TSTP Solution File: SCT026-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SCT026-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n003.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 : Sun May 5 09:00:26 EDT 2024
% Result : Unsatisfiable 0.21s 0.50s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 528
% Syntax : Number of formulae : 894 ( 341 unt; 0 def)
% Number of atoms : 1813 ( 222 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 1590 ( 671 ~; 642 |; 0 &)
% ( 277 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 301 ( 299 usr; 278 prp; 0-3 aty)
% Number of functors : 50 ( 50 usr; 7 con; 0-5 aty)
% Number of variables : 1627 (1627 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3039,plain,
$false,
inference(avatar_sat_refutation,[],[f629,f634,f639,f644,f649,f654,f659,f664,f669,f674,f678,f682,f686,f690,f694,f698,f702,f706,f710,f714,f718,f722,f726,f730,f734,f738,f742,f746,f750,f754,f758,f762,f766,f770,f774,f778,f782,f786,f790,f796,f800,f805,f810,f814,f818,f822,f826,f830,f835,f839,f843,f847,f851,f855,f861,f868,f872,f876,f880,f885,f889,f893,f897,f901,f905,f909,f913,f917,f921,f925,f930,f934,f938,f942,f946,f950,f955,f985,f989,f993,f997,f1001,f1005,f1009,f1013,f1017,f1021,f1025,f1030,f1035,f1056,f1060,f1071,f1075,f1079,f1083,f1087,f1091,f1095,f1099,f1103,f1107,f1111,f1115,f1119,f1123,f1127,f1131,f1135,f1139,f1143,f1163,f1180,f1185,f1189,f1193,f1197,f1201,f1205,f1209,f1213,f1217,f1221,f1245,f1295,f1300,f1312,f1316,f1320,f1324,f1328,f1332,f1336,f1340,f1344,f1348,f1352,f1356,f1360,f1364,f1368,f1372,f1376,f1380,f1384,f1388,f1392,f1401,f1405,f1409,f1413,f1417,f1421,f1442,f1610,f1623,f1627,f1631,f1635,f1639,f1643,f1647,f1651,f1655,f1659,f1663,f1667,f1671,f1675,f1679,f1683,f1687,f1691,f1695,f1699,f1703,f1707,f1711,f1715,f1719,f1723,f1727,f1732,f1969,f1975,f2002,f2006,f2010,f2014,f2023,f2027,f2031,f2035,f2039,f2043,f2047,f2051,f2055,f2059,f2063,f2067,f2072,f2077,f2081,f2184,f2188,f2200,f2225,f2229,f2233,f2237,f2241,f2245,f2249,f2253,f2257,f2261,f2265,f2269,f2273,f2277,f2282,f2286,f2291,f2423,f2427,f2431,f2435,f2439,f2443,f2447,f2451,f2455,f2459,f2463,f2467,f2471,f2475,f2479,f2483,f2487,f2491,f2495,f2499,f2503,f2507,f2580,f2714,f2718,f2722,f2726,f2730,f2734,f2738,f2742,f2746,f2750,f2754,f2758,f2762,f2766,f2770,f2778,f2782,f2786,f2790,f2897,f2989,f3003,f3007,f3011,f3015,f3019,f3023,f3027,f3031,f3035,f3038]) ).
fof(f3038,plain,
( ~ spl0_77
| ~ spl0_268 ),
inference(avatar_contradiction_clause,[],[f3037]) ).
fof(f3037,plain,
( $false
| ~ spl0_77
| ~ spl0_268 ),
inference(resolution,[],[f2988,f954]) ).
fof(f954,plain,
( ! [X0] : c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,X0)
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f953]) ).
fof(f953,plain,
( spl0_77
<=> ! [X0] : c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f2988,plain,
( ! [X0] : ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ spl0_268 ),
inference(avatar_component_clause,[],[f2987]) ).
fof(f2987,plain,
( spl0_268
<=> ! [X0] : ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f3035,plain,
spl0_277,
inference(avatar_split_clause,[],[f295,f3033]) ).
fof(f3033,plain,
( spl0_277
<=> ! [X0,X1] : c_lessequals(c_Relation_OId__on(X0,X1),c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X1,tc_bool),X1),X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f295,axiom,
! [X0,X1] : c_lessequals(c_Relation_OId__on(X0,X1),c_Product__Type_OSigma(X0,c_COMBK(X0,tc_fun(X1,tc_bool),X1),X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__subset__Times_0) ).
fof(f3031,plain,
spl0_276,
inference(avatar_split_clause,[],[f245,f3029]) ).
fof(f3029,plain,
( spl0_276
<=> ! [X3,X11,X5,X1] :
( hBOOL(hAPP(X3,X5))
| ~ c_in(X5,c_Wellfounded_Oacc(X11,X1),X1)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X3,X11,X1),c_Wellfounded_Oacc(X11,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f245,axiom,
! [X3,X11,X1,X5] :
( hBOOL(hAPP(X3,X5))
| ~ c_in(X5,c_Wellfounded_Oacc(X11,X1),X1)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X3,X11,X1),c_Wellfounded_Oacc(X11,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct__rule_0) ).
fof(f3027,plain,
spl0_275,
inference(avatar_split_clause,[],[f240,f3025]) ).
fof(f3025,plain,
( spl0_275
<=> ! [X3,X11,X5,X1] :
( hBOOL(hAPP(X3,X5))
| ~ c_in(X5,c_Wellfounded_Oacc(X11,X1),X1)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X3,X11,X1),c_Wellfounded_Oacc(X11,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f240,axiom,
! [X3,X11,X1,X5] :
( hBOOL(hAPP(X3,X5))
| ~ c_in(X5,c_Wellfounded_Oacc(X11,X1),X1)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X3,X11,X1),c_Wellfounded_Oacc(X11,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct_0) ).
fof(f3023,plain,
spl0_274,
inference(avatar_split_clause,[],[f188,f3021]) ).
fof(f3021,plain,
( spl0_274
<=> ! [X4,X0,X12,X1] :
( ~ c_in(X4,X12,X1)
| ~ c_lessequals(X0,X12,tc_fun(X1,tc_bool))
| c_lessequals(c_Set_Oinsert(X4,X0,X1),X12,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f188,axiom,
! [X0,X1,X4,X12] :
( ~ c_in(X4,X12,X1)
| ~ c_lessequals(X0,X12,tc_fun(X1,tc_bool))
| c_lessequals(c_Set_Oinsert(X4,X0,X1),X12,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).
fof(f3019,plain,
spl0_273,
inference(avatar_split_clause,[],[f175,f3017]) ).
fof(f3017,plain,
( spl0_273
<=> ! [X5,X9,X10,X12,X1] : c_Set_Oimage(X9,c_Set_Oinsert(X5,X12,X10),X10,X1) = c_Set_Oinsert(hAPP(X9,X5),c_Set_Oimage(X9,X12,X10,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f175,axiom,
! [X10,X1,X9,X5,X12] : c_Set_Oimage(X9,c_Set_Oinsert(X5,X12,X10),X10,X1) = c_Set_Oinsert(hAPP(X9,X5),c_Set_Oimage(X9,X12,X10,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__insert_0) ).
fof(f3015,plain,
spl0_272,
inference(avatar_split_clause,[],[f125,f3013]) ).
fof(f3013,plain,
( spl0_272
<=> ! [X4,X0,X12,X1] :
( c_in(X4,X0,X1)
| c_lessequals(X0,X12,tc_fun(X1,tc_bool))
| ~ c_lessequals(X0,c_Set_Oinsert(X4,X12,X1),tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f125,axiom,
! [X0,X1,X4,X12] :
( c_in(X4,X0,X1)
| c_lessequals(X0,X12,tc_fun(X1,tc_bool))
| ~ c_lessequals(X0,c_Set_Oinsert(X4,X12,X1),tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
fof(f3011,plain,
spl0_271,
inference(avatar_split_clause,[],[f40,f3009]) ).
fof(f3009,plain,
( spl0_271
<=> ! [X4,X0,X12,X1] :
( ~ c_in(X4,X12,X1)
| ~ c_in(X4,X0,X1)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f40,axiom,
! [X0,X1,X4,X12] :
( ~ c_in(X4,X12,X1)
| ~ c_in(X4,X0,X1)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
fof(f3007,plain,
spl0_270,
inference(avatar_split_clause,[],[f7,f3005]) ).
fof(f3005,plain,
( spl0_270
<=> ! [X5,X1,X7] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X5,X7,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f7,axiom,
! [X1,X7,X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X5,c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X5,X7,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__binary_0) ).
fof(f3003,plain,
spl0_269,
inference(avatar_split_clause,[],[f1,f3001]) ).
fof(f3001,plain,
( spl0_269
<=> ! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X2,X1)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X0
| ~ c_lessequals(X0,c_Relation_OImage(X2,X0,X1,X1),tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ c_Wellfounded_Owf(X2,X1)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X0
| ~ c_lessequals(X0,c_Relation_OImage(X2,X0,X1,X1),tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wfE__pf_0) ).
fof(f2989,plain,
( spl0_268
| ~ spl0_207
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f2945,f2756,f2198,f2987]) ).
fof(f2198,plain,
( spl0_207
<=> ! [X0] : ~ c_in(c_Arrow__Order__Mirabelle_Omktop(X0,v_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f2756,plain,
( spl0_259
<=> ! [X4,X48] :
( ~ c_in(X48,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Arrow__Order__Mirabelle_Omktop(X48,X4),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f2945,plain,
( ! [X0] : ~ c_in(X0,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ spl0_207
| ~ spl0_259 ),
inference(resolution,[],[f2757,f2199]) ).
fof(f2199,plain,
( ! [X0] : ~ c_in(c_Arrow__Order__Mirabelle_Omktop(X0,v_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ spl0_207 ),
inference(avatar_component_clause,[],[f2198]) ).
fof(f2757,plain,
( ! [X48,X4] :
( c_in(c_Arrow__Order__Mirabelle_Omktop(X48,X4),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(X48,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ spl0_259 ),
inference(avatar_component_clause,[],[f2756]) ).
fof(f2897,plain,
( spl0_267
| ~ spl0_69
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f2015,f1967,f919,f2895]) ).
fof(f2895,plain,
( spl0_267
<=> ! [X0] :
( ~ c_in(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_Wellfounded_Owf(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f919,plain,
( spl0_69
<=> ! [X11,X4,X1] :
( ~ c_Wellfounded_Owf(X11,X1)
| c_in(X4,c_Wellfounded_Oacc(X11,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1967,plain,
( spl0_184
<=> ! [X0] :
( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Transitive__Closure_Ortrancl(X0,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f2015,plain,
( ! [X0] :
( ~ c_in(c_Transitive__Closure_Ortrancl(c_Wellfounded_Oacc(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_Wellfounded_Owf(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) )
| ~ spl0_69
| ~ spl0_184 ),
inference(resolution,[],[f1968,f920]) ).
fof(f920,plain,
( ! [X11,X1,X4] :
( c_in(X4,c_Wellfounded_Oacc(X11,X1),X1)
| ~ c_Wellfounded_Owf(X11,X1) )
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f919]) ).
fof(f1968,plain,
( ! [X0] :
( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Transitive__Closure_Ortrancl(X0,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f1967]) ).
fof(f2790,plain,
spl0_266,
inference(avatar_split_clause,[],[f471,f2788]) ).
fof(f2788,plain,
( spl0_266
<=> ! [X18,X4,X11,X0,X1] :
( ~ c_Relation_Orefl__on(X0,X11,X1)
| c_in(X4,X0,X1)
| ~ c_in(c_Pair(X4,X18,X1,X1),X11,tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f471,axiom,
! [X0,X11,X1,X18,X4] :
( ~ c_Relation_Orefl__on(X0,X11,X1)
| c_in(X4,X0,X1)
| ~ c_in(c_Pair(X4,X18,X1,X1),X11,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onD1_0) ).
fof(f2786,plain,
spl0_265,
inference(avatar_split_clause,[],[f470,f2784]) ).
fof(f2784,plain,
( spl0_265
<=> ! [X18,X4,X11,X0,X1] :
( ~ c_Relation_Orefl__on(X0,X11,X1)
| c_in(X18,X0,X1)
| ~ c_in(c_Pair(X4,X18,X1,X1),X11,tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f470,axiom,
! [X0,X11,X1,X18,X4] :
( ~ c_Relation_Orefl__on(X0,X11,X1)
| c_in(X18,X0,X1)
| ~ c_in(c_Pair(X4,X18,X1,X1),X11,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onD2_0) ).
fof(f2782,plain,
spl0_264,
inference(avatar_split_clause,[],[f469,f2780]) ).
fof(f2780,plain,
( spl0_264
<=> ! [X4,X11,X0,X1] :
( ~ c_Relation_Orefl__on(X0,X11,X1)
| ~ c_in(X4,X0,X1)
| c_in(c_Pair(X4,X4,X1,X1),X11,tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f469,axiom,
! [X0,X11,X1,X4] :
( ~ c_Relation_Orefl__on(X0,X11,X1)
| ~ c_in(X4,X0,X1)
| c_in(c_Pair(X4,X4,X1,X1),X11,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__def_1) ).
fof(f2778,plain,
spl0_263,
inference(avatar_split_clause,[],[f467,f2776]) ).
fof(f2776,plain,
( spl0_263
<=> ! [X10,X0,X12,X5,X1,X7] :
( c_in(X5,X0,X1)
| ~ c_in(c_Pair(X5,X7,X1,X10),c_Product__Type_OSigma(X0,X12,X1,X10),tc_prod(X1,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f467,axiom,
! [X10,X0,X1,X7,X5,X12] :
( c_in(X5,X0,X1)
| ~ c_in(c_Pair(X5,X7,X1,X10),c_Product__Type_OSigma(X0,X12,X1,X10),tc_prod(X1,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaD1_0) ).
fof(f2770,plain,
spl0_262,
inference(avatar_split_clause,[],[f461,f2768]) ).
fof(f2768,plain,
( spl0_262
<=> ! [X18,X4,X11,X0,X1] :
( ~ c_Equiv__Relations_Oequiv(X0,X11,X1)
| c_in(X4,X0,X1)
| ~ c_in(c_Pair(X4,X18,X1,X1),X11,tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f461,axiom,
! [X0,X11,X1,X18,X4] :
( ~ c_Equiv__Relations_Oequiv(X0,X11,X1)
| c_in(X4,X0,X1)
| ~ c_in(c_Pair(X4,X18,X1,X1),X11,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).
fof(f2766,plain,
spl0_261,
inference(avatar_split_clause,[],[f460,f2764]) ).
fof(f2764,plain,
( spl0_261
<=> ! [X18,X4,X11,X0,X1] :
( ~ c_Equiv__Relations_Oequiv(X0,X11,X1)
| c_in(X18,X0,X1)
| ~ c_in(c_Pair(X4,X18,X1,X1),X11,tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f460,axiom,
! [X0,X11,X1,X18,X4] :
( ~ c_Equiv__Relations_Oequiv(X0,X11,X1)
| c_in(X18,X0,X1)
| ~ c_in(c_Pair(X4,X18,X1,X1),X11,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).
fof(f2762,plain,
spl0_260,
inference(avatar_split_clause,[],[f446,f2760]) ).
fof(f2760,plain,
( spl0_260
<=> ! [X4,X48] :
( ~ c_in(X48,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Arrow__Order__Mirabelle_Omkbot(X48,X4),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f446,axiom,
! [X48,X4] :
( ~ c_in(X48,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Arrow__Order__Mirabelle_Omkbot(X48,X4),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mkbot__Lin_0) ).
fof(f2758,plain,
spl0_259,
inference(avatar_split_clause,[],[f445,f2756]) ).
fof(f445,axiom,
! [X48,X4] :
( ~ c_in(X48,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| c_in(c_Arrow__Order__Mirabelle_Omktop(X48,X4),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mktop__Lin_0) ).
fof(f2754,plain,
spl0_258,
inference(avatar_split_clause,[],[f432,f2752]) ).
fof(f2752,plain,
( spl0_258
<=> ! [X0,X8,X16,X1] :
( ~ c_in(X0,X16,X1)
| ~ c_in(X16,X8,tc_fun(X1,tc_bool))
| c_in(X0,c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f432,axiom,
! [X0,X1,X8,X16] :
( ~ c_in(X0,X16,X1)
| ~ c_in(X16,X8,tc_fun(X1,tc_bool))
| c_in(X0,c_Complete__Lattice_OSup__class_OSup(X8,tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnionI_0) ).
fof(f2750,plain,
spl0_257,
inference(avatar_split_clause,[],[f431,f2748]) ).
fof(f2748,plain,
( spl0_257
<=> ! [X0,X8,X16,X1] :
( c_in(X0,X16,X1)
| ~ c_in(X16,X8,tc_fun(X1,tc_bool))
| ~ c_in(X0,c_Complete__Lattice_OInf__class_OInf(X8,tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f431,axiom,
! [X0,X1,X8,X16] :
( c_in(X0,X16,X1)
| ~ c_in(X16,X8,tc_fun(X1,tc_bool))
| ~ c_in(X0,c_Complete__Lattice_OInf__class_OInf(X8,tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_InterD_0) ).
fof(f2746,plain,
spl0_256,
inference(avatar_split_clause,[],[f303,f2744]) ).
fof(f2744,plain,
( spl0_256
<=> ! [X41,X1,X42] :
( ~ c_lessequals(X42,X41,tc_fun(tc_prod(X1,X1),tc_bool))
| c_lessequals(c_Wellfounded_Oacc(X41,X1),c_Wellfounded_Oacc(X42,X1),tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f303,axiom,
! [X41,X1,X42] :
( ~ c_lessequals(X42,X41,tc_fun(tc_prod(X1,X1),tc_bool))
| c_lessequals(c_Wellfounded_Oacc(X41,X1),c_Wellfounded_Oacc(X42,X1),tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__subset_0) ).
