TSTP Solution File: SWW305+1 by SnakeForV-SAT---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SWW305+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n025.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 : Wed Aug 31 19:18:59 EDT 2022
% Result : Theorem 91.41s 12.02s
% Output : Refutation 91.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 823
% Syntax : Number of formulae : 2604 (1308 unt; 0 def)
% Number of atoms : 4841 (1829 equ)
% Maximal formula atoms : 22 ( 1 avg)
% Number of connectives : 3582 (1345 ~;1335 |; 281 &)
% ( 481 <=>; 140 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 517 ( 515 usr; 425 prp; 0-5 aty)
% Number of functors : 138 ( 138 usr; 46 con; 0-6 aty)
% Number of variables : 1008 ( 996 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f38366,plain,
$false,
inference(avatar_smt_refutation,[],[f28661,f28666,f28671,f28679,f28685,f28690,f28695,f28700,f28705,f28710,f28715,f28720,f28725,f28730,f28735,f28740,f28745,f28750,f28755,f28760,f28765,f28770,f28775,f28780,f28785,f28790,f28795,f28800,f28805,f28810,f28815,f28820,f28826,f28831,f28837,f28843,f28848,f28853,f28858,f28890,f28896,f28904,f28909,f28916,f28917,f28922,f28927,f28932,f28937,f28938,f28946,f28951,f28956,f28962,f28967,f28972,f28990,f28995,f29000,f29005,f29010,f29016,f29021,f29022,f29027,f29033,f29040,f29048,f29053,f29058,f29063,f29069,f29074,f29080,f29085,f29096,f29102,f29107,f29115,f29126,f29131,f29140,f29147,f29154,f29160,f29165,f29170,f29176,f29182,f29187,f29193,f29198,f29220,f29225,f29249,f29254,f29262,f29267,f29273,f29290,f29291,f29301,f29309,f29322,f29328,f29333,f29341,f29351,f29356,f29375,f29383,f29395,f29403,f29411,f29417,f29425,f29430,f29440,f29446,f29460,f29466,f29472,f29477,f29482,f29488,f29494,f29501,f29510,f29515,f29520,f29528,f29538,f29638,f29648,f29662,f29672,f29678,f29683,f29689,f29694,f29707,f29714,f29720,f29729,f29734,f29739,f30135,f30141,f30173,f30202,f30207,f30214,f30219,f30224,f30243,f30271,f30277,f30282,f30294,f30304,f30317,f30322,f30328,f30338,f30379,f30386,f30392,f30423,f30430,f30450,f30455,f30475,f30497,f30515,f30520,f30531,f30558,f30565,f30570,f30579,f30604,f30609,f30615,f30633,f30640,f30672,f30680,f30686,f30718,f30738,f30770,f30775,f30785,f30818,f30871,f30896,f30901,f30908,f30913,f30936,f30957,f30963,f30972,f30993,f31026,f31034,f31043,f31052,f31057,f31063,f31135,f31186,f31197,f31205,f31211,f31220,f31229,f31239,f31249,f31306,f31311,f31361,f31379,f31385,f31390,f31399,f31404,f31413,f31430,f31503,f31508,f31513,f31561,f31566,f31593,f31602,f31607,f31613,f31618,f31628,f31641,f31650,f31675,f31680,f31685,f31690,f31698,f31703,f31712,f31723,f31771,f31778,f31798,f32352,f32361,f32387,f32394,f32401,f32426,f32446,f32541,f32549,f32558,f32568,f32609,f32614,f32620,f32630,f32856,f33028,f33095,f33625,f33632,f33641,f33666,f33671,f33679,f33684,f33690,f33700,f33708,f33745,f33756,f33761,f33818,f33831,f33844,f33852,f33913,f33919,f33924,f33940,f33945,f33971,f34016,f34149,f34156,f34244,f34272,f34277,f34532,f34544,f34550,f34555,f34565,f34597,f34681,f34696,f34702,f34710,f34716,f34721,f34741,f34794,f34800,f34817,f34829,f35197,f35238,f35252,f35304,f35309,f35320,f35337,f35345,f35382,f35390,f35436,f35452,f35458,f35469,f35496,f35508,f35515,f35520,f35539,f35562,f35567,f35579,f35587,f35595,f35601,f35619,f35628,f35637,f35643,f35677,f35697,f35702,f35746,f35751,f35760,f35769,f35851,f35878,f35880,f35909,f35911,f35921,f35927,f35929,f35935,f35942,f35953,f36003,f36010,f36028,f36041,f36071,f36075,f36081,f36087,f36561,f36584,f36592,f36598,f36676,f36701,f36780,f36790,f36830,f36858,f36861,f36879,f36890,f36905,f36911,f36920,f36926,f36932,f36941,f36948,f36978,f36984,f36991,f37328,f37333,f37338,f37343,f37355,f37360,f37366,f37400,f37406,f37420,f37428,f37433,f37442,f37454,f37459,f37465,f37471,f37478,f37484,f37490,f37496,f37502,f37510,f37533,f37540,f37545,f37575,f37581,f37587,f37593,f37599,f37604,f37621,f37628,f37634,f37648,f37658,f37728,f37733,f37738,f37748,f37754,f37757,f37770,f37773,f37775,f37782,f37784,f37793,f38186,f38361]) ).
fof(f38361,plain,
( ~ spl574_399
| spl574_424 ),
inference(avatar_split_clause,[],[f38360,f38183,f37487]) ).
fof(f37487,plain,
( spl574_399
<=> c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_399])]) ).
fof(f38183,plain,
( spl574_424
<=> c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q))),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_424])]) ).
fof(f38360,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)))
| spl574_424 ),
inference(backward_demodulation,[],[f38185,f38357]) ).
fof(f38357,plain,
! [X26,X24,X25] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24,tc_HOL_Obool)),X25),hAPP(c_fequal,X26)) = hAPP(hAPP(c_Set_Oinsert(X24),X26),X25),
inference(forward_demodulation,[],[f38314,f34306]) ).
fof(f34306,plain,
! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_fequal,X0),
inference(forward_demodulation,[],[f24698,f21003]) ).
fof(f21003,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(cnf_transformation,[],[f6935]) ).
fof(f6935,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(rectify,[],[f765]) ).
fof(f765,axiom,
! [X17,X4] : hAPP(c_Set_OCollect(X4),X17) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(f24698,plain,
! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X0)),
inference(cnf_transformation,[],[f9402]) ).
fof(f9402,plain,
! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X0)),
inference(rectify,[],[f789]) ).
fof(f789,axiom,
! [X5,X4] : hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X4),hAPP(c_fequal,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__conv2) ).
fof(f38314,plain,
! [X26,X24,X25] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24,tc_HOL_Obool)),X25),hAPP(hAPP(c_Set_Oinsert(X24),X26),c_Orderings_Obot__class_Obot(tc_fun(X24,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X24),X26),X25),
inference(superposition,[],[f26015,f21712]) ).
fof(f21712,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) = X1,
inference(cnf_transformation,[],[f9102]) ).
fof(f9102,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) = X1,
inference(rectify,[],[f93]) ).
fof(f93,axiom,
! [X4,X21] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X21),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))) = X21,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__empty__right) ).
fof(f26015,plain,
! [X2,X3,X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X0),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_Set_Oinsert(X2),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X0),X1)),
inference(cnf_transformation,[],[f19081]) ).
fof(f19081,plain,
! [X0,X1,X2,X3] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X0),hAPP(hAPP(c_Set_Oinsert(X2),X3),X1)) = hAPP(hAPP(c_Set_Oinsert(X2),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X0),X1)),
inference(rectify,[],[f7780]) ).
fof(f7780,plain,
! [X2,X3,X1,X0] : hAPP(hAPP(c_Set_Oinsert(X1),X0),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X0),X3)),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X5,X4,X21,X23] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X21),hAPP(hAPP(c_Set_Oinsert(X4),X5),X23)) = hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X21),X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__insert__right) ).
fof(f38185,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q))),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)))
| spl574_424 ),
inference(avatar_component_clause,[],[f38183]) ).
fof(f38186,plain,
( ~ spl574_424
| spl574_370 ),
inference(avatar_split_clause,[],[f38181,f36876,f38183]) ).
fof(f36876,plain,
( spl574_370
<=> c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY)),v_Q)),hAPP(c_fequal,v_pn))),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),v_Q)),hAPP(c_fequal,v_pn))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_370])]) ).
fof(f38181,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q))),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)))
| spl574_370 ),
inference(forward_demodulation,[],[f38180,f20556]) ).
fof(f20556,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(hAPP(c_COMBB(X2,X5,X1),X3),X0),X4) = hAPP(X3,hAPP(X0,X4)),
inference(cnf_transformation,[],[f14900]) ).
fof(f14900,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(hAPP(c_COMBB(X2,X5,X1),X3),X0),X4) = hAPP(X3,hAPP(X0,X4)),
inference(rectify,[],[f8357]) ).
fof(f8357,plain,
! [X1,X5,X2,X4,X0,X3] : hAPP(X4,hAPP(X1,X0)) = hAPP(hAPP(hAPP(c_COMBB(X2,X3,X5),X4),X1),X0),
inference(rectify,[],[f5206]) ).
fof(f5206,axiom,
! [X29,X16,X20,X4,X17,X38] : hAPP(hAPP(hAPP(c_COMBB(X20,X4,X38),X17),X16),X29) = hAPP(X17,hAPP(X16,X29)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(f38180,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_fequal,hAPP(hAPP(hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY),v_pn),v_Q))),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)))
| spl574_370 ),
inference(forward_demodulation,[],[f38179,f23322]) ).
fof(f23322,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(X2,X3),X1) = hAPP(hAPP(hAPP(c_COMBC(X4,X5,X0),X2),X1),X3),
inference(cnf_transformation,[],[f17027]) ).
fof(f17027,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(X2,X3),X1) = hAPP(hAPP(hAPP(c_COMBC(X4,X5,X0),X2),X1),X3),
inference(rectify,[],[f5714]) ).
fof(f5714,plain,
! [X3,X4,X0,X5,X1,X2] : hAPP(hAPP(X0,X5),X4) = hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X0),X4),X5),
inference(rectify,[],[f5207]) ).
fof(f5207,axiom,
! [X17,X20,X38,X4,X16,X29] : hAPP(hAPP(hAPP(c_COMBC(X20,X38,X4),X17),X16),X29) = hAPP(hAPP(X17,X29),X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBC__1) ).
fof(f38179,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_fequal,hAPP(hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY)),v_Q),v_pn))),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)))
| spl574_370 ),
inference(forward_demodulation,[],[f38178,f38174]) ).
fof(f38174,plain,
! [X2,X3,X0,X1] : hAPP(c_Set_Oimage(X0,X1,X2),hAPP(c_fequal,X3)) = hAPP(c_fequal,hAPP(X2,X3)),
inference(forward_demodulation,[],[f38173,f34306]) ).
fof(f38173,plain,
! [X2,X3,X0,X1] : hAPP(c_Set_Oimage(X0,X1,X2),hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))) = hAPP(c_fequal,hAPP(X2,X3)),
inference(forward_demodulation,[],[f38147,f34306]) ).
fof(f38147,plain,
! [X2,X3,X0,X1] : hAPP(c_Set_Oimage(X0,X1,X2),hAPP(hAPP(c_Set_Oinsert(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(superposition,[],[f24290,f28349]) ).
fof(f28349,plain,
! [X2,X3,X0] : hAPP(c_Set_Oimage(X2,X3,X0),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)),
inference(equality_resolution,[],[f23889]) ).
fof(f23889,plain,
! [X2,X3,X0,X1] :
( hAPP(c_Set_Oimage(X2,X3,X0),X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != X1 ),
inference(cnf_transformation,[],[f17478]) ).
fof(f17478,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X1
| hAPP(c_Set_Oimage(X2,X3,X0),X1) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) )
& ( hAPP(c_Set_Oimage(X2,X3,X0),X1) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != X1 ) ),
inference(rectify,[],[f17477]) ).
fof(f17477,plain,
! [X0,X2,X3,X1] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) = X2
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(c_Set_Oimage(X3,X1,X0),X2) )
& ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X3,X1,X0),X2)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) != X2 ) ),
inference(nnf_transformation,[],[f5964]) ).
fof(f5964,plain,
! [X0,X2,X3,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) = X2
<=> c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X3,X1,X0),X2) ),
inference(rectify,[],[f89]) ).
fof(f89,axiom,
! [X1,X4,X21,X20] :
( c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X20,X4,X1),X21)
<=> c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)) = X21 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__is__empty) ).
fof(f24290,plain,
! [X2,X3,X0,X1,X4] : hAPP(hAPP(c_Set_Oinsert(X3),hAPP(X2,X4)),hAPP(c_Set_Oimage(X1,X3,X2),X0)) = hAPP(c_Set_Oimage(X1,X3,X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X0)),
inference(cnf_transformation,[],[f17798]) ).
fof(f17798,plain,
! [X0,X1,X2,X3,X4] : hAPP(hAPP(c_Set_Oinsert(X3),hAPP(X2,X4)),hAPP(c_Set_Oimage(X1,X3,X2),X0)) = hAPP(c_Set_Oimage(X1,X3,X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X0)),
inference(rectify,[],[f9926]) ).
fof(f9926,plain,
! [X0,X1,X4,X2,X3] : hAPP(c_Set_Oimage(X1,X2,X4),hAPP(hAPP(c_Set_Oinsert(X1),X3),X0)) = hAPP(hAPP(c_Set_Oinsert(X2),hAPP(X4,X3)),hAPP(c_Set_Oimage(X1,X2,X4),X0)),
inference(rectify,[],[f95]) ).
fof(f95,axiom,
! [X23,X20,X4,X5,X1] : hAPP(c_Set_Oimage(X20,X4,X1),hAPP(hAPP(c_Set_Oinsert(X20),X5),X23)) = hAPP(hAPP(c_Set_Oinsert(X4),hAPP(X1,X5)),hAPP(c_Set_Oimage(X20,X4,X1),X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__insert) ).
fof(f38178,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY)),v_Q)),hAPP(c_fequal,v_pn))),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)))
| spl574_370 ),
inference(forward_demodulation,[],[f38177,f20556]) ).
fof(f38177,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY)),v_Q)),hAPP(c_fequal,v_pn))),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody),v_pn)),v_Q)))
| spl574_370 ),
inference(forward_demodulation,[],[f38176,f20556]) ).
fof(f38176,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY)),v_Q)),hAPP(c_fequal,v_pn))),hAPP(c_fequal,hAPP(hAPP(hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody)),v_pn),v_Q)))
| spl574_370 ),
inference(forward_demodulation,[],[f38175,f23322]) ).
fof(f38175,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY)),v_Q)),hAPP(c_fequal,v_pn))),hAPP(c_fequal,hAPP(hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),v_Q),v_pn)))
| spl574_370 ),
inference(backward_demodulation,[],[f36878,f38174]) ).
fof(f36878,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY)),v_Q)),hAPP(c_fequal,v_pn))),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),v_Q)),hAPP(c_fequal,v_pn)))
| spl574_370 ),
inference(avatar_component_clause,[],[f36876]) ).
fof(f37793,plain,
( spl574_423
| ~ spl574_358
| ~ spl574_410 ),
inference(avatar_split_clause,[],[f37788,f37601,f36038,f37790]) ).
fof(f37790,plain,
( spl574_423
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_423])]) ).
fof(f36038,plain,
( spl574_358
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_358])]) ).
fof(f37601,plain,
( spl574_410
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_410])]) ).
fof(f37788,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl574_358
| ~ spl574_410 ),
inference(forward_demodulation,[],[f37603,f36040]) ).
fof(f36040,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl574_358 ),
inference(avatar_component_clause,[],[f36038]) ).
fof(f37603,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))
| ~ spl574_410 ),
inference(avatar_component_clause,[],[f37601]) ).
fof(f37784,plain,
( ~ spl574_411
| ~ spl574_97
| spl574_376 ),
inference(avatar_split_clause,[],[f37783,f36938,f29259,f37618]) ).
fof(f37618,plain,
( spl574_411
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_411])]) ).
fof(f29259,plain,
( spl574_97
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_97])]) ).
fof(f36938,plain,
( spl574_376
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_376])]) ).
fof(f37783,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl574_97
| spl574_376 ),
inference(forward_demodulation,[],[f36940,f29261]) ).
fof(f29261,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat)
| ~ spl574_97 ),
inference(avatar_component_clause,[],[f29259]) ).
fof(f36940,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| spl574_376 ),
inference(avatar_component_clause,[],[f36938]) ).
fof(f37782,plain,
( spl574_422
| ~ spl574_358
| ~ spl574_413 ),
inference(avatar_split_clause,[],[f37777,f37631,f36038,f37779]) ).
fof(f37779,plain,
( spl574_422
<=> hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_422])]) ).
fof(f37631,plain,
( spl574_413
<=> hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))) = hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_413])]) ).
fof(f37777,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl574_358
| ~ spl574_413 ),
inference(forward_demodulation,[],[f37633,f36040]) ).
fof(f37633,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))) = hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl574_413 ),
inference(avatar_component_clause,[],[f37631]) ).
fof(f37775,plain,
( ~ spl574_411
| ~ spl574_97
| spl574_152
| ~ spl574_223 ),
inference(avatar_split_clause,[],[f37774,f31382,f30211,f29259,f37618]) ).
fof(f30211,plain,
( spl574_152
<=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_152])]) ).
fof(f31382,plain,
( spl574_223
<=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_223])]) ).
fof(f37774,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl574_97
| spl574_152
| ~ spl574_223 ),
inference(forward_demodulation,[],[f36936,f29261]) ).
fof(f36936,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| spl574_152
| ~ spl574_223 ),
inference(forward_demodulation,[],[f30212,f31384]) ).
fof(f31384,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ spl574_223 ),
inference(avatar_component_clause,[],[f31382]) ).
fof(f30212,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| spl574_152 ),
inference(avatar_component_clause,[],[f30211]) ).
fof(f37773,plain,
( ~ spl574_411
| ~ spl574_97
| spl574_152
| ~ spl574_396 ),
inference(avatar_split_clause,[],[f37772,f37468,f30211,f29259,f37618]) ).
fof(f37468,plain,
( spl574_396
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_396])]) ).
fof(f37772,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl574_97
| spl574_152
| ~ spl574_396 ),
inference(forward_demodulation,[],[f37771,f37470]) ).
fof(f37470,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl574_396 ),
inference(avatar_component_clause,[],[f37468]) ).
fof(f37771,plain,
( hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat)) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl574_97
| spl574_152 ),
inference(forward_demodulation,[],[f30212,f29261]) ).
fof(f37770,plain,
( spl574_421
| ~ spl574_418
| ~ spl574_420 ),
inference(avatar_split_clause,[],[f37765,f37751,f37735,f37767]) ).
fof(f37767,plain,
( spl574_421
<=> hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_421])]) ).
fof(f37735,plain,
( spl574_418
<=> hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_418])]) ).
fof(f37751,plain,
( spl574_420
<=> hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_420])]) ).
fof(f37765,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl574_418
| ~ spl574_420 ),
inference(forward_demodulation,[],[f37753,f37737]) ).
fof(f37737,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl574_418 ),
inference(avatar_component_clause,[],[f37735]) ).
fof(f37753,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl574_420 ),
inference(avatar_component_clause,[],[f37751]) ).
fof(f37757,plain,
( spl574_411
| ~ spl574_97
| ~ spl574_152
| ~ spl574_396 ),
inference(avatar_split_clause,[],[f37756,f37468,f30211,f29259,f37618]) ).
fof(f37756,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl574_97
| ~ spl574_152
| ~ spl574_396 ),
inference(forward_demodulation,[],[f37755,f37470]) ).
fof(f37755,plain,
( hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl574_97
| ~ spl574_152 ),
inference(forward_demodulation,[],[f30213,f29261]) ).
fof(f30213,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl574_152 ),
inference(avatar_component_clause,[],[f30211]) ).
fof(f37754,plain,
( spl574_420
| ~ spl574_358
| ~ spl574_359 ),
inference(avatar_split_clause,[],[f37749,f36068,f36038,f37751]) ).
fof(f36068,plain,
( spl574_359
<=> hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_359])]) ).
fof(f37749,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl574_358
| ~ spl574_359 ),
inference(forward_demodulation,[],[f36070,f36040]) ).
fof(f36070,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))
| ~ spl574_359 ),
inference(avatar_component_clause,[],[f36068]) ).
fof(f37748,plain,
( spl574_419
| ~ spl574_348
| ~ spl574_358 ),
inference(avatar_split_clause,[],[f37701,f36038,f35875,f37745]) ).
fof(f37745,plain,
( spl574_419
<=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint))))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_419])]) ).
fof(f35875,plain,
( spl574_348
<=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_348])]) ).
fof(f37701,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint))))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl574_348
| ~ spl574_358 ),
inference(backward_demodulation,[],[f35877,f36040]) ).
fof(f35877,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))
| ~ spl574_348 ),
inference(avatar_component_clause,[],[f35875]) ).
fof(f37738,plain,
( spl574_418
| ~ spl574_347
| ~ spl574_358 ),
inference(avatar_split_clause,[],[f37700,f36038,f35848,f37735]) ).
fof(f35848,plain,
( spl574_347
<=> hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_347])]) ).
fof(f37700,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl574_347
| ~ spl574_358 ),
inference(backward_demodulation,[],[f35850,f36040]) ).
fof(f35850,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))
| ~ spl574_347 ),
inference(avatar_component_clause,[],[f35848]) ).
fof(f37733,plain,
( spl574_417
| ~ spl574_355
| ~ spl574_358 ),
inference(avatar_split_clause,[],[f37704,f36038,f36000,f37730]) ).
fof(f37730,plain,
( spl574_417
<=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_417])]) ).
fof(f36000,plain,
( spl574_355
<=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_355])]) ).
fof(f37704,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl574_355
| ~ spl574_358 ),
inference(backward_demodulation,[],[f36002,f36040]) ).
fof(f36002,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))
| ~ spl574_355 ),
inference(avatar_component_clause,[],[f36000]) ).
fof(f37728,plain,
( spl574_416
| ~ spl574_349
| ~ spl574_358 ),
inference(avatar_split_clause,[],[f37702,f36038,f35906,f37725]) ).
fof(f37725,plain,
( spl574_416
<=> hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_416])]) ).
fof(f35906,plain,
( spl574_349
<=> hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_349])]) ).
fof(f37702,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl574_349
| ~ spl574_358 ),
inference(backward_demodulation,[],[f35908,f36040]) ).
fof(f35908,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))
| ~ spl574_349 ),
inference(avatar_component_clause,[],[f35906]) ).
fof(f37658,plain,
( spl574_415
| ~ spl574_20
| ~ spl574_74
| ~ spl574_95 ),
inference(avatar_split_clause,[],[f37569,f29246,f29077,f28752,f37655]) ).
fof(f37655,plain,
( spl574_415
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_415])]) ).
fof(f28752,plain,
( spl574_20
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl574_20])]) ).
fof(f29077,plain,
( spl574_74
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_74])]) ).
fof(f29246,plain,
( spl574_95
<=> c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_95])]) ).
fof(f37569,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))
| ~ spl574_20
| ~ spl574_74
| ~ spl574_95 ),
inference(forward_demodulation,[],[f37568,f28754]) ).
fof(f28754,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls
| ~ spl574_20 ),
inference(avatar_component_clause,[],[f28752]) ).
fof(f37568,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))
| ~ spl574_74
| ~ spl574_95 ),
inference(forward_demodulation,[],[f37567,f21216]) ).
fof(f21216,plain,
! [X0,X1] : hAPP(c_Fun_Oid(X0),X1) = X1,
inference(cnf_transformation,[],[f15386]) ).
fof(f15386,plain,
! [X0,X1] : hAPP(c_Fun_Oid(X0),X1) = X1,
inference(rectify,[],[f7492]) ).
fof(f7492,plain,
! [X1,X0] : hAPP(c_Fun_Oid(X1),X0) = X0,
inference(rectify,[],[f735]) ).
fof(f735,axiom,
! [X118,X34] : hAPP(c_Fun_Oid(X34),X118) = X118,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__def) ).
fof(f37567,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Fun_Oid(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))
| ~ spl574_74
| ~ spl574_95 ),
inference(forward_demodulation,[],[f37566,f29248]) ).
fof(f29248,plain,
( c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint)
| ~ spl574_95 ),
inference(avatar_component_clause,[],[f29246]) ).
fof(f37566,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))
| ~ spl574_74 ),
inference(forward_demodulation,[],[f37565,f27421]) ).
fof(f27421,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(definition_unfolding,[],[f22454,f20650]) ).
fof(f20650,plain,
! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f9741]) ).
fof(f9741,plain,
! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(rectify,[],[f2703]) ).
fof(f2703,axiom,
! [X106] : c_Int_Osucc(X106) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X106),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__def) ).
fof(f22454,plain,
! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OMin),
inference(cnf_transformation,[],[f6775]) ).
fof(f6775,plain,
! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OMin),
inference(rectify,[],[f2947]) ).
fof(f2947,axiom,
! [X106] : c_Int_Osucc(X106) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X106),c_Int_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I2_J) ).
fof(f37565,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl574_74 ),
inference(forward_demodulation,[],[f37564,f23929]) ).
fof(f23929,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X0) = X0,
inference(cnf_transformation,[],[f9866]) ).
fof(f9866,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X0) = X0,
inference(rectify,[],[f2679]) ).
fof(f2679,axiom,
! [X106] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X106) = X106,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls) ).
fof(f37564,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl574_74 ),
inference(forward_demodulation,[],[f37563,f23560]) ).
fof(f23560,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0)),
inference(cnf_transformation,[],[f7421]) ).
fof(f7421,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0)),
inference(rectify,[],[f1703]) ).
fof(f1703,axiom,
! [X31,X33,X32] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X33),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X32),X31)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X33),X31)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
fof(f37563,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl574_74 ),
inference(forward_demodulation,[],[f37562,f23560]) ).
fof(f37562,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl574_74 ),
inference(forward_demodulation,[],[f37561,f25075]) ).
fof(f25075,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0),
inference(cnf_transformation,[],[f18346]) ).
fof(f18346,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0),
inference(rectify,[],[f9798]) ).
fof(f9798,plain,
! [X1,X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0),
inference(rectify,[],[f1704]) ).
fof(f1704,axiom,
! [X151,X31] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X151),X31) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X31),X151),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).
fof(f37561,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))))
| ~ spl574_74 ),
inference(forward_demodulation,[],[f37560,f23929]) ).
fof(f37560,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))))
| ~ spl574_74 ),
inference(forward_demodulation,[],[f37559,f23560]) ).
fof(f37559,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))))
| ~ spl574_74 ),
inference(forward_demodulation,[],[f37558,f23560]) ).
fof(f37558,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))))
| ~ spl574_74 ),
inference(forward_demodulation,[],[f37557,f23560]) ).
fof(f37557,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))))
| ~ spl574_74 ),
inference(forward_demodulation,[],[f37556,f24146]) ).
fof(f24146,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X2)),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1)),
inference(cnf_transformation,[],[f8905]) ).
fof(f8905,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X2)),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1)),
inference(rectify,[],[f1702]) ).
fof(f1702,axiom,
! [X153,X154,X152] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X153),X152)),X154) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X153),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X152),X154)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(f37556,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))))
| ~ spl574_74 ),
inference(forward_demodulation,[],[f37555,f23929]) ).
fof(f37555,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))))
| ~ spl574_74 ),
inference(forward_demodulation,[],[f37554,f23560]) ).
fof(f37554,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))))
| ~ spl574_74 ),
inference(forward_demodulation,[],[f37553,f23560]) ).
fof(f37553,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))))
| ~ spl574_74 ),
inference(forward_demodulation,[],[f37552,f23929]) ).
fof(f37552,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))))))
| ~ spl574_74 ),
inference(forward_demodulation,[],[f37551,f23560]) ).
fof(f37551,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))))))
| ~ spl574_74 ),
inference(forward_demodulation,[],[f37550,f23560]) ).
fof(f37550,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))))))
| ~ spl574_74 ),
inference(forward_demodulation,[],[f37549,f24146]) ).
fof(f37549,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))))
| ~ spl574_74 ),
inference(forward_demodulation,[],[f37548,f24146]) ).
fof(f37548,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))))
| ~ spl574_74 ),
inference(forward_demodulation,[],[f29079,f24146]) ).
fof(f29079,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))
| ~ spl574_74 ),
inference(avatar_component_clause,[],[f29077]) ).
fof(f37648,plain,
( spl574_414
| ~ spl574_20
| ~ spl574_97
| ~ spl574_361 ),
inference(avatar_split_clause,[],[f37643,f36084,f29259,f28752,f37645]) ).
fof(f37645,plain,
( spl574_414
<=> c_Int_OPls = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_414])]) ).
fof(f36084,plain,
( spl574_361
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_361])]) ).
fof(f37643,plain,
( c_Int_OPls = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))))
| ~ spl574_20
| ~ spl574_97
| ~ spl574_361 ),
inference(forward_demodulation,[],[f37642,f28754]) ).
fof(f37642,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))))
| ~ spl574_97
| ~ spl574_361 ),
inference(forward_demodulation,[],[f36086,f29261]) ).
fof(f36086,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| ~ spl574_361 ),
inference(avatar_component_clause,[],[f36084]) ).
fof(f37634,plain,
( spl574_413
| ~ spl574_396
| ~ spl574_403 ),
inference(avatar_split_clause,[],[f37629,f37530,f37468,f37631]) ).
fof(f37530,plain,
( spl574_403
<=> hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_403])]) ).
fof(f37629,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))) = hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl574_396
| ~ spl574_403 ),
inference(forward_demodulation,[],[f37532,f37470]) ).
fof(f37532,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| ~ spl574_403 ),
inference(avatar_component_clause,[],[f37530]) ).
fof(f37628,plain,
( spl574_412
| ~ spl574_97
| ~ spl574_374 ),
inference(avatar_split_clause,[],[f37623,f36923,f29259,f37625]) ).
fof(f37625,plain,
( spl574_412
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_412])]) ).
fof(f36923,plain,
( spl574_374
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_374])]) ).
fof(f37623,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))))
| ~ spl574_97
| ~ spl574_374 ),
inference(forward_demodulation,[],[f36925,f29261]) ).
fof(f36925,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| ~ spl574_374 ),
inference(avatar_component_clause,[],[f36923]) ).
fof(f37621,plain,
( spl574_411
| ~ spl574_97
| ~ spl574_376 ),
inference(avatar_split_clause,[],[f37616,f36938,f29259,f37618]) ).
fof(f37616,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl574_97
| ~ spl574_376 ),
inference(forward_demodulation,[],[f36939,f29261]) ).
fof(f36939,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl574_376 ),
inference(avatar_component_clause,[],[f36938]) ).
fof(f37604,plain,
( spl574_410
| ~ spl574_20
| ~ spl574_95
| ~ spl574_135 ),
inference(avatar_split_clause,[],[f36976,f29659,f29246,f28752,f37601]) ).
fof(f29659,plain,
( spl574_135
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_135])]) ).
fof(f36976,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))
| ~ spl574_20
| ~ spl574_95
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36975,f28754]) ).
fof(f36975,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))
| ~ spl574_95
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36974,f21216]) ).
fof(f36974,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Fun_Oid(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))))
| ~ spl574_95
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36973,f29248]) ).
fof(f36973,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36972,f27421]) ).
fof(f36972,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36971,f23560]) ).
fof(f36971,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36970,f23560]) ).
fof(f36970,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36969,f25075]) ).
fof(f36969,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36968,f23929]) ).
fof(f36968,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36967,f23560]) ).
fof(f36967,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36966,f23560]) ).
fof(f36966,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36965,f23560]) ).
fof(f36965,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)))))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36964,f23929]) ).
fof(f36964,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))))))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36963,f23560]) ).
fof(f36963,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))))))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36962,f23560]) ).
fof(f36962,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))))))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36961,f23560]) ).
fof(f36961,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))))))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36960,f23929]) ).
fof(f36960,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)))))))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36959,f23560]) ).
fof(f36959,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)))))))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36958,f23560]) ).
fof(f36958,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)))))))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36957,f23560]) ).
fof(f36957,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)))))))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36956,f24146]) ).
fof(f36956,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))))))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36955,f24146]) ).
fof(f36955,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)))))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36954,f24146]) ).
fof(f36954,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36953,f24146]) ).
fof(f36953,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OPls)),c_Int_OMin)))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36952,f23929]) ).
fof(f36952,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OPls)),c_Int_OMin))))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36951,f23560]) ).
fof(f36951,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OPls)),c_Int_OMin))))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36950,f24146]) ).
fof(f36950,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OPls)),c_Int_OMin)))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f36949,f24146]) ).
fof(f36949,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OPls))),c_Int_OMin))))
| ~ spl574_135 ),
inference(forward_demodulation,[],[f29661,f27698]) ).
fof(f27698,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OMin) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(definition_unfolding,[],[f24704,f23060]) ).
fof(f23060,plain,
! [X0] : c_Int_Opred(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f9106]) ).
fof(f9106,plain,
! [X0] : c_Int_Opred(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(rectify,[],[f2695]) ).
fof(f2695,axiom,
! [X106] : c_Int_Opred(X106) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X106),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__def) ).
fof(f24704,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OMin) = c_Int_Opred(X0),
inference(cnf_transformation,[],[f6568]) ).
fof(f6568,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OMin) = c_Int_Opred(X0),
inference(rectify,[],[f2943]) ).
fof(f2943,axiom,
! [X106] : c_Int_Opred(X106) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X106),c_Int_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Min__right) ).
fof(f29661,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl574_135 ),
inference(avatar_component_clause,[],[f29659]) ).
fof(f37599,plain,
( spl574_409
| ~ spl574_97
| ~ spl574_363 ),
inference(avatar_split_clause,[],[f37594,f36581,f29259,f37596]) ).
fof(f37596,plain,
( spl574_409
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Obot__class_Obot(tc_Nat_Onat))),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_409])]) ).
fof(f36581,plain,
( spl574_363
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_363])]) ).
fof(f37594,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Obot__class_Obot(tc_Nat_Onat))),c_Int_OPls))
| ~ spl574_97
| ~ spl574_363 ),
inference(forward_demodulation,[],[f36583,f29261]) ).
fof(f36583,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_OPls))
| ~ spl574_363 ),
inference(avatar_component_clause,[],[f36581]) ).
fof(f37593,plain,
( spl574_408
| ~ spl574_97
| ~ spl574_353 ),
inference(avatar_split_clause,[],[f37588,f35939,f29259,f37590]) ).
fof(f37590,plain,
( spl574_408
<=> hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)) = hAPP(c_fequal,c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_408])]) ).
fof(f35939,plain,
( spl574_353
<=> hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_fequal,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_353])]) ).
fof(f37588,plain,
( hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)) = hAPP(c_fequal,c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl574_97
| ~ spl574_353 ),
inference(forward_demodulation,[],[f35941,f29261]) ).
fof(f35941,plain,
( hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_fequal,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl574_353 ),
inference(avatar_component_clause,[],[f35939]) ).
fof(f37587,plain,
( spl574_407
| ~ spl574_97
| ~ spl574_372 ),
inference(avatar_split_clause,[],[f37582,f36902,f29259,f37584]) ).
fof(f37584,plain,
( spl574_407
<=> c_Int_OPls = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_407])]) ).
fof(f36902,plain,
( spl574_372
<=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl574_372])]) ).
fof(f37582,plain,
( c_Int_OPls = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl574_97
| ~ spl574_372 ),
inference(forward_demodulation,[],[f36904,f29261]) ).
fof(f36904,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Int_OPls
| ~ spl574_372 ),
inference(avatar_component_clause,[],[f36902]) ).
fof(f37581,plain,
( spl574_406
| ~ spl574_97
| ~ spl574_366 ),
inference(avatar_split_clause,[],[f37576,f36673,f29259,f37578]) ).
fof(f37578,plain,
( spl574_406
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_406])]) ).
fof(f36673,plain,
( spl574_366
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_366])]) ).
fof(f37576,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls)
| ~ spl574_97
| ~ spl574_366 ),
inference(forward_demodulation,[],[f36675,f29261]) ).
fof(f36675,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls)
| ~ spl574_366 ),
inference(avatar_component_clause,[],[f36673]) ).
fof(f37575,plain,
( spl574_405
| ~ spl574_20
| ~ spl574_249 ),
inference(avatar_split_clause,[],[f37570,f31768,f28752,f37572]) ).
fof(f37572,plain,
( spl574_405
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_405])]) ).
fof(f31768,plain,
( spl574_249
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_249])]) ).
fof(f37570,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl574_20
| ~ spl574_249 ),
inference(forward_demodulation,[],[f31770,f28754]) ).
fof(f31770,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl574_249 ),
inference(avatar_component_clause,[],[f31768]) ).
fof(f37545,plain,
( spl574_328
| ~ spl574_95
| ~ spl574_102 ),
inference(avatar_split_clause,[],[f37544,f29299,f29246,f35513]) ).
fof(f35513,plain,
( spl574_328
<=> ! [X0] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_328])]) ).
fof(f29299,plain,
( spl574_102
<=> ! [X1] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_102])]) ).
fof(f37544,plain,
( ! [X1] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| ~ spl574_95
| ~ spl574_102 ),
inference(forward_demodulation,[],[f37543,f21216]) ).
fof(f37543,plain,
( ! [X1] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Fun_Oid(tc_Int_Oint),X1)))
| ~ spl574_95
| ~ spl574_102 ),
inference(forward_demodulation,[],[f29300,f29248]) ).
fof(f29300,plain,
( ! [X1] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)))
| ~ spl574_102 ),
inference(avatar_component_clause,[],[f29299]) ).
fof(f37540,plain,
( spl574_404
| ~ spl574_124
| ~ spl574_227 ),
inference(avatar_split_clause,[],[f37534,f31410,f29479,f37537]) ).
fof(f37537,plain,
( spl574_404
<=> c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_404])]) ).
fof(f29479,plain,
( spl574_124
<=> c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_124])]) ).
fof(f31410,plain,
( spl574_227
<=> c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral ),
introduced(avatar_definition,[new_symbols(naming,[spl574_227])]) ).
fof(f37534,plain,
( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
| ~ spl574_124
| ~ spl574_227 ),
inference(backward_demodulation,[],[f29481,f31412]) ).
fof(f31412,plain,
( c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral
| ~ spl574_227 ),
inference(avatar_component_clause,[],[f31410]) ).
fof(f29481,plain,
( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
| ~ spl574_124 ),
inference(avatar_component_clause,[],[f29479]) ).
fof(f37533,plain,
( spl574_403
| ~ spl574_95
| ~ spl574_97
| ~ spl574_251 ),
inference(avatar_split_clause,[],[f37528,f31795,f29259,f29246,f37530]) ).
fof(f31795,plain,
( spl574_251
<=> hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_251])]) ).
fof(f37528,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| ~ spl574_95
| ~ spl574_97
| ~ spl574_251 ),
inference(forward_demodulation,[],[f37527,f29261]) ).
fof(f37527,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))
| ~ spl574_95
| ~ spl574_251 ),
inference(forward_demodulation,[],[f37526,f21216]) ).
fof(f37526,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Fun_Oid(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))
| ~ spl574_95
| ~ spl574_251 ),
inference(forward_demodulation,[],[f37525,f29248]) ).
fof(f37525,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))
| ~ spl574_251 ),
inference(forward_demodulation,[],[f37524,f27421]) ).
fof(f37524,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl574_251 ),
inference(forward_demodulation,[],[f37523,f23560]) ).
fof(f37523,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl574_251 ),
inference(forward_demodulation,[],[f37522,f23560]) ).
fof(f37522,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl574_251 ),
inference(forward_demodulation,[],[f37521,f25075]) ).
fof(f37521,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))
| ~ spl574_251 ),
inference(forward_demodulation,[],[f37520,f24146]) ).
