TSTP Solution File: SCT061-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT061-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:50:19 EDT 2023
% Result : Unsatisfiable 11.03s 3.41s
% Output : Refutation 12.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 734
% Syntax : Number of formulae : 1346 ( 327 unt; 123 typ; 0 def)
% Number of atoms : 2844 ( 597 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 23943 (1408 ~;1621 |; 0 &;20914 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 314 ( 314 >; 0 *; 0 +; 0 <<)
% Number of symbols : 125 ( 123 usr; 14 con; 0-7 aty)
% Number of variables : 4310 ( 0 ^;4310 !; 0 ?;4310 :)
% Comments :
%------------------------------------------------------------------------------
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thf(124,axiom,
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( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ D ) @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseD_0) ).
thf(892,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ D ) @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(371,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_5) ).
thf(1411,plain,
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( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(531,axiom,
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( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ( B = A )
| ~ ( c_in @ A @ E @ C )
| ~ ( c_in @ B @ E @ C )
| ~ ( c_Relation_Ototal__on @ E @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_0) ).
thf(1767,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ( B = A )
| ~ ( c_in @ A @ E @ C )
| ~ ( c_in @ B @ E @ C )
| ~ ( c_Relation_Ototal__on @ E @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(104,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(846,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(596,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Oantisym @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__def_0) ).
thf(1899,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Oantisym @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(565,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ A @ C @ C @ C ) @ ( c_Relation_Orel__comp @ B @ A @ C @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_1) ).
thf(1840,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ A @ C @ C @ C ) @ ( c_Relation_Orel__comp @ B @ A @ C @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(73,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__right_0) ).
thf(777,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(449,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_1) ).
thf(1586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(411,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).
thf(1501,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(586,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ E @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ A @ B @ D @ E ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ D @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ A @ B @ D @ E ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ E @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ D @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_Arrow__Order__Mirabelle_OIIA @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_1) ).
thf(1879,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ E @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ A @ B @ D @ E ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ D @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ A @ B @ D @ E ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ E @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ D @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_Arrow__Order__Mirabelle_OIIA @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(335,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ D ) @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseI_0) ).
thf(1337,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ D ) @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(185,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(1024,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(397,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ E @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Orefl__on @ B @ E @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD1_0) ).
thf(1469,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ E @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Orefl__on @ B @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(252,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( A = D )
| ~ ( c_lessequals @ E @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Sigma__aux_0) ).
thf(1168,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( A = D )
| ~ ( c_lessequals @ E @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(66,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).
thf(760,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Relation_OId @ B ) @ C @ B @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_R__O__Id_0) ).
thf(628,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Relation_OId @ B ) @ C @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(188,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) )
| ~ ( c_Wellfounded_Owf @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_0) ).
thf(1031,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) )
| ~ ( c_Wellfounded_Owf @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(324,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
| ~ ( c_Wellfounded_Oacyclic @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_1) ).
thf(1315,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
| ~ ( c_Wellfounded_Oacyclic @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(570,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ B @ A @ C @ D ) @ D @ D ) @ B @ ( tc_prod @ D @ D ) )
| ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_0) ).
thf(1850,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ B @ A @ C @ D ) @ D @ D ) @ B @ ( tc_prod @ D @ D ) )
| ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(213,axiom,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(1083,plain,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(156,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainI_0) ).
thf(962,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(555,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ C @ D ) ) )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_2) ).
thf(1818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ C @ D ) ) )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(315,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_5) ).
thf(1295,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(435,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(1554,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(225,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ~ ( c_in @ ( c_Pair @ F @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__cut__apply_0) ).
thf(1110,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ~ ( c_in @ ( c_Pair @ F @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(266,axiom,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(1200,plain,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(272,axiom,
( ( c_Relation_ORange @ v_r @ t_a @ t_b )
= ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ t_a @ t_b ) @ v_r ) @ t_b @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__def__raw_0) ).
thf(1211,plain,
( ( c_Relation_ORange @ v_r @ t_a @ t_b )
= ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ t_a @ t_b ) @ v_r ) @ t_b @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(762,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(453,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ A @ B @ C @ D @ E ) @ A @ D )
| ~ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_0) ).
thf(1596,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ A @ B @ C @ D @ E ) @ A @ D )
| ~ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).
thf(683,plain,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(311,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Product__Type_OSigma @ ( c_Relation_OField @ A @ B ) @ ( c_COMBK @ ( c_Relation_OField @ A @ B ) @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Field2_0) ).
thf(1290,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Product__Type_OSigma @ ( c_Relation_OField @ A @ B ) @ ( c_COMBK @ ( c_Relation_OField @ A @ B ) @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(464,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) @ ( tc_prod @ B @ B ) )
| ~ ( c_Wellfounded_Oacyclic @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__def_0) ).
thf(1618,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) @ ( tc_prod @ B @ B ) )
| ~ ( c_Wellfounded_Oacyclic @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(442,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= B )
| ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(1569,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= B )
| ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(208,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) ) @ A @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__empty_0) ).
thf(1073,plain,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) ) @ A @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(513,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ C @ B ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ C @ B ) @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) @ ( tc_prod @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__trancl__rD_0) ).
thf(1728,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ C @ B ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ C @ B ) @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) @ ( tc_prod @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(542,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(1793,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(382,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
thf(1437,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(193,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ B @ A @ C ) @ A @ C @ C ) @ B @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_0) ).
thf(1041,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ B @ A @ C ) @ A @ C @ C ) @ B @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(254,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__Int__distrib1_0) ).
thf(1173,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(524,axiom,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ A )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ A ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_4) ).
thf(1750,plain,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ A )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ A ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(163,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(977,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(607,axiom,
! [A: $i] : ( c_Wellfounded_Owf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__empty_0) ).
thf(1924,plain,
! [A: $i] : ( c_Wellfounded_Owf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(176,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(1005,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(385,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ C ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ D @ ( v_sko__local__X3__1 @ C @ D @ A @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ ( v_sko__local__X3__1 @ C @ D @ A @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ D @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_3_1) ).
thf(1443,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ C ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ D @ ( v_sko__local__X3__1 @ C @ D @ A @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ ( v_sko__local__X3__1 @ C @ D @ A @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ D @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(551,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
| ~ ( c_in @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(1808,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
| ~ ( c_in @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(116,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Osym @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__def_0) ).
thf(873,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Osym @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(269,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(1205,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(3,negated_conjecture,
! [A: $i] :
( ( c_in @ ( c_Pair @ v_b____ @ v_a____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( c_Fun_Ocomp @ ( c_Relation_Oconverse @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(614,plain,
! [A: $i] :
( ( c_in @ ( c_Pair @ v_b____ @ v_a____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( c_Fun_Ocomp @ ( c_Relation_Oconverse @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(496,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Relation_Oinv__image @ B @ C @ D @ A ) )
= ( c_Relation_Oinv__image @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ B ) @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__inv__image_0) ).
thf(1692,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Relation_Oinv__image @ B @ C @ D @ A ) )
= ( c_Relation_Oinv__image @ ( hAPP @ ( c_Relation_Oconverse @ D @ D ) @ B ) @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
thf(677,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(409,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ ( c_Relation_Orel__comp @ C @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_0) ).
thf(1497,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ ( c_Relation_Orel__comp @ C @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(459,axiom,
c_in @ ( c_Fun_Ocomp @ ( c_Relation_Oconverse @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cP_0) ).
thf(1608,plain,
c_in @ ( c_Fun_Ocomp @ ( c_Relation_Oconverse @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(480,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_2) ).
thf(1655,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(238,axiom,
class_Lattices_Odistrib__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(1137,plain,
class_Lattices_Odistrib__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(83,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(797,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(582,axiom,
! [A: $i] : ( c_Relation_Oantisym @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__empty_0) ).
thf(1872,plain,
! [A: $i] : ( c_Relation_Oantisym @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(91,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(814,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(296,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Relation_ODomain @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__empty__iff_0) ).
thf(1260,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Relation_ODomain @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(605,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ B @ E @ C )
| ~ ( c_lessequals @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__equiv__class_0) ).
thf(1919,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ B @ E @ C )
| ~ ( c_lessequals @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(148,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_1) ).
thf(945,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(392,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ C @ D ) @ ( c_Wellfounded_Oacc @ C @ D ) @ D )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_0) ).
thf(1458,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ C @ D ) @ ( c_Wellfounded_Oacc @ C @ D ) @ D )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
thf(670,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(747,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(133,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ A @ C @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ B @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_3) ).
thf(913,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ A @ C @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ B @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(278,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Wellfounded_Oacyclic @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__subset_0) ).
thf(1222,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Wellfounded_Oacyclic @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(141,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_in @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(930,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_in @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(264,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(1196,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(522,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(1746,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(233,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ B @ D @ C ) @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ E @ B @ C )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_1) ).
thf(1127,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ B @ D @ C ) @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ E @ B @ C )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(361,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ A @ B @ C )
= ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ B @ C ) @ A ) @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__def_0) ).
thf(1391,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ A @ B @ C )
= ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ B @ C ) @ A ) @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(346,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(1359,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(455,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_1) ).
thf(1601,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(349,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) )
| ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ A @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_1) ).
thf(1366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) )
| ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ A @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(590,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ A @ B @ C @ D @ E ) @ A @ D )
| ~ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_1) ).
thf(1887,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ A @ B @ C @ D @ E ) @ A @ D )
| ~ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(651,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(75,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(782,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(384,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Wellfounded_Owf @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Int1_0) ).
thf(1441,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Wellfounded_Owf @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(161,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_OImage @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_Equiv__Relations_Oequiv @ D @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__self_0) ).
thf(973,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_OImage @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_Equiv__Relations_Oequiv @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(121,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortrancl__def_0) ).
thf(885,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(478,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ A @ C @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_2) ).
thf(1650,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ A @ C @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(606,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ C ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ F ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ ( v_sko__local__X2__1 @ F @ C @ D @ A @ E @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ F @ ( v_sko__local__X2__1 @ F @ C @ D @ A @ E @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ F @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( E = A )
| ( D = B )
| ( A = B )
| ( D = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_2_2) ).
thf(1921,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ C ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ F ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ ( v_sko__local__X2__1 @ F @ C @ D @ A @ E @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ F @ ( v_sko__local__X2__1 @ F @ C @ D @ A @ E @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ F @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( E = A )
| ( D = B )
| ( A = B )
| ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(598,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_FuncSet_OPi @ B @ C @ D @ E ) @ ( tc_fun @ D @ E ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ B @ C @ A @ D @ E ) @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__I_H_0) ).
thf(1904,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_FuncSet_OPi @ B @ C @ D @ E ) @ ( tc_fun @ D @ E ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ B @ C @ A @ D @ E ) @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(418,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ D @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1 @ A @ B @ D ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ D @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_Arrow__Order__Mirabelle_Ounanimity @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_unanimity__def_0) ).
thf(1518,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ D @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1 @ A @ B @ D ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ D @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_Arrow__Order__Mirabelle_Ounanimity @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(298,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(1265,plain,
class_Orderings_Opreorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(466,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(1623,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(402,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
thf(1482,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(370,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__trancl_0) ).
thf(1409,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(379,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(1430,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(316,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(1298,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId @ A ) @ B @ A @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id_0) ).
thf(719,plain,
! [B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId @ A ) @ B @ A @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(76,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
thf(785,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(331,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
| ~ ( c_Relation_Osym @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_1) ).
thf(1330,plain,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
| ~ ( c_Relation_Osym @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(328,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(1323,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(558,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ B @ A @ C @ D ) @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ B @ D ) @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_0) ).
thf(1826,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ B @ A @ C @ D ) @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ B @ D ) @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(323,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ A @ C @ D ) @ ( c_Relation_ORange @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Un__eq_0) ).
thf(1313,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ A @ C @ D ) @ ( c_Relation_ORange @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(415,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_2) ).
thf(1511,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(135,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(917,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(445,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ C ) ) )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ t_a ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_2) ).
thf(1577,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ C ) ) )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ t_a ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(390,axiom,
! [B: $i,A: $i] : ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Int__converse_0) ).
thf(1455,plain,
! [B: $i,A: $i] : ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(561,axiom,
! [B: $i,A: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ A )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ A ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ A ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ A ) @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ A ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ A ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ A ) @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_7) ).
thf(1832,plain,
! [B: $i,A: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ A )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ A ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ A ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ A ) @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ A ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ A ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ A ) @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(143,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Product__Type_OSigma @ E @ F @ C @ D ) @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ B @ ( hAPP @ F @ A ) @ D )
| ~ ( c_in @ A @ E @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaI_0) ).
thf(934,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Product__Type_OSigma @ E @ F @ C @ D ) @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ B @ ( hAPP @ F @ A ) @ D )
| ~ ( c_in @ A @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(431,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(1545,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(547,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ ( hAPP @ C @ B ) @ D )
| ~ ( c_in @ B @ E @ F )
| ~ ( c_in @ A @ ( c_FuncSet_OPi @ E @ C @ F @ D ) @ ( tc_fun @ F @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__mem_0) ).
thf(1800,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ ( hAPP @ C @ B ) @ D )
| ~ ( c_in @ B @ E @ F )
| ~ ( c_in @ A @ ( c_FuncSet_OPi @ E @ C @ F @ D ) @ ( tc_fun @ F @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(592,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(1892,plain,
class_Orderings_Oorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(244,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_Orel__comp @ A @ B @ C @ C @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ A @ D @ C @ C @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C @ C @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_union__comp__emptyR_0) ).
thf(1147,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_Orel__comp @ A @ B @ C @ C @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ A @ D @ C @ C @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C @ C @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(289,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ A @ B @ C ) @ A @ C )
| ~ ( c_in @ D @ A @ C )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_0) ).
