TSTP Solution File: LCL755-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL755-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 18:55:30 EDT 2023
% Result : Unsatisfiable 0.29s 0.55s
% Output : Refutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 109
% Syntax : Number of formulae : 172 ( 102 unt; 0 def)
% Number of atoms : 253 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 132 ( 51 ~; 26 |; 0 &)
% ( 55 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 91 ( 89 usr; 56 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 71 (; 71 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1075,plain,
$false,
inference(avatar_sat_refutation,[],[f818,f822,f827,f832,f837,f842,f847,f852,f857,f862,f867,f872,f877,f882,f887,f892,f897,f902,f907,f912,f917,f922,f927,f932,f937,f942,f947,f952,f957,f962,f967,f972,f977,f981,f985,f989,f993,f997,f1001,f1005,f1009,f1013,f1017,f1021,f1027,f1032,f1036,f1040,f1044,f1048,f1052,f1056,f1060,f1064,f1068,f1074]) ).
fof(f1074,plain,
( ~ spl0_2
| spl0_46 ),
inference(avatar_contradiction_clause,[],[f1073]) ).
fof(f1073,plain,
( $false
| ~ spl0_2
| spl0_46 ),
inference(resolution,[],[f1031,f821]) ).
fof(f821,plain,
( ! [X11,X9] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X9),X11))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f820]) ).
fof(f820,plain,
( spl0_2
<=> ! [X9,X11] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X9),X11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f1031,plain,
( ~ c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))
| spl0_46 ),
inference(avatar_component_clause,[],[f1029]) ).
fof(f1029,plain,
( spl0_46
<=> c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f1068,plain,
spl0_55,
inference(avatar_split_clause,[],[f692,f1066]) ).
fof(f1066,plain,
( spl0_55
<=> ! [X9,X15] :
( ~ c_InductTermi_OIT(X15)
| c_InductTermi_OIT(c_Lambda_Olift(X15,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f692,axiom,
! [X9,X15] :
( ~ c_InductTermi_OIT(X15)
| c_InductTermi_OIT(c_Lambda_Olift(X15,X9)) ),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_lift__IT_0) ).
fof(f1064,plain,
spl0_54,
inference(avatar_split_clause,[],[f689,f1062]) ).
fof(f1062,plain,
( spl0_54
<=> ! [X37,X30,X31] : c_Lambda_OdB_OApp(X30,X31) != c_Lambda_OdB_OVar(X37) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f689,axiom,
! [X31,X37,X30] : c_Lambda_OdB_OApp(X30,X31) != c_Lambda_OdB_OVar(X37),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_dB_Osimps_I4_J_0) ).
fof(f1060,plain,
spl0_53,
inference(avatar_split_clause,[],[f667,f1058]) ).
fof(f1058,plain,
( spl0_53
<=> ! [X29,X36,X28] : c_Lambda_OdB_OApp(X28,X29) != c_Lambda_OdB_OAbs(X36) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f667,axiom,
! [X28,X29,X36] : c_Lambda_OdB_OApp(X28,X29) != c_Lambda_OdB_OAbs(X36),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_dB_Osimps_I8_J_0) ).
fof(f1056,plain,
spl0_52,
inference(avatar_split_clause,[],[f581,f1054]) ).
fof(f1054,plain,
( spl0_52
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f581,axiom,
! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X1,X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_order__eq__refl_0) ).
fof(f1052,plain,
spl0_51,
inference(avatar_split_clause,[],[f580,f1050]) ).
fof(f1050,plain,
( spl0_51
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f580,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_order__eq__iff_0) ).
fof(f1048,plain,
spl0_50,
inference(avatar_split_clause,[],[f364,f1046]) ).
fof(f1046,plain,
( spl0_50
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f364,axiom,
! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_order__less__irrefl_0) ).
fof(f1044,plain,
spl0_49,
inference(avatar_split_clause,[],[f363,f1042]) ).
fof(f1042,plain,
( spl0_49
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f363,axiom,
! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_linorder__neq__iff_1) ).
fof(f1040,plain,
spl0_48,
inference(avatar_split_clause,[],[f362,f1038]) ).