fof(f37520,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OMin))))
| ~ spl574_251 ),
inference(forward_demodulation,[],[f37519,f24146]) ).
fof(f37519,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Int_OMin)))
| ~ spl574_251 ),
inference(forward_demodulation,[],[f37518,f23929]) ).
fof(f37518,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Int_OMin))))
| ~ spl574_251 ),
inference(forward_demodulation,[],[f37517,f24146]) ).
fof(f37517,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Int_OMin)))
| ~ spl574_251 ),
inference(forward_demodulation,[],[f37516,f23929]) ).
fof(f37516,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Int_OMin))))
| ~ spl574_251 ),
inference(forward_demodulation,[],[f37515,f24146]) ).
fof(f37515,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Int_OMin)))
| ~ spl574_251 ),
inference(forward_demodulation,[],[f37514,f23929]) ).
fof(f37514,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Int_OMin))))
| ~ spl574_251 ),
inference(forward_demodulation,[],[f37513,f24146]) ).
fof(f37513,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Int_OMin)))
| ~ spl574_251 ),
inference(forward_demodulation,[],[f37512,f23929]) ).
fof(f37512,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Int_OMin))))
| ~ spl574_251 ),
inference(forward_demodulation,[],[f37511,f24146]) ).
fof(f37511,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Int_OMin)))
| ~ spl574_251 ),
inference(forward_demodulation,[],[f31797,f27698]) ).
fof(f31797,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl574_251 ),
inference(avatar_component_clause,[],[f31795]) ).
fof(f37510,plain,
( spl574_402
| ~ spl574_97
| ~ spl574_147 ),
inference(avatar_split_clause,[],[f37505,f30132,f29259,f37507]) ).
fof(f37507,plain,
( spl574_402
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_402])]) ).
fof(f30132,plain,
( spl574_147
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_147])]) ).
fof(f37505,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue)
| ~ spl574_97
| ~ spl574_147 ),
inference(forward_demodulation,[],[f30134,f29261]) ).
fof(f30134,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue)
| ~ spl574_147 ),
inference(avatar_component_clause,[],[f30132]) ).
fof(f37502,plain,
( spl574_401
| ~ spl574_9
| ~ spl574_97 ),
inference(avatar_split_clause,[],[f37497,f29259,f28697,f37499]) ).
fof(f37499,plain,
( spl574_401
<=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_401])]) ).
fof(f28697,plain,
( spl574_9
<=> hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_9])]) ).
fof(f37497,plain,
( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl574_9
| ~ spl574_97 ),
inference(forward_demodulation,[],[f28699,f29261]) ).
fof(f28699,plain,
( hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| ~ spl574_9 ),
inference(avatar_component_clause,[],[f28697]) ).
fof(f37496,plain,
( spl574_400
| ~ spl574_215 ),
inference(avatar_split_clause,[],[f37491,f31217,f37493]) ).
fof(f37493,plain,
( spl574_400
<=> c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_400])]) ).
fof(f31217,plain,
( spl574_215
<=> c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_215])]) ).
fof(f37491,plain,
( c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))
| ~ spl574_215 ),
inference(forward_demodulation,[],[f31219,f34306]) ).
fof(f31219,plain,
( c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool))))
| ~ spl574_215 ),
inference(avatar_component_clause,[],[f31217]) ).
fof(f37490,plain,
( spl574_399
| ~ spl574_89 ),
inference(avatar_split_clause,[],[f37485,f29179,f37487]) ).
fof(f29179,plain,
( spl574_89
<=> c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_89])]) ).
fof(f37485,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(c_fequal,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)))
| ~ spl574_89 ),
inference(forward_demodulation,[],[f29181,f34306]) ).
fof(f29181,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
| ~ spl574_89 ),
inference(avatar_component_clause,[],[f29179]) ).
fof(f37484,plain,
( spl574_398
| ~ spl574_97
| ~ spl574_116 ),
inference(avatar_split_clause,[],[f37217,f29422,f29259,f37481]) ).
fof(f37481,plain,
( spl574_398
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_398])]) ).
fof(f29422,plain,
( spl574_116
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_116])]) ).
fof(f37217,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse)
| ~ spl574_97
| ~ spl574_116 ),
inference(backward_demodulation,[],[f29424,f29261]) ).
fof(f29424,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse)
| ~ spl574_116 ),
inference(avatar_component_clause,[],[f29422]) ).
fof(f37478,plain,
( spl574_397
| ~ spl574_97
| ~ spl574_121 ),
inference(avatar_split_clause,[],[f37219,f29463,f29259,f37475]) ).
fof(f37475,plain,
( spl574_397
<=> c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_397])]) ).
fof(f29463,plain,
( spl574_121
<=> hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_121])]) ).
fof(f37219,plain,
( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl574_97
| ~ spl574_121 ),
inference(backward_demodulation,[],[f29465,f29261]) ).
fof(f29465,plain,
( hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ spl574_121 ),
inference(avatar_component_clause,[],[f29463]) ).
fof(f37471,plain,
( spl574_396
| ~ spl574_97
| ~ spl574_223 ),
inference(avatar_split_clause,[],[f37240,f31382,f29259,f37468]) ).
fof(f37240,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl574_97
| ~ spl574_223 ),
inference(backward_demodulation,[],[f31384,f29261]) ).
fof(f37465,plain,
( ~ spl574_395
| spl574_51
| ~ spl574_97 ),
inference(avatar_split_clause,[],[f37208,f29259,f28943,f37462]) ).
fof(f37462,plain,
( spl574_395
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_395])]) ).
fof(f28943,plain,
( spl574_51
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_51])]) ).
fof(f37208,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| spl574_51
| ~ spl574_97 ),
inference(backward_demodulation,[],[f28945,f29261]) ).
fof(f28945,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| spl574_51 ),
inference(avatar_component_clause,[],[f28943]) ).
fof(f37459,plain,
( spl574_394
| ~ spl574_42
| ~ spl574_97 ),
inference(avatar_split_clause,[],[f37207,f29259,f28893,f37456]) ).
fof(f37456,plain,
( spl574_394
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_394])]) ).
fof(f28893,plain,
( spl574_42
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_42])]) ).
fof(f37207,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP)
| ~ spl574_42
| ~ spl574_97 ),
inference(backward_demodulation,[],[f28895,f29261]) ).
fof(f28895,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP)
| ~ spl574_42 ),
inference(avatar_component_clause,[],[f28893]) ).
fof(f37454,plain,
( spl574_393
| ~ spl574_97
| ~ spl574_183 ),
inference(avatar_split_clause,[],[f37227,f30630,f29259,f37451]) ).
fof(f37451,plain,
( spl574_393
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_393])]) ).
fof(f30630,plain,
( spl574_183
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_183])]) ).
fof(f37227,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse)
| ~ spl574_97
| ~ spl574_183 ),
inference(backward_demodulation,[],[f30632,f29261]) ).
fof(f30632,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse)
| ~ spl574_183 ),
inference(avatar_component_clause,[],[f30630]) ).
fof(f37442,plain,
( spl574_392
| ~ spl574_97
| ~ spl574_120 ),
inference(avatar_split_clause,[],[f37218,f29457,f29259,f37439]) ).
fof(f37439,plain,
( spl574_392
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_392])]) ).
fof(f29457,plain,
( spl574_120
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_120])]) ).
fof(f37218,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue)
| ~ spl574_97
| ~ spl574_120 ),
inference(backward_demodulation,[],[f29459,f29261]) ).
fof(f29459,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue)
| ~ spl574_120 ),
inference(avatar_component_clause,[],[f29457]) ).
fof(f37433,plain,
( spl574_391
| ~ spl574_97
| ~ spl574_279 ),
inference(avatar_split_clause,[],[f37250,f33742,f29259,f37430]) ).
fof(f37430,plain,
( spl574_391
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_391])]) ).
fof(f33742,plain,
( spl574_279
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_279])]) ).
fof(f37250,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))
| ~ spl574_97
| ~ spl574_279 ),
inference(backward_demodulation,[],[f33744,f29261]) ).
fof(f33744,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))
| ~ spl574_279 ),
inference(avatar_component_clause,[],[f33742]) ).
fof(f37428,plain,
( spl574_390
| ~ spl574_97
| ~ spl574_98 ),
inference(avatar_split_clause,[],[f37212,f29264,f29259,f37425]) ).
fof(f37425,plain,
( spl574_390
<=> c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_390])]) ).
fof(f29264,plain,
( spl574_98
<=> c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_98])]) ).
fof(f37212,plain,
( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl574_97
| ~ spl574_98 ),
inference(backward_demodulation,[],[f29266,f29261]) ).
fof(f29266,plain,
( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl574_98 ),
inference(avatar_component_clause,[],[f29264]) ).
fof(f37420,plain,
( spl574_389
| ~ spl574_97
| ~ spl574_240 ),
inference(avatar_split_clause,[],[f37242,f31638,f29259,f37417]) ).
fof(f37417,plain,
( spl574_389
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_389])]) ).
fof(f31638,plain,
( spl574_240
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_240])]) ).
fof(f37242,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl574_97
| ~ spl574_240 ),
inference(backward_demodulation,[],[f31640,f29261]) ).
fof(f31640,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl574_240 ),
inference(avatar_component_clause,[],[f31638]) ).
fof(f37406,plain,
( spl574_388
| ~ spl574_97
| ~ spl574_174 ),
inference(avatar_split_clause,[],[f37225,f30517,f29259,f37403]) ).
fof(f37403,plain,
( spl574_388
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_388])]) ).
fof(f30517,plain,
( spl574_174
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_174])]) ).
fof(f37225,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl574_97
| ~ spl574_174 ),
inference(backward_demodulation,[],[f30519,f29261]) ).
fof(f30519,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl574_174 ),
inference(avatar_component_clause,[],[f30517]) ).
fof(f37400,plain,
( ~ spl574_386
| spl574_387
| ~ spl574_97 ),
inference(avatar_split_clause,[],[f37392,f29259,f37398,f37394]) ).
fof(f37394,plain,
( spl574_386
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_386])]) ).
fof(f37398,plain,
( spl574_387
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) != hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),X0))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X0),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),c_Orderings_Obot__class_Obot(tc_Nat_Onat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_387])]) ).
fof(f37392,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) != hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X0),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),c_Orderings_Obot__class_Obot(tc_Nat_Onat))) )
| ~ spl574_97 ),
inference(forward_subsumption_demodulation,[],[f37391,f37367]) ).
fof(f37367,plain,
( ! [X0] :
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),c_Orderings_Obot__class_Obot(tc_Nat_Onat))) )
| ~ spl574_97 ),
inference(forward_demodulation,[],[f37143,f29261]) ).
fof(f37143,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Orderings_Obot__class_Obot(tc_Nat_Onat) = X0 )
| ~ spl574_97 ),
inference(backward_demodulation,[],[f26169,f29261]) ).
fof(f26169,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f19194]) ).
fof(f19194,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ),
inference(nnf_transformation,[],[f6704]) ).
fof(f6704,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(rectify,[],[f569]) ).
fof(f569,axiom,
! [X74] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X74
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X74),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).
fof(f37391,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| c_Orderings_Obot__class_Obot(tc_Nat_Onat) != hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X0),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),X0)) )
| ~ spl574_97 ),
inference(forward_demodulation,[],[f37390,f37027]) ).
fof(f37027,plain,
( ! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),X0) = X0
| ~ spl574_97 ),
inference(backward_demodulation,[],[f21331,f29261]) ).
fof(f21331,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(cnf_transformation,[],[f5696]) ).
fof(f5696,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f1021]) ).
fof(f1021,axiom,
! [X75] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X75) = X75,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(f37390,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| c_Orderings_Obot__class_Obot(tc_Nat_Onat) != hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X0)),X0),X1)) )
| ~ spl574_97 ),
inference(forward_subsumption_demodulation,[],[f37389,f22689]) ).
fof(f22689,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X1)) ),
inference(cnf_transformation,[],[f16543]) ).
fof(f16543,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X1))
| X0 = X1 ),
inference(rectify,[],[f11502]) ).
fof(f11502,plain,
! [X1,X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0))
| X0 = X1 ),
inference(flattening,[],[f11501]) ).
fof(f11501,plain,
! [X1,X0] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0)) ),
inference(ennf_transformation,[],[f8405]) ).
fof(f8405,plain,
! [X1,X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X1))
=> X0 = X1 ) ),
inference(rectify,[],[f526]) ).
fof(f526,axiom,
! [X75,X99] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X99),X75))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X75),X99))
=> X75 = X99 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).
fof(f37389,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))
| c_Orderings_Obot__class_Obot(tc_Nat_Onat) != hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X0)),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),c_Orderings_Obot__class_Obot(tc_Nat_Onat))) )
| ~ spl574_97 ),
inference(forward_subsumption_demodulation,[],[f37388,f37367]) ).
fof(f37388,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) != hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X0))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X0)),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1))) )
| ~ spl574_97 ),
inference(forward_subsumption_demodulation,[],[f37387,f22689]) ).
fof(f37387,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))
| c_Orderings_Obot__class_Obot(tc_Nat_Onat) != hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X0)),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),c_Orderings_Obot__class_Obot(tc_Nat_Onat))) )
| ~ spl574_97 ),
inference(forward_demodulation,[],[f37386,f29261]) ).
fof(f37386,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) != hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X0)),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ~ spl574_97 ),
inference(forward_demodulation,[],[f37241,f29261]) ).
fof(f37241,plain,
( ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X0)),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1))) )
| ~ spl574_97 ),
inference(backward_demodulation,[],[f31555,f29261]) ).
fof(f31555,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X0)),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1) ),
inference(forward_demodulation,[],[f28111,f25994]) ).
fof(f25994,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1),
inference(cnf_transformation,[],[f9850]) ).
fof(f9850,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1),
inference(rectify,[],[f1144]) ).
fof(f1144,axiom,
! [X99,X75] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X99),X75) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X75),X99),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(f28111,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X0)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(equality_resolution,[],[f21067]) ).
fof(f21067,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X0),X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X0)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)) != X2 ),
inference(cnf_transformation,[],[f15284]) ).
fof(f15284,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X0),X1))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1) )
| ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1))) ) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X0)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)) != X2 )
& ( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1) )
& ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1))) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)),X0)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)) = X2 )
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X0),X1)) ) ),
inference(rectify,[],[f15283]) ).
fof(f15283,plain,
! [X0,X2,X1] :
( ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X0),X2))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2) )
| ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2))) ) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X0)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)) != X1 )
& ( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2) )
& ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2))) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X0)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)) = X1 )
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X0),X2)) ) ),
inference(flattening,[],[f15282]) ).
fof(f15282,plain,
! [X0,X2,X1] :
( ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X0),X2))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2) )
| ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2))) ) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X0)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)) != X1 )
& ( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2) )
& ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2))) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X0)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)) = X1 )
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X0),X2)) ) ),
inference(nnf_transformation,[],[f10770]) ).
fof(f10770,plain,
! [X0,X2,X1] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X0),X2))
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2) )
& ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2))) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X0)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)) = X1 ) ),
inference(ennf_transformation,[],[f6453]) ).
fof(f6453,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2)),X0)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)) = X1
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2))) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X2) ) )
<=> hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X0),X2)) ),
inference(rectify,[],[f3156]) ).
fof(f3156,axiom,
! [X74,X77,X218] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X74
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X218) )
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X218)),X74)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X218)) = X77
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X74
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X74))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X218)),X74))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X218))) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X74))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X74),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X218)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X218)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ) )
<=> hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X77,X74),X218)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__def) ).
fof(f37366,plain,
( spl574_385
| ~ spl574_97
| ~ spl574_158 ),
inference(avatar_split_clause,[],[f37223,f30279,f29259,f37363]) ).
fof(f37363,plain,
( spl574_385
<=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Obot__class_Obot(tc_Nat_Onat)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Obot__class_Obot(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_385])]) ).
fof(f30279,plain,
( spl574_158
<=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_158])]) ).
fof(f37223,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Obot__class_Obot(tc_Nat_Onat)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| ~ spl574_97
| ~ spl574_158 ),
inference(backward_demodulation,[],[f30281,f29261]) ).
fof(f30281,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ spl574_158 ),
inference(avatar_component_clause,[],[f30279]) ).
fof(f37360,plain,
( spl574_384
| ~ spl574_2
| ~ spl574_97 ),
inference(avatar_split_clause,[],[f37204,f29259,f28663,f37357]) ).
fof(f37357,plain,
( spl574_384
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_384])]) ).
fof(f28663,plain,
( spl574_2
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_2])]) ).
fof(f37204,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)
| ~ spl574_2
| ~ spl574_97 ),
inference(backward_demodulation,[],[f28665,f29261]) ).
fof(f28665,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)
| ~ spl574_2 ),
inference(avatar_component_clause,[],[f28663]) ).
fof(f37355,plain,
( spl574_383
| ~ spl574_41
| ~ spl574_97 ),
inference(avatar_split_clause,[],[f37206,f29259,f28887,f37352]) ).
fof(f37352,plain,
( spl574_383
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_383])]) ).
fof(f28887,plain,
( spl574_41
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_41])]) ).
fof(f37206,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP)
| ~ spl574_41
| ~ spl574_97 ),
inference(backward_demodulation,[],[f28889,f29261]) ).
fof(f28889,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP)
| ~ spl574_41 ),
inference(avatar_component_clause,[],[f28887]) ).
fof(f37343,plain,
( spl574_382
| ~ spl574_97
| ~ spl574_320 ),
inference(avatar_split_clause,[],[f37279,f35342,f29259,f37340]) ).
fof(f37340,plain,
( spl574_382
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_382])]) ).
fof(f35342,plain,
( spl574_320
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_320])]) ).
fof(f37279,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))
| ~ spl574_97
| ~ spl574_320 ),
inference(backward_demodulation,[],[f35344,f29261]) ).
fof(f35344,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))
| ~ spl574_320 ),
inference(avatar_component_clause,[],[f35342]) ).
fof(f37338,plain,
( spl574_381
| ~ spl574_97
| ~ spl574_345 ),
inference(avatar_split_clause,[],[f37282,f35757,f29259,f37335]) ).
fof(f37335,plain,
( spl574_381
<=> c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_381])]) ).
fof(f35757,plain,
( spl574_345
<=> c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_345])]) ).
fof(f37282,plain,
( c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl574_97
| ~ spl574_345 ),
inference(backward_demodulation,[],[f35759,f29261]) ).
fof(f35759,plain,
( c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl574_345 ),
inference(avatar_component_clause,[],[f35757]) ).
fof(f37333,plain,
( spl574_380
| ~ spl574_34
| ~ spl574_97 ),
inference(avatar_split_clause,[],[f37205,f29259,f28823,f37330]) ).
fof(f37330,plain,
( spl574_380
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_380])]) ).
fof(f28823,plain,
( spl574_34
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_34])]) ).
fof(f37205,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ spl574_34
| ~ spl574_97 ),
inference(backward_demodulation,[],[f28825,f29261]) ).
fof(f28825,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ spl574_34 ),
inference(avatar_component_clause,[],[f28823]) ).
fof(f37328,plain,
( spl574_379
| ~ spl574_97
| ~ spl574_133 ),
inference(avatar_split_clause,[],[f37221,f29635,f29259,f37325]) ).
fof(f37325,plain,
( spl574_379
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),c_List_Olist_ONil(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_379])]) ).
fof(f29635,plain,
( spl574_133
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),c_List_Olist_ONil(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_133])]) ).
fof(f37221,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),c_List_Olist_ONil(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl574_97
| ~ spl574_133 ),
inference(backward_demodulation,[],[f29637,f29261]) ).
fof(f29637,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),c_List_Olist_ONil(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl574_133 ),
inference(avatar_component_clause,[],[f29635]) ).
fof(f36991,plain,
( ~ spl574_378
| ~ spl574_95
| spl574_304 ),
inference(avatar_split_clause,[],[f36986,f34707,f29246,f36988]) ).
fof(f36988,plain,
( spl574_378
<=> c_Int_OPls = hAPP(c_Fun_Oid(tc_Int_Oint),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_378])]) ).
fof(f34707,plain,
( spl574_304
<=> hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),c_Int_OPls) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_304])]) ).
fof(f36986,plain,
( c_Int_OPls != hAPP(c_Fun_Oid(tc_Int_Oint),c_Int_OMin)
| ~ spl574_95
| spl574_304 ),
inference(forward_demodulation,[],[f36985,f21216]) ).
fof(f36985,plain,
( hAPP(c_Fun_Oid(tc_Int_Oint),c_Int_OMin) != hAPP(c_Fun_Oid(tc_Int_Oint),c_Int_OPls)
| ~ spl574_95
| spl574_304 ),
inference(forward_demodulation,[],[f34709,f29248]) ).
fof(f34709,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),c_Int_OMin)
| spl574_304 ),
inference(avatar_component_clause,[],[f34707]) ).
fof(f36984,plain,
( spl574_377
| ~ spl574_263 ),
inference(avatar_split_clause,[],[f36979,f32611,f36981]) ).
fof(f36981,plain,
( spl574_377
<=> c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Product__Type_Ointernal__split(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_377])]) ).
fof(f32611,plain,
( spl574_263
<=> c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Ointernal__split(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_263])]) ).
fof(f36979,plain,
( c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Product__Type_Ointernal__split(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))
| ~ spl574_263 ),
inference(forward_demodulation,[],[f32613,f21003]) ).
fof(f32613,plain,
( c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Ointernal__split(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat))))
| ~ spl574_263 ),
inference(avatar_component_clause,[],[f32611]) ).
fof(f36978,plain,
( spl574_356
| ~ spl574_286 ),
inference(avatar_split_clause,[],[f36977,f33916,f36007]) ).
fof(f36007,plain,
( spl574_356
<=> c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_356])]) ).
fof(f33916,plain,
( spl574_286
<=> c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_286])]) ).
fof(f36977,plain,
( c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),c_Int_OMin)
| ~ spl574_286 ),
inference(forward_demodulation,[],[f33918,f27421]) ).
fof(f33918,plain,
( c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OMin)
| ~ spl574_286 ),
inference(avatar_component_clause,[],[f33916]) ).
fof(f36948,plain,
( spl574_347
| ~ spl574_223
| ~ spl574_256 ),
inference(avatar_split_clause,[],[f36947,f32423,f31382,f35848]) ).
fof(f32423,plain,
( spl574_256
<=> hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_256])]) ).
fof(f36947,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))
| ~ spl574_223
| ~ spl574_256 ),
inference(forward_demodulation,[],[f36946,f31384]) ).
fof(f36946,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))
| ~ spl574_256 ),
inference(forward_demodulation,[],[f36945,f27421]) ).
fof(f36945,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl574_256 ),
inference(forward_demodulation,[],[f36944,f23929]) ).
fof(f36944,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl574_256 ),
inference(forward_demodulation,[],[f36943,f23929]) ).
fof(f36943,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl574_256 ),
inference(forward_demodulation,[],[f36942,f23929]) ).
fof(f36942,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ spl574_256 ),
inference(forward_demodulation,[],[f32425,f23929]) ).
fof(f32425,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))
| ~ spl574_256 ),
inference(avatar_component_clause,[],[f32423]) ).
fof(f36941,plain,
( ~ spl574_376
| spl574_152
| ~ spl574_223 ),
inference(avatar_split_clause,[],[f36936,f31382,f30211,f36938]) ).
fof(f36932,plain,
( spl574_375
| ~ spl574_201 ),
inference(avatar_split_clause,[],[f36927,f30960,f36929]) ).
fof(f36929,plain,
( spl574_375
<=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_375])]) ).
fof(f30960,plain,
( spl574_201
<=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_201])]) ).
fof(f36927,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),c_Int_OPls)
| ~ spl574_201 ),
inference(forward_demodulation,[],[f30962,f27421]) ).
fof(f30962,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OPls)
| ~ spl574_201 ),
inference(avatar_component_clause,[],[f30960]) ).
fof(f36926,plain,
( spl574_374
| ~ spl574_160 ),
inference(avatar_split_clause,[],[f36921,f30301,f36923]) ).
fof(f30301,plain,
( spl574_160
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_160])]) ).
fof(f36921,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| ~ spl574_160 ),
inference(forward_demodulation,[],[f30303,f34306]) ).
fof(f30303,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))
| ~ spl574_160 ),
inference(avatar_component_clause,[],[f30301]) ).
fof(f36920,plain,
( spl574_357
| ~ spl574_59 ),
inference(avatar_split_clause,[],[f36919,f28992,f36025]) ).
fof(f36025,plain,
( spl574_357
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_357])]) ).
fof(f28992,plain,
( spl574_59
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_59])]) ).
fof(f36919,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))
| ~ spl574_59 ),
inference(forward_demodulation,[],[f36918,f27421]) ).
fof(f36918,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl574_59 ),
inference(forward_demodulation,[],[f36917,f25075]) ).
fof(f36917,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))
| ~ spl574_59 ),
inference(forward_demodulation,[],[f36916,f23929]) ).
fof(f36916,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))
| ~ spl574_59 ),
inference(forward_demodulation,[],[f36915,f23560]) ).
fof(f36915,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))
| ~ spl574_59 ),
inference(forward_demodulation,[],[f28994,f24146]) ).
fof(f28994,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))
| ~ spl574_59 ),
inference(avatar_component_clause,[],[f28992]) ).
fof(f36911,plain,
( spl574_373
| ~ spl574_20
| ~ spl574_297 ),
inference(avatar_split_clause,[],[f36906,f34547,f28752,f36908]) ).
fof(f36908,plain,
( spl574_373
<=> c_Nat__Transfer_Ois__nat(c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_373])]) ).
fof(f34547,plain,
( spl574_297
<=> c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_297])]) ).
fof(f36906,plain,
( c_Nat__Transfer_Ois__nat(c_Int_OPls)
| ~ spl574_20
| ~ spl574_297 ),
inference(forward_demodulation,[],[f34549,f28754]) ).
fof(f34549,plain,
( c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl574_297 ),
inference(avatar_component_clause,[],[f34547]) ).
fof(f36905,plain,
( spl574_372
| ~ spl574_20
| ~ spl574_55 ),
inference(avatar_split_clause,[],[f36900,f28964,f28752,f36902]) ).
fof(f28964,plain,
( spl574_55
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_55])]) ).
fof(f36900,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Int_OPls
| ~ spl574_20
| ~ spl574_55 ),
inference(forward_demodulation,[],[f28966,f28754]) ).
fof(f28966,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl574_55 ),
inference(avatar_component_clause,[],[f28964]) ).
fof(f36890,plain,
( spl574_371
| ~ spl574_20
| ~ spl574_301 ),
inference(avatar_split_clause,[],[f36885,f34678,f28752,f36887]) ).
fof(f36887,plain,
( spl574_371
<=> c_Int_OPls = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_371])]) ).
fof(f34678,plain,
( spl574_301
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_301])]) ).
fof(f36885,plain,
( c_Int_OPls = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Int_OPls)
| ~ spl574_20
| ~ spl574_301 ),
inference(forward_demodulation,[],[f34680,f28754]) ).
fof(f34680,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl574_301 ),
inference(avatar_component_clause,[],[f34678]) ).
fof(f36879,plain,
( ~ spl574_370
| spl574_182 ),
inference(avatar_split_clause,[],[f36874,f30612,f36876]) ).
fof(f30612,plain,
( spl574_182
<=> c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY)),v_Q)),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pn),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_HOL_Obool))))),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),v_Q)),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pn),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_HOL_Obool))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_182])]) ).
fof(f36874,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY)),v_Q)),hAPP(c_fequal,v_pn))),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),v_Q)),hAPP(c_fequal,v_pn)))
| spl574_182 ),
inference(forward_demodulation,[],[f30614,f34306]) ).
fof(f30614,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY)),v_Q)),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pn),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_HOL_Obool))))),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),v_Q)),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pn),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_HOL_Obool)))))
| spl574_182 ),
inference(avatar_component_clause,[],[f30612]) ).
fof(f36861,plain,
( ~ spl574_362
| spl574_38 ),
inference(avatar_split_clause,[],[f36860,f28845,f36558]) ).
fof(f36558,plain,
( spl574_362
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_362])]) ).
fof(f28845,plain,
( spl574_38
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_38])]) ).
fof(f36860,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OPls))
| spl574_38 ),
inference(forward_demodulation,[],[f28847,f22630]) ).
fof(f22630,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0,
inference(cnf_transformation,[],[f6416]) ).
fof(f6416,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0,
inference(rectify,[],[f2650]) ).
fof(f2650,axiom,
! [X106] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X106) = X106,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__is__id) ).
fof(f28847,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls)))
| spl574_38 ),
inference(avatar_component_clause,[],[f28845]) ).
fof(f36858,plain,
( spl574_347
| ~ spl574_81
| ~ spl574_223 ),
inference(avatar_split_clause,[],[f36857,f31382,f29128,f35848]) ).
fof(f29128,plain,
( spl574_81
<=> hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_81])]) ).
fof(f36857,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))
| ~ spl574_81
| ~ spl574_223 ),
inference(forward_demodulation,[],[f36856,f31384]) ).
fof(f36856,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36855,f27421]) ).
fof(f36855,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36854,f23560]) ).
fof(f36854,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36853,f23560]) ).
fof(f36853,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36852,f25075]) ).
fof(f36852,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36851,f23929]) ).
fof(f36851,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36850,f23560]) ).
fof(f36850,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36849,f23560]) ).
fof(f36849,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36848,f23560]) ).
fof(f36848,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)))))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36847,f23929]) ).
fof(f36847,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))))))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36846,f23560]) ).
fof(f36846,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))))))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36845,f23560]) ).
fof(f36845,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))))))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36844,f23560]) ).
fof(f36844,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))))))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36843,f24146]) ).
fof(f36843,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)))))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36842,f24146]) ).
fof(f36842,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin))))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36841,f23929]) ).
fof(f36841,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin)))))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36840,f23560]) ).
fof(f36840,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin)))))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36839,f23560]) ).
fof(f36839,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin)))))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36838,f23929]) ).
fof(f36838,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin))))))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36837,f23560]) ).
fof(f36837,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin))))))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36836,f23560]) ).
fof(f36836,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin))))))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36835,f24146]) ).
fof(f36835,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin)))))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36834,f24146]) ).
fof(f36834,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin))))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36833,f24146]) ).
fof(f36833,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin)))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f36832,f24146]) ).
fof(f36832,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))
| ~ spl574_81 ),
inference(forward_demodulation,[],[f29130,f27698]) ).
fof(f29130,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl574_81 ),
inference(avatar_component_clause,[],[f29128]) ).
fof(f36830,plain,
( spl574_295
| ~ spl574_75 ),
inference(avatar_split_clause,[],[f36829,f29082,f34529]) ).
fof(f34529,plain,
( spl574_295
<=> c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_295])]) ).
fof(f29082,plain,
( spl574_75
<=> c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_75])]) ).
fof(f36829,plain,
( c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl574_75 ),
inference(forward_demodulation,[],[f36828,f27421]) ).
fof(f36828,plain,
( c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl574_75 ),
inference(forward_demodulation,[],[f36827,f25075]) ).
fof(f36827,plain,
( c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl574_75 ),
inference(forward_demodulation,[],[f36826,f23929]) ).
fof(f36826,plain,
( c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl574_75 ),
inference(forward_demodulation,[],[f36825,f23560]) ).
fof(f36825,plain,
( c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl574_75 ),
inference(forward_demodulation,[],[f29084,f24146]) ).
fof(f29084,plain,
( c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl574_75 ),
inference(avatar_component_clause,[],[f29082]) ).
fof(f36790,plain,
( ~ spl574_369
| ~ spl574_20
| spl574_196 ),
inference(avatar_split_clause,[],[f36431,f30898,f28752,f36787]) ).
fof(f36787,plain,
( spl574_369
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl574_369])]) ).
fof(f30898,plain,
( spl574_196
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_196])]) ).
fof(f36431,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Int_OPls
| ~ spl574_20
| spl574_196 ),
inference(backward_demodulation,[],[f30900,f28754]) ).
fof(f30900,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| spl574_196 ),
inference(avatar_component_clause,[],[f30898]) ).
fof(f36780,plain,
( spl574_368
| ~ spl574_20
| ~ spl574_274 ),
inference(avatar_split_clause,[],[f36475,f33676,f28752,f36777]) ).
fof(f36777,plain,
( spl574_368
<=> c_Nitpick_OFrac = hAPP(c_Product__Type_Ointernal__split(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_368])]) ).
fof(f33676,plain,
( spl574_274
<=> c_Nitpick_OFrac = hAPP(c_Product__Type_Ointernal__split(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_274])]) ).
fof(f36475,plain,
( c_Nitpick_OFrac = hAPP(c_Product__Type_Ointernal__split(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl574_20
| ~ spl574_274 ),
inference(backward_demodulation,[],[f33678,f28754]) ).
fof(f33678,plain,
( c_Nitpick_OFrac = hAPP(c_Product__Type_Ointernal__split(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl574_274 ),
inference(avatar_component_clause,[],[f33676]) ).
fof(f36701,plain,
( spl574_367
| ~ spl574_20
| ~ spl574_64 ),
inference(avatar_split_clause,[],[f36397,f29018,f28752,f36698]) ).
fof(f36698,plain,
( spl574_367
<=> c_Int_OPls = hAPP(c_Code__Numeral_Oint__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_367])]) ).
fof(f29018,plain,
( spl574_64
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_64])]) ).
fof(f36397,plain,
( c_Int_OPls = hAPP(c_Code__Numeral_Oint__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))
| ~ spl574_20
| ~ spl574_64 ),
inference(backward_demodulation,[],[f29020,f28754]) ).
fof(f29020,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))
| ~ spl574_64 ),
inference(avatar_component_clause,[],[f29018]) ).
fof(f36676,plain,
( spl574_366
| ~ spl574_20
| ~ spl574_203 ),
inference(avatar_split_clause,[],[f36433,f30990,f28752,f36673]) ).
fof(f30990,plain,
( spl574_203
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_203])]) ).
fof(f36433,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls)
| ~ spl574_20
| ~ spl574_203 ),
inference(backward_demodulation,[],[f30992,f28754]) ).
fof(f30992,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl574_203 ),
inference(avatar_component_clause,[],[f30990]) ).
fof(f36598,plain,
( spl574_365
| ~ spl574_20
| ~ spl574_311 ),
inference(avatar_split_clause,[],[f36490,f34826,f28752,f36595]) ).
fof(f36595,plain,
( spl574_365
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_365])]) ).
fof(f34826,plain,
( spl574_311
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_311])]) ).
fof(f36490,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl574_20
| ~ spl574_311 ),
inference(backward_demodulation,[],[f34828,f28754]) ).
fof(f34828,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl574_311 ),
inference(avatar_component_clause,[],[f34826]) ).
fof(f36592,plain,
( spl574_364
| ~ spl574_11
| ~ spl574_20 ),
inference(avatar_split_clause,[],[f36393,f28752,f28707,f36589]) ).
fof(f36589,plain,
( spl574_364
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Int_OPls)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_364])]) ).
fof(f28707,plain,
( spl574_11
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_11])]) ).
fof(f36393,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Int_OPls)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl574_11
| ~ spl574_20 ),
inference(backward_demodulation,[],[f28709,f28754]) ).
fof(f28709,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl574_11 ),
inference(avatar_component_clause,[],[f28707]) ).
fof(f36584,plain,
( spl574_363
| ~ spl574_20
| ~ spl574_49 ),
inference(avatar_split_clause,[],[f36395,f28934,f28752,f36581]) ).
fof(f28934,plain,
( spl574_49
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_49])]) ).
fof(f36395,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_OPls))
| ~ spl574_20
| ~ spl574_49 ),
inference(backward_demodulation,[],[f28936,f28754]) ).
fof(f28936,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ spl574_49 ),
inference(avatar_component_clause,[],[f28934]) ).
fof(f36561,plain,
( ~ spl574_362
| ~ spl574_20
| spl574_25 ),
inference(avatar_split_clause,[],[f36394,f28777,f28752,f36558]) ).
fof(f28777,plain,
( spl574_25
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_25])]) ).
fof(f36394,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OPls))
| ~ spl574_20
| spl574_25 ),
inference(backward_demodulation,[],[f28779,f28754]) ).
fof(f28779,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| spl574_25 ),
inference(avatar_component_clause,[],[f28777]) ).
fof(f36087,plain,
( spl574_361
| ~ spl574_293 ),
inference(avatar_split_clause,[],[f36082,f34241,f36084]) ).
fof(f34241,plain,
( spl574_293
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_COMBC(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_fequal),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_293])]) ).
fof(f36082,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| ~ spl574_293 ),
inference(forward_demodulation,[],[f34243,f34307]) ).
fof(f34307,plain,
! [X0,X1] : hAPP(c_fequal,X1) = hAPP(hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_fequal),X1),
inference(backward_demodulation,[],[f33101,f34306]) ).
fof(f33101,plain,
! [X0,X1] : hAPP(hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_fequal),X1) = hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),
inference(backward_demodulation,[],[f21912,f21003]) ).
fof(f21912,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X0),hAPP(hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_fequal),X1)) = hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),
inference(cnf_transformation,[],[f15926]) ).
fof(f15926,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X0),hAPP(hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_fequal),X1)) = hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),
inference(rectify,[],[f10104]) ).
fof(f10104,plain,
! [X1,X0] : hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X0)) = hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(rectify,[],[f788]) ).
fof(f788,axiom,
! [X5,X4] : hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__conv) ).
fof(f34243,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_COMBC(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_fequal),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| ~ spl574_293 ),
inference(avatar_component_clause,[],[f34241]) ).
fof(f36081,plain,
( spl574_360
| ~ spl574_309 ),
inference(avatar_split_clause,[],[f36076,f34797,f36078]) ).
fof(f36078,plain,
( spl574_360
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_360])]) ).
fof(f34797,plain,
( spl574_309
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),c_Int_OMin))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_309])]) ).
fof(f36076,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin))
| ~ spl574_309 ),
inference(forward_demodulation,[],[f34799,f34859]) ).
fof(f34859,plain,
! [X0] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0) = X0,
inference(backward_demodulation,[],[f23272,f22630]) ).
fof(f23272,plain,
! [X0] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0),
inference(cnf_transformation,[],[f5732]) ).
fof(f5732,plain,
! [X0] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0),
inference(rectify,[],[f2654]) ).
fof(f2654,axiom,
! [X151] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X151) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X151),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__number__of__def) ).
fof(f34799,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),c_Int_OMin)))
| ~ spl574_309 ),
inference(avatar_component_clause,[],[f34797]) ).
fof(f36075,plain,
( spl574_357
| ~ spl574_223
| ~ spl574_261 ),
inference(avatar_split_clause,[],[f36074,f32565,f31382,f36025]) ).
fof(f32565,plain,
( spl574_261
<=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_261])]) ).
fof(f36074,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))
| ~ spl574_223
| ~ spl574_261 ),
inference(forward_demodulation,[],[f36073,f31384]) ).
fof(f36073,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))
| ~ spl574_261 ),
inference(forward_demodulation,[],[f36072,f27421]) ).
fof(f36072,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl574_261 ),
inference(forward_demodulation,[],[f32567,f23929]) ).
fof(f32567,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl574_261 ),
inference(avatar_component_clause,[],[f32565]) ).
fof(f36071,plain,
( spl574_359
| ~ spl574_91 ),
inference(avatar_split_clause,[],[f36066,f29190,f36068]) ).
fof(f29190,plain,
( spl574_91
<=> hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_91])]) ).
fof(f36066,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36065,f27421]) ).
fof(f36065,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36064,f23560]) ).
fof(f36064,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36063,f23560]) ).
fof(f36063,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36062,f25075]) ).
fof(f36062,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36061,f23929]) ).
fof(f36061,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36060,f23560]) ).
fof(f36060,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36059,f23560]) ).
fof(f36059,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36058,f23560]) ).
fof(f36058,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)))))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36057,f23929]) ).
fof(f36057,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))))))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36056,f23560]) ).