thf(1247,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ A @ B @ C ) @ A @ C )
| ~ ( c_in @ D @ A @ C )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(227,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Relation_Orefl__on @ B @ E @ C )
| ~ ( c_Relation_Orefl__on @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Int_0) ).
thf(1115,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Relation_Orefl__on @ B @ E @ C )
| ~ ( c_Relation_Orefl__on @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(611,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Wellfounded_Oacc @ A @ B ) @ ( c_Wellfounded_Oacc @ C @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__subset_0) ).
thf(1931,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Wellfounded_Oacc @ A @ B ) @ ( c_Wellfounded_Oacc @ C @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(474,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Oantisym @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisymD_0) ).
thf(1641,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Oantisym @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(554,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ C @ B @ D @ E ) @ F @ ( tc_prod @ D @ E ) )
| ~ ( c_in @ ( c_Pair @ C @ A @ D @ E ) @ F @ ( tc_prod @ D @ E ) )
| ~ ( c_Relation_Osingle__valued @ F @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valuedD_0) ).
thf(1815,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ C @ B @ D @ E ) @ F @ ( tc_prod @ D @ E ) )
| ~ ( c_in @ ( c_Pair @ C @ A @ D @ E ) @ F @ ( tc_prod @ D @ E ) )
| ~ ( c_Relation_Osingle__valued @ F @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(347,axiom,
( ( c_Relation_OField @ v_r @ t_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ v_r @ t_a @ t_a ) @ ( c_Relation_ORange @ v_r @ t_a @ t_a ) @ ( tc_fun @ t_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__def__raw_0) ).
thf(1362,plain,
( ( c_Relation_OField @ v_r @ t_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ v_r @ t_a @ t_a ) @ ( c_Relation_ORange @ v_r @ t_a @ t_a ) @ ( tc_fun @ t_a @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(283,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Int2_0) ).
thf(1232,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(568,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ C ) @ B )
| ~ ( c_Relation_Orefl__on @ A @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).
thf(1847,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ C ) @ B )
| ~ ( c_Relation_Orefl__on @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(638,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(107,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
thf(853,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(215,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_Orel__comp @ A @ B @ C @ C @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ D @ B @ C @ C @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ B @ C @ C @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_union__comp__emptyL_0) ).
thf(1087,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_Orel__comp @ A @ B @ C @ C @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ D @ B @ C @ C @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) )
| ( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ B @ C @ C @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(416,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__Un__distrib1_0) ).
thf(1514,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(326,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ D @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ A @ B @ E @ D ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ E @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ A @ B @ E @ D ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ D @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ E @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_Arrow__Order__Mirabelle_OIIA @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_2) ).
thf(1319,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ D @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ A @ B @ E @ D ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ E @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ A @ B @ E @ D ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ D @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ E @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_Arrow__Order__Mirabelle_OIIA @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(502,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__rtrancl_0) ).
thf(1704,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(115,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
!= ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(870,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
!= ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(401,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ C ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ F ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ F @ ( v_sko__local__X2__1 @ C @ F @ A @ D @ B @ E ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ ( v_sko__local__X2__1 @ C @ F @ A @ D @ B @ E ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ F @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( B = D )
| ( A = E )
| ( D = E )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_2_3) ).
thf(1479,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ C ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ F ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ F @ ( v_sko__local__X2__1 @ C @ F @ A @ D @ B @ E ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ ( v_sko__local__X2__1 @ C @ F @ A @ D @ B @ E ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ F @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( B = D )
| ( A = E )
| ( D = E )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(460,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ A @ D ) @ ( tc_prod @ D @ D ) )
| ( B = C )
| ~ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclE_1) ).
thf(1609,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ A @ D ) @ ( tc_prod @ D @ D ) )
| ( B = C )
| ~ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ A @ B ) @ ( c_Wellfounded_Oacc @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acc__iff_1) ).
thf(969,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ A @ B ) @ ( c_Wellfounded_Oacc @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(340,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ E )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ A @ D @ C @ E ) @ ( c_Product__Type_OSigma @ B @ D @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Int__distrib1_0) ).
thf(1347,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ E )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ A @ D @ C @ E ) @ ( c_Product__Type_OSigma @ B @ D @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(443,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ A @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) @ C ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__empty2_0) ).
thf(1572,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ A @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) @ C ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(180,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
thf(1013,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(70,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ F @ C @ E @ G )
= ( c_Relation_Orel__comp @ A @ ( c_Relation_Orel__comp @ B @ F @ D @ E @ G ) @ C @ D @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_O__assoc_0) ).
thf(770,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ F @ C @ E @ G )
= ( c_Relation_Orel__comp @ A @ ( c_Relation_Orel__comp @ B @ F @ D @ E @ G ) @ C @ D @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(584,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(1875,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(536,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__subset_0) ).
thf(1778,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(138,axiom,
c_in @ v_P_H____ @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_A_I5_J_0) ).
thf(924,plain,
c_in @ v_P_H____ @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(395,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C ) @ ( c_Product__Type_OSigma @ E @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ E @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ F @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_1) ).
thf(1465,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C ) @ ( c_Product__Type_OSigma @ E @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ E @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ F @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(388,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfD_0) ).
thf(1450,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(352,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__reflcl_0) ).
thf(1373,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(601,axiom,
! [B: $i,A: $i] :
~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(1911,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
thf(623,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(492,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(1682,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(559,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ E @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ A @ E @ C @ D ) @ ( c_Relation_OImage @ B @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Image_0) ).
thf(1828,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ E @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ A @ E @ C @ D ) @ ( c_Relation_OImage @ B @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(145,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
!= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C )
| ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ D @ E @ C )
| ~ ( c_in @ B @ E @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_3) ).
thf(937,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
!= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C )
| ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ D @ E @ C )
| ~ ( c_in @ B @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(357,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Osingle__valued @ D @ C @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__confluent_0) ).
thf(1383,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Osingle__valued @ D @ C @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(490,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
thf(1677,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(87,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(806,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(258,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Product__Type_OSigma @ A @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C )
!= ( c_Product__Type_OSigma @ E @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C ) )
| ~ ( c_in @ F @ B @ C )
| ( A = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__eq__cancel2_0) ).
thf(1183,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Product__Type_OSigma @ A @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C )
!= ( c_Product__Type_OSigma @ E @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C ) )
| ~ ( c_in @ F @ B @ C )
| ( A = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(94,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_0) ).
thf(821,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(318,axiom,
! [B: $i,A: $i] :
( ( c_Arrow__Order__Mirabelle_Ounanimity @ A )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3 @ A ) @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4 @ A ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ A ) @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_unanimity__def_2) ).
thf(1302,plain,
! [B: $i,A: $i] :
( ( c_Arrow__Order__Mirabelle_Ounanimity @ A )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3 @ A ) @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4 @ A ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ A ) @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(484,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).
thf(1664,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(333,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_1) ).
thf(1334,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
thf(646,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(574,axiom,
c_in @ v_P____ @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_A_I4_J_0) ).
thf(1858,plain,
c_in @ v_P____ @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(578,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( c_in @ A @ D @ C )
| ~ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(1864,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( c_in @ A @ D @ C )
| ~ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(165,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_in @ A @ C @ D )
| ~ ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).
thf(981,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_in @ A @ C @ D )
| ~ ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
!= B )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
thf(687,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
!= B )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__comp__rtrancl__eq_0) ).
thf(866,plain,
! [B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(545,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__apply_0) ).
thf(1796,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(229,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_1) ).
thf(1119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(342,axiom,
! [B: $i,A: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ A )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ A ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ A ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ A ) @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ A ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ A ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ A ) @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_6) ).
thf(1351,plain,
! [B: $i,A: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ A )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ A ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ A ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ A ) @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ A ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ A ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ A ) @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
thf(660,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(173,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ ( c_Relation_Orel__comp @ C @ D @ A @ E @ B ) )
= ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ E @ B ) @ D ) @ ( hAPP @ ( c_Relation_Oconverse @ A @ E ) @ C ) @ B @ E @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rel__comp_0) ).
thf(998,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ ( c_Relation_Orel__comp @ C @ D @ A @ E @ B ) )
= ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ E @ B ) @ D ) @ ( hAPP @ ( c_Relation_Oconverse @ A @ E ) @ C ) @ B @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(339,axiom,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ A )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ A ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_5) ).
thf(1345,plain,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ A )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ A ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(380,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__type_0) ).
thf(1433,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(368,axiom,
! [A: $i] :
( ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iff_1) ).
thf(1405,plain,
! [A: $i] :
( ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(267,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(1201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(440,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) )
| ~ ( c_Wellfounded_Owf @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_0) ).
thf(1564,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) )
| ~ ( c_Wellfounded_Owf @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(274,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(1215,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(634,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(594,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ A @ B @ C ) @ A @ C )
| ~ ( c_in @ B @ ( c_Relation_OId__on @ A @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_0) ).
thf(1896,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ A @ B @ C ) @ A @ C )
| ~ ( c_in @ B @ ( c_Relation_OId__on @ A @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(118,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(877,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(36,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
thf(692,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(222,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ E ) @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__iff_1) ).
thf(1104,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ E ) @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(499,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Or__into__trancl_0) ).
thf(1697,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__rtrancl_0) ).
thf(849,plain,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(577,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).
thf(1863,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(457,axiom,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_1) ).
thf(1604,plain,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp__self__comp_0) ).
thf(793,plain,
! [B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(139,axiom,
v_b____ != v_c____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_A_I2_J_0) ).
thf(925,plain,
v_b____ != v_c____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(246,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) @ C @ D )
= ( c_Set_Oinsert @ B @ ( c_Relation_ORange @ E @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__insert_0) ).
thf(1153,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) @ C @ D )
= ( c_Set_Oinsert @ B @ ( c_Relation_ORange @ E @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(538,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B )
!= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B ) )
| ~ ( c_in @ D @ E @ B )
| ~ ( c_in @ A @ E @ B )
| ~ ( c_Equiv__Relations_Oequiv @ E @ C @ B )
| ( c_in @ ( c_Pair @ A @ D @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff2_0) ).
thf(1783,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B )
!= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B ) )
| ~ ( c_in @ D @ E @ B )
| ~ ( c_in @ A @ E @ B )
| ~ ( c_Equiv__Relations_Oequiv @ E @ C @ B )
| ( c_in @ ( c_Pair @ A @ D @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(322,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(1311,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(603,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ( c_in @ D @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(1915,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ( c_in @ D @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(504,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ A @ B @ C ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ C @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_0) ).
thf(1708,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ A @ B @ C ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ C @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(205,axiom,
! [B: $i,A: $i] :
( ( c_Relation_OField @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
= ( c_Relation_OField @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__converse_0) ).
thf(1067,plain,
! [B: $i,A: $i] :
( ( c_Relation_OField @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
= ( c_Relation_OField @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(517,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ D ) @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseD_0) ).
thf(1736,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ D ) @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ORange @ A @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__range_0) ).
thf(714,plain,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ORange @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(580,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) )
| ~ ( c_Wellfounded_Owf @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_0) ).
thf(1868,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) )
| ~ ( c_Wellfounded_Owf @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(196,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
| ~ ( c_Nitpick_Orefl_H @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_0) ).
thf(1047,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
| ~ ( c_Nitpick_Orefl_H @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(514,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ B @ A @ C ) @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_1) ).
thf(1730,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ B @ A @ C ) @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclD_0) ).
thf(1057,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(152,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ A @ B @ C @ D @ E )
!= ( c_Fun_Ocomp @ F @ G @ H @ D @ E ) )
| ( ( hAPP @ A @ ( hAPP @ B @ I ) )
= ( hAPP @ F @ ( hAPP @ G @ I ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).
thf(952,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ A @ B @ C @ D @ E )
!= ( c_Fun_Ocomp @ F @ G @ H @ D @ E ) )
| ( ( hAPP @ A @ ( hAPP @ B @ I ) )
= ( hAPP @ F @ ( hAPP @ G @ I ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(344,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_1) ).
thf(1355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(293,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(1255,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(485,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ B @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Ocases_0) ).
thf(1666,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ B @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).
thf(630,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(286,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(1238,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(359,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
thf(1387,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(511,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ ( c_Product__Type_OSigma @ F @ ( c_COMBK @ G @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ B @ ( c_Product__Type_OSigma @ H @ ( c_COMBK @ G @ ( tc_fun @ E @ tc_bool ) @ D ) @ D @ E ) @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Product__Type_OSigma @ F @ ( c_COMBK @ H @ ( tc_fun @ D @ tc_bool ) @ C ) @ C @ D ) @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__subset__Sigma_0) ).
thf(1723,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ ( c_Product__Type_OSigma @ F @ ( c_COMBK @ G @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ B @ ( c_Product__Type_OSigma @ H @ ( c_COMBK @ G @ ( tc_fun @ E @ tc_bool ) @ D ) @ D @ E ) @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Product__Type_OSigma @ F @ ( c_COMBK @ H @ ( tc_fun @ D @ tc_bool ) @ C ) @ C @ D ) @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(957,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(125,axiom,
! [A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__empty_0) ).
thf(894,plain,
! [A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(96,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(825,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(338,axiom,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_1) ).
thf(1343,plain,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(231,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
thf(1123,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( c_Relation_Orel__comp @ A @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__left_0) ).
thf(862,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( c_Relation_Orel__comp @ A @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(557,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId__on @ A @ B ) @ C @ B @ B )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id__on_0) ).
thf(1824,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId__on @ A @ B ) @ C @ B @ B )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(788,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(588,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
thf(1883,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(438,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ C ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__empty1_0) ).
thf(1560,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ C ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(376,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_0) ).
thf(1423,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(563,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(1837,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(119,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ B @ A @ C @ D ) @ D @ D ) @ B @ ( tc_prod @ D @ D ) )
| ( A = C )
| ~ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclE_0) ).
