i > $i > $i ).
thf(c_Main_Olistrel__Cons1__2_decl,type,
c_Main_Olistrel__Cons1__2: $i > $i > $i > $i > $i > $i ).
thf(c_union_decl,type,
c_union: $i > $i > $i > $i ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(c_Nat_Osize_decl,type,
c_Nat_Osize: $i > $i > $i ).
thf(c_List_Olex_decl,type,
c_List_Olex: $i > $i > $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(class_Finite__Set_Ofinite_decl,type,
class_Finite__Set_Ofinite: $i > $o ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(c_less_decl,type,
c_less: $i > $i > $i > $o ).
thf(c_Wellfounded__Recursion_Owf_decl,type,
c_Wellfounded__Recursion_Owf: $i > $i > $o ).
thf(c_List_Olists_decl,type,
c_List_Olists: $i > $i > $i ).
thf(c_Relation_Oconverse_decl,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(c_Transitive__Closure_Ortrancl_decl,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_Relation_ORange_decl,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(c_List_Olist_ONil_decl,type,
c_List_Olist_ONil: $i ).
thf(c_Relation_OId_decl,type,
c_Relation_OId: $i ).
thf(c_Wellfounded__Relations_Oless__than_decl,type,
c_Wellfounded__Relations_Oless__than: $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_Relation_Orel__comp_decl,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(c_Transitive__Closure_Otrancl_decl,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_List_Onth_decl,type,
c_List_Onth: $i > $i > $i > $i ).
thf(c_List_Ozip_decl,type,
c_List_Ozip: $i > $i > $i > $i > $i ).
thf(c_plus_decl,type,
c_plus: $i > $i > $i > $i ).
thf(c_List_Olexord_decl,type,
c_List_Olexord: $i > $i > $i ).
thf(c_Relation_OImage_decl,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_Wellfounded__Recursion_Oacyclic_decl,type,
c_Wellfounded__Recursion_Oacyclic: $i > $i > $o ).
thf(c_Relation_Odiag_decl,type,
c_Relation_Odiag: $i > $i > $i ).
thf(c_IntDef_Ointrel_decl,type,
c_IntDef_Ointrel: $i ).
thf(c_Relation_ODomain_decl,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(c_Main_OImageE__1_decl,type,
c_Main_OImageE__1: $i > $i > $i > $i > $i > $i ).
thf(c_fst_decl,type,
c_fst: $i > $i > $i > $i ).
thf(c_snd_decl,type,
c_snd: $i > $i > $i > $i ).
thf(c_List_Olenlex_decl,type,
c_List_Olenlex: $i > $i > $i ).
thf(c_Set_Ocontents_decl,type,
c_Set_Ocontents: $i > $i > $i ).
thf(c_List_Olistset_decl,type,
c_List_Olistset: $i > $i > $i ).
thf(c_IntDef_OInteg_decl,type,
c_IntDef_OInteg: $i ).
thf(v_cl_decl,type,
v_cl: $i ).
thf(c_Main_ORangeE__1_decl,type,
c_Main_ORangeE__1: $i > $i > $i > $i > $i ).
thf(c_Main_Otrans__def__1_decl,type,
c_Main_Otrans__def__1: $i > $i > $i ).
thf(c_Main_Otrans__def__2_decl,type,
c_Main_Otrans__def__2: $i > $i > $i ).
thf(c_Wellfounded__Relations_Olex__prod_decl,type,
c_Wellfounded__Relations_Olex__prod: $i > $i > $i > $i > $i ).
thf(c_Main_Otrans__def__3_decl,type,
c_Main_Otrans__def__3: $i > $i > $i ).
thf(c_Main_OconverseE__1_decl,type,
c_Main_OconverseE__1: $i > $i > $i > $i > $i ).
thf(c_Main_OconverseE__2_decl,type,
c_Main_OconverseE__2: $i > $i > $i > $i > $i ).
thf(v_A_decl,type,
v_A: $i ).
thf(c_Main_Olexord__Nil__left__1_decl,type,
c_Main_Olexord__Nil__left__1: $i > $i > $i ).
thf(c_Main_Olexord__Nil__left__2_decl,type,
c_Main_Olexord__Nil__left__2: $i > $i > $i ).
thf(c_Infinite__Set_Oatmost__one_decl,type,
c_Infinite__Set_Oatmost__one: $i > $i > $o ).
thf(c_Main_Orel__compE__1_decl,type,
c_Main_Orel__compE__1: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_Orel__compE__3_decl,type,
c_Main_Orel__compE__3: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_Osurj__pair__1_decl,type,
c_Main_Osurj__pair__1: $i > $i > $i > $i ).
thf(c_Main_Osurj__pair__2_decl,type,
c_Main_Osurj__pair__2: $i > $i > $i > $i ).
thf(c_Main_OdiagE__1_decl,type,
c_Main_OdiagE__1: $i > $i > $i > $i ).
thf(c_Main_Orel__compE__2_decl,type,
c_Main_Orel__compE__2: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Main_Oall__not__in__conv__1_decl,type,
c_Main_Oall__not__in__conv__1: $i > $i > $i ).
thf(c_Main_OIdE__1_decl,type,
c_Main_OIdE__1: $i > $i > $i ).
thf(c_Main_ODomainE__1_decl,type,
c_Main_ODomainE__1: $i > $i > $i > $i > $i ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( A @ c_in ) ) )
| ~ ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Otrans ) )
| ~ ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Opset ) ) @ c_Relation_Orefl ) ) )
| ~ ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Oantisym ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_3) ).