fof(f2742,plain,
spl0_255,
inference(avatar_split_clause,[],[f275,f2740]) ).
fof(f2740,plain,
( spl0_255
<=> ! [X0,X8,X12,X1] :
( ~ c_lessequals(X0,X12,tc_fun(X1,tc_bool))
| ~ c_lessequals(X12,X8,tc_fun(X1,tc_bool))
| c_lessequals(X0,X8,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f275,axiom,
! [X0,X1,X8,X12] :
( ~ c_lessequals(X0,X12,tc_fun(X1,tc_bool))
| ~ c_lessequals(X12,X8,tc_fun(X1,tc_bool))
| c_lessequals(X0,X8,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).
fof(f2738,plain,
spl0_254,
inference(avatar_split_clause,[],[f203,f2736]) ).
fof(f2736,plain,
( spl0_254
<=> ! [X23,X8,X5,X1] :
( ~ c_lessequals(X8,X23,tc_fun(X1,tc_bool))
| c_lessequals(c_Set_Oinsert(X5,X8,X1),c_Set_Oinsert(X5,X23,X1),tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f203,axiom,
! [X1,X8,X5,X23] :
( ~ c_lessequals(X8,X23,tc_fun(X1,tc_bool))
| c_lessequals(c_Set_Oinsert(X5,X8,X1),c_Set_Oinsert(X5,X23,X1),tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).
fof(f2734,plain,
spl0_253,
inference(avatar_split_clause,[],[f192,f2732]) ).
fof(f2732,plain,
( spl0_253
<=> ! [X11,X1,X19] :
( ~ c_lessequals(X11,X19,tc_fun(tc_prod(X1,X1),tc_bool))
| c_lessequals(c_Relation_OField(X11,X1),c_Relation_OField(X19,X1),tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f192,axiom,
! [X11,X1,X19] :
( ~ c_lessequals(X11,X19,tc_fun(tc_prod(X1,X1),tc_bool))
| c_lessequals(c_Relation_OField(X11,X1),c_Relation_OField(X19,X1),tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mono__Field_0) ).
fof(f2730,plain,
( spl0_252
| ~ spl0_154
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f2116,f2008,f1440,f2728]) ).
fof(f2728,plain,
( spl0_252
<=> ! [X2,X0,X1] : ~ c_in(c_Set_Oinsert(X0,c_Set_Oinsert(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,X2),X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f1440,plain,
( spl0_154
<=> ! [X0,X1] : ~ c_in(c_Set_Oinsert(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,X1),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f2008,plain,
( spl0_188
<=> ! [X18,X4,X0,X1] : c_Set_Oinsert(X4,c_Set_Oinsert(X18,X0,X1),X1) = c_Set_Oinsert(X18,c_Set_Oinsert(X4,X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f2116,plain,
( ! [X2,X0,X1] : ~ c_in(c_Set_Oinsert(X0,c_Set_Oinsert(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1,X2),X2),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ spl0_154
| ~ spl0_188 ),
inference(superposition,[],[f1441,f2009]) ).
fof(f2009,plain,
( ! [X0,X18,X1,X4] : c_Set_Oinsert(X4,c_Set_Oinsert(X18,X0,X1),X1) = c_Set_Oinsert(X18,c_Set_Oinsert(X4,X0,X1),X1)
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f2008]) ).
fof(f1441,plain,
( ! [X0,X1] : ~ c_in(c_Set_Oinsert(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,X1),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ spl0_154 ),
inference(avatar_component_clause,[],[f1440]) ).
fof(f2726,plain,
spl0_251,
inference(avatar_split_clause,[],[f191,f2724]) ).
fof(f2724,plain,
( spl0_251
<=> ! [X12,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f191,axiom,
! [X0,X1,X12] : c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
fof(f2722,plain,
spl0_250,
inference(avatar_split_clause,[],[f26,f2720]) ).
fof(f2720,plain,
( spl0_250
<=> ! [X14,X10,X2,X1] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X10),tc_bool)) = c_Relation_Orel__comp(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X14,X10),tc_bool)),X1,X14,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f26,axiom,
! [X2,X10,X1,X14] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X10),tc_bool)) = c_Relation_Orel__comp(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X14,X10),tc_bool)),X1,X14,X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__empty2_0) ).
fof(f2718,plain,
spl0_249,
inference(avatar_split_clause,[],[f25,f2716]) ).
fof(f2716,plain,
( spl0_249
<=> ! [X14,X10,X2,X1] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X10),tc_bool)) = c_Relation_Orel__comp(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X14),tc_bool)),X2,X1,X14,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f25,axiom,
! [X2,X10,X1,X14] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X10),tc_bool)) = c_Relation_Orel__comp(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X14),tc_bool)),X2,X1,X14,X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__empty1_0) ).
fof(f2714,plain,
spl0_248,
inference(avatar_split_clause,[],[f18,f2712]) ).
fof(f2712,plain,
( spl0_248
<=> ! [X5,X1,X7] :
( X5 = X7
| c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) != c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f18,axiom,
! [X1,X7,X5] :
( X5 = X7
| c_Set_Oinsert(X7,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) != c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
fof(f2580,plain,
( spl0_247
| spl0_10
| ~ spl0_184
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f2202,f2079,f1967,f671,f2578]) ).
fof(f2578,plain,
( spl0_247
<=> ! [X0] : ~ c_in(c_Transitive__Closure_Ortrancl(c_Arrow__Order__Mirabelle_Omkbot(X0,v_a),tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f671,plain,
( spl0_10
<=> v_a = v_b ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f2079,plain,
( spl0_204
<=> ! [X18,X48,X4] :
( X4 = X18
| c_in(c_Pair(X4,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X48,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f2202,plain,
( ! [X0] :
( v_a = v_b
| ~ c_in(c_Transitive__Closure_Ortrancl(c_Arrow__Order__Mirabelle_Omkbot(X0,v_a),tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ spl0_184
| ~ spl0_204 ),
inference(resolution,[],[f2080,f1968]) ).
fof(f2080,plain,
( ! [X48,X18,X4] :
( c_in(c_Pair(X4,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X48,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X18 )
| ~ spl0_204 ),
inference(avatar_component_clause,[],[f2079]) ).
fof(f2507,plain,
spl0_246,
inference(avatar_split_clause,[],[f553,f2505]) ).
fof(f2505,plain,
( spl0_246
<=> ! [X1,X10] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Relation_ORange(c_Relation_Oconverse(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X10),tc_bool)),X1,X10),X10,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f553,plain,
! [X10,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Relation_ORange(c_Relation_Oconverse(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X10),tc_bool)),X1,X10),X10,X1),
inference(definition_unfolding,[],[f21,f398]) ).
fof(f398,axiom,
! [X10,X11,X1] : c_Relation_ODomain(X11,X1,X10) = c_Relation_ORange(c_Relation_Oconverse(X11,X1,X10),X10,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__converse_0) ).
fof(f21,axiom,
! [X10,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Relation_ODomain(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X10),tc_bool)),X1,X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__empty_0) ).
fof(f2503,plain,
spl0_245,
inference(avatar_split_clause,[],[f549,f2501]) ).
fof(f2501,plain,
( spl0_245
<=> ! [X11,X1] : c_Relation_Orel__comp(X11,c_Transitive__Closure_Ortrancl(X11,X1),X1,X1,X1) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X11,X1),X11,X1,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f549,plain,
! [X11,X1] : c_Relation_Orel__comp(X11,c_Transitive__Closure_Ortrancl(X11,X1),X1,X1,X1) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X11,X1),X11,X1,X1,X1),
inference(definition_unfolding,[],[f238,f237]) ).
fof(f237,axiom,
! [X11,X1] : c_Transitive__Closure_Otrancl(X11,X1) = c_Relation_Orel__comp(X11,c_Transitive__Closure_Ortrancl(X11,X1),X1,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__unfold__left_0) ).
fof(f238,axiom,
! [X11,X1] : c_Transitive__Closure_Otrancl(X11,X1) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X11,X1),X11,X1,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__unfold__right_0) ).
fof(f2499,plain,
spl0_244,
inference(avatar_split_clause,[],[f463,f2497]) ).
fof(f2497,plain,
( spl0_244
<=> ! [X5,X11,X10,X1,X7] :
( c_in(X7,c_Relation_ORange(X11,X1,X10),X10)
| ~ c_in(c_Pair(X5,X7,X1,X10),X11,tc_prod(X1,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f463,axiom,
! [X10,X11,X1,X7,X5] :
( c_in(X7,c_Relation_ORange(X11,X1,X10),X10)
| ~ c_in(c_Pair(X5,X7,X1,X10),X11,tc_prod(X1,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_RangeI_0) ).
fof(f2495,plain,
spl0_243,
inference(avatar_split_clause,[],[f393,f2493]) ).
fof(f2493,plain,
( spl0_243
<=> ! [X2,X10,X9,X1] : c_Relation_Oconverse(c_Relation_Oinv__image(X2,X9,X10,X1),X1,X1) = c_Relation_Oinv__image(c_Relation_Oconverse(X2,X10,X10),X9,X10,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f393,axiom,
! [X2,X10,X1,X9] : c_Relation_Oconverse(c_Relation_Oinv__image(X2,X9,X10,X1),X1,X1) = c_Relation_Oinv__image(c_Relation_Oconverse(X2,X10,X10),X9,X10,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__inv__image_0) ).
fof(f2491,plain,
spl0_242,
inference(avatar_split_clause,[],[f332,f2489]) ).
fof(f2489,plain,
( spl0_242
<=> ! [X11,X1] :
( c_Nitpick_Orefl_H(X11,X1)
| ~ c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X11,X1),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X11,X1),X1,X1),X11,tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f332,axiom,
! [X11,X1] :
( c_Nitpick_Orefl_H(X11,X1)
| ~ c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X11,X1),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(X11,X1),X1,X1),X11,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_1) ).
fof(f2487,plain,
spl0_241,
inference(avatar_split_clause,[],[f323,f2485]) ).
fof(f2485,plain,
( spl0_241
<=> ! [X0,X1,X8] :
( c_in(X0,c_Complete__Lattice_OInf__class_OInf(X8,tc_fun(X1,tc_bool)),X1)
| c_in(c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X0,X8,X1),X8,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f323,axiom,
! [X0,X1,X8] :
( c_in(X0,c_Complete__Lattice_OInf__class_OInf(X8,tc_fun(X1,tc_bool)),X1)
| c_in(c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X0,X8,X1),X8,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_InterI_0) ).
fof(f2483,plain,
spl0_240,
inference(avatar_split_clause,[],[f321,f2481]) ).
fof(f2481,plain,
( spl0_240
<=> ! [X11,X0,X16,X1] :
( c_in(c_List_Osko__Equiv__Relations__XquotientE__1__1(X0,X16,X11,X1),X0,X1)
| ~ c_in(X16,c_Equiv__Relations_Oquotient(X0,X11,X1),tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f321,axiom,
! [X0,X11,X1,X16] :
( c_in(c_List_Osko__Equiv__Relations__XquotientE__1__1(X0,X16,X11,X1),X0,X1)
| ~ c_in(X16,c_Equiv__Relations_Oquotient(X0,X11,X1),tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_quotientE_1) ).
fof(f2479,plain,
spl0_239,
inference(avatar_split_clause,[],[f252,f2477]) ).
fof(f2477,plain,
( spl0_239
<=> ! [X11,X0,X10,X1,X7] :
( ~ c_in(X7,c_Relation_OImage(X11,X0,X10,X1),X1)
| c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X0,X7,X11,X10,X1),X0,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f252,axiom,
! [X10,X0,X11,X1,X7] :
( ~ c_in(X7,c_Relation_OImage(X11,X0,X10,X1),X1)
| c_in(c_ATP__Linkup_Osko__Relation__XImageE__1__1(X0,X7,X11,X10,X1),X0,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ImageE_1) ).
fof(f2475,plain,
spl0_238,
inference(avatar_split_clause,[],[f251,f2473]) ).
fof(f2473,plain,
( spl0_238
<=> ! [X11,X0,X10,X1,X7] :
( ~ c_in(X7,c_Relation_OImage(X11,X0,X10,X1),X1)
| c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X0,X7,X11,X10,X1),X0,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f251,axiom,
! [X10,X0,X11,X1,X7] :
( ~ c_in(X7,c_Relation_OImage(X11,X0,X10,X1),X1)
| c_in(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1(X0,X7,X11,X10,X1),X0,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__iff_0) ).
fof(f2471,plain,
spl0_237,
inference(avatar_split_clause,[],[f247,f2469]) ).
fof(f2469,plain,
( spl0_237
<=> ! [X3,X11,X5,X1] :
( hBOOL(hAPP(X3,X5))
| ~ c_in(X5,c_Wellfounded_Oacc(X11,X1),X1)
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X3,X11,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f247,axiom,
! [X3,X11,X1,X5] :
( hBOOL(hAPP(X3,X5))
| ~ c_in(X5,c_Wellfounded_Oacc(X11,X1),X1)
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1(X3,X11,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct_2) ).
fof(f2467,plain,
spl0_236,
inference(avatar_split_clause,[],[f243,f2465]) ).
fof(f2465,plain,
( spl0_236
<=> ! [X3,X11,X5,X1] :
( hBOOL(hAPP(X3,X5))
| ~ c_in(X5,c_Wellfounded_Oacc(X11,X1),X1)
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X3,X11,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f243,axiom,
! [X3,X11,X1,X5] :
( hBOOL(hAPP(X3,X5))
| ~ c_in(X5,c_Wellfounded_Oacc(X11,X1),X1)
| ~ hBOOL(hAPP(X3,c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1(X3,X11,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct__rule_2) ).
fof(f2463,plain,
spl0_235,
inference(avatar_split_clause,[],[f200,f2461]) ).
fof(f2461,plain,
( spl0_235
<=> ! [X4,X0,X12,X1] :
( ~ hBOOL(hAPP(X0,X4))
| ~ hBOOL(hAPP(X12,X4))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f200,axiom,
! [X0,X1,X4,X12] :
( ~ hBOOL(hAPP(X0,X4))
| ~ hBOOL(hAPP(X12,X4))
| hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1I_0) ).
fof(f2459,plain,
spl0_234,
inference(avatar_split_clause,[],[f179,f2457]) ).
fof(f2457,plain,
( spl0_234
<=> ! [X18,X4,X1,X24] :
( ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X4,X18,X1)
| ~ c_lessequals(X4,X24,X1)
| c_lessequals(X4,c_Lattices_Olower__semilattice__class_Oinf(X18,X24,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f179,axiom,
! [X1,X18,X4,X24] :
( ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X4,X18,X1)
| ~ c_lessequals(X4,X24,X1)
| c_lessequals(X4,c_Lattices_Olower__semilattice__class_Oinf(X18,X24,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
fof(f2455,plain,
spl0_233,
inference(avatar_split_clause,[],[f166,f2453]) ).
fof(f2453,plain,
( spl0_233
<=> ! [X18,X4,X1,X24] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1),X24,X1) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X18,X24,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f166,axiom,
! [X1,X18,X4,X24] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1),X24,X1) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X18,X24,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
fof(f2451,plain,
spl0_232,
inference(avatar_split_clause,[],[f165,f2449]) ).
fof(f2449,plain,
( spl0_232
<=> ! [X24,X4,X18,X1] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X18,X24,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X18,c_Lattices_Olower__semilattice__class_Oinf(X4,X24,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f165,axiom,
! [X1,X18,X4,X24] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X18,X24,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X18,c_Lattices_Olower__semilattice__class_Oinf(X4,X24,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
fof(f2447,plain,
( spl0_231
| spl0_10
| ~ spl0_184
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2190,f2075,f1967,f671,f2445]) ).
fof(f2445,plain,
( spl0_231
<=> ! [X0] : ~ c_in(c_Transitive__Closure_Ortrancl(c_Arrow__Order__Mirabelle_Omktop(X0,v_b),tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f2075,plain,
( spl0_203
<=> ! [X13,X4,X48] :
( X4 = X13
| c_in(c_Pair(X13,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X48,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f2190,plain,
( ! [X0] :
( v_a = v_b
| ~ c_in(c_Transitive__Closure_Ortrancl(c_Arrow__Order__Mirabelle_Omktop(X0,v_b),tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ spl0_184
| ~ spl0_203 ),
inference(resolution,[],[f2076,f1968]) ).
fof(f2076,plain,
( ! [X48,X4,X13] :
( c_in(c_Pair(X13,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X48,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| X4 = X13 )
| ~ spl0_203 ),
inference(avatar_component_clause,[],[f2075]) ).
fof(f2443,plain,
spl0_230,
inference(avatar_split_clause,[],[f164,f2441]) ).
fof(f2441,plain,
( spl0_230
<=> ! [X24,X4,X18,X1] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X18,X24,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X18,c_Lattices_Olower__semilattice__class_Oinf(X4,X24,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f164,axiom,
! [X1,X18,X4,X24] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X18,X24,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X18,c_Lattices_Olower__semilattice__class_Oinf(X4,X24,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
fof(f2439,plain,
spl0_229,
inference(avatar_split_clause,[],[f163,f2437]) ).
fof(f2437,plain,
( spl0_229
<=> ! [X18,X4,X1,X24] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1),X24,X1) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X18,X24,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f163,axiom,
! [X1,X18,X4,X24] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1),X24,X1) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X18,X24,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
fof(f2435,plain,
spl0_228,
inference(avatar_split_clause,[],[f118,f2433]) ).
fof(f2433,plain,
( spl0_228
<=> ! [X0,X8,X12,X1] :
( c_lessequals(X8,X12,tc_fun(X1,tc_bool))
| ~ c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f118,axiom,
! [X0,X1,X8,X12] :
( c_lessequals(X8,X12,tc_fun(X1,tc_bool))
| ~ c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
fof(f2431,plain,
spl0_227,
inference(avatar_split_clause,[],[f117,f2429]) ).