thf(879,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtranclE__1__1 @ B @ A @ C @ D ) @ D @ D ) @ B @ ( tc_prod @ D @ D ) )
| ( A = C )
| ~ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(256,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) )
| ~ ( c_in @ ( c_Pair @ C @ C @ A @ A ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) @ ( tc_prod @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__tranclI_0) ).
thf(1178,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) )
| ~ ( c_in @ ( c_Pair @ C @ C @ A @ A ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) @ ( tc_prod @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
thf(665,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(494,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_1) ).
thf(1687,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(467,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_OId @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_0) ).
thf(1624,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_OId @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(98,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(830,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(249,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(1159,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(211,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ A @ B @ C @ D ) @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ C @ D ) @ ( tc_prod @ D @ D ) )
| ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_0) ).
thf(1079,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ A @ B @ C @ D ) @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ C @ D ) @ ( tc_prod @ D @ D ) )
| ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(369,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(1407,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(471,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( A = D )
| ~ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(1634,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( A = D )
| ~ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
thf(1291,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(519,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ C ) ) )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ t_a ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_2) ).
thf(1740,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ C ) ) )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ t_a ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(223,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ E ) @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseI_0) ).
thf(1106,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( hAPP @ ( c_Relation_Oconverse @ D @ C ) @ E ) @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(366,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ A @ B )
| ~ ( c_Relation_Oantisym @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_0) ).
thf(1402,plain,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ A @ B )
| ~ ( c_Relation_Oantisym @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(742,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(242,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ A @ B @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).
thf(1143,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ A @ B @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(529,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ A @ B @ C @ D ) @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) )
| ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_1) ).
thf(1762,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ A @ B @ C @ D ) @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) )
| ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(150,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Obounded__lattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(948,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Obounded__lattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(549,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) )
| ~ ( c_Wellfounded_Owf @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_0) ).
thf(1804,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) )
| ~ ( c_Wellfounded_Owf @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(330,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ A @ C @ D @ E ) @ C @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_1) ).
thf(1328,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ A @ C @ D @ E ) @ C @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(203,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_1) ).
thf(1064,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(281,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
= ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converse_0) ).
thf(1227,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
= ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(377,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(1425,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(219,axiom,
! [B: $i,A: $i] :
( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ B @ A @ A @ A )
!= B )
| ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ B @ A @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__equivI_0) ).
thf(1096,plain,
! [B: $i,A: $i] :
( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ B @ A @ A @ A )
!= B )
| ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ B @ A @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(239,axiom,
class_Orderings_Obot @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(1138,plain,
class_Orderings_Obot @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(168,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
thf(989,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(364,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ D ) @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Int_0) ).
thf(1397,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ D ) @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(284,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_0) ).
thf(1234,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(429,axiom,
! [A: $i] :
( ( c_Relation_OField @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__empty_0) ).
thf(1541,plain,
! [A: $i] :
( ( c_Relation_OField @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(301,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ D ) @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Un_0) ).
thf(1270,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ D ) @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(533,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ A @ B @ C @ D @ E @ F @ G ) @ E @ G ) @ C @ ( tc_prod @ E @ G ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ E @ F ) @ ( c_Relation_Orel__comp @ C @ D @ E @ G @ F ) @ ( tc_prod @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_0) ).
thf(1772,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ A @ B @ C @ D @ E @ F @ G ) @ E @ G ) @ C @ ( tc_prod @ E @ G ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ E @ F ) @ ( c_Relation_Orel__comp @ C @ D @ E @ G @ F ) @ ( tc_prod @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(425,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(1534,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(543,axiom,
class_Lattices_Oupper__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(1794,plain,
class_Lattices_Oupper__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(182,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).
thf(1017,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(353,axiom,
class_Lattices_Olower__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(1375,plain,
class_Lattices_Olower__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(230,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(1121,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(573,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(1856,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(51,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(725,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(407,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(1493,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(482,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ C ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ ( v_sko__local__X3__1 @ D @ C @ B @ A ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ D @ ( v_sko__local__X3__1 @ D @ C @ B @ A ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ D @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_3_0) ).
thf(1659,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ C ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ ( v_sko__local__X3__1 @ D @ C @ B @ A ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ D @ ( v_sko__local__X3__1 @ D @ C @ B @ A ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ D @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(313,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
= ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converse_0) ).
thf(1292,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
= ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(448,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ A @ B @ C @ D ) @ E @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Product__Type_OSigma @ F @ ( c_COMBK @ E @ ( tc_fun @ D @ tc_bool ) @ C ) @ C @ D ) @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__subset_0) ).
thf(1584,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ A @ B @ C @ D ) @ E @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Product__Type_OSigma @ F @ ( c_COMBK @ E @ ( tc_fun @ D @ tc_bool ) @ C ) @ C @ D ) @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(386,axiom,
! [A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) @ A )
= ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__empty_0) ).
thf(1446,plain,
! [A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) @ A )
= ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(270,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ B @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__mono_0) ).
thf(1207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ B @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(374,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(1419,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(128,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Recdef_Ocut @ A @ B @ C @ D @ E )
= ( c_Recdef_Ocut @ F @ B @ C @ D @ E ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ F @ B @ C @ D @ E ) @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_1) ).
thf(901,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Recdef_Ocut @ A @ B @ C @ D @ E )
= ( c_Recdef_Ocut @ F @ B @ C @ D @ E ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ F @ B @ C @ D @ E ) @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(209,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ A @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_1) ).
thf(1075,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ A @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(372,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ C ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ F ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ ( v_sko__local__X1__1 @ F @ C @ D @ A @ E @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ F @ ( v_sko__local__X1__1 @ F @ C @ D @ A @ E @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ F @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( E = A )
| ( D = B )
| ( A = B )
| ( D = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_1_0) ).
thf(1414,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ C ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ F ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ ( v_sko__local__X1__1 @ F @ C @ D @ A @ E @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ F @ ( v_sko__local__X1__1 @ F @ C @ D @ A @ E @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ F @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( E = A )
| ( D = B )
| ( A = B )
| ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(566,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B ) )
| ~ ( c_in @ ( c_Pair @ A @ D @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
| ~ ( c_in @ D @ E @ B )
| ~ ( c_in @ A @ E @ B )
| ~ ( c_Equiv__Relations_Oequiv @ E @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff2_1) ).
thf(1842,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B )
= ( c_Equiv__Relations_Oquotient @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C @ B ) )
| ~ ( c_in @ ( c_Pair @ A @ D @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
| ~ ( c_in @ D @ E @ B )
| ~ ( c_in @ A @ E @ B )
| ~ ( c_Equiv__Relations_Oequiv @ E @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(552,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_bool ) ) @ D ) @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_1) ).
thf(1810,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_bool ) ) @ D ) @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(541,axiom,
! [B: $i,A: $i] :
( ( c_Relation_OField @ A @ B )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ A @ B @ B ) @ ( c_Relation_ORange @ A @ B @ B ) @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__def_0) ).
thf(1791,plain,
! [B: $i,A: $i] :
( ( c_Relation_OField @ A @ B )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ A @ B @ B ) @ ( c_Relation_ORange @ A @ B @ B ) @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(591,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ~ ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
thf(1889,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ~ ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(475,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__trancl_0) ).
thf(1644,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(461,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl_0) ).
thf(1612,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(192,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(1039,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(247,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
thf(1155,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(521,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) ) @ C @ A @ B @ D )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ D ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__empty1_0) ).
thf(1744,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) ) @ C @ A @ B @ D )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ D ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(837,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(701,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ A @ B @ C ) @ B @ C @ C ) @ A @ ( tc_prod @ C @ C ) )
| ( c_in @ B @ ( c_Wellfounded_Oacc @ A @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_0) ).
thf(1266,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ A @ B @ C ) @ B @ C @ C ) @ A @ ( tc_prod @ C @ C ) )
| ( c_in @ B @ ( c_Wellfounded_Oacc @ A @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(486,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
| ~ ( c_Relation_Oantisym @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_1) ).
thf(1668,plain,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A )
| ~ ( c_Relation_Oantisym @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(434,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ A @ B @ B @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OId @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Int__subset_0) ).
thf(1552,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ A @ B @ B @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OId @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(262,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_Oinv__image @ D @ E @ F @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ E @ A ) @ ( hAPP @ E @ B ) @ F @ F ) @ D @ ( tc_prod @ F @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_1) ).
thf(1192,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_Oinv__image @ D @ E @ F @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ E @ A ) @ ( hAPP @ E @ B ) @ F @ F ) @ D @ ( tc_prod @ F @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(201,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(1060,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(911,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(49,axiom,
! [B: $i,A: $i] : ( c_Relation_Osym @ ( c_Relation_OId__on @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id__on_0) ).
thf(721,plain,
! [B: $i,A: $i] : ( c_Relation_Osym @ ( c_Relation_OId__on @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(571,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(1852,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(507,axiom,
! [A: $i] :
( ( c_Relation_OId__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__empty_0) ).
thf(1715,plain,
! [A: $i] :
( ( c_Relation_OId__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(509,axiom,
class_HOL_Oord @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(1720,plain,
class_HOL_Oord @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= B )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
thf(779,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= B )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(535,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(1776,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(297,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D )
| ~ ( c_in @ ( c_Pair @ E @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_1) ).
thf(1263,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D )
| ~ ( c_in @ ( c_Pair @ E @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(450,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ E @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ A @ B @ D @ E ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ D @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ A @ B @ D @ E ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ E @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ D @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_Arrow__Order__Mirabelle_OIIA @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_3) ).
thf(1588,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ E @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ A @ B @ D @ E ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ D @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ A @ B @ D @ E ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ E @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ D @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_Arrow__Order__Mirabelle_OIIA @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(220,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) @ C @ D )
= ( c_Set_Oinsert @ A @ ( c_Relation_ODomain @ E @ C @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__insert_0) ).
thf(1099,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) @ C @ D )
= ( c_Set_Oinsert @ A @ ( c_Relation_ODomain @ E @ C @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(245,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Relation_OImage @ C @ A @ B @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__pf_0) ).
thf(1150,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Relation_OImage @ C @ A @ B @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(1249,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(423,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_in @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(1530,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_in @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(428,axiom,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ A )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ A ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ A ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ A @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ A ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ A ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ A ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ A @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ A ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_9) ).
thf(1539,plain,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ A )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ A ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ A ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ A @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ A ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ A ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ A ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ A @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ A ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(391,axiom,
! [A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(1456,plain,
! [A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(235,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(1131,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(654,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(528,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_3) ).
thf(1759,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(362,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Osingle__valued @ A @ B @ C )
| ~ ( c_Relation_Osingle__valued @ D @ B @ C )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__subset_0) ).
thf(1393,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Osingle__valued @ A @ B @ C )
| ~ ( c_Relation_Osingle__valued @ D @ B @ C )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(468,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Relation_Osym @ B @ C )
| ~ ( c_Relation_Osym @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Int_0) ).
thf(1627,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Relation_Osym @ B @ C )
| ~ ( c_Relation_Osym @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(421,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
!= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( c_in @ D @ ( c_Relation_OField @ A @ C ) @ C )
| ~ ( c_in @ B @ ( c_Relation_OField @ A @ C ) @ C )
| ~ ( c_Relation_Oantisym @ A @ C )
| ~ ( c_Relation_Orefl__on @ ( c_Relation_OField @ A @ C ) @ A @ C )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Refl__antisym__eq__Image1__Image1__iff_0) ).
thf(1525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
!= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( c_in @ D @ ( c_Relation_OField @ A @ C ) @ C )
| ~ ( c_in @ B @ ( c_Relation_OField @ A @ C ) @ C )
| ~ ( c_Relation_Oantisym @ A @ C )
| ~ ( c_Relation_Orefl__on @ ( c_Relation_OField @ A @ C ) @ A @ C )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(80,axiom,
! [A: $i] : ( c_Relation_Osym @ ( c_Relation_OId @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id_0) ).
thf(792,plain,
! [A: $i] : ( c_Relation_Osym @ ( c_Relation_OId @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(498,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__trancl2_0) ).
thf(1695,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(309,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(1286,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(207,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
thf(1071,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(186,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ C ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ D @ ( v_sko__local__X3__1 @ C @ D @ A @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ ( v_sko__local__X3__1 @ C @ D @ A @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ D @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_3_3) ).
thf(1026,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ C ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ D @ ( v_sko__local__X3__1 @ C @ D @ A @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ ( v_sko__local__X3__1 @ C @ D @ A @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ D @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(463,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ A @ B @ C @ D @ E ) @ B @ D @ E ) @ C @ ( tc_prod @ D @ E ) )
| ~ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_1) ).
thf(1616,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ A @ B @ C @ D @ E ) @ B @ D @ E ) @ C @ ( tc_prod @ D @ E ) )
| ~ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(515,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__mono_0) ).
thf(1732,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(68,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ C @ E )
| ~ ( c_Relation_Osingle__valued @ B @ D @ E )
| ~ ( c_Relation_Osingle__valued @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__rel__comp_0) ).
thf(765,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ C @ E )
| ~ ( c_Relation_Osingle__valued @ B @ D @ E )
| ~ ( c_Relation_Osingle__valued @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(506,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(1712,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(199,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B )
= B )
| ~ ( c_Relation_Osym @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_0) ).
thf(1054,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B )
= B )
| ~ ( c_Relation_Osym @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(260,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_2) ).
thf(1187,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(674,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(662,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(47,axiom,
! [B: $i,A: $i] : ( c_Relation_Orefl__on @ A @ ( c_Relation_OId__on @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Id__on_0) ).
thf(718,plain,
! [B: $i,A: $i] : ( c_Relation_Orefl__on @ A @ ( c_Relation_OId__on @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ A @ B @ B @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__Int__subset_0) ).
thf(906,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ A @ B @ B @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( ( c_Nitpick_Orefl_H @ A @ B )
| ~ ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ A @ B ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_1) ).