thf(172,plain,
! [B: $i,A: $i] :
( ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( A @ c_in ) ) )
| ~ ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Otrans ) )
| ~ ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Opset ) ) @ c_Relation_Orefl ) ) )
| ~ ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Oantisym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(173,plain,
! [B: $i,A: $i] :
( ( tc_Product__Type_Ounit @ ( B @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( A @ c_in ) ) )
| ~ ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Otrans ) )
| ~ ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Opset ) ) @ c_Relation_Orefl ) ) )
| ~ ( B @ ( tc_Product__Type_Ounit @ ( B @ ( A @ c_Tarski_Opotype_Oorder ) ) @ c_Relation_Oantisym ) ) ),
inference(cnf,[status(esa)],[172]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ ( A @ ( c_Relation_OId @ c_Relation_Oconverse ) ) )
= c_Relation_OId ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__Id_0) ).
thf(336,plain,
! [A: $i] :
( ( A @ ( A @ ( c_Relation_OId @ c_Relation_Oconverse ) ) )
= c_Relation_OId ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(141,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_1) ).
thf(479,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( 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)],[141]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( c_emptyset @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__inject__dest_0) ).
thf(347,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)],[82]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).
thf(333,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( C @ ( A @ c_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(136,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( E @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( F @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_1) ).
thf(468,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( E @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( F @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(142,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( B @ ( A @ c_Main_OIdE__1 ) @ ( B @ ( A @ c_Main_OIdE__1 ) @ c_Pair ) ) ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).
thf(481,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( B @ ( A @ c_Main_OIdE__1 ) @ ( B @ ( A @ c_Main_OIdE__1 ) @ c_Pair ) ) ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(84,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Relation_Odiag ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Odiag__empty_0) ).
thf(352,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Relation_Odiag ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(161,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_0) ).
thf(523,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)],[161]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).
thf(217,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)],[23]) ).
thf(66,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_0) ).
thf(308,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)],[66]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_Relation_ORange ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__empty_0) ).
thf(246,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_Relation_ORange ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(247,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_Relation_ORange ) ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[246]) ).
thf(16,axiom,
! [A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ( A @ tc_set @ class_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_3) ).
thf(202,plain,
! [A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite )
| ( A @ tc_set @ class_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_1) ).
thf(408,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(3,negated_conjecture,
~ ( t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_c @ ( v_a @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(170,plain,
~ ( t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_c @ ( v_a @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(99,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( C @ ( C @ tc_prod ) @ ( F @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_0) ).
thf(384,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( C @ ( C @ tc_prod ) @ ( F @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(166,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
thf(533,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)],[166]) ).
thf(150,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_snd ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Osnd__conv_0) ).
thf(500,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_snd ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(138,axiom,
! [B: $i,A: $i] :
( ( A = c_emptyset )
| ( B @ ( A @ ( B @ ( A @ c_Main_Oall__not__in__conv__1 ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).
thf(472,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)],[138]) ).
thf(5,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
| ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_0) ).
thf(174,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
| ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).
thf(185,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)],[9]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
thf(320,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(101,axiom,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Olistset ) )
= ( A @ tc_List_Olist @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__1_0) ).
thf(389,plain,
! [A: $i] :
( ( A @ ( c_List_Olist_ONil @ c_List_Olistset ) )
= ( A @ tc_List_Olist @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(93,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olenlex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).
thf(372,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olenlex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(152,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_Main_Otrans__def__3 ) @ ( B @ ( A @ c_Main_Otrans__def__2 ) @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Otrans__def_2) ).
thf(504,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_Main_Otrans__def__3 ) @ ( B @ ( A @ c_Main_Otrans__def__2 ) @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
thf(357,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( B @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( D @ c_List_Olists ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).
thf(196,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)],[13]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
thf(460,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(105,axiom,
tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( v_cl @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Ocl_A_58_APartialOrder_0) ).
thf(396,plain,
tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( v_cl @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(171,plain,
~ ( t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_c @ ( v_a @ c_Pair ) ) ) @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[170]) ).
thf(557,plain,
( ( ( t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_c @ ( v_a @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( v_cl @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[396,171]) ).
thf(558,plain,
( ( t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_c @ ( v_a @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( v_cl @ c_in ) ) ) ),
inference(simp,[status(thm)],[557]) ).
thf(559,plain,
( ( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) )
!= ( t_a @ ( t_a @ tc_prod ) ) )
| ( c_Tarski_OPartialOrder != v_r )
| ( ( t_a @ ( t_a @ ( v_c @ ( v_a @ c_Pair ) ) ) )
!= v_cl ) ),
inference(simp,[status(thm)],[558]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).
thf(284,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(115,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
thf(416,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)],[115]) ).
thf(57,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_1) ).
thf(289,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)],[57]) ).
thf(44,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( E @ tc_prod ) @ ( A @ ( C @ ( E @ ( B @ ( D @ c_List_Ozip ) ) ) @ c_List_Onth ) ) )
= ( C @ ( E @ ( C @ ( A @ ( B @ c_List_Onth ) ) @ ( E @ ( A @ ( D @ c_List_Onth ) ) @ c_Pair ) ) ) ) )
| ~ ( tc_nat @ ( E @ tc_List_Olist @ ( D @ c_Nat_Osize ) @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__zip_0) ).
thf(261,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( E @ tc_prod ) @ ( A @ ( C @ ( E @ ( B @ ( D @ c_List_Ozip ) ) ) @ c_List_Onth ) ) )
= ( C @ ( E @ ( C @ ( A @ ( B @ c_List_Onth ) ) @ ( E @ ( A @ ( D @ c_List_Onth ) ) @ c_Pair ) ) ) ) )
| ~ ( tc_nat @ ( E @ tc_List_Olist @ ( D @ c_Nat_Osize ) @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
thf(215,plain,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(216,plain,
! [B: $i,A: $i] :
( ( B @ ( c_emptyset @ ( A @ c_union ) ) )
= A ),
inference(lifteq,[status(thm)],[215]) ).
thf(139,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( C @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( A @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Otrans__def_0) ).
thf(475,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( C @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( A @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(6,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_0) ).
thf(177,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(178,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[177]) ).