fof(f36056,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))))))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36055,f23560]) ).
fof(f36055,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))))))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36054,f23560]) ).
fof(f36054,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))))))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36053,f24146]) ).
fof(f36053,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)))))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36052,f24146]) ).
fof(f36052,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin))))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36051,f23929]) ).
fof(f36051,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin)))))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36050,f23560]) ).
fof(f36050,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin)))))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36049,f23560]) ).
fof(f36049,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin)))))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36048,f23929]) ).
fof(f36048,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin))))))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36047,f23560]) ).
fof(f36047,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin))))))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36046,f23560]) ).
fof(f36046,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin))))))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36045,f24146]) ).
fof(f36045,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin)))))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36044,f24146]) ).
fof(f36044,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin))))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36043,f24146]) ).
fof(f36043,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin)))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f36042,f24146]) ).
fof(f36042,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))
| ~ spl574_91 ),
inference(forward_demodulation,[],[f29192,f27698]) ).
fof(f29192,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl574_91 ),
inference(avatar_component_clause,[],[f29190]) ).
fof(f36041,plain,
( spl574_358
| ~ spl574_170 ),
inference(avatar_split_clause,[],[f36036,f30447,f36038]) ).
fof(f30447,plain,
( spl574_170
<=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_170])]) ).
fof(f36036,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl574_170 ),
inference(forward_demodulation,[],[f36035,f31242]) ).
fof(f31242,plain,
! [X0,X1] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X0,X1)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X0))),
inference(forward_demodulation,[],[f20544,f25075]) ).
fof(f20544,plain,
! [X0,X1] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X0,X1)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X0)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(cnf_transformation,[],[f7271]) ).
fof(f7271,plain,
! [X0,X1] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X0,X1)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X0)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(rectify,[],[f1913]) ).
fof(f1913,axiom,
! [X130,X129] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X130,X129)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X129),X130)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__atLeastAtMost__int) ).
fof(f36035,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))
| ~ spl574_170 ),
inference(forward_demodulation,[],[f36034,f27421]) ).
fof(f36034,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl574_170 ),
inference(forward_demodulation,[],[f36033,f23929]) ).
fof(f36033,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl574_170 ),
inference(forward_demodulation,[],[f36032,f23929]) ).
fof(f36032,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl574_170 ),
inference(forward_demodulation,[],[f36031,f23929]) ).
fof(f36031,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ spl574_170 ),
inference(forward_demodulation,[],[f36030,f23929]) ).
fof(f36030,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))
| ~ spl574_170 ),
inference(forward_demodulation,[],[f36029,f34871]) ).
fof(f34871,plain,
! [X0] : hAPP(c_Int_Onat,X0) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0),
inference(backward_demodulation,[],[f29188,f34859]) ).
fof(f29188,plain,
! [X0] : hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0),
inference(forward_demodulation,[],[f26924,f23272]) ).
fof(f26924,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),
inference(cnf_transformation,[],[f9050]) ).
fof(f9050,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),
inference(rectify,[],[f2655]) ).
fof(f2655,axiom,
! [X148] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X148) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X148)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__def) ).
fof(f36029,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))
| ~ spl574_170 ),
inference(forward_demodulation,[],[f30449,f34859]) ).
fof(f30449,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ spl574_170 ),
inference(avatar_component_clause,[],[f30447]) ).
fof(f36028,plain,
( spl574_357
| ~ spl574_161 ),
inference(avatar_split_clause,[],[f36023,f30314,f36025]) ).
fof(f30314,plain,
( spl574_161
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_161])]) ).
fof(f36023,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))
| ~ spl574_161 ),
inference(forward_demodulation,[],[f36022,f27421]) ).
fof(f36022,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl574_161 ),
inference(forward_demodulation,[],[f30316,f23929]) ).
fof(f30316,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl574_161 ),
inference(avatar_component_clause,[],[f30314]) ).
fof(f36010,plain,
( spl574_356
| ~ spl574_62 ),
inference(avatar_split_clause,[],[f36005,f29007,f36007]) ).
fof(f29007,plain,
( spl574_62
<=> c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_62])]) ).
fof(f36005,plain,
( c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),c_Int_OMin)
| ~ spl574_62 ),
inference(forward_demodulation,[],[f36004,f27421]) ).
fof(f36004,plain,
( c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OMin)
| ~ spl574_62 ),
inference(forward_demodulation,[],[f29009,f25075]) ).
fof(f29009,plain,
( c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),c_Int_OMin)
| ~ spl574_62 ),
inference(avatar_component_clause,[],[f29007]) ).
fof(f36003,plain,
( spl574_355
| ~ spl574_3 ),
inference(avatar_split_clause,[],[f35998,f28668,f36000]) ).
fof(f28668,plain,
( spl574_3
<=> c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_3])]) ).
fof(f35998,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35997,f27421]) ).
fof(f35997,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35996,f23560]) ).
fof(f35996,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35995,f23560]) ).
fof(f35995,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35994,f25075]) ).
fof(f35994,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35993,f23929]) ).
fof(f35993,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35992,f23560]) ).
fof(f35992,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35991,f23560]) ).
fof(f35991,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35990,f23560]) ).
fof(f35990,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)))))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35989,f23929]) ).
fof(f35989,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))))))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35988,f23560]) ).
fof(f35988,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))))))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35987,f23560]) ).
fof(f35987,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))))))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35986,f23560]) ).
fof(f35986,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))))))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35985,f24146]) ).
fof(f35985,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)))))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35984,f24146]) ).
fof(f35984,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin))))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35983,f23929]) ).
fof(f35983,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin)))))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35982,f23560]) ).
fof(f35982,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin)))))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35981,f23560]) ).
fof(f35981,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin)))))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35980,f23929]) ).
fof(f35980,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin))))))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35979,f23560]) ).
fof(f35979,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin))))))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35978,f23560]) ).
fof(f35978,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin))))))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35977,f24146]) ).
fof(f35977,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin)))))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35976,f24146]) ).
fof(f35976,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin))))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35975,f24146]) ).
fof(f35975,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin)))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35974,f24146]) ).
fof(f35974,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f35973,f27698]) ).
fof(f35973,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl574_3 ),
inference(forward_demodulation,[],[f28670,f22630]) ).
fof(f28670,plain,
( c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl574_3 ),
inference(avatar_component_clause,[],[f28668]) ).
fof(f35953,plain,
( spl574_354
| ~ spl574_234 ),
inference(avatar_split_clause,[],[f35948,f31590,f35950]) ).
fof(f35950,plain,
( spl574_354
<=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_354])]) ).
fof(f31590,plain,
( spl574_234
<=> c_Nat__Transfer_Ois__nat(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_234])]) ).
fof(f35948,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))
| ~ spl574_234 ),
inference(forward_demodulation,[],[f35947,f27421]) ).
fof(f35947,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl574_234 ),
inference(forward_demodulation,[],[f35946,f23929]) ).
fof(f35946,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl574_234 ),
inference(forward_demodulation,[],[f35945,f23929]) ).
fof(f35945,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl574_234 ),
inference(forward_demodulation,[],[f35944,f23929]) ).
fof(f35944,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl574_234 ),
inference(forward_demodulation,[],[f35943,f23929]) ).
fof(f35943,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ spl574_234 ),
inference(forward_demodulation,[],[f31592,f34859]) ).
fof(f31592,plain,
( c_Nat__Transfer_Ois__nat(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))
| ~ spl574_234 ),
inference(avatar_component_clause,[],[f31590]) ).
fof(f35942,plain,
( spl574_353
| ~ spl574_15 ),
inference(avatar_split_clause,[],[f35937,f28727,f35939]) ).
fof(f28727,plain,
( spl574_15
<=> hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_15])]) ).
fof(f35937,plain,
( hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_fequal,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl574_15 ),
inference(forward_demodulation,[],[f28729,f34306]) ).
fof(f28729,plain,
( hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| ~ spl574_15 ),
inference(avatar_component_clause,[],[f28727]) ).
fof(f35935,plain,
( spl574_352
| ~ spl574_60 ),
inference(avatar_split_clause,[],[f35930,f28997,f35932]) ).
fof(f35932,plain,
( spl574_352
<=> c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_352])]) ).
fof(f28997,plain,
( spl574_60
<=> c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_60])]) ).
fof(f35930,plain,
( c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))
| ~ spl574_60 ),
inference(forward_demodulation,[],[f28999,f34306]) ).
fof(f28999,plain,
( c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool))))
| ~ spl574_60 ),
inference(avatar_component_clause,[],[f28997]) ).
fof(f35929,plain,
( spl574_20
| ~ spl574_184 ),
inference(avatar_split_clause,[],[f35928,f30637,f28752]) ).
fof(f30637,plain,
( spl574_184
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_184])]) ).
fof(f35928,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls
| ~ spl574_184 ),
inference(forward_demodulation,[],[f30639,f22630]) ).
fof(f30639,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls)
| ~ spl574_184 ),
inference(avatar_component_clause,[],[f30637]) ).
fof(f35927,plain,
( ~ spl574_351
| ~ spl574_98
| spl574_109 ),
inference(avatar_split_clause,[],[f35922,f29353,f29264,f35924]) ).
fof(f35924,plain,
( spl574_351
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_351])]) ).
fof(f29353,plain,
( spl574_109
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_109])]) ).
fof(f35922,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
| ~ spl574_98
| spl574_109 ),
inference(forward_demodulation,[],[f29355,f29266]) ).
fof(f29355,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| spl574_109 ),
inference(avatar_component_clause,[],[f29353]) ).
fof(f35921,plain,
( spl574_350
| ~ spl574_37 ),
inference(avatar_split_clause,[],[f35916,f28840,f35918]) ).
fof(f35918,plain,
( spl574_350
<=> c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_350])]) ).
fof(f28840,plain,
( spl574_37
<=> c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_37])]) ).
fof(f35916,plain,
( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))
| ~ spl574_37 ),
inference(forward_demodulation,[],[f35915,f27421]) ).
fof(f35915,plain,
( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl574_37 ),
inference(forward_demodulation,[],[f35914,f25075]) ).
fof(f35914,plain,
( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))
| ~ spl574_37 ),
inference(forward_demodulation,[],[f35913,f23929]) ).
fof(f35913,plain,
( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))
| ~ spl574_37 ),
inference(forward_demodulation,[],[f35912,f23560]) ).
fof(f35912,plain,
( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))
| ~ spl574_37 ),
inference(forward_demodulation,[],[f28842,f24146]) ).
fof(f28842,plain,
( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))
| ~ spl574_37 ),
inference(avatar_component_clause,[],[f28840]) ).
fof(f35911,plain,
( spl574_99
| ~ spl574_144
| ~ spl574_223 ),
inference(avatar_split_clause,[],[f35910,f31382,f29726,f29270]) ).
fof(f29270,plain,
( spl574_99
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_99])]) ).
fof(f29726,plain,
( spl574_144
<=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_144])]) ).
fof(f35910,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl574_144
| ~ spl574_223 ),
inference(forward_demodulation,[],[f29728,f31384]) ).
fof(f29728,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl574_144 ),
inference(avatar_component_clause,[],[f29726]) ).
fof(f35909,plain,
( spl574_349
| ~ spl574_66
| ~ spl574_223 ),
inference(avatar_split_clause,[],[f35904,f31382,f29030,f35906]) ).
fof(f29030,plain,
( spl574_66
<=> hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_66])]) ).
fof(f35904,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))
| ~ spl574_66
| ~ spl574_223 ),
inference(forward_demodulation,[],[f35903,f31384]) ).
fof(f35903,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))
| ~ spl574_66 ),
inference(forward_demodulation,[],[f35902,f27421]) ).
fof(f35902,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl574_66 ),
inference(forward_demodulation,[],[f35901,f23929]) ).
fof(f35901,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl574_66 ),
inference(forward_demodulation,[],[f35900,f23560]) ).
fof(f35900,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl574_66 ),
inference(forward_demodulation,[],[f35899,f23560]) ).
fof(f35899,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl574_66 ),
inference(forward_demodulation,[],[f35898,f25075]) ).
fof(f35898,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))
| ~ spl574_66 ),
inference(forward_demodulation,[],[f35897,f23929]) ).
fof(f35897,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))
| ~ spl574_66 ),
inference(forward_demodulation,[],[f35896,f23560]) ).
fof(f35896,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))
| ~ spl574_66 ),
inference(forward_demodulation,[],[f35895,f23560]) ).
fof(f35895,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))
| ~ spl574_66 ),
inference(forward_demodulation,[],[f35894,f23560]) ).
fof(f35894,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ spl574_66 ),
inference(forward_demodulation,[],[f35893,f24146]) ).
fof(f35893,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))
| ~ spl574_66 ),
inference(forward_demodulation,[],[f35892,f23929]) ).
fof(f35892,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))
| ~ spl574_66 ),
inference(forward_demodulation,[],[f35891,f23560]) ).
fof(f35891,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))
| ~ spl574_66 ),
inference(forward_demodulation,[],[f35890,f23560]) ).
fof(f35890,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))
| ~ spl574_66 ),
inference(forward_demodulation,[],[f35889,f23929]) ).
fof(f35889,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))))
| ~ spl574_66 ),
inference(forward_demodulation,[],[f35888,f23560]) ).
fof(f35888,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))))
| ~ spl574_66 ),
inference(forward_demodulation,[],[f35887,f23560]) ).
fof(f35887,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))))
| ~ spl574_66 ),
inference(forward_demodulation,[],[f35886,f24146]) ).
fof(f35886,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))
| ~ spl574_66 ),
inference(forward_demodulation,[],[f35885,f24146]) ).
fof(f35885,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))
| ~ spl574_66 ),
inference(forward_demodulation,[],[f29032,f24146]) ).
fof(f29032,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))
| ~ spl574_66 ),
inference(avatar_component_clause,[],[f29030]) ).
fof(f35880,plain,
( spl574_205
| ~ spl574_56
| ~ spl574_223 ),
inference(avatar_split_clause,[],[f35879,f31382,f28969,f31031]) ).
fof(f31031,plain,
( spl574_205
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_205])]) ).
fof(f28969,plain,
( spl574_56
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_56])]) ).
fof(f35879,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl574_56
| ~ spl574_223 ),
inference(forward_demodulation,[],[f28971,f31384]) ).
fof(f28971,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ spl574_56 ),
inference(avatar_component_clause,[],[f28969]) ).
fof(f35878,plain,
( spl574_348
| ~ spl574_173 ),
inference(avatar_split_clause,[],[f35873,f30494,f35875]) ).
fof(f30494,plain,
( spl574_173
<=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_173])]) ).
fof(f35873,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))
| ~ spl574_173 ),
inference(forward_demodulation,[],[f35872,f23929]) ).
fof(f35872,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))))
| ~ spl574_173 ),
inference(forward_demodulation,[],[f35871,f23929]) ).
fof(f35871,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))))
| ~ spl574_173 ),
inference(forward_demodulation,[],[f35870,f23929]) ).
fof(f35870,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))))))
| ~ spl574_173 ),
inference(forward_demodulation,[],[f35869,f23929]) ).
fof(f35869,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))
| ~ spl574_173 ),
inference(forward_demodulation,[],[f35868,f27421]) ).
fof(f35868,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl574_173 ),
inference(forward_demodulation,[],[f35867,f23560]) ).
fof(f35867,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl574_173 ),
inference(forward_demodulation,[],[f35866,f23560]) ).
fof(f35866,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl574_173 ),
inference(forward_demodulation,[],[f35865,f25075]) ).
fof(f35865,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))
| ~ spl574_173 ),
inference(forward_demodulation,[],[f35864,f24146]) ).
fof(f35864,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OMin))
| ~ spl574_173 ),
inference(forward_demodulation,[],[f35863,f24146]) ).
fof(f35863,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Int_OMin)
| ~ spl574_173 ),
inference(forward_demodulation,[],[f35862,f23929]) ).
fof(f35862,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Int_OMin))
| ~ spl574_173 ),
inference(forward_demodulation,[],[f35861,f24146]) ).
fof(f35861,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Int_OMin)
| ~ spl574_173 ),
inference(forward_demodulation,[],[f35860,f23929]) ).
fof(f35860,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Int_OMin))
| ~ spl574_173 ),
inference(forward_demodulation,[],[f35859,f24146]) ).
fof(f35859,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Int_OMin)
| ~ spl574_173 ),
inference(forward_demodulation,[],[f35858,f23929]) ).
fof(f35858,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Int_OMin))
| ~ spl574_173 ),
inference(forward_demodulation,[],[f35857,f24146]) ).
fof(f35857,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Int_OMin)
| ~ spl574_173 ),
inference(forward_demodulation,[],[f35856,f23929]) ).
fof(f35856,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Int_OMin))
| ~ spl574_173 ),
inference(forward_demodulation,[],[f35855,f24146]) ).
fof(f35855,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Int_OMin)
| ~ spl574_173 ),
inference(forward_demodulation,[],[f35854,f27698]) ).
fof(f35854,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl574_173 ),
inference(forward_demodulation,[],[f35853,f23185]) ).
fof(f23185,plain,
! [X0,X1] : hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),X1)) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X0)),
inference(cnf_transformation,[],[f6872]) ).
fof(f6872,plain,
! [X0,X1] : hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),X1)) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X0)),
inference(rectify,[],[f1839]) ).
fof(f1839,axiom,
! [X129,X130] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X130,X129)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X129),X130)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__greaterThanAtMost__int) ).
fof(f35853,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl574_173 ),
inference(forward_demodulation,[],[f35852,f34871]) ).
fof(f35852,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl574_173 ),
inference(forward_demodulation,[],[f30496,f34859]) ).
fof(f30496,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl574_173 ),
inference(avatar_component_clause,[],[f30494]) ).
fof(f35851,plain,
( spl574_347
| ~ spl574_195 ),
inference(avatar_split_clause,[],[f35846,f30893,f35848]) ).
fof(f30893,plain,
( spl574_195
<=> hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_195])]) ).
fof(f35846,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))
| ~ spl574_195 ),
inference(forward_demodulation,[],[f35845,f27421]) ).
fof(f35845,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl574_195 ),
inference(forward_demodulation,[],[f35844,f23560]) ).
fof(f35844,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl574_195 ),
inference(forward_demodulation,[],[f35843,f23560]) ).
fof(f35843,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl574_195 ),
inference(forward_demodulation,[],[f35842,f25075]) ).
fof(f35842,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))
| ~ spl574_195 ),
inference(forward_demodulation,[],[f35841,f24146]) ).
fof(f35841,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OMin)))
| ~ spl574_195 ),
inference(forward_demodulation,[],[f35840,f24146]) ).
fof(f35840,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Int_OMin))
| ~ spl574_195 ),
inference(forward_demodulation,[],[f35839,f23929]) ).
fof(f35839,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Int_OMin))) = hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl574_195 ),
inference(forward_demodulation,[],[f35838,f24146]) ).
fof(f35838,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Int_OMin))
| ~ spl574_195 ),
inference(forward_demodulation,[],[f35837,f23929]) ).
fof(f35837,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Int_OMin))) = hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl574_195 ),
inference(forward_demodulation,[],[f35836,f24146]) ).
fof(f35836,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Int_OMin))
| ~ spl574_195 ),
inference(forward_demodulation,[],[f35835,f23929]) ).
fof(f35835,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))),c_Int_OMin)))
| ~ spl574_195 ),
inference(forward_demodulation,[],[f35834,f24146]) ).
fof(f35834,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Int_OMin))
| ~ spl574_195 ),
inference(forward_demodulation,[],[f35833,f23929]) ).
fof(f35833,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),c_Int_OMin)))
| ~ spl574_195 ),
inference(forward_demodulation,[],[f35832,f24146]) ).
fof(f35832,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Int_OMin))
| ~ spl574_195 ),
inference(forward_demodulation,[],[f30895,f27698]) ).
fof(f30895,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl574_195 ),
inference(avatar_component_clause,[],[f30893]) ).
fof(f35769,plain,
spl574_346,
inference(avatar_split_clause,[],[f22989,f35766]) ).
fof(f35766,plain,
( spl574_346
<=> class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_346])]) ).
fof(f22989,plain,
class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5176]) ).
fof(f5176,axiom,
class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult) ).
fof(f35760,plain,
spl574_345,
inference(avatar_split_clause,[],[f25601,f35757]) ).
fof(f25601,plain,
c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f1976]) ).
fof(f1976,axiom,
c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast__0) ).
fof(f35751,plain,
spl574_344,
inference(avatar_split_clause,[],[f24071,f35748]) ).
fof(f35748,plain,
( spl574_344
<=> class_Groups_Oone(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_344])]) ).
fof(f24071,plain,
class_Groups_Oone(tc_Int_Oint),
inference(cnf_transformation,[],[f5075]) ).
fof(f5075,axiom,
class_Groups_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
fof(f35746,plain,
spl574_343,
inference(avatar_split_clause,[],[f22458,f35743]) ).
fof(f35743,plain,
( spl574_343
<=> class_Rings_Ocomm__ring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_343])]) ).
fof(f22458,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5052]) ).
fof(f5052,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(f35702,plain,
spl574_342,
inference(avatar_split_clause,[],[f25606,f35699]) ).
fof(f35699,plain,
( spl574_342
<=> class_Int_Oring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_342])]) ).
fof(f25606,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(cnf_transformation,[],[f5061]) ).
fof(f5061,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
fof(f35697,plain,
spl574_341,
inference(avatar_split_clause,[],[f23947,f35694]) ).
fof(f35694,plain,
( spl574_341
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_341])]) ).
fof(f23947,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(cnf_transformation,[],[f5008]) ).
fof(f5008,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f35677,plain,
spl574_340,
inference(avatar_split_clause,[],[f23526,f35674]) ).
fof(f35674,plain,
( spl574_340
<=> class_Rings_Ocomm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_340])]) ).
fof(f23526,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5102]) ).
fof(f5102,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
fof(f35643,plain,
spl574_339,
inference(avatar_split_clause,[],[f22443,f35640]) ).
fof(f35640,plain,
( spl574_339
<=> class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_339])]) ).
fof(f22443,plain,
class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5178]) ).
fof(f5178,axiom,
class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring) ).
fof(f35637,plain,
spl574_338,
inference(avatar_split_clause,[],[f23546,f35634]) ).
fof(f35634,plain,
( spl574_338
<=> class_Rings_Olinordered__semidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_338])]) ).
fof(f23546,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(cnf_transformation,[],[f5027]) ).
fof(f5027,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
fof(f35628,plain,
spl574_337,
inference(avatar_split_clause,[],[f25552,f35625]) ).
fof(f35625,plain,
( spl574_337
<=> class_Rings_Ono__zero__divisors(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_337])]) ).
fof(f25552,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(cnf_transformation,[],[f5097]) ).
fof(f5097,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
fof(f35619,plain,
spl574_336,
inference(avatar_split_clause,[],[f20590,f35616]) ).
fof(f35616,plain,
( spl574_336
<=> class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_336])]) ).
fof(f20590,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(cnf_transformation,[],[f5089]) ).
fof(f5089,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(f35601,plain,
spl574_335,
inference(avatar_split_clause,[],[f21227,f35598]) ).
fof(f35598,plain,
( spl574_335
<=> class_Rings_Oordered__comm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_335])]) ).
fof(f21227,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5022]) ).
fof(f5022,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
fof(f35595,plain,
spl574_334,
inference(avatar_split_clause,[],[f24593,f35592]) ).
fof(f35592,plain,
( spl574_334
<=> class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_334])]) ).
fof(f24593,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5086]) ).
fof(f5086,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
fof(f35587,plain,
spl574_333,
inference(avatar_split_clause,[],[f25070,f35584]) ).
fof(f35584,plain,
( spl574_333
<=> class_Lattices_Osemilattice__inf(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_333])]) ).
fof(f25070,plain,
class_Lattices_Osemilattice__inf(tc_Int_Oint),
inference(cnf_transformation,[],[f5030]) ).
fof(f5030,axiom,
class_Lattices_Osemilattice__inf(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Osemilattice__inf) ).
fof(f35579,plain,
spl574_262,
inference(avatar_split_clause,[],[f35578,f32606]) ).
fof(f32606,plain,
( spl574_262
<=> c_List_Olist_ONil(tc_Nat_Onat) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_262])]) ).
fof(f35578,plain,
c_List_Olist_ONil(tc_Nat_Onat) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(forward_demodulation,[],[f28595,f21540]) ).
fof(f21540,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f8306]) ).
fof(f8306,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rectify,[],[f1731]) ).
fof(f1731,axiom,
! [X77] : c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X77),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan0) ).
fof(f28595,plain,
! [X0] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f27937]) ).
fof(f27937,plain,
! [X0,X1] :
( c_List_Olist_ONil(tc_Nat_Onat) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X0),X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(definition_unfolding,[],[f26543,f24709]) ).
fof(f24709,plain,
! [X0,X1] : c_List_Oupt(X0,X1) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X0),X1)),
inference(cnf_transformation,[],[f18111]) ).
fof(f18111,plain,
! [X0,X1] : c_List_Oupt(X0,X1) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X0),X1)),
inference(rectify,[],[f9077]) ).
fof(f9077,plain,
! [X1,X0] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0)) = c_List_Oupt(X1,X0),
inference(rectify,[],[f4547]) ).
fof(f4547,axiom,
! [X74,X77] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X77),X74)) = c_List_Oupt(X77,X74),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__list__of__set__range) ).
fof(f26543,plain,
! [X0,X1] :
( c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f19462]) ).
fof(f19462,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0))
| c_List_Olist_ONil(tc_Nat_Onat) != c_List_Oupt(X0,X1) )
& ( c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X0,X1)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0)) ) ) ),
inference(flattening,[],[f19461]) ).
fof(f19461,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0))
| c_List_Olist_ONil(tc_Nat_Onat) != c_List_Oupt(X0,X1) )
& ( c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X0,X1)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0)) ) ) ),
inference(nnf_transformation,[],[f5924]) ).
fof(f5924,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0)) )
<=> c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X0,X1) ),
inference(rectify,[],[f4538]) ).
fof(f4538,axiom,
! [X124,X137] :
( c_List_Oupt(X124,X137) = c_List_Olist_ONil(tc_Nat_Onat)
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X137),X124))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X137 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__eq__Nil__conv) ).
fof(f35567,plain,
spl574_332,
inference(avatar_split_clause,[],[f24664,f35564]) ).
fof(f35564,plain,
( spl574_332
<=> class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_332])]) ).
fof(f24664,plain,
class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint),
inference(cnf_transformation,[],[f5028]) ).
fof(f5028,axiom,
class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Lazy__Sequence_Osmall__lazy) ).
fof(f35562,plain,
spl574_331,
inference(avatar_split_clause,[],[f25204,f35559]) ).
fof(f35559,plain,
( spl574_331
<=> c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_331])]) ).
fof(f25204,plain,
c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls),
inference(cnf_transformation,[],[f2681]) ).
fof(f2681,axiom,
c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Pls) ).
fof(f35539,plain,
spl574_330,
inference(avatar_split_clause,[],[f22656,f35536]) ).
fof(f35536,plain,
( spl574_330
<=> class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_330])]) ).
fof(f22656,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5034]) ).
fof(f5034,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(f35520,plain,
spl574_329,
inference(avatar_split_clause,[],[f20692,f35517]) ).
fof(f35517,plain,
( spl574_329
<=> class_Divides_Oring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_329])]) ).
fof(f20692,plain,
class_Divides_Oring__div(tc_Int_Oint),
inference(cnf_transformation,[],[f5058]) ).
fof(f5058,axiom,
class_Divides_Oring__div(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Oring__div) ).
fof(f35515,plain,
( spl574_223
| spl574_328 ),
inference(avatar_split_clause,[],[f35511,f35513,f31382]) ).
fof(f35511,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(forward_subsumption_demodulation,[],[f35510,f35177]) ).
fof(f35177,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X0) ),
inference(forward_demodulation,[],[f34873,f34871]) ).
fof(f34873,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) ),
inference(backward_demodulation,[],[f29285,f34859]) ).
fof(f29285,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) ),
inference(forward_demodulation,[],[f22370,f23272]) ).
fof(f22370,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(cnf_transformation,[],[f13969]) ).
fof(f13969,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) ),
inference(ennf_transformation,[],[f9639]) ).
fof(f9639,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) ),
inference(rectify,[],[f2659]) ).
fof(f2659,axiom,
! [X148] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X148)))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X148) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__imp__number__of__eq__0) ).
fof(f35510,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X0)) ),
inference(forward_demodulation,[],[f35509,f22630]) ).
fof(f35509,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X0)) ),
inference(forward_demodulation,[],[f20927,f34871]) ).
fof(f20927,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(cnf_transformation,[],[f13366]) ).
fof(f13366,plain,
! [X0] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X0)) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) ),
inference(ennf_transformation,[],[f8724]) ).
fof(f8724,plain,
! [X0] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X0)) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ) ),
inference(rectify,[],[f2722]) ).
fof(f2722,axiom,
! [X148] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X148)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X148)) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X148)) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X148)))
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X148)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__nat__number__of) ).
fof(f35508,plain,
spl574_327,
inference(avatar_split_clause,[],[f35503,f35505]) ).
fof(f35505,plain,
( spl574_327
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_327])]) ).
fof(f35503,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),c_Int_OMin),
inference(forward_demodulation,[],[f28416,f22630]) ).
fof(f28416,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),
inference(equality_resolution,[],[f28415]) ).
fof(f28415,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X0 ),
inference(equality_resolution,[],[f24685]) ).
fof(f24685,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X1
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X0 ),
inference(cnf_transformation,[],[f18093]) ).
fof(f18093,plain,
! [X0,X1] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X1
& hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X0 )
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X0 )
| c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1) )
& ( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1)
| ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X1
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X0 )
& ( c_Groups_Oone__class_Oone(tc_Int_Oint) != X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X0 ) ) ) ),
inference(rectify,[],[f18092]) ).
fof(f18092,plain,
! [X1,X0] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X0
& hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X1 )
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 )
| c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) )
& ( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
| ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X0
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X1 )
& ( c_Groups_Oone__class_Oone(tc_Int_Oint) != X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X1 ) ) ) ),
inference(flattening,[],[f18091]) ).
fof(f18091,plain,
! [X1,X0] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X0
& hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X1 )
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 )
| c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) )
& ( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
| ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X0
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X1 )
& ( c_Groups_Oone__class_Oone(tc_Int_Oint) != X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X1 ) ) ) ),
inference(nnf_transformation,[],[f6746]) ).
fof(f6746,plain,
! [X1,X0] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X0
& hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X1 )
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 ) )
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) ),
inference(rectify,[],[f2960]) ).
fof(f2960,axiom,
! [X74,X77] :
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X77),X74)
<=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X74
& hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X77 )
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X77
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X74 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__eq__1__iff) ).
fof(f35496,plain,
spl574_326,
inference(avatar_split_clause,[],[f26751,f35493]) ).
fof(f35493,plain,
( spl574_326
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_326])]) ).
fof(f26751,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5165]) ).
fof(f5165,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add) ).
fof(f35469,plain,
spl574_223,
inference(avatar_split_clause,[],[f20150,f31382]) ).
fof(f20150,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(cnf_transformation,[],[f1090]) ).
fof(f1090,axiom,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).
fof(f35458,plain,
spl574_325,
inference(avatar_split_clause,[],[f22438,f35455]) ).
fof(f35455,plain,
( spl574_325
<=> c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_325])]) ).
fof(f22438,plain,
c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)),
inference(cnf_transformation,[],[f2081]) ).
fof(f2081,axiom,
c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__atMost__UNIV) ).
fof(f35452,plain,
spl574_324,
inference(avatar_split_clause,[],[f24534,f35449]) ).
fof(f35449,plain,
( spl574_324
<=> class_Nat_Osize(tc_Com_Ostate) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_324])]) ).
fof(f24534,plain,
class_Nat_Osize(tc_Com_Ostate),
inference(cnf_transformation,[],[f5142]) ).
fof(f5142,axiom,
class_Nat_Osize(tc_Com_Ostate),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Com__Ostate__Nat_Osize) ).
fof(f35436,plain,
spl574_323,
inference(avatar_split_clause,[],[f23724,f35433]) ).
fof(f35433,plain,
( spl574_323
<=> class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_323])]) ).
fof(f23724,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(cnf_transformation,[],[f5014]) ).
fof(f5014,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).
fof(f35390,plain,
spl574_322,
inference(avatar_split_clause,[],[f25159,f35387]) ).
fof(f35387,plain,
( spl574_322
<=> class_Int_Onumber__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_322])]) ).
fof(f25159,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5062]) ).
fof(f5062,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).
fof(f35382,plain,
spl574_321,
inference(avatar_split_clause,[],[f35377,f35379]) ).
fof(f35379,plain,
( spl574_321
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_321])]) ).
fof(f35377,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(forward_demodulation,[],[f35376,f27421]) ).
fof(f35376,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f35375,f25075]) ).
fof(f35375,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),
inference(forward_demodulation,[],[f35374,f23929]) ).
fof(f35374,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))),
inference(forward_demodulation,[],[f35373,f23560]) ).
fof(f35373,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),
inference(forward_demodulation,[],[f27789,f24146]) ).
fof(f27789,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),
inference(definition_unfolding,[],[f25475,f24559]) ).
fof(f24559,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)),X0) = c_Int_OBit1(X0),
inference(cnf_transformation,[],[f9125]) ).
fof(f9125,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)),X0) = c_Int_OBit1(X0),
inference(rectify,[],[f2751]) ).
fof(f2751,axiom,
! [X106] : c_Int_OBit1(X106) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X106)),X106),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(f25475,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
inference(cnf_transformation,[],[f2766]) ).
fof(f2766,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__num__one) ).
fof(f35345,plain,
spl574_320,
inference(avatar_split_clause,[],[f24260,f35342]) ).
fof(f24260,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
inference(cnf_transformation,[],[f2982]) ).
fof(f2982,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Osize_I1_J) ).
fof(f35337,plain,
spl574_319,
inference(avatar_split_clause,[],[f24510,f35334]) ).
fof(f35334,plain,
( spl574_319
<=> class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_319])]) ).
fof(f24510,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5085]) ).
fof(f5085,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
fof(f35320,plain,
spl574_318,
inference(avatar_split_clause,[],[f27355,f35317]) ).
fof(f35317,plain,
( spl574_318
<=> c_Wellfounded_Oless__than = hAPP(hAPP(c_Relation_Orel__comp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Wellfounded_Opred__nat),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_318])]) ).
fof(f27355,plain,
c_Wellfounded_Oless__than = hAPP(hAPP(c_Relation_Orel__comp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Wellfounded_Opred__nat),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)),
inference(definition_unfolding,[],[f21956,f20934]) ).
fof(f20934,plain,
! [X0,X1] : hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X0),c_Transitive__Closure_Ortrancl(X1,X0)) = c_Transitive__Closure_Otrancl(X1,X0),
inference(cnf_transformation,[],[f7087]) ).
fof(f7087,plain,
! [X0,X1] : hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X0),c_Transitive__Closure_Ortrancl(X1,X0)) = c_Transitive__Closure_Otrancl(X1,X0),
inference(rectify,[],[f3553]) ).
fof(f3553,axiom,
! [X97,X4] : c_Transitive__Closure_Otrancl(X4,X97) = hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X97),c_Transitive__Closure_Ortrancl(X4,X97)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__unfold__left) ).
fof(f21956,plain,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(cnf_transformation,[],[f3500]) ).
fof(f3500,axiom,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__than__def) ).
fof(f35309,plain,
spl574_317,
inference(avatar_split_clause,[],[f24935,f35306]) ).
fof(f35306,plain,
( spl574_317
<=> class_Nat_Osize(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_317])]) ).
fof(f24935,plain,
class_Nat_Osize(tc_Nat_Onat),
inference(cnf_transformation,[],[f5123]) ).
fof(f5123,axiom,
class_Nat_Osize(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Nat_Osize) ).
fof(f35304,plain,
spl574_316,
inference(avatar_split_clause,[],[f27527,f35301]) ).
fof(f35301,plain,
( spl574_316
<=> c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Ointernal__split(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_316])]) ).
fof(f27527,plain,
c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Ointernal__split(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))),
inference(definition_unfolding,[],[f23335,f23198]) ).
fof(f23198,plain,
! [X2,X0,X1] : c_Product__Type_Oprod_Oprod__case(X2,X0,X1) = c_Product__Type_Ointernal__split(X2,X0,X1),
inference(cnf_transformation,[],[f16931]) ).
fof(f16931,plain,
! [X0,X1,X2] : c_Product__Type_Oprod_Oprod__case(X2,X0,X1) = c_Product__Type_Ointernal__split(X2,X0,X1),
inference(rectify,[],[f5940]) ).
fof(f5940,plain,
! [X1,X0,X2] : c_Product__Type_Ointernal__split(X2,X1,X0) = c_Product__Type_Oprod_Oprod__case(X2,X1,X0),
inference(rectify,[],[f3877]) ).
fof(f3877,axiom,
! [X38,X20,X4] : c_Product__Type_Oprod_Oprod__case(X4,X20,X38) = c_Product__Type_Ointernal__split(X4,X20,X38),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_internal__split__def) ).
fof(f23335,plain,
c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))),
inference(cnf_transformation,[],[f3390]) ).
fof(f3390,axiom,
c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__nat__def) ).
fof(f35252,plain,
spl574_315,
inference(avatar_split_clause,[],[f24845,f35249]) ).
fof(f35249,plain,
( spl574_315
<=> class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_315])]) ).
fof(f24845,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f5018]) ).
fof(f5018,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
fof(f35238,plain,
( spl574_157
| spl574_314 ),
inference(avatar_split_clause,[],[f35234,f35236,f30275]) ).
fof(f30275,plain,
( spl574_157
<=> ! [X1] :
( ~ class_Int_Onumber__ring(X1)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_157])]) ).
fof(f35236,plain,
( spl574_314
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_314])]) ).
fof(f35234,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_subsumption_demodulation,[],[f35233,f28036]) ).
fof(f28036,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X0)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ),
inference(equality_resolution,[],[f20168]) ).
fof(f20168,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f14633]) ).
fof(f14633,plain,
! [X0,X1] :
( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) )
| hAPP(c_Int_Onat,X0) != X1 )
& ( hAPP(c_Int_Onat,X0) = X1
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
& hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != X0 )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ) ),
inference(rectify,[],[f14632]) ).
fof(f14632,plain,
! [X1,X0] :
( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
| hAPP(c_Int_Onat,X1) != X0 )
& ( hAPP(c_Int_Onat,X1) = X0
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
& hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != X1 )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
inference(flattening,[],[f14631]) ).
fof(f14631,plain,
! [X1,X0] :
( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
| hAPP(c_Int_Onat,X1) != X0 )
& ( hAPP(c_Int_Onat,X1) = X0
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
& hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != X1 )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
inference(nnf_transformation,[],[f10747]) ).
fof(f10747,plain,
! [X1,X0] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
<=> hAPP(c_Int_Onat,X1) = X0 ),
inference(ennf_transformation,[],[f8998]) ).
fof(f8998,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1 )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
<=> hAPP(c_Int_Onat,X1) = X0 ),
inference(rectify,[],[f1882]) ).
fof(f1882,axiom,
! [X77,X145] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X145))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X77 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X145))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X77) = X145 ) )
<=> hAPP(c_Int_Onat,X145) = X77 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__iff2) ).
fof(f35233,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onat,X0)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f34902,f34871]) ).
fof(f34902,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| ~ class_Int_Onumber__ring(X1) ),
inference(backward_demodulation,[],[f33636,f34859]) ).
fof(f33636,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)))
| ~ class_Int_Onumber__ring(X1)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ),
inference(forward_demodulation,[],[f23301,f23272]) ).
fof(f23301,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ class_Int_Onumber__ring(X1) ),
inference(cnf_transformation,[],[f13451]) ).
fof(f13451,plain,
! [X0,X1] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| hAPP(c_Int_Onumber__class_Onumber__of(X1),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ) )
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f10053]) ).