thf(1135,plain,
! [B: $i,A: $i] :
( ( c_Nitpick_Orefl_H @ A @ B )
| ~ ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ A @ B ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ~ ( c_Equiv__Relations_Oequiv @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Orefl__on_0) ).
thf(750,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ~ ( c_Equiv__Relations_Oequiv @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).
thf(618,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(526,axiom,
! [B: $i,A: $i] :
( ( ( c_Relation_Orel__comp @ A @ A @ B @ B @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) )
| ( c_Wellfounded_Owf @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__no__loop_0) ).
thf(1754,plain,
! [B: $i,A: $i] :
( ( ( c_Relation_Orel__comp @ A @ A @ B @ B @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) )
| ( c_Wellfounded_Owf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(491,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ A @ B @ C @ D ) @ A @ D @ C ) @ B @ ( tc_prod @ D @ C ) )
| ~ ( c_in @ A @ ( c_Relation_ORange @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_0) ).
thf(1680,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ A @ B @ C @ D ) @ A @ D @ C ) @ B @ ( tc_prod @ D @ C ) )
| ~ ( c_in @ A @ ( c_Relation_ORange @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(403,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_0) ).
thf(1483,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(303,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ A @ B @ C ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( B = A )
| ~ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_0) ).
thf(1273,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ A @ B @ C ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) )
| ( B = A )
| ~ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(108,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
thf(856,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(60,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
| ~ ( c_Relation_Osym @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__inv__image_0) ).
thf(745,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
| ~ ( c_Relation_Osym @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(305,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Odistrib__lattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
thf(1278,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Odistrib__lattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(599,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(1906,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(432,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
| ~ ( c_in @ A @ D @ B )
| ~ ( c_Relation_Orefl__on @ D @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_1) ).
thf(1548,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
| ~ ( c_in @ A @ D @ B )
| ~ ( c_Relation_Orefl__on @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(609,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
| ~ ( c_Wellfounded_Owf @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__irrefl_0) ).
thf(1927,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
| ~ ( c_Wellfounded_Owf @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(470,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ A @ B @ C @ D ) @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) )
| ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_0) ).
thf(1631,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ A @ B @ C @ D ) @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) )
| ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ODomain @ A @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__domain_0) ).
thf(733,plain,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ODomain @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(360,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(1389,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(465,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_OId__on @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).
thf(1620,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_OId__on @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(525,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ E @ ( tc_prod @ C @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ B @ E @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).
thf(1752,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ E @ ( tc_prod @ C @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ B @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(426,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(1535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(419,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(1520,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(405,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ B @ D @ C ) @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ E @ B @ C )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_1) ).
thf(1488,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ B @ D @ C ) @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ E @ B @ C )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(129,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(904,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ C ) @ C )
| ( c_in @ ( c_Pair @ A @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_1) ).
thf(975,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ C ) @ C )
| ( c_in @ ( c_Pair @ A @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(177,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ C @ D ) @ ( c_Wellfounded_Oacc @ C @ D ) @ D )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_0) ).
thf(1007,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ C @ D ) @ ( c_Wellfounded_Oacc @ C @ D ) @ D )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(694,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(843,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(232,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_0) ).
thf(1125,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(479,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(1652,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(610,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ D @ A @ C @ C ) @ E @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Orefl__on @ B @ E @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD2_0) ).
thf(1929,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ D @ A @ C @ C ) @ E @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Orefl__on @ B @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(117,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(875,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(711,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(544,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(1795,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(501,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_0) ).
thf(1701,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(641,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(539,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq_0) ).
thf(1786,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(144,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Relation_ODomain @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ A @ C @ D ) @ ( c_Relation_ODomain @ B @ C @ D ) @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Int__subset_0) ).
thf(936,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Relation_ODomain @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ A @ C @ D ) @ ( c_Relation_ODomain @ B @ C @ D ) @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(351,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_in @ C @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_0) ).
thf(1371,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_in @ C @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(77,axiom,
! [B: $i,A: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId__on @ A @ B ) @ B @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id__on_0) ).
thf(787,plain,
! [B: $i,A: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId__on @ A @ B ) @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(332,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ A @ B @ C @ D @ E ) @ A @ D )
| ~ ( c_in @ C @ ( c_Product__Type_OSigma @ A @ B @ D @ E ) @ ( tc_prod @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaE_0) ).
thf(1332,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigmaE__1__1 @ A @ B @ C @ D @ E ) @ A @ D )
| ~ ( c_in @ C @ ( c_Product__Type_OSigma @ A @ B @ D @ E ) @ ( tc_prod @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(217,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(1092,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(295,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ A @ B @ C @ D @ E @ F @ G ) @ B @ G @ F ) @ D @ ( tc_prod @ G @ F ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ E @ F ) @ ( c_Relation_Orel__comp @ C @ D @ E @ G @ F ) @ ( tc_prod @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_1) ).
thf(1258,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ A @ B @ C @ D @ E @ F @ G ) @ B @ G @ F ) @ D @ ( tc_prod @ G @ F ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ E @ F ) @ ( c_Relation_Orel__comp @ C @ D @ E @ G @ F ) @ ( tc_prod @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(149,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Relation_ORange @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ORange @ A @ C @ D ) @ ( c_Relation_ORange @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Int__subset_0) ).
thf(947,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Relation_ORange @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ORange @ A @ C @ D ) @ ( c_Relation_ORange @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(279,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(1224,plain,
class_Lattices_Olattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(489,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Equiv__Relations_Ocongruent @ A @ ( hAPP @ B @ C ) @ D @ E )
| ~ ( c_in @ C @ F @ G )
| ~ ( c_Equiv__Relations_Ocongruent2 @ H @ A @ B @ G @ D @ E )
| ~ ( c_Equiv__Relations_Oequiv @ F @ H @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent2__implies__congruent_0) ).
thf(1675,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Equiv__Relations_Ocongruent @ A @ ( hAPP @ B @ C ) @ D @ E )
| ~ ( c_in @ C @ F @ G )
| ~ ( c_Equiv__Relations_Ocongruent2 @ H @ A @ B @ G @ D @ E )
| ~ ( c_Equiv__Relations_Oequiv @ F @ H @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(240,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(1139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(412,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ C @ D ) ) )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_2) ).
thf(1503,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ C @ D ) ) )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(530,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ D @ A @ C @ C ) @ E @ ( tc_prod @ C @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ B @ E @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).
thf(1765,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ D @ A @ C @ C ) @ E @ ( tc_prod @ C @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ B @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(216,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_FuncSet_OPi @ B @ C @ D @ E ) @ ( tc_fun @ D @ E ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ B @ C @ A @ D @ E ) @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__I_0) ).
thf(1090,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_FuncSet_OPi @ B @ C @ D @ E ) @ ( tc_fun @ D @ E ) )
| ( c_in @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ B @ C @ A @ D @ E ) @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(136,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ D ) @ E ) )
| ~ ( c_in @ ( c_Pair @ C @ E @ F @ F ) @ G @ ( tc_prod @ F @ F ) )
| ~ ( c_in @ ( c_Pair @ B @ D @ H @ H ) @ I @ ( tc_prod @ H @ H ) )
| ~ ( c_Equiv__Relations_Ocongruent2 @ I @ G @ A @ H @ F @ J ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent2_Ocongruent2_0) ).
thf(919,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ D ) @ E ) )
| ~ ( c_in @ ( c_Pair @ C @ E @ F @ F ) @ G @ ( tc_prod @ F @ F ) )
| ~ ( c_in @ ( c_Pair @ B @ D @ H @ H ) @ I @ ( tc_prod @ H @ H ) )
| ~ ( c_Equiv__Relations_Ocongruent2 @ I @ G @ A @ H @ F @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(804,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(164,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) ) @ F @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ B @ F @ D @ E ) @ ( c_Relation_Orel__comp @ A @ C @ F @ D @ E ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib_0) ).
thf(979,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) ) @ F @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ B @ F @ D @ E ) @ ( c_Relation_Orel__comp @ A @ C @ F @ D @ E ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(263,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_in @ D @ A @ C )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(1194,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_in @ D @ A @ C )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(271,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Un_0) ).
thf(1209,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(307,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ C ) @ B @ A )
= ( c_Relation_ODomain @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__converse_0) ).
thf(1282,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ C ) @ B @ A )
= ( c_Relation_ODomain @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ B @ C )
| ~ ( c_Relation_Ototal__on @ A @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_0) ).
thf(1117,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ B @ C )
| ~ ( c_Relation_Ototal__on @ A @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(341,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ ( c_Relation_Orel__comp @ F @ G @ C @ D @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ B @ G @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ F @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__mono_0) ).
thf(1349,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ ( c_Relation_Orel__comp @ F @ G @ C @ D @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ B @ G @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ F @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(172,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_FuncSet_OPi @ B @ C @ D @ E ) @ ( tc_fun @ D @ E ) )
| ~ ( c_in @ ( hAPP @ A @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ B @ C @ A @ D @ E ) ) @ ( hAPP @ C @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ B @ C @ A @ D @ E ) ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__I_H_1) ).
thf(996,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_FuncSet_OPi @ B @ C @ D @ E ) @ ( tc_fun @ D @ E ) )
| ~ ( c_in @ ( hAPP @ A @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ B @ C @ A @ D @ E ) ) @ ( hAPP @ C @ ( c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 @ B @ C @ A @ D @ E ) ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(456,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(1603,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(737,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(320,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) @ D @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__empty2_0) ).
thf(1307,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) @ D @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(255,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
thf(1175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(444,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( B = D )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_3) ).
thf(1574,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( B = D )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(550,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_in @ A @ C @ D )
| ~ ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).
thf(1806,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_in @ A @ C @ D )
| ~ ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(179,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ B @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downward_0) ).
thf(1011,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ B @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(649,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(194,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(1043,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(354,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_0) ).
thf(1376,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(383,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Relation_OId__on @ B @ A ) )
= ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id__on_0) ).
thf(1439,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Relation_OId__on @ B @ A ) )
= ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(123,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) @ D @ D ) @ E @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ F @ F ) @ ( c_Relation_Oinv__image @ E @ A @ D @ F ) @ ( tc_prod @ F @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_0) ).
thf(890,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) @ D @ D ) @ E @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ F @ F ) @ ( c_Relation_Oinv__image @ E @ A @ D @ F ) @ ( tc_prod @ F @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(89,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(811,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(109,axiom,
! [A: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId @ A ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id_0) ).
thf(858,plain,
! [A: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId @ A ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(816,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(329,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( B = D )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_2) ).
thf(1325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( B = D )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(187,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ A @ C @ D @ E ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ A @ C @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ B @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_1) ).
thf(1029,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ A @ C @ D @ E ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__2 @ A @ C @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ B @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(964,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
thf(668,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(142,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ B @ ( c_Relation_OImage @ E @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).
thf(932,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ B @ ( c_Relation_OImage @ E @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(556,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( B = F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
thf(1820,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( B = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(585,axiom,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_Ounanimity @ A )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ A ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_unanimity__def_1) ).
thf(1877,plain,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_Ounanimity @ A )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ A ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(398,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ D @ E @ C )
| ~ ( c_in @ B @ E @ C )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_1) ).
thf(1471,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ D @ E @ C )
| ~ ( c_in @ B @ E @ C )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(65,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).
thf(758,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(336,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ A @ C @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_3) ).
thf(1339,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ A @ C @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ A @ B )
| ~ ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Osym_0) ).
thf(799,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ A @ B )
| ~ ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(600,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OField @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OField @ A @ C ) @ ( c_Relation_OField @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__Un_0) ).
thf(1909,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OField @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OField @ A @ C ) @ ( c_Relation_OField @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trancl_0) ).
thf(626,plain,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(134,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(915,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(436,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_in @ C @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_0) ).
thf(1556,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_in @ C @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a )
| ~ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(393,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ B @ C @ D @ E @ F ) )
!= ( hAPP @ B @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ B @ C @ D @ E @ F ) ) )
| ( ( c_Recdef_Ocut @ A @ C @ D @ E @ F )
= ( c_Recdef_Ocut @ B @ C @ D @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_2) ).
thf(1460,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ B @ C @ D @ E @ F ) )
!= ( hAPP @ B @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ B @ C @ D @ E @ F ) ) )
| ( ( c_Recdef_Ocut @ A @ C @ D @ E @ F )
= ( c_Recdef_Ocut @ B @ C @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(147,axiom,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ A )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ A ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ A ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ A @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ A ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ A ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ A ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ A @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ A ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_8) ).
thf(943,plain,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ A )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ A ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ A ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ A @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__3 @ A ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__4 @ A ) @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__5 @ A ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ A @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__2 @ A ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(184,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ A @ B @ C ) @ A @ C )
| ~ ( c_in @ D @ A @ C )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_0) ).
thf(1022,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ A @ B @ C ) @ A @ C )
| ~ ( c_in @ D @ A @ C )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(166,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ A @ B ) @ B @ B ) )
| ~ ( c_in @ A @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdE_0) ).
thf(983,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ A @ B ) @ B @ B ) )
| ~ ( c_in @ A @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(265,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D )
| ~ ( c_in @ ( c_Pair @ E @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeI_0) ).
thf(1198,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D )
| ~ ( c_in @ ( c_Pair @ E @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(399,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ A @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__Lin_1) ).
thf(1474,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ A @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(500,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Orel__comp @ E @ F @ C @ G @ D ) @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ H @ B @ G @ D ) @ F @ ( tc_prod @ G @ D ) )
| ~ ( c_in @ ( c_Pair @ A @ H @ C @ G ) @ E @ ( tc_prod @ C @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compI_0) ).