thf(179,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ c_List_Olist_OCons ) ) )
= D ) ),
inference(lifteq,[status(thm)],[178]) ).
thf(95,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Transitive__Closure_Otrancl ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__empty_0) ).
thf(375,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Transitive__Closure_Otrancl ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(376,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Transitive__Closure_Otrancl ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[375]) ).
thf(157,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( E @ c_List_Olist_OCons ) ) @ ( C @ ( A @ ( E @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_3) ).
thf(514,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( E @ c_List_Olist_OCons ) ) @ ( C @ ( A @ ( E @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(353,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Relation_Odiag ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[352]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_union ) ) )
= ( D @ ( D @ ( C @ ( A @ c_union ) ) @ ( B @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).
thf(211,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)],[20]) ).
thf(40,axiom,
tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).
thf(253,plain,
tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Wellfounded__Recursion_Owf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(106,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oequiv__intrel__iff_1) ).
thf(397,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)],[106]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_Oconverse ) ) )
= ( B @ ( A @ c_Relation_Odiag ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__diag_0) ).
thf(280,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)],[53]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_2) ).
thf(221,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ ( c_emptyset @ c_union ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onot__Cons__self_0) ).
thf(243,plain,
! [C: $i,B: $i,A: $i] :
( A
!= ( C @ ( A @ ( B @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( C @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).
thf(527,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( C @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ ( C @ ( A @ ( B @ c_Main_OdiagE__1 ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_Odiag ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(18,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) )
= ( C @ tc_List_Olist @ ( E @ c_Nat_Osize ) ) )
| ( A = D )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_2) ).
thf(206,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) )
= ( C @ tc_List_Olist @ ( E @ c_Nat_Osize ) ) )
| ( A = D )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2_0) ).
thf(248,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(97,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ ( c_Relation_OId @ c_Relation_OImage ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__Id_0) ).
thf(380,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ ( c_Relation_OId @ c_Relation_OImage ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_insert ) ) )
= ( C @ ( B @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).
thf(233,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)],[31]) ).
thf(129,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_0) ).
thf(452,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ tc_prod ) @ ( c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(156,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_1) ).
thf(512,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)],[156]) ).
thf(125,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( B @ ( A @ ( D @ c_in ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( A @ c_Infinite__Set_Oatmost__one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Oatmost__one__unique_0) ).
thf(439,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)],[125]) ).
thf(24,axiom,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).
thf(219,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(220,plain,
! [B: $i,A: $i] :
~ ( B @ tc_set @ ( c_emptyset @ ( A @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[219]) ).
thf(90,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__domain_0) ).
thf(366,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)],[90]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( B @ ( A @ ( c_Relation_OId @ c_Relation_Orel__comp ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OId__O__R_0) ).
thf(302,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( B @ ( A @ ( c_Relation_OId @ c_Relation_Orel__comp ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(1,negated_conjecture,
t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_b @ ( v_a @ c_Pair ) ) ) @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(168,plain,
t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_b @ ( v_a @ c_Pair ) ) ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(537,plain,
( ( ( t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_c @ ( v_a @ c_Pair ) ) ) @ c_in ) ) )
!= ( t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_b @ ( v_a @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[168,171]) ).
thf(538,plain,
( ( t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_c @ ( v_a @ c_Pair ) ) ) @ c_in ) ) )
!= ( t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_b @ ( v_a @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[537]) ).
thf(539,plain,
( ( ( t_a @ ( t_a @ tc_prod ) )
!= ( t_a @ ( t_a @ tc_prod ) ) )
| ( v_r != v_r )
| ( ( t_a @ ( t_a @ ( v_c @ ( v_a @ c_Pair ) ) ) )
!= ( t_a @ ( t_a @ ( v_b @ ( v_a @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[538]) ).
thf(540,plain,
( ( t_a @ ( t_a @ ( v_c @ ( v_a @ c_Pair ) ) ) )
!= ( t_a @ ( t_a @ ( v_b @ ( v_a @ c_Pair ) ) ) ) ),
inference(simp,[status(thm)],[539]) ).
thf(560,plain,
( ( t_a != t_a )
| ( t_a != t_a )
| ( v_c != v_b )
| ( v_a != v_a ) ),
inference(simp,[status(thm)],[540]) ).
thf(561,plain,
v_c != v_b,
inference(simp,[status(thm)],[560]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_ORange ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__diag_0) ).
thf(392,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_ORange ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(119,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( C @ ( C @ tc_prod ) @ ( F @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_0) ).
thf(424,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( C @ ( C @ tc_prod ) @ ( F @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(121,axiom,
( v_A
= ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Opset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
thf(429,plain,
( v_A
= ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Opset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) @ ( B @ ( A @ c_List_Olistrel ) @ c_Relation_OImage ) ) ) )
= ( B @ tc_List_Olist @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil_0) ).
thf(275,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) @ ( B @ ( A @ c_List_Olistrel ) @ c_Relation_OImage ) ) ) )
= ( B @ tc_List_Olist @ ( c_emptyset @ ( c_List_Olist_ONil @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Transitive__Closure_Ortrancl ) )
= c_Relation_OId ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__empty_0) ).
thf(251,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Transitive__Closure_Ortrancl ) )
= c_Relation_OId ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(252,plain,
! [A: $i] :
( ( A @ ( c_emptyset @ c_Transitive__Closure_Ortrancl ) )
= c_Relation_OId ),
inference(lifteq,[status(thm)],[251]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).
thf(361,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
thf(329,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(29,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( C @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_1) ).
thf(229,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( C @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(143,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).
thf(484,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(159,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( F @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( E @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_2) ).
thf(519,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( F @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( E @ ( A @ c_List_Olist_OCons ) ) @ 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)],[159]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).
thf(317,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)],[70]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
thf(403,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( B @ ( C @ c_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(10,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( F @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( E @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ tc_List_Olist @ ( E @ c_Nat_Osize ) )
!= ( C @ tc_List_Olist @ ( F @ c_Nat_Osize ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_4) ).