fof(f2429,plain,
( spl0_227
<=> ! [X0,X8,X12,X1] :
( c_lessequals(X8,X0,tc_fun(X1,tc_bool))
| ~ c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f117,axiom,
! [X0,X1,X8,X12] :
( c_lessequals(X8,X0,tc_fun(X1,tc_bool))
| ~ c_lessequals(X8,c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
fof(f2427,plain,
spl0_226,
inference(avatar_split_clause,[],[f78,f2425]) ).
fof(f2425,plain,
( spl0_226
<=> ! [X0,X12,X6,X1] :
( ~ c_in(X6,X0,X1)
| ~ c_in(X6,X12,X1)
| c_in(X6,c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f78,axiom,
! [X0,X1,X6,X12] :
( ~ c_in(X6,X0,X1)
| ~ c_in(X6,X12,X1)
| c_in(X6,c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntI_0) ).
fof(f2423,plain,
spl0_225,
inference(avatar_split_clause,[],[f58,f2421]) ).
fof(f2421,plain,
( spl0_225
<=> ! [X11,X1,X10] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X1),tc_bool)) = X11
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Relation_ORange(X11,X10,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f58,axiom,
! [X10,X11,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X1),tc_bool)) = X11
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Relation_ORange(X11,X10,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__empty__iff_0) ).
fof(f2291,plain,
( spl0_224
| spl0_10
| ~ spl0_12
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f2203,f2079,f680,f671,f2289]) ).
fof(f2289,plain,
( spl0_224
<=> ! [X0] : ~ c_in(c_Arrow__Order__Mirabelle_Omkbot(X0,v_a),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f680,plain,
( spl0_12
<=> ! [X4] :
( ~ c_in(X4,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f2203,plain,
( ! [X0] :
( v_a = v_b
| ~ c_in(c_Arrow__Order__Mirabelle_Omkbot(X0,v_a),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ spl0_12
| ~ spl0_204 ),
inference(resolution,[],[f2080,f681]) ).
fof(f681,plain,
( ! [X4] :
( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(X4,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f680]) ).
fof(f2286,plain,
spl0_223,
inference(avatar_split_clause,[],[f614,f2284]) ).
fof(f2284,plain,
( spl0_223
<=> ! [X2,X1] :
( c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) != c_Relation_Orel__comp(X2,X2,X1,X1,X1)
| c_Wellfounded_Owf(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f614,plain,
! [X2,X1] :
( c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) != c_Relation_Orel__comp(X2,X2,X1,X1,X1)
| c_Wellfounded_Owf(X2,X1) ),
inference(forward_demodulation,[],[f59,f17]) ).
fof(f17,axiom,
! [X1] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)) = c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__empty_0) ).
fof(f59,axiom,
! [X2,X1] :
( c_Wellfounded_Owf(X2,X1)
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)) != c_Relation_Orel__comp(X2,X2,X1,X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__no__loop_0) ).
fof(f2282,plain,
spl0_222,
inference(avatar_split_clause,[],[f545,f2280]) ).
fof(f2280,plain,
( spl0_222
<=> ! [X11,X1] : c_Relation_ORange(X11,X1,X1) = c_Relation_ORange(c_Relation_Orel__comp(X11,c_Transitive__Closure_Ortrancl(X11,X1),X1,X1,X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f545,plain,
! [X11,X1] : c_Relation_ORange(X11,X1,X1) = c_Relation_ORange(c_Relation_Orel__comp(X11,c_Transitive__Closure_Ortrancl(X11,X1),X1,X1,X1),X1,X1),
inference(definition_unfolding,[],[f384,f237]) ).
fof(f384,axiom,
! [X11,X1] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X11,X1),X1,X1) = c_Relation_ORange(X11,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__range_0) ).
fof(f2277,plain,
spl0_221,
inference(avatar_split_clause,[],[f541,f2275]) ).
fof(f2275,plain,
( spl0_221
<=> ! [X2,X1] : c_Transitive__Closure_Ortrancl(X2,X1) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X2,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X1),X1),X1,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f541,plain,
! [X2,X1] : c_Transitive__Closure_Ortrancl(X2,X1) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X2,X1),c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X2,X1),X1),X1,X1,X1),
inference(definition_unfolding,[],[f291,f237]) ).
fof(f291,axiom,
! [X2,X1] : c_Transitive__Closure_Ortrancl(X2,X1) = c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X2,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__trancl__absorb_0) ).
fof(f2273,plain,
spl0_220,
inference(avatar_split_clause,[],[f459,f2271]) ).
fof(f2271,plain,
( spl0_220
<=> ! [X4,X0,X1] :
( ~ c_in(X4,X0,X1)
| c_in(c_Pair(X4,X4,X1,X1),c_Relation_OId__on(X0,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f459,axiom,
! [X0,X1,X4] :
( ~ c_in(X4,X0,X1)
| c_in(c_Pair(X4,X4,X1,X1),c_Relation_OId__on(X0,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).
fof(f2269,plain,
spl0_219,
inference(avatar_split_clause,[],[f458,f2267]) ).
fof(f2267,plain,
( spl0_219
<=> ! [X18,X4,X0,X1] :
( c_in(X4,X0,X1)
| ~ c_in(c_Pair(X4,X18,X1,X1),c_Relation_OId__on(X0,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f458,axiom,
! [X0,X1,X18,X4] :
( c_in(X4,X0,X1)
| ~ c_in(c_Pair(X4,X18,X1,X1),c_Relation_OId__on(X0,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).
fof(f2265,plain,
spl0_218,
inference(avatar_split_clause,[],[f305,f2263]) ).
fof(f2263,plain,
( spl0_218
<=> ! [X43,X10,X4,X9,X1] :
( ~ class_HOL_Oord(X10)
| ~ c_lessequals(X9,X43,tc_fun(X1,X10))
| c_lessequals(hAPP(X9,X4),hAPP(X43,X4),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f305,axiom,
! [X10,X1,X9,X4,X43] :
( ~ class_HOL_Oord(X10)
| ~ c_lessequals(X9,X43,tc_fun(X1,X10))
| c_lessequals(hAPP(X9,X4),hAPP(X43,X4),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).
fof(f2261,plain,
spl0_217,
inference(avatar_split_clause,[],[f249,f2259]) ).
fof(f2259,plain,
( spl0_217
<=> ! [X12,X0,X1] :
( ~ c_in(X12,X0,tc_fun(X1,tc_bool))
| c_lessequals(X12,c_Complete__Lattice_OSup__class_OSup(X0,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f249,axiom,
! [X0,X1,X12] :
( ~ c_in(X12,X0,tc_fun(X1,tc_bool))
| c_lessequals(X12,c_Complete__Lattice_OSup__class_OSup(X0,tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Union__upper_0) ).
fof(f2257,plain,
spl0_216,
inference(avatar_split_clause,[],[f246,f2255]) ).
fof(f2255,plain,
( spl0_216
<=> ! [X4,X11,X3] :
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X3,X11)))
| ~ c_in(X4,c_Wellfounded_Oacc(X11,t_a),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f246,axiom,
! [X3,X11,X4] :
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X3,v_sko__Wellfounded__Xacc__Xinducts__1(X3,X11)))
| ~ c_in(X4,c_Wellfounded_Oacc(X11,t_a),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinducts_2) ).
fof(f2253,plain,
spl0_215,
inference(avatar_split_clause,[],[f242,f2251]) ).
fof(f2251,plain,
( spl0_215
<=> ! [X4,X11,X3] :
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X3,X11)))
| ~ c_in(X4,c_Wellfounded_Oacc(X11,t_a),t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f242,axiom,
! [X3,X11,X4] :
( hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(X3,v_sko__Wellfounded__Xacc__Xinduct__1(X3,X11)))
| ~ c_in(X4,c_Wellfounded_Oacc(X11,t_a),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinduct_2) ).
fof(f2249,plain,
spl0_214,
inference(avatar_split_clause,[],[f236,f2247]) ).
fof(f2247,plain,
( spl0_214
<=> ! [X12,X0,X1] :
( ~ c_in(X12,X0,tc_fun(X1,tc_bool))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X0,tc_fun(X1,tc_bool)),X12,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f236,axiom,
! [X0,X1,X12] :
( ~ c_in(X12,X0,tc_fun(X1,tc_bool))
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X0,tc_fun(X1,tc_bool)),X12,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inter__lower_0) ).
fof(f2245,plain,
spl0_213,
inference(avatar_split_clause,[],[f208,f2243]) ).
fof(f2243,plain,
( spl0_213
<=> ! [X29,X4,X1] :
( ~ c_Finite__Set_Ofinite(X4,X1)
| ~ c_in(X4,X29,tc_fun(X1,tc_bool))
| c_Finite__Set_Ofinite(c_Complete__Lattice_OInf__class_OInf(X29,tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f208,axiom,
! [X29,X1,X4] :
( ~ c_Finite__Set_Ofinite(X4,X1)
| ~ c_in(X4,X29,tc_fun(X1,tc_bool))
| c_Finite__Set_Ofinite(c_Complete__Lattice_OInf__class_OInf(X29,tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Inter_0) ).
fof(f2241,plain,
spl0_212,
inference(avatar_split_clause,[],[f170,f2239]) ).
fof(f2239,plain,
( spl0_212
<=> ! [X11,X1,X19] :
( ~ c_Relation_Otrans(X11,X1)
| ~ c_Relation_Otrans(X19,X1)
| c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(X11,X19,tc_fun(tc_prod(X1,X1),tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f170,axiom,
! [X11,X1,X19] :
( ~ c_Relation_Otrans(X11,X1)
| ~ c_Relation_Otrans(X19,X1)
| c_Relation_Otrans(c_Lattices_Olower__semilattice__class_Oinf(X11,X19,tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__Int_0) ).
fof(f2237,plain,
spl0_211,
inference(avatar_split_clause,[],[f162,f2235]) ).
fof(f2235,plain,
( spl0_211
<=> ! [X11,X1] :
( ~ c_Relation_Otrans(X11,X1)
| c_lessequals(c_Relation_Orel__comp(X11,X11,X1,X1,X1),X11,tc_fun(tc_prod(X1,X1),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f162,axiom,
! [X11,X1] :
( ~ c_Relation_Otrans(X11,X1)
| c_lessequals(c_Relation_Orel__comp(X11,X11,X1,X1,X1),X11,tc_fun(tc_prod(X1,X1),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__O__subset_0) ).
fof(f2233,plain,
spl0_210,
inference(avatar_split_clause,[],[f143,f2231]) ).
fof(f2231,plain,
( spl0_210
<=> ! [X10,X9,X0,X12,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| c_Finite__Set_Ofinite(X12,X10)
| ~ c_lessequals(X12,c_Set_Oimage(X9,X0,X1,X10),tc_fun(X10,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f143,axiom,
! [X10,X0,X1,X9,X12] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| c_Finite__Set_Ofinite(X12,X10)
| ~ c_lessequals(X12,c_Set_Oimage(X9,X0,X1,X10),tc_fun(X10,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__surj_0) ).
fof(f2229,plain,
spl0_209,
inference(avatar_split_clause,[],[f73,f2227]) ).
fof(f2227,plain,
( spl0_209
<=> ! [X11,X1,X19] :
( ~ c_Relation_Osym(X11,X1)
| ~ c_Relation_Osym(X19,X1)
| c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X11,X19,tc_fun(tc_prod(X1,X1),tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f73,axiom,
! [X11,X1,X19] :
( ~ c_Relation_Osym(X11,X1)
| ~ c_Relation_Osym(X19,X1)
| c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X11,X19,tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Int_0) ).
fof(f2225,plain,
spl0_208,
inference(avatar_split_clause,[],[f24,f2223]) ).
fof(f2223,plain,
( spl0_208
<=> ! [X10,X0,X9,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)) = X0
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oimage(X9,X0,X10,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f24,axiom,
! [X10,X0,X1,X9] :
( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)) = X0
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oimage(X9,X0,X10,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
fof(f2200,plain,
( spl0_207
| spl0_10
| ~ spl0_12
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2191,f2075,f680,f671,f2198]) ).
fof(f2191,plain,
( ! [X0] :
( v_a = v_b
| ~ c_in(c_Arrow__Order__Mirabelle_Omktop(X0,v_b),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ spl0_12
| ~ spl0_203 ),
inference(resolution,[],[f2076,f681]) ).
fof(f2188,plain,
( spl0_206
| ~ spl0_128
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f2073,f2070,f1314,f2186]) ).
fof(f2186,plain,
( spl0_206
<=> ! [X2,X1,X10] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1),X2,X1,X1,X10) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f1314,plain,
( spl0_128
<=> ! [X1] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)) = c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f2070,plain,
( spl0_202
<=> ! [X2,X1,X10] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X2,X1,X1,X10) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f2073,plain,
( ! [X2,X10,X1] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1),X2,X1,X1,X10) = X2
| ~ spl0_128
| ~ spl0_202 ),
inference(forward_demodulation,[],[f2071,f1315]) ).
fof(f1315,plain,
( ! [X1] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)) = c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f1314]) ).
fof(f2071,plain,
( ! [X2,X10,X1] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X2,X1,X1,X10) = X2
| ~ spl0_202 ),
inference(avatar_component_clause,[],[f2070]) ).
fof(f2184,plain,
( spl0_205
| ~ spl0_128
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2068,f2065,f1314,f2182]) ).
fof(f2182,plain,
( spl0_205
<=> ! [X2,X1,X10] : c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10),X10),X1,X10,X10) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f2065,plain,
( spl0_201
<=> ! [X2,X1,X10] : c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_bool)),X10),X1,X10,X10) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f2068,plain,
( ! [X2,X10,X1] : c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10),X10),X1,X10,X10) = X2
| ~ spl0_128
| ~ spl0_201 ),
inference(forward_demodulation,[],[f2066,f1315]) ).
fof(f2066,plain,
( ! [X2,X10,X1] : c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_bool)),X10),X1,X10,X10) = X2
| ~ spl0_201 ),
inference(avatar_component_clause,[],[f2065]) ).
fof(f2081,plain,
spl0_204,
inference(avatar_split_clause,[],[f611,f2079]) ).
fof(f611,plain,
! [X48,X18,X4] :
( X4 = X18
| c_in(c_Pair(X4,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X48,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(duplicate_literal_removal,[],[f438]) ).
fof(f438,axiom,
! [X48,X18,X4] :
( X4 = X18
| X4 = X18
| c_in(c_Pair(X4,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X48,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_4) ).
fof(f2077,plain,
spl0_203,
inference(avatar_split_clause,[],[f610,f2075]) ).
fof(f610,plain,
! [X48,X4,X13] :
( X4 = X13
| c_in(c_Pair(X13,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X48,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
inference(duplicate_literal_removal,[],[f443]) ).
fof(f443,axiom,
! [X48,X4,X13] :
( X4 = X13
| X4 = X13
| c_in(c_Pair(X13,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X48,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_4) ).
fof(f2072,plain,
spl0_202,
inference(avatar_split_clause,[],[f544,f2070]) ).
fof(f544,plain,
! [X2,X10,X1] : c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X2,X1,X1,X10) = X2,
inference(definition_unfolding,[],[f372,f23]) ).
fof(f23,axiom,
! [X1] : c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) = c_Relation_OId(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__empty_0) ).
fof(f372,axiom,
! [X2,X10,X1] : c_Relation_Orel__comp(c_Relation_OId(X1),X2,X1,X1,X10) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__O__R_0) ).
fof(f2067,plain,
spl0_201,
inference(avatar_split_clause,[],[f543,f2065]) ).
fof(f543,plain,
! [X2,X10,X1] : c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_bool)),X10),X1,X10,X10) = X2,
inference(definition_unfolding,[],[f373,f23]) ).
fof(f373,axiom,
! [X2,X10,X1] : c_Relation_Orel__comp(X2,c_Relation_OId(X10),X1,X10,X10) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_R__O__Id_0) ).
fof(f2063,plain,
( spl0_200
| ~ spl0_137
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f2017,f1967,f1350,f2061]) ).
fof(f2061,plain,
( spl0_200
<=> ! [X0,X1] : ~ c_in(c_Transitive__Closure_Ortrancl(c_Set_Oinsert(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,X1),tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f1350,plain,
( spl0_137
<=> ! [X0,X3,X2,X1] : c_in(X0,c_Set_Oinsert(X0,X1,X2),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f2017,plain,
( ! [X0,X1] : ~ c_in(c_Transitive__Closure_Ortrancl(c_Set_Oinsert(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,X1),tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ spl0_137
| ~ spl0_184 ),
inference(resolution,[],[f1968,f1351]) ).
fof(f1351,plain,
( ! [X2,X3,X0,X1] : c_in(X0,c_Set_Oinsert(X0,X1,X2),X3)
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1350]) ).
fof(f2059,plain,
spl0_199,
inference(avatar_split_clause,[],[f533,f2057]) ).
fof(f2057,plain,
( spl0_199
<=> ! [X11,X1,X10] : c_Relation_ORange(X11,X10,X1) = c_Relation_ORange(c_Relation_Oconverse(c_Relation_Oconverse(X11,X10,X1),X1,X10),X10,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f533,plain,
! [X10,X11,X1] : c_Relation_ORange(X11,X10,X1) = c_Relation_ORange(c_Relation_Oconverse(c_Relation_Oconverse(X11,X10,X1),X1,X10),X10,X1),
inference(definition_unfolding,[],[f408,f398]) ).
fof(f408,axiom,
! [X10,X11,X1] : c_Relation_ORange(X11,X10,X1) = c_Relation_ODomain(c_Relation_Oconverse(X11,X10,X1),X1,X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__def_0) ).