fof(f10053,plain,
! [X1,X0] :
( class_Int_Onumber__ring(X1)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> hAPP(c_Int_Onumber__class_Onumber__of(X1),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ) ) ),
inference(rectify,[],[f2592]) ).
fof(f2592,axiom,
! [X148,X34] :
( class_Int_Onumber__ring(X34)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X148)))
=> c_Groups_Ozero__class_Ozero(X34) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X34),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X148)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X148)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X34),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X148)) = hAPP(c_Int_Onumber__class_Onumber__of(X34),X148) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__number__of__lemma) ).
fof(f35197,plain,
( spl574_312
| spl574_313 ),
inference(avatar_split_clause,[],[f35190,f35195,f35192]) ).
fof(f35192,plain,
( spl574_312
<=> ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_312])]) ).
fof(f35195,plain,
( spl574_313
<=> ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_313])]) ).
fof(f35190,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 ),
inference(forward_subsumption_demodulation,[],[f35189,f35177]) ).
fof(f35189,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| hAPP(c_Int_Onat,X1) = hAPP(c_Int_Onat,X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(forward_demodulation,[],[f35188,f34871]) ).
fof(f35188,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onat,X0) ),
inference(forward_demodulation,[],[f35187,f34859]) ).
fof(f35187,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onat,X0) ),
inference(forward_demodulation,[],[f35186,f34859]) ).
fof(f35186,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onat,X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_demodulation,[],[f34864,f34871]) ).
fof(f34864,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1) ),
inference(backward_demodulation,[],[f28876,f34859]) ).
fof(f28876,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1) ),
inference(forward_demodulation,[],[f28875,f23272]) ).
fof(f28875,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f28860,f23272]) ).
fof(f28860,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0))) ),
inference(backward_demodulation,[],[f20788,f23272]) ).
fof(f20788,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f15069]) ).
fof(f15069,plain,
! [X0,X1] :
( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| X0 = X1 )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) ) ) ) )
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
| ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
& ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
& X0 != X1 )
| ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) ) ) ) ) ),
inference(rectify,[],[f15068]) ).
fof(f15068,plain,
! [X1,X0] :
( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| X0 = X1 )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) ) ) ) )
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
| ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
& ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
& X0 != X1 )
| ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) ) ) ) ) ),
inference(flattening,[],[f15067]) ).
fof(f15067,plain,
! [X1,X0] :
( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| X0 = X1 )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) ) ) ) )
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
| ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
& ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
& X0 != X1 )
| ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) ) ) ) ) ),
inference(nnf_transformation,[],[f11366]) ).
fof(f11366,plain,
! [X1,X0] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| X0 = X1 )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) ) ) ) )
<=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) ),
inference(ennf_transformation,[],[f6972]) ).
fof(f6972,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
=> X0 = X1 ) ) ) )
<=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) ),
inference(rectify,[],[f2661]) ).
fof(f2661,axiom,
! [X95,X196] :
( ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X95)))
=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X196)))
=> X95 = X196 )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X196)))
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X95) ) ) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X95)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X196)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
<=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X95) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X196) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__nat__number__of) ).
fof(f34829,plain,
spl574_311,
inference(avatar_split_clause,[],[f26230,f34826]) ).
fof(f26230,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(cnf_transformation,[],[f1793]) ).
fof(f1793,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(f34817,plain,
( spl574_310
| spl574_102 ),
inference(avatar_split_clause,[],[f34813,f29299,f34815]) ).
fof(f34815,plain,
( spl574_310
<=> ! [X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_310])]) ).
fof(f34813,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) ),
inference(forward_subsumption_demodulation,[],[f34812,f29285]) ).
fof(f34812,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f34811,f23272]) ).
fof(f34811,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f22645,f23272]) ).
fof(f22645,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ),
inference(cnf_transformation,[],[f16512]) ).
fof(f16512,plain,
! [X0,X1] :
( ( ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) )
& ( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ) ),
inference(rectify,[],[f11593]) ).
fof(f11593,plain,
! [X1,X0] :
( ( ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) )
& ( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) ),
inference(ennf_transformation,[],[f9971]) ).
fof(f9971,plain,
! [X0,X1] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
=> hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) ) ) ) ),
inference(rectify,[],[f2664]) ).
fof(f2664,axiom,
! [X148,X195] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X148)))
=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X195)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X148) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X148),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X195)) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X195)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X148),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X195)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X148),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X195))) ) ) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X148)))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X148),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X195)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__nat__number__of) ).
fof(f34800,plain,
spl574_309,
inference(avatar_split_clause,[],[f34795,f34797]) ).
fof(f34795,plain,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),c_Int_OMin))),
inference(forward_demodulation,[],[f20918,f23272]) ).
fof(f20918,plain,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
inference(cnf_transformation,[],[f2940]) ).
fof(f2940,axiom,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__number__of__Min) ).
fof(f34794,plain,
spl574_308,
inference(avatar_split_clause,[],[f26997,f34791]) ).
fof(f34791,plain,
( spl574_308
<=> c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_308])]) ).
fof(f26997,plain,
c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f3270]) ).
fof(f3270,axiom,
c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__strict__def) ).
fof(f34741,plain,
spl574_307,
inference(avatar_split_clause,[],[f26853,f34738]) ).
fof(f34738,plain,
( spl574_307
<=> class_Lattices_Olattice(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_307])]) ).
fof(f26853,plain,
class_Lattices_Olattice(tc_Nat_Onat),
inference(cnf_transformation,[],[f5112]) ).
fof(f5112,axiom,
class_Lattices_Olattice(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).
fof(f34721,plain,
spl574_306,
inference(avatar_split_clause,[],[f26437,f34718]) ).
fof(f34718,plain,
( spl574_306
<=> class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_306])]) ).
fof(f26437,plain,
class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5200]) ).
fof(f5200,axiom,
class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Int_Onumber) ).
fof(f34716,plain,
spl574_305,
inference(avatar_split_clause,[],[f21982,f34713]) ).
fof(f34713,plain,
( spl574_305
<=> class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_305])]) ).
fof(f21982,plain,
class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5181]) ).
fof(f5181,axiom,
class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1) ).
fof(f34710,plain,
~ spl574_304,
inference(avatar_split_clause,[],[f34705,f34707]) ).
fof(f34705,plain,
hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),c_Int_OMin),
inference(forward_demodulation,[],[f34704,f23272]) ).
fof(f34704,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),c_Int_OMin),
inference(forward_demodulation,[],[f21048,f23272]) ).
fof(f21048,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
inference(cnf_transformation,[],[f2937]) ).
fof(f2937,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__Pls__Min) ).
fof(f34702,plain,
spl574_303,
inference(avatar_split_clause,[],[f34697,f34699]) ).
fof(f34699,plain,
( spl574_303
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),c_Int_OPls))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_303])]) ).
fof(f34697,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),c_Int_OPls))),
inference(forward_demodulation,[],[f26235,f23272]) ).
fof(f26235,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
inference(cnf_transformation,[],[f2700]) ).
fof(f2700,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of2) ).
fof(f34696,plain,
spl574_302,
inference(avatar_split_clause,[],[f21101,f34693]) ).
fof(f34693,plain,
( spl574_302
<=> class_Power_Opower(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_302])]) ).
fof(f21101,plain,
class_Power_Opower(tc_Nat_Onat),
inference(cnf_transformation,[],[f5119]) ).
fof(f5119,axiom,
class_Power_Opower(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
fof(f34681,plain,
spl574_301,
inference(avatar_split_clause,[],[f28520,f34678]) ).
fof(f28520,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(equality_resolution,[],[f25840]) ).
fof(f25840,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0) ),
inference(cnf_transformation,[],[f10925]) ).
fof(f10925,plain,
! [X0] :
( ( ( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0) ) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0) ) ),
inference(ennf_transformation,[],[f6050]) ).
fof(f6050,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0) ) ) ) ),
inference(rectify,[],[f1723]) ).
fof(f1723,axiom,
! [X104] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X104
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X104) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X104
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X104))
=> c_Groups_Osgn__class_Osgn(tc_Int_Oint,X104) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X104))
=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X104) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zsgn__def) ).
fof(f34597,plain,
spl574_300,
inference(avatar_split_clause,[],[f21870,f34594]) ).
fof(f34594,plain,
( spl574_300
<=> class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_300])]) ).
fof(f21870,plain,
class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5194]) ).
fof(f5194,axiom,
class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Oorder) ).
fof(f34565,plain,
spl574_299,
inference(avatar_split_clause,[],[f24495,f34562]) ).
fof(f34562,plain,
( spl574_299
<=> class_Groups_Omonoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_299])]) ).
fof(f24495,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5109]) ).
fof(f5109,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(f34555,plain,
spl574_298,
inference(avatar_split_clause,[],[f19979,f34552]) ).
fof(f34552,plain,
( spl574_298
<=> class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_298])]) ).
fof(f19979,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f5033]) ).
fof(f5033,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
fof(f34550,plain,
spl574_297,
inference(avatar_split_clause,[],[f23533,f34547]) ).
fof(f23533,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f1928]) ).
fof(f1928,axiom,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J) ).
fof(f34544,plain,
spl574_296,
inference(avatar_split_clause,[],[f21306,f34541]) ).
fof(f34541,plain,
( spl574_296
<=> class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_296])]) ).
fof(f21306,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5167]) ).
fof(f5167,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add) ).
fof(f34532,plain,
spl574_295,
inference(avatar_split_clause,[],[f34527,f34529]) ).
fof(f34527,plain,
c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(forward_demodulation,[],[f34526,f27421]) ).
fof(f34526,plain,
c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(forward_demodulation,[],[f34525,f25075]) ).
fof(f34525,plain,
c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(forward_demodulation,[],[f34524,f23929]) ).
fof(f34524,plain,
c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(forward_demodulation,[],[f34523,f23560]) ).
fof(f34523,plain,
c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(forward_demodulation,[],[f28384,f24146]) ).
fof(f28384,plain,
c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(equality_resolution,[],[f27648]) ).
fof(f27648,plain,
! [X0] :
( c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)),X0)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Int_OPls != X0 ),
inference(definition_unfolding,[],[f24300,f27035]) ).
fof(f27035,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)),X0)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_OBit0(X0),
inference(definition_unfolding,[],[f23459,f23060,f24559]) ).
fof(f23459,plain,
! [X0] : c_Int_OBit0(X0) = c_Int_Opred(c_Int_OBit1(X0)),
inference(cnf_transformation,[],[f8018]) ).
fof(f8018,plain,
! [X0] : c_Int_OBit0(X0) = c_Int_Opred(c_Int_OBit1(X0)),
inference(rectify,[],[f2831]) ).
fof(f2831,axiom,
! [X106] : c_Int_OBit0(X106) = c_Int_Opred(c_Int_OBit1(X106)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__Bit1) ).
fof(f24300,plain,
! [X0] :
( c_Int_OPls = c_Int_OBit0(X0)
| c_Int_OPls != X0 ),
inference(cnf_transformation,[],[f17802]) ).
fof(f17802,plain,
! [X0] :
( ( c_Int_OPls = c_Int_OBit0(X0)
| c_Int_OPls != X0 )
& ( c_Int_OPls = X0
| c_Int_OPls != c_Int_OBit0(X0) ) ),
inference(nnf_transformation,[],[f7100]) ).
fof(f7100,plain,
! [X0] :
( c_Int_OPls = c_Int_OBit0(X0)
<=> c_Int_OPls = X0 ),
inference(rectify,[],[f2804]) ).
fof(f2804,axiom,
! [X105] :
( c_Int_OPls = X105
<=> c_Int_OPls = c_Int_OBit0(X105) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I44_J) ).
fof(f34277,plain,
spl574_294,
inference(avatar_split_clause,[],[f26150,f34274]) ).
fof(f34274,plain,
( spl574_294
<=> class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_294])]) ).
fof(f26150,plain,
class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5192]) ).
fof(f5192,axiom,
class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0) ).
fof(f34272,plain,
spl574_55,
inference(avatar_split_clause,[],[f28140,f28964]) ).
fof(f28140,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f21445]) ).
fof(f21445,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f15557]) ).
fof(f15557,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ),
inference(nnf_transformation,[],[f8120]) ).
fof(f8120,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) ),
inference(rectify,[],[f1593]) ).
fof(f1593,axiom,
! [X74] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X74) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X74 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__eq__0__conv) ).
fof(f34244,plain,
spl574_293,
inference(avatar_split_clause,[],[f34239,f34241]) ).
fof(f34239,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_COMBC(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_fequal),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(forward_demodulation,[],[f22178,f33101]) ).
fof(f22178,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(cnf_transformation,[],[f3288]) ).
fof(f3288,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__int__def) ).
fof(f34156,plain,
spl574_292,
inference(avatar_split_clause,[],[f23709,f34153]) ).
fof(f34153,plain,
( spl574_292
<=> class_Groups_Oone(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_292])]) ).
fof(f23709,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(cnf_transformation,[],[f5122]) ).
fof(f5122,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
fof(f34149,plain,
spl574_291,
inference(avatar_split_clause,[],[f21764,f34146]) ).
fof(f34146,plain,
( spl574_291
<=> c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_291])]) ).
fof(f21764,plain,
c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)),
inference(cnf_transformation,[],[f3765]) ).
fof(f3765,axiom,
c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__greaterThan__UNIV) ).
fof(f34016,plain,
spl574_290,
inference(avatar_split_clause,[],[f22036,f34013]) ).
fof(f34013,plain,
( spl574_290
<=> class_Orderings_Obot(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_290])]) ).
fof(f22036,plain,
class_Orderings_Obot(tc_Nat_Onat),
inference(cnf_transformation,[],[f5117]) ).
fof(f5117,axiom,
class_Orderings_Obot(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Obot) ).
fof(f33971,plain,
( spl574_102
| spl574_289 ),
inference(avatar_split_clause,[],[f33967,f33969,f29299]) ).
fof(f33969,plain,
( spl574_289
<=> ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_289])]) ).
fof(f33967,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0))) ),
inference(forward_subsumption_demodulation,[],[f33966,f29285]) ).
fof(f33966,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) ),
inference(forward_demodulation,[],[f33965,f23272]) ).
fof(f33965,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f33964,f23272]) ).
fof(f33964,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) ),
inference(forward_demodulation,[],[f20783,f23272]) ).
fof(f20783,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(cnf_transformation,[],[f15069]) ).
fof(f33945,plain,
spl574_288,
inference(avatar_split_clause,[],[f21402,f33942]) ).
fof(f33942,plain,
( spl574_288
<=> class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_288])]) ).
fof(f21402,plain,
class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5190]) ).
fof(f5190,axiom,
class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add) ).
fof(f33940,plain,
spl574_287,
inference(avatar_split_clause,[],[f28123,f33937]) ).
fof(f33937,plain,
( spl574_287
<=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_287])]) ).
fof(f28123,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f28122]) ).
fof(f28122,plain,
! [X0] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X0)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0 ),
inference(equality_resolution,[],[f21163]) ).
fof(f21163,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0 ),
inference(cnf_transformation,[],[f15345]) ).
fof(f15345,plain,
! [X0,X1] :
( ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 )
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) )
& ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0 ) ),
inference(rectify,[],[f15344]) ).
fof(f15344,plain,
! [X1,X0] :
( ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) )
& ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ),
inference(flattening,[],[f15343]) ).
fof(f15343,plain,
! [X1,X0] :
( ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) )
& ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ),
inference(nnf_transformation,[],[f9153]) ).
fof(f9153,plain,
! [X1,X0] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
<=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) ),
inference(rectify,[],[f1474]) ).
fof(f1474,axiom,
! [X77,X74] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X77
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X74 )
<=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X77),X74) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
fof(f33924,plain,
spl574_205,
inference(avatar_split_clause,[],[f25382,f31031]) ).
fof(f25382,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f1775]) ).
fof(f1775,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I2_J) ).
fof(f33919,plain,
spl574_286,
inference(avatar_split_clause,[],[f33914,f33916]) ).
fof(f33914,plain,
c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OMin),
inference(forward_demodulation,[],[f27271,f25075]) ).
fof(f27271,plain,
c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),c_Int_OMin),
inference(definition_unfolding,[],[f21390,f24559]) ).
fof(f21390,plain,
c_Int_OMin = c_Int_OBit1(c_Int_OMin),
inference(cnf_transformation,[],[f2925]) ).
fof(f2925,axiom,
c_Int_OMin = c_Int_OBit1(c_Int_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__Min) ).
fof(f33913,plain,
spl574_285,
inference(avatar_split_clause,[],[f21632,f33910]) ).
fof(f33910,plain,
( spl574_285
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_285])]) ).
fof(f21632,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(cnf_transformation,[],[f5076]) ).
fof(f5076,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f33852,plain,
spl574_284,
inference(avatar_split_clause,[],[f24661,f33849]) ).
fof(f33849,plain,
( spl574_284
<=> c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_284])]) ).
fof(f24661,plain,
c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),
inference(cnf_transformation,[],[f1316]) ).
fof(f1316,axiom,
c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__nat__def) ).
fof(f33844,plain,
spl574_283,
inference(avatar_split_clause,[],[f25926,f33841]) ).
fof(f33841,plain,
( spl574_283
<=> class_Orderings_Owellorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_283])]) ).
fof(f25926,plain,
class_Orderings_Owellorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5103]) ).
fof(f5103,axiom,
class_Orderings_Owellorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Owellorder) ).
fof(f33831,plain,
spl574_203,
inference(avatar_split_clause,[],[f20393,f30990]) ).
fof(f20393,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f1842]) ).
fof(f1842,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I1_J) ).
fof(f33818,plain,
spl574_282,
inference(avatar_split_clause,[],[f27945,f33815]) ).
fof(f33815,plain,
( spl574_282
<=> c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Transitive__Closure_Ortrancl(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_282])]) ).
fof(f27945,plain,
c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Transitive__Closure_Ortrancl(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)))),
inference(definition_unfolding,[],[f26577,f22552]) ).
fof(f22552,plain,
! [X0] : c_Relation_OId(X0) = c_Transitive__Closure_Ortrancl(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(cnf_transformation,[],[f8225]) ).
fof(f8225,plain,
! [X0] : c_Relation_OId(X0) = c_Transitive__Closure_Ortrancl(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(rectify,[],[f3548]) ).
fof(f3548,axiom,
! [X4] : c_Relation_OId(X4) = c_Transitive__Closure_Ortrancl(X4,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__empty) ).
fof(f26577,plain,
c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))),
inference(cnf_transformation,[],[f3568]) ).
fof(f3568,axiom,
c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__leq__def) ).
fof(f33761,plain,
spl574_281,
inference(avatar_split_clause,[],[f24274,f33758]) ).
fof(f33758,plain,
( spl574_281
<=> class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_281])]) ).
fof(f24274,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f5093]) ).
fof(f5093,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(f33756,plain,
~ spl574_280,
inference(avatar_split_clause,[],[f25765,f33753]) ).
fof(f33753,plain,
( spl574_280
<=> hBOOL(c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_280])]) ).
fof(f25765,plain,
~ hBOOL(c_fFalse),
inference(cnf_transformation,[],[f5211]) ).
fof(f5211,axiom,
~ hBOOL(c_fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fFalse__1) ).
fof(f33745,plain,
spl574_279,
inference(avatar_split_clause,[],[f21242,f33742]) ).
fof(f21242,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
inference(cnf_transformation,[],[f3215]) ).
fof(f3215,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Osize_I3_J) ).
fof(f33708,plain,
spl574_278,
inference(avatar_split_clause,[],[f24561,f33705]) ).
fof(f33705,plain,
( spl574_278
<=> class_Rings_Oring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_278])]) ).
fof(f24561,plain,
class_Rings_Oring(tc_Int_Oint),
inference(cnf_transformation,[],[f5072]) ).
fof(f5072,axiom,
class_Rings_Oring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
fof(f33700,plain,
spl574_277,
inference(avatar_split_clause,[],[f22812,f33697]) ).
fof(f33697,plain,
( spl574_277
<=> c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_277])]) ).
fof(f22812,plain,
c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)),
inference(cnf_transformation,[],[f2086]) ).
fof(f2086,axiom,
c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__atLeast__UNIV) ).
fof(f33690,plain,
spl574_276,
inference(avatar_split_clause,[],[f26573,f33687]) ).
fof(f33687,plain,
( spl574_276
<=> class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_276])]) ).
fof(f26573,plain,
class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5168]) ).
fof(f5168,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add) ).
fof(f33684,plain,
spl574_275,
inference(avatar_split_clause,[],[f24305,f33681]) ).
fof(f33681,plain,
( spl574_275
<=> c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_275])]) ).
fof(f24305,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f4337]) ).
fof(f4337,axiom,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__code__numeral__def) ).
fof(f33679,plain,
spl574_274,
inference(avatar_split_clause,[],[f27543,f33676]) ).
fof(f27543,plain,
c_Nitpick_OFrac = hAPP(c_Product__Type_Ointernal__split(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(definition_unfolding,[],[f23469,f23198]) ).
fof(f23469,plain,
c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(cnf_transformation,[],[f2973]) ).
fof(f2973,axiom,
c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_OFrac__def) ).
fof(f33671,plain,
spl574_273,
inference(avatar_split_clause,[],[f25543,f33668]) ).
fof(f33668,plain,
( spl574_273
<=> class_Enum_Oenum(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_273])]) ).
fof(f25543,plain,
class_Enum_Oenum(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5158]) ).
fof(f5158,axiom,
class_Enum_Oenum(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Enum_Oenum) ).
fof(f33666,plain,
spl574_272,
inference(avatar_split_clause,[],[f20462,f33663]) ).
fof(f33663,plain,
( spl574_272
<=> class_Rings_Osemiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_272])]) ).
fof(f20462,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(cnf_transformation,[],[f5055]) ).
fof(f5055,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
fof(f33641,plain,
spl574_271,
inference(avatar_split_clause,[],[f23530,f33638]) ).
fof(f33638,plain,
( spl574_271
<=> class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_271])]) ).
fof(f23530,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f5094]) ).
fof(f5094,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
fof(f33632,plain,
spl574_270,
inference(avatar_split_clause,[],[f25599,f33629]) ).
fof(f33629,plain,
( spl574_270
<=> c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_270])]) ).
fof(f25599,plain,
c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f4341]) ).
fof(f4341,axiom,
c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__code) ).
fof(f33625,plain,
spl574_269,
inference(avatar_split_clause,[],[f25169,f33622]) ).
fof(f33622,plain,
( spl574_269
<=> class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_269])]) ).
fof(f25169,plain,
class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5185]) ).
fof(f5185,axiom,
class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0) ).
fof(f33095,plain,
spl574_268,
inference(avatar_split_clause,[],[f22503,f33092]) ).
fof(f33092,plain,
( spl574_268
<=> class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_268])]) ).
fof(f22503,plain,
class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5172]) ).
fof(f5172,axiom,
class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add) ).
fof(f33028,plain,
spl574_267,
inference(avatar_split_clause,[],[f20414,f33025]) ).
fof(f33025,plain,
( spl574_267
<=> class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_267])]) ).
fof(f20414,plain,
class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5201]) ).
fof(f5201,axiom,
class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oone) ).
fof(f32856,plain,
( ~ spl574_51
| spl574_266 ),
inference(avatar_split_clause,[],[f32852,f32854,f28943]) ).
fof(f32854,plain,
( spl574_266
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_266])]) ).
fof(f32852,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(forward_subsumption_demodulation,[],[f32851,f26954]) ).
fof(f26954,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ),
inference(cnf_transformation,[],[f19773]) ).
fof(f19773,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(nnf_transformation,[],[f8389]) ).
fof(f8389,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ),
inference(rectify,[],[f538]) ).
fof(f538,axiom,
! [X74] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X74))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X74 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).
fof(f32851,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(forward_demodulation,[],[f32850,f23929]) ).
fof(f32850,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) ),
inference(forward_demodulation,[],[f32849,f23560]) ).
fof(f32849,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
inference(forward_demodulation,[],[f32848,f23929]) ).
fof(f32848,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) ),
inference(forward_demodulation,[],[f32847,f24146]) ).
fof(f32847,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
inference(forward_demodulation,[],[f32846,f30826]) ).
fof(f30826,plain,
! [X0] : hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0)),
inference(backward_demodulation,[],[f29759,f30820]) ).
fof(f30820,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0))),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(forward_demodulation,[],[f27856,f25075]) ).
fof(f27856,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)),X0)),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(definition_unfolding,[],[f25962,f27035]) ).
fof(f25962,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0) = c_Int_OBit0(X0),
inference(cnf_transformation,[],[f6146]) ).
fof(f6146,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0) = c_Int_OBit0(X0),
inference(rectify,[],[f2811]) ).
fof(f2811,axiom,
! [X106] : c_Int_OBit0(X106) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X106),X106),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(f29759,plain,
! [X0] : hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(backward_demodulation,[],[f27436,f25075]) ).
fof(f27436,plain,
! [X0] : hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)),X0)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(definition_unfolding,[],[f22555,f27035]) ).
fof(f22555,plain,
! [X0] : hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X0)),
inference(cnf_transformation,[],[f8221]) ).
fof(f8221,plain,
! [X0] : hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X0)),
inference(rectify,[],[f2836]) ).
fof(f2836,axiom,
! [X145] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X145)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X145)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__Bit0) ).
fof(f32846,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) ),
inference(forward_demodulation,[],[f32845,f23929]) ).
fof(f32845,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ),
inference(forward_demodulation,[],[f32844,f23560]) ).
fof(f32844,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ),
inference(forward_demodulation,[],[f32843,f23929]) ).
fof(f32843,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ),
inference(forward_demodulation,[],[f32842,f24146]) ).
fof(f32842,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ),
inference(forward_demodulation,[],[f32841,f23929]) ).
fof(f32841,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))) ),
inference(forward_demodulation,[],[f32660,f30826]) ).
fof(f32660,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ),
inference(backward_demodulation,[],[f29994,f23929]) ).
fof(f29994,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ),
inference(forward_demodulation,[],[f29993,f25075]) ).
fof(f29993,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ),
inference(forward_demodulation,[],[f29992,f25075]) ).
fof(f29992,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))))) ),
inference(forward_demodulation,[],[f29823,f25075]) ).
fof(f29823,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ),
inference(backward_demodulation,[],[f29468,f25075]) ).
fof(f29468,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))))) ),
inference(forward_demodulation,[],[f29467,f27436]) ).
fof(f29467,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) ),
inference(forward_demodulation,[],[f27189,f27436]) ).
fof(f27189,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) ),
inference(definition_unfolding,[],[f20853,f27035,f24559,f27035,f24559]) ).
fof(f20853,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
inference(cnf_transformation,[],[f15124]) ).
fof(f15124,plain,
! [X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
inference(nnf_transformation,[],[f5539]) ).
fof(f5539,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
inference(rectify,[],[f2903]) ).
fof(f2903,axiom,
! [X77] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X77,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X77,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod2__gr__0) ).
fof(f32630,plain,
~ spl574_265,
inference(avatar_split_clause,[],[f23519,f32627]) ).
fof(f32627,plain,
( spl574_265
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_265])]) ).
fof(f23519,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(cnf_transformation,[],[f2928]) ).
fof(f2928,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I20_J) ).
fof(f32620,plain,
spl574_264,
inference(avatar_split_clause,[],[f23790,f32617]) ).
fof(f32617,plain,
( spl574_264
<=> c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_264])]) ).
fof(f23790,plain,
c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of),
inference(cnf_transformation,[],[f4369]) ).
fof(f4369,axiom,
c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__of__def) ).
fof(f32614,plain,
spl574_263,
inference(avatar_split_clause,[],[f27781,f32611]) ).
fof(f27781,plain,
c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Ointernal__split(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
inference(definition_unfolding,[],[f25435,f23198]) ).
fof(f25435,plain,
c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
inference(cnf_transformation,[],[f3360]) ).
fof(f3360,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__less) ).
fof(f32609,plain,
spl574_262,
inference(avatar_split_clause,[],[f32604,f32606]) ).
fof(f32604,plain,
c_List_Olist_ONil(tc_Nat_Onat) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(forward_demodulation,[],[f27776,f21540]) ).
fof(f27776,plain,
! [X0] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definition_unfolding,[],[f25419,f24709]) ).
fof(f25419,plain,
! [X0] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f5620]) ).
fof(f5620,plain,
! [X0] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rectify,[],[f4537]) ).
fof(f4537,axiom,
! [X104] : c_List_Oupt(X104,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__0) ).
fof(f32568,plain,
spl574_261,
inference(avatar_split_clause,[],[f32563,f32565]) ).
fof(f32563,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f32562,f25075]) ).
fof(f32562,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))),
inference(forward_demodulation,[],[f32561,f23560]) ).
fof(f32561,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),
inference(forward_demodulation,[],[f27307,f24146]) ).
fof(f27307,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),
inference(definition_unfolding,[],[f21610,f24559]) ).
fof(f21610,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
inference(cnf_transformation,[],[f2772]) ).
fof(f2772,axiom,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__1__eq__Suc__0) ).
fof(f32558,plain,
spl574_260,
inference(avatar_split_clause,[],[f24990,f32555]) ).
fof(f32555,plain,
( spl574_260
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_260])]) ).
fof(f24990,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(cnf_transformation,[],[f5078]) ).
fof(f5078,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f32549,plain,
spl574_259,
inference(avatar_split_clause,[],[f21606,f32546]) ).
fof(f32546,plain,
( spl574_259
<=> class_Rings_Omult__zero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_259])]) ).
fof(f21606,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(cnf_transformation,[],[f5059]) ).
fof(f5059,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
fof(f32541,plain,
spl574_258,
inference(avatar_split_clause,[],[f32536,f32538]) ).
fof(f32538,plain,
( spl574_258
<=> c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_258])]) ).
fof(f32536,plain,
c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(forward_demodulation,[],[f32535,f25075]) ).
fof(f32535,plain,
c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(forward_demodulation,[],[f32534,f23560]) ).
fof(f32534,plain,
c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(forward_demodulation,[],[f27888,f24146]) ).
fof(f27888,plain,
c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(definition_unfolding,[],[f26216,f27035]) ).
fof(f26216,plain,
c_Int_OPls = c_Int_OBit0(c_Int_OPls),
inference(cnf_transformation,[],[f2802]) ).
fof(f2802,axiom,
c_Int_OPls = c_Int_OBit0(c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__Pls) ).
fof(f32446,plain,
spl574_257,
inference(avatar_split_clause,[],[f26418,f32443]) ).
fof(f32443,plain,
( spl574_257
<=> class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_257])]) ).
fof(f26418,plain,
class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5193]) ).
fof(f5193,axiom,
class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero) ).
fof(f32426,plain,
spl574_256,
inference(avatar_split_clause,[],[f32421,f32423]) ).
fof(f32421,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))),
inference(forward_demodulation,[],[f32420,f23560]) ).
fof(f32420,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))),
inference(forward_demodulation,[],[f32419,f23560]) ).
fof(f32419,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))),
inference(forward_demodulation,[],[f32418,f25075]) ).
fof(f32418,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))))),
inference(forward_demodulation,[],[f32417,f23560]) ).
fof(f32417,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))))),
inference(forward_demodulation,[],[f32416,f23560]) ).
fof(f32416,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))))))),
inference(forward_demodulation,[],[f32415,f23560]) ).
fof(f32415,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)))))))),
inference(forward_demodulation,[],[f32414,f23560]) ).
fof(f32414,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)))))))),
inference(forward_demodulation,[],[f32413,f23560]) ).
fof(f32413,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)))))))),
inference(forward_demodulation,[],[f32412,f23560]) ).
fof(f32412,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)))))))),
inference(forward_demodulation,[],[f32411,f24146]) ).
fof(f32411,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))))))),
inference(forward_demodulation,[],[f32410,f24146]) ).
fof(f32410,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin)))))),
inference(forward_demodulation,[],[f32409,f23560]) ).
fof(f32409,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin)))))),
inference(forward_demodulation,[],[f32408,f23560]) ).
fof(f32408,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin)))))),
inference(forward_demodulation,[],[f32407,f23560]) ).
fof(f32407,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin)))))),
inference(forward_demodulation,[],[f32406,f23560]) ).
fof(f32406,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin)))))),
inference(forward_demodulation,[],[f32405,f24146]) ).
fof(f32405,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin))))),
inference(forward_demodulation,[],[f32404,f24146]) ).
fof(f32404,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin)))),
inference(forward_demodulation,[],[f32403,f24146]) ).
fof(f32403,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Int_OMin))),
inference(forward_demodulation,[],[f32402,f24146]) ).
fof(f32402,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OMin)),
inference(forward_demodulation,[],[f27525,f27698]) ).
fof(f27525,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(definition_unfolding,[],[f23296,f27035,f24559]) ).
fof(f23296,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(cnf_transformation,[],[f2857]) ).
fof(f2857,axiom,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__2__eq__2) ).
fof(f32401,plain,
spl574_220,
inference(avatar_split_clause,[],[f28525,f31308]) ).
fof(f31308,plain,
( spl574_220
<=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_220])]) ).
fof(f28525,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f28524]) ).
fof(f28524,plain,
! [X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(equality_resolution,[],[f25872]) ).
fof(f25872,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(cnf_transformation,[],[f18964]) ).
fof(f18964,plain,
! [X0,X1] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0 ) ) )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 )
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) ) ),
inference(flattening,[],[f18963]) ).
fof(f18963,plain,
! [X0,X1] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0 ) ) )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 )
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) ) ),
inference(nnf_transformation,[],[f6242]) ).
fof(f6242,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 ) ) ),
inference(rectify,[],[f1084]) ).
fof(f1084,axiom,
! [X74,X77] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X77),X74)
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X77
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X74 )
| ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X77
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X74 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).
fof(f32394,plain,
spl574_255,
inference(avatar_split_clause,[],[f20094,f32391]) ).
fof(f32391,plain,
( spl574_255
<=> class_Divides_Osemiring__div(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_255])]) ).
fof(f20094,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(cnf_transformation,[],[f5101]) ).
fof(f5101,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).
fof(f32387,plain,
spl574_254,
inference(avatar_split_clause,[],[f23205,f32384]) ).
fof(f32384,plain,
( spl574_254
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_254])]) ).
fof(f23205,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5169]) ).
fof(f5169,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add) ).
fof(f32361,plain,
spl574_253,
inference(avatar_split_clause,[],[f23048,f32358]) ).
fof(f32358,plain,
( spl574_253
<=> class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_253])]) ).
fof(f23048,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5041]) ).
fof(f5041,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(f32352,plain,
~ spl574_252,
inference(avatar_split_clause,[],[f24344,f32349]) ).
fof(f32349,plain,
( spl574_252
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_252])]) ).
fof(f24344,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
inference(cnf_transformation,[],[f2920]) ).
fof(f2920,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I7_J) ).
fof(f31798,plain,
spl574_251,
inference(avatar_split_clause,[],[f31793,f31795]) ).
fof(f31793,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f31792,f23560]) ).
fof(f31792,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f31791,f23560]) ).
fof(f31791,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f31790,f25075]) ).
fof(f31790,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f31789,f23560]) ).
fof(f31789,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f31788,f23560]) ).
fof(f31788,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f31787,f23560]) ).
fof(f31787,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f31786,f24146]) ).
fof(f31786,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f31785,f23560]) ).
fof(f31785,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f31784,f23560]) ).
fof(f31784,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f31783,f23560]) ).
fof(f31783,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f31782,f23560]) ).
fof(f31782,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f31781,f24146]) ).
fof(f31781,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f31780,f24146]) ).
fof(f31780,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f31779,f24146]) ).
fof(f31779,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f27600,f23272]) ).
fof(f27600,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(definition_unfolding,[],[f23877,f27035,f24559]) ).
fof(f23877,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(cnf_transformation,[],[f2888]) ).
fof(f2888,axiom,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__2) ).
fof(f31778,plain,
spl574_250,
inference(avatar_split_clause,[],[f21321,f31775]) ).
fof(f31775,plain,
( spl574_250
<=> c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_250])]) ).
fof(f21321,plain,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)),
inference(cnf_transformation,[],[f3274]) ).
fof(f3274,axiom,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__rpair__set) ).
fof(f31771,plain,
spl574_249,
inference(avatar_split_clause,[],[f26671,f31768]) ).
fof(f26671,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(cnf_transformation,[],[f1698]) ).
fof(f1698,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__less__1) ).
fof(f31723,plain,
spl574_248,
inference(avatar_split_clause,[],[f19996,f31720]) ).
fof(f31720,plain,
( spl574_248
<=> class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_248])]) ).
fof(f19996,plain,
class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5180]) ).
fof(f5180,axiom,
class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add) ).
fof(f31712,plain,
( spl574_102
| spl574_55 ),
inference(avatar_split_clause,[],[f31711,f28964,f29299]) ).
fof(f31711,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0))) ),
inference(forward_subsumption_demodulation,[],[f31710,f29285]) ).
fof(f31710,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ),
inference(forward_demodulation,[],[f23930,f23272]) ).
fof(f23930,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(cnf_transformation,[],[f12030]) ).
fof(f12030,plain,
! [X0] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ) ),
inference(ennf_transformation,[],[f8751]) ).
fof(f8751,plain,
! [X0] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ) ),
inference(rectify,[],[f2663]) ).
fof(f2663,axiom,
! [X148] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X148)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X148) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X148)) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X148)))
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X148)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__nat__number__of) ).
fof(f31703,plain,
spl574_247,
inference(avatar_split_clause,[],[f25885,f31700]) ).
fof(f31700,plain,
( spl574_247
<=> class_Rings_Ocomm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_247])]) ).
fof(f25885,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5044]) ).
fof(f5044,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(f31698,plain,
spl574_246,
inference(avatar_split_clause,[],[f25950,f31695]) ).
fof(f31695,plain,
( spl574_246
<=> class_Groups_Osemigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_246])]) ).
fof(f25950,plain,
class_Groups_Osemigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5100]) ).
fof(f5100,axiom,
class_Groups_Osemigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Osemigroup__add) ).
fof(f31690,plain,
spl574_245,
inference(avatar_split_clause,[],[f21292,f31687]) ).
fof(f31687,plain,
( spl574_245
<=> class_Rings_Oordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_245])]) ).
fof(f21292,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5035]) ).
fof(f5035,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
fof(f31685,plain,
spl574_244,
inference(avatar_split_clause,[],[f23211,f31682]) ).
fof(f31682,plain,
( spl574_244
<=> class_Int_Onumber(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_244])]) ).
fof(f23211,plain,
class_Int_Onumber(tc_Int_Oint),
inference(cnf_transformation,[],[f5074]) ).
fof(f5074,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber) ).
fof(f31680,plain,
spl574_243,
inference(avatar_split_clause,[],[f23713,f31677]) ).
fof(f31677,plain,
( spl574_243
<=> class_Groups_Oab__semigroup__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_243])]) ).
fof(f23713,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f5032]) ).
fof(f5032,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(f31675,plain,
spl574_242,
inference(avatar_split_clause,[],[f21975,f31672]) ).
fof(f31672,plain,
( spl574_242
<=> c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_242])]) ).
fof(f21975,plain,
c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel),
inference(cnf_transformation,[],[f3278]) ).
fof(f3278,axiom,
c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__intrel) ).
fof(f31650,plain,
spl574_241,
inference(avatar_split_clause,[],[f22302,f31647]) ).
fof(f31647,plain,
( spl574_241
<=> class_Nat_Osize(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_241])]) ).
fof(f22302,plain,
class_Nat_Osize(tc_HOL_Obool),
inference(cnf_transformation,[],[f5141]) ).
fof(f5141,axiom,
class_Nat_Osize(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Nat_Osize) ).
fof(f31641,plain,
spl574_240,
inference(avatar_split_clause,[],[f31636,f31638]) ).
fof(f31636,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_demodulation,[],[f31635,f28309]) ).
fof(f28309,plain,
! [X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
inference(equality_resolution,[],[f23283]) ).
fof(f23283,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f16996]) ).
fof(f16996,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
inference(flattening,[],[f16995]) ).