thf(188,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( F @ ( B @ c_List_Olist_OCons ) ) @ ( C @ ( E @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ tc_List_Olist @ ( E @ c_Nat_Osize ) )
!= ( C @ tc_List_Olist @ ( F @ c_Nat_Osize ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(100,axiom,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
thf(387,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(388,plain,
! [B: $i,A: $i] :
~ ( B @ ( c_emptyset @ ( A @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[387]) ).
thf(2,negated_conjecture,
t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_c @ ( v_b @ c_Pair ) ) ) @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(169,plain,
t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_c @ ( v_b @ c_Pair ) ) ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(117,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).
thf(420,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( c_emptyset @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
thf(256,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)],[42]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_1) ).
thf(488,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( 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)],[145]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).
thf(266,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( C @ ( B @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_plus ) ) @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(87,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(359,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(360,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_less ) ) ),
inference(polarity_switch,[status(thm)],[359]) ).
thf(154,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_0) ).
thf(508,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_less ) ) )
| ~ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_Wellfounded__Relations_Oless__than @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(164,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
thf(530,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)],[164]) ).
thf(578,plain,
! [B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_b @ ( v_a @ c_Pair ) ) ) @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[168,388]) ).
thf(579,plain,
! [B: $i,A: $i] :
( ( t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_b @ ( v_a @ c_Pair ) ) ) @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[578]) ).
thf(583,plain,
! [B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_prod ) )
!= B )
| ( c_emptyset != v_r )
| ( ( t_a @ ( t_a @ ( v_b @ ( v_a @ c_Pair ) ) ) )
!= A ) ),
inference(simp,[status(thm)],[579]) ).
thf(586,plain,
c_emptyset != v_r,
inference(simp,[status(thm)],[583]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_ODomain ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__diag_0) ).
thf(343,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Odiag ) @ c_Relation_ODomain ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oconverse ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__converse_0) ).
thf(237,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)],[33]) ).
thf(61,axiom,
! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
thf(298,plain,
! [B: $i,A: $i] : ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olists ) @ ( c_List_Olist_ONil @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_Main_Otrans__def__2 ) @ ( B @ ( A @ c_Main_Otrans__def__1 ) @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Otrans__def_1) ).
thf(412,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_Main_Otrans__def__2 ) @ ( B @ ( A @ c_Main_Otrans__def__1 ) @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(430,plain,
( ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Opset ) ) )
= v_A ),
inference(lifteq,[status(thm)],[429]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__notin__lex_0) ).
thf(264,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(175,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( D @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_List_Olist_OCons ) ) ) )
| ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[174]) ).
thf(176,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( ( D @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_List_Olist_OCons ) ) )
= A ) ),
inference(lifteq,[status(thm)],[175]) ).
thf(566,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_c @ ( v_b @ c_Pair ) ) ) @ c_in ) ) )
!= ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true
| ( ( D @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_List_Olist_OCons ) ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[169,176]) ).
thf(567,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_c @ ( v_b @ c_Pair ) ) ) @ c_in ) ) )
!= ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) )
| ( ( D @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_List_Olist_OCons ) ) )
= A ) ),
inference(simp,[status(thm)],[566]) ).
thf(573,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) )
!= ( t_a @ ( t_a @ tc_prod ) ) )
| ( ( D @ ( E @ c_List_Olistrel ) )
!= v_r )
| ( ( t_a @ ( t_a @ ( v_c @ ( v_b @ c_Pair ) ) ) )
!= ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) ) )
| ( ( D @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__2 ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_List_Olist_OCons ) ) )
= A ) ),
inference(simp,[status(thm)],[567]) ).
thf(7,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_OPartialOrder @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_1) ).
thf(180,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_OPartialOrder @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(60,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( E @ c_List_Olist_OCons ) ) @ ( C @ ( A @ ( E @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_5) ).
thf(296,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( E @ c_List_Olist_OCons ) ) @ ( C @ ( A @ ( E @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(58,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/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oequiv__intrel__iff_0) ).
thf(291,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)],[58]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_union ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
thf(204,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ c_union ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(43,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__range_0) ).
thf(259,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)],[43]) ).
thf(11,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) )
= ( C @ tc_List_Olist @ ( E @ c_Nat_Osize ) ) )
| ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( E @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_3) ).
thf(191,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_List_Olist @ ( B @ c_Nat_Osize ) )
= ( C @ tc_List_Olist @ ( E @ c_Nat_Osize ) ) )
| ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( E @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(108,axiom,
tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Otrans ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__less__than_0) ).
thf(402,plain,
tc_nat @ ( c_Wellfounded__Relations_Oless__than @ c_Relation_Otrans ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(102,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ tc_prod ) @ tc_set @ ( c_IntDef_OInteg @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ ( c_IntDef_Ointrel @ c_Relation_OImage ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ointrel_A_96_96_A_123_Ix1_M_Ay1_J_125_A_58_AInteg_A_61_61_ATrue_0) ).
thf(391,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ tc_prod ) @ tc_set @ ( c_IntDef_OInteg @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( tc_nat @ ( tc_nat @ tc_prod ) @ ( c_emptyset @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_insert ) ) @ ( c_IntDef_Ointrel @ c_Relation_OImage ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(127,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/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_0) ).
thf(445,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)],[127]) ).
thf(98,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Set_Ocontents ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).
thf(382,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ c_Set_Ocontents ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex_0) ).
thf(313,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olex ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(149,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_fst ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Ofst__conv_0) ).
thf(498,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_fst ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(135,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__rtrancl_0) ).
thf(466,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(83,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
thf(350,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(110,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( C @ ( D @ ( B @ ( A @ c_Main_ORangeE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).
thf(406,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( C @ ( D @ ( B @ ( A @ c_Main_ORangeE__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_1) ).