fof(f2055,plain,
spl0_198,
inference(avatar_split_clause,[],[f413,f2053]) ).
fof(f2053,plain,
( spl0_198
<=> ! [X18,X4,X0,X1] :
( X4 = X18
| ~ c_in(c_Pair(X4,X18,X1,X1),c_Relation_OId__on(X0,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f413,axiom,
! [X0,X18,X1,X4] :
( X4 = X18
| ~ c_in(c_Pair(X4,X18,X1,X1),c_Relation_OId__on(X0,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).
fof(f2051,plain,
spl0_197,
inference(avatar_split_clause,[],[f401,f2049]) ).
fof(f2049,plain,
( spl0_197
<=> ! [X11,X0,X1] :
( ~ c_Equiv__Relations_Oequiv(X0,X11,X1)
| c_Relation_Orel__comp(c_Relation_Oconverse(X11,X1,X1),X11,X1,X1,X1) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f401,axiom,
! [X0,X11,X1] :
( ~ c_Equiv__Relations_Oequiv(X0,X11,X1)
| c_Relation_Orel__comp(c_Relation_Oconverse(X11,X1,X1),X11,X1,X1,X1) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__comp__eq_0) ).
fof(f2047,plain,
spl0_196,
inference(avatar_split_clause,[],[f326,f2045]) ).
fof(f2045,plain,
( spl0_196
<=> ! [X6,X0,X1] :
( c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X0,X6,X1),X0,X1)
| ~ c_in(X6,c_Relation_OId__on(X0,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f326,axiom,
! [X0,X1,X6] :
( c_in(c_ATP__Linkup_Osko__Relation__XId__onE__1__1(X0,X6,X1),X0,X1)
| ~ c_in(X6,c_Relation_OId__on(X0,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__onE_0) ).
fof(f2043,plain,
spl0_195,
inference(avatar_split_clause,[],[f287,f2041]) ).
fof(f2041,plain,
( spl0_195
<=> ! [X0,X12,X1] :
( X0 = X12
| ~ c_lessequals(X0,X12,tc_fun(X1,tc_bool))
| ~ c_lessequals(X12,X0,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f287,axiom,
! [X0,X1,X12] :
( X0 = X12
| ~ c_lessequals(X0,X12,tc_fun(X1,tc_bool))
| ~ c_lessequals(X12,X0,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).
fof(f2039,plain,
spl0_194,
inference(avatar_split_clause,[],[f244,f2037]) ).
fof(f2037,plain,
( spl0_194
<=> ! [X2,X1,X4] :
( c_in(X4,c_Wellfounded_Oacc(X2,X1),X1)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X2,X4,X1),c_Wellfounded_Oacc(X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f244,axiom,
! [X2,X1,X4] :
( c_in(X4,c_Wellfounded_Oacc(X2,X1),X1)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1(X2,X4,X1),c_Wellfounded_Oacc(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__acc__down_1) ).
fof(f2035,plain,
spl0_193,
inference(avatar_split_clause,[],[f241,f2033]) ).
fof(f2033,plain,
( spl0_193
<=> ! [X11,X4,X1] :
( c_in(X4,c_Wellfounded_Oacc(X11,X1),X1)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X11,X4,X1),c_Wellfounded_Oacc(X11,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f241,axiom,
! [X11,X1,X4] :
( c_in(X4,c_Wellfounded_Oacc(X11,X1),X1)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1(X11,X4,X1),c_Wellfounded_Oacc(X11,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_OaccI_1) ).
fof(f2031,plain,
spl0_192,
inference(avatar_split_clause,[],[f239,f2029]) ).
fof(f2029,plain,
( spl0_192
<=> ! [X0,X1,X8] :
( ~ c_in(X0,c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X0,X8,X1),X1)
| c_in(X0,c_Complete__Lattice_OInf__class_OInf(X8,tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f239,axiom,
! [X0,X1,X8] :
( ~ c_in(X0,c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1(X0,X8,X1),X1)
| c_in(X0,c_Complete__Lattice_OInf__class_OInf(X8,tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_InterI_1) ).
fof(f2027,plain,
spl0_191,
inference(avatar_split_clause,[],[f146,f2025]) ).
fof(f2025,plain,
( spl0_191
<=> ! [X5,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X5,X0,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Complete__Lattice_OInf__class_OInf(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f146,axiom,
! [X0,X1,X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X5,X0,X1),X1) = c_Lattices_Olower__semilattice__class_Oinf(X5,c_Complete__Lattice_OInf__class_OInf(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__insert_0) ).
fof(f2023,plain,
spl0_190,
inference(avatar_split_clause,[],[f145,f2021]) ).
fof(f2021,plain,
( spl0_190
<=> ! [X0,X12,X1,X7] :
( ~ c_lessequals(X0,X12,tc_fun(X1,tc_bool))
| c_lessequals(X0,c_Set_Oinsert(X7,X12,X1),tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f145,axiom,
! [X0,X1,X7,X12] :
( ~ c_lessequals(X0,X12,tc_fun(X1,tc_bool))
| c_lessequals(X0,c_Set_Oinsert(X7,X12,X1),tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
fof(f2014,plain,
spl0_189,
inference(avatar_split_clause,[],[f144,f2012]) ).
fof(f2012,plain,
( spl0_189
<=> ! [X12,X0,X1,X4] :
( c_lessequals(X0,X12,tc_fun(X1,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X4,X0,X1),X12,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f144,axiom,
! [X0,X1,X4,X12] :
( c_lessequals(X0,X12,tc_fun(X1,tc_bool))
| ~ c_lessequals(c_Set_Oinsert(X4,X0,X1),X12,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).
fof(f2010,plain,
spl0_188,
inference(avatar_split_clause,[],[f139,f2008]) ).
fof(f139,axiom,
! [X0,X18,X1,X4] : c_Set_Oinsert(X4,c_Set_Oinsert(X18,X0,X1),X1) = c_Set_Oinsert(X18,c_Set_Oinsert(X4,X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).
fof(f2006,plain,
spl0_187,
inference(avatar_split_clause,[],[f47,f2004]) ).
fof(f2004,plain,
( spl0_187
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X0
| ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f47,axiom,
! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = X0
| ~ c_lessequals(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).
fof(f2002,plain,
spl0_186,
inference(avatar_split_clause,[],[f13,f2000]) ).
fof(f2000,plain,
( spl0_186
<=> ! [X12,X1,X10] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X10),tc_bool)) = c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X12,X1,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f13,axiom,
! [X10,X1,X12] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X10),tc_bool)) = c_Product__Type_OSigma(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X12,X1,X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sigma__empty1_0) ).
fof(f1975,plain,
( spl0_185
| ~ spl0_128
| ~ spl0_182 ),
inference(avatar_split_clause,[],[f1728,f1725,f1314,f1973]) ).
fof(f1973,plain,
( spl0_185
<=> ! [X0,X1] : c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1),X0,X1,X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f1725,plain,
( spl0_182
<=> ! [X0,X1] : c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X0,X1,X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f1728,plain,
( ! [X0,X1] : c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1),X0,X1,X1) = X0
| ~ spl0_128
| ~ spl0_182 ),
inference(forward_demodulation,[],[f1726,f1315]) ).
fof(f1726,plain,
( ! [X0,X1] : c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X0,X1,X1) = X0
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f1725]) ).
fof(f1969,plain,
( spl0_184
| ~ spl0_12
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f1962,f1709,f680,f1967]) ).
fof(f1709,plain,
( spl0_178
<=> ! [X11,X1,X30] :
( ~ c_in(X30,X11,tc_prod(X1,X1))
| c_in(X30,c_Transitive__Closure_Ortrancl(X11,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1962,plain,
( ! [X0] :
( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Transitive__Closure_Ortrancl(X0,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ spl0_12
| ~ spl0_178 ),
inference(resolution,[],[f1710,f681]) ).
fof(f1710,plain,
( ! [X11,X1,X30] :
( c_in(X30,c_Transitive__Closure_Ortrancl(X11,X1),tc_prod(X1,X1))
| ~ c_in(X30,X11,tc_prod(X1,X1)) )
| ~ spl0_178 ),
inference(avatar_component_clause,[],[f1709]) ).
fof(f1732,plain,
spl0_183,
inference(avatar_split_clause,[],[f542,f1730]) ).
fof(f1730,plain,
( spl0_183
<=> ! [X2,X1] : c_Transitive__Closure_Ortrancl(X2,X1) = c_Transitive__Closure_Ortrancl(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X1),X1,X1,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f542,plain,
! [X2,X1] : c_Transitive__Closure_Ortrancl(X2,X1) = c_Transitive__Closure_Ortrancl(c_Relation_Orel__comp(X2,c_Transitive__Closure_Ortrancl(X2,X1),X1,X1,X1),X1),
inference(definition_unfolding,[],[f266,f237]) ).
fof(f266,axiom,
! [X2,X1] : c_Transitive__Closure_Ortrancl(X2,X1) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X2,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).
fof(f1727,plain,
spl0_182,
inference(avatar_split_clause,[],[f540,f1725]) ).
fof(f540,plain,
! [X0,X1] : c_Relation_OImage(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X0,X1,X1) = X0,
inference(definition_unfolding,[],[f380,f23]) ).
fof(f380,axiom,
! [X0,X1] : c_Relation_OImage(c_Relation_OId(X1),X0,X1,X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Id_0) ).
fof(f1723,plain,
spl0_181,
inference(avatar_split_clause,[],[f504,f1721]) ).
fof(f1721,plain,
( spl0_181
<=> ! [X49,X10,X50,X5,X1,X7] :
( X5 = X49
| c_Pair(X5,X7,X1,X10) != c_Pair(X49,X50,X1,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f504,axiom,
! [X50,X10,X49,X1,X7,X5] :
( X5 = X49
| c_Pair(X5,X7,X1,X10) != c_Pair(X49,X50,X1,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
fof(f1719,plain,
spl0_180,
inference(avatar_split_clause,[],[f503,f1717]) ).
fof(f1717,plain,
( spl0_180
<=> ! [X5,X49,X7,X50,X10,X1] :
( X7 = X50
| c_Pair(X5,X7,X1,X10) != c_Pair(X49,X50,X1,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f503,axiom,
! [X50,X10,X49,X1,X7,X5] :
( X7 = X50
| c_Pair(X5,X7,X1,X10) != c_Pair(X49,X50,X1,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
fof(f1715,plain,
spl0_179,
inference(avatar_split_clause,[],[f405,f1713]) ).
fof(f1713,plain,
( spl0_179
<=> ! [X11,X0,X1] :
( ~ c_Equiv__Relations_Oequiv(X0,X11,X1)
| c_Complete__Lattice_OSup__class_OSup(c_Equiv__Relations_Oquotient(X0,X11,X1),tc_fun(X1,tc_bool)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f405,axiom,
! [X0,X11,X1] :
( ~ c_Equiv__Relations_Oequiv(X0,X11,X1)
| c_Complete__Lattice_OSup__class_OSup(c_Equiv__Relations_Oquotient(X0,X11,X1),tc_fun(X1,tc_bool)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Union__quotient_0) ).
fof(f1711,plain,
spl0_178,
inference(avatar_split_clause,[],[f310,f1709]) ).
fof(f310,axiom,
! [X11,X1,X30] :
( ~ c_in(X30,X11,tc_prod(X1,X1))
| c_in(X30,c_Transitive__Closure_Ortrancl(X11,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).
fof(f1707,plain,
spl0_177,
inference(avatar_split_clause,[],[f308,f1705]) ).
fof(f1705,plain,
( spl0_177
<=> ! [X0,X12,X6,X1] :
( ~ c_in(X6,X0,X1)
| c_in(X6,X12,X1)
| ~ c_lessequals(X0,X12,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f308,axiom,
! [X0,X1,X6,X12] :
( ~ c_in(X6,X0,X1)
| c_in(X6,X12,X1)
| ~ c_lessequals(X0,X12,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).
fof(f1703,plain,
spl0_176,
inference(avatar_split_clause,[],[f288,f1701]) ).
fof(f1701,plain,
( spl0_176
<=> ! [X2,X1] : c_Transitive__Closure_Ortrancl(X2,X1) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X2,X1),c_Transitive__Closure_Ortrancl(X2,X1),X1,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f288,axiom,
! [X2,X1] : c_Transitive__Closure_Ortrancl(X2,X1) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X2,X1),c_Transitive__Closure_Ortrancl(X2,X1),X1,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__idemp__self__comp_0) ).
fof(f1699,plain,
spl0_175,
inference(avatar_split_clause,[],[f279,f1697]) ).
fof(f1697,plain,
( spl0_175
<=> ! [X24,X4,X18,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X18,X4,X1)
| ~ c_lessequals(X24,X18,X1)
| c_lessequals(X24,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f279,axiom,
! [X1,X18,X4,X24] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X18,X4,X1)
| ~ c_lessequals(X24,X18,X1)
| c_lessequals(X24,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f1695,plain,
( spl0_174
| ~ spl0_121
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f1594,f1403,f1211,f1693]) ).
fof(f1693,plain,
( spl0_174
<=> ! [X0,X1] : ~ c_Wellfounded_Owf(c_Transitive__Closure_Ortrancl(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f1211,plain,
( spl0_121
<=> ! [X11,X5,X1] : c_in(c_Pair(X5,X5,X1,X1),c_Transitive__Closure_Ortrancl(X11,X1),tc_prod(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f1403,plain,
( spl0_149
<=> ! [X11,X5,X1] :
( ~ c_Wellfounded_Owf(X11,X1)
| ~ c_in(c_Pair(X5,X5,X1,X1),X11,tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1594,plain,
( ! [X0,X1] : ~ c_Wellfounded_Owf(c_Transitive__Closure_Ortrancl(X0,X1),X1)
| ~ spl0_121
| ~ spl0_149 ),
inference(resolution,[],[f1404,f1212]) ).
fof(f1212,plain,
( ! [X11,X1,X5] : c_in(c_Pair(X5,X5,X1,X1),c_Transitive__Closure_Ortrancl(X11,X1),tc_prod(X1,X1))
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f1211]) ).
fof(f1404,plain,
( ! [X11,X1,X5] :
( ~ c_in(c_Pair(X5,X5,X1,X1),X11,tc_prod(X1,X1))
| ~ c_Wellfounded_Owf(X11,X1) )
| ~ spl0_149 ),
inference(avatar_component_clause,[],[f1403]) ).
fof(f1691,plain,
spl0_173,
inference(avatar_split_clause,[],[f278,f1689]) ).
fof(f1689,plain,
( spl0_173
<=> ! [X18,X4,X1,X24] :
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X18,X1)
| ~ c_lessequals(X18,X24,X1)
| c_lessequals(X4,X24,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f278,axiom,
! [X1,X18,X4,X24] :
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X18,X1)
| ~ c_lessequals(X18,X24,X1)
| c_lessequals(X4,X24,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f1687,plain,
spl0_172,
inference(avatar_split_clause,[],[f273,f1685]) ).
fof(f1685,plain,
( spl0_172
<=> ! [X11,X1,X30] :
( ~ c_Wellfounded_Owf(X11,X1)
| c_Wellfounded_Owf(X30,X1)
| ~ c_lessequals(X30,X11,tc_fun(tc_prod(X1,X1),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f273,axiom,
! [X11,X1,X30] :
( ~ c_Wellfounded_Owf(X11,X1)
| c_Wellfounded_Owf(X30,X1)
| ~ c_lessequals(X30,X11,tc_fun(tc_prod(X1,X1),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__subset_0) ).
fof(f1683,plain,
spl0_171,
inference(avatar_split_clause,[],[f270,f1681]) ).
fof(f1681,plain,
( spl0_171
<=> ! [X11,X1,X19] :
( ~ c_Relation_Oantisym(X19,X1)
| c_Relation_Oantisym(X11,X1)
| ~ c_lessequals(X11,X19,tc_fun(tc_prod(X1,X1),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f270,axiom,
! [X11,X1,X19] :
( ~ c_Relation_Oantisym(X19,X1)
| c_Relation_Oantisym(X11,X1)
| ~ c_lessequals(X11,X19,tc_fun(tc_prod(X1,X1),tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__subset_0) ).
fof(f1679,plain,
spl0_170,
inference(avatar_split_clause,[],[f269,f1677]) ).
fof(f1677,plain,
( spl0_170
<=> ! [X31,X4,X3,X1] :
( ~ hBOOL(hAPP(X3,X4))
| hBOOL(hAPP(X31,X4))
| ~ c_lessequals(X3,X31,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f269,axiom,
! [X31,X3,X1,X4] :
( ~ hBOOL(hAPP(X3,X4))
| hBOOL(hAPP(X31,X4))
| ~ c_lessequals(X3,X31,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
fof(f1675,plain,
spl0_169,
inference(avatar_split_clause,[],[f255,f1673]) ).
fof(f1673,plain,
( spl0_169
<=> ! [X31,X11,X13,X1] :
( ~ c_Wellfounded_Owf(X11,X1)
| ~ c_in(X13,X31,X1)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X31,X11,X1),X31,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f255,axiom,
! [X31,X11,X1,X13] :
( ~ c_Wellfounded_Owf(X11,X1)
| ~ c_in(X13,X31,X1)
| c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1(X31,X11,X1),X31,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__eq__minimal_0) ).
fof(f1671,plain,
spl0_168,
inference(avatar_split_clause,[],[f254,f1669]) ).
fof(f1669,plain,
( spl0_168
<=> ! [X31,X4,X2,X1] :
( ~ c_Wellfounded_Owf(X2,X1)
| ~ c_in(X4,X31,X1)
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X31,X2,X1),X31,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f254,axiom,
! [X2,X31,X1,X4] :
( ~ c_Wellfounded_Owf(X2,X1)
| ~ c_in(X4,X31,X1)
| c_in(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1(X31,X2,X1),X31,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wfE__min_0) ).