fof(f16995,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
inference(nnf_transformation,[],[f8441]) ).
fof(f8441,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) ),
inference(rectify,[],[f1394]) ).
fof(f1394,axiom,
! [X77,X74] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X77
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X74 )
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X77),X74) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__is__0) ).
fof(f31635,plain,
! [X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_demodulation,[],[f28623,f28309]) ).
fof(f28623,plain,
! [X2,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)),
inference(equality_resolution,[],[f26806]) ).
fof(f26806,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f13573]) ).
fof(f13573,plain,
! [X0,X1,X2] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ),
inference(ennf_transformation,[],[f8364]) ).
fof(f8364,plain,
! [X1,X0,X2] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2)) ) ),
inference(rectify,[],[f2381]) ).
fof(f2381,axiom,
! [X106,X99,X75] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X106
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X106),X99)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X106),X75)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X106
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X99),X75) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X106),X99)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X106),X75)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__div__cancel__disj) ).
fof(f31628,plain,
spl574_239,
inference(avatar_split_clause,[],[f20726,f31625]) ).
fof(f31625,plain,
( spl574_239
<=> class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_239])]) ).
fof(f20726,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5095]) ).
fof(f5095,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(f31618,plain,
spl574_238,
inference(avatar_split_clause,[],[f26998,f31615]) ).
fof(f31615,plain,
( spl574_238
<=> class_Groups_Ominus(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_238])]) ).
fof(f26998,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(cnf_transformation,[],[f5069]) ).
fof(f5069,axiom,
class_Groups_Ominus(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).
fof(f31613,plain,
spl574_237,
inference(avatar_split_clause,[],[f23260,f31610]) ).
fof(f31610,plain,
( spl574_237
<=> class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_237])]) ).
fof(f23260,plain,
class_Nat_Osize(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5202]) ).
fof(f5202,axiom,
class_Nat_Osize(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Nat_Osize) ).
fof(f31607,plain,
spl574_236,
inference(avatar_split_clause,[],[f20506,f31604]) ).
fof(f31604,plain,
( spl574_236
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_236])]) ).
fof(f20506,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5077]) ).
fof(f5077,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f31602,plain,
spl574_235,
inference(avatar_split_clause,[],[f25769,f31599]) ).
fof(f31599,plain,
( spl574_235
<=> class_Rings_Ozero__neq__one(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_235])]) ).
fof(f25769,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(cnf_transformation,[],[f5047]) ).
fof(f5047,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(f31593,plain,
spl574_234,
inference(avatar_split_clause,[],[f31588,f31590]) ).
fof(f31588,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))),
inference(forward_demodulation,[],[f31587,f23560]) ).
fof(f31587,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))),
inference(forward_demodulation,[],[f31586,f23560]) ).
fof(f31586,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))),
inference(forward_demodulation,[],[f31585,f25075]) ).
fof(f31585,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))))),
inference(forward_demodulation,[],[f31584,f23560]) ).
fof(f31584,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))))),
inference(forward_demodulation,[],[f31583,f23560]) ).
fof(f31583,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))))),
inference(forward_demodulation,[],[f31582,f23560]) ).
fof(f31582,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))))),
inference(forward_demodulation,[],[f31581,f24146]) ).
fof(f31581,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))))),
inference(forward_demodulation,[],[f31580,f23560]) ).
fof(f31580,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))))),
inference(forward_demodulation,[],[f31579,f23560]) ).
fof(f31579,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))))),
inference(forward_demodulation,[],[f31578,f23560]) ).
fof(f31578,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))))),
inference(forward_demodulation,[],[f31577,f23560]) ).
fof(f31577,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))))),
inference(forward_demodulation,[],[f31576,f24146]) ).
fof(f31576,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f31575,f24146]) ).
fof(f31575,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f31574,f24146]) ).
fof(f31574,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(forward_demodulation,[],[f27110,f23272]) ).
fof(f27110,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(definition_unfolding,[],[f20226,f24559,f24559]) ).
fof(f20226,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
inference(cnf_transformation,[],[f2769]) ).
fof(f2769,axiom,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J) ).
fof(f31566,plain,
spl574_233,
inference(avatar_split_clause,[],[f25264,f31563]) ).
fof(f31563,plain,
( spl574_233
<=> class_Finite__Set_Ofinite(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_233])]) ).
fof(f25264,plain,
class_Finite__Set_Ofinite(tc_HOL_Obool),
inference(cnf_transformation,[],[f5132]) ).
fof(f5132,axiom,
class_Finite__Set_Ofinite(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).
fof(f31561,plain,
spl574_232,
inference(avatar_split_clause,[],[f28180,f31558]) ).
fof(f31558,plain,
( spl574_232
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_232])]) ).
fof(f28180,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(equality_resolution,[],[f28179]) ).
fof(f28179,plain,
! [X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(equality_resolution,[],[f21722]) ).
fof(f21722,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f15768]) ).
fof(f15768,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))) ) ),
inference(flattening,[],[f15767]) ).
fof(f15767,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))) ) ),
inference(nnf_transformation,[],[f9081]) ).
fof(f9081,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))))
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) ),
inference(rectify,[],[f1589]) ).
fof(f1589,axiom,
! [X74,X77] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X77
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X74 )
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X74)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X77)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__zle__neg) ).
fof(f31513,plain,
spl574_231,
inference(avatar_split_clause,[],[f20557,f31510]) ).
fof(f31510,plain,
( spl574_231
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_231])]) ).
fof(f20557,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(cnf_transformation,[],[f2926]) ).
fof(f2926,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I2_J) ).
fof(f31508,plain,
spl574_230,
inference(avatar_split_clause,[],[f23538,f31505]) ).
fof(f31505,plain,
( spl574_230
<=> class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_230])]) ).
fof(f23538,plain,
class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5198]) ).
fof(f5198,axiom,
class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Power_Opower) ).
fof(f31503,plain,
spl574_229,
inference(avatar_split_clause,[],[f23204,f31500]) ).
fof(f31500,plain,
( spl574_229
<=> class_Orderings_Otop(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_229])]) ).
fof(f23204,plain,
class_Orderings_Otop(tc_HOL_Obool),
inference(cnf_transformation,[],[f5135]) ).
fof(f5135,axiom,
class_Orderings_Otop(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
fof(f31430,plain,
spl574_228,
inference(avatar_split_clause,[],[f26649,f31427]) ).
fof(f31427,plain,
( spl574_228
<=> class_Groups_Ogroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_228])]) ).
fof(f26649,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5057]) ).
fof(f5057,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
fof(f31413,plain,
spl574_227,
inference(avatar_split_clause,[],[f20530,f31410]) ).
fof(f20530,plain,
c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral,
inference(cnf_transformation,[],[f4378]) ).
fof(f4378,axiom,
c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subtract__code__numeral__def) ).
fof(f31404,plain,
spl574_226,
inference(avatar_split_clause,[],[f25858,f31401]) ).
fof(f31401,plain,
( spl574_226
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_226])]) ).
fof(f25858,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))),
inference(cnf_transformation,[],[f979]) ).
fof(f979,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__UNIV__unit) ).
fof(f31399,plain,
spl574_225,
inference(avatar_split_clause,[],[f31394,f31396]) ).
fof(f31396,plain,
( spl574_225
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_225])]) ).
fof(f31394,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(forward_demodulation,[],[f31393,f30820]) ).
fof(f31393,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))),c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(forward_demodulation,[],[f27970,f25075]) ).
fof(f27970,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),c_Int_OMin)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(definition_unfolding,[],[f26767,f23060,f27035]) ).
fof(f26767,plain,
c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
inference(cnf_transformation,[],[f2944]) ).
fof(f2944,axiom,
c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__Min) ).
fof(f31390,plain,
~ spl574_224,
inference(avatar_split_clause,[],[f20133,f31387]) ).
fof(f31387,plain,
( spl574_224
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_224])]) ).
fof(f20133,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f853]) ).
fof(f853,axiom,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_infinite__UNIV__nat) ).
fof(f31385,plain,
spl574_223,
inference(avatar_split_clause,[],[f31380,f31382]) ).
fof(f31380,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(forward_demodulation,[],[f28255,f28551]) ).
fof(f28551,plain,
! [X1] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f26119]) ).
fof(f26119,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f19160]) ).
fof(f19160,plain,
! [X0,X1] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ),
inference(rectify,[],[f12003]) ).
fof(f12003,plain,
! [X1,X0] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ),
inference(ennf_transformation,[],[f9088]) ).
fof(f9088,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) ) ),
inference(rectify,[],[f2199]) ).
fof(f2199,axiom,
! [X168,X99] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X99
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X168),X99) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X168),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X168),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X99),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X99
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X168),X99) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__if) ).
fof(f28255,plain,
! [X0] : hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f22595]) ).
fof(f22595,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f16470]) ).
fof(f16470,plain,
! [X0,X1] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) ) ),
inference(rectify,[],[f16469]) ).
fof(f16469,plain,
! [X1,X0] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0) ) ),
inference(flattening,[],[f16468]) ).
fof(f16468,plain,
! [X1,X0] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0) ) ),
inference(nnf_transformation,[],[f6815]) ).
fof(f6815,plain,
! [X1,X0] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ) ),
inference(rectify,[],[f2207]) ).
fof(f2207,axiom,
! [X77,X22] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X22
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X77 )
<=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22),X77) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
fof(f31379,plain,
spl574_222,
inference(avatar_split_clause,[],[f23288,f31376]) ).
fof(f31376,plain,
( spl574_222
<=> class_Rings_Omult__zero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_222])]) ).
fof(f23288,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(cnf_transformation,[],[f5113]) ).
fof(f5113,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
fof(f31361,plain,
spl574_221,
inference(avatar_split_clause,[],[f26631,f31358]) ).
fof(f31358,plain,
( spl574_221
<=> class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_221])]) ).
fof(f26631,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5010]) ).
fof(f5010,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
fof(f31311,plain,
spl574_220,
inference(avatar_split_clause,[],[f28270,f31308]) ).
fof(f28270,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f28269]) ).
fof(f28269,plain,
! [X0] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0 ),
inference(equality_resolution,[],[f22682]) ).
fof(f22682,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0 ),
inference(cnf_transformation,[],[f16541]) ).
fof(f16541,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 )
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1) )
& ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)
| ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0 ) ) ) ),
inference(flattening,[],[f16540]) ).
fof(f16540,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 )
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1) )
& ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)
| ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0 ) ) ) ),
inference(nnf_transformation,[],[f7098]) ).
fof(f7098,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 ) )
<=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1) ),
inference(rectify,[],[f1083]) ).
fof(f1083,axiom,
! [X77,X74] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X77),X74)
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X77
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X74 )
| ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X77
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X74 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).
fof(f31306,plain,
spl574_219,
inference(avatar_split_clause,[],[f20107,f31303]) ).
fof(f31303,plain,
( spl574_219
<=> class_Groups_Ominus(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_219])]) ).
fof(f20107,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(cnf_transformation,[],[f5139]) ).
fof(f5139,axiom,
class_Groups_Ominus(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
fof(f31249,plain,
spl574_218,
inference(avatar_split_clause,[],[f25930,f31246]) ).
fof(f31246,plain,
( spl574_218
<=> class_Power_Opower(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_218])]) ).
fof(f25930,plain,
class_Power_Opower(tc_Int_Oint),
inference(cnf_transformation,[],[f5070]) ).
fof(f5070,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
fof(f31239,plain,
spl574_217,
inference(avatar_split_clause,[],[f24511,f31236]) ).
fof(f31236,plain,
( spl574_217
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_217])]) ).
fof(f24511,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(cnf_transformation,[],[f2927]) ).
fof(f2927,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I23_J) ).
fof(f31229,plain,
spl574_216,
inference(avatar_split_clause,[],[f19852,f31226]) ).
fof(f31226,plain,
( spl574_216
<=> class_Orderings_Opreorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_216])]) ).
fof(f19852,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5106]) ).
fof(f5106,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(f31220,plain,
spl574_215,
inference(avatar_split_clause,[],[f24438,f31217]) ).
fof(f24438,plain,
c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
inference(cnf_transformation,[],[f3268]) ).
fof(f3268,axiom,
c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__weak__def) ).
fof(f31211,plain,
spl574_214,
inference(avatar_split_clause,[],[f22911,f31208]) ).
fof(f31208,plain,
( spl574_214
<=> class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_214])]) ).
fof(f22911,plain,
class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5177]) ).
fof(f5177,axiom,
class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add) ).
fof(f31205,plain,
spl574_213,
inference(avatar_split_clause,[],[f21906,f31202]) ).
fof(f31202,plain,
( spl574_213
<=> c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_213])]) ).
fof(f21906,plain,
c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
inference(cnf_transformation,[],[f1938]) ).
fof(f1938,axiom,
c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J) ).
fof(f31197,plain,
spl574_212,
inference(avatar_split_clause,[],[f24393,f31194]) ).
fof(f31194,plain,
( spl574_212
<=> c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_212])]) ).
fof(f24393,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(cnf_transformation,[],[f3393]) ).
fof(f3393,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__pred__nat) ).
fof(f31186,plain,
~ spl574_211,
inference(avatar_split_clause,[],[f20600,f31183]) ).
fof(f31183,plain,
( spl574_211
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_211])]) ).
fof(f20600,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(cnf_transformation,[],[f2064]) ).
fof(f2064,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__1) ).
fof(f31135,plain,
spl574_210,
inference(avatar_split_clause,[],[f26713,f31132]) ).
fof(f31132,plain,
( spl574_210
<=> c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_210])]) ).
fof(f26713,plain,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f3362]) ).
fof(f3362,axiom,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__pair__less) ).
fof(f31063,plain,
spl574_209,
inference(avatar_split_clause,[],[f24213,f31060]) ).
fof(f31060,plain,
( spl574_209
<=> c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_209])]) ).
fof(f24213,plain,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)),
inference(cnf_transformation,[],[f3269]) ).
fof(f3269,axiom,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__rpair__set) ).
fof(f31057,plain,
spl574_208,
inference(avatar_split_clause,[],[f26582,f31054]) ).
fof(f31054,plain,
( spl574_208
<=> class_Lattices_Obounded__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_208])]) ).
fof(f26582,plain,
class_Lattices_Obounded__lattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f4986]) ).
fof(f4986,axiom,
class_Lattices_Obounded__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice) ).
fof(f31052,plain,
spl574_207,
inference(avatar_split_clause,[],[f21611,f31049]) ).
fof(f31049,plain,
( spl574_207
<=> class_Orderings_Obot(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_207])]) ).
fof(f21611,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(cnf_transformation,[],[f5137]) ).
fof(f5137,axiom,
class_Orderings_Obot(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
fof(f31043,plain,
spl574_206,
inference(avatar_split_clause,[],[f20484,f31040]) ).
fof(f31040,plain,
( spl574_206
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_206])]) ).
fof(f20484,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(cnf_transformation,[],[f5006]) ).
fof(f5006,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f31034,plain,
spl574_205,
inference(avatar_split_clause,[],[f22207,f31031]) ).
fof(f22207,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f1605]) ).
fof(f1605,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__1) ).
fof(f31026,plain,
spl574_204,
inference(avatar_split_clause,[],[f23203,f31023]) ).
fof(f31023,plain,
( spl574_204
<=> class_Rings_Osemiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_204])]) ).
fof(f23203,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5063]) ).
fof(f5063,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
fof(f30993,plain,
spl574_203,
inference(avatar_split_clause,[],[f26858,f30990]) ).
fof(f26858,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f1843]) ).
fof(f1843,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0) ).
fof(f30972,plain,
spl574_202,
inference(avatar_split_clause,[],[f22131,f30969]) ).
fof(f30969,plain,
( spl574_202
<=> class_Orderings_Oord(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_202])]) ).
fof(f22131,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(cnf_transformation,[],[f5116]) ).
fof(f5116,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(f30963,plain,
spl574_201,
inference(avatar_split_clause,[],[f30958,f30960]) ).
fof(f30958,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OPls),
inference(forward_demodulation,[],[f27921,f25075]) ).
fof(f27921,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls),
inference(definition_unfolding,[],[f26442,f24559]) ).
fof(f26442,plain,
c_Int_OBit1(c_Int_OPls) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin),
inference(cnf_transformation,[],[f2958]) ).
fof(f2958,axiom,
c_Int_OBit1(c_Int_OPls) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Min) ).
fof(f30957,plain,
spl574_200,
inference(avatar_split_clause,[],[f23964,f30954]) ).
fof(f30954,plain,
( spl574_200
<=> class_Divides_Osemiring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_200])]) ).
fof(f23964,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(cnf_transformation,[],[f5043]) ).
fof(f5043,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).
fof(f30936,plain,
spl574_199,
inference(avatar_split_clause,[],[f23076,f30933]) ).
fof(f30933,plain,
( spl574_199
<=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_OMin ),
introduced(avatar_definition,[new_symbols(naming,[spl574_199])]) ).
fof(f23076,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_OMin,
inference(cnf_transformation,[],[f2938]) ).
fof(f2938,axiom,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_OMin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int_OMin__def) ).
fof(f30913,plain,
spl574_198,
inference(avatar_split_clause,[],[f26061,f30910]) ).
fof(f30910,plain,
( spl574_198
<=> class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_198])]) ).
fof(f26061,plain,
class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5166]) ).
fof(f5166,axiom,
class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict) ).
fof(f30908,plain,
( spl574_102
| spl574_197 ),
inference(avatar_split_clause,[],[f30904,f30906,f29299]) ).
fof(f30906,plain,
( spl574_197
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_197])]) ).
fof(f30904,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1))) ),
inference(forward_subsumption_demodulation,[],[f30903,f29285]) ).
fof(f30903,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(forward_demodulation,[],[f30902,f23272]) ).
fof(f30902,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(forward_demodulation,[],[f20790,f23272]) ).
fof(f20790,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f15069]) ).
fof(f30901,plain,
~ spl574_196,
inference(avatar_split_clause,[],[f26319,f30898]) ).
fof(f26319,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(cnf_transformation,[],[f1708]) ).
fof(f1708,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
fof(f30896,plain,
spl574_195,
inference(avatar_split_clause,[],[f30891,f30893]) ).
fof(f30891,plain,
hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f30890,f25771]) ).
fof(f25771,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f9260]) ).
fof(f9260,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rectify,[],[f987]) ).
fof(f987,axiom,
! [X75] : hAPP(c_Nat_OSuc,X75) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X75),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(f30890,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f30889,f23560]) ).
fof(f30889,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f30888,f23560]) ).
fof(f30888,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f30887,f25075]) ).
fof(f30887,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f30886,f23560]) ).
fof(f30886,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f30885,f23560]) ).
fof(f30885,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f30884,f25075]) ).
fof(f30884,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f30883,f23560]) ).
fof(f30883,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f30882,f23560]) ).
fof(f30882,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f30881,f23560]) ).
fof(f30881,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f30880,f25075]) ).
fof(f30880,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f30879,f23560]) ).
fof(f30879,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f30878,f23560]) ).
fof(f30878,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f30877,f25075]) ).
fof(f30877,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f27966,f23560]) ).
fof(f27966,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(definition_unfolding,[],[f26739,f27035,f24559]) ).
fof(f26739,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f2873]) ).
fof(f2873,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__add__1) ).
fof(f30871,plain,
spl574_194,
inference(avatar_split_clause,[],[f22205,f30868]) ).
fof(f30868,plain,
( spl574_194
<=> class_Rings_Ono__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_194])]) ).
fof(f22205,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f5037]) ).
fof(f5037,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(f30818,plain,
~ spl574_193,
inference(avatar_split_clause,[],[f21945,f30815]) ).
fof(f30815,plain,
( spl574_193
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_193])]) ).
fof(f21945,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(cnf_transformation,[],[f2675]) ).
fof(f2675,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I2_J) ).
fof(f30785,plain,
spl574_192,
inference(avatar_split_clause,[],[f26810,f30782]) ).
fof(f30782,plain,
( spl574_192
<=> class_Orderings_Oorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_192])]) ).
fof(f26810,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(cnf_transformation,[],[f5060]) ).
fof(f5060,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
fof(f30775,plain,
spl574_191,
inference(avatar_split_clause,[],[f23989,f30772]) ).
fof(f30772,plain,
( spl574_191
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_191])]) ).
fof(f23989,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5080]) ).
fof(f5080,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add) ).
fof(f30770,plain,
spl574_190,
inference(avatar_split_clause,[],[f22635,f30767]) ).
fof(f30767,plain,
( spl574_190
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_190])]) ).
fof(f22635,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5162]) ).
fof(f5162,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f30738,plain,
spl574_189,
inference(avatar_split_clause,[],[f25285,f30735]) ).
fof(f30735,plain,
( spl574_189
<=> class_Nat_Osemiring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_189])]) ).
fof(f25285,plain,
class_Nat_Osemiring__char__0(tc_Int_Oint),
inference(cnf_transformation,[],[f5045]) ).
fof(f5045,axiom,
class_Nat_Osemiring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Nat_Osemiring__char__0) ).
fof(f30718,plain,
spl574_188,
inference(avatar_split_clause,[],[f23763,f30715]) ).
fof(f30715,plain,
( spl574_188
<=> class_Lattices_Olattice(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_188])]) ).
fof(f23763,plain,
class_Lattices_Olattice(tc_Int_Oint),
inference(cnf_transformation,[],[f5056]) ).
fof(f5056,axiom,
class_Lattices_Olattice(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Olattice) ).
fof(f30686,plain,
spl574_187,
inference(avatar_split_clause,[],[f23604,f30683]) ).
fof(f30683,plain,
( spl574_187
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_187])]) ).
fof(f23604,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5011]) ).
fof(f5011,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__semigroup__add) ).
fof(f30680,plain,
spl574_186,
inference(avatar_split_clause,[],[f24562,f30677]) ).
fof(f30677,plain,
( spl574_186
<=> class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_186])]) ).
fof(f24562,plain,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
inference(cnf_transformation,[],[f5126]) ).
fof(f5126,axiom,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).
fof(f30672,plain,
spl574_185,
inference(avatar_split_clause,[],[f21595,f30669]) ).
fof(f30669,plain,
( spl574_185
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_185])]) ).
fof(f21595,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(cnf_transformation,[],[f5050]) ).
fof(f5050,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
fof(f30640,plain,
spl574_184,
inference(avatar_split_clause,[],[f24956,f30637]) ).
fof(f24956,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
inference(cnf_transformation,[],[f2689]) ).
fof(f2689,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__is__num__zero) ).
fof(f30633,plain,
spl574_183,
inference(avatar_split_clause,[],[f20151,f30630]) ).
fof(f20151,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse),
inference(cnf_transformation,[],[f3880]) ).
fof(f3880,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bool_Osize_I2_J) ).
fof(f30615,plain,
~ spl574_182,
inference(avatar_split_clause,[],[f25383,f30612]) ).
fof(f25383,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY)),v_Q)),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pn),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_HOL_Obool))))),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),v_Q)),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pn),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_HOL_Obool))))),
inference(cnf_transformation,[],[f6408]) ).
fof(f6408,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY)),v_Q)),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pn),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_HOL_Obool))))),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),v_Q)),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pn),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_HOL_Obool))))),
inference(flattening,[],[f5226]) ).
fof(f5226,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY)),v_Q)),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pn),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_HOL_Obool))))),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),v_Q)),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pn),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_HOL_Obool))))),
inference(negated_conjecture,[],[f5225]) ).
fof(f5225,conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),c_Com_Ocom_OBODY)),v_Q)),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pn),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_HOL_Obool))))),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a),hAPP(hAPP(c_COMBC(tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_COMBB(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Option_Othe(tc_Com_Ocom)),c_Com_Obody))),v_Q)),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),v_pn),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_HOL_Obool))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f30609,plain,
spl574_181,
inference(avatar_split_clause,[],[f26779,f30606]) ).
fof(f30606,plain,
( spl574_181
<=> class_Lattices_Oboolean__algebra(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_181])]) ).
fof(f26779,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(cnf_transformation,[],[f5130]) ).
fof(f5130,axiom,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
fof(f30604,plain,
spl574_180,
inference(avatar_split_clause,[],[f25300,f30601]) ).
fof(f30601,plain,
( spl574_180
<=> c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_180])]) ).
fof(f25300,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls),
inference(cnf_transformation,[],[f2965]) ).
fof(f2965,axiom,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__code__numeral__code) ).
fof(f30579,plain,
spl574_179,
inference(avatar_split_clause,[],[f21436,f30576]) ).
fof(f30576,plain,
( spl574_179
<=> class_Rings_Oidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_179])]) ).
fof(f21436,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(cnf_transformation,[],[f5073]) ).
fof(f5073,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
fof(f30570,plain,
spl574_178,
inference(avatar_split_clause,[],[f22501,f30567]) ).
fof(f30567,plain,
( spl574_178
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_178])]) ).
fof(f22501,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5017]) ).
fof(f5017,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
fof(f30565,plain,
spl574_177,
inference(avatar_split_clause,[],[f26285,f30562]) ).
fof(f30562,plain,
( spl574_177
<=> class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_177])]) ).
fof(f26285,plain,
class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5191]) ).
fof(f5191,axiom,
class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1) ).
fof(f30558,plain,
( spl574_176
| spl574_57 ),
inference(avatar_split_clause,[],[f28428,f28984,f30556]) ).
fof(f30556,plain,
( spl574_176
<=> ! [X0] : hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_176])]) ).
fof(f28984,plain,
( spl574_57
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_57])]) ).
fof(f28428,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(equality_resolution,[],[f24805]) ).
fof(f24805,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 ),
inference(cnf_transformation,[],[f18149]) ).
fof(f18149,plain,
! [X0,X1] :
( ( c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)) = c_Nitpick_Onorm__frac(X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ( ( hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X0,X1)
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X0),X1)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1))) = c_Nitpick_Onorm__frac(X0,X1) ) ) ) ),
inference(rectify,[],[f11308]) ).
fof(f11308,plain,
! [X1,X0] :
( ( c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)) = c_Nitpick_Onorm__frac(X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ( ( hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X1,X0)
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| c_Nitpick_Onorm__frac(X1,X0) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X1),X0)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0))) ) ) ) ),
inference(flattening,[],[f11307]) ).
fof(f11307,plain,
! [X1,X0] :
( ( c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)) = c_Nitpick_Onorm__frac(X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ( ( c_Nitpick_Onorm__frac(X1,X0) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X1),X0)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1 )
& ( hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X1,X0)
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 ) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(ennf_transformation,[],[f6253]) ).
fof(f6253,plain,
! [X1,X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)) = c_Nitpick_Onorm__frac(X1,X0) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( ( ~ ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1 )
=> c_Nitpick_Onorm__frac(X1,X0) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X1),X0)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0))) )
& ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 )
=> hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X1,X0) ) ) ) ),
inference(rectify,[],[f3025]) ).
fof(f3025,axiom,
! [X26,X5] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( ( ~ ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X26
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X5 )
=> c_Nitpick_Onorm__frac(X5,X26) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X5),X26)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X5))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26))) )
& ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X26
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X5 )
=> c_Nitpick_Onorm__frac(X5,X26) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Nitpick_Onorm__frac(X5,X26) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X5),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__frac_Osimps) ).
fof(f30531,plain,
spl574_175,
inference(avatar_split_clause,[],[f21189,f30528]) ).
fof(f30528,plain,
( spl574_175
<=> class_Groups_Ocomm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_175])]) ).
fof(f21189,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5038]) ).
fof(f5038,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(f30520,plain,
spl574_174,
inference(avatar_split_clause,[],[f24425,f30517]) ).
fof(f24425,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f3127]) ).
fof(f3127,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I1_J) ).
fof(f30515,plain,
spl574_118,
inference(avatar_split_clause,[],[f20035,f29438]) ).
fof(f29438,plain,
( spl574_118
<=> ! [X0] : hAPP(c_Nat_OSuc,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_118])]) ).
fof(f20035,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
inference(cnf_transformation,[],[f9983]) ).
fof(f9983,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
inference(rectify,[],[f988]) ).
fof(f988,axiom,
! [X75] : hAPP(c_Nat_OSuc,X75) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X75),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(f30497,plain,
spl574_173,
inference(avatar_split_clause,[],[f30492,f30494]) ).
fof(f30492,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f30491,f23560]) ).
fof(f30491,plain,
hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f30490,f23560]) ).
fof(f30490,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f30489,f25075]) ).
fof(f30489,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f30488,f23560]) ).
fof(f30488,plain,
hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f30487,f23560]) ).
fof(f30487,plain,
hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f30486,f25075]) ).
fof(f30486,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f30485,f23560]) ).
fof(f30485,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f30484,f23560]) ).
fof(f30484,plain,
hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f30483,f23560]) ).
fof(f30483,plain,
hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f30482,f25075]) ).
fof(f30482,plain,
hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f30481,f23560]) ).
fof(f30481,plain,
hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f30480,f23560]) ).
fof(f30480,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f30479,f23272]) ).
fof(f30479,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f30478,f25075]) ).
fof(f30478,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f27356,f23560]) ).
fof(f27356,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(definition_unfolding,[],[f21959,f27035,f24559,f27035,f24559]) ).
fof(f21959,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(cnf_transformation,[],[f2869]) ).
fof(f2869,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I3_J) ).
fof(f30475,plain,
spl574_172,
inference(avatar_split_clause,[],[f22004,f30472]) ).
fof(f30472,plain,
( spl574_172
<=> class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_172])]) ).
fof(f22004,plain,
class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5175]) ).
fof(f5175,axiom,
class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult) ).
fof(f30455,plain,
spl574_171,
inference(avatar_split_clause,[],[f20385,f30452]) ).
fof(f30452,plain,
( spl574_171
<=> class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_171])]) ).
fof(f20385,plain,
class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5171]) ).
fof(f5171,axiom,
class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring) ).
fof(f30450,plain,
spl574_170,
inference(avatar_split_clause,[],[f30445,f30447]) ).
fof(f30445,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),
inference(forward_demodulation,[],[f30444,f23560]) ).
fof(f30444,plain,
hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))),
inference(forward_demodulation,[],[f30443,f23560]) ).
fof(f30443,plain,
hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))),
inference(forward_demodulation,[],[f30442,f25075]) ).
fof(f30442,plain,
hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))))),
inference(forward_demodulation,[],[f30441,f23560]) ).
fof(f30441,plain,
hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))))),
inference(forward_demodulation,[],[f30440,f23560]) ).
fof(f30440,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))))) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))))),
inference(forward_demodulation,[],[f30439,f25075]) ).
fof(f30439,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))))) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f30438,f23560]) ).
fof(f30438,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))))) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f30437,f23560]) ).
fof(f30437,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))))) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f30436,f23560]) ).
fof(f30436,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))))) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f30435,f25075]) ).
fof(f30435,plain,
hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f30434,f23560]) ).
fof(f30434,plain,
hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f30433,f23272]) ).
fof(f30433,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f30432,f23560]) ).
fof(f30432,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f30431,f25075]) ).
fof(f30431,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OPls)))),
inference(forward_demodulation,[],[f27773,f23560]) ).
fof(f27773,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(definition_unfolding,[],[f25403,f24559,f24559,f24559,f24559]) ).
fof(f25403,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
inference(cnf_transformation,[],[f2776]) ).
fof(f2776,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I4_J) ).
fof(f30430,plain,
spl574_169,
inference(avatar_split_clause,[],[f25857,f30427]) ).
fof(f30427,plain,
( spl574_169
<=> c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_169])]) ).
fof(f25857,plain,
c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f3279]) ).
fof(f3279,axiom,
c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__less__def) ).
fof(f30423,plain,
spl574_168,
inference(avatar_split_clause,[],[f22858,f30420]) ).
fof(f30420,plain,
( spl574_168
<=> class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_168])]) ).
fof(f22858,plain,
class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5187]) ).
fof(f5187,axiom,
class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder) ).
fof(f30392,plain,
spl574_167,
inference(avatar_split_clause,[],[f25996,f30389]) ).
fof(f30389,plain,
( spl574_167
<=> class_Enum_Oenum(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_167])]) ).
fof(f25996,plain,
class_Enum_Oenum(tc_HOL_Obool),
inference(cnf_transformation,[],[f5140]) ).
fof(f5140,axiom,
class_Enum_Oenum(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Enum_Oenum) ).
fof(f30386,plain,
spl574_166,
inference(avatar_split_clause,[],[f23697,f30383]) ).
fof(f30383,plain,
( spl574_166
<=> class_Lattices_Osemilattice__sup(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_166])]) ).
fof(f23697,plain,
class_Lattices_Osemilattice__sup(tc_Int_Oint),
inference(cnf_transformation,[],[f5029]) ).
fof(f5029,axiom,
class_Lattices_Osemilattice__sup(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Osemilattice__sup) ).
fof(f30379,plain,
spl574_165,
inference(avatar_split_clause,[],[f21793,f30376]) ).
fof(f30376,plain,
( spl574_165
<=> c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_165])]) ).
fof(f21793,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(cnf_transformation,[],[f1606]) ).
fof(f1606,axiom,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__int) ).
fof(f30338,plain,
spl574_164,
inference(avatar_split_clause,[],[f25524,f30335]) ).
fof(f30335,plain,
( spl574_164
<=> class_Orderings_Oord(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_164])]) ).
fof(f25524,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(cnf_transformation,[],[f5064]) ).
fof(f5064,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
fof(f30328,plain,
spl574_163,
inference(avatar_split_clause,[],[f23683,f30325]) ).
fof(f30325,plain,
( spl574_163
<=> hBOOL(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_163])]) ).
fof(f23683,plain,
hBOOL(c_fTrue),
inference(cnf_transformation,[],[f5212]) ).
fof(f5212,axiom,
hBOOL(c_fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fTrue__1) ).
fof(f30322,plain,
spl574_162,
inference(avatar_split_clause,[],[f22522,f30319]) ).
fof(f30319,plain,
( spl574_162
<=> class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_162])]) ).
fof(f22522,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5013]) ).
fof(f5013,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
fof(f30317,plain,
spl574_161,
inference(avatar_split_clause,[],[f30312,f30314]) ).
fof(f30312,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f30311,f25075]) ).
fof(f30311,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))),
inference(forward_demodulation,[],[f27488,f25075]) ).
fof(f27488,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),
inference(definition_unfolding,[],[f22986,f24559]) ).
fof(f22986,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
inference(cnf_transformation,[],[f2768]) ).
fof(f2768,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Numeral1__eq1__nat) ).
fof(f30304,plain,
spl574_160,
inference(avatar_split_clause,[],[f23246,f30301]) ).
fof(f23246,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(cnf_transformation,[],[f3284]) ).
fof(f3284,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__int__def) ).
fof(f30294,plain,
spl574_159,
inference(avatar_split_clause,[],[f25630,f30291]) ).
fof(f30291,plain,
( spl574_159
<=> class_Lattices_Osemilattice__sup(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_159])]) ).
fof(f25630,plain,
class_Lattices_Osemilattice__sup(tc_Nat_Onat),
inference(cnf_transformation,[],[f5090]) ).
fof(f5090,axiom,
class_Lattices_Osemilattice__sup(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__sup) ).
fof(f30282,plain,
spl574_158,
inference(avatar_split_clause,[],[f28278,f30279]) ).
fof(f28278,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f28277]) ).
fof(f28277,plain,
! [X0] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(equality_resolution,[],[f22739]) ).
fof(f22739,plain,
! [X0,X1] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f16580]) ).
fof(f16580,plain,
! [X0,X1] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) ) ),
inference(flattening,[],[f16579]) ).
fof(f16579,plain,
! [X0,X1] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) ) ),
inference(nnf_transformation,[],[f7447]) ).
fof(f7447,plain,
! [X0,X1] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(rectify,[],[f1590]) ).
fof(f1590,axiom,
! [X77,X74] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X77) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X74))
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X77
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X74 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__eq__positive) ).
fof(f30277,plain,
( spl574_102
| spl574_157 ),
inference(avatar_split_clause,[],[f30273,f30275,f29299]) ).
fof(f30273,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(forward_subsumption_demodulation,[],[f30272,f29285]) ).
fof(f30272,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)))
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f20074,f23272]) ).
fof(f20074,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ class_Int_Onumber__ring(X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(cnf_transformation,[],[f13701]) ).
fof(f13701,plain,
! [X0,X1] :
( ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(X1),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) )
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f8077]) ).
fof(f8077,plain,
! [X1,X0] :
( class_Int_Onumber__ring(X1)
=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> hAPP(c_Int_Onumber__class_Onumber__of(X1),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ) ) ),
inference(rectify,[],[f2593]) ).
fof(f2593,axiom,
! [X148,X34] :
( class_Int_Onumber__ring(X34)
=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X148)))
=> c_Groups_Ozero__class_Ozero(X34) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X34),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X148)) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X148)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X34),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X148)) = hAPP(c_Int_Onumber__class_Onumber__of(X34),X148) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__number__of__eq) ).
fof(f30271,plain,
spl574_156,
inference(avatar_split_clause,[],[f21430,f30268]) ).
fof(f30268,plain,
( spl574_156
<=> class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_156])]) ).
fof(f21430,plain,
class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5199]) ).
fof(f5199,axiom,
class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ozero) ).
fof(f30243,plain,
spl574_155,
inference(avatar_split_clause,[],[f24391,f30240]) ).
fof(f30240,plain,
( spl574_155
<=> class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_155])]) ).
fof(f24391,plain,
class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5174]) ).
fof(f5174,axiom,
class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom) ).
fof(f30224,plain,
spl574_154,
inference(avatar_split_clause,[],[f21151,f30221]) ).
fof(f30221,plain,
( spl574_154
<=> class_Lattices_Osemilattice__inf(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_154])]) ).
fof(f21151,plain,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
inference(cnf_transformation,[],[f5091]) ).
fof(f5091,axiom,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__inf) ).
fof(f30219,plain,
spl574_153,
inference(avatar_split_clause,[],[f23065,f30216]) ).
fof(f30216,plain,
( spl574_153
<=> c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_153])]) ).
fof(f23065,plain,
c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),
inference(cnf_transformation,[],[f1317]) ).
fof(f1317,axiom,
c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__nat__def) ).
fof(f30214,plain,
( spl574_102
| spl574_152 ),
inference(avatar_split_clause,[],[f30209,f30211,f29299]) ).
fof(f30209,plain,
! [X0] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0))) ),
inference(forward_subsumption_demodulation,[],[f30208,f29285]) ).
fof(f30208,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)))
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ),
inference(forward_demodulation,[],[f22042,f23272]) ).
fof(f22042,plain,
! [X0] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(cnf_transformation,[],[f11464]) ).
fof(f11464,plain,
! [X0] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) ),
inference(ennf_transformation,[],[f5516]) ).
fof(f5516,plain,
! [X0] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ) ),
inference(rectify,[],[f2646]) ).
fof(f2646,axiom,
! [X195] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X195)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X195)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X195))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X195)))
=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X195)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__mod__nat__number__of) ).
fof(f30207,plain,
spl574_151,
inference(avatar_split_clause,[],[f26492,f30204]) ).
fof(f30204,plain,
( spl574_151
<=> class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_151])]) ).
fof(f26492,plain,
class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5182]) ).
fof(f5182,axiom,
class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add) ).
fof(f30202,plain,
( spl574_102
| spl574_150 ),
inference(avatar_split_clause,[],[f30198,f30200,f29299]) ).
fof(f30200,plain,
( spl574_150
<=> ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_150])]) ).
fof(f30198,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1))) ),
inference(forward_subsumption_demodulation,[],[f30197,f29285]) ).
fof(f30197,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) ),
inference(forward_demodulation,[],[f30196,f23272]) ).
fof(f30196,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) ),
inference(forward_demodulation,[],[f30195,f23272]) ).
fof(f30195,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1))) ),
inference(forward_demodulation,[],[f20791,f23272]) ).
fof(f20791,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) ),
inference(cnf_transformation,[],[f15069]) ).
fof(f30173,plain,
spl574_149,
inference(avatar_split_clause,[],[f21341,f30170]) ).