thf(274,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( D @ c_List_Olexord ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( C @ ( B @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).
thf(377,plain,
! [C: $i,B: $i,A: $i] :
( c_emptyset
!= ( C @ ( B @ ( A @ c_insert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(123,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).
thf(434,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__1 ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Main_OconverseE__2 ) ) ) @ c_Pair ) ) ) ) )
| ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__not__empty_0) ).
thf(271,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(140,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_2) ).
thf(477,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_union ) ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Oreflcl__trancl_0) ).
thf(345,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_union ) ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(167,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).
thf(535,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)],[167]) ).
thf(21,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_OPartialOrder @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_2) ).
thf(213,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_OPartialOrder @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).
thf(198,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)],[14]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).
thf(330,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_plus ) ) @ ( tc_nat @ ( A @ ( C @ c_plus ) ) @ c_less ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(133,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( F @ tc_prod ) @ ( C @ ( D @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).
thf(462,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( F @ tc_prod ) @ ( C @ ( D @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(160,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).
thf(521,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)],[160]) ).
thf(52,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_0) ).
thf(278,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)],[52]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( D @ ( A @ c_plus ) ) )
= ( tc_nat @ ( B @ ( C @ c_plus ) ) ) )
| ~ ( 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 ) @ ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_Pair ) ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ointrel__iff_0) ).
thf(455,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( D @ ( A @ c_plus ) ) )
= ( tc_nat @ ( B @ ( C @ c_plus ) ) ) )
| ~ ( 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 ) @ ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_Pair ) ) ) @ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(26,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_1) ).
thf(223,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__2 ) ) ) ) @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(541,plain,
( ( ( t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_c @ ( v_b @ c_Pair ) ) ) @ c_in ) ) )
!= ( t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_c @ ( v_a @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[169,171]) ).
thf(542,plain,
( ( t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_c @ ( v_b @ c_Pair ) ) ) @ c_in ) ) )
!= ( t_a @ ( t_a @ tc_prod ) @ ( v_r @ ( t_a @ ( t_a @ ( v_c @ ( v_a @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[541]) ).
thf(543,plain,
( ( ( t_a @ ( t_a @ tc_prod ) )
!= ( t_a @ ( t_a @ tc_prod ) ) )
| ( v_r != v_r )
| ( ( t_a @ ( t_a @ ( v_c @ ( v_b @ c_Pair ) ) ) )
!= ( t_a @ ( t_a @ ( v_c @ ( v_a @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[542]) ).
thf(544,plain,
( ( t_a @ ( t_a @ ( v_c @ ( v_b @ c_Pair ) ) ) )
!= ( t_a @ ( t_a @ ( v_c @ ( v_a @ c_Pair ) ) ) ) ),
inference(simp,[status(thm)],[543]) ).
thf(562,plain,
( ( t_a != t_a )
| ( t_a != t_a )
| ( v_c != v_c )
| ( v_b != v_a ) ),
inference(simp,[status(thm)],[544]) ).
thf(563,plain,
v_b != v_a,
inference(simp,[status(thm)],[562]) ).
thf(62,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_insert ) ) )
!= ( C @ ( c_emptyset @ ( D @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_0) ).
thf(299,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)],[62]) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_union ) ) )
= A ),
inference(lifteq,[status(thm)],[225]) ).
thf(124,axiom,
( v_r
= ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Oorder ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
thf(437,plain,
( v_r
= ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Oorder ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(438,plain,
( ( tc_Product__Type_Ounit @ ( t_a @ ( v_cl @ c_Tarski_Opotype_Oorder ) ) )
= v_r ),
inference(lifteq,[status(thm)],[437]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( A @ c_Main_Olexord__Nil__left__2 ) @ ( B @ ( A @ c_Main_Olexord__Nil__left__1 ) @ c_List_Olist_OCons ) ) ) )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olexord ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_0) ).
thf(431,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( B @ ( B @ ( A @ c_Main_Olexord__Nil__left__2 ) @ ( B @ ( A @ c_Main_Olexord__Nil__left__1 ) @ c_List_Olist_OCons ) ) ) )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olexord ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( A @ ( c_List_Olist_ONil @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(35,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( E @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( F @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_1) ).
thf(241,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( E @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( F @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( F @ c_List_Olex ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(104,axiom,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).
thf(394,plain,
! [B: $i,A: $i] :
~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_plus ) ) @ c_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(65,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_1) ).
thf(306,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)],[65]) ).
thf(146,axiom,
! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_1) ).
thf(490,plain,
! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(94,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonI_0) ).
thf(374,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( c_emptyset @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(19,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_2) ).
thf(209,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( C @ ( B @ ( A @ ( D @ ( E @ c_Main_Olistrel__Cons1__1 ) ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ tc_prod ) @ ( C @ ( E @ c_List_Olistrel ) @ ( C @ tc_List_Olist @ ( C @ tc_List_Olist @ ( D @ ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(158,axiom,
! [D: $i,C: $i,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 ) @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Pair ) ) ) @ ( tc_nat @ ( tc_nat @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( D @ ( C @ c_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ointrel__iff_1) ).
thf(516,plain,
! [D: $i,C: $i,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 ) @ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Pair ) ) ) @ ( tc_nat @ ( tc_nat @ ( D @ ( A @ c_Pair ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( ( tc_nat @ ( B @ ( A @ c_plus ) ) )
!= ( tc_nat @ ( D @ ( C @ c_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(131,axiom,
! [C: $i,B: $i,A: $i] :
( A
= ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_Osurj__pair__2 ) ) @ ( C @ ( B @ ( A @ c_Main_Osurj__pair__1 ) ) @ c_Pair ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Osurj__pair_0) ).