fof(f1667,plain,
spl0_167,
inference(avatar_split_clause,[],[f210,f1665]) ).
fof(f1665,plain,
( spl0_167
<=> ! [X12,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)) = c_Relation_OImage(c_Relation_OId__on(X0,X1),X12,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f210,axiom,
! [X0,X1,X12] : c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)) = c_Relation_OImage(c_Relation_OId__on(X0,X1),X12,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Id__on_0) ).
fof(f1663,plain,
spl0_166,
inference(avatar_split_clause,[],[f190,f1661]) ).
fof(f1661,plain,
( spl0_166
<=> ! [X18,X1,X4] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f190,axiom,
! [X1,X18,X4] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
fof(f1659,plain,
spl0_165,
inference(avatar_split_clause,[],[f189,f1657]) ).
fof(f1657,plain,
( spl0_165
<=> ! [X18,X1,X4] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f189,axiom,
! [X1,X18,X4] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
fof(f1655,plain,
spl0_164,
inference(avatar_split_clause,[],[f152,f1653]) ).
fof(f1653,plain,
( spl0_164
<=> ! [X18,X4,X0,X1] :
( X4 = X18
| hBOOL(hAPP(X0,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X18,X0,X1),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f152,axiom,
! [X0,X18,X1,X4] :
( X4 = X18
| hBOOL(hAPP(X0,X4))
| ~ hBOOL(hAPP(c_Set_Oinsert(X18,X0,X1),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).
fof(f1651,plain,
( spl0_163
| ~ spl0_123
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1585,f1399,f1219,f1649]) ).
fof(f1649,plain,
( spl0_163
<=> ! [X0,X1] : ~ c_Nitpick_Orefl_H(c_Arrow__Order__Mirabelle_Omkbot(X0,X1),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f1219,plain,
( spl0_123
<=> ! [X13,X4,X48] : ~ c_in(c_Pair(X13,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X48,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1399,plain,
( spl0_148
<=> ! [X11,X4,X1] :
( ~ c_Nitpick_Orefl_H(X11,X1)
| c_in(c_Pair(X4,X4,X1,X1),X11,tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f1585,plain,
( ! [X0,X1] : ~ c_Nitpick_Orefl_H(c_Arrow__Order__Mirabelle_Omkbot(X0,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_123
| ~ spl0_148 ),
inference(resolution,[],[f1400,f1220]) ).
fof(f1220,plain,
( ! [X48,X4,X13] : ~ c_in(c_Pair(X13,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X48,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f1219]) ).
fof(f1400,plain,
( ! [X11,X1,X4] :
( c_in(c_Pair(X4,X4,X1,X1),X11,tc_prod(X1,X1))
| ~ c_Nitpick_Orefl_H(X11,X1) )
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f1399]) ).
fof(f1647,plain,
spl0_162,
inference(avatar_split_clause,[],[f138,f1645]) ).
fof(f1645,plain,
( spl0_162
<=> ! [X12,X0,X1] :
( ~ c_lessequals(X0,X12,tc_fun(X1,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f138,axiom,
! [X0,X1,X12] :
( ~ c_lessequals(X0,X12,tc_fun(X1,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
fof(f1643,plain,
spl0_161,
inference(avatar_split_clause,[],[f137,f1641]) ).
fof(f1641,plain,
( spl0_161
<=> ! [X12,X0,X1] :
( ~ c_lessequals(X12,X0,tc_fun(X1,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f137,axiom,
! [X0,X1,X12] :
( ~ c_lessequals(X12,X0,tc_fun(X1,tc_bool))
| c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)) = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
fof(f1639,plain,
spl0_160,
inference(avatar_split_clause,[],[f89,f1637]) ).
fof(f1637,plain,
( spl0_160
<=> ! [X4,X0,X9,X22,X1] :
( ~ c_in(X4,X0,X22)
| c_in(hAPP(X9,X4),c_Set_Oimage(X9,X0,X22,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f89,axiom,
! [X0,X1,X9,X4,X22] :
( ~ c_in(X4,X0,X22)
| c_in(hAPP(X9,X4),c_Set_Oimage(X9,X0,X22,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
fof(f1635,plain,
spl0_159,
inference(avatar_split_clause,[],[f81,f1633]) ).
fof(f1633,plain,
( spl0_159
<=> ! [X7,X0,X5,X1] :
( X5 = X7
| c_in(X5,X0,X1)
| ~ c_in(X5,c_Set_Oinsert(X7,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f81,axiom,
! [X0,X1,X7,X5] :
( X5 = X7
| c_in(X5,X0,X1)
| ~ c_in(X5,c_Set_Oinsert(X7,X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).
fof(f1631,plain,
spl0_158,
inference(avatar_split_clause,[],[f42,f1629]) ).
fof(f1629,plain,
( spl0_158
<=> ! [X1,X10] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X1),tc_bool)),X10,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f42,axiom,
! [X10,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Relation_ORange(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X1),tc_bool)),X10,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__empty_0) ).
fof(f1627,plain,
spl0_157,
inference(avatar_split_clause,[],[f35,f1625]) ).
fof(f1625,plain,
( spl0_157
<=> ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f35,axiom,
! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
fof(f1623,plain,
spl0_156,
inference(avatar_split_clause,[],[f34,f1621]) ).
fof(f1621,plain,
( spl0_156
<=> ! [X12,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X12,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f34,axiom,
! [X1,X12] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X12,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
fof(f1610,plain,
( spl0_155
| ~ spl0_122
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1584,f1399,f1215,f1608]) ).
fof(f1608,plain,
( spl0_155
<=> ! [X0,X1] : ~ c_Nitpick_Orefl_H(c_Arrow__Order__Mirabelle_Omktop(X0,X1),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1215,plain,
( spl0_122
<=> ! [X4,X48,X18] : ~ c_in(c_Pair(X4,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X48,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f1584,plain,
( ! [X0,X1] : ~ c_Nitpick_Orefl_H(c_Arrow__Order__Mirabelle_Omktop(X0,X1),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_122
| ~ spl0_148 ),
inference(resolution,[],[f1400,f1216]) ).
fof(f1216,plain,
( ! [X48,X18,X4] : ~ c_in(c_Pair(X4,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X48,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f1215]) ).
fof(f1442,plain,
( spl0_154
| ~ spl0_12
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1395,f1350,f680,f1440]) ).
fof(f1395,plain,
( ! [X0,X1] : ~ c_in(c_Set_Oinsert(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,X1),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ spl0_12
| ~ spl0_137 ),
inference(resolution,[],[f1351,f681]) ).
fof(f1421,plain,
( spl0_153
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f1296,f1293,f1419]) ).
fof(f1419,plain,
( spl0_153
<=> ! [X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Relation_OField(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f1293,plain,
( spl0_125
<=> ! [X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Relation_OField(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1296,plain,
( ! [X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Relation_OField(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1)
| ~ spl0_125 ),
inference(forward_demodulation,[],[f1294,f17]) ).
fof(f1294,plain,
( ! [X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Relation_OField(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f1293]) ).
fof(f1417,plain,
spl0_152,
inference(avatar_split_clause,[],[f560,f1415]) ).
fof(f1415,plain,
( spl0_152
<=> ! [X11,X1] :
( ~ c_Wellfounded_Owf(X11,X1)
| c_Wellfounded_Owf(c_Relation_Orel__comp(X11,c_Transitive__Closure_Ortrancl(X11,X1),X1,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f560,plain,
! [X11,X1] :
( ~ c_Wellfounded_Owf(X11,X1)
| c_Wellfounded_Owf(c_Relation_Orel__comp(X11,c_Transitive__Closure_Ortrancl(X11,X1),X1,X1,X1),X1) ),
inference(definition_unfolding,[],[f391,f237]) ).
fof(f391,axiom,
! [X11,X1] :
( ~ c_Wellfounded_Owf(X11,X1)
| c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X11,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__trancl_0) ).
fof(f1413,plain,
spl0_151,
inference(avatar_split_clause,[],[f559,f1411]) ).
fof(f1411,plain,
( spl0_151
<=> ! [X11,X1] :
( ~ c_Relation_Osym(X11,X1)
| c_Relation_Osym(c_Relation_Orel__comp(X11,c_Transitive__Closure_Ortrancl(X11,X1),X1,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f559,plain,
! [X11,X1] :
( ~ c_Relation_Osym(X11,X1)
| c_Relation_Osym(c_Relation_Orel__comp(X11,c_Transitive__Closure_Ortrancl(X11,X1),X1,X1,X1),X1) ),
inference(definition_unfolding,[],[f367,f237]) ).
fof(f367,axiom,
! [X11,X1] :
( ~ c_Relation_Osym(X11,X1)
| c_Relation_Osym(c_Transitive__Closure_Otrancl(X11,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__trancl_0) ).
fof(f1409,plain,
spl0_150,
inference(avatar_split_clause,[],[f558,f1407]) ).
fof(f1407,plain,
( spl0_150
<=> ! [X11,X1] :
( ~ c_Relation_Otrans(X11,X1)
| c_Relation_Orel__comp(X11,c_Transitive__Closure_Ortrancl(X11,X1),X1,X1,X1) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f558,plain,
! [X11,X1] :
( ~ c_Relation_Otrans(X11,X1)
| c_Relation_Orel__comp(X11,c_Transitive__Closure_Ortrancl(X11,X1),X1,X1,X1) = X11 ),
inference(definition_unfolding,[],[f74,f237]) ).
fof(f74,axiom,
! [X11,X1] :
( ~ c_Relation_Otrans(X11,X1)
| c_Transitive__Closure_Otrancl(X11,X1) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__id_0) ).
fof(f1405,plain,
spl0_149,
inference(avatar_split_clause,[],[f417,f1403]) ).
fof(f417,axiom,
! [X11,X1,X5] :
( ~ c_Wellfounded_Owf(X11,X1)
| ~ c_in(c_Pair(X5,X5,X1,X1),X11,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__irrefl_0) ).
fof(f1401,plain,
spl0_148,
inference(avatar_split_clause,[],[f416,f1399]) ).
fof(f416,axiom,
! [X11,X1,X4] :
( ~ c_Nitpick_Orefl_H(X11,X1)
| c_in(c_Pair(X4,X4,X1,X1),X11,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_0) ).
fof(f1392,plain,
spl0_147,
inference(avatar_split_clause,[],[f283,f1390]) ).
fof(f1390,plain,
( spl0_147
<=> ! [X18,X1,X4] :
( ~ class_Orderings_Oorder(X1)
| X4 = X18
| ~ c_lessequals(X18,X4,X1)
| ~ c_lessequals(X4,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f283,axiom,
! [X1,X18,X4] :
( ~ class_Orderings_Oorder(X1)
| X4 = X18
| ~ c_lessequals(X18,X4,X1)
| ~ c_lessequals(X4,X18,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
fof(f1388,plain,
spl0_146,
inference(avatar_split_clause,[],[f280,f1386]) ).
fof(f1386,plain,
( spl0_146
<=> ! [X11,X1] : c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X11,X1,X1),X1) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X11,X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f280,axiom,
! [X11,X1] : c_Transitive__Closure_Ortrancl(c_Relation_Oconverse(X11,X1,X1),X1) = c_Relation_Oconverse(c_Transitive__Closure_Ortrancl(X11,X1),X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__converse_0) ).
fof(f1384,plain,
spl0_145,
inference(avatar_split_clause,[],[f209,f1382]) ).
fof(f1382,plain,
( spl0_145
<=> ! [X11,X1] : c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X11,c_Relation_Oconverse(X11,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f209,axiom,
! [X11,X1] : c_Relation_Osym(c_Lattices_Olower__semilattice__class_Oinf(X11,c_Relation_Oconverse(X11,X1,X1),tc_fun(tc_prod(X1,X1),tc_bool)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Int__converse_0) ).
fof(f1380,plain,
spl0_144,
inference(avatar_split_clause,[],[f194,f1378]) ).
fof(f1378,plain,
( spl0_144
<=> ! [X11,X1,X28] :
( ~ c_Wellfounded_Owf(X11,X1)
| c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X28,X11,tc_fun(tc_prod(X1,X1),tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f194,axiom,
! [X28,X11,X1] :
( ~ c_Wellfounded_Owf(X11,X1)
| c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X28,X11,tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__Int2_0) ).
fof(f1376,plain,
spl0_143,
inference(avatar_split_clause,[],[f193,f1374]) ).
fof(f1374,plain,
( spl0_143
<=> ! [X11,X1,X28] :
( ~ c_Wellfounded_Owf(X11,X1)
| c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X11,X28,tc_fun(tc_prod(X1,X1),tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f193,axiom,
! [X28,X11,X1] :
( ~ c_Wellfounded_Owf(X11,X1)
| c_Wellfounded_Owf(c_Lattices_Olower__semilattice__class_Oinf(X11,X28,tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__Int1_0) ).
fof(f1372,plain,
spl0_142,
inference(avatar_split_clause,[],[f133,f1370]) ).
fof(f1370,plain,
( spl0_142
<=> ! [X12,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X12,X0,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f133,axiom,
! [X0,X1,X12] : c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X12,X0,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__commute_0) ).
fof(f1368,plain,
spl0_141,
inference(avatar_split_clause,[],[f129,f1366]) ).
fof(f1366,plain,
( spl0_141
<=> ! [X4,X0,X12,X1] :
( c_in(X4,X12,X1)
| ~ c_lessequals(c_Set_Oinsert(X4,X0,X1),X12,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f129,axiom,
! [X0,X1,X4,X12] :
( c_in(X4,X12,X1)
| ~ c_lessequals(c_Set_Oinsert(X4,X0,X1),X12,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).
fof(f1364,plain,
spl0_140,
inference(avatar_split_clause,[],[f114,f1362]) ).
fof(f1362,plain,
( spl0_140
<=> ! [X4,X7,X5,X1] :
( ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X5,X4,X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X7,X1),X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f114,axiom,
! [X1,X7,X4,X5] :
( ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X5,X4,X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X7,X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI1_0) ).
fof(f1360,plain,
spl0_139,
inference(avatar_split_clause,[],[f113,f1358]) ).
fof(f1358,plain,
( spl0_139
<=> ! [X4,X5,X1,X7] :
( ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X7,X4,X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X7,X1),X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f113,axiom,
! [X1,X7,X4,X5] :
( ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X7,X4,X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X5,X7,X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI2_0) ).
fof(f1356,plain,
spl0_138,
inference(avatar_split_clause,[],[f112,f1354]) ).
fof(f1354,plain,
( spl0_138
<=> ! [X18,X4,X1,X24] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(X4,X18,X1)
| ~ c_lessequals(X4,c_Lattices_Olower__semilattice__class_Oinf(X18,X24,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f112,axiom,
! [X1,X18,X4,X24] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(X4,X18,X1)
| ~ c_lessequals(X4,c_Lattices_Olower__semilattice__class_Oinf(X18,X24,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
fof(f1352,plain,
( spl0_137
| ~ spl0_36
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f862,f837,f776,f1350]) ).
fof(f776,plain,
( spl0_36
<=> ! [X4,X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X4,X0,X1),X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f837,plain,
( spl0_50
<=> ! [X4,X1,X40] :
( ~ hBOOL(hAPP(X40,X4))
| c_in(X4,X40,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f862,plain,
( ! [X2,X3,X0,X1] : c_in(X0,c_Set_Oinsert(X0,X1,X2),X3)
| ~ spl0_36
| ~ spl0_50 ),
inference(resolution,[],[f838,f777]) ).
fof(f777,plain,
( ! [X0,X1,X4] : hBOOL(hAPP(c_Set_Oinsert(X4,X0,X1),X4))
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f776]) ).
fof(f838,plain,
( ! [X40,X1,X4] :
( ~ hBOOL(hAPP(X40,X4))
| c_in(X4,X40,X1) )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f837]) ).
fof(f1348,plain,
spl0_136,
inference(avatar_split_clause,[],[f111,f1346]) ).
fof(f1346,plain,
( spl0_136
<=> ! [X24,X4,X18,X1] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(X4,X24,X1)
| ~ c_lessequals(X4,c_Lattices_Olower__semilattice__class_Oinf(X18,X24,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f111,axiom,
! [X1,X18,X4,X24] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(X4,X24,X1)
| ~ c_lessequals(X4,c_Lattices_Olower__semilattice__class_Oinf(X18,X24,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
fof(f1344,plain,
spl0_135,
inference(avatar_split_clause,[],[f86,f1342]) ).
fof(f1342,plain,
( spl0_135
<=> ! [X0,X12,X6,X1] :
( c_in(X6,X0,X1)
| ~ c_in(X6,c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f86,axiom,
! [X0,X1,X6,X12] :
( c_in(X6,X0,X1)
| ~ c_in(X6,c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_0) ).
fof(f1340,plain,
spl0_134,
inference(avatar_split_clause,[],[f85,f1338]) ).
fof(f1338,plain,
( spl0_134
<=> ! [X0,X12,X6,X1] :
( c_in(X6,X12,X1)
| ~ c_in(X6,c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f85,axiom,
! [X0,X1,X6,X12] :
( c_in(X6,X12,X1)
| ~ c_in(X6,c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_1) ).
fof(f1336,plain,
spl0_133,
inference(avatar_split_clause,[],[f71,f1334]) ).
fof(f1334,plain,
( spl0_133
<=> ! [X4,X0,X12,X1] :
( hBOOL(hAPP(X0,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f71,axiom,
! [X0,X1,X4,X12] :
( hBOOL(hAPP(X0,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_0) ).
fof(f1332,plain,
spl0_132,
inference(avatar_split_clause,[],[f70,f1330]) ).
fof(f1330,plain,
( spl0_132
<=> ! [X4,X0,X12,X1] :
( hBOOL(hAPP(X12,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f70,axiom,
! [X0,X1,X4,X12] :
( hBOOL(hAPP(X12,X4))
| ~ hBOOL(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_1) ).