thf(1699,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Orel__comp @ E @ F @ C @ G @ D ) @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ H @ B @ G @ D ) @ F @ ( tc_prod @ G @ D ) )
| ~ ( c_in @ ( c_Pair @ A @ H @ C @ G ) @ E @ ( tc_prod @ C @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(155,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) )
| ( c_in @ B @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
thf(959,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) )
| ( c_in @ B @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(273,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainE_0) ).
thf(1213,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acyclic_0) ).
thf(636,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ B @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ A @ B @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__trancl_H_0) ).
thf(1015,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ B @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ A @ B @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ B @ A @ A @ A )
= B )
| ~ ( c_Equiv__Relations_Oequiv @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__comp__eq_0) ).
thf(986,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ B @ A @ A @ A )
= B )
| ~ ( c_Equiv__Relations_Oequiv @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(226,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards__aux_0) ).
thf(1113,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(400,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(1477,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(851,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
thf(658,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(439,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(1562,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_1) ).
thf(685,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(253,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ A @ D ) @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_1) ).
thf(1171,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ A @ D ) @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(422,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(1528,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
| ~ ( c_Wellfounded_Owf @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__inv__image_0) ).
thf(868,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
| ~ ( c_Wellfounded_Owf @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(174,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B )
!= B )
| ( c_Relation_Osym @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).
thf(1000,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B )
!= B )
| ( c_Relation_Osym @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(381,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__trans_0) ).
thf(1435,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(348,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_1) ).
thf(1364,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(291,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Relation_Osingle__valued @ ( hAPP @ ( c_Relation_Oconverse @ D @ E ) @ A ) @ E @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__eq_0) ).
thf(1250,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Relation_Osingle__valued @ ( hAPP @ ( c_Relation_Oconverse @ D @ E ) @ A ) @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(497,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdI_0) ).
thf(1694,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(137,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ B @ A @ C @ D ) @ D @ D ) @ B @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_0) ).
thf(922,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ B @ A @ C @ D ) @ D @ D ) @ B @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(50,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
thf(722,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(190,axiom,
v_a____ != v_c____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_A_I3_J_0) ).
thf(1034,plain,
v_a____ != v_c____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(483,axiom,
! [B: $i,A: $i] :
~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(1662,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(268,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Relation_Orefl__on @ B @ E @ C )
| ~ ( c_Relation_Orefl__on @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Un_0) ).
thf(1203,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Relation_Orefl__on @ B @ E @ C )
| ~ ( c_Relation_Orefl__on @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(396,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl2_0) ).
thf(1467,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(493,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
thf(1684,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(17,axiom,
c_Arrow__Order__Mirabelle_OIIA @ v_F,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_I3_J_0) ).
thf(648,plain,
c_Arrow__Order__Mirabelle_OIIA @ v_F,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Oantisym @ A @ B )
| ~ ( c_Relation_Oantisym @ C @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__subset_0) ).
thf(1081,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Oantisym @ A @ B )
| ~ ( c_Relation_Oantisym @ C @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(243,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_Wellfounded_Oacyclic @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_2) ).
thf(1145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_Wellfounded_Oacyclic @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(197,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Recdef_Ocut @ A @ B @ C @ D @ E )
!= ( c_Recdef_Ocut @ F @ B @ C @ D @ E ) )
| ( ( hAPP @ A @ G )
= ( hAPP @ F @ G ) )
| ~ ( c_in @ ( c_Pair @ G @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_0) ).
thf(1049,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Recdef_Ocut @ A @ B @ C @ D @ E )
!= ( c_Recdef_Ocut @ F @ B @ C @ D @ E ) )
| ( ( hAPP @ A @ G )
= ( hAPP @ F @ G ) )
| ~ ( c_in @ ( c_Pair @ G @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = B )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_4) ).
thf(1304,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(583,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ A @ ( hAPP @ B @ C ) )
= ( hAPP @ ( c_Fun_Ocomp @ A @ B @ D @ E @ F ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
thf(1873,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ A @ ( hAPP @ B @ C ) )
= ( hAPP @ ( c_Fun_Ocomp @ A @ B @ D @ E @ F ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
thf(795,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(680,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(257,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ C @ C ) @ A @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ B @ C )
| ~ ( c_Wellfounded_Owf @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__compatible_0) ).
thf(1181,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ C @ C ) @ A @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ B @ C )
| ~ ( c_Wellfounded_Owf @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(823,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(567,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ A @ C @ D ) @ ( c_Relation_ODomain @ B @ C @ D ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Un__eq_0) ).
thf(1845,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ A @ C @ D ) @ ( c_Relation_ODomain @ B @ C @ D ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(523,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) )
| ~ ( c_in @ F @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_0) ).
thf(1748,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) )
| ~ ( c_in @ F @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(546,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(1798,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(705,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(280,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ocomp @ A @ ( c_Fun_Ocomp @ B @ C @ D @ E @ F ) @ E @ G @ F )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ A @ B @ E @ G @ D ) @ C @ D @ G @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__assoc_0) ).
thf(1225,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ocomp @ A @ ( c_Fun_Ocomp @ B @ C @ D @ E @ F ) @ E @ G @ F )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ A @ B @ E @ G @ D ) @ C @ D @ G @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(122,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ C ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ F ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ ( v_sko__local__X2__1 @ F @ C @ D @ A @ E @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ F @ ( v_sko__local__X2__1 @ F @ C @ D @ A @ E @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ F @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( E = A )
| ( D = B )
| ( A = B )
| ( D = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_2_0) ).
thf(887,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ C ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ F ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ ( v_sko__local__X2__1 @ F @ C @ D @ A @ E @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ F @ ( v_sko__local__X2__1 @ F @ C @ D @ A @ E @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ F @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( E = A )
| ( D = B )
| ( A = B )
| ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(160,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__rtrancl_0) ).
thf(971,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(441,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oinsert @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(1566,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oinsert @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(477,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Set_Oinsert @ A @ D @ C ) )
| ( c_in @ A @ D @ C )
| ( c_in @ A @ B @ C )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(1647,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Set_Oinsert @ A @ D @ C ) )
| ( c_in @ A @ D @ C )
| ( c_in @ A @ B @ C )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(350,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
thf(1368,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(537,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(1780,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(170,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_FuncSet_OPi @ B @ C @ D @ E ) @ ( tc_fun @ D @ E ) )
| ~ ( c_in @ ( hAPP @ A @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ B @ C @ A @ D @ E ) ) @ ( hAPP @ C @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ B @ C @ A @ D @ E ) ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__I_1) ).
thf(993,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_FuncSet_OPi @ B @ C @ D @ E ) @ ( tc_fun @ D @ E ) )
| ~ ( c_in @ ( hAPP @ A @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ B @ C @ A @ D @ E ) ) @ ( hAPP @ C @ ( c_FuncSet_Osko__FuncSet__XPi__I__1__1 @ B @ C @ A @ D @ E ) ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(175,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold_0) ).
thf(1003,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(532,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__empty_0) ).
thf(1770,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(35,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(690,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(417,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Product__Type_OSigma @ E @ F @ C @ D ) @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ B @ ( hAPP @ F @ A ) @ D )
| ~ ( c_in @ A @ E @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__Sigma__iff_2) ).
thf(1516,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Product__Type_OSigma @ E @ F @ C @ D ) @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ B @ ( hAPP @ F @ A ) @ D )
| ~ ( c_in @ A @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(454,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ A @ B @ C ) @ B @ t_a @ t_a ) @ C @ ( tc_prod @ t_a @ t_a ) )
| ( B = A )
| ~ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ocases_1) ).
thf(1598,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xrtrancl__Xcases__1 @ A @ B @ C ) @ B @ t_a @ t_a ) @ C @ ( tc_prod @ t_a @ t_a ) )
| ( B = A )
| ~ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ ( c_Transitive__Closure_Ortrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(410,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ~ ( c_Relation_Orefl__on @ A @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).
thf(1499,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ~ ( c_Relation_Orefl__on @ A @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(28,axiom,
! [A: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id_0) ).
thf(673,plain,
! [A: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(259,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__subset_0) ).
thf(1186,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(840,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
thf(808,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(446,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(1579,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(334,axiom,
! [A: $i] : ( c_Relation_Orefl__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__empty_0) ).
thf(1336,plain,
! [A: $i] : ( c_Relation_Orefl__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(277,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ A @ B )
| ~ ( c_Relation_Osym @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_0) ).
thf(1220,plain,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ A @ B )
| ~ ( c_Relation_Osym @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(317,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ A @ B ) @ ( c_Wellfounded_Oacc @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfI_0) ).
thf(1300,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ A @ B ) @ ( c_Wellfounded_Oacc @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(389,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ C ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ F ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ ( v_sko__local__X1__1 @ F @ C @ D @ A @ E @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ F @ ( v_sko__local__X1__1 @ F @ C @ D @ A @ E @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ F @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( E = A )
| ( D = B )
| ( A = B )
| ( D = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_1_1) ).
thf(1452,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ C ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ F ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ ( v_sko__local__X1__1 @ F @ C @ D @ A @ E @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ F @ ( v_sko__local__X1__1 @ F @ C @ D @ A @ E @ B ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ F @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( E = A )
| ( D = B )
| ( A = B )
| ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(472,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( hAPP @ B @ C ) @ D )
| ~ ( c_in @ ( c_Pair @ C @ A @ E @ D ) @ ( c_Product__Type_OSigma @ F @ B @ E @ D ) @ ( tc_prod @ E @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD2_0) ).
thf(1637,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( hAPP @ B @ C ) @ D )
| ~ ( c_in @ ( c_Pair @ C @ A @ E @ D ) @ ( c_Product__Type_OSigma @ F @ B @ E @ D ) @ ( tc_prod @ E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(325,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ A @ C @ D @ E ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ A @ C @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__induct_0) ).
thf(1317,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__1 @ A @ C @ D @ E ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__rtrancl__induct__1__2 @ A @ C @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(560,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) ) @ A @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__empty_0) ).
thf(1830,plain,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ B ) @ tc_bool ) ) @ A @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(214,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ A @ B @ C @ D @ E ) @ B @ D @ E ) @ C @ ( tc_prod @ D @ E ) )
| ~ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_0) ).
thf(1085,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ A @ B @ C @ D @ E ) @ B @ D @ E ) @ C @ ( tc_prod @ D @ E ) )
| ~ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(481,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) @ B @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__by__empty_0) ).
thf(1658,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) @ B @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(518,axiom,
! [A: $i] :
( ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iff_0) ).
thf(1738,plain,
! [A: $i] :
( ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(276,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(1218,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(367,axiom,
! [B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(1404,plain,
! [B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(59,axiom,
c_Arrow__Order__Mirabelle_Ounanimity @ v_F,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_u_0) ).
thf(744,plain,
c_Arrow__Order__Mirabelle_Ounanimity @ v_F,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(430,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_0) ).
thf(1543,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(241,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( hAPP @ D @ A ) @ ( hAPP @ E @ A ) @ F )
| ~ ( c_in @ D @ ( c_FuncSet_OPi @ B @ E @ C @ F ) @ ( tc_fun @ C @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PiE_0) ).
thf(1141,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( hAPP @ D @ A ) @ ( hAPP @ E @ A ) @ F )
| ~ ( c_in @ D @ ( c_FuncSet_OPi @ B @ E @ C @ F ) @ ( tc_fun @ C @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(2,negated_conjecture,
! [A: $i] :
( ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ v_b____ @ v_a____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( c_Fun_Ocomp @ ( c_Relation_Oconverse @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(613,plain,
! [A: $i] :
( ( c_in @ ( c_Pair @ v_b____ @ v_c____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P_H____ @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ v_b____ @ v_a____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ ( c_Fun_Ocomp @ ( c_Relation_Oconverse @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ v_P____ @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(308,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ A ) @ C ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__converse_0) ).
thf(1284,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ ( hAPP @ ( c_Relation_Oconverse @ B @ A ) @ C ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(343,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_bool ) ) @ D ) @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_0) ).
thf(1353,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_bool ) ) @ D ) @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(112,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
| ~ ( c_Wellfounded_Oacyclic @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__impl__antisym__rtrancl_0) ).
thf(864,plain,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
| ~ ( c_Wellfounded_Oacyclic @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(378,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(1427,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(218,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ A @ B @ C ) @ ( c_Relation_ODomain @ D @ B @ C ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__mono_0) ).
thf(1094,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ A @ B @ C ) @ ( c_Relation_ODomain @ D @ B @ C ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(487,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
thf(1670,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(508,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
!= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( c_in @ D @ E @ C )
| ~ ( c_in @ B @ E @ C )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C )
| ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_0) ).
thf(1717,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
!= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ~ ( c_in @ D @ E @ C )
| ~ ( c_in @ B @ E @ C )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C )
| ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(859,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(595,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).
thf(1898,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(569,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(1849,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(294,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(1257,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
thf(656,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(548,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_1) ).
thf(1802,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(404,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= ( hAPP @ B @ C ) )
| ~ ( c_in @ B @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_Arrow__Order__Mirabelle_Odictator @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dictator__def_0) ).
thf(1485,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= ( hAPP @ B @ C ) )
| ~ ( c_in @ B @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_Arrow__Order__Mirabelle_Odictator @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(198,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ A @ B @ C @ D ) @ ( c_Relation_OImage @ E @ F @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ F @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ E @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__mono_0) ).
thf(1052,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ A @ B @ C @ D ) @ ( c_Relation_OImage @ E @ F @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ F @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ E @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(587,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__asym_0) ).
thf(1881,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(302,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Relation_OImage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).
thf(1272,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Relation_OImage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(1,negated_conjecture,
v_b____ = v_a____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(612,plain,
v_b____ = v_a____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(287,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = A )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_4) ).
thf(1240,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = A )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(169,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Relation_OId__on @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).