thf(458,plain,
! [C: $i,B: $i,A: $i] :
( A
= ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_Osurj__pair__2 ) ) @ ( C @ ( B @ ( A @ c_Main_Osurj__pair__1 ) ) @ c_Pair ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( C @ ( B @ ( A @ c_insert ) ) @ c_union ) ) )
= ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_insert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).
thf(194,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)],[12]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
thf(525,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(59,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_Relation_ODomain ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__empty_0) ).
thf(294,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_Relation_ODomain ) ) )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(295,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( c_emptyset @ c_Relation_ODomain ) ) )
= c_emptyset ),
inference(lifteq,[status(thm)],[294]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).
thf(282,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)],[54]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olexord ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__right_0) ).
thf(414,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olexord ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(73,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( c_List_Olist_ONil @ c_List_Ozip ) ) ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Nil_0) ).
thf(327,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( c_List_Olist_ONil @ c_List_Ozip ) ) ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1_0) ).
thf(310,plain,
! [C: $i,B: $i,A: $i] :
( c_List_Olist_ONil
!= ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(151,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).
thf(502,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)],[151]) ).
thf(79,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).
thf(338,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)],[79]) ).
thf(137,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_0) ).
thf(470,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)],[137]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = c_emptyset )
| ( ( C @ ( B @ ( A @ c_union ) ) )
!= c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).
thf(182,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)],[8]) ).
thf(576,plain,
! [B: $i,A: $i] :
( ( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( v_cl @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[396,388]) ).
thf(577,plain,
! [B: $i,A: $i] :
( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) @ ( c_Tarski_OPartialOrder @ ( v_cl @ c_in ) ) )
!= ( B @ ( c_emptyset @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[576]) ).
thf(582,plain,
! [B: $i,A: $i] :
( ( ( tc_Product__Type_Ounit @ ( t_a @ tc_Tarski_Opotype_Opotype__ext__type ) )
!= B )
| ( c_emptyset != c_Tarski_OPartialOrder )
| ( v_cl != A ) ),
inference(simp,[status(thm)],[577]) ).
thf(585,plain,
c_emptyset != c_Tarski_OPartialOrder,
inference(simp,[status(thm)],[582]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Ozip ) ) ) )
= c_List_Olist_ONil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip_Osimps__1_0) ).
thf(370,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( c_List_Olist_ONil @ ( A @ c_List_Ozip ) ) ) )
= c_List_Olist_ONil ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(128,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__not__refl_0) ).
thf(450,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)],[128]) ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( c_emptyset @ ( A @ c_Relation_OImage ) ) ) )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__empty_0) ).
thf(368,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)],[91]) ).
thf(249,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= c_List_Olist_ONil ),
inference(polarity_switch,[status(thm)],[248]) ).
thf(250,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= c_List_Olist_ONil ),
inference(lifteq,[status(thm)],[249]) ).
thf(30,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_OPartialOrder @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OPartialOrder__iff_0) ).
thf(231,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_OPartialOrder @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_union ) ) @ c_Transitive__Closure_Otrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__reflcl_0) ).
thf(304,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_union ) ) @ c_Transitive__Closure_Otrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(116,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Relation_Otrans ) )
| ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_Main_Otrans__def__3 ) @ ( B @ ( A @ c_Main_Otrans__def__1 ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Otrans__def_3) ).
thf(418,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Relation_Otrans ) )
| ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_Main_Otrans__def__3 ) @ ( B @ ( A @ c_Main_Otrans__def__1 ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(155,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Main_ODomainE__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).
thf(510,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Main_ODomainE__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( c_Relation_OId @ ( A @ c_Relation_Orel__comp ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OR__O__Id_0) ).
thf(287,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( c_Relation_OId @ ( A @ c_Relation_Orel__comp ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).
thf(235,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( C @ ( D @ ( A @ c_List_Olist_OCons ) ) @ c_in ) ) )
| ~ ( C @ tc_List_Olist @ ( C @ ( B @ c_List_Olists ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(69,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).
thf(315,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( D @ ( B @ ( A @ ( C @ c_Main_OImageE__1 ) ) ) ) @ c_in ) ) )
| ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(112,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/sandbox2/benchmark/theBenchmark.p',clsarity_prod_0) ).
thf(410,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)],[112]) ).
thf(118,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/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_0) ).
thf(422,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)],[118]) ).
thf(272,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_emptyset ),
inference(polarity_switch,[status(thm)],[271]) ).
thf(273,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_insert ) ) )
!= c_emptyset ),
inference(lifteq,[status(thm)],[272]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp_0) ).
thf(239,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(107,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_union ) ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__reflcl_0) ).
thf(400,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ tc_prod ) @ ( c_Relation_OId @ ( A @ c_union ) ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
thf(532,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(153,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/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
thf(506,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)],[153]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).
thf(268,plain,
! [C: $i,B: $i,A: $i] :
( ( A = c_List_Olist_ONil )
| ~ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ tc_prod ) @ ( B @ ( C @ c_List_Olistrel ) @ ( B @ tc_List_Olist @ ( B @ tc_List_Olist @ ( c_List_Olist_ONil @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(134,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).
thf(464,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__2 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(76,axiom,
tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
thf(332,plain,
tc_Product__Type_Ounit @ class_Finite__Set_Ofinite,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_2) ).
thf(427,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_insert ) ) @ c_Wellfounded__Recursion_Oacyclic ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(15,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( B @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_2) ).
thf(200,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( B @ ( D @ ( C @ ( B @ ( A @ ( E @ c_Main_Olistrel__Cons2__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ tc_prod ) @ ( D @ ( E @ c_List_Olistrel ) @ ( D @ tc_List_Olist @ ( D @ tc_List_Olist @ ( D @ ( C @ ( B @ c_List_Olist_OCons ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(51,axiom,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
thf(277,plain,
! [A: $i] : ( A @ ( c_emptyset @ c_Wellfounded__Recursion_Owf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(126,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).