fof(f30170,plain,
( spl574_149
<=> class_Groups_Oabs__if(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_149])]) ).
fof(f21341,plain,
class_Groups_Oabs__if(tc_Int_Oint),
inference(cnf_transformation,[],[f5067]) ).
fof(f5067,axiom,
class_Groups_Oabs__if(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oabs__if) ).
fof(f30141,plain,
spl574_148,
inference(avatar_split_clause,[],[f26469,f30138]) ).
fof(f30138,plain,
( spl574_148
<=> class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_148])]) ).
fof(f26469,plain,
class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5195]) ).
fof(f5195,axiom,
class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring) ).
fof(f30135,plain,
spl574_147,
inference(avatar_split_clause,[],[f27010,f30132]) ).
fof(f27010,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue),
inference(cnf_transformation,[],[f4751]) ).
fof(f4751,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bool_Osize_I3_J) ).
fof(f29739,plain,
spl574_146,
inference(avatar_split_clause,[],[f20672,f29736]) ).
fof(f29736,plain,
( spl574_146
<=> class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_146])]) ).
fof(f20672,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5083]) ).
fof(f5083,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(f29734,plain,
spl574_145,
inference(avatar_split_clause,[],[f24311,f29731]) ).
fof(f29731,plain,
( spl574_145
<=> class_Rings_Oring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_145])]) ).
fof(f24311,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5068]) ).
fof(f5068,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
fof(f29729,plain,
spl574_144,
inference(avatar_split_clause,[],[f20731,f29726]) ).
fof(f20731,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f1863]) ).
fof(f1863,axiom,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1) ).
fof(f29720,plain,
spl574_143,
inference(avatar_split_clause,[],[f20421,f29717]) ).
fof(f29717,plain,
( spl574_143
<=> class_Nat_Osemiring__char__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_143])]) ).
fof(f20421,plain,
class_Nat_Osemiring__char__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f5104]) ).
fof(f5104,axiom,
class_Nat_Osemiring__char__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Nat_Osemiring__char__0) ).
fof(f29714,plain,
spl574_142,
inference(avatar_split_clause,[],[f28039,f29711]) ).
fof(f29711,plain,
( spl574_142
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_142])]) ).
fof(f28039,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f28038]) ).
fof(f28038,plain,
! [X1] :
( hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(equality_resolution,[],[f20166]) ).
fof(f20166,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f14633]) ).
fof(f29707,plain,
spl574_141,
inference(avatar_split_clause,[],[f24326,f29704]) ).
fof(f29704,plain,
( spl574_141
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_141])]) ).
fof(f24326,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5009]) ).
fof(f5009,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
fof(f29694,plain,
spl574_140,
inference(avatar_split_clause,[],[f23707,f29691]) ).
fof(f29691,plain,
( spl574_140
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_140])]) ).
fof(f23707,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5164]) ).
fof(f5164,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict) ).
fof(f29689,plain,
( spl574_102
| spl574_139 ),
inference(avatar_split_clause,[],[f29685,f29687,f29299]) ).
fof(f29687,plain,
( spl574_139
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_139])]) ).
fof(f29685,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1))) ),
inference(forward_subsumption_demodulation,[],[f29684,f29285]) ).
fof(f29684,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1))) ),
inference(forward_demodulation,[],[f22643,f23272]) ).
fof(f22643,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(cnf_transformation,[],[f16512]) ).
fof(f29683,plain,
spl574_138,
inference(avatar_split_clause,[],[f23050,f29680]) ).
fof(f29680,plain,
( spl574_138
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_138])]) ).
fof(f23050,plain,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5157]) ).
fof(f5157,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).
fof(f29678,plain,
~ spl574_137,
inference(avatar_split_clause,[],[f26179,f29675]) ).
fof(f29675,plain,
( spl574_137
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_137])]) ).
fof(f26179,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f1779]) ).
fof(f1779,axiom,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_infinite__UNIV__int) ).
fof(f29672,plain,
spl574_136,
inference(avatar_split_clause,[],[f25050,f29669]) ).
fof(f29669,plain,
( spl574_136
<=> class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_136])]) ).
fof(f25050,plain,
class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5156]) ).
fof(f5156,axiom,
class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy) ).
fof(f29662,plain,
spl574_135,
inference(avatar_split_clause,[],[f29657,f29659]) ).
fof(f29657,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
inference(forward_demodulation,[],[f29656,f23560]) ).
fof(f29656,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
inference(forward_demodulation,[],[f27911,f23272]) ).
fof(f27911,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
inference(definition_unfolding,[],[f26378,f27035,f24559]) ).
fof(f26378,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(cnf_transformation,[],[f2861]) ).
fof(f2861,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
fof(f29648,plain,
spl574_134,
inference(avatar_split_clause,[],[f24643,f29645]) ).
fof(f29645,plain,
( spl574_134
<=> class_Lattices_Osemilattice__sup(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_134])]) ).
fof(f24643,plain,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
inference(cnf_transformation,[],[f5127]) ).
fof(f5127,axiom,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__sup) ).
fof(f29638,plain,
spl574_133,
inference(avatar_split_clause,[],[f29632,f29635]) ).
fof(f29632,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),c_List_Olist_ONil(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(backward_demodulation,[],[f29284,f28018]) ).
fof(f28018,plain,
! [X2,X0,X1] : c_List_Olist_ONil(X0) = hAPP(hAPP(c_List_Omap(X2,X0),X1),c_List_Olist_ONil(X2)),
inference(equality_resolution,[],[f19974]) ).
fof(f19974,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_List_Omap(X2,X0),X1),X3) = c_List_Olist_ONil(X0)
| c_List_Olist_ONil(X2) != X3 ),
inference(cnf_transformation,[],[f14486]) ).
fof(f14486,plain,
! [X0,X1,X2,X3] :
( ( hAPP(hAPP(c_List_Omap(X2,X0),X1),X3) = c_List_Olist_ONil(X0)
| c_List_Olist_ONil(X2) != X3 )
& ( c_List_Olist_ONil(X2) = X3
| hAPP(hAPP(c_List_Omap(X2,X0),X1),X3) != c_List_Olist_ONil(X0) ) ),
inference(rectify,[],[f14485]) ).
fof(f14485,plain,
! [X3,X0,X1,X2] :
( ( c_List_Olist_ONil(X3) = hAPP(hAPP(c_List_Omap(X1,X3),X0),X2)
| c_List_Olist_ONil(X1) != X2 )
& ( c_List_Olist_ONil(X1) = X2
| c_List_Olist_ONil(X3) != hAPP(hAPP(c_List_Omap(X1,X3),X0),X2) ) ),
inference(nnf_transformation,[],[f7314]) ).
fof(f7314,plain,
! [X3,X0,X1,X2] :
( c_List_Olist_ONil(X3) = hAPP(hAPP(c_List_Omap(X1,X3),X0),X2)
<=> c_List_Olist_ONil(X1) = X2 ),
inference(rectify,[],[f4311]) ).
fof(f4311,axiom,
! [X1,X20,X250,X4] :
( c_List_Olist_ONil(X20) = X250
<=> c_List_Olist_ONil(X4) = hAPP(hAPP(c_List_Omap(X20,X4),X1),X250) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__is__Nil__conv) ).
fof(f29284,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X0,tc_Nat_Onat),X1),c_List_Olist_ONil(X0)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_demodulation,[],[f27095,f26092]) ).
fof(f26092,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X0)),c_List_Olist_ONil(X0)),
inference(cnf_transformation,[],[f9874]) ).
fof(f9874,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X0)),c_List_Olist_ONil(X0)),
inference(rectify,[],[f4066]) ).
fof(f4066,axiom,
! [X34] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X34)),c_List_Olist_ONil(X34)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osize_I3_J) ).
fof(f27095,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X0,tc_Nat_Onat),X1),c_List_Olist_ONil(X0)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X0)),c_List_Olist_ONil(X0))),
inference(definition_unfolding,[],[f20099,f24663]) ).
fof(f24663,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X0,tc_Nat_Onat),X1),X2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X0)),X2)) = c_List_Olist_Olist__size(X0,X1,X2),
inference(cnf_transformation,[],[f18075]) ).
fof(f18075,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X0,tc_Nat_Onat),X1),X2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X0)),X2)) = c_List_Olist_Olist__size(X0,X1,X2),
inference(rectify,[],[f9873]) ).
fof(f9873,plain,
! [X0,X2,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X0,tc_Nat_Onat),X2),X1))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X0)),X1)) = c_List_Olist_Olist__size(X0,X2,X1),
inference(rectify,[],[f4351]) ).
fof(f4351,axiom,
! [X4,X250,X1] : c_List_Olist_Olist__size(X4,X1,X250) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X4,tc_Nat_Onat),X1),X250))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X250)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__size__conv__listsum) ).
fof(f20099,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_List_Olist_Olist__size(X0,X1,c_List_Olist_ONil(X0)),
inference(cnf_transformation,[],[f14582]) ).
fof(f14582,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_List_Olist_Olist__size(X0,X1,c_List_Olist_ONil(X0)),
inference(rectify,[],[f5277]) ).
fof(f5277,plain,
! [X1,X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_List_Olist_Olist__size(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f4059]) ).
fof(f4059,axiom,
! [X100,X4] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_List_Olist_Olist__size(X4,X100,c_List_Olist_ONil(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osize_I1_J) ).
fof(f29538,plain,
spl574_132,
inference(avatar_split_clause,[],[f20283,f29535]) ).
fof(f29535,plain,
( spl574_132
<=> class_Rings_Olinordered__idom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_132])]) ).
fof(f20283,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(cnf_transformation,[],[f5040]) ).
fof(f5040,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
fof(f29528,plain,
spl574_131,
inference(avatar_split_clause,[],[f26117,f29525]) ).
fof(f29525,plain,
( spl574_131
<=> c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_131])]) ).
fof(f26117,plain,
c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(cnf_transformation,[],[f4365]) ).
fof(f4365,axiom,
c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition__code__numeral) ).
fof(f29520,plain,
spl574_130,
inference(avatar_split_clause,[],[f22338,f29517]) ).
fof(f29517,plain,
( spl574_130
<=> class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_130])]) ).
fof(f22338,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5016]) ).
fof(f5016,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
fof(f29515,plain,
spl574_129,
inference(avatar_split_clause,[],[f25341,f29512]) ).
fof(f29512,plain,
( spl574_129
<=> class_Orderings_Oorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_129])]) ).
fof(f25341,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f5134]) ).
fof(f5134,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(f29510,plain,
spl574_128,
inference(avatar_split_clause,[],[f24586,f29507]) ).
fof(f29507,plain,
( spl574_128
<=> c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_128])]) ).
fof(f24586,plain,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f3273]) ).
fof(f3273,axiom,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__strict__def) ).
fof(f29501,plain,
spl574_127,
inference(avatar_split_clause,[],[f22741,f29498]) ).
fof(f29498,plain,
( spl574_127
<=> class_Rings_Olinordered__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_127])]) ).
fof(f22741,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5023]) ).
fof(f5023,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
fof(f29494,plain,
spl574_126,
inference(avatar_split_clause,[],[f23503,f29491]) ).
fof(f29491,plain,
( spl574_126
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_126])]) ).
fof(f23503,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(cnf_transformation,[],[f2932]) ).
fof(f2932,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I6_J) ).
fof(f29488,plain,
spl574_125,
inference(avatar_split_clause,[],[f21204,f29485]) ).
fof(f29485,plain,
( spl574_125
<=> class_Rings_Ozero__neq__one(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_125])]) ).
fof(f21204,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(cnf_transformation,[],[f5105]) ).
fof(f5105,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(f29482,plain,
spl574_124,
inference(avatar_split_clause,[],[f22166,f29479]) ).
fof(f22166,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),
inference(cnf_transformation,[],[f2919]) ).
fof(f2919,axiom,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral__zero__minus__one) ).
fof(f29477,plain,
spl574_123,
inference(avatar_split_clause,[],[f20277,f29474]) ).
fof(f29474,plain,
( spl574_123
<=> class_Rings_Osemiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_123])]) ).
fof(f20277,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5115]) ).
fof(f5115,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
fof(f29472,plain,
( ~ spl574_51
| spl574_122 ),
inference(avatar_split_clause,[],[f19963,f29470,f28943]) ).
fof(f29470,plain,
( spl574_122
<=> ! [X2,X0,X1] :
( hAPP(c_Finite__Set_Ocard(X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X0),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2),X0)),hAPP(c_Finite__Set_Ocard(X2),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_122])]) ).
fof(f19963,plain,
! [X2,X0,X1] :
( hAPP(c_Finite__Set_Ocard(X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X0),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2),X0)),hAPP(c_Finite__Set_Ocard(X2),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X0)) ),
inference(cnf_transformation,[],[f14479]) ).
fof(f14479,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X0))
| hAPP(c_Finite__Set_Ocard(X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X0),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2),X0)),hAPP(c_Finite__Set_Ocard(X2),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
| ( hBOOL(hAPP(hAPP(c_member(X2),sK8(X0,X1,X2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X0),X1)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f14477,f14478]) ).
fof(f14478,plain,
! [X0,X1,X2] :
( ? [X3] : hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X0),X1)))
=> hBOOL(hAPP(hAPP(c_member(X2),sK8(X0,X1,X2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X0),X1))) ),
introduced(choice_axiom,[]) ).
fof(f14477,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X0))
| hAPP(c_Finite__Set_Ocard(X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X0),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2),X0)),hAPP(c_Finite__Set_Ocard(X2),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
| ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X0),X1)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(rectify,[],[f13100]) ).
fof(f13100,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X0)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(flattening,[],[f13099]) ).
fof(f13099,plain,
! [X2,X1,X0] :
( hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X0))
| ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X0)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(ennf_transformation,[],[f9953]) ).
fof(f9953,plain,
! [X2,X1,X0] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
=> ( ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X1),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X0)))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
=> hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X0)) ) ) ),
inference(rectify,[],[f1138]) ).
fof(f1138,axiom,
! [X23,X4,X21] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X21))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X23))
=> ( ( ? [X2] : hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X21),X23)))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X4),X21)),hAPP(c_Finite__Set_Ocard(X4),X23)) = hAPP(c_Finite__Set_Ocard(X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X21),X23)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Ounion__inter__neutral) ).
fof(f29466,plain,
spl574_121,
inference(avatar_split_clause,[],[f22870,f29463]) ).
fof(f22870,plain,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(cnf_transformation,[],[f1561]) ).
fof(f1561,axiom,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__0) ).
fof(f29460,plain,
spl574_120,
inference(avatar_split_clause,[],[f23695,f29457]) ).
fof(f23695,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue),
inference(cnf_transformation,[],[f3881]) ).
fof(f3881,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bool_Osize_I1_J) ).
fof(f29446,plain,
spl574_119,
inference(avatar_split_clause,[],[f21536,f29443]) ).
fof(f29443,plain,
( spl574_119
<=> class_Rings_Oordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_119])]) ).
fof(f21536,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5048]) ).
fof(f5048,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
fof(f29440,plain,
( spl574_118
| spl574_102 ),
inference(avatar_split_clause,[],[f29436,f29299,f29438]) ).
fof(f29436,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)))
| hAPP(c_Nat_OSuc,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
inference(forward_demodulation,[],[f29435,f21331]) ).
fof(f29435,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1))) ),
inference(forward_subsumption_demodulation,[],[f29434,f29285]) ).
fof(f29434,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X0)) ),
inference(forward_demodulation,[],[f20902,f23272]) ).
fof(f20902,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(cnf_transformation,[],[f15164]) ).
fof(f15164,plain,
! [X0,X1] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X1))),X0) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X0)) ) ),
inference(rectify,[],[f11361]) ).
fof(f11361,plain,
! [X1,X0] :
( ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X0))),X1)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ) ),
inference(ennf_transformation,[],[f5511]) ).
fof(f5511,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X0))),X1) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ) ),
inference(rectify,[],[f2669]) ).
fof(f2669,axiom,
! [X148,X75] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X148)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X75) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X148)),X75)) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X148)))
=> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X148)),X75)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X148))),X75) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__nat__number__of__add) ).
fof(f29430,plain,
spl574_117,
inference(avatar_split_clause,[],[f27108,f29427]) ).
fof(f29427,plain,
( spl574_117
<=> c_Int_OMin = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_117])]) ).
fof(f27108,plain,
c_Int_OMin = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(definition_unfolding,[],[f20143,f23060]) ).
fof(f20143,plain,
c_Int_OMin = c_Int_Opred(c_Int_OPls),
inference(cnf_transformation,[],[f2941]) ).
fof(f2941,axiom,
c_Int_OMin = c_Int_Opred(c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__Pls) ).
fof(f29425,plain,
spl574_116,
inference(avatar_split_clause,[],[f23200,f29422]) ).
fof(f23200,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse),
inference(cnf_transformation,[],[f4752]) ).
fof(f4752,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bool_Osize_I4_J) ).
fof(f29417,plain,
spl574_115,
inference(avatar_split_clause,[],[f23014,f29414]) ).
fof(f29414,plain,
( spl574_115
<=> class_Groups_Ouminus(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_115])]) ).
fof(f23014,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(cnf_transformation,[],[f5138]) ).
fof(f5138,axiom,
class_Groups_Ouminus(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).
fof(f29411,plain,
spl574_114,
inference(avatar_split_clause,[],[f23075,f29408]) ).
fof(f29408,plain,
( spl574_114
<=> class_Rings_Olinordered__ring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_114])]) ).
fof(f23075,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5020]) ).
fof(f5020,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
fof(f29403,plain,
( spl574_102
| spl574_113 ),
inference(avatar_split_clause,[],[f29399,f29401,f29299]) ).
fof(f29401,plain,
( spl574_113
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_113])]) ).
fof(f29399,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1))) ),
inference(forward_subsumption_demodulation,[],[f29398,f29285]) ).
fof(f29398,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ),
inference(forward_demodulation,[],[f23643,f23272]) ).
fof(f23643,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(cnf_transformation,[],[f17296]) ).
fof(f17296,plain,
! [X0,X1] :
( ( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ) ),
inference(rectify,[],[f12129]) ).
fof(f12129,plain,
! [X1,X0] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) ) ),
inference(ennf_transformation,[],[f6428]) ).
fof(f6428,plain,
! [X1,X0] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ) ),
inference(rectify,[],[f2666]) ).
fof(f2666,axiom,
! [X148,X195] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X148)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X148)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X195)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X148)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X195))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X148)))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X148)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X195)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__nat__number__of) ).
fof(f29395,plain,
spl574_112,
inference(avatar_split_clause,[],[f25877,f29392]) ).
fof(f29392,plain,
( spl574_112
<=> class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_112])]) ).
fof(f25877,plain,
class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5188]) ).
fof(f5188,axiom,
class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder) ).
fof(f29383,plain,
spl574_111,
inference(avatar_split_clause,[],[f23892,f29380]) ).
fof(f29380,plain,
( spl574_111
<=> class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_111])]) ).
fof(f23892,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5087]) ).
fof(f5087,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(f29375,plain,
spl574_110,
inference(avatar_split_clause,[],[f27430,f29372]) ).
fof(f29372,plain,
( spl574_110
<=> c_Int_OPls = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_110])]) ).
fof(f27430,plain,
c_Int_OPls = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(definition_unfolding,[],[f22531,f20650]) ).
fof(f22531,plain,
c_Int_OPls = c_Int_Osucc(c_Int_OMin),
inference(cnf_transformation,[],[f2946]) ).
fof(f2946,axiom,
c_Int_OPls = c_Int_Osucc(c_Int_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__Min) ).
fof(f29356,plain,
~ spl574_109,
inference(avatar_split_clause,[],[f28335,f29353]) ).
fof(f28335,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(equality_resolution,[],[f23564]) ).
fof(f23564,plain,
! [X0] :
( hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X0)) ),
inference(cnf_transformation,[],[f17224]) ).
fof(f17224,plain,
! [X0] :
( ( hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X0))
| hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 ) ),
inference(nnf_transformation,[],[f9740]) ).
fof(f9740,plain,
! [X0] :
( hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X0)) ),
inference(rectify,[],[f4352]) ).
fof(f4352,axiom,
! [X124] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X124))
<=> hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X124 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral__not__eq__zero) ).
fof(f29351,plain,
spl574_108,
inference(avatar_split_clause,[],[f23082,f29348]) ).
fof(f29348,plain,
( spl574_108
<=> class_Rings_Osemiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_108])]) ).
fof(f23082,plain,
class_Rings_Osemiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5054]) ).
fof(f5054,axiom,
class_Rings_Osemiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).
fof(f29341,plain,
spl574_107,
inference(avatar_split_clause,[],[f24916,f29338]) ).
fof(f29338,plain,
( spl574_107
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_107])]) ).
fof(f24916,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5163]) ).
fof(f5163,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f29333,plain,
spl574_106,
inference(avatar_split_clause,[],[f20475,f29330]) ).
fof(f29330,plain,
( spl574_106
<=> class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_106])]) ).
fof(f20475,plain,
class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5179]) ).
fof(f5179,axiom,
class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors) ).
fof(f29328,plain,
spl574_105,
inference(avatar_split_clause,[],[f19960,f29325]) ).
fof(f29325,plain,
( spl574_105
<=> class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_105])]) ).
fof(f19960,plain,
class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5173]) ).
fof(f5173,axiom,
class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring) ).
fof(f29322,plain,
spl574_104,
inference(avatar_split_clause,[],[f20369,f29319]) ).
fof(f29319,plain,
( spl574_104
<=> class_Groups_Ominus(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_104])]) ).
fof(f20369,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(cnf_transformation,[],[f5118]) ).
fof(f5118,axiom,
class_Groups_Ominus(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
fof(f29309,plain,
spl574_103,
inference(avatar_split_clause,[],[f19920,f29306]) ).
fof(f29306,plain,
( spl574_103
<=> class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_103])]) ).
fof(f19920,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5012]) ).
fof(f5012,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
fof(f29301,plain,
( spl574_101
| spl574_102 ),
inference(avatar_split_clause,[],[f29294,f29299,f29296]) ).
fof(f29296,plain,
( spl574_101
<=> ! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_101])]) ).
fof(f29294,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) ),
inference(forward_subsumption_demodulation,[],[f29293,f29285]) ).
fof(f29293,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X1)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(forward_demodulation,[],[f29292,f23272]) ).
fof(f29292,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(forward_demodulation,[],[f20793,f23272]) ).
fof(f20793,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(cnf_transformation,[],[f15069]) ).
fof(f29291,plain,
spl574_62,
inference(avatar_split_clause,[],[f28594,f29007]) ).
fof(f28594,plain,
c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),c_Int_OMin),
inference(equality_resolution,[],[f27931]) ).
fof(f27931,plain,
! [X0] :
( c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)),X0)
| c_Int_OMin != X0 ),
inference(definition_unfolding,[],[f26495,f24559]) ).
fof(f26495,plain,
! [X0] :
( c_Int_OMin = c_Int_OBit1(X0)
| c_Int_OMin != X0 ),
inference(cnf_transformation,[],[f19421]) ).
fof(f19421,plain,
! [X0] :
( ( c_Int_OMin = X0
| c_Int_OMin != c_Int_OBit1(X0) )
& ( c_Int_OMin = c_Int_OBit1(X0)
| c_Int_OMin != X0 ) ),
inference(nnf_transformation,[],[f5722]) ).
fof(f5722,plain,
! [X0] :
( c_Int_OMin = X0
<=> c_Int_OMin = c_Int_OBit1(X0) ),
inference(rectify,[],[f2924]) ).
fof(f2924,axiom,
! [X130] :
( c_Int_OBit1(X130) = c_Int_OMin
<=> c_Int_OMin = X130 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I43_J) ).
fof(f29290,plain,
spl574_100,
inference(avatar_split_clause,[],[f22992,f29287]) ).
fof(f29287,plain,
( spl574_100
<=> class_Groups_Ouminus(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_100])]) ).
fof(f22992,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(cnf_transformation,[],[f5065]) ).
fof(f5065,axiom,
class_Groups_Ouminus(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).
fof(f29273,plain,
spl574_99,
inference(avatar_split_clause,[],[f20877,f29270]) ).
fof(f20877,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f1848]) ).
fof(f1848,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I2_J) ).
fof(f29267,plain,
spl574_98,
inference(avatar_split_clause,[],[f23408,f29264]) ).
fof(f23408,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f4338]) ).
fof(f4338,axiom,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__code__numeral__def) ).
fof(f29262,plain,
spl574_97,
inference(avatar_split_clause,[],[f26988,f29259]) ).
fof(f26988,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat),
inference(cnf_transformation,[],[f567]) ).
fof(f567,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__nat__def) ).
fof(f29254,plain,
spl574_96,
inference(avatar_split_clause,[],[f24570,f29251]) ).
fof(f29251,plain,
( spl574_96
<=> class_Rings_Olinordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_96])]) ).
fof(f24570,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5088]) ).
fof(f5088,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
fof(f29249,plain,
spl574_95,
inference(avatar_split_clause,[],[f25436,f29246]) ).
fof(f25436,plain,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
inference(cnf_transformation,[],[f1972]) ).
fof(f1972,axiom,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__eq__id) ).
fof(f29225,plain,
spl574_94,
inference(avatar_split_clause,[],[f27724,f29222]) ).
fof(f29222,plain,
( spl574_94
<=> c_List_Olist_ONil(tc_Nat_Onat) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),c_List_Olist_ONil(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_94])]) ).
fof(f27724,plain,
c_List_Olist_ONil(tc_Nat_Onat) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),c_List_Olist_ONil(tc_Int_Oint)),
inference(definition_unfolding,[],[f24948,f23386]) ).
fof(f23386,plain,
! [X0] : c_List_Oreturn__list(X0) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X0),
inference(cnf_transformation,[],[f7868]) ).
fof(f7868,plain,
! [X0] : c_List_Oreturn__list(X0) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X0),
inference(rectify,[],[f4653]) ).
fof(f4653,axiom,
! [X130] : c_List_Oreturn__list(X130) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X130),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_return__list__def) ).
fof(f24948,plain,
c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)),
inference(cnf_transformation,[],[f4640]) ).
fof(f4640,axiom,
c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__list__functions_I2_J) ).
fof(f29220,plain,
spl574_93,
inference(avatar_split_clause,[],[f21831,f29217]) ).
fof(f29217,plain,
( spl574_93
<=> class_Rings_Oordered__ring__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_93])]) ).
fof(f21831,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(cnf_transformation,[],[f5036]) ).
fof(f5036,axiom,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).
fof(f29198,plain,
spl574_92,
inference(avatar_split_clause,[],[f26906,f29195]) ).
fof(f29195,plain,
( spl574_92
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_92])]) ).
fof(f26906,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5084]) ).
fof(f5084,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(f29193,plain,
spl574_91,
inference(avatar_split_clause,[],[f27989,f29190]) ).
fof(f27989,plain,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(definition_unfolding,[],[f26909,f27035,f24559]) ).
fof(f26909,plain,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(cnf_transformation,[],[f2842]) ).
fof(f2842,axiom,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__UNIV__bool) ).
fof(f29187,plain,
spl574_90,
inference(avatar_split_clause,[],[f20759,f29184]) ).
fof(f29184,plain,
( spl574_90
<=> class_Groups_Oab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_90])]) ).
fof(f20759,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5046]) ).
fof(f5046,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
fof(f29182,plain,
spl574_89,
inference(avatar_split_clause,[],[f22314,f29179]) ).
fof(f22314,plain,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5224]) ).
fof(f5224,axiom,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Com_Ocom_OBODY,v_pn)),v_Q)),v_G),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_Q)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f29176,plain,
spl574_88,
inference(avatar_split_clause,[],[f26214,f29173]) ).
fof(f29173,plain,
( spl574_88
<=> class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_88])]) ).
fof(f26214,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f5081]) ).
fof(f5081,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
fof(f29170,plain,
spl574_87,
inference(avatar_split_clause,[],[f26411,f29167]) ).
fof(f29167,plain,
( spl574_87
<=> class_Orderings_Olinorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_87])]) ).
fof(f26411,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5107]) ).
fof(f5107,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(f29165,plain,
spl574_86,
inference(avatar_split_clause,[],[f23468,f29162]) ).
fof(f29162,plain,
( spl574_86
<=> class_Orderings_Oord(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_86])]) ).
fof(f23468,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(cnf_transformation,[],[f5136]) ).
fof(f5136,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(f29160,plain,
spl574_85,
inference(avatar_split_clause,[],[f22926,f29157]) ).
fof(f29157,plain,
( spl574_85
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_85])]) ).
fof(f22926,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f5079]) ).
fof(f5079,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
fof(f29154,plain,
spl574_84,
inference(avatar_split_clause,[],[f26171,f29151]) ).
fof(f29151,plain,
( spl574_84
<=> class_Rings_Osemiring__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_84])]) ).
fof(f26171,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f5111]) ).
fof(f5111,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(f29147,plain,
spl574_83,
inference(avatar_split_clause,[],[f24902,f29144]) ).
fof(f29144,plain,
( spl574_83
<=> class_Int_Onumber(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_83])]) ).
fof(f24902,plain,
class_Int_Onumber(tc_Nat_Onat),
inference(cnf_transformation,[],[f5121]) ).
fof(f5121,axiom,
class_Int_Onumber(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).
fof(f29140,plain,
spl574_82,
inference(avatar_split_clause,[],[f24000,f29137]) ).
fof(f29137,plain,
( spl574_82
<=> class_Rings_Olinordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_82])]) ).
fof(f24000,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5039]) ).
fof(f5039,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
fof(f29131,plain,
spl574_81,
inference(avatar_split_clause,[],[f27859,f29128]) ).
fof(f27859,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(definition_unfolding,[],[f25981,f27035,f24559]) ).
fof(f25981,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(cnf_transformation,[],[f2858]) ).
fof(f2858,axiom,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I115_J) ).
fof(f29126,plain,
spl574_80,
inference(avatar_split_clause,[],[f22164,f29123]) ).
fof(f29123,plain,
( spl574_80
<=> class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_80])]) ).
fof(f22164,plain,
class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5189]) ).
fof(f5189,axiom,
class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult) ).
fof(f29115,plain,
spl574_79,
inference(avatar_split_clause,[],[f24690,f29112]) ).
fof(f29112,plain,
( spl574_79
<=> c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_79])]) ).
fof(f24690,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f3353]) ).
fof(f3353,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__less__than) ).
fof(f29107,plain,
spl574_78,
inference(avatar_split_clause,[],[f23569,f29104]) ).
fof(f29104,plain,
( spl574_78
<=> class_Orderings_Oorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_78])]) ).
fof(f23569,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5114]) ).
fof(f5114,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(f29102,plain,
spl574_77,
inference(avatar_split_clause,[],[f25351,f29099]) ).
fof(f29099,plain,
( spl574_77
<=> class_Groups_Omonoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_77])]) ).
fof(f25351,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f5108]) ).
fof(f5108,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(f29096,plain,
spl574_76,
inference(avatar_split_clause,[],[f22610,f29093]) ).
fof(f29093,plain,
( spl574_76
<=> class_Orderings_Opreorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_76])]) ).
fof(f22610,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f5131]) ).
fof(f5131,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(f29085,plain,
spl574_75,
inference(avatar_split_clause,[],[f28325,f29082]) ).
fof(f28325,plain,
c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(equality_resolution,[],[f27540]) ).
fof(f27540,plain,
! [X0] :
( c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)),X0)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Int_OPls != X0 ),
inference(definition_unfolding,[],[f23463,f27035]) ).
fof(f23463,plain,
! [X0] :
( c_Int_OPls = c_Int_OBit0(X0)
| c_Int_OPls != X0 ),
inference(cnf_transformation,[],[f17145]) ).
fof(f17145,plain,
! [X0] :
( ( c_Int_OPls = c_Int_OBit0(X0)
| c_Int_OPls != X0 )
& ( c_Int_OPls = X0
| c_Int_OPls != c_Int_OBit0(X0) ) ),
inference(nnf_transformation,[],[f9834]) ).
fof(f9834,plain,
! [X0] :
( c_Int_OPls = c_Int_OBit0(X0)
<=> c_Int_OPls = X0 ),
inference(rectify,[],[f2803]) ).
fof(f2803,axiom,
! [X130] :
( c_Int_OPls = c_Int_OBit0(X130)
<=> c_Int_OPls = X130 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I38_J) ).
fof(f29080,plain,
spl574_74,
inference(avatar_split_clause,[],[f29075,f29077]) ).
fof(f29075,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f27496,f23272]) ).
fof(f27496,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(definition_unfolding,[],[f23025,f24559,f24559]) ).
fof(f23025,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))),
inference(cnf_transformation,[],[f2774]) ).
fof(f2774,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
fof(f29074,plain,
spl574_73,
inference(avatar_split_clause,[],[f20105,f29071]) ).
fof(f29071,plain,
( spl574_73
<=> class_Lattices_Odistrib__lattice(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_73])]) ).
fof(f20105,plain,
class_Lattices_Odistrib__lattice(tc_Nat_Onat),
inference(cnf_transformation,[],[f5092]) ).
fof(f5092,axiom,
class_Lattices_Odistrib__lattice(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Odistrib__lattice) ).
fof(f29069,plain,
spl574_72,
inference(avatar_split_clause,[],[f20929,f29066]) ).
fof(f29066,plain,
( spl574_72
<=> class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_72])]) ).
fof(f20929,plain,
class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5184]) ).
fof(f5184,axiom,
class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring) ).
fof(f29063,plain,
spl574_71,
inference(avatar_split_clause,[],[f25146,f29060]) ).
fof(f29060,plain,
( spl574_71
<=> class_Orderings_Opreorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_71])]) ).
fof(f25146,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(cnf_transformation,[],[f5049]) ).
fof(f5049,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
fof(f29058,plain,
~ spl574_70,
inference(avatar_split_clause,[],[f24113,f29055]) ).
fof(f29055,plain,
( spl574_70
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_70])]) ).
fof(f24113,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(cnf_transformation,[],[f2686]) ).
fof(f2686,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I1_J) ).
fof(f29053,plain,
~ spl574_69,
inference(avatar_split_clause,[],[f22233,f29050]) ).
fof(f29050,plain,
( spl574_69
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_69])]) ).
fof(f22233,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(cnf_transformation,[],[f2931]) ).
fof(f2931,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I3_J) ).
fof(f29048,plain,
spl574_68,
inference(avatar_split_clause,[],[f23991,f29045]) ).
fof(f29045,plain,
( spl574_68
<=> class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_68])]) ).
fof(f23991,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f5021]) ).
fof(f5021,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
fof(f29040,plain,
spl574_67,
inference(avatar_split_clause,[],[f22796,f29037]) ).
fof(f29037,plain,
( spl574_67
<=> class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_67])]) ).
fof(f22796,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5082]) ).
fof(f5082,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(f29033,plain,
spl574_66,
inference(avatar_split_clause,[],[f27816,f29030]) ).
fof(f27816,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),
inference(definition_unfolding,[],[f25749,f24559,f24559]) ).
fof(f25749,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(cnf_transformation,[],[f2771]) ).
fof(f2771,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__3__eq__3) ).
fof(f29027,plain,
spl574_65,
inference(avatar_split_clause,[],[f25238,f29024]) ).
fof(f29024,plain,
( spl574_65
<=> class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_65])]) ).
fof(f25238,plain,
class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5183]) ).
fof(f5183,axiom,
class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div) ).
fof(f29022,plain,
spl574_55,
inference(avatar_split_clause,[],[f23951,f28964]) ).
fof(f23951,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f1788]) ).
fof(f1788,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I1_J) ).
fof(f29021,plain,
spl574_64,
inference(avatar_split_clause,[],[f28414,f29018]) ).
fof(f28414,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
inference(equality_resolution,[],[f24681]) ).
fof(f24681,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X0
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,X0) ),
inference(cnf_transformation,[],[f10948]) ).
fof(f10948,plain,
! [X0] :
( ( ( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| hAPP(c_Code__Numeral_Oint__of,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( hAPP(c_Code__Numeral_Oint__of,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) )
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X0
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,X0) ) ),
inference(ennf_transformation,[],[f5650]) ).
fof(f5650,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X0
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,X0) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X0
=> ( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> hAPP(c_Code__Numeral_Oint__of,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> hAPP(c_Code__Numeral_Oint__of,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ) ) ),
inference(rectify,[],[f2913]) ).
fof(f2913,axiom,
! [X106] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X106
=> ( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X106,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> hAPP(c_Code__Numeral_Oint__of,X106) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X106),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X106,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> hAPP(c_Code__Numeral_Oint__of,X106) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X106),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X106
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,X106) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__of__code) ).
fof(f29016,plain,
spl574_63,
inference(avatar_split_clause,[],[f24390,f29013]) ).
fof(f29013,plain,
( spl574_63
<=> class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_63])]) ).
fof(f24390,plain,
class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5186]) ).
fof(f5186,axiom,
class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one) ).
fof(f29010,plain,
spl574_62,
inference(avatar_split_clause,[],[f28549,f29007]) ).
fof(f28549,plain,
c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),c_Int_OMin),
inference(equality_resolution,[],[f27871]) ).
fof(f27871,plain,
! [X0] :
( c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)),X0)
| c_Int_OMin != X0 ),
inference(definition_unfolding,[],[f26101,f24559]) ).
fof(f26101,plain,
! [X0] :
( c_Int_OMin = c_Int_OBit1(X0)
| c_Int_OMin != X0 ),
inference(cnf_transformation,[],[f19150]) ).
fof(f19150,plain,
! [X0] :
( ( c_Int_OMin = X0
| c_Int_OMin != c_Int_OBit1(X0) )
& ( c_Int_OMin = c_Int_OBit1(X0)
| c_Int_OMin != X0 ) ),
inference(nnf_transformation,[],[f8413]) ).
fof(f8413,plain,
! [X0] :
( c_Int_OMin = X0
<=> c_Int_OMin = c_Int_OBit1(X0) ),
inference(rectify,[],[f2923]) ).
fof(f2923,axiom,
! [X105] :
( c_Int_OMin = X105
<=> c_Int_OBit1(X105) = c_Int_OMin ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I47_J) ).
fof(f29005,plain,
spl574_61,
inference(avatar_split_clause,[],[f26090,f29002]) ).
fof(f29002,plain,
( spl574_61
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_61])]) ).
fof(f26090,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5007]) ).
fof(f5007,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f29000,plain,
spl574_60,
inference(avatar_split_clause,[],[f26763,f28997]) ).
fof(f26763,plain,
c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
inference(cnf_transformation,[],[f3267]) ).
fof(f3267,axiom,
c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__weak__def) ).
fof(f28995,plain,
spl574_59,
inference(avatar_split_clause,[],[f27690,f28992]) ).
fof(f27690,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),
inference(definition_unfolding,[],[f24656,f24559]) ).
fof(f24656,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
inference(cnf_transformation,[],[f2767]) ).
fof(f2767,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__numeral__1__eq__1) ).
fof(f28990,plain,
( spl574_57
| spl574_58 ),
inference(avatar_split_clause,[],[f28244,f28988,f28984]) ).
fof(f28988,plain,
( spl574_58
<=> ! [X1] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))
| hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_58])]) ).
fof(f28244,plain,
! [X1] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))
| hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(equality_resolution,[],[f22466]) ).
fof(f22466,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X0)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X1,X0) ),
inference(cnf_transformation,[],[f10827]) ).
fof(f10827,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X0)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)) = c_Nitpick_Onorm__frac(X1,X0) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ( ( c_Nitpick_Onorm__frac(X1,X0) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X1),X0)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 )
| hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X1,X0) ) ) ) ) ),
inference(flattening,[],[f10826]) ).
fof(f10826,plain,
! [X1,X0] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)) = c_Nitpick_Onorm__frac(X1,X0) )
& ( ( ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 )
| hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X1,X0) )
& ( c_Nitpick_Onorm__frac(X1,X0) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X1),X0)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X0))) ),
inference(ennf_transformation,[],[f6947]) ).