thf(991,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Relation_OId__on @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(375,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ D @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ A @ B @ E @ D ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ E @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ A @ B @ E @ D ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ D @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ E @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_Arrow__Order__Mirabelle_OIIA @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IIA__def_0) ).
thf(1421,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ D @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ A @ B @ E @ D ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ E @ ( v_sko__Arrow__Order__Mirabelle__XIIA__def__1 @ A @ B @ E @ D ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ D @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ E @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_Arrow__Order__Mirabelle_OIIA @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(564,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Relation_OId__on @ A @ B ) @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ A @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__subset__Times_0) ).
thf(1839,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Relation_OId__on @ A @ B ) @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ A @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(275,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ A @ B )
| ~ ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_0) ).
thf(1216,plain,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ A @ B )
| ~ ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(579,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
thf(1866,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(516,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).
thf(1734,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(224,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ A @ C @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ B @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_2) ).
thf(1108,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ A @ C @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ B @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(248,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__comp__subset_0) ).
thf(1157,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Relation_Orel__comp @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(327,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ C ) @ B )
| ~ ( c_Relation_Ototal__on @ A @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_1) ).
thf(1321,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ C ) @ B )
| ~ ( c_Relation_Ototal__on @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(562,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ~ ( c_in @ ( c_Pair @ F @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut__apply_0) ).
thf(1834,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ~ ( c_in @ ( c_Pair @ F @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(602,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ~ ( c_in @ ( c_Pair @ F @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) )
| ~ ( c_in @ F @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).
thf(1913,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ~ ( c_in @ ( c_Pair @ F @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) )
| ~ ( c_in @ F @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(387,axiom,
! [B: $i,A: $i] :
( ( c_Arrow__Order__Mirabelle_Odictator @ A @ B )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ A @ B ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dictator__def_1) ).
thf(1448,plain,
! [B: $i,A: $i] :
( ( c_Arrow__Order__Mirabelle_Odictator @ A @ B )
| ( c_in @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ A @ B ) @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(261,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( c_in @ A @ ( c_Relation_ODomain @ D @ C @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_0) ).
thf(1189,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( c_in @ A @ ( c_Relation_ODomain @ D @ C @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(476,axiom,
! [B: $i,A: $i] : ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__empty_0) ).
thf(1646,plain,
! [B: $i,A: $i] : ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(473,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ C @ D )
| ~ ( c_in @ B @ E @ F )
| ~ ( c_in @ A @ ( c_FuncSet_OPi @ E @ ( c_COMBK @ C @ ( tc_fun @ D @ tc_bool ) @ F ) @ F @ D ) @ ( tc_fun @ F @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funcset__mem_0) ).
thf(1639,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ C @ D )
| ~ ( c_in @ B @ E @ F )
| ~ ( c_in @ A @ ( c_FuncSet_OPi @ E @ ( c_COMBK @ C @ ( tc_fun @ D @ tc_bool ) @ F ) @ F @ D ) @ ( tc_fun @ F @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(221,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(1101,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(469,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OField @ A @ B ) @ ( c_Relation_OField @ C @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mono__Field_0) ).
thf(1629,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OField @ A @ B ) @ ( c_Relation_OField @ C @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(632,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(572,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OId @ B ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__unfold_0) ).
thf(1854,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OId @ B ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ A @ B @ B ) @ ( c_Relation_ORange @ C @ B @ B ) @ ( tc_fun @ B @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_Wellfounded_Owf @ C @ B )
| ~ ( c_Wellfounded_Owf @ A @ B )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Un_0) ).
thf(1244,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ A @ B @ B ) @ ( c_Relation_ORange @ C @ B @ B ) @ ( tc_fun @ B @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_Wellfounded_Owf @ C @ B )
| ~ ( c_Wellfounded_Owf @ A @ B )
| ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(420,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
| ~ ( c_in @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(1523,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
| ~ ( c_in @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_OId @ A ) @ B @ A @ A @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__O__R_0) ).
thf(731,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_OId @ A ) @ B @ A @ A @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(304,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Osym @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_symD_0) ).
thf(1276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Osym @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(451,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( c_Transitive__Closure_Ortrancl @ C @ B ) )
| ~ ( c_lessequals @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset_0) ).
thf(1590,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( c_Transitive__Closure_Ortrancl @ C @ B ) )
| ~ ( c_lessequals @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(292,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ A @ B @ C ) @ B @ t_a @ t_a ) @ C @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ C @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_1) ).
thf(1253,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ A @ B @ C ) @ B @ t_a @ t_a ) @ C @ ( tc_prod @ t_a @ t_a ) )
| ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ C @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
thf(699,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(90,axiom,
! [B: $i,A: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId__on @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id__on_0) ).
thf(813,plain,
! [B: $i,A: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId__on @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(358,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Relation_Osym @ B @ C )
| ~ ( c_Relation_Osym @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un_0) ).
thf(1385,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Relation_Osym @ B @ C )
| ~ ( c_Relation_Osym @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(510,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
thf(1721,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(337,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl__absorb_0) ).
thf(1341,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(126,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ B @ A @ C ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ B @ A @ C ) @ C @ C ) )
| ~ ( c_in @ A @ ( c_Relation_OId__on @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_1) ).
thf(896,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ B @ A @ C ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ B @ A @ C ) @ C @ C ) )
| ~ ( c_in @ A @ ( c_Relation_OId__on @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(202,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ A @ B @ C @ D ) @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) )
| ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_1) ).
thf(1062,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ A @ B @ C @ D ) @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) )
| ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(414,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ E @ ( tc_prod @ D @ D ) )
| ~ ( c_Equiv__Relations_Ocongruent @ E @ A @ D @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent_Ocongruent_0) ).
thf(1508,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ E @ ( tc_prod @ D @ D ) )
| ~ ( c_Equiv__Relations_Ocongruent @ E @ A @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(171,axiom,
! [B: $i,A: $i] : ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un__converse_0) ).
thf(995,plain,
! [B: $i,A: $i] : ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( hAPP @ ( c_Relation_Oconverse @ B @ B ) @ A ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(437,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__subset_0) ).
thf(1558,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(576,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ E ) @ ( c_Product__Type_OSigma @ B @ F @ C @ E ) @ ( tc_prod @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD1_0) ).
thf(1861,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ E ) @ ( c_Product__Type_OSigma @ B @ F @ C @ E ) @ ( tc_prod @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(495,axiom,
! [B: $i,A: $i] :
( ( ( hAPP @ A @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ A @ B ) )
!= ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ A @ B ) @ B ) )
| ( c_Arrow__Order__Mirabelle_Odictator @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dictator__def_2) ).
thf(1689,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ A @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ A @ B ) )
!= ( hAPP @ ( v_sko__Arrow__Order__Mirabelle__Xdictator__def__1 @ A @ B ) @ B ) )
| ( c_Arrow__Order__Mirabelle_Odictator @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(314,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(1294,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(503,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_1) ).
thf(1706,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(210,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(1077,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(899,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(195,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ D ) @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseI_0) ).
thf(1045,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ D ) @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(593,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(1893,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(321,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
thf(1309,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(46,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(716,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(250,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( A = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
thf(1161,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( A = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(462,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(1614,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(236,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ E @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Equiv__Relations_Oequiv @ F @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__nondisjoint_0) ).
thf(1133,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ E @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( c_Relation_OImage @ D @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Equiv__Relations_Oequiv @ F @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
thf(620,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(752,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(534,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
| ~ ( c_Relation_Oantisym @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_1) ).
thf(1774,plain,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
| ~ ( c_Relation_Oantisym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(282,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
= B )
| ~ ( c_in @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(1229,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
= B )
| ~ ( c_in @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(363,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__trancl_0) ).
thf(1395,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(818,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(488,axiom,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_Ounanimity @ A )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3 @ A ) @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4 @ A ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ A @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ A ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_unanimity__def_3) ).
thf(1673,plain,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_Ounanimity @ A )
| ~ ( c_in @ ( c_Pair @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__3 @ A ) @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__4 @ A ) @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ A @ ( v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2 @ A ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(79,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).
thf(790,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(527,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(1757,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(55,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__absorb_0) ).
thf(735,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(512,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(1725,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(306,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(1280,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(833,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(158,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl1_0) ).
thf(967,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(151,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ C @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ C @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Sigma_0) ).
thf(950,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ C @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ C @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(100,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
thf(835,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(452,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_A_I1_J_0) ).
thf(1593,plain,
v_a____ != v_b____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(356,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(1380,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(575,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset__rtrancl_0) ).
thf(1859,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(801,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(408,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(1495,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(69,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(767,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(540,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ E @ C @ D @ F )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ E @ C @ D @ F ) @ ( c_Relation_Orel__comp @ B @ E @ C @ D @ F ) @ ( tc_fun @ ( tc_prod @ C @ F ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib2_0) ).
thf(1789,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ E @ C @ D @ F )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ E @ C @ D @ F ) @ ( c_Relation_Orel__comp @ B @ E @ C @ D @ F ) @ ( tc_fun @ ( tc_prod @ C @ F ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(97,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Id__on_0) ).
thf(828,plain,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(204,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
| ~ ( c_in @ A @ D @ B )
| ~ ( c_Relation_Orefl__on @ D @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD_0) ).
thf(1065,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
| ~ ( c_in @ A @ D @ B )
| ~ ( c_Relation_Orefl__on @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(696,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(251,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_0) ).
thf(1165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(955,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(189,axiom,
class_Lattices_Obounded__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(1033,plain,
class_Lattices_Obounded__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(310,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
thf(1288,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(505,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_1) ).
thf(1710,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) )
| ~ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(520,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ A @ B @ C @ D ) @ A @ D @ C ) @ B @ ( tc_prod @ D @ C ) )
| ~ ( c_in @ A @ ( c_Relation_ORange @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeE_0) ).
thf(1742,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ A @ B @ C @ D ) @ A @ D @ C ) @ B @ ( tc_prod @ D @ C ) )
| ~ ( c_in @ A @ ( c_Relation_ORange @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(140,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards_0) ).
thf(928,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(285,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ A @ D @ C @ E ) @ ( c_Product__Type_OSigma @ B @ D @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Un__distrib1_0) ).
thf(1236,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ A @ D @ C @ E ) @ ( c_Product__Type_OSigma @ B @ D @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(234,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ C ) @ B @ A )
= ( c_Relation_ORange @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__converse_0) ).
thf(1129,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( hAPP @ ( c_Relation_Oconverse @ A @ B ) @ C ) @ B @ A )
= ( c_Relation_ORange @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(300,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ D ) @ E ) @ ( tc_prod @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseD_0) ).
thf(1268,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ ( hAPP @ ( c_Relation_Oconverse @ C @ D ) @ E ) @ ( tc_prod @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(424,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(1532,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(427,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_reflcl__trancl_0) ).
thf(1537,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(355,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(1378,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(345,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_COMBK @ ( c_Set_Oinsert @ D @ E @ F ) @ ( tc_fun @ F @ tc_bool ) @ C ) @ C @ F )
= ( c_Set_Oinsert @ ( c_Pair @ A @ D @ C @ F ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ ( c_Set_Oinsert @ D @ E @ F ) @ ( tc_fun @ F @ tc_bool ) @ C ) @ C @ F ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_COMBK @ E @ ( tc_fun @ F @ tc_bool ) @ C ) @ C @ F ) @ ( tc_fun @ ( tc_prod @ C @ F ) @ tc_bool ) ) @ ( tc_prod @ C @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__times__insert_0) ).
thf(1357,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_COMBK @ ( c_Set_Oinsert @ D @ E @ F ) @ ( tc_fun @ F @ tc_bool ) @ C ) @ C @ F )
= ( c_Set_Oinsert @ ( c_Pair @ A @ D @ C @ F ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ ( c_Set_Oinsert @ D @ E @ F ) @ ( tc_fun @ F @ tc_bool ) @ C ) @ C @ F ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_COMBK @ E @ ( tc_fun @ F @ tc_bool ) @ C ) @ C @ F ) @ ( tc_fun @ ( tc_prod @ C @ F ) @ tc_bool ) ) @ ( tc_prod @ C @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(131,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Relation_ORange @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__empty__iff_0) ).
thf(908,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Relation_ORange @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(608,axiom,
! [A: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Relation_OId @ A ) )
= ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id_0) ).
thf(1925,plain,
! [A: $i] :
( ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Relation_OId @ A ) )
= ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(597,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_0) ).
thf(1902,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(589,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId__on @ C @ B ) @ ( tc_prod @ B @ B ) )
| ~ ( c_in @ A @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).
thf(1885,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId__on @ C @ B ) @ ( tc_prod @ B @ B ) )
| ~ ( c_in @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(728,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(57,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
thf(740,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(447,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(1582,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(183,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
!= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ D @ E @ C )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class_0) ).
thf(1019,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C )
!= ( c_Relation_OImage @ A @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C @ C ) )
| ( c_in @ ( c_Pair @ B @ D @ C @ C ) @ A @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ D @ E @ C )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(644,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(433,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
thf(1550,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(413,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
!= ( hAPP @ D @ ( hAPP @ E @ F ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ G @ H @ I ) @ C )
= ( hAPP @ ( c_Fun_Ocomp @ D @ E @ J @ H @ K ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__cong_0) ).
thf(1505,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
!= ( hAPP @ D @ ( hAPP @ E @ F ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ G @ H @ I ) @ C )
= ( hAPP @ ( c_Fun_Ocomp @ D @ E @ J @ H @ K ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(365,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ C ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ F ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ F @ ( v_sko__local__X2__1 @ C @ F @ A @ D @ B @ E ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ ( v_sko__local__X2__1 @ C @ F @ A @ D @ B @ E ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ F @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( B = D )
| ( A = E )
| ( D = E )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_2_1) ).