thf(442,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( E @ ( F @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__3 ) ) ) ) ) @ ( F @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Main_Orel__compE__1 ) ) ) ) ) @ c_Pair ) ) ) ) )
| ~ ( E @ ( F @ tc_prod ) @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(72,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( ( C @ ( B @ ( A @ c_List_Olist_OCons ) ) )
!= ( C @ ( E @ ( D @ c_List_Olist_OCons ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).
thf(322,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)],[72]) ).
thf(144,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/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Cons__Cons_0) ).
thf(486,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)],[144]) ).
thf(337,plain,
! [A: $i] :
( ( A @ ( A @ ( c_Relation_OId @ c_Relation_Oconverse ) ) )
= c_Relation_OId ),
inference(lifteq,[status(thm)],[336]) ).
thf(85,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = A )
| ( ( B @ ( c_emptyset @ ( A @ c_insert ) ) )
!= ( B @ ( D @ ( C @ c_insert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_0) ).
thf(354,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)],[85]) ).
thf(147,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/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_1) ).
thf(491,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)],[147]) ).
thf(148,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/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
thf(496,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)],[148]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ ( B @ ( A @ c_snd ) ) @ ( C @ ( B @ ( A @ c_fst ) ) @ c_Pair ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Opair__collapse_0) ).
thf(364,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ ( B @ ( A @ c_snd ) ) @ ( C @ ( B @ ( A @ c_fst ) ) @ c_Pair ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp__self__comp_0) ).
thf(254,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
thf(227,plain,
! [B: $i,A: $i] :
( ( B @ tc_List_Olist @ ( B @ ( A @ c_List_Olex ) @ c_Wellfounded__Recursion_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded__Recursion_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(2795,plain,
$false,
inference(e,[status(thm)],[173,336,479,347,333,468,481,352,523,217,308,247,202,408,170,384,533,500,472,174,185,320,389,372,504,357,196,460,559,284,416,289,261,216,475,179,376,514,353,211,253,397,280,221,396,243,527,206,248,380,233,452,512,439,220,366,302,561,392,424,429,275,252,361,329,229,484,519,317,403,188,388,169,420,256,488,225,266,360,508,530,586,343,237,298,412,430,264,573,375,180,296,176,291,204,259,191,402,391,445,382,313,498,466,350,540,406,172,219,274,377,434,271,477,387,345,535,213,251,198,330,462,521,278,455,223,563,299,226,438,431,241,394,306,490,374,209,516,458,194,525,295,282,414,327,310,502,338,470,359,544,177,182,585,370,450,368,250,231,304,171,418,510,287,235,246,315,410,168,422,273,239,294,437,400,532,506,268,464,332,427,200,277,442,322,486,337,354,215,491,496,364,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT281-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40 % Computer : n001.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 25 20:29:56 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.31/1.25 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.04/1.86 % [INFO] Parsing done (614ms).
% 3.04/1.88 % [INFO] Running in sequential loop mode.
% 3.83/2.25 % [INFO] eprover registered as external prover.
% 3.83/2.26 % [INFO] Scanning for conjecture ...
% 4.77/2.54 % [INFO] Found a conjecture (or negated_conjecture) and 2747 axioms. Running axiom selection ...
% 5.68/2.77 % [INFO] Axiom selection finished. Selected 164 axioms (removed 2583 axioms).
% 6.28/2.90 % [INFO] Problem is propositional (TPTP CNF).
% 6.28/2.92 % [INFO] Type checking passed.
% 6.28/2.92 % [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 ...
% 32.61/7.86 % External prover 'e' found a proof!
% 32.61/7.86 % [INFO] Killing All external provers ...
% 32.61/7.86 % Time passed: 7264ms (effective reasoning time: 5970ms)