fof(f1328,plain,
spl0_131,
inference(avatar_split_clause,[],[f52,f1326]) ).
fof(f1326,plain,
( spl0_131
<=> ! [X5,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f52,axiom,
! [X1,X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Complete__Lattice_OSup__class_OSup(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).
fof(f1324,plain,
spl0_130,
inference(avatar_split_clause,[],[f31,f1322]) ).
fof(f1322,plain,
( spl0_130
<=> ! [X2,X1,X10] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Relation_OImage(X2,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f31,axiom,
! [X2,X10,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Relation_OImage(X2,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__empty_0) ).
fof(f1320,plain,
spl0_129,
inference(avatar_split_clause,[],[f22,f1318]) ).
fof(f1318,plain,
( spl0_129
<=> ! [X5,X1,X7] :
( X5 = X7
| ~ c_in(X7,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f22,axiom,
! [X1,X7,X5] :
( X5 = X7
| ~ c_in(X7,c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).
fof(f1316,plain,
spl0_128,
inference(avatar_split_clause,[],[f17,f1314]) ).
fof(f1312,plain,
spl0_127,
inference(avatar_split_clause,[],[f11,f1310]) ).
fof(f1310,plain,
( spl0_127
<=> ! [X9,X1,X10] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Set_Oimage(X9,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f11,axiom,
! [X10,X1,X9] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Set_Oimage(X9,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_bool)),X10,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
fof(f1300,plain,
spl0_126,
inference(avatar_split_clause,[],[f10,f1298]) ).
fof(f1298,plain,
( spl0_126
<=> ! [X5,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f10,axiom,
! [X1,X5] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Complete__Lattice_OInf__class_OInf(c_Set_Oinsert(X5,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).
fof(f1295,plain,
spl0_125,
inference(avatar_split_clause,[],[f8,f1293]) ).
fof(f8,axiom,
! [X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) = c_Relation_OField(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Field__empty_0) ).
fof(f1245,plain,
( spl0_124
| ~ spl0_77
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f1041,f991,f953,f1243]) ).
fof(f1243,plain,
( spl0_124
<=> ! [X0] : c_Arrow__Order__Mirabelle_OLin = c_Set_Oinsert(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f991,plain,
( spl0_80
<=> ! [X5,X0,X1] :
( ~ c_in(X5,X0,X1)
| c_Set_Oinsert(X5,X0,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f1041,plain,
( ! [X0] : c_Arrow__Order__Mirabelle_OLin = c_Set_Oinsert(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,X0)
| ~ spl0_77
| ~ spl0_80 ),
inference(resolution,[],[f992,f954]) ).
fof(f992,plain,
( ! [X0,X1,X5] :
( ~ c_in(X5,X0,X1)
| c_Set_Oinsert(X5,X0,X1) = X0 )
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f991]) ).
fof(f1221,plain,
spl0_123,
inference(avatar_split_clause,[],[f440,f1219]) ).
fof(f440,axiom,
! [X48,X4,X13] : ~ c_in(c_Pair(X13,X4,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omkbot(X48,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_0) ).
fof(f1217,plain,
spl0_122,
inference(avatar_split_clause,[],[f436,f1215]) ).
fof(f436,axiom,
! [X48,X18,X4] : ~ c_in(c_Pair(X4,X18,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Arrow__Order__Mirabelle_Omktop(X48,X4),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_0) ).
fof(f1213,plain,
spl0_121,
inference(avatar_split_clause,[],[f261,f1211]) ).
fof(f261,axiom,
! [X11,X1,X5] : c_in(c_Pair(X5,X5,X1,X1),c_Transitive__Closure_Ortrancl(X11,X1),tc_prod(X1,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).
fof(f1209,plain,
spl0_120,
inference(avatar_split_clause,[],[f256,f1207]) ).
fof(f1207,plain,
( spl0_120
<=> ! [X4,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ c_in(X4,X0,X1)
| c_lessequals(X4,c_Complete__Lattice_OSup__class_OSup(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f256,axiom,
! [X0,X1,X4] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ c_in(X4,X0,X1)
| c_lessequals(X4,c_Complete__Lattice_OSup__class_OSup(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
fof(f1205,plain,
spl0_119,
inference(avatar_split_clause,[],[f248,f1203]) ).
fof(f1203,plain,
( spl0_119
<=> ! [X4,X0,X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ c_in(X4,X0,X1)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X0,X1),X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f248,axiom,
! [X0,X1,X4] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| ~ c_in(X4,X0,X1)
| c_lessequals(c_Complete__Lattice_OInf__class_OInf(X0,X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__lower_0) ).
fof(f1201,plain,
spl0_118,
inference(avatar_split_clause,[],[f198,f1199]) ).
fof(f1199,plain,
( spl0_118
<=> ! [X12,X0,X1] :
( ~ c_Finite__Set_Ofinite(X12,X1)
| c_Finite__Set_Ofinite(X0,X1)
| ~ c_lessequals(X0,X12,tc_fun(X1,tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f198,axiom,
! [X0,X1,X12] :
( ~ c_Finite__Set_Ofinite(X12,X1)
| c_Finite__Set_Ofinite(X0,X1)
| ~ c_lessequals(X0,X12,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
fof(f1197,plain,
spl0_117,
inference(avatar_split_clause,[],[f151,f1195]) ).
fof(f1195,plain,
( spl0_117
<=> ! [X4,X0,X1] : c_Set_Oinsert(X4,X0,X1) = c_Set_Oinsert(X4,c_Set_Oinsert(X4,X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f151,axiom,
! [X0,X1,X4] : c_Set_Oinsert(X4,X0,X1) = c_Set_Oinsert(X4,c_Set_Oinsert(X4,X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
fof(f1193,plain,
spl0_116,
inference(avatar_split_clause,[],[f136,f1191]) ).
fof(f1191,plain,
( spl0_116
<=> ! [X18,X1,X4] :
( ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X4,X18,X1)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f136,axiom,
! [X1,X18,X4] :
( ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X4,X18,X1)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
fof(f1189,plain,
spl0_115,
inference(avatar_split_clause,[],[f135,f1187]) ).
fof(f1187,plain,
( spl0_115
<=> ! [X18,X1,X4] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(X4,X18,X1)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f135,axiom,
! [X1,X18,X4] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(X4,X18,X1)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1) != X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
fof(f1185,plain,
spl0_114,
inference(avatar_split_clause,[],[f134,f1183]) ).
fof(f1183,plain,
( spl0_114
<=> ! [X4,X1,X18] :
( ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X18,X4,X1)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1) = X18 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f134,axiom,
! [X1,X18,X4] :
( ~ class_Lattices_Olower__semilattice(X1)
| ~ c_lessequals(X18,X4,X1)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1) = X18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
fof(f1180,plain,
spl0_113,
inference(avatar_split_clause,[],[f50,f1178]) ).
fof(f1178,plain,
( spl0_113
<=> ! [X1] : c_Relation_Orefl__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f50,axiom,
! [X1] : c_Relation_Orefl__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__empty_0) ).
fof(f1163,plain,
( spl0_112
| ~ spl0_12
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1151,f1081,f680,f1161]) ).
fof(f1161,plain,
( spl0_112
<=> ! [X0,X1] :
( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Set_Oinsert(X1,X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f1081,plain,
( spl0_96
<=> ! [X5,X7,X12,X1] :
( ~ c_in(X5,X12,X1)
| c_in(X5,c_Set_Oinsert(X7,X12,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1151,plain,
( ! [X0,X1] :
( ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Set_Oinsert(X1,X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ spl0_12
| ~ spl0_96 ),
inference(resolution,[],[f1082,f681]) ).
fof(f1082,plain,
( ! [X1,X7,X5,X12] :
( c_in(X5,c_Set_Oinsert(X7,X12,X1),X1)
| ~ c_in(X5,X12,X1) )
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f1081]) ).
fof(f1143,plain,
spl0_111,
inference(avatar_split_clause,[],[f539,f1141]) ).
fof(f1141,plain,
( spl0_111
<=> ! [X0,X1] : c_Relation_ORange(c_Relation_Oconverse(c_Relation_OId__on(X0,X1),X1,X1),X1,X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f539,plain,
! [X0,X1] : c_Relation_ORange(c_Relation_Oconverse(c_Relation_OId__on(X0,X1),X1,X1),X1,X1) = X0,
inference(definition_unfolding,[],[f381,f398]) ).
fof(f381,axiom,
! [X0,X1] : c_Relation_ODomain(c_Relation_OId__on(X0,X1),X1,X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).
fof(f1139,plain,
spl0_110,
inference(avatar_split_clause,[],[f410,f1137]) ).
fof(f1137,plain,
( spl0_110
<=> ! [X11,X0,X1] :
( ~ c_Relation_Ototal__on(X0,X11,X1)
| c_Relation_Ototal__on(X0,c_Relation_Oconverse(X11,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f410,axiom,
! [X0,X11,X1] :
( ~ c_Relation_Ototal__on(X0,X11,X1)
| c_Relation_Ototal__on(X0,c_Relation_Oconverse(X11,X1,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__converse_1) ).
fof(f1135,plain,
spl0_109,
inference(avatar_split_clause,[],[f409,f1133]) ).
fof(f1133,plain,
( spl0_109
<=> ! [X11,X0,X1] :
( c_Relation_Ototal__on(X0,X11,X1)
| ~ c_Relation_Ototal__on(X0,c_Relation_Oconverse(X11,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f409,axiom,
! [X0,X11,X1] :
( c_Relation_Ototal__on(X0,X11,X1)
| ~ c_Relation_Ototal__on(X0,c_Relation_Oconverse(X11,X1,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__converse_0) ).
fof(f1131,plain,
spl0_108,
inference(avatar_split_clause,[],[f379,f1129]) ).
fof(f1129,plain,
( spl0_108
<=> ! [X2,X1] :
( c_Wellfounded_Owf(X2,X1)
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X2,X2,X1,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f379,axiom,
! [X2,X1] :
( c_Wellfounded_Owf(X2,X1)
| ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X2,X2,X1,X1,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__comp__self_1) ).
fof(f1127,plain,
spl0_107,
inference(avatar_split_clause,[],[f378,f1125]) ).
fof(f1125,plain,
( spl0_107
<=> ! [X2,X1] :
( ~ c_Wellfounded_Owf(X2,X1)
| c_Wellfounded_Owf(c_Relation_Orel__comp(X2,X2,X1,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f378,axiom,
! [X2,X1] :
( ~ c_Wellfounded_Owf(X2,X1)
| c_Wellfounded_Owf(c_Relation_Orel__comp(X2,X2,X1,X1,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__comp__self_0) ).
fof(f1123,plain,
spl0_106,
inference(avatar_split_clause,[],[f377,f1121]) ).
fof(f1121,plain,
( spl0_106
<=> ! [X11,X0,X1] :
( ~ c_Relation_Orefl__on(X0,X11,X1)
| c_Relation_Orefl__on(X0,c_Relation_Oconverse(X11,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f377,axiom,
! [X0,X11,X1] :
( ~ c_Relation_Orefl__on(X0,X11,X1)
| c_Relation_Orefl__on(X0,c_Relation_Oconverse(X11,X1,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).
fof(f1119,plain,
spl0_105,
inference(avatar_split_clause,[],[f376,f1117]) ).
fof(f1117,plain,
( spl0_105
<=> ! [X11,X0,X1] :
( c_Relation_Orefl__on(X0,X11,X1)
| ~ c_Relation_Orefl__on(X0,c_Relation_Oconverse(X11,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f376,axiom,
! [X0,X11,X1] :
( c_Relation_Orefl__on(X0,X11,X1)
| ~ c_Relation_Orefl__on(X0,c_Relation_Oconverse(X11,X1,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).
fof(f1115,plain,
spl0_104,
inference(avatar_split_clause,[],[f325,f1113]) ).
fof(f1113,plain,
( spl0_104
<=> ! [X11,X1] :
( c_Wellfounded_Owf(X11,X1)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X11,X1),c_Wellfounded_Oacc(X11,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f325,axiom,
! [X11,X1] :
( c_Wellfounded_Owf(X11,X1)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X11,X1),c_Wellfounded_Oacc(X11,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__acc__iff_1) ).
fof(f1111,plain,
spl0_103,
inference(avatar_split_clause,[],[f324,f1109]) ).
fof(f1109,plain,
( spl0_103
<=> ! [X11,X1] :
( c_Wellfounded_Owf(X11,X1)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X11,X1),c_Wellfounded_Oacc(X11,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f324,axiom,
! [X11,X1] :
( c_Wellfounded_Owf(X11,X1)
| ~ c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X11,X1),c_Wellfounded_Oacc(X11,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__wfI_0) ).
fof(f1107,plain,
spl0_102,
inference(avatar_split_clause,[],[f184,f1105]) ).
fof(f1105,plain,
( spl0_102
<=> ! [X12,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)),X12,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f184,axiom,
! [X0,X1,X12] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)),X12,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
fof(f1103,plain,
( ~ spl0_2
| spl0_101
| ~ spl0_55
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f1063,f911,f859,f1101,f631]) ).
fof(f631,plain,
( spl0_2
<=> class_Lattices_Olower__semilattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f1101,plain,
( spl0_101
<=> ! [X0] : c_lessequals(X0,X0,tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f859,plain,
( spl0_55
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f911,plain,
( spl0_67
<=> ! [X4,X1,X18] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1),X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1063,plain,
( ! [X0] :
( c_lessequals(X0,X0,tc_bool)
| ~ class_Lattices_Olower__semilattice(tc_bool) )
| ~ spl0_55
| ~ spl0_67 ),
inference(superposition,[],[f912,f860]) ).
fof(f860,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f859]) ).
fof(f912,plain,
( ! [X18,X1,X4] :
( c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1),X4,X1)
| ~ class_Lattices_Olower__semilattice(X1) )
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f911]) ).
fof(f1099,plain,
spl0_100,
inference(avatar_split_clause,[],[f183,f1097]) ).
fof(f1097,plain,
( spl0_100
<=> ! [X12,X0,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f183,axiom,
! [X0,X1,X12] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X0,X12,tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
fof(f1095,plain,
spl0_99,
inference(avatar_split_clause,[],[f132,f1093]) ).
fof(f1093,plain,
( spl0_99
<=> ! [X4,X1,X18] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1) = c_Lattices_Olower__semilattice__class_Oinf(X18,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f132,axiom,
! [X1,X18,X4] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1) = c_Lattices_Olower__semilattice__class_Oinf(X18,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__commute_0) ).
fof(f1091,plain,
spl0_98,
inference(avatar_split_clause,[],[f131,f1089]) ).
fof(f1089,plain,
( spl0_98
<=> ! [X4,X1,X18] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1) = c_Lattices_Olower__semilattice__class_Oinf(X18,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f131,axiom,
! [X1,X18,X4] :
( ~ class_Lattices_Olattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1) = c_Lattices_Olower__semilattice__class_Oinf(X18,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
fof(f1087,plain,
spl0_97,
inference(avatar_split_clause,[],[f128,f1085]) ).
fof(f1085,plain,
( spl0_97
<=> ! [X4,X0,X1,X18] :
( ~ hBOOL(hAPP(X0,X4))
| hBOOL(hAPP(c_Set_Oinsert(X18,X0,X1),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f128,axiom,
! [X0,X18,X1,X4] :
( ~ hBOOL(hAPP(X0,X4))
| hBOOL(hAPP(c_Set_Oinsert(X18,X0,X1),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).
fof(f1083,plain,
spl0_96,
inference(avatar_split_clause,[],[f80,f1081]) ).
fof(f80,axiom,
! [X1,X7,X5,X12] :
( ~ c_in(X5,X12,X1)
| c_in(X5,c_Set_Oinsert(X7,X12,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).
fof(f1079,plain,
spl0_95,
inference(avatar_split_clause,[],[f76,f1077]) ).
fof(f1077,plain,
( spl0_95
<=> ! [X20,X21,X1] :
( ~ c_Finite__Set_Ofinite(X20,X1)
| c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X20,X21,tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f76,axiom,
! [X21,X1,X20] :
( ~ c_Finite__Set_Ofinite(X20,X1)
| c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X20,X21,tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_0) ).
fof(f1075,plain,
spl0_94,
inference(avatar_split_clause,[],[f75,f1073]) ).
fof(f1073,plain,
( spl0_94
<=> ! [X20,X21,X1] :
( ~ c_Finite__Set_Ofinite(X21,X1)
| c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X20,X21,tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f75,axiom,
! [X21,X1,X20] :
( ~ c_Finite__Set_Ofinite(X21,X1)
| c_Finite__Set_Ofinite(c_Lattices_Olower__semilattice__class_Oinf(X20,X21,tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_1) ).
fof(f1071,plain,
spl0_93,
inference(avatar_split_clause,[],[f37,f1069]) ).
fof(f1069,plain,
( spl0_93
<=> ! [X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Orderings_Obot__class_Obot(X1) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f37,axiom,
! [X1] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X1)
| c_Orderings_Obot__class_Obot(X1) = c_Complete__Lattice_OSup__class_OSup(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
fof(f1060,plain,
( spl0_92
| ~ spl0_89 ),
inference(avatar_split_clause,[],[f1031,f1028,f1058]) ).
fof(f1058,plain,
( spl0_92
<=> ! [X1] : c_Relation_Osym(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f1028,plain,
( spl0_89
<=> ! [X1] : c_Relation_Osym(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f1031,plain,
( ! [X1] : c_Relation_Osym(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1),X1)
| ~ spl0_89 ),
inference(forward_demodulation,[],[f1029,f17]) ).
fof(f1029,plain,
( ! [X1] : c_Relation_Osym(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1)
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f1028]) ).