fof(f1038,plain,
( spl0_48
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f362,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_order__less__le_1) ).
fof(f1036,plain,
spl0_47,
inference(avatar_split_clause,[],[f311,f1034]) ).
fof(f1034,plain,
( spl0_47
<=> ! [X8] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X8),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f311,axiom,
! [X8] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X8),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_zero__less__Suc_0) ).
fof(f1032,plain,
( ~ spl0_46
| spl0_33
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f1022,f1019,f974,f1029]) ).
fof(f974,plain,
( spl0_33
<=> c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f1019,plain,
( spl0_44
<=> ! [X34] :
( ~ c_InductTermi_OIT(X34)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f1022,plain,
( ~ c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))
| spl0_33
| ~ spl0_44 ),
inference(resolution,[],[f1020,f976]) ).
fof(f976,plain,
( ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja))))
| spl0_33 ),
inference(avatar_component_clause,[],[f974]) ).
fof(f1020,plain,
( ! [X34] :
( c_InductTermi_OIT(c_Lambda_OdB_OAbs(X34))
| ~ c_InductTermi_OIT(X34) )
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f1019]) ).
fof(f1027,plain,
spl0_45,
inference(avatar_split_clause,[],[f176,f1024]) ).
fof(f1024,plain,
( spl0_45
<=> c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f176,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_One__nat__def_0) ).
fof(f1021,plain,
spl0_44,
inference(avatar_split_clause,[],[f710,f1019]) ).
fof(f710,axiom,
! [X34] :
( ~ c_InductTermi_OIT(X34)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(X34)) ),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_Lambda_0) ).
fof(f1017,plain,
spl0_43,
inference(avatar_split_clause,[],[f685,f1015]) ).
fof(f1015,plain,
( spl0_43
<=> ! [X38] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X38) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f685,axiom,
! [X38] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X38),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_nat_Osimps_I3_J_0) ).
fof(f1013,plain,
spl0_42,
inference(avatar_split_clause,[],[f681,f1011]) ).
fof(f1011,plain,
( spl0_42
<=> ! [X1] : c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f681,axiom,
! [X1] : c_HOL_Oord__class_Oless(X1,c_Suc(X1),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_less__Suc__eq_2) ).
fof(f1009,plain,
spl0_41,
inference(avatar_split_clause,[],[f675,f1007]) ).
fof(f1007,plain,
( spl0_41
<=> ! [X8] : ~ c_lessequals(c_Suc(X8),X8,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f675,axiom,
! [X8] : ~ c_lessequals(c_Suc(X8),X8,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_Suc__n__not__le__n_0) ).
fof(f1005,plain,
spl0_40,
inference(avatar_split_clause,[],[f666,f1003]) ).
fof(f1003,plain,
( spl0_40
<=> ! [X36,X37] : c_Lambda_OdB_OAbs(X36) != c_Lambda_OdB_OVar(X37) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f666,axiom,
! [X36,X37] : c_Lambda_OdB_OAbs(X36) != c_Lambda_OdB_OVar(X37),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_dB_Osimps_I7_J_0) ).
fof(f1001,plain,
spl0_39,
inference(avatar_split_clause,[],[f342,f999]) ).
fof(f999,plain,
( spl0_39
<=> ! [X8] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f342,axiom,
! [X8] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_le0_0) ).
fof(f997,plain,
spl0_38,
inference(avatar_split_clause,[],[f147,f995]) ).
fof(f995,plain,
( spl0_38
<=> ! [X8] : ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f147,axiom,
! [X8] : ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_not__less0_0) ).
fof(f993,plain,
spl0_37,
inference(avatar_split_clause,[],[f683,f991]) ).
fof(f991,plain,
( spl0_37
<=> ! [X9,X15] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X9),X15) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f683,axiom,
! [X9,X15] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X9),X15),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_beta__cases_I1_J_0) ).
fof(f989,plain,
spl0_36,
inference(avatar_split_clause,[],[f673,f987]) ).
fof(f987,plain,
( spl0_36
<=> ! [X8] : c_Suc(X8) != X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f673,axiom,
! [X8] : c_Suc(X8) != X8,
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_Suc__n__not__n_0) ).