% 32.61/7.86 % Axioms used in derivation (164): cls_List_Olistrel__Cons1_0, cls_Relation_Otrans__def_3, cls_Relation_ODomain__empty_0, cls_Transitive__Closure_Otrancl__range_0, cls_Nat_Onat__add__left__cancel__less_1, cls_Set_Osingleton__insert__inj__eq_0, cls_List_Olists_ONil_0, cls_List_Onth__zip_0, cls_Relation_OImageI_0, cls_List_Olistrel__Cons2_1, cls_Relation_ODomain__diag_0, cls_List_OCons__in__lex_1, cls_Relation_ORange__diag_0, cls_List_Olexord__cons__cons_2, cls_Nat_Onat__add__right__cancel_0, clsarity_prod_0, cls_Wellfounded__Recursion_Owf__insert_0, cls_Product__Type_Ofst__conv_0, cls_IntDef_Ointrel_A_96_96_A_123_Ix1_M_Ay1_J_125_A_58_AInteg_A_61_61_ATrue_0, cls_Transitive__Closure_Otrancl_Or__into__trancl_0, cls_Set_Osingleton__inject__dest_0, cls_Relation_OImageE_0, cls_Transitive__Closure_Ortrancl__reflcl_0, cls_List_Olexord__Nil__left_0, cls_Wellfounded__Relations_Owf__lex__prod_0, cls_Nat_Oless__irrefl_0, cls_List_Olistrel__Nil1_0, cls_Transitive__Closure_Ortrancl__idemp_0, cls_List_Olist_Oinject_1, cls_Relation_Oconverse__converse_0, cls_Relation_OconverseE_1, cls_Set_Osingleton__insert__inj__eq_H_0, cls_Product__Type_Osurj__pair_0, cls_Relation_Orel__compE_0, cls_Relation_Opair__in__Id__conv_0, cls_Relation_ORangeE_0, cls_List_OCons__in__lex_0, cls_Nat_Onat__add__left__cancel__less_0, cls_List_OCons__in__lex_5, cls_Wellfounded__Recursion_Oacyclic__converse_1, cls_Relation_OdiagI_0, cls_IntDef_Ointrel__iff_1, cls_Transitive__Closure_Ortrancl__empty_0, cls_List_OlistsE_0, cls_Tarski_OPartialOrder__iff_0, cls_List_Olistrel__Cons2_0, cls_Relation_ODomainI_0, cls_List_Olexord__cons__cons_1, cls_Tarski_OA_A_61_61_Apset_Acl_0, cls_Set_OUn__iff_0, cls_List_Owf__lex_0, cls_Set_OUn__empty_1, cls_Relation_OImage__Id_0, cls_Wellfounded__Recursion_Oacyclic__insert_1, cls_Relation_Orel__compE_2, cls_Set_Oinsert__iff_2, cls_List_ONil2__notin__lex_0, cls_Relation_OImageE_1, cls_Relation_OdiagE_0, cls_Set_OsingletonD__dest_0, clsarity_set_3, cls_Relation_OImage__singleton__iff_1, cls_Set_Oinsert__not__empty_0, cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0, cls_Transitive__Closure_Otrancl__empty_0, cls_List_OCons__in__lex_4, cls_Relation_Oconverse__iff_1, cls_List_ONil__notin__lex_0, cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0, cls_List_Olist_Oinject_0, cls_Set_Oempty__iff_0, cls_Wellfounded__Recursion_Owf__not__refl_0, cls_Tarski_Ocl_A_58_APartialOrder_0, cls_Set_OsingletonI_0, cls_Relation_ORange__empty_0, cls_List_Ozip_Osimps__1_0, cls_Relation_OImage__empty_0, cls_Relation_OconverseE_0, cls_Set_Oall__not__in__conv_0, cls_Set_Oinsert__iff_1, cls_Relation_Oconverse__diag_0, cls_Relation_ORangeI_0, cls_Relation_OId__O__R_0, cls_Infinite__Set_Oatmost__one__unique_0, cls_Relation_Opair__in__Id__conv_1, cls_Wellfounded__Relations_Otrans__less__than_0, cls_IntDef_Ointrel__iff_0, cls_Tarski_Or_A_61_61_Aorder_Acl_0, cls_Set_OUn__insert__left_0, cls_Wellfounded__Recursion_Oacyclic__converse_0, cls_Wellfounded__Recursion_Owf__insert_2, cls_Set_OUn__insert__right_0, cls_Nat_Onot__add__less1_0, cls_Relation_OR__O__Id_0, cls_List_Olist_Odistinct__2_0, cls_List_Olistrel__Nil_0, cls_IntDef_Oequiv__intrel__iff_0, cls_Product__Type_OPair__eq_1, cls_Wellfounded__Recursion_Owf__empty_0, cls_Wellfounded__Relations_Owf__less__than_0, cls_Transitive__Closure_Or__into__rtrancl_0, cls_List_OCons__in__lex_3, cls_Relation_Oconverse__iff_0, cls_Tarski_OPartialOrder__iff_2, cls_List_Olistrel__Cons1_2, cls_List_OlistsE_1, cls_Relation_OImage__singleton__iff_0, cls_List_Onot__Cons__self_0, cls_Set_OUn__iff_1, cls_Relation_Otrans__def_0, cls_Wellfounded__Recursion_Oacyclic__insert_2, cls_Tarski_OPartialOrder__iff_1, cls_Relation_Orel__compI_0, cls_List_Olist_Odistinct__1_0, cls_Set_Oempty__not__insert_0, cls_Wellfounded__Relations_Oless__than__iff_1, cls_Nat_Onot__add__less2_0, cls_List_Olistrel__Nil2_0, cls_Transitive__Closure_Otrancl__domain_0, cls_List_Olexord__Nil__right_0, cls_Relation_OdiagE_1, cls_Wellfounded__Relations_Otrans__lex__prod_0, cls_Relation_Odiag__empty_0, cls_Set_OUn__empty__left_0, cls_Set_OUn__empty__right_0, cls_Transitive__Closure_Otrancl__reflcl_0, cls_Wellfounded__Recursion_Owf__insert_1, cls_List_Olistrel__Cons2_2, cls_List_Olistrel__Cons1_1, cls_Set_Ocontents__eq_0, cls_List_Ozip__Nil_0, cls_Relation_ODomainE_0, cls_List_Olexord__cons__cons_3, cls_IntDef_Oequiv__intrel__iff_1, cls_Relation_Otrans__def_2, cls_Nat_Onat__add__left__cancel_0, clsarity_Product____Type__Ounit_0, cls_List_Olistset_Osimps__1_0, cls_Product__Type_OPair__eq_0, cls_List_Olexord__Nil__left_1, cls_Transitive__Closure_Oreflcl__trancl_0, cls_List_Ozip__Cons__Cons_0, cls_List_Olexord__cons__cons_0, cls_List_OCons__in__lex_2, cls_Transitive__Closure_Ortrancl__idemp__self__comp_0, cls_Product__Type_Osnd__conv_0, cls_Relation_Otrans__def_1, cls_Set_OUn__empty_0, cls_Set_Oinsert__absorb2_0, cls_Set_Onot__psubset__empty_0, cls_Set_Oinsert__iff_0, cls_Wellfounded__Recursion_Oacyclic__insert_0, cls_Set_OUn__empty_2, cls_List_Owf__lenlex_0, cls_Relation_OIdE_0, cls_Set_OUn__iff_2, cls_Relation_Orel__compE_1, cls_Product__Type_Opair__collapse_0, cls_Wellfounded__Relations_Oless__than__iff_0, cls_Set_OUn__absorb_0, cls_List_Olists_OCons_0, cls_Tarski_OPartialOrder__iff_3, cls_Transitive__Closure_Otrancl__into__rtrancl_0, cls_Relation_Oconverse__Id_0
% 32.61/7.86 % No. of inferences in proof: 384
% 32.61/7.86 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7264 ms resp. 5970 ms w/o parsing
% 29.32/8.01 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 29.32/8.02 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------