fof(f1056,plain,
( spl0_91
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f1026,f1023,f1054]) ).
fof(f1054,plain,
( spl0_91
<=> ! [X1] : c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f1023,plain,
( spl0_88
<=> ! [X1] : c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f1026,plain,
( ! [X1] : c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1),X1)
| ~ spl0_88 ),
inference(forward_demodulation,[],[f1024,f17]) ).
fof(f1024,plain,
( ! [X1] : c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1)
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f1023]) ).
fof(f1035,plain,
spl0_90,
inference(avatar_split_clause,[],[f537,f1033]) ).
fof(f1033,plain,
( spl0_90
<=> ! [X11,X1] : c_Relation_Otrans(c_Relation_Orel__comp(X11,c_Transitive__Closure_Ortrancl(X11,X1),X1,X1,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f537,plain,
! [X11,X1] : c_Relation_Otrans(c_Relation_Orel__comp(X11,c_Transitive__Closure_Ortrancl(X11,X1),X1,X1,X1),X1),
inference(definition_unfolding,[],[f140,f237]) ).
fof(f140,axiom,
! [X11,X1] : c_Relation_Otrans(c_Transitive__Closure_Otrancl(X11,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__trancl_0) ).
fof(f1030,plain,
spl0_89,
inference(avatar_split_clause,[],[f536,f1028]) ).
fof(f536,plain,
! [X1] : c_Relation_Osym(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1),
inference(definition_unfolding,[],[f371,f23]) ).
fof(f371,axiom,
! [X1] : c_Relation_Osym(c_Relation_OId(X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Id_0) ).
fof(f1025,plain,
spl0_88,
inference(avatar_split_clause,[],[f534,f1023]) ).
fof(f534,plain,
! [X1] : c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),X1),
inference(definition_unfolding,[],[f397,f23]) ).
fof(f397,axiom,
! [X1] : c_Relation_Oantisym(c_Relation_OId(X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__Id_0) ).
fof(f1021,plain,
spl0_87,
inference(avatar_split_clause,[],[f395,f1019]) ).
fof(f1019,plain,
( spl0_87
<=> ! [X0,X1] : c_Relation_OId__on(X0,X1) = c_Relation_Oconverse(c_Relation_OId__on(X0,X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f395,axiom,
! [X0,X1] : c_Relation_OId__on(X0,X1) = c_Relation_Oconverse(c_Relation_OId__on(X0,X1),X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__Id__on_0) ).
fof(f1017,plain,
spl0_86,
inference(avatar_split_clause,[],[f389,f1015]) ).
fof(f1015,plain,
( spl0_86
<=> ! [X10,X11,X9,X1] :
( ~ c_Relation_Osym(X11,X1)
| c_Relation_Osym(c_Relation_Oinv__image(X11,X9,X1,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f389,axiom,
! [X10,X11,X1,X9] :
( ~ c_Relation_Osym(X11,X1)
| c_Relation_Osym(c_Relation_Oinv__image(X11,X9,X1,X10),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__inv__image_0) ).
fof(f1013,plain,
spl0_85,
inference(avatar_split_clause,[],[f388,f1011]) ).
fof(f1011,plain,
( spl0_85
<=> ! [X10,X11,X9,X1] :
( ~ c_Wellfounded_Owf(X11,X1)
| c_Wellfounded_Owf(c_Relation_Oinv__image(X11,X9,X1,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f388,axiom,
! [X10,X11,X1,X9] :
( ~ c_Wellfounded_Owf(X11,X1)
| c_Wellfounded_Owf(c_Relation_Oinv__image(X11,X9,X1,X10),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__inv__image_0) ).
fof(f1009,plain,
spl0_84,
inference(avatar_split_clause,[],[f172,f1007]) ).
fof(f1007,plain,
( spl0_84
<=> ! [X20,X27,X1,X10] :
( ~ c_Finite__Set_Ofinite(X20,X1)
| c_Finite__Set_Ofinite(c_Set_Oimage(X27,X20,X1,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f172,axiom,
! [X10,X1,X27,X20] :
( ~ c_Finite__Set_Ofinite(X20,X1)
| c_Finite__Set_Ofinite(c_Set_Oimage(X27,X20,X1,X10),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
fof(f1005,plain,
spl0_83,
inference(avatar_split_clause,[],[f158,f1003]) ).
fof(f1003,plain,
( spl0_83
<=> ! [X10,X11,X9,X1] :
( ~ c_Relation_Otrans(X11,X1)
| c_Relation_Otrans(c_Relation_Oinv__image(X11,X9,X1,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f158,axiom,
! [X10,X11,X1,X9] :
( ~ c_Relation_Otrans(X11,X1)
| c_Relation_Otrans(c_Relation_Oinv__image(X11,X9,X1,X10),X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__inv__image_0) ).
fof(f1001,plain,
( spl0_82
| ~ spl0_12
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f965,f919,f680,f999]) ).
fof(f999,plain,
( spl0_82
<=> ! [X0] :
( ~ c_Wellfounded_Owf(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Wellfounded_Oacc(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f965,plain,
( ! [X0] :
( ~ c_Wellfounded_Owf(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))
| ~ c_in(c_Wellfounded_Oacc(X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) )
| ~ spl0_12
| ~ spl0_69 ),
inference(resolution,[],[f920,f681]) ).
fof(f997,plain,
spl0_81,
inference(avatar_split_clause,[],[f130,f995]) ).
fof(f995,plain,
( spl0_81
<=> ! [X11,X1] : c_Relation_OField(X11,X1) = c_Relation_OField(c_Relation_Oconverse(X11,X1,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f130,axiom,
! [X11,X1] : c_Relation_OField(X11,X1) = c_Relation_OField(c_Relation_Oconverse(X11,X1,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Field__converse_0) ).
fof(f993,plain,
spl0_80,
inference(avatar_split_clause,[],[f88,f991]) ).
fof(f88,axiom,
! [X0,X1,X5] :
( ~ c_in(X5,X0,X1)
| c_Set_Oinsert(X5,X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
fof(f989,plain,
spl0_79,
inference(avatar_split_clause,[],[f33,f987]) ).
fof(f987,plain,
( spl0_79
<=> ! [X4,X1] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Obot__class_Obot(X1) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f33,axiom,
! [X1,X4] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Obot__class_Obot(X1) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
fof(f985,plain,
spl0_78,
inference(avatar_split_clause,[],[f32,f983]) ).
fof(f983,plain,
( spl0_78
<=> ! [X4,X1] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Obot__class_Obot(X1) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Orderings_Obot__class_Obot(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f32,axiom,
! [X1,X4] :
( ~ class_Lattices_Obounded__lattice(X1)
| c_Orderings_Obot__class_Obot(X1) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Orderings_Obot__class_Obot(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
fof(f955,plain,
( spl0_77
| ~ spl0_50
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f926,f882,f837,f953]) ).
fof(f882,plain,
( spl0_60
<=> hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f926,plain,
( ! [X0] : c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,X0)
| ~ spl0_50
| ~ spl0_60 ),
inference(resolution,[],[f884,f838]) ).
fof(f884,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f882]) ).
fof(f950,plain,
spl0_76,
inference(avatar_split_clause,[],[f403,f948]) ).
fof(f948,plain,
( spl0_76
<=> ! [X11,X1] :
( ~ c_Relation_Oantisym(X11,X1)
| c_Relation_Oantisym(c_Relation_Oconverse(X11,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f403,axiom,
! [X11,X1] :
( ~ c_Relation_Oantisym(X11,X1)
| c_Relation_Oantisym(c_Relation_Oconverse(X11,X1,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__converse_1) ).
fof(f946,plain,
spl0_75,
inference(avatar_split_clause,[],[f402,f944]) ).
fof(f944,plain,
( spl0_75
<=> ! [X11,X1] :
( c_Relation_Oantisym(X11,X1)
| ~ c_Relation_Oantisym(c_Relation_Oconverse(X11,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f402,axiom,
! [X11,X1] :
( c_Relation_Oantisym(X11,X1)
| ~ c_Relation_Oantisym(c_Relation_Oconverse(X11,X1,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__converse_0) ).
fof(f942,plain,
spl0_74,
inference(avatar_split_clause,[],[f400,f940]) ).
fof(f940,plain,
( spl0_74
<=> ! [X11,X1,X10] : c_Relation_Oconverse(c_Relation_Oconverse(X11,X1,X10),X10,X1) = X11 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f400,axiom,
! [X10,X11,X1] : c_Relation_Oconverse(c_Relation_Oconverse(X11,X1,X10),X10,X1) = X11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__converse_0) ).
fof(f938,plain,
spl0_73,
inference(avatar_split_clause,[],[f383,f936]) ).
fof(f936,plain,
( spl0_73
<=> ! [X11,X1] :
( c_Relation_Osym(X11,X1)
| c_Relation_Oconverse(X11,X1,X1) != X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f383,axiom,
! [X11,X1] :
( c_Relation_Osym(X11,X1)
| c_Relation_Oconverse(X11,X1,X1) != X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).
fof(f934,plain,
spl0_72,
inference(avatar_split_clause,[],[f382,f932]) ).
fof(f932,plain,
( spl0_72
<=> ! [X11,X1] :
( ~ c_Relation_Osym(X11,X1)
| c_Relation_Oconverse(X11,X1,X1) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f382,axiom,
! [X11,X1] :
( ~ c_Relation_Osym(X11,X1)
| c_Relation_Oconverse(X11,X1,X1) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_0) ).
fof(f930,plain,
spl0_71,
inference(avatar_split_clause,[],[f369,f928]) ).
fof(f928,plain,
( spl0_71
<=> ! [X11,X1] :
( ~ c_Relation_Osym(X11,X1)
| c_Relation_Osym(c_Relation_Oconverse(X11,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f369,axiom,
! [X11,X1] :
( ~ c_Relation_Osym(X11,X1)
| c_Relation_Osym(c_Relation_Oconverse(X11,X1,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__converse_1) ).
fof(f925,plain,
spl0_70,
inference(avatar_split_clause,[],[f368,f923]) ).
fof(f923,plain,
( spl0_70
<=> ! [X11,X1] :
( c_Relation_Osym(X11,X1)
| ~ c_Relation_Osym(c_Relation_Oconverse(X11,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f368,axiom,
! [X11,X1] :
( c_Relation_Osym(X11,X1)
| ~ c_Relation_Osym(c_Relation_Oconverse(X11,X1,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__converse_0) ).
fof(f921,plain,
spl0_69,
inference(avatar_split_clause,[],[f366,f919]) ).
fof(f366,axiom,
! [X11,X1,X4] :
( ~ c_Wellfounded_Owf(X11,X1)
| c_in(X4,c_Wellfounded_Oacc(X11,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__wfD_0) ).
fof(f917,plain,
spl0_68,
inference(avatar_split_clause,[],[f264,f915]) ).
fof(f915,plain,
( spl0_68
<=> ! [X11,X1] : c_Transitive__Closure_Ortrancl(X11,X1) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X11,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f264,axiom,
! [X11,X1] : c_Transitive__Closure_Ortrancl(X11,X1) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X11,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).
fof(f913,plain,
spl0_67,
inference(avatar_split_clause,[],[f182,f911]) ).
fof(f182,axiom,
! [X1,X18,X4] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le1_0) ).
fof(f909,plain,
spl0_66,
inference(avatar_split_clause,[],[f181,f907]) ).
fof(f907,plain,
( spl0_66
<=> ! [X18,X1,X4] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1),X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f181,axiom,
! [X1,X18,X4] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1),X18,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le2_0) ).
fof(f905,plain,
spl0_65,
inference(avatar_split_clause,[],[f177,f903]) ).
fof(f903,plain,
( spl0_65
<=> ! [X18,X1,X4] :
( ~ class_Lattices_Olattice(X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1),X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f177,axiom,
! [X1,X18,X4] :
( ~ class_Lattices_Olattice(X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1),X18,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
fof(f901,plain,
spl0_64,
inference(avatar_split_clause,[],[f176,f899]) ).
fof(f899,plain,
( spl0_64
<=> ! [X4,X1,X18] :
( ~ class_Lattices_Olattice(X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1),X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f176,axiom,
! [X1,X18,X4] :
( ~ class_Lattices_Olattice(X1)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
fof(f897,plain,
spl0_63,
inference(avatar_split_clause,[],[f157,f895]) ).
fof(f895,plain,
( spl0_63
<=> ! [X5,X0,X1] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| c_Finite__Set_Ofinite(c_Set_Oinsert(X5,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f157,axiom,
! [X0,X1,X5] :
( ~ c_Finite__Set_Ofinite(X0,X1)
| c_Finite__Set_Ofinite(c_Set_Oinsert(X5,X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_1) ).
fof(f893,plain,
spl0_62,
inference(avatar_split_clause,[],[f156,f891]) ).
fof(f891,plain,
( spl0_62
<=> ! [X5,X0,X1] :
( c_Finite__Set_Ofinite(X0,X1)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X5,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f156,axiom,
! [X0,X1,X5] :
( c_Finite__Set_Ofinite(X0,X1)
| ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X5,X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_0) ).
fof(f889,plain,
spl0_61,
inference(avatar_split_clause,[],[f155,f887]) ).
fof(f887,plain,
( spl0_61
<=> ! [X12,X5,X1] : c_lessequals(X12,c_Set_Oinsert(X5,X12,X1),tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f155,axiom,
! [X1,X5,X12] : c_lessequals(X12,c_Set_Oinsert(X5,X12,X1),tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
fof(f885,plain,
( spl0_60
| ~ spl0_49
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f864,f841,f832,f882]) ).
fof(f832,plain,
( spl0_49
<=> c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f841,plain,
( spl0_51
<=> ! [X4,X1,X40] :
( ~ c_in(X4,X40,X1)
| hBOOL(hAPP(X40,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f864,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1))
| ~ spl0_49
| ~ spl0_51 ),
inference(resolution,[],[f842,f834]) ).
fof(f834,plain,
( c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f832]) ).
fof(f842,plain,
( ! [X40,X1,X4] :
( ~ c_in(X4,X40,X1)
| hBOOL(hAPP(X40,X4)) )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f841]) ).
fof(f880,plain,
spl0_59,
inference(avatar_split_clause,[],[f149,f878]) ).
fof(f878,plain,
( spl0_59
<=> ! [X11,X1] :
( ~ c_Relation_Otrans(X11,X1)
| c_Relation_Otrans(c_Relation_Oconverse(X11,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f149,axiom,
! [X11,X1] :
( ~ c_Relation_Otrans(X11,X1)
| c_Relation_Otrans(c_Relation_Oconverse(X11,X1,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__converse_1) ).
fof(f876,plain,
spl0_58,
inference(avatar_split_clause,[],[f148,f874]) ).
fof(f874,plain,
( spl0_58
<=> ! [X11,X1] :
( c_Relation_Otrans(X11,X1)
| ~ c_Relation_Otrans(c_Relation_Oconverse(X11,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f148,axiom,
! [X11,X1] :
( c_Relation_Otrans(X11,X1)
| ~ c_Relation_Otrans(c_Relation_Oconverse(X11,X1,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__converse_0) ).
fof(f872,plain,
spl0_57,
inference(avatar_split_clause,[],[f49,f870]) ).
fof(f870,plain,
( spl0_57
<=> ! [X5,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X5,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f49,axiom,
! [X0,X1,X5] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)) != c_Set_Oinsert(X5,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
fof(f868,plain,
spl0_56,
inference(avatar_split_clause,[],[f27,f866]) ).
fof(f866,plain,
( spl0_56
<=> ! [X0,X1] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f27,axiom,
! [X0,X1] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X0,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
fof(f861,plain,
( spl0_55
| ~ spl0_2
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f856,f808,f631,f859]) ).
fof(f808,plain,
( spl0_43
<=> ! [X4,X1] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X4,X1) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f856,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0
| ~ spl0_2
| ~ spl0_43 ),
inference(resolution,[],[f809,f633]) ).
fof(f633,plain,
( class_Lattices_Olower__semilattice(tc_bool)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f631]) ).
fof(f809,plain,
( ! [X1,X4] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X4,X1) = X4 )
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f808]) ).
fof(f855,plain,
( spl0_54
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f801,f798,f853]) ).
fof(f853,plain,
( spl0_54
<=> ! [X1] : c_Wellfounded_Owf(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f798,plain,
( spl0_41
<=> ! [X1] : c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f801,plain,
( ! [X1] : c_Wellfounded_Owf(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),X1)
| ~ spl0_41 ),
inference(forward_demodulation,[],[f799,f17]) ).
fof(f799,plain,
( ! [X1] : c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f798]) ).
fof(f851,plain,
spl0_53,
inference(avatar_split_clause,[],[f516,f849]) ).
fof(f849,plain,
( spl0_53
<=> ! [X52,X51] :
( ~ class_Finite__Set_Ofinite_Ofinite(X51)
| ~ class_Finite__Set_Ofinite_Ofinite(X52)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X51,X52)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f516,axiom,
! [X51,X52] :
( ~ class_Finite__Set_Ofinite_Ofinite(X51)
| ~ class_Finite__Set_Ofinite_Ofinite(X52)
| class_Finite__Set_Ofinite_Ofinite(tc_fun(X51,X52)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
fof(f847,plain,
spl0_52,
inference(avatar_split_clause,[],[f512,f845]) ).
fof(f845,plain,
( spl0_52
<=> ! [X52,X51] :
( ~ class_Finite__Set_Ofinite_Ofinite(X51)
| ~ class_Finite__Set_Ofinite_Ofinite(X52)
| class_Finite__Set_Ofinite_Ofinite(tc_prod(X51,X52)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f512,axiom,
! [X51,X52] :
( ~ class_Finite__Set_Ofinite_Ofinite(X51)
| ~ class_Finite__Set_Ofinite_Ofinite(X52)
| class_Finite__Set_Ofinite_Ofinite(tc_prod(X51,X52)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_prod__Finite__Set_Ofinite_Ofinite) ).