thf(1399,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ C ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ F ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ D @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ F @ ( v_sko__local__X2__1 @ C @ F @ A @ D @ B @ E ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ ( v_sko__local__X2__1 @ C @ F @ A @ D @ B @ E ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ F @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( B = D )
| ( A = E )
| ( D = E )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(458,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) @ A )
| ~ ( c_Wellfounded_Owf @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__converse__trancl_0) ).
thf(1606,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) @ A )
| ~ ( c_Wellfounded_Owf @ ( hAPP @ ( c_Relation_Oconverse @ A @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(146,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ C ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ ( v_sko__local__X3__1 @ D @ C @ B @ A ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ D @ ( v_sko__local__X3__1 @ D @ C @ B @ A ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ D @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_3_2) ).
thf(940,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ C ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_F @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ ( v_sko__local__X3__1 @ D @ C @ B @ A ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ D @ ( v_sko__local__X3__1 @ D @ C @ B @ A ) ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ~ ( c_in @ D @ c_Arrow__Order__Mirabelle_OProf @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(178,axiom,
! [B: $i,A: $i] :
~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(1009,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(394,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ A @ C @ D @ E ) @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ B @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__induct_0) ).
thf(1463,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xrtrancl__induct__1__1 @ A @ C @ D @ E ) @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( c_in @ ( c_Pair @ C @ B @ E @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ E ) @ ( tc_prod @ E @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(553,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_in @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(1812,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_in @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(206,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__r__into__trancl_0) ).
thf(1069,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(708,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ~ ( c_in @ B @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
thf(882,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ~ ( c_in @ B @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(406,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
thf(1490,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(191,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ A @ B @ C ) @ ( c_Wellfounded_Oacc @ A @ C ) @ C )
| ( c_in @ B @ ( c_Wellfounded_Oacc @ A @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_1) ).
thf(1037,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ A @ B @ C ) @ ( c_Wellfounded_Oacc @ A @ C ) @ C )
| ( c_in @ B @ ( c_Wellfounded_Oacc @ A @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__trancl_0) ).
thf(775,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(604,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_OField @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) @ ( c_Relation_OField @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__insert_0) ).
thf(1917,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_OField @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) @ ( c_Relation_OField @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(64,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= C )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
thf(755,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= C )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(373,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_OImage @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D @ E ) @ E )
| ~ ( c_in @ ( c_Pair @ C @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_1) ).
thf(1417,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_OImage @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D @ E ) @ E )
| ~ ( c_in @ ( c_Pair @ C @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(581,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ~ ( c_in @ ( c_Pair @ F @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) )
| ~ ( c_in @ F @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_2) ).
thf(1870,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ~ ( c_in @ ( c_Pair @ F @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) )
| ~ ( c_in @ F @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(1933,plain,
$false,
inference(e,[status(thm)],[892,1411,1767,846,1899,1840,777,1586,1501,1879,1337,1024,1469,1168,760,628,1031,1315,1850,1083,962,1818,1295,1554,1110,1200,1211,762,1596,683,1290,1618,1569,1073,1728,1793,1437,1041,1173,1750,977,1924,1005,1443,1808,873,1205,614,1692,677,1497,1608,1655,1137,797,1872,814,1260,1919,945,1458,670,747,913,1222,930,1196,1746,1127,1391,1359,1601,1366,1887,651,782,1441,973,885,1650,1921,1904,1518,1265,1623,1482,1409,1430,1298,719,785,1330,1323,1826,1313,1511,917,1577,1455,1832,934,1545,1800,1892,1147,1247,1115,1931,1641,1815,1362,1232,1847,638,853,1087,1514,1319,1704,870,1479,1609,969,1347,1572,1013,770,1875,1778,924,1465,1450,1373,1911,623,1682,1828,937,1383,1677,806,1183,821,1302,1664,1334,646,1858,1864,981,687,866,1796,1119,1351,660,998,1345,1433,1405,1201,1564,1215,634,1896,877,692,1104,1697,849,1863,1604,793,925,1153,1783,1311,1915,1708,1067,1736,714,1868,1047,1730,1057,952,1355,1255,1666,630,1238,1387,1723,957,894,825,1343,1123,862,1824,788,1883,1560,1423,1837,879,1178,665,1687,1624,830,1159,1079,1407,1634,1291,1740,1106,1402,742,1143,1762,948,1804,1328,1064,1227,1425,1096,1138,989,1397,1234,1541,1270,1772,1534,1794,1017,1375,1121,1856,725,1493,1659,1292,1584,1446,1207,1419,901,1075,1414,1842,1810,1791,1889,1644,1612,1039,1155,1744,837,701,1266,1668,1552,1192,1060,911,721,1852,1715,1720,779,1776,1263,1588,1099,1150,1249,1530,1539,1456,1131,654,1759,1393,1627,1525,792,1695,1286,1071,1026,1616,1732,765,1712,1054,1187,674,662,718,906,1135,750,618,1754,1680,1483,1273,856,745,1278,1906,1548,1927,1631,733,1389,772,1620,1752,1535,1520,1488,904,975,1007,694,843,1125,1652,1929,875,711,1795,1701,641,1786,936,1371,787,1332,1092,1258,947,1224,1675,1139,1503,1765,1090,919,804,979,1194,1209,1282,1117,1349,996,1603,737,1307,1175,1574,1806,1011,649,1043,1376,1439,890,811,858,816,1325,1029,964,668,932,1820,1877,1471,758,1339,799,1909,626,915,1556,1460,943,1022,983,1198,1474,1699,959,1213,636,1015,986,1113,1477,851,658,1562,685,1171,1528,868,1000,1435,1364,1250,1694,922,722,1034,1662,1203,1467,1684,648,1081,1145,1049,1304,1873,795,680,1181,823,1845,1748,1798,705,1225,887,971,1566,1647,1368,1780,993,1003,1770,690,1516,1598,1499,673,1186,840,808,1579,1336,1220,1300,1452,1637,1317,1830,1085,1658,1738,1218,1404,744,1543,703,1141,613,1284,1353,864,1427,1094,1670,1717,859,1898,1849,1257,656,1802,1485,1052,1881,1272,612,1240,991,1421,1839,1216,1866,1734,1108,1157,1321,1834,1913,1448,1189,1646,1639,1101,1629,632,1854,1244,1523,731,1276,1590,1253,699,813,1385,1721,1341,896,1062,1508,995,1558,1861,1689,1294,1706,1077,899,1045,1893,1309,716,1161,1614,1133,620,752,1774,1229,1395,818,1673,790,1757,735,1725,1280,833,967,950,835,1593,1380,1859,801,1495,767,1789,828,1065,696,1165,955,1033,1288,1710,1742,928,1236,1129,1268,1532,1537,1378,1357,908,1925,1902,1885,728,740,1582,1019,644,1550,1505,1399,1606,940,1009,1463,1812,1069,708,882,1490,1037,775,1917,755,1417,1870]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT061-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 15:54:36 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.82/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.50/1.07 % [INFO] Parsing done (232ms).
% 1.50/1.08 % [INFO] Running in sequential loop mode.
% 2.22/1.28 % [INFO] eprover registered as external prover.
% 2.22/1.28 % [INFO] cvc4 registered as external prover.
% 2.22/1.28 % [INFO] Scanning for conjecture ...
% 2.73/1.41 % [INFO] Found a conjecture and 610 axioms. Running axiom selection ...
% 3.37/1.55 % [INFO] Axiom selection finished. Selected 608 axioms (removed 2 axioms).
% 4.03/1.73 % [INFO] Problem is propositional (TPTP CNF).
% 4.03/1.74 % [INFO] Type checking passed.
% 4.03/1.74 % [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 ...
% 11.03/3.41 % External prover 'e' found a proof!
% 11.03/3.41 % [INFO] Killing All external provers ...
% 11.03/3.41 % Time passed: 2903ms (effective reasoning time: 2331ms)
% 11.03/3.41 % Solved by 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)>
% 11.03/3.41 % Axioms used in derivation (608): cls_inf__sup__absorb_0, cls_trancl__converseD_0, cls_converse__tranclE_1, cls_in__mktop_1, cls_rtrancl__idemp_0, cls_equiv__class__eq__iff_0, cls_sym__conv__converse__eq_1, cls_cuts__eq_1, cls_Int__Un__distrib_0, clsarity_fun__Lattices_Olower__semilattice, cls_Range__Un__eq_0, cls_inf__sup__aci_I2_J_0, cls_rtrancl__induct_3, cls_PiE_0, cls_Int__absorb2_0, cls_sym__Int__converse_0, cls_subset__insert_1, cls_2_0, cls_sup__ge1_0, cls_IIA__def_6, cls_insertE_0, cls_u_0, cls_congruent_Ocongruent_0, cls_rtrancl__converseD_0, cls_Un__subset__iff_0, cls_Pi__I_0, cls_cP_0, cls_wf__subset_0, cls_union__comp__emptyL_0, cls_order__eq__iff_0, cls_total__on__def_0, cls_converseI_0, cls_equalityI_0, cls_Id__onE_0, cls_insert__inter__insert_0, cls_iff_1, cls_single__valuedD_0, cls_wf__acyclic_0, cls_trancl__subset__Sigma__aux_0, cls_rtrancl_Ocases_0, cls_tranclD2_0, cls_Un__empty__left_0, cls_wfE__min_0, cls_single__valued__Id__on_0, cls_le__funD_0, cls_subset__empty_1, cls_Pi__mem_0, cls_rel__comp__empty1_0, cls_Image__singleton__iff_0, cls_sup__bot__right_0, cls_insert__code_1, cls_trancl_Ocases_0, clsarity_bool__Lattices_Olower__semilattice, cls_Id__O__R_0, cls_le__iff__inf_1, clsarity_fun__Orderings_Oorder, cls_COMBK__def_0, cls_acc__wfD_0, cls_distrib__sup__le_0, cls_Int__mono_0, cls_Range__def_0, cls_inf__sup__aci_I6_J_0, cls_Id__on__eqI_0, cls_A_I3_J_0, cls_Un__upper1_0, cls_Un__commute_0, cls_acc_Oinduct_2, cls_UnCI_1, cls_tranclD_0, cls_Sigma__empty1_0, cls_Int__insert__left_0, cls_insert__absorb_0, cls_comp__equivI_0, cls_empty__iff_0, cls_le__inf__iff_1, cls_mem__def_1, cls_A_I5_J_0, cls_wf__inv__image_0, cls_equiv__class__self_0, cls_Int__subset__iff_2, cls_Domain__iff_0, cls_wf__no__loop_0, cls_Int__Un__distrib2_0, cls_rtrancl__trans_0, cls_inf1E_1, cls_Domain__empty_0, cls_insert__iff_1, cls_wf__union__compatible_0, cls_insert__subset_0, cls_inf__sup__distrib1_0, cls_wf__empty_0, cls_Int__absorb1_0, cls_sup__inf__distrib2_0, cls_antisymD_0, cls_refl__on__converse_0, cls_le__sup__iff_0, cls_wf__induct__rule_0, cls_Image__Un_0, cls_in__mkbot_4, cls_Field__converse_0, clsarity_fun__Lattices_Oupper__semilattice, cls_set__rev__