fof(f985,plain,
spl0_35,
inference(avatar_split_clause,[],[f579,f983]) ).
fof(f983,plain,
( spl0_35
<=> ! [X1] : c_lessequals(X1,X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f579,axiom,
! [X1] : c_lessequals(X1,X1,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_eq__imp__le_0) ).
fof(f981,plain,
spl0_34,
inference(avatar_split_clause,[],[f360,f979]) ).
fof(f979,plain,
( spl0_34
<=> ! [X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f360,axiom,
! [X1] : ~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_nat__less__le_1) ).
fof(f977,plain,
~ spl0_33,
inference(avatar_split_clause,[],[f725,f974]) ).
fof(f725,axiom,
~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_conjecture_2) ).
fof(f972,plain,
spl0_32,
inference(avatar_split_clause,[],[f755,f969]) ).
fof(f969,plain,
( spl0_32
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f755,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__Orderings_Oorder) ).
fof(f967,plain,
spl0_31,
inference(avatar_split_clause,[],[f754,f964]) ).
fof(f964,plain,
( spl0_31
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f754,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__Orderings_Olinorder) ).
fof(f962,plain,
spl0_30,
inference(avatar_split_clause,[],[f753,f959]) ).
fof(f959,plain,
( spl0_30
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f753,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__Orderings_Opreorder) ).
fof(f957,plain,
spl0_29,
inference(avatar_split_clause,[],[f752,f954]) ).
fof(f954,plain,
( spl0_29
<=> class_Divides_Osemiring__div(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f752,axiom,
class_Divides_Osemiring__div(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__Divides_Osemiring__div) ).
fof(f952,plain,
spl0_28,
inference(avatar_split_clause,[],[f751,f949]) ).
fof(f949,plain,
( spl0_28
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f751,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f947,plain,
spl0_27,
inference(avatar_split_clause,[],[f750,f944]) ).
fof(f944,plain,
( spl0_27
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f750,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(f942,plain,
spl0_26,
inference(avatar_split_clause,[],[f749,f939]) ).
fof(f939,plain,
( spl0_26
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f749,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(f937,plain,
spl0_25,
inference(avatar_split_clause,[],[f748,f934]) ).
fof(f934,plain,
( spl0_25
<=> class_Ring__and__Field_Omult__mono(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f748,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(f932,plain,
spl0_24,
inference(avatar_split_clause,[],[f747,f929]) ).
fof(f929,plain,
( spl0_24
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f747,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f927,plain,
spl0_23,
inference(avatar_split_clause,[],[f746,f924]) ).
fof(f924,plain,
( spl0_23
<=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f746,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(f922,plain,
spl0_22,
inference(avatar_split_clause,[],[f745,f919]) ).
fof(f919,plain,
( spl0_22
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f745,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(f917,plain,
spl0_21,
inference(avatar_split_clause,[],[f744,f914]) ).
fof(f914,plain,
( spl0_21
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f744,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f912,plain,
spl0_20,
inference(avatar_split_clause,[],[f743,f909]) ).
fof(f909,plain,
( spl0_20
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f743,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(f907,plain,
spl0_19,
inference(avatar_split_clause,[],[f742,f904]) ).
fof(f904,plain,
( spl0_19
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f742,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f902,plain,
spl0_18,
inference(avatar_split_clause,[],[f741,f899]) ).
fof(f899,plain,
( spl0_18
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f741,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
fof(f897,plain,
spl0_17,
inference(avatar_split_clause,[],[f740,f894]) ).
fof(f894,plain,
( spl0_17
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f740,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f892,plain,
spl0_16,
inference(avatar_split_clause,[],[f739,f889]) ).
fof(f889,plain,
( spl0_16
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f739,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f887,plain,
spl0_15,
inference(avatar_split_clause,[],[f738,f884]) ).
fof(f884,plain,
( spl0_15
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f738,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f882,plain,
spl0_14,
inference(avatar_split_clause,[],[f737,f879]) ).
fof(f879,plain,
( spl0_14
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f737,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(f877,plain,
spl0_13,
inference(avatar_split_clause,[],[f736,f874]) ).