fof(f843,plain,
spl0_51,
inference(avatar_split_clause,[],[f509,f841]) ).
fof(f509,axiom,
! [X40,X1,X4] :
( ~ c_in(X4,X40,X1)
| hBOOL(hAPP(X40,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
fof(f839,plain,
spl0_50,
inference(avatar_split_clause,[],[f508,f837]) ).
fof(f508,axiom,
! [X40,X1,X4] :
( ~ hBOOL(hAPP(X40,X4))
| c_in(X4,X40,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
fof(f835,plain,
spl0_49,
inference(avatar_split_clause,[],[f448,f832]) ).
fof(f448,axiom,
c_in(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linear__alt_0) ).
fof(f830,plain,
spl0_48,
inference(avatar_split_clause,[],[f404,f828]) ).
fof(f828,plain,
( spl0_48
<=> ! [X11,X0,X1] :
( ~ c_Equiv__Relations_Oequiv(X0,X11,X1)
| c_Relation_Orefl__on(X0,X11,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f404,axiom,
! [X0,X11,X1] :
( ~ c_Equiv__Relations_Oequiv(X0,X11,X1)
| c_Relation_Orefl__on(X0,X11,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv_Orefl__on_0) ).
fof(f826,plain,
spl0_47,
inference(avatar_split_clause,[],[f399,f824]) ).
fof(f824,plain,
( spl0_47
<=> ! [X0,X1] : c_Relation_ORange(c_Relation_OId__on(X0,X1),X1,X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f399,axiom,
! [X0,X1] : c_Relation_ORange(c_Relation_OId__on(X0,X1),X1,X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__Id__on_0) ).
fof(f822,plain,
spl0_46,
inference(avatar_split_clause,[],[f300,f820]) ).
fof(f820,plain,
( spl0_46
<=> ! [X11,X1] :
( ~ c_Relation_Osym(X11,X1)
| c_Relation_Osym(c_Transitive__Closure_Ortrancl(X11,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f300,axiom,
! [X11,X1] :
( ~ c_Relation_Osym(X11,X1)
| c_Relation_Osym(c_Transitive__Closure_Ortrancl(X11,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__rtrancl_0) ).
fof(f818,plain,
spl0_45,
inference(avatar_split_clause,[],[f298,f816]) ).
fof(f816,plain,
( spl0_45
<=> ! [X3,X31,X10,X1] : hAPP(c_COMBK(X3,X1,X10),X31) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f298,axiom,
! [X31,X3,X10,X1] : hAPP(c_COMBK(X3,X1,X10),X31) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
fof(f814,plain,
spl0_44,
inference(avatar_split_clause,[],[f196,f812]) ).
fof(f812,plain,
( spl0_44
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_fun(X1,tc_bool)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f196,axiom,
! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_fun(X1,tc_bool)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
fof(f810,plain,
spl0_43,
inference(avatar_split_clause,[],[f195,f808]) ).
fof(f195,axiom,
! [X1,X4] :
( ~ class_Lattices_Olower__semilattice(X1)
| c_Lattices_Olower__semilattice__class_Oinf(X4,X4,X1) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).
fof(f805,plain,
spl0_42,
inference(avatar_split_clause,[],[f41,f803]) ).
fof(f803,plain,
( spl0_42
<=> ! [X1] : c_Relation_Oantisym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f41,axiom,
! [X1] : c_Relation_Oantisym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__empty_0) ).
fof(f800,plain,
spl0_41,
inference(avatar_split_clause,[],[f14,f798]) ).
fof(f14,axiom,
! [X1] : c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_bool)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__empty_0) ).
fof(f796,plain,
( spl0_40
| ~ spl0_12
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f791,f772,f680,f794]) ).
fof(f794,plain,
( spl0_40
<=> ! [X0] : ~ c_in(c_Set_Oinsert(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f772,plain,
( spl0_35
<=> ! [X4,X0,X1] : c_in(X4,c_Set_Oinsert(X4,X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f791,plain,
( ! [X0] : ~ c_in(c_Set_Oinsert(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ spl0_12
| ~ spl0_35 ),
inference(resolution,[],[f773,f681]) ).
fof(f773,plain,
( ! [X0,X1,X4] : c_in(X4,c_Set_Oinsert(X4,X0,X1),X1)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f772]) ).
fof(f790,plain,
spl0_39,
inference(avatar_split_clause,[],[f532,f788]) ).
fof(f788,plain,
( spl0_39
<=> ! [X16,X17,X1] :
( X16 = X17
| ~ c_fequal(X16,X17,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f532,axiom,
! [X1,X16,X17] :
( X16 = X17
| ~ c_fequal(X16,X17,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f786,plain,
spl0_38,
inference(avatar_split_clause,[],[f406,f784]) ).
fof(f784,plain,
( spl0_38
<=> ! [X11,X0,X1] :
( c_Relation_Osym(X11,X1)
| ~ c_Equiv__Relations_Oequiv(X0,X11,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f406,axiom,
! [X0,X11,X1] :
( c_Relation_Osym(X11,X1)
| ~ c_Equiv__Relations_Oequiv(X0,X11,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv_Osym_0) ).
fof(f782,plain,
spl0_37,
inference(avatar_split_clause,[],[f204,f780]) ).
fof(f780,plain,
( spl0_37
<=> ! [X11,X0,X1] :
( c_Relation_Otrans(X11,X1)
| ~ c_Equiv__Relations_Oequiv(X0,X11,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f204,axiom,
! [X0,X11,X1] :
( c_Relation_Otrans(X11,X1)
| ~ c_Equiv__Relations_Oequiv(X0,X11,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv_Otrans_0) ).
fof(f778,plain,
spl0_36,
inference(avatar_split_clause,[],[f187,f776]) ).
fof(f187,axiom,
! [X0,X1,X4] : hBOOL(hAPP(c_Set_Oinsert(X4,X0,X1),X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
fof(f774,plain,
spl0_35,
inference(avatar_split_clause,[],[f82,f772]) ).
fof(f82,axiom,
! [X0,X1,X4] : c_in(X4,c_Set_Oinsert(X4,X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).
fof(f770,plain,
spl0_34,
inference(avatar_split_clause,[],[f51,f768]) ).
fof(f768,plain,
( spl0_34
<=> ! [X11,X1] : c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X11,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f51,axiom,
! [X11,X1] : c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X11,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__empty_0) ).
fof(f766,plain,
spl0_33,
inference(avatar_split_clause,[],[f38,f764]) ).
fof(f764,plain,
( spl0_33
<=> ! [X4,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f38,axiom,
! [X1,X4] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
fof(f762,plain,
spl0_32,
inference(avatar_split_clause,[],[f29,f760]) ).
fof(f760,plain,
( spl0_32
<=> ! [X4,X1] :
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f29,axiom,
! [X1,X4] :
( ~ class_Orderings_Obot(X1)
| c_lessequals(c_Orderings_Obot__class_Obot(X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
fof(f758,plain,
spl0_31,
inference(avatar_split_clause,[],[f4,f756]) ).
fof(f756,plain,
( spl0_31
<=> ! [X6,X1] : ~ c_in(X6,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f4,axiom,
! [X1,X6] : ~ c_in(X6,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).
fof(f754,plain,
spl0_30,
inference(avatar_split_clause,[],[f521,f752]) ).
fof(f752,plain,
( spl0_30
<=> ! [X52,X51] :
( ~ class_HOL_Oord(X52)
| class_HOL_Oord(tc_fun(X51,X52)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f521,axiom,
! [X51,X52] :
( ~ class_HOL_Oord(X52)
| class_HOL_Oord(tc_fun(X51,X52)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
fof(f750,plain,
spl0_29,
inference(avatar_split_clause,[],[f520,f748]) ).
fof(f748,plain,
( spl0_29
<=> ! [X52,X51] :
( ~ class_Orderings_Obot(X52)
| class_Orderings_Obot(tc_fun(X51,X52)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f520,axiom,
! [X51,X52] :
( ~ class_Orderings_Obot(X52)
| class_Orderings_Obot(tc_fun(X51,X52)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
fof(f746,plain,
spl0_28,
inference(avatar_split_clause,[],[f519,f744]) ).
fof(f744,plain,
( spl0_28
<=> ! [X52,X51] :
( ~ class_Orderings_Oorder(X52)
| class_Orderings_Oorder(tc_fun(X51,X52)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f519,axiom,
! [X51,X52] :
( ~ class_Orderings_Oorder(X52)
| class_Orderings_Oorder(tc_fun(X51,X52)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f742,plain,
spl0_27,
inference(avatar_split_clause,[],[f518,f740]) ).
fof(f740,plain,
( spl0_27
<=> ! [X52,X51] :
( ~ class_Lattices_Olattice(X52)
| class_Lattices_Olattice(tc_fun(X51,X52)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f518,axiom,
! [X51,X52] :
( ~ class_Lattices_Olattice(X52)
| class_Lattices_Olattice(tc_fun(X51,X52)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
fof(f738,plain,
spl0_26,
inference(avatar_split_clause,[],[f517,f736]) ).
fof(f736,plain,
( spl0_26
<=> ! [X52,X51] :
( ~ class_Orderings_Opreorder(X52)
| class_Orderings_Opreorder(tc_fun(X51,X52)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f517,axiom,
! [X51,X52] :
( ~ class_Orderings_Opreorder(X52)
| class_Orderings_Opreorder(tc_fun(X51,X52)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f734,plain,
spl0_25,
inference(avatar_split_clause,[],[f515,f732]) ).
fof(f732,plain,
( spl0_25
<=> ! [X52,X51] :
( ~ class_Lattices_Obounded__lattice(X52)
| class_Lattices_Obounded__lattice(tc_fun(X51,X52)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f515,axiom,
! [X51,X52] :
( ~ class_Lattices_Obounded__lattice(X52)
| class_Lattices_Obounded__lattice(tc_fun(X51,X52)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
fof(f730,plain,
spl0_24,
inference(avatar_split_clause,[],[f514,f728]) ).
fof(f728,plain,
( spl0_24
<=> ! [X52,X51] :
( ~ class_Lattices_Olattice(X52)
| class_Lattices_Olower__semilattice(tc_fun(X51,X52)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f514,axiom,
! [X51,X52] :
( ~ class_Lattices_Olattice(X52)
| class_Lattices_Olower__semilattice(tc_fun(X51,X52)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
fof(f726,plain,
spl0_23,
inference(avatar_split_clause,[],[f513,f724]) ).
fof(f724,plain,
( spl0_23
<=> ! [X52,X51] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X52)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X51,X52)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f513,axiom,
! [X51,X52] :
( ~ class_Complete__Lattice_Ocomplete__lattice(X52)
| class_Complete__Lattice_Ocomplete__lattice(tc_fun(X51,X52)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(f722,plain,
spl0_22,
inference(avatar_split_clause,[],[f387,f720]) ).
fof(f720,plain,
( spl0_22
<=> ! [X0,X1] : c_Relation_Orefl__on(X0,c_Relation_OId__on(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f387,axiom,
! [X0,X1] : c_Relation_Orefl__on(X0,c_Relation_OId__on(X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__Id__on_0) ).
fof(f718,plain,
spl0_21,
inference(avatar_split_clause,[],[f276,f716]) ).
fof(f716,plain,
( spl0_21
<=> ! [X0,X1] : c_lessequals(X0,X0,tc_fun(X1,tc_bool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f276,axiom,
! [X0,X1] : c_lessequals(X0,X0,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).
fof(f714,plain,
spl0_20,
inference(avatar_split_clause,[],[f272,f712]) ).
fof(f712,plain,
( spl0_20
<=> ! [X4,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X4,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f272,axiom,
! [X1,X4] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X4,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f710,plain,
spl0_19,
inference(avatar_split_clause,[],[f271,f708]) ).
fof(f708,plain,
( spl0_19
<=> ! [X4,X1] :
( ~ class_Orderings_Opreorder(X1)
| c_lessequals(X4,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f271,axiom,
! [X1,X4] :
( ~ class_Orderings_Opreorder(X1)
| c_lessequals(X4,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f706,plain,
spl0_18,
inference(avatar_split_clause,[],[f36,f704]) ).
fof(f704,plain,
( spl0_18
<=> ! [X1] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f36,axiom,
! [X1] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
fof(f702,plain,
spl0_17,
inference(avatar_split_clause,[],[f386,f700]) ).
fof(f700,plain,
( spl0_17
<=> ! [X0,X1] : c_Relation_Osym(c_Relation_OId__on(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f386,axiom,
! [X0,X1] : c_Relation_Osym(c_Relation_OId__on(X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Id__on_0) ).
fof(f698,plain,
spl0_16,
inference(avatar_split_clause,[],[f374,f696]) ).
fof(f696,plain,
( spl0_16
<=> ! [X0,X1] : c_Relation_Oantisym(c_Relation_OId__on(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f374,axiom,
! [X0,X1] : c_Relation_Oantisym(c_Relation_OId__on(X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__Id__on_0) ).
fof(f694,plain,
spl0_15,
inference(avatar_split_clause,[],[f147,f692]) ).
fof(f692,plain,
( spl0_15
<=> ! [X11,X1] : c_Relation_Otrans(c_Transitive__Closure_Ortrancl(X11,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f147,axiom,
! [X11,X1] : c_Relation_Otrans(c_Transitive__Closure_Ortrancl(X11,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__rtrancl_0) ).
fof(f690,plain,
spl0_14,
inference(avatar_split_clause,[],[f119,f688]) ).
fof(f688,plain,
( spl0_14
<=> ! [X0,X1] : c_Relation_Otrans(c_Relation_OId__on(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f119,axiom,
! [X0,X1] : c_Relation_Otrans(c_Relation_OId__on(X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__Id__on_0) ).
fof(f686,plain,
spl0_13,
inference(avatar_split_clause,[],[f68,f684]) ).
fof(f684,plain,
( spl0_13
<=> ! [X0,X1] :
( ~ class_Finite__Set_Ofinite_Ofinite(X1)
| c_Finite__Set_Ofinite(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f68,axiom,
! [X0,X1] :
( ~ class_Finite__Set_Ofinite_Ofinite(X1)
| c_Finite__Set_Ofinite(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_0) ).
fof(f682,plain,
spl0_12,
inference(avatar_split_clause,[],[f511,f680]) ).
fof(f511,axiom,
! [X4] :
( ~ c_in(X4,c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))
| ~ c_in(c_Pair(v_a,v_b,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f678,plain,
spl0_11,
inference(avatar_split_clause,[],[f531,f676]) ).
fof(f676,plain,
( spl0_11
<=> ! [X4,X1] : c_fequal(X4,X4,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f531,axiom,
! [X1,X4] : c_fequal(X4,X4,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f674,plain,
~ spl0_10,
inference(avatar_split_clause,[],[f505,f671]) ).
fof(f505,axiom,
v_a != v_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_assms_0) ).
fof(f669,plain,
spl0_9,
inference(avatar_split_clause,[],[f530,f666]) ).
fof(f666,plain,
( spl0_9
<=> class_HOL_Oord(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f530,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
fof(f664,plain,
spl0_8,
inference(avatar_split_clause,[],[f529,f661]) ).
fof(f661,plain,
( spl0_8
<=> class_Orderings_Obot(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f529,axiom,
class_Orderings_Obot(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
fof(f659,plain,
spl0_7,
inference(avatar_split_clause,[],[f528,f656]) ).
fof(f656,plain,
( spl0_7
<=> class_Orderings_Oorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f528,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
fof(f654,plain,
spl0_6,
inference(avatar_split_clause,[],[f527,f651]) ).
fof(f651,plain,
( spl0_6
<=> class_Lattices_Olattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f527,axiom,
class_Lattices_Olattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
fof(f649,plain,
spl0_5,
inference(avatar_split_clause,[],[f526,f646]) ).
fof(f646,plain,
( spl0_5
<=> class_Orderings_Opreorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f526,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
fof(f644,plain,
spl0_4,
inference(avatar_split_clause,[],[f525,f641]) ).
fof(f641,plain,
( spl0_4
<=> class_Finite__Set_Ofinite_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f525,axiom,
class_Finite__Set_Ofinite_Ofinite(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
fof(f639,plain,
spl0_3,
inference(avatar_split_clause,[],[f524,f636]) ).
fof(f636,plain,
( spl0_3
<=> class_Lattices_Obounded__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f524,axiom,
class_Lattices_Obounded__lattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
fof(f634,plain,
spl0_2,
inference(avatar_split_clause,[],[f523,f631]) ).
fof(f523,axiom,
class_Lattices_Olower__semilattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
fof(f629,plain,
spl0_1,
inference(avatar_split_clause,[],[f522,f626]) ).
fof(f626,plain,
( spl0_1
<=> class_Complete__Lattice_Ocomplete__lattice(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f522,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SCT026-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 13:15:05 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (18791)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.40 % (18794)WARNING: value z3 for option sas not known
% 0.14/0.40 % (18792)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.40 % (18797)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.40 % (18796)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.40 % (18795)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.40 % (18794)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.40 % (18793)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.40 % (18798)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.50 % (18796)First to succeed.
% 0.21/0.50 % (18796)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-18791"
% 0.21/0.50 % (18796)Refutation found. Thanks to Tanya!
% 0.21/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.51 % (18796)------------------------------
% 0.21/0.51 % (18796)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.51 % (18796)Termination reason: Refutation
% 0.21/0.51
% 0.21/0.51 % (18796)Memory used [KB]: 2503
% 0.21/0.51 % (18796)Time elapsed: 0.103 s
% 0.21/0.51 % (18796)Instructions burned: 178 (million)
% 0.21/0.51 % (18791)Success in time 0.14 s
%------------------------------------------------------------------------------