fof(f6947,plain,
! [X1,X0] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X0)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)) = c_Nitpick_Onorm__frac(X1,X0) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 )
=> hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X1,X0) )
& ( ~ ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 )
=> c_Nitpick_Onorm__frac(X1,X0) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X1),X0)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0))) ) ) ) ) ),
inference(rectify,[],[f3114]) ).
fof(f3114,axiom,
! [X26,X5] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X5),X26)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( ( ~ ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X5
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X26 )
=> c_Nitpick_Onorm__frac(X5,X26) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X5),X26)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X5))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26))) )
& ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X26
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X5 )
=> c_Nitpick_Onorm__frac(X5,X26) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Nitpick_Onorm__frac(X5,X26) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X5),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__frac_Opsimps) ).
fof(f28972,plain,
spl574_56,
inference(avatar_split_clause,[],[f22001,f28969]) ).
fof(f22001,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[],[f1614]) ).
fof(f1614,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__Suc0__eq__1) ).
fof(f28967,plain,
spl574_55,
inference(avatar_split_clause,[],[f24555,f28964]) ).
fof(f24555,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f1592]) ).
fof(f1592,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0) ).
fof(f28962,plain,
spl574_54,
inference(avatar_split_clause,[],[f23467,f28959]) ).
fof(f28959,plain,
( spl574_54
<=> class_Nat_Osize(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_54])]) ).
fof(f23467,plain,
class_Nat_Osize(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5159]) ).
fof(f5159,axiom,
class_Nat_Osize(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Nat_Osize) ).
fof(f28956,plain,
spl574_53,
inference(avatar_split_clause,[],[f21316,f28953]) ).
fof(f28953,plain,
( spl574_53
<=> class_Groups_Osgn__if(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_53])]) ).
fof(f21316,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(cnf_transformation,[],[f5066]) ).
fof(f5066,axiom,
class_Groups_Osgn__if(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).
fof(f28951,plain,
spl574_52,
inference(avatar_split_clause,[],[f24268,f28948]) ).
fof(f28948,plain,
( spl574_52
<=> class_Nat_Osize(tc_Code__Evaluation_Oterm) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_52])]) ).
fof(f24268,plain,
class_Nat_Osize(tc_Code__Evaluation_Oterm),
inference(cnf_transformation,[],[f5160]) ).
fof(f5160,axiom,
class_Nat_Osize(tc_Code__Evaluation_Oterm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Evaluation__Oterm__Nat_Osize) ).
fof(f28946,plain,
( spl574_50
| ~ spl574_51 ),
inference(avatar_split_clause,[],[f22173,f28943,f28940]) ).
fof(f28940,plain,
( spl574_50
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_50])]) ).
fof(f22173,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X1),X0) ),
inference(cnf_transformation,[],[f16137]) ).
fof(f16137,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X1),X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(X1),sK153(X0,X1)),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK153])],[f16135,f16136]) ).
fof(f16136,plain,
! [X0,X1] :
( ? [X2] : hBOOL(hAPP(hAPP(c_member(X1),X2),X0))
=> hBOOL(hAPP(hAPP(c_member(X1),sK153(X0,X1)),X0)) ),
introduced(choice_axiom,[]) ).
fof(f16135,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X1),X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
& ? [X2] : hBOOL(hAPP(hAPP(c_member(X1),X2),X0)) ) ),
inference(rectify,[],[f11270]) ).
fof(f11270,plain,
! [X1,X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X0),X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
& ? [X2] : hBOOL(hAPP(hAPP(c_member(X0),X2),X1)) ) ),
inference(flattening,[],[f11269]) ).
fof(f11269,plain,
! [X1,X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X0),X1)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
& ? [X2] : hBOOL(hAPP(hAPP(c_member(X0),X2),X1)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1)) ),
inference(ennf_transformation,[],[f9097]) ).
fof(f9097,plain,
! [X1,X0] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1))
=> ( ( ? [X2] : hBOOL(hAPP(hAPP(c_member(X0),X2),X1))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X0),X1) ) ),
inference(rectify,[],[f2560]) ).
fof(f2560,axiom,
! [X4,X21] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X21))
=> ( ( ? [X2] : hBOOL(hAPP(hAPP(c_member(X4),X2),X21))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X4),X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oneutral) ).
fof(f28938,plain,
~ spl574_16,
inference(avatar_split_clause,[],[f25025,f28732]) ).
fof(f28732,plain,
( spl574_16
<=> c_Int_OPls = c_Int_OMin ),
introduced(avatar_definition,[new_symbols(naming,[spl574_16])]) ).
fof(f25025,plain,
c_Int_OPls != c_Int_OMin,
inference(cnf_transformation,[],[f2922]) ).
fof(f2922,axiom,
c_Int_OPls != c_Int_OMin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I40_J) ).
fof(f28937,plain,
spl574_49,
inference(avatar_split_clause,[],[f28584,f28934]) ).
fof(f28584,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(equality_resolution,[],[f26440]) ).
fof(f26440,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f19381]) ).
fof(f19381,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ),
inference(nnf_transformation,[],[f8513]) ).
fof(f8513,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(rectify,[],[f1591]) ).
fof(f1591,axiom,
! [X74] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X74)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X74 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__le__0__conv) ).
fof(f28932,plain,
spl574_48,
inference(avatar_split_clause,[],[f21957,f28929]) ).
fof(f28929,plain,
( spl574_48
<=> class_Lattices_Olattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_48])]) ).
fof(f21957,plain,
class_Lattices_Olattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f5133]) ).
fof(f5133,axiom,
class_Lattices_Olattice(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
fof(f28927,plain,
spl574_47,
inference(avatar_split_clause,[],[f23261,f28924]) ).
fof(f28924,plain,
( spl574_47
<=> c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_47])]) ).
fof(f23261,plain,
c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel),
inference(cnf_transformation,[],[f3296]) ).
fof(f3296,axiom,
c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Integ__def) ).
fof(f28922,plain,
spl574_46,
inference(avatar_split_clause,[],[f23123,f28919]) ).
fof(f28919,plain,
( spl574_46
<=> c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_46])]) ).
fof(f23123,plain,
c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg),
inference(cnf_transformation,[],[f3299]) ).
fof(f3299,axiom,
c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition__Integ) ).
fof(f28917,plain,
spl574_2,
inference(avatar_split_clause,[],[f22204,f28663]) ).
fof(f22204,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
inference(cnf_transformation,[],[f2687]) ).
fof(f2687,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I113_J) ).
fof(f28916,plain,
spl574_45,
inference(avatar_split_clause,[],[f22935,f28913]) ).
fof(f28913,plain,
( spl574_45
<=> class_Nat_Osize(tc_Com_Ocom) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_45])]) ).
fof(f22935,plain,
class_Nat_Osize(tc_Com_Ocom),
inference(cnf_transformation,[],[f5005]) ).
fof(f5005,axiom,
class_Nat_Osize(tc_Com_Ocom),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Com__Ocom__Nat_Osize) ).
fof(f28909,plain,
spl574_44,
inference(avatar_split_clause,[],[f22885,f28906]) ).
fof(f28906,plain,
( spl574_44
<=> class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_44])]) ).
fof(f22885,plain,
class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5196]) ).
fof(f5196,axiom,
class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Oord) ).
fof(f28904,plain,
spl574_43,
inference(avatar_split_clause,[],[f23079,f28901]) ).
fof(f28901,plain,
( spl574_43
<=> class_Rings_Oordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_43])]) ).
fof(f23079,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5096]) ).
fof(f5096,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
fof(f28896,plain,
spl574_42,
inference(avatar_split_clause,[],[f21303,f28893]) ).
fof(f21303,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP),
inference(cnf_transformation,[],[f1188]) ).
fof(f1188,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osize_I1_J) ).
fof(f28890,plain,
spl574_41,
inference(avatar_split_clause,[],[f23823,f28887]) ).
fof(f23823,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP),
inference(cnf_transformation,[],[f1186]) ).
fof(f1186,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osize_I9_J) ).
fof(f28858,plain,
spl574_40,
inference(avatar_split_clause,[],[f20374,f28855]) ).
fof(f28855,plain,
( spl574_40
<=> class_Rings_Olinordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_40])]) ).
fof(f20374,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5026]) ).
fof(f5026,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
fof(f28853,plain,
spl574_39,
inference(avatar_split_clause,[],[f23686,f28850]) ).
fof(f28850,plain,
( spl574_39
<=> class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_39])]) ).
fof(f23686,plain,
class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
inference(cnf_transformation,[],[f5125]) ).
fof(f5125,axiom,
class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__top) ).
fof(f28848,plain,
~ spl574_38,
inference(avatar_split_clause,[],[f26381,f28845]) ).
fof(f26381,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
inference(cnf_transformation,[],[f2691]) ).
fof(f2691,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__number__of__Pls) ).
fof(f28843,plain,
spl574_37,
inference(avatar_split_clause,[],[f27850,f28840]) ).
fof(f27850,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),
inference(definition_unfolding,[],[f25914,f24559]) ).
fof(f25914,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)),
inference(cnf_transformation,[],[f2971]) ).
fof(f2971,axiom,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__code__numeral__code) ).
fof(f28837,plain,
spl574_36,
inference(avatar_split_clause,[],[f20563,f28834]) ).
fof(f28834,plain,
( spl574_36
<=> class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_36])]) ).
fof(f20563,plain,
class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5170]) ).
fof(f5170,axiom,
class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring) ).
fof(f28831,plain,
spl574_35,
inference(avatar_split_clause,[],[f26471,f28828]) ).
fof(f28828,plain,
( spl574_35
<=> class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_35])]) ).
fof(f26471,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5098]) ).
fof(f5098,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(f28826,plain,
spl574_34,
inference(avatar_split_clause,[],[f28821,f28823]) ).
fof(f28821,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(backward_demodulation,[],[f28427,f28551]) ).
fof(f28427,plain,
! [X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(equality_resolution,[],[f24796]) ).
fof(f24796,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f18143]) ).
fof(f18143,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))) ) ),
inference(rectify,[],[f18142]) ).
fof(f18142,plain,
! [X1,X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1))) ) ),
inference(flattening,[],[f18141]) ).
fof(f18141,plain,
! [X1,X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1))) ) ),
inference(nnf_transformation,[],[f9790]) ).
fof(f9790,plain,
! [X1,X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) ),
inference(rectify,[],[f2209]) ).
fof(f2209,axiom,
! [X22,X74] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X22),X74)))
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X74
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
fof(f28820,plain,
spl574_33,
inference(avatar_split_clause,[],[f20618,f28817]) ).
fof(f28817,plain,
( spl574_33
<=> class_Lattices_Odistrib__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_33])]) ).
fof(f20618,plain,
class_Lattices_Odistrib__lattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f5129]) ).
fof(f5129,axiom,
class_Lattices_Odistrib__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Odistrib__lattice) ).
fof(f28815,plain,
spl574_32,
inference(avatar_split_clause,[],[f24626,f28812]) ).
fof(f28812,plain,
( spl574_32
<=> class_Lattices_Odistrib__lattice(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_32])]) ).
fof(f24626,plain,
class_Lattices_Odistrib__lattice(tc_Int_Oint),
inference(cnf_transformation,[],[f5031]) ).
fof(f5031,axiom,
class_Lattices_Odistrib__lattice(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Odistrib__lattice) ).
fof(f28810,plain,
spl574_31,
inference(avatar_split_clause,[],[f23678,f28807]) ).
fof(f28807,plain,
( spl574_31
<=> class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_31])]) ).
fof(f23678,plain,
class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5197]) ).
fof(f5197,axiom,
class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ominus) ).
fof(f28805,plain,
spl574_30,
inference(avatar_split_clause,[],[f24123,f28802]) ).
fof(f28802,plain,
( spl574_30
<=> c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_30])]) ).
fof(f24123,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f1931]) ).
fof(f1931,axiom,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J) ).
fof(f28800,plain,
spl574_29,
inference(avatar_split_clause,[],[f20007,f28797]) ).
fof(f28797,plain,
( spl574_29
<=> class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_29])]) ).
fof(f20007,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(cnf_transformation,[],[f5099]) ).
fof(f5099,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(f28795,plain,
spl574_28,
inference(avatar_split_clause,[],[f26515,f28792]) ).
fof(f28792,plain,
( spl574_28
<=> c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_28])]) ).
fof(f26515,plain,
c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)),
inference(cnf_transformation,[],[f2080]) ).
fof(f2080,axiom,
c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__lessThan__UNIV) ).
fof(f28790,plain,
spl574_27,
inference(avatar_split_clause,[],[f24620,f28787]) ).
fof(f28787,plain,
( spl574_27
<=> class_Rings_Osemiring__1(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_27])]) ).
fof(f24620,plain,
class_Rings_Osemiring__1(tc_Nat_Onat),
inference(cnf_transformation,[],[f5110]) ).
fof(f5110,axiom,
class_Rings_Osemiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).
fof(f28785,plain,
spl574_26,
inference(avatar_split_clause,[],[f27388,f28782]) ).
fof(f28782,plain,
( spl574_26
<=> c_Divides_OnegateSnd = hAPP(c_Product__Type_Ointernal__split(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Fun_Oid(tc_Int_Oint)))),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_26])]) ).
fof(f27388,plain,
c_Divides_OnegateSnd = hAPP(c_Product__Type_Ointernal__split(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Fun_Oid(tc_Int_Oint)))),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),
inference(definition_unfolding,[],[f22156,f27041]) ).
fof(f27041,plain,
! [X2,X3,X0,X1] : hAPP(c_Product__Type_Ointernal__split(X2,X3,tc_prod(X2,X1)),hAPP(hAPP(c_COMBC(X2,tc_fun(X3,X1),tc_fun(X3,tc_prod(X2,X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X2,X1)),tc_fun(tc_fun(X3,X1),tc_fun(X3,tc_prod(X2,X1))),X2),c_COMBB(X1,tc_prod(X2,X1),X3)),hAPP(hAPP(c_COMBB(X2,tc_fun(X1,tc_prod(X2,X1)),X2),c_Product__Type_OPair(X2,X1)),c_Fun_Oid(X2)))),X0)) = c_Product__Type_Oapsnd(X3,X1,X2,X0),
inference(definition_unfolding,[],[f26494,f27040]) ).
fof(f27040,plain,
! [X2,X3,X0,X1,X4,X5] : c_Product__Type_Omap__pair(X5,X2,X4,X0,X1,X3) = hAPP(c_Product__Type_Ointernal__split(X5,X4,tc_prod(X2,X0)),hAPP(hAPP(c_COMBC(X5,tc_fun(X4,X0),tc_fun(X4,tc_prod(X2,X0))),hAPP(hAPP(c_COMBB(tc_fun(X0,tc_prod(X2,X0)),tc_fun(tc_fun(X4,X0),tc_fun(X4,tc_prod(X2,X0))),X5),c_COMBB(X0,tc_prod(X2,X0),X4)),hAPP(hAPP(c_COMBB(X2,tc_fun(X0,tc_prod(X2,X0)),X5),c_Product__Type_OPair(X2,X0)),X1))),X3)),
inference(definition_unfolding,[],[f21555,f23198]) ).
fof(f21555,plain,
! [X2,X3,X0,X1,X4,X5] : c_Product__Type_Omap__pair(X5,X2,X4,X0,X1,X3) = hAPP(c_Product__Type_Oprod_Oprod__case(X5,X4,tc_prod(X2,X0)),hAPP(hAPP(c_COMBC(X5,tc_fun(X4,X0),tc_fun(X4,tc_prod(X2,X0))),hAPP(hAPP(c_COMBB(tc_fun(X0,tc_prod(X2,X0)),tc_fun(tc_fun(X4,X0),tc_fun(X4,tc_prod(X2,X0))),X5),c_COMBB(X0,tc_prod(X2,X0),X4)),hAPP(hAPP(c_COMBB(X2,tc_fun(X0,tc_prod(X2,X0)),X5),c_Product__Type_OPair(X2,X0)),X1))),X3)),
inference(cnf_transformation,[],[f15637]) ).
fof(f15637,plain,
! [X0,X1,X2,X3,X4,X5] : c_Product__Type_Omap__pair(X5,X2,X4,X0,X1,X3) = hAPP(c_Product__Type_Oprod_Oprod__case(X5,X4,tc_prod(X2,X0)),hAPP(hAPP(c_COMBC(X5,tc_fun(X4,X0),tc_fun(X4,tc_prod(X2,X0))),hAPP(hAPP(c_COMBB(tc_fun(X0,tc_prod(X2,X0)),tc_fun(tc_fun(X4,X0),tc_fun(X4,tc_prod(X2,X0))),X5),c_COMBB(X0,tc_prod(X2,X0),X4)),hAPP(hAPP(c_COMBB(X2,tc_fun(X0,tc_prod(X2,X0)),X5),c_Product__Type_OPair(X2,X0)),X1))),X3)),
inference(rectify,[],[f8409]) ).
fof(f8409,plain,
! [X3,X5,X4,X0,X2,X1] : c_Product__Type_Omap__pair(X1,X4,X2,X3,X5,X0) = hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_prod(X4,X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(X2,X3),tc_fun(X2,tc_prod(X4,X3))),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_prod(X4,X3)),tc_fun(tc_fun(X2,X3),tc_fun(X2,tc_prod(X4,X3))),X1),c_COMBB(X3,tc_prod(X4,X3),X2)),hAPP(hAPP(c_COMBB(X4,tc_fun(X3,tc_prod(X4,X3)),X1),c_Product__Type_OPair(X4,X3)),X5))),X0)),
inference(rectify,[],[f3316]) ).
fof(f3316,axiom,
! [X0,X4,X20,X93,X38,X1] : c_Product__Type_Omap__pair(X4,X38,X20,X93,X1,X0) = hAPP(c_Product__Type_Oprod_Oprod__case(X4,X20,tc_prod(X38,X93)),hAPP(hAPP(c_COMBC(X4,tc_fun(X20,X93),tc_fun(X20,tc_prod(X38,X93))),hAPP(hAPP(c_COMBB(tc_fun(X93,tc_prod(X38,X93)),tc_fun(tc_fun(X20,X93),tc_fun(X20,tc_prod(X38,X93))),X4),c_COMBB(X93,tc_prod(X38,X93),X20)),hAPP(hAPP(c_COMBB(X38,tc_fun(X93,tc_prod(X38,X93)),X4),c_Product__Type_OPair(X38,X93)),X1))),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__def) ).
fof(f26494,plain,
! [X2,X3,X0,X1] : c_Product__Type_Omap__pair(X2,X2,X3,X1,c_Fun_Oid(X2),X0) = c_Product__Type_Oapsnd(X3,X1,X2,X0),
inference(cnf_transformation,[],[f19420]) ).
fof(f19420,plain,
! [X0,X1,X2,X3] : c_Product__Type_Omap__pair(X2,X2,X3,X1,c_Fun_Oid(X2),X0) = c_Product__Type_Oapsnd(X3,X1,X2,X0),
inference(rectify,[],[f6957]) ).
fof(f6957,plain,
! [X3,X1,X2,X0] : c_Product__Type_Omap__pair(X2,X2,X0,X1,c_Fun_Oid(X2),X3) = c_Product__Type_Oapsnd(X0,X1,X2,X3),
inference(rectify,[],[f3313]) ).
fof(f3313,axiom,
! [X20,X38,X4,X1] : c_Product__Type_Oapsnd(X20,X38,X4,X1) = c_Product__Type_Omap__pair(X4,X4,X20,X38,c_Fun_Oid(X4),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apsnd__def) ).
fof(f22156,plain,
c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
inference(cnf_transformation,[],[f3077]) ).
fof(f3077,axiom,
c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negateSnd__def) ).
fof(f28780,plain,
~ spl574_25,
inference(avatar_split_clause,[],[f21141,f28777]) ).
fof(f21141,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(cnf_transformation,[],[f2061]) ).
fof(f2061,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__0) ).
fof(f28775,plain,
spl574_24,
inference(avatar_split_clause,[],[f22534,f28772]) ).
fof(f28772,plain,
( spl574_24
<=> class_Groups_Ozero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_24])]) ).
fof(f22534,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(cnf_transformation,[],[f5071]) ).
fof(f5071,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
fof(f28770,plain,
spl574_23,
inference(avatar_split_clause,[],[f28444,f28767]) ).
fof(f28767,plain,
( spl574_23
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_23])]) ).
fof(f28444,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f28443]) ).
fof(f28443,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(equality_resolution,[],[f25037]) ).
fof(f25037,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f18319]) ).
fof(f18319,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) ) ),
inference(flattening,[],[f18318]) ).
fof(f18318,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) ) ),
inference(nnf_transformation,[],[f10051]) ).
fof(f10051,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) ),
inference(rectify,[],[f1019]) ).
fof(f1019,axiom,
! [X74,X77] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X77),X74)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X77
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X74 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).
fof(f28765,plain,
spl574_22,
inference(avatar_split_clause,[],[f24793,f28762]) ).
fof(f28762,plain,
( spl574_22
<=> class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_22])]) ).
fof(f24793,plain,
class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f5124]) ).
fof(f5124,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice) ).
fof(f28760,plain,
spl574_21,
inference(avatar_split_clause,[],[f20817,f28757]) ).
fof(f28757,plain,
( spl574_21
<=> class_Groups_Ozero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_21])]) ).
fof(f20817,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f5120]) ).
fof(f5120,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(f28755,plain,
spl574_20,
inference(avatar_split_clause,[],[f23612,f28752]) ).
fof(f23612,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls,
inference(cnf_transformation,[],[f2677]) ).
fof(f2677,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(f28750,plain,
spl574_19,
inference(avatar_split_clause,[],[f20145,f28747]) ).
fof(f28747,plain,
( spl574_19
<=> class_Lattices_Osemilattice__inf(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_19])]) ).
fof(f20145,plain,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
inference(cnf_transformation,[],[f5128]) ).
fof(f5128,axiom,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
fof(f28745,plain,
spl574_18,
inference(avatar_split_clause,[],[f26594,f28742]) ).
fof(f28742,plain,
( spl574_18
<=> class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_18])]) ).
fof(f26594,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5024]) ).
fof(f5024,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
fof(f28740,plain,
spl574_17,
inference(avatar_split_clause,[],[f23690,f28737]) ).
fof(f28737,plain,
( spl574_17
<=> class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_17])]) ).
fof(f23690,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5025]) ).
fof(f5025,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(f28735,plain,
~ spl574_16,
inference(avatar_split_clause,[],[f22985,f28732]) ).
fof(f22985,plain,
c_Int_OPls != c_Int_OMin,
inference(cnf_transformation,[],[f2921]) ).
fof(f2921,axiom,
c_Int_OPls != c_Int_OMin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I37_J) ).
fof(f28730,plain,
spl574_15,
inference(avatar_split_clause,[],[f23903,f28727]) ).
fof(f23903,plain,
hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(cnf_transformation,[],[f1609]) ).
fof(f1609,axiom,
hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atMost__0) ).
fof(f28725,plain,
spl574_14,
inference(avatar_split_clause,[],[f23785,f28722]) ).
fof(f28722,plain,
( spl574_14
<=> class_Groups_Omonoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_14])]) ).
fof(f23785,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f5051]) ).
fof(f5051,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(f28720,plain,
spl574_13,
inference(avatar_split_clause,[],[f20106,f28717]) ).
fof(f28717,plain,
( spl574_13
<=> class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_13])]) ).
fof(f20106,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5015]) ).
fof(f5015,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
fof(f28715,plain,
spl574_12,
inference(avatar_split_clause,[],[f22270,f28712]) ).
fof(f28712,plain,
( spl574_12
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_12])]) ).
fof(f22270,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f1714]) ).
fof(f1714,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__0) ).
fof(f28710,plain,
spl574_11,
inference(avatar_split_clause,[],[f28295,f28707]) ).
fof(f28295,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(equality_resolution,[],[f23042]) ).
fof(f23042,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X0)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ),
inference(cnf_transformation,[],[f16822]) ).
fof(f16822,plain,
! [X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X0)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X0)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(nnf_transformation,[],[f7550]) ).
fof(f7550,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X0)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ),
inference(rectify,[],[f2038]) ).
fof(f2038,axiom,
! [X30] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X30)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zabs__less__one__iff) ).
fof(f28705,plain,
spl574_10,
inference(avatar_split_clause,[],[f25755,f28702]) ).
fof(f28702,plain,
( spl574_10
<=> class_Groups_Osemigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_10])]) ).
fof(f25755,plain,
class_Groups_Osemigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5042]) ).
fof(f5042,axiom,
class_Groups_Osemigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osemigroup__add) ).
fof(f28700,plain,
spl574_9,
inference(avatar_split_clause,[],[f25997,f28697]) ).
fof(f25997,plain,
hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(cnf_transformation,[],[f1834]) ).
fof(f1834,axiom,
hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThan__0) ).
fof(f28695,plain,
spl574_8,
inference(avatar_split_clause,[],[f25921,f28692]) ).
fof(f28692,plain,
( spl574_8
<=> c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_8])]) ).
fof(f25921,plain,
c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat),
inference(cnf_transformation,[],[f4345]) ).
fof(f4345,axiom,
c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__code__numeral__def) ).
fof(f28690,plain,
spl574_7,
inference(avatar_split_clause,[],[f20779,f28687]) ).
fof(f28687,plain,
( spl574_7
<=> class_Groups_Omonoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_7])]) ).
fof(f20779,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5053]) ).
fof(f5053,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
fof(f28685,plain,
spl574_6,
inference(avatar_split_clause,[],[f24023,f28682]) ).
fof(f28682,plain,
( spl574_6
<=> class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_6])]) ).
fof(f24023,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5019]) ).
fof(f5019,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
fof(f28679,plain,
( ~ spl574_4
| spl574_5 ),
inference(avatar_split_clause,[],[f28020,f28677,f28673]) ).
fof(f28673,plain,
( spl574_4
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_4])]) ).
fof(f28677,plain,
( spl574_5
<=> ! [X1] :
( hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_5])]) ).
fof(f28020,plain,
! [X1] :
( hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(equality_resolution,[],[f27072]) ).
fof(f27072,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),X1)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(definition_unfolding,[],[f19990,f23874]) ).
fof(f23874,plain,
! [X0,X1] : c_Divides_Odivmod__int(X0,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),X1)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1)),
inference(cnf_transformation,[],[f6924]) ).
fof(f6924,plain,
! [X0,X1] : c_Divides_Odivmod__int(X0,X1) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),X1)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1)),
inference(rectify,[],[f3002]) ).
fof(f3002,axiom,
! [X168,X158] : c_Divides_Odivmod__int(X168,X158) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X168),X158)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X168,X158)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__mod__div) ).
fof(f19990,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Divides_Odivmod__int(X0,X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(cnf_transformation,[],[f13280]) ).
fof(f13280,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| ( ( ( ( hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))) = c_Divides_Odivmod__int(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Divides_Odivmod__int(X0,X1) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| c_Divides_OposDivAlg(X0,X1) = c_Divides_Odivmod__int(X0,X1) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| c_Divides_Odivmod__int(X0,X1) = c_Divides_OnegDivAlg(X0,X1) )
& ( c_Divides_Odivmod__int(X0,X1) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) ) ) ),
inference(ennf_transformation,[],[f6325]) ).
fof(f6325,plain,
! [X1,X0] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
=> c_Divides_Odivmod__int(X0,X1) = c_Divides_OnegDivAlg(X0,X1) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
=> c_Divides_Odivmod__int(X0,X1) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
=> c_Divides_OposDivAlg(X0,X1) = c_Divides_Odivmod__int(X0,X1) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
=> ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
=> hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))) = c_Divides_Odivmod__int(X0,X1) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
=> hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Divides_Odivmod__int(X0,X1) ) ) ) ) ) ),
inference(rectify,[],[f3073]) ).
fof(f3073,axiom,
! [X37,X36] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
=> ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X37
=> c_Divides_Odivmod__int(X37,X36) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X37),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X36))) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X37
=> c_Divides_Odivmod__int(X37,X36) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
=> c_Divides_Odivmod__int(X37,X36) = c_Divides_OposDivAlg(X37,X36) ) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
=> c_Divides_Odivmod__int(X37,X36) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X37),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X36))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
=> c_Divides_Odivmod__int(X37,X36) = c_Divides_OnegDivAlg(X37,X36) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__def) ).
fof(f28671,plain,
spl574_3,
inference(avatar_split_clause,[],[f27487,f28668]) ).
fof(f27487,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(definition_unfolding,[],[f22978,f27035,f24559]) ).
fof(f22978,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(cnf_transformation,[],[f2850]) ).
fof(f2850,axiom,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J) ).
fof(f28666,plain,
spl574_2,
inference(avatar_split_clause,[],[f25058,f28663]) ).
fof(f25058,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
inference(cnf_transformation,[],[f2688]) ).
fof(f2688,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__Pls) ).
fof(f28661,plain,
spl574_1,
inference(avatar_split_clause,[],[f26503,f28658]) ).
fof(f28658,plain,
( spl574_1
<=> c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl574_1])]) ).
fof(f26503,plain,
c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f4870]) ).
fof(f4870,axiom,
c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__than) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.07 % Problem : SWW305+1 : TPTP v8.1.0. Released v5.2.0.
% 0.05/0.07 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.07/0.26 % Computer : n025.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Tue Aug 30 20:38:30 EDT 2022
% 0.07/0.26 % CPUTime :
% 0.37/0.65 % (15205)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/498Mi)
% 0.37/0.66 % (15197)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/68Mi)
% 0.37/0.67 % (15189)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/51Mi)
% 0.37/0.69 % (15185)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/37Mi)
% 0.37/0.69 % (15196)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/99Mi)
% 0.37/0.69 % (15210)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/177Mi)
% 0.37/0.69 % (15203)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/176Mi)
% 0.37/0.70 % (15194)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/100Mi)
% 0.37/0.70 % (15202)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/100Mi)
% 0.37/0.71 % (15186)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/51Mi)
% 0.37/0.71 % (15187)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/51Mi)
% 0.37/0.71 % (15193)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/50Mi)
% 0.37/0.72 % (15183)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/191324Mi)
% 0.37/0.72 % (15207)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/482Mi)
% 0.37/0.72 % (15211)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/439Mi)
% 0.37/0.72 % (15188)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/48Mi)
% 0.37/0.72 % (15212)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/355Mi)
% 0.37/0.72 % (15199)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/99Mi)
% 0.37/0.73 % (15198)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/75Mi)
% 0.37/0.73 % (15204)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/138Mi)
% 0.37/0.73 % (15184)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/50Mi)
% 0.37/0.73 % (15192)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/51Mi)
% 0.37/0.73 % (15190)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/7Mi)
% 0.37/0.73 % (15195)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/101Mi)
% 0.37/0.73 % (15209)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/68Mi)
% 0.37/0.74 % (15206)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/467Mi)
% 0.37/0.74 % (15208)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/500Mi)
% 0.37/0.74 % (15201)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/100Mi)
% 0.37/0.74 % (15200)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/59Mi)
% 0.37/0.75 % (15191)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/2Mi)
% 0.37/0.76 % (15190)Instruction limit reached!
% 0.37/0.76 % (15190)------------------------------
% 0.37/0.76 % (15190)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.37/0.76 % (15190)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.37/0.76 % (15190)Termination reason: Unknown
% 0.37/0.76 % (15190)Termination phase: Preprocessing 1
% 0.37/0.76
% 0.37/0.76 % (15190)Memory used [KB]: 7291
% 0.37/0.76 % (15190)Time elapsed: 0.009 s
% 0.37/0.76 % (15190)Instructions burned: 7 (million)
% 0.37/0.76 % (15190)------------------------------
% 0.37/0.76 % (15190)------------------------------
% 0.37/0.77 % (15191)Instruction limit reached!
% 0.37/0.77 % (15191)------------------------------
% 0.37/0.77 % (15191)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.37/0.77 % (15191)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.37/0.77 % (15191)Termination reason: Unknown
% 0.37/0.77 % (15191)Termination phase: shuffling
% 0.37/0.77
% 0.41/0.77 % (15191)Memory used [KB]: 6652
% 0.41/0.77 % (15191)Time elapsed: 0.003 s
% 0.41/0.77 % (15191)Instructions burned: 2 (million)
% 0.41/0.77 % (15191)------------------------------
% 0.41/0.77 % (15191)------------------------------
% 0.41/0.79 % (15189)Instruction limit reached!
% 0.41/0.79 % (15189)------------------------------
% 0.41/0.79 % (15189)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.41/0.79 % (15189)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.41/0.79 % (15189)Termination reason: Unknown
% 0.41/0.79 % (15189)Termination phase: Preprocessing 1
% 0.41/0.79
% 0.41/0.79 % (15189)Memory used [KB]: 10234
% 0.41/0.79 % (15189)Time elapsed: 0.057 s
% 0.41/0.79 % (15189)Instructions burned: 52 (million)
% 0.41/0.79 % (15189)------------------------------
% 0.41/0.79 % (15189)------------------------------
% 0.41/0.80 % (15185)Instruction limit reached!
% 0.41/0.80 % (15185)------------------------------
% 0.41/0.80 % (15185)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.41/0.80 % (15185)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.41/0.80 % (15185)Termination reason: Unknown
% 0.41/0.80 % (15185)Termination phase: SInE selection
% 0.41/0.80
% 0.41/0.80 % (15185)Memory used [KB]: 7291
% 0.41/0.80 % (15185)Time elapsed: 0.047 s
% 0.41/0.80 % (15185)Instructions burned: 37 (million)
% 0.41/0.80 % (15185)------------------------------
% 0.41/0.80 % (15185)------------------------------
% 0.41/0.80 % (15197)Instruction limit reached!
% 0.41/0.80 % (15197)------------------------------
% 0.41/0.80 % (15197)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.41/0.80 % (15197)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.41/0.80 % (15197)Termination reason: Unknown
% 0.41/0.80 % (15197)Termination phase: Preprocessing 1
% 0.41/0.80
% 0.41/0.80 % (15197)Memory used [KB]: 10874
% 0.41/0.80 % (15197)Time elapsed: 0.067 s
% 0.41/0.80 % (15197)Instructions burned: 69 (million)
% 0.41/0.80 % (15197)------------------------------
% 0.41/0.80 % (15197)------------------------------
% 0.41/0.82 % (15186)Instruction limit reached!
% 0.41/0.82 % (15186)------------------------------
% 0.41/0.82 % (15186)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.41/0.82 % (15186)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.41/0.82 % (15186)Termination reason: Unknown
% 0.41/0.82 % (15186)Termination phase: Preprocessing 1
% 0.41/0.82
% 0.41/0.82 % (15186)Memory used [KB]: 10362
% 0.41/0.82 % (15186)Time elapsed: 0.029 s
% 0.41/0.82 % (15186)Instructions burned: 52 (million)
% 0.41/0.82 % (15186)------------------------------
% 0.41/0.82 % (15186)------------------------------
% 0.41/0.83 % (15193)Instruction limit reached!
% 0.41/0.83 % (15193)------------------------------
% 0.41/0.83 % (15193)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.41/0.83 % (15193)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.41/0.83 % (15193)Termination reason: Unknown
% 0.41/0.83 % (15193)Termination phase: Preprocessing 1
% 0.41/0.83
% 0.41/0.83 % (15193)Memory used [KB]: 10234
% 0.41/0.83 % (15193)Time elapsed: 0.033 s
% 0.41/0.83 % (15193)Instructions burned: 51 (million)
% 0.41/0.83 % (15193)------------------------------
% 0.41/0.83 % (15193)------------------------------
% 0.75/0.83 % (15188)Instruction limit reached!
% 0.75/0.83 % (15188)------------------------------
% 0.75/0.83 % (15188)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.75/0.83 % (15188)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.75/0.83 % (15188)Termination reason: Unknown
% 0.75/0.83 % (15188)Termination phase: Preprocessing 1
% 0.75/0.83
% 0.75/0.83 % (15188)Memory used [KB]: 10106
% 0.75/0.83 % (15188)Time elapsed: 0.031 s
% 0.75/0.83 % (15188)Instructions burned: 48 (million)
% 0.75/0.83 % (15188)------------------------------
% 0.75/0.83 % (15188)------------------------------
% 0.75/0.83 % (15196)Instruction limit reached!
% 0.75/0.83 % (15196)------------------------------
% 0.75/0.83 % (15196)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.75/0.83 % (15196)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.75/0.83 % (15196)Termination reason: Unknown
% 0.75/0.83 % (15196)Termination phase: Preprocessing 1
% 0.75/0.83
% 0.75/0.83 % (15196)Memory used [KB]: 12025
% 0.75/0.83 % (15196)Time elapsed: 0.060 s
% 0.75/0.83 % (15196)Instructions burned: 99 (million)
% 0.75/0.83 % (15196)------------------------------
% 0.75/0.83 % (15196)------------------------------
% 0.75/0.83 % (15184)Instruction limit reached!
% 0.75/0.83 % (15184)------------------------------
% 0.75/0.83 % (15184)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.75/0.83 % (15184)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.75/0.83 % (15184)Termination reason: Unknown
% 0.75/0.83 % (15184)Termination phase: Preprocessing 1
% 0.75/0.83
% 0.75/0.83 % (15184)Memory used [KB]: 10234
% 0.75/0.83 % (15184)Time elapsed: 0.032 s
% 0.75/0.83 % (15184)Instructions burned: 51 (million)
% 0.75/0.83 % (15184)------------------------------
% 0.75/0.83 % (15184)------------------------------
% 0.75/0.84 % (15192)Instruction limit reached!
% 0.75/0.84 % (15192)------------------------------
% 0.75/0.84 % (15192)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.75/0.84 % (15192)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.75/0.84 % (15192)Termination reason: Unknown
% 0.75/0.84 % (15192)Termination phase: Preprocessing 1
% 0.75/0.84
% 0.75/0.84 % (15192)Memory used [KB]: 10234
% 0.75/0.84 % (15192)Time elapsed: 0.032 s
% 0.75/0.84 % (15192)Instructions burned: 51 (million)
% 0.75/0.84 % (15192)------------------------------
% 0.75/0.84 % (15192)------------------------------
% 0.75/0.85 % (15187)Instruction limit reached!
% 0.75/0.85 % (15187)------------------------------
% 0.75/0.85 % (15187)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.75/0.85 % (15187)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.75/0.85 % (15187)Termination reason: Unknown
% 0.75/0.85 % (15187)Termination phase: Preprocessing 1
% 0.75/0.85
% 0.75/0.85 % (15187)Memory used [KB]: 7931
% 0.75/0.85 % (15187)Time elapsed: 0.039 s
% 0.75/0.85 % (15187)Instructions burned: 51 (million)
% 0.75/0.85 % (15187)------------------------------
% 0.75/0.85 % (15187)------------------------------
% 1.25/0.86 % (15198)Instruction limit reached!
% 1.25/0.86 % (15198)------------------------------
% 1.25/0.86 % (15198)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.25/0.86 % (15198)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.25/0.86 % (15198)Termination reason: Unknown
% 1.25/0.86 % (15198)Termination phase: Preprocessing 1
% 1.25/0.86
% 1.25/0.86 % (15198)Memory used [KB]: 11257
% 1.25/0.86 % (15198)Time elapsed: 0.055 s
% 1.25/0.86 % (15198)Instructions burned: 77 (million)
% 1.25/0.86 % (15198)------------------------------
% 1.25/0.86 % (15198)------------------------------
% 1.25/0.87 % (15209)Instruction limit reached!
% 1.25/0.87 % (15209)------------------------------
% 1.25/0.87 % (15209)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.25/0.87 % (15209)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.25/0.87 % (15209)Termination reason: Unknown
% 1.25/0.87 % (15209)Termination phase: Preprocessing 1
% 1.25/0.87
% 1.25/0.87 % (15209)Memory used [KB]: 10874
% 1.25/0.87 % (15209)Time elapsed: 0.048 s
% 1.25/0.87 % (15209)Instructions burned: 68 (million)
% 1.25/0.87 % (15209)------------------------------
% 1.25/0.87 % (15209)------------------------------
% 1.25/0.87 % (15213)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=388:si=on:rawr=on:rtra=on_0 on theBenchmark for (2995ds/388Mi)
% 1.25/0.87 % (15200)Instruction limit reached!