fof(f874,plain,
( spl0_13
<=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f736,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
fof(f872,plain,
spl0_12,
inference(avatar_split_clause,[],[f735,f869]) ).
fof(f869,plain,
( spl0_12
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f735,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(f867,plain,
spl0_11,
inference(avatar_split_clause,[],[f734,f864]) ).
fof(f864,plain,
( spl0_11
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f734,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f862,plain,
spl0_10,
inference(avatar_split_clause,[],[f733,f859]) ).
fof(f859,plain,
( spl0_10
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f733,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f857,plain,
spl0_9,
inference(avatar_split_clause,[],[f732,f854]) ).
fof(f854,plain,
( spl0_9
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f732,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f852,plain,
spl0_8,
inference(avatar_split_clause,[],[f731,f849]) ).
fof(f849,plain,
( spl0_8
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f731,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f847,plain,
spl0_7,
inference(avatar_split_clause,[],[f730,f844]) ).
fof(f844,plain,
( spl0_7
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f730,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
fof(f842,plain,
spl0_6,
inference(avatar_split_clause,[],[f729,f839]) ).
fof(f839,plain,
( spl0_6
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f729,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f837,plain,
spl0_5,
inference(avatar_split_clause,[],[f728,f834]) ).
fof(f834,plain,
( spl0_5
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f728,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f832,plain,
spl0_4,
inference(avatar_split_clause,[],[f727,f829]) ).
fof(f829,plain,
( spl0_4
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f727,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f827,plain,
spl0_3,
inference(avatar_split_clause,[],[f726,f824]) ).
fof(f824,plain,
( spl0_3
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f726,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f822,plain,
spl0_2,
inference(avatar_split_clause,[],[f724,f820]) ).
fof(f724,axiom,
! [X11,X9] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(X9),X11)),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_conjecture_1) ).
fof(f818,plain,
spl0_1,
inference(avatar_split_clause,[],[f723,f815]) ).
fof(f815,plain,
( spl0_1
<=> c_InductTermi_OIT(v_ra) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f723,axiom,
c_InductTermi_OIT(v_ra),
file('/export/starexec/sandbox2/tmp/tmp.SZN0HMcnOx/Vampire---4.8_27236',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.19 % Problem : LCL755-1 : TPTP v8.1.2. Released v4.1.0.
% 0.20/0.21 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.22/0.43 % Computer : n027.cluster.edu
% 0.22/0.43 % Model : x86_64 x86_64
% 0.22/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.43 % Memory : 8042.1875MB
% 0.22/0.43 % OS : Linux 3.10.0-693.el7.x86_64
% 0.22/0.43 % CPULimit : 300
% 0.22/0.43 % WCLimit : 300
% 0.22/0.43 % DateTime : Wed Aug 30 15:20:54 EDT 2023
% 0.22/0.43 % CPUTime :
% 0.29/0.49 % (27443)Running in auto input_syntax mode. Trying TPTP
% 0.29/0.52 % (27502)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.29/0.52 % (27504)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.29/0.52 % (27506)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.29/0.52 % (27505)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.29/0.52 % (27508)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.29/0.52 % (27509)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.29/0.52 % (27511)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.29/0.54 % (27508)First to succeed.
% 0.29/0.55 % (27509)Also succeeded, but the first one will report.
% 0.29/0.55 % (27508)Refutation found. Thanks to Tanya!
% 0.29/0.55 % SZS status Unsatisfiable for Vampire---4
% 0.29/0.55 % SZS output start Proof for Vampire---4
% See solution above
% 0.29/0.55 % (27508)------------------------------
% 0.29/0.55 % (27508)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.29/0.55 % (27508)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.29/0.55 % (27508)Termination reason: Refutation
% 0.29/0.55
% 0.29/0.55 % (27508)Memory used [KB]: 6780
% 0.29/0.55 % (27508)Time elapsed: 0.029 s
% 0.29/0.55 % (27508)------------------------------
% 0.29/0.55 % (27508)------------------------------
% 0.29/0.55 % (27443)Success in time 0.105 s
% 0.29/0.55 % Vampire---4.8 exiting
%------------------------------------------------------------------------------