mp_0, cls_inf__left__commute_0, cls_Range__empty__iff_0, cls_Times__subset__cancel2_1, cls_acc_Oinducts_0, cls_converse__rtrancl__induct_3, cls_dictator__def_0, cls_congruent2_Ocongruent2_0, cls_inf__commute_0, cls_DomainE_0, cls_subset__insert__iff_2, cls_Range__Id__on_0, cls_refl__on__Id__on_0, cls_IIA__def_7, cls_Un__left__commute_0, cls_rtrancl__into__trancl1_0, cls_trancl__subset__Field2_0, cls_single__valued__Id_0, cls_rtrancl__trancl__absorb_0, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_cut__apply_0, cls_Pi__I_H_1, cls_wf__converse__trancl_0, cls_IIA__def_2, cls_Un__Int__distrib2_0, cls_Int__empty__right_0, cls_Image__iff_0, cls_sym__Id__on_0, cls_rel__compEpair_0, cls_sym__Id_0, cls_equiv__class__eq__iff_3, cls_le__supI_0, cls_rtrancl__mono_0, cls_Un__subset__iff_1, cls_rtrancl__unfold_0, cls_Un__empty_2, cls_le__iff__sup_1, cls_antisym__converse_0, cls_Image__subset_0, cls_wf__insert_0, cls_1_0, cls_IIA__def_8, cls_converse__rtranclE_1, cls_converse__rtrancl__into__rtrancl_0, cls_wfE__min_1, cls_rtrancl__reflcl_0, cls_Image__empty_0, clsarity_fun__Orderings_Obot, cls_Image__iff_1, cls_le__supE_1, cls_le__iff__sup_0, cls_Sigma__empty2_0, cls_order__eq__refl_0, cls_rtrancl__induct_2, cls_eq__equiv__class__iff2_1, cls_in__mktop_3, cls_rel__comp__distrib2_0, cls_wf__induct_1, cls_tranclE_1, cls_wf__acc__iff_1, cls_sym__trancl_0, cls_cuts__eq_0, cls_acc__wfI_0, cls_SigmaI_0, cls_IIA__def_5, cls_Un__absorb2_0, cls_trancl__into__trancl2_0, cls_inf__sup__aci_I8_J_0, cls_rtrancl__eq__or__trancl_0, cls_trancl__empty_0, cls_less__by__empty_0, cls_Un__empty__right_0, cls_insert__ident_0, cls_Image__Id__on_0, cls_Range__converse_0, cls_refl__on__empty_0, cls_r__into__trancl_H_0, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_2_1, cls_sup__eq__bot__eq2_0, cls_refl__on__def_1, cls_Int__insert__right_1, cls_sym__Un_0, cls_r__r__into__trancl_0, cls_trancl_Ocases_1, cls_wf__trancl_0, cls_rtrancl__converse_0, cls_A_I2_J_0, cls_wf__induct__rule_1, cls_Range__Int__subset_0, cls_RangeE_0, cls_unanimity__def_3, cls_antisym__reflcl_1, cls_Range__def__raw_0, cls_antisym__Id__on_0, cls_UnCI_0, cls_not__acc__down_1, cls_Un__upper2_0, cls_2_3, cls_subset__iff_0, cls_insert__code_2, cls_wf__comp__self_0, clsarity_fun__HOL_Oord, cls_Field__Un_0, cls_single__valued__rel__comp_0, cls_subset__empty_0, cls_in__mkbot_3, cls_rev__predicate1D_0, cls_converse__Un_0, cls_singleton__iff_1, cls_r__comp__rtrancl__eq_0, cls_rel__comp__distrib_0, cls_equiv__class__eq_0, cls_sym__converse_1, cls_wf__eq__minimal_0, cls_rtrancl_Ocases_1, cls_Range__iff_1, cls_wf__def_1, cls_tranclD_1, cls_Range__iff_0, cls_acc__induct_2, cls_doubleton__eq__iff_2, cls_unanimity__def_0, cls_acc__downwards__aux_0, cls_Domain__Int__subset_0, cls_inf__absorb2_0, cls_wf__comp__self_1, clsarity_bool__Lattices_Oupper__semilattice, cls_Un__insert__left_0, cls_inf__sup__ord_I2_J_0, cls_wf__irrefl_0, cls_rtrancl__Un__rtrancl_0, cls_Id__on__iff_0, cls_IdE_0, cls_SigmaD2_0, cls_set__eq__subset_2, cls_Un__mono_0, cls_insert__subset_1, cls_Int__empty__left_0, cls_Image__singleton__iff_1, cls_pair__in__Id__conv_0, cls_Field__def_0, cls_Range__insert_0, cls_sym__inv__image_0, cls_rtrancl__induct_1, cls_ex__in__conv_0, cls_sup__commute_0, cls_inf__sup__aci_I3_J_0, cls_trancl__reflcl_0, cls_trancl__domain_0, cls_converse__Id__on_0, cls_Int__insert__left_1, cls_converse__rtranclE_0, cls_le__inf__iff_0, cls_Int__subset__iff_1, cls_irrefl__tranclI_0, cls_rtrancl__reflcl__absorb_0, cls_DomainI_0, cls_Un__subset__iff_2, clsarity_fun__Lattices_Olattice, cls_wf__asym_0, cls_linorder__linear_0, cls_Un__empty_0, cls_in__mktop_5, cls_Int__assoc_0, cls_acc_Oinduct_1, cls_order__antisym_0, cls_order__trans_0, cls_acc__downwards_0, cls_wf__eq__minimal_1, cls_Times__subset__cancel2_0, cls_sym__rtrancl_0, cls_subset__trans_0, cls_inf__le2_0, cls_refl__onD2_0, cls_in__mktop_0, cls_converse__rtrancl__induct_2, cls_acc_Ocases_0, cls_insert__is__Un_0, cls_SigmaD1_0, cls_Domain__Un__eq_0, cls_Image__iff_2, cls_empty__not__insert_0, cls_sup__assoc_0, cls_Image__Int__subset_0, cls_acc_Oinduct_0, cls_A_I1_J_0, cls_in__mkbot_2, cls_Id__on__subset__Times_0, cls_insertI1_0, cls_Id__onE_1, cls_eq__equiv__class__iff2_0, cls_mono__Field_0, cls_le__sup__iff_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, cls_Un__Int__crazy_0, clsarity_bool__Orderings_Opreorder, cls_le__supE_0, cls_rel__comp__empty2_0, cls_rtrancl__eq__or__trancl_1, cls_Field__insert_0, cls_acyclic__def_0, cls_acyclic__insert_1, cls_Refl__antisym__eq__Image1__Image1__iff_0, cls_3_3, cls_in__mktop_4, cls_Int__commute_0, cls_wfE__pf_0, cls_sup__least_0, cls_tranclE_0, cls_rev__ImageI_0, cls_Domain__converse_0, cls_trancl__converseI_0, cls_empty__subsetI_0, cls_doubleton__eq__iff_0, cls_inf__sup__aci_I1_J_0, cls_dictator__def_2, cls_Un__absorb1_0, cls_sym__converse_0, cls_sup1E_0, cls_in__inv__image_1, cls_distrib__inf__le_0, cls_converse__iff_1, cls_refl__onD_0, cls_1_1, cls_subset__refl_0, cls_Pair__eq_0, cls_rtranclE_0, cls_singletonE_0, cls_Nitpick_Ortrancl__def_0, cls_total__on__empty_0, cls_IIA__def_4, cls_Image__mono_0, cls_R__O__Id_0, cls_rtrancl__Int__subset_0, cls_insertCI_0, cls_le__infE_0, cls_pair__in__Id__conv_1, cls_Range__empty_0, cls_le__inf__iff_2, cls_tranclD2_1, cls_subset__equiv__class_0, cls_trancl__into__rtrancl_0, cls_reflcl__trancl_0, cls_union__comp__emptyR_0, cls_sup1CI_1, cls_ImageE_1, cls_order__eq__iff_2, cls_le__infI1_0, cls_bot1E_0, cls_trancl__unfold__left_0, cls_inf__assoc_0, cls_rtrancl__trancl__trancl_0, cls_refl__on__Un_0, cls_Int__lower2_0, cls_rel__compI_0, cls_2_2, cls_insert__mono_0, cls_le__supI2_0, cls_IIA__def_9, cls_bex__empty_0, cls_Pi__I_1, cls_in__rtrancl__UnI_1, cls_Sigma__Un__distrib1_0, cls_Int__absorb_0, cls_converse__Id_0, cls_o__eq__dest_0, cls_Un__assoc_0, cls_unanimity__def_2, cls_antisym__reflcl_0, cls_Int__left__absorb_0, cls_wf__union__merge_0, cls_doubleton__eq__iff_3, cls_inf__sup__ord_I4_J_0, cls_total__on__converse_1, cls_acc__subset_0, cls_o__eq__dest__lhs_0, cls_converse__inv__image_0, cls_unanimity__def_1, cls_ImageE_0, cls_wf__def_0, cls_equiv_Osym_0, cls_UnE_0, cls_subset__insertI2_0, cls_converseD_0, cls_acc_OaccI_0, cls_3_0, cls_Un__absorb_0, cls_antisym__Id_0, cls_trancl__rtrancl__absorb_0, cls_order__antisym__conv_0, cls_Int__lower1_0, cls_converse__rtrancl__induct_1, clsarity_bool__Lattices_Olattice, cls_Domain__empty__iff_0, cls_Int__subset__iff_0, cls_trancl__range_0, cls_refl__on__converse_1, cls_refl__onD1_0, clsarity_bool__Lattices_Obounded__lattice, cls_inf__sup__ord_I1_J_0, cls_le__infI_0, cls_Nitpick_Orefl_H__def_0, cls_Domain__Id__on_0, cls_equiv__type_0, cls_rtrancl__subset_0, cls_rtrancl__into__trancl2_0, cls_Un__Int__distrib_0, cls_Not__Domain__rtrancl_0, cls_converse__rel__comp_0, cls_insert__subset_2, cls_le__supI1_0, cls_rtrancl__converseI_0, cls_sup__left__idem_0, cls_subsetD_0, cls_symD_0, cls_single__valued__confluent_0, cls_acc_Oinducts_2, cls_acyclic__insert_2, cls_antisym__empty_0, cls_inf__bot__left_0, cls_inf1I_0, cls_equiv_Orefl__on_0, cls_SigmaE_0, cls_sym__def_0, cls_assms_I3_J_0, cls_insert__not__empty_0, cls_Image__Id_0, cls_Int__left__commute_0, cls_le__sup__iff_2, cls_inf__idem_0, cls_trancl__Int__subset_0, clsarity_fun__Lattices_Obounded__lattice, cls_equiv__class__subset_0, cls_insert__absorb2_0, cls_IdI_0, cls_inf__sup__aci_I4_J_0, cls_irrefl__trancl__rD_0, cls_sup__inf__absorb_0, cls_xt1_I6_J_0, cls_acc__induct_1, cls_Un__Int__assoc__eq_1, cls_eq__equiv__class__iff_0, cls_converse__converse_0, cls_Id__on__empty_0, cls_IIA__def_1, cls_wf__induct_0, cls_acyclic__converse_0, cls_subset__singletonD_0, cls_RangeI_0, cls_Int__iff_2, cls_doubleton__eq__iff_1, cls_rtrancl__induct_0, cls_rtrancl_Ortrancl__refl_0, cls_Id__on__iff_1, cls_eq__equiv__class_0, cls_inf__greatest_0, cls_equiv__class__eq__iff_1, cls_cuts__eq_2, cls_in__mkbot_1, cls_tfl__wf__induct_0, cls_in__mktop_2, cls_IntI_0, cls_in__inv__image_0, cls_IIA__def_3, cls_Times__Un__distrib1_0, cls_Un__left__absorb_0, cls_converse__tranclE_0, cls_rtrancl__eq__or__trancl_2, cls_funcset__mem_0, cls_insert__times__insert_0, cls_trancl_Or__into__trancl_0, cls_singleton__inject_0, cls_tfl__wf__induct_1, cls_Un__empty_1, cls_comp__cong_0, cls_le__iff__inf_0, cls_subset__insert_0, cls_sup__idem_0, cls_emptyE_0, cls_antisym__subset_0, cls_acyclic__insert_0, cls_inf__sup__ord_I3_J_0, cls_congruent2__implies__congruent_0, cls_inf__sup__aci_I5_J_0, cls_sup__eq__bot__eq1_0, cls_comm__monoid__add_Ononempty__iff_2, cls_Times__eq__cancel2_0, cls_3_2, cls_rtrancl_Ortrancl__into__rtrancl_0, clsarity_fun__Orderings_Opreorder, cls_IntE_1, cls_rtrancl__subset__rtrancl_0, cls_trancl__unfold__right_0, cls_Int__greatest_0, cls_Domain__insert_0, cls_sup__ge2_0, cls_sym__Un__converse_0, cls_sym__conv__converse__eq_0, cls_IntE_0, cls_in__mkbot_5, cls_Un__least_0, cls_in__rtrancl__UnI_0, cls_trancl__rtrancl__trancl_0, cls_sup1CI_0, cls_subset__Un__eq_1, cls_sup__left__commute_0, cls_rel__comp__subset__Sigma_0, cls_A_I4_J_0, cls_le__infE_1, cls_iff_0, cls_mem__Sigma__iff_2, cls_refl__on__Int_0, cls_wf__Int1_0, cls_r__into__rtrancl_0, cls_rtrancl__Un__subset_0, cls_rtrancl__idemp__self__comp_0, cls_insertCI_1, cls_doubleton__eq__iff_4, cls_rtranclD_0, cls_wf__insert_2, clsarity_bool__Lattices_Odistrib__lattice, cls_acc__downward_0, cls_acc__induct__rule_1, cls_trancl__mono_0, cls_acyclic__subset_0, cls_acc__induct_0, cls_inf__le1_0, cls_rel__comp__mono_0, cls_refl__on__comp__subset_0, cls_inf__left__idem_0, cls_single__valued__subset_0, cls_acc_OaccI_1, cls_insert__code_0, cls_subset__insertI_0, cls_acc_Oinducts_1, cls_trancl__unfold_0, cls_Domain__mono_0, cls_Transitive__Closure_Otrancl__into__trancl_0, cls_antisym__def_0, cls_Image__Int__eq_0, cls_total__on__converse_0, cls_Sigma__Int__distrib1_0, cls_Field__def__raw_0, cls_converse__rtrancl__induct_0, cls_IIA__def_0, cls_trancl__trans_0, cls_Un__Image_0, cls_equiv__class__nondisjoint_0, cls_equiv__comp__eq_0, cls_converse__Int_0, cls_le__infI2_0, cls_disjoint__iff__not__equal_0, cls_Not__Domain__rtrancl_1, cls_rtrancl__empty_0, cls_Nitpick_Orefl_H__def_1, cls_Un__Int__assoc__eq_0, cls_refl__on__def_0, cls_Domain__iff_1, cls_sup__bot__left_0, cls_acc__induct__rule_0, cls_wf__insert_1, cls_sup__inf__distrib1_0, cls_insert__commute_0, cls_trancl__subset__Sigma_0, cls_complete__Lin_1, cls_insert__iff_2, cls_rtranclE_1, cls_equiv__class__eq__iff_2, cls_3_1, cls_Un__insert__right_0, cls_acyclic__impl__antisym__rtrancl_0, cls_equalityE_0, cls_sym__Int_0, cls_trancl__converse_0, cls_Times__Int__distrib1_0, cls_acyclic__converse_1, cls_wf__Un_0, cls_antisym__converse_1, cls_Pair__eq_1, cls_Pi__I_H_0, cls_inf__sup__distrib2_0, cls_wf__Int2_0, clsarity_fun__Lattices_Odistrib__lattice, cls_wf__union__merge_1, cls_O__assoc_0, cls_Field__empty_0, cls_o__apply_0, cls_inf__bot__right_0, cls_sup__absorb1_0, cls_not__acc__down_0, cls_rel__compEpair_1, cls_in__mkbot_0, cls_ball__empty_0, cls_Int__insert__right_0, cls_eq__equiv__class__iff_1, cls_acc__induct__rule_2, cls_tfl__cut__apply_0, cls_subset__insert__iff_1, cls_predicate1D_0, cls_inf1E_0, cls_o__assoc_0, cls_dictator__def_1
% 11.03/3.41 % No. of inferences in proof: 1223
% 11.03/3.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2903 ms resp. 2331 ms w/o parsing
% 12.13/3.63 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.13/3.63 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------