% 1.25/0.87 % (15200)------------------------------
% 1.25/0.87 % (15200)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.25/0.87 % (15200)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.25/0.87 % (15200)Termination reason: Unknown
% 1.25/0.87 % (15200)Termination phase: Preprocessing 1
% 1.25/0.87
% 1.25/0.87 % (15200)Memory used [KB]: 10490
% 1.25/0.87 % (15200)Time elapsed: 0.037 s
% 1.25/0.87 % (15200)Instructions burned: 60 (million)
% 1.25/0.87 % (15200)------------------------------
% 1.25/0.87 % (15200)------------------------------
% 1.25/0.87 % (15194)Instruction limit reached!
% 1.25/0.87 % (15194)------------------------------
% 1.25/0.87 % (15194)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.25/0.87 % (15194)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.25/0.87 % (15194)Termination reason: Unknown
% 1.25/0.87 % (15194)Termination phase: Preprocessing 1
% 1.25/0.87
% 1.25/0.87 % (15194)Memory used [KB]: 12153
% 1.25/0.87 % (15194)Time elapsed: 0.058 s
% 1.25/0.87 % (15194)Instructions burned: 100 (million)
% 1.25/0.87 % (15194)------------------------------
% 1.25/0.87 % (15194)------------------------------
% 1.25/0.89 % (15216)ott+1_1:2_i=920:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/920Mi)
% 1.25/0.89 % (15202)Instruction limit reached!
% 1.25/0.89 % (15202)------------------------------
% 1.25/0.89 % (15202)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.25/0.89 % (15202)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.25/0.89 % (15202)Termination reason: Unknown
% 1.25/0.89 % (15202)Termination phase: Preprocessing 1
% 1.25/0.89
% 1.25/0.89 % (15202)Memory used [KB]: 8571
% 1.25/0.89 % (15202)Time elapsed: 0.064 s
% 1.25/0.89 % (15202)Instructions burned: 100 (million)
% 1.25/0.89 % (15202)------------------------------
% 1.25/0.89 % (15202)------------------------------
% 1.25/0.91 % (15215)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/90Mi)
% 1.25/0.91 % (15214)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=211:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/211Mi)
% 1.25/0.92 % (15195)Instruction limit reached!
% 1.25/0.92 % (15195)------------------------------
% 1.25/0.92 % (15195)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.25/0.92 % (15199)Instruction limit reached!
% 1.25/0.92 % (15199)------------------------------
% 1.25/0.92 % (15199)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.25/0.92 % (15199)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.25/0.92 % (15199)Termination reason: Unknown
% 1.25/0.92 % (15199)Termination phase: Preprocessing 1
% 1.25/0.92
% 1.25/0.92 % (15199)Memory used [KB]: 12025
% 1.25/0.92 % (15199)Time elapsed: 0.057 s
% 1.25/0.92 % (15199)Instructions burned: 99 (million)
% 1.25/0.92 % (15199)------------------------------
% 1.25/0.92 % (15199)------------------------------
% 1.25/0.92 % (15195)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.25/0.92 % (15195)Termination reason: Unknown
% 1.25/0.92 % (15195)Termination phase: Preprocessing 1
% 1.25/0.92
% 1.25/0.92 % (15195)Memory used [KB]: 12153
% 1.25/0.92 % (15195)Time elapsed: 0.077 s
% 1.25/0.92 % (15195)Instructions burned: 101 (million)
% 1.25/0.92 % (15195)------------------------------
% 1.25/0.92 % (15195)------------------------------
% 1.25/0.92 % (15201)Instruction limit reached!
% 1.25/0.92 % (15201)------------------------------
% 1.25/0.92 % (15201)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.25/0.92 % (15201)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.25/0.92 % (15201)Termination reason: Unknown
% 1.25/0.92 % (15201)Termination phase: Preprocessing 1
% 1.25/0.92
% 1.25/0.92 % (15201)Memory used [KB]: 12153
% 1.25/0.92 % (15201)Time elapsed: 0.065 s
% 1.25/0.92 % (15201)Instructions burned: 101 (million)
% 1.25/0.92 % (15201)------------------------------
% 1.25/0.92 % (15201)------------------------------
% 1.91/0.95 % (15217)ott+1_1:7_bd=off:i=934:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/934Mi)
% 1.91/0.95 % (15203)Instruction limit reached!
% 1.91/0.95 % (15203)------------------------------
% 1.91/0.95 % (15203)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.91/0.95 % (15203)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.91/0.95 % (15203)Termination reason: Unknown
% 1.91/0.95 % (15203)Termination phase: Unused predicate definition removal
% 1.91/0.95
% 1.91/0.95 % (15203)Memory used [KB]: 12792
% 1.91/0.95 % (15203)Time elapsed: 0.105 s
% 1.91/0.95 % (15203)Instructions burned: 177 (million)
% 1.91/0.95 % (15203)------------------------------
% 1.91/0.95 % (15203)------------------------------
% 1.91/0.96 % (15221)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=940:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/940Mi)
% 1.91/0.96 % (15219)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=655:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/655Mi)
% 1.91/0.96 % (15218)ott+10_1:50_bsr=unit_only:drc=off:fd=preordered:sp=frequency:i=747:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/747Mi)
% 2.15/0.97 WARNING Broken Constraint: if sine_depth(2) has been set then sine_selection(off) is not equal to off
% 2.15/0.97 % (15222)ott+11_4:1_br=off:fde=none:s2a=on:sd=2:sp=frequency:urr=on:i=981:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/981Mi)
% 2.15/0.97 % (15223)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/90Mi)
% 2.15/0.98 % (15220)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/68Mi)
% 2.15/0.98 % (15224)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=2016:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/2016Mi)
% 2.15/0.99 % (15204)Instruction limit reached!
% 2.15/0.99 % (15204)------------------------------
% 2.15/0.99 % (15204)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.15/0.99 % (15204)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.15/0.99 % (15204)Termination reason: Unknown
% 2.15/0.99 % (15204)Termination phase: Preprocessing 3
% 2.15/0.99
% 2.15/0.99 % (15204)Memory used [KB]: 14839
% 2.15/0.99 % (15204)Time elapsed: 0.117 s
% 2.15/0.99 % (15204)Instructions burned: 138 (million)
% 2.15/0.99 % (15204)------------------------------
% 2.15/0.99 % (15204)------------------------------
% 2.15/1.00 % (15225)dis+10_1:2_atotf=0.3:i=3735:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/3735Mi)
% 2.15/1.01 % (15227)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=4959:si=on:rawr=on:rtra=on_0 on theBenchmark for (2993ds/4959Mi)
% 2.15/1.01 % (15226)ott+11_9:8_add=large:afp=10:amm=off:fsd=on:fsr=off:lma=on:nm=0:nwc=2.4:s2a=on:s2agt=10:sas=z3:sp=reverse_arity:tha=some:thi=overlap:i=4958:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/4958Mi)
% 2.15/1.02 % (15228)ott+10_1:1_kws=precedence:tgt=ground:i=4756:si=on:rawr=on:rtra=on_0 on theBenchmark for (2993ds/4756Mi)
% 2.15/1.02 % (15210)Instruction limit reached!
% 2.15/1.02 % (15210)------------------------------
% 2.15/1.02 % (15210)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.15/1.02 % (15210)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.15/1.02 % (15210)Termination reason: Unknown
% 2.15/1.02 % (15210)Termination phase: Preprocessing 3
% 2.15/1.02
% 2.15/1.02 % (15210)Memory used [KB]: 16119
% 2.15/1.02 % (15210)Time elapsed: 0.108 s
% 2.15/1.02 % (15210)Instructions burned: 179 (million)
% 2.15/1.02 % (15210)------------------------------
% 2.15/1.02 % (15210)------------------------------
% 2.15/1.03 % (15229)ott+3_1:1_atotf=0.2:fsr=off:kws=precedence:sp=weighted_frequency:spb=intro:tgt=ground:i=4931:si=on:rawr=on:rtra=on_0 on theBenchmark for (2993ds/4931Mi)
% 2.15/1.03 % (15230)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2993ds/68Mi)
% 2.42/1.05 % (15231)ott+11_9:8_amm=off:bsd=on:etr=on:fsd=on:fsr=off:lma=on:newcnf=on:nm=0:nwc=3.0:s2a=on:s2agt=10:sas=z3:tha=some:i=1824:si=on:rawr=on:rtra=on_0 on theBenchmark for (2993ds/1824Mi)
% 2.42/1.06 % (15215)Instruction limit reached!
% 2.42/1.06 % (15215)------------------------------
% 2.42/1.06 % (15215)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.42/1.06 % (15232)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=2134:si=on:rawr=on:rtra=on_0 on theBenchmark for (2993ds/2134Mi)
% 2.42/1.06 % (15215)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.42/1.06 % (15215)Termination reason: Unknown
% 2.42/1.06 % (15215)Termination phase: Preprocessing 1
% 2.42/1.06
% 2.42/1.06 % (15215)Memory used [KB]: 10362
% 2.42/1.06 % (15215)Time elapsed: 0.071 s
% 2.42/1.06 % (15215)Instructions burned: 91 (million)
% 2.42/1.06 % (15215)------------------------------
% 2.42/1.06 % (15215)------------------------------
% 2.42/1.06 % (15233)ott-1_1:1_sp=const_frequency:i=2891:si=on:rawr=on:rtra=on_0 on theBenchmark for (2993ds/2891Mi)
% 4.38/1.09 % (15234)dis+2_1:64_add=large:bce=on:bd=off:i=4585:si=on:rawr=on:rtra=on_0 on theBenchmark for (2992ds/4585Mi)
% 4.38/1.11 % (15220)Instruction limit reached!
% 4.38/1.11 % (15220)------------------------------
% 4.38/1.11 % (15220)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 4.38/1.11 % (15220)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 4.38/1.11 % (15220)Termination reason: Unknown
% 4.38/1.11 % (15220)Termination phase: Preprocessing 1
% 4.38/1.11
% 4.38/1.11 % (15220)Memory used [KB]: 10874
% 4.38/1.11 % (15220)Time elapsed: 0.038 s
% 4.38/1.11 % (15220)Instructions burned: 68 (million)
% 4.38/1.11 % (15220)------------------------------
% 4.38/1.11 % (15220)------------------------------
% 4.38/1.12 % (15230)Instruction limit reached!
% 4.38/1.12 % (15230)------------------------------
% 4.38/1.12 % (15230)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 4.86/1.15 % (15230)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 4.86/1.15 % (15230)Termination reason: Unknown
% 4.86/1.15 % (15230)Termination phase: Preprocessing 1
% 4.86/1.15
% 4.86/1.15 % (15230)Memory used [KB]: 10874
% 4.86/1.15 % (15230)Time elapsed: 0.047 s
% 4.86/1.15 % (15230)Instructions burned: 70 (million)
% 4.86/1.15 % (15230)------------------------------
% 4.86/1.15 % (15230)------------------------------
% 4.86/1.17 % (15223)Instruction limit reached!
% 4.86/1.17 % (15223)------------------------------
% 4.86/1.17 % (15223)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 5.07/1.17 % (15235)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2992ds/90Mi)
% 5.07/1.18 % (15223)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 5.07/1.18 % (15223)Termination reason: Unknown
% 5.07/1.18 % (15223)Termination phase: Preprocessing 1
% 5.07/1.18
% 5.07/1.18 % (15223)Memory used [KB]: 10362
% 5.07/1.18 % (15223)Time elapsed: 0.055 s
% 5.07/1.18 % (15223)Instructions burned: 90 (million)
% 5.07/1.18 % (15223)------------------------------
% 5.07/1.18 % (15223)------------------------------
% 5.07/1.21 % (15236)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=2016:si=on:rawr=on:rtra=on_0 on theBenchmark for (2991ds/2016Mi)
% 5.07/1.22 % (15237)dis+10_1:2_atotf=0.3:i=8004:si=on:rawr=on:rtra=on_0 on theBenchmark for (2991ds/8004Mi)
% 5.70/1.27 % (15238)ott+11_9:8_add=large:afp=10:amm=off:fsd=on:fsr=off:lma=on:nm=0:nwc=2.4:s2a=on:s2agt=10:sas=z3:sp=reverse_arity:tha=some:thi=overlap:i=9965:si=on:rawr=on:rtra=on_0 on theBenchmark for (2991ds/9965Mi)
% 5.70/1.30 % (15214)Instruction limit reached!
% 5.70/1.30 % (15214)------------------------------
% 5.70/1.30 % (15214)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 5.70/1.30 % (15214)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 5.70/1.30 % (15214)Termination reason: Unknown
% 5.70/1.30 % (15214)Termination phase: Preprocessing 3
% 5.70/1.30
% 5.70/1.30 % (15214)Memory used [KB]: 17142
% 5.70/1.30 % (15214)Time elapsed: 0.114 s
% 5.70/1.30 % (15214)Instructions burned: 212 (million)
% 5.70/1.30 % (15214)------------------------------
% 5.70/1.30 % (15214)------------------------------
% 6.24/1.33 % (15239)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=9877:si=on:rawr=on:rtra=on_0 on theBenchmark for (2990ds/9877Mi)
% 6.52/1.37 % (15235)Instruction limit reached!
% 6.52/1.37 % (15235)------------------------------
% 6.52/1.37 % (15235)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 6.52/1.37 % (15235)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 6.52/1.37 % (15235)Termination reason: Unknown
% 6.52/1.37 % (15235)Termination phase: Preprocessing 1
% 6.52/1.37
% 6.52/1.37 % (15235)Memory used [KB]: 10362
% 6.52/1.37 % (15235)Time elapsed: 0.061 s
% 6.52/1.37 % (15235)Instructions burned: 90 (million)
% 6.52/1.37 % (15235)------------------------------
% 6.52/1.37 % (15235)------------------------------
% 6.52/1.38 % (15212)Instruction limit reached!
% 6.52/1.38 % (15212)------------------------------
% 6.52/1.38 % (15212)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 6.52/1.38 % (15212)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 6.52/1.38 % (15212)Termination reason: Unknown
% 6.52/1.38 % (15212)Termination phase: Property scanning
% 6.52/1.38
% 6.52/1.38 % (15212)Memory used [KB]: 22131
% 6.52/1.38 % (15212)Time elapsed: 0.191 s
% 6.52/1.38 % (15212)Instructions burned: 356 (million)
% 6.52/1.38 % (15212)------------------------------
% 6.52/1.38 % (15212)------------------------------
% 6.52/1.39 % (15211)Instruction limit reached!
% 6.52/1.39 % (15211)------------------------------
% 6.52/1.39 % (15211)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 6.52/1.39 % (15211)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 6.52/1.39 % (15211)Termination reason: Unknown
% 6.52/1.39 % (15211)Termination phase: Property scanning
% 6.52/1.39
% 6.52/1.39 % (15211)Memory used [KB]: 22131
% 6.52/1.39 % (15211)Time elapsed: 0.270 s
% 6.52/1.39 % (15211)Instructions burned: 441 (million)
% 6.52/1.39 % (15211)------------------------------
% 6.52/1.39 % (15211)------------------------------
% 6.52/1.43 % (15205)Instruction limit reached!
% 6.52/1.43 % (15205)------------------------------
% 6.52/1.43 % (15205)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 6.52/1.43 % (15205)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 6.52/1.43 % (15205)Termination reason: Unknown
% 6.52/1.43 % (15205)Termination phase: Function definition elimination
% 6.52/1.43
% 6.52/1.43 % (15205)Memory used [KB]: 22259
% 6.52/1.43 % (15205)Time elapsed: 0.268 s
% 6.52/1.43 % (15205)Instructions burned: 499 (million)
% 6.52/1.43 % (15205)------------------------------
% 6.52/1.43 % (15205)------------------------------
% 7.02/1.44 % (15240)ins+10_1:16_bce=on:fde=unused:igpr=on:igs=35:igwr=on:sp=const_frequency:tgt=full:to=lpo:i=9902:si=on:rawr=on:rtra=on_0 on theBenchmark for (2989ds/9902Mi)
% 7.02/1.45 % (15213)Instruction limit reached!
% 7.02/1.45 % (15213)------------------------------
% 7.02/1.45 % (15213)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 7.02/1.45 % (15213)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 7.02/1.45 % (15213)Termination reason: Unknown
% 7.02/1.45 % (15213)Termination phase: Property scanning
% 7.02/1.45
% 7.02/1.45 % (15213)Memory used [KB]: 22131
% 7.02/1.45 % (15213)Time elapsed: 0.212 s
% 7.02/1.45 % (15213)Instructions burned: 389 (million)
% 7.02/1.45 % (15213)------------------------------
% 7.02/1.45 % (15213)------------------------------
% 7.17/1.47 % (15206)Instruction limit reached!
% 7.17/1.47 % (15206)------------------------------
% 7.17/1.47 % (15206)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 7.17/1.47 % (15206)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 7.17/1.47 % (15206)Termination reason: Unknown
% 7.17/1.47 % (15206)Termination phase: Property scanning
% 7.17/1.47
% 7.17/1.47 % (15206)Memory used [KB]: 22131
% 7.17/1.47 % (15206)Time elapsed: 0.235 s
% 7.17/1.47 % (15206)Instructions burned: 468 (million)
% 7.17/1.47 % (15206)------------------------------
% 7.17/1.47 % (15206)------------------------------
% 7.17/1.48 % (15207)Instruction limit reached!
% 7.17/1.48 % (15207)------------------------------
% 7.17/1.48 % (15207)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 7.17/1.48 % (15207)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 7.17/1.48 % (15207)Termination reason: Unknown
% 7.17/1.48 % (15207)Termination phase: Function definition elimination
% 7.17/1.48
% 7.17/1.48 % (15207)Memory used [KB]: 22387
% 7.17/1.48 % (15207)Time elapsed: 0.223 s
% 7.17/1.48 % (15207)Instructions burned: 483 (million)
% 7.17/1.48 % (15207)------------------------------
% 7.17/1.48 % (15207)------------------------------
% 7.17/1.50 % (15241)ott+11_9:8_amm=off:bsd=on:etr=on:fsd=on:fsr=off:lma=on:newcnf=on:nm=0:nwc=3.0:s2a=on:s2agt=10:sas=z3:tha=some:i=1824:si=on:rawr=on:rtra=on_0 on theBenchmark for (2988ds/1824Mi)
% 7.52/1.53 % (15242)dis+2_1:64_add=large:bce=on:bd=off:i=9989:si=on:rawr=on:rtra=on_0 on theBenchmark for (2988ds/9989Mi)
% 7.52/1.54 % (15243)ott-11_1:32_i=9707:si=on:rawr=on:rtra=on_0 on theBenchmark for (2988ds/9707Mi)
% 7.52/1.55 % (15208)Instruction limit reached!
% 7.52/1.55 % (15208)------------------------------
% 7.52/1.55 % (15208)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 7.65/1.56 % (15208)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 7.65/1.56 % (15208)Termination reason: Unknown
% 7.65/1.56 % (15208)Termination phase: Function definition elimination
% 7.65/1.56
% 7.65/1.56 % (15208)Memory used [KB]: 22515
% 7.65/1.56 % (15208)Time elapsed: 0.233 s
% 7.65/1.56 % (15208)Instructions burned: 500 (million)
% 7.65/1.56 % (15208)------------------------------
% 7.65/1.56 % (15208)------------------------------
% 7.65/1.57 % (15245)ott+3_1:1_abs=on:anc=none:bs=on:fsr=off:spb=goal_then_units:i=44001:si=on:rawr=on:rtra=on_0 on theBenchmark for (2988ds/44001Mi)
% 7.65/1.58 % (15244)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2988ds/90Mi)
% 7.65/1.61 % (15246)ott+11_9:8_add=large:afp=10:amm=off:fsd=on:fsr=off:lma=on:nm=0:nwc=2.4:s2a=on:s2agt=10:sas=z3:sp=reverse_arity:tha=some:thi=overlap:i=4958:si=on:rawr=on:rtra=on_0 on theBenchmark for (2987ds/4958Mi)
% 7.65/1.62 % (15247)ott+1_27:428_av=off:awrs=converge:awrsf=8:bsr=unit_only:drc=off:fd=preordered:newcnf=on:nwc=1.5:skr=on:slsq=on:slsqc=2:slsql=off:slsqr=1,4:sp=reverse_frequency:uwa=one_side_constant:i=35256:si=on:rawr=on:rtra=on_0 on theBenchmark for (2987ds/35256Mi)
% 9.12/1.73 % (15248)dis+1002_1:1_fde=unused:nwc=10.0:s2a=on:s2at=3.0:sac=on:i=32293:si=on:rawr=on:rtra=on_0 on theBenchmark for (2987ds/32293Mi)
% 9.72/1.77 % (15244)Instruction limit reached!
% 9.72/1.77 % (15244)------------------------------
% 9.72/1.77 % (15244)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 9.87/1.78 % (15244)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 9.87/1.78 % (15244)Termination reason: Unknown
% 9.87/1.78 % (15244)Termination phase: Preprocessing 1
% 9.87/1.78
% 9.87/1.78 % (15244)Memory used [KB]: 10362
% 9.87/1.78 % (15244)Time elapsed: 0.055 s
% 9.87/1.78 % (15244)Instructions burned: 91 (million)
% 9.87/1.78 % (15244)------------------------------
% 9.87/1.78 % (15244)------------------------------
% 10.47/1.92 % (15249)ott+21_1:28_afr=on:anc=all_dependent:bs=on:bsr=unit_only:nicw=on:sp=const_frequency:uhcvi=on:i=37001:si=on:rawr=on:rtra=on_0 on theBenchmark for (2984ds/37001Mi)
% 11.08/1.95 % (15219)Instruction limit reached!
% 11.08/1.95 % (15219)------------------------------
% 11.08/1.95 % (15219)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 11.08/1.95 % (15219)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 11.08/1.95 % (15219)Termination reason: Unknown
% 11.08/1.95 % (15219)Termination phase: Property scanning
% 11.08/1.95
% 11.08/1.95 % (15219)Memory used [KB]: 22899
% 11.08/1.95 % (15219)Time elapsed: 0.290 s
% 11.08/1.95 % (15219)Instructions burned: 656 (million)
% 11.08/1.95 % (15219)------------------------------
% 11.08/1.95 % (15219)------------------------------
% 11.52/2.03 % (15218)Instruction limit reached!
% 11.52/2.03 % (15218)------------------------------
% 11.52/2.03 % (15218)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 11.52/2.03 % (15218)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 11.52/2.03 % (15218)Termination reason: Unknown
% 11.52/2.03 % (15218)Termination phase: Saturation
% 11.52/2.03
% 11.52/2.03 % (15218)Memory used [KB]: 28272
% 11.52/2.03 % (15218)Time elapsed: 0.313 s
% 11.52/2.03 % (15218)Instructions burned: 748 (million)
% 11.52/2.03 % (15218)------------------------------
% 11.52/2.03 % (15218)------------------------------
% 12.05/2.06 % (15250)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=10187:si=on:rawr=on:rtra=on_0 on theBenchmark for (2983ds/10187Mi)
% 12.53/2.14 % (15221)Instruction limit reached!
% 12.53/2.14 % (15221)------------------------------
% 12.53/2.14 % (15221)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 12.93/2.15 % (15221)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 12.93/2.15 % (15221)Termination reason: Unknown
% 12.93/2.15 % (15221)Termination phase: Saturation
% 12.93/2.15
% 12.93/2.15 % (15221)Memory used [KB]: 28528
% 12.93/2.15 % (15221)Time elapsed: 0.398 s
% 12.93/2.15 % (15221)Instructions burned: 941 (million)
% 12.93/2.15 % (15221)------------------------------
% 12.93/2.15 % (15221)------------------------------
% 12.93/2.20 % (15251)ott+3_1:1_atotf=0.2:fsr=off:kws=precedence:sp=weighted_frequency:spb=intro:tgt=ground:i=29337:si=on:rawr=on:rtra=on_0 on theBenchmark for (2982ds/29337Mi)
% 13.59/2.25 % (15217)Instruction limit reached!
% 13.59/2.25 % (15217)------------------------------
% 13.59/2.25 % (15217)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 13.59/2.25 % (15217)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 13.59/2.25 % (15217)Termination reason: Unknown
% 13.59/2.25 % (15217)Termination phase: Saturation
% 13.59/2.25
% 13.59/2.25 % (15217)Memory used [KB]: 29551
% 13.59/2.25 % (15217)Time elapsed: 0.536 s
% 13.59/2.25 % (15217)Instructions burned: 935 (million)
% 13.59/2.25 % (15217)------------------------------
% 13.59/2.25 % (15217)------------------------------
% 13.59/2.26 % (15252)ins+10_1:16_bce=on:fde=unused:igpr=on:igs=35:igwr=on:sp=const_frequency:tgt=full:to=lpo:i=10147:si=on:rawr=on:rtra=on_0 on theBenchmark for (2981ds/10147Mi)
% 13.59/2.28 % (15216)Instruction limit reached!
% 13.59/2.28 % (15216)------------------------------
% 13.59/2.28 % (15216)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 14.01/2.29 % (15216)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 14.01/2.29 % (15216)Termination reason: Unknown
% 14.01/2.29 % (15216)Termination phase: Saturation
% 14.01/2.29
% 14.01/2.29 % (15216)Memory used [KB]: 30958
% 14.01/2.29 % (15216)Time elapsed: 0.446 s
% 14.01/2.29 % (15216)Instructions burned: 921 (million)
% 14.01/2.29 % (15216)------------------------------
% 14.01/2.29 % (15216)------------------------------
% 14.50/2.39 % (15253)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=38056:si=on:rawr=on:rtra=on_0 on theBenchmark for (2980ds/38056Mi)
% 14.82/2.44 % (15254)fmb+10_1:1_dr=on:fmbsr=2.0:newcnf=on:nm=2:i=33239:si=on:rawr=on:rtra=on_0 on theBenchmark for (2979ds/33239Mi)
% 15.11/2.54 % (15222)Instruction limit reached!
% 15.11/2.54 % (15222)------------------------------
% 15.11/2.54 % (15222)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 15.76/2.55 % (15222)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 15.76/2.55 % (15222)Termination reason: Unknown
% 15.76/2.55 % (15222)Termination phase: Saturation
% 15.76/2.55
% 15.76/2.55 % (15222)Memory used [KB]: 31854
% 15.76/2.55 % (15222)Time elapsed: 0.512 s
% 15.76/2.55 % (15222)Instructions burned: 982 (million)
% 15.76/2.55 % (15222)------------------------------
% 15.76/2.55 % (15222)------------------------------
% 16.65/2.68 % (15255)fmb+10_1:1_fmbas=predicate:gsp=on:nm=2:i=20987:si=on:rawr=on:rtra=on_0 on theBenchmark for (2977ds/20987Mi)
% 25.59/3.75 % (15231)Instruction limit reached!
% 25.59/3.75 % (15231)------------------------------
% 25.59/3.75 % (15231)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 25.59/3.75 % (15231)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 25.59/3.75 % (15231)Termination reason: Unknown
% 25.59/3.75 % (15231)Termination phase: Saturation
% 25.59/3.75
% 25.59/3.75 % (15231)Memory used [KB]: 31854
% 25.59/3.75 % (15231)Time elapsed: 0.981 s
% 25.59/3.75 % (15231)Instructions burned: 1826 (million)
% 25.59/3.75 % (15231)------------------------------
% 25.59/3.75 % (15231)------------------------------
% 26.48/3.86 % (15256)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=49917:si=on:rawr=on:rtra=on_0 on theBenchmark for (2965ds/49917Mi)
% 29.75/4.30 % (15241)Instruction limit reached!
% 29.75/4.30 % (15241)------------------------------
% 29.75/4.30 % (15241)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 29.75/4.30 % (15241)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 29.75/4.30 % (15241)Termination reason: Unknown
% 29.75/4.30 % (15241)Termination phase: Saturation
% 29.75/4.30
% 29.75/4.30 % (15241)Memory used [KB]: 31470
% 29.75/4.30 % (15241)Time elapsed: 0.862 s
% 29.75/4.30 % (15241)Instructions burned: 1824 (million)
% 29.75/4.30 % (15241)------------------------------
% 29.75/4.30 % (15241)------------------------------
% 30.64/4.41 % (15224)Instruction limit reached!
% 30.64/4.41 % (15224)------------------------------
% 30.64/4.41 % (15224)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 30.64/4.41 % (15224)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 30.64/4.41 % (15224)Termination reason: Unknown
% 30.64/4.41 % (15224)Termination phase: Saturation
% 30.64/4.41
% 30.64/4.41 % (15224)Memory used [KB]: 32110
% 30.64/4.41 % (15224)Time elapsed: 3.530 s
% 30.64/4.41 % (15224)Instructions burned: 2017 (million)
% 30.64/4.41 % (15224)------------------------------
% 30.64/4.41 % (15224)------------------------------
% 30.64/4.44 % (15232)Instruction limit reached!
% 30.64/4.44 % (15232)------------------------------
% 30.64/4.44 % (15232)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 30.64/4.44 % (15232)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 30.64/4.44 % (15232)Termination reason: Unknown
% 30.64/4.44 % (15232)Termination phase: Saturation
% 30.64/4.44
% 30.64/4.44 % (15232)Memory used [KB]: 46438
% 30.64/4.44 % (15232)Time elapsed: 3.469 s
% 30.64/4.44 % (15232)Instructions burned: 2134 (million)
% 30.64/4.44 % (15232)------------------------------
% 30.64/4.44 % (15232)------------------------------
% 31.14/4.44 % (15257)dis+2_1:64_add=large:bce=on:bd=off:i=19144:si=on:rawr=on:rtra=on_0 on theBenchmark for (2959ds/19144Mi)
% 31.32/4.49 % (15236)Instruction limit reached!
% 31.32/4.49 % (15236)------------------------------
% 31.32/4.49 % (15236)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 31.32/4.49 % (15236)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 31.32/4.49 % (15236)Termination reason: Unknown
% 31.32/4.49 % (15236)Termination phase: Saturation
% 31.32/4.49
% 31.32/4.49 % (15236)Memory used [KB]: 32622
% 31.32/4.49 % (15236)Time elapsed: 3.378 s
% 31.32/4.49 % (15236)Instructions burned: 2016 (million)
% 31.32/4.49 % (15236)------------------------------
% 31.32/4.49 % (15236)------------------------------
% 31.32/4.52 % (15258)dis+10_1:128_bd=off:lcm=predicate:sac=on:sp=reverse_arity:urr=on:i=27492:si=on:rawr=on:rtra=on_0 on theBenchmark for (2958ds/27492Mi)
% 32.01/4.61 % (15259)ott-11_1:32_i=6101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2958ds/6101Mi)
% 32.54/4.66 % (15260)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2957ds/90Mi)
% 33.95/4.83 % (15260)Instruction limit reached!
% 33.95/4.83 % (15260)------------------------------
% 33.95/4.83 % (15260)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 33.95/4.84 % (15260)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 33.95/4.84 % (15260)Termination reason: Unknown
% 33.95/4.84 % (15260)Termination phase: Preprocessing 1
% 33.95/4.84
% 33.95/4.84 % (15260)Memory used [KB]: 10362
% 33.95/4.84 % (15260)Time elapsed: 0.056 s
% 33.95/4.84 % (15260)Instructions burned: 91 (million)
% 33.95/4.84 % (15260)------------------------------
% 33.95/4.84 % (15260)------------------------------
% 35.07/4.98 % (15261)ott+11_1:128_av=off:bd=off:bsr=unit_only:fd=preordered:to=lpo:updr=off:i=91600:si=on:rawr=on:rtra=on_0 on theBenchmark for (2954ds/91600Mi)
% 46.37/6.36 % (15233)Instruction limit reached!
% 46.37/6.36 % (15233)------------------------------
% 46.37/6.36 % (15233)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 46.37/6.36 % (15233)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 46.37/6.36 % (15233)Termination reason: Unknown
% 46.37/6.36 % (15233)Termination phase: Saturation
% 46.37/6.36
% 46.37/6.36 % (15233)Memory used [KB]: 43368
% 46.37/6.36 % (15233)Time elapsed: 4.744 s
% 46.37/6.36 % (15233)Instructions burned: 2891 (million)
% 46.37/6.36 % (15233)------------------------------
% 46.37/6.36 % (15233)------------------------------
% 47.13/6.49 % (15262)ott+11_9:8_add=large:afp=10:amm=off:fsd=on:fsr=off:lma=on:nm=0:nwc=2.4:s2a=on:s2agt=10:sas=z3:sp=reverse_arity:tha=some:thi=overlap:i=7127:si=on:rawr=on:rtra=on_0 on theBenchmark for (2939ds/7127Mi)
% 53.56/7.28 % (15225)Instruction limit reached!
% 53.56/7.28 % (15225)------------------------------
% 53.56/7.28 % (15225)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 53.56/7.28 % (15225)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 53.56/7.28 % (15225)Termination reason: Unknown
% 53.56/7.28 % (15225)Termination phase: Saturation
% 53.56/7.28
% 53.56/7.28 % (15225)Memory used [KB]: 61406
% 53.56/7.28 % (15225)Time elapsed: 6.374 s
% 53.56/7.28 % (15225)Instructions burned: 3735 (million)
% 53.56/7.28 % (15225)------------------------------
% 53.56/7.28 % (15225)------------------------------
% 55.14/7.46 % (15263)ott+1_27:428_av=off:awrs=converge:awrsf=8:bsr=unit_only:drc=off:fd=preordered:newcnf=on:nwc=1.5:skr=on:slsq=on:slsqc=2:slsql=off:slsqr=1,4:sp=reverse_frequency:uwa=one_side_constant:i=35256:si=on:rawr=on:rtra=on_0 on theBenchmark for (2929ds/35256Mi)
% 59.24/8.01 % (15234)Instruction limit reached!
% 59.24/8.01 % (15234)------------------------------
% 59.24/8.01 % (15234)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 59.24/8.01 % (15234)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 59.24/8.01 % (15234)Termination reason: Unknown
% 59.24/8.01 % (15234)Termination phase: Saturation
% 59.24/8.01
% 59.24/8.01 % (15234)Memory used [KB]: 48485
% 59.24/8.01 % (15234)Time elapsed: 6.964 s
% 59.24/8.01 % (15234)Instructions burned: 4586 (million)
% 59.24/8.01 % (15234)------------------------------
% 59.24/8.01 % (15234)------------------------------
% 60.68/8.17 % (15264)dis+1002_1:1_fde=unused:nwc=10.0:s2a=on:s2at=3.0:sac=on:i=32293:si=on:rawr=on:rtra=on_0 on theBenchmark for (2922ds/32293Mi)
% 67.76/9.14 % (15226)Instruction limit reached!
% 67.76/9.14 % (15226)------------------------------
% 67.76/9.14 % (15226)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 68.52/9.14 % (15226)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 68.52/9.14 % (15226)Termination reason: Unknown
% 68.52/9.14 % (15226)Termination phase: Saturation
% 68.52/9.14
% 68.52/9.14 % (15226)Memory used [KB]: 38378
% 68.52/9.14 % (15226)Time elapsed: 3.0000 s
% 68.52/9.14 % (15226)Instructions burned: 4958 (million)
% 68.52/9.14 % (15226)------------------------------
% 68.52/9.14 % (15226)------------------------------
% 69.50/9.27 % (15265)ott+3_1:1_atotf=0.2:fsr=off:kws=precedence:sp=weighted_frequency:spb=intro:tgt=ground:i=29337:si=on:rawr=on:rtra=on_0 on theBenchmark for (2911ds/29337Mi)
% 71.35/9.53 % (15227)Instruction limit reached!
% 71.35/9.53 % (15227)------------------------------
% 71.35/9.53 % (15227)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 71.35/9.53 % (15227)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 71.35/9.53 % (15227)Termination reason: Unknown
% 71.35/9.53 % (15227)Termination phase: Saturation
% 71.35/9.53
% 71.35/9.53 % (15227)Memory used [KB]: 85073
% 71.35/9.53 % (15227)Time elapsed: 8.526 s
% 71.35/9.53 % (15227)Instructions burned: 4959 (million)
% 71.35/9.53 % (15227)------------------------------
% 71.35/9.53 % (15227)------------------------------
% 72.59/9.66 % (15246)Instruction limit reached!
% 72.59/9.66 % (15246)------------------------------
% 72.59/9.66 % (15246)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 72.59/9.67 % (15266)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=99860:si=on:rawr=on:rtra=on_0 on theBenchmark for (2907ds/99860Mi)
% 72.59/9.67 % (15246)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 72.59/9.67 % (15246)Termination reason: Unknown
% 72.59/9.67 % (15246)Termination phase: Saturation
% 72.59/9.67
% 72.59/9.67 % (15246)Memory used [KB]: 38634
% 72.59/9.67 % (15246)Time elapsed: 2.747 s
% 72.59/9.67 % (15246)Instructions burned: 4959 (million)
% 72.59/9.67 % (15246)------------------------------
% 72.59/9.67 % (15246)------------------------------
% 73.70/9.82 % (15267)fmb+10_1:1_fmbas=expand:i=96985:si=on:rawr=on:rtra=on_0 on theBenchmark for (2905ds/96985Mi)
% 74.25/9.88 % (15228)Instruction limit reached!
% 74.25/9.88 % (15228)------------------------------
% 74.25/9.88 % (15228)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 74.25/9.89 % (15228)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 74.25/9.89 % (15228)Termination reason: Unknown
% 74.25/9.89 % (15228)Termination phase: Saturation
% 74.25/9.89
% 74.25/9.89 % (15228)Memory used [KB]: 50916
% 74.25/9.89 % (15228)Time elapsed: 6.434 s
% 74.25/9.89 % (15228)Instructions burned: 4756 (million)
% 74.25/9.89 % (15228)------------------------------
% 74.25/9.89 % (15228)------------------------------
% 75.09/10.03 % (15268)fmb+10_1:1_bce=on:dr=on:fmbsr=1.47:gsp=on:nm=2:skr=on:i=99648:si=on:rawr=on:rtra=on_0 on theBenchmark for (2903ds/99648Mi)
% 79.88/10.63 % (15229)Instruction limit reached!
% 79.88/10.63 % (15229)------------------------------
% 79.88/10.63 % (15229)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 80.45/10.64 % (15229)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 80.45/10.64 % (15229)Termination reason: Unknown
% 80.45/10.64 % (15229)Termination phase: Saturation
% 80.45/10.64
% 80.45/10.64 % (15229)Memory used [KB]: 92493
% 80.45/10.64 % (15229)Time elapsed: 9.721 s
% 80.45/10.64 % (15229)Instructions burned: 4931 (million)
% 80.45/10.64 % (15229)------------------------------
% 80.45/10.64 % (15229)------------------------------
% 81.46/10.77 % (15269)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=99882:si=on:rawr=on:rtra=on_0 on theBenchmark for (2896ds/99882Mi)
% 89.89/11.85 % (15238)First to succeed.
% 91.41/12.02 % (15238)Refutation found. Thanks to Tanya!
% 91.41/12.02 % SZS status Theorem for theBenchmark
% 91.41/12.02 % SZS output start Proof for theBenchmark
% See solution above
% 91.41/12.04 % (15238)------------------------------
% 91.41/12.04 % (15238)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 91.41/12.04 % (15238)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 91.41/12.04 % (15238)Termination reason: Refutation
% 91.41/12.04
% 91.41/12.04 % (15238)Memory used [KB]: 41321
% 91.41/12.04 % (15238)Time elapsed: 10.611 s
% 91.41/12.04 % (15238)Instructions burned: 6728 (million)
% 91.41/12.04 % (15238)------------------------------
% 91.41/12.04 % (15238)------------------------------
% 91.41/12.04 % (15182)Success in time 11.774 s
%------------------------------------------------------------------------------