TSTP Solution File: GEO048-3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GEO048-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -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 : Tue Apr 30 11:13:23 EDT 2024
% Result : Unsatisfiable 0.15s 0.41s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 119
% Syntax : Number of formulae : 197 ( 82 unt; 0 def)
% Number of atoms : 453 ( 59 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 443 ( 187 ~; 195 |; 0 &)
% ( 61 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 65 ( 63 usr; 62 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-6 aty)
% Number of variables : 376 ( 376 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f591,plain,
$false,
inference(avatar_sat_refutation,[],[f84,f89,f94,f99,f104,f109,f114,f119,f124,f129,f134,f138,f142,f146,f150,f154,f158,f162,f166,f172,f176,f180,f184,f199,f205,f211,f215,f219,f223,f227,f231,f235,f240,f244,f277,f282,f286,f302,f306,f310,f332,f349,f353,f370,f374,f378,f382,f386,f430,f434,f461,f466,f470,f488,f492,f514,f523,f537,f546,f563,f573,f590]) ).
fof(f590,plain,
( ~ spl0_8
| ~ spl0_33
| ~ spl0_50
| spl0_52 ),
inference(avatar_split_clause,[],[f524,f463,f432,f237,f116]) ).
fof(f116,plain,
( spl0_8
<=> between(u,x,u1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f237,plain,
( spl0_33
<=> between(w,v1,u1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f432,plain,
( spl0_50
<=> ! [X10,X0,X5,X3,X1] :
( ~ between(X10,X3,X5)
| ~ between(X1,X0,X5)
| between(X0,inner_pasch(X10,X3,X5,X0,X1),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f463,plain,
( spl0_52
<=> between(v1,inner_pasch(u,x,u1,v1,w),u) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f524,plain,
( ~ between(w,v1,u1)
| ~ between(u,x,u1)
| ~ spl0_50
| spl0_52 ),
inference(resolution,[],[f465,f433]) ).
fof(f433,plain,
( ! [X3,X10,X0,X1,X5] :
( between(X0,inner_pasch(X10,X3,X5,X0,X1),X10)
| ~ between(X1,X0,X5)
| ~ between(X10,X3,X5) )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f432]) ).
fof(f465,plain,
( ~ between(v1,inner_pasch(u,x,u1,v1,w),u)
| spl0_52 ),
inference(avatar_component_clause,[],[f463]) ).
fof(f573,plain,
spl0_61,
inference(avatar_split_clause,[],[f6,f571]) ).
fof(f571,plain,
( spl0_61
<=> ! [X2,X3,X9,X0,X8,X6,X1,X7] :
( X0 = X1
| ~ between(X6,X7,X8)
| ~ between(X0,X1,X2)
| ~ equidistant(X1,X3,X7,X9)
| ~ equidistant(X0,X3,X6,X9)
| ~ equidistant(X1,X2,X7,X8)
| ~ equidistant(X0,X1,X6,X7)
| equidistant(X2,X3,X8,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f6,axiom,
! [X2,X3,X0,X1,X8,X6,X9,X7] :
( X0 = X1
| ~ between(X6,X7,X8)
| ~ between(X0,X1,X2)
| ~ equidistant(X1,X3,X7,X9)
| ~ equidistant(X0,X3,X6,X9)
| ~ equidistant(X1,X2,X7,X8)
| ~ equidistant(X0,X1,X6,X7)
| equidistant(X2,X3,X8,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_five_segment) ).
fof(f563,plain,
spl0_60,
inference(avatar_split_clause,[],[f13,f561]) ).
fof(f561,plain,
( spl0_60
<=> ! [X2,X3,X0,X5,X1] :
( X3 = X5
| between(X2,X0,X1)
| between(X1,X2,X0)
| between(X0,X1,X2)
| ~ equidistant(X2,X5,X2,X3)
| ~ equidistant(X1,X5,X1,X3)
| ~ equidistant(X0,X5,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f13,axiom,
! [X2,X3,X0,X1,X5] :
( X3 = X5
| between(X2,X0,X1)
| between(X1,X2,X0)
| between(X0,X1,X2)
| ~ equidistant(X2,X5,X2,X3)
| ~ equidistant(X1,X5,X1,X3)
| ~ equidistant(X0,X5,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upper_dimension) ).
fof(f546,plain,
spl0_59,
inference(avatar_split_clause,[],[f18,f544]) ).
fof(f544,plain,
( spl0_59
<=> ! [X6,X10,X9,X0,X5,X3] :
( ~ between(X3,X5,X0)
| ~ between(X10,X3,X0)
| ~ equidistant(X10,X0,X10,X6)
| ~ equidistant(X10,X3,X10,X9)
| equidistant(X10,X5,X10,continuous(X10,X3,X9,X5,X0,X6)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f18,axiom,
! [X3,X10,X0,X6,X9,X5] :
( ~ between(X3,X5,X0)
| ~ between(X10,X3,X0)
| ~ equidistant(X10,X0,X10,X6)
| ~ equidistant(X10,X3,X10,X9)
| equidistant(X10,X5,X10,continuous(X10,X3,X9,X5,X0,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity2) ).
fof(f537,plain,
spl0_58,
inference(avatar_split_clause,[],[f17,f535]) ).
fof(f535,plain,
( spl0_58
<=> ! [X6,X10,X9,X0,X5,X3] :
( ~ between(X3,X5,X0)
| ~ between(X10,X3,X0)
| ~ equidistant(X10,X0,X10,X6)
| ~ equidistant(X10,X3,X10,X9)
| between(X9,continuous(X10,X3,X9,X5,X0,X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f17,axiom,
! [X3,X10,X0,X6,X9,X5] :
( ~ between(X3,X5,X0)
| ~ between(X10,X3,X0)
| ~ equidistant(X10,X0,X10,X6)
| ~ equidistant(X10,X3,X10,X9)
| between(X9,continuous(X10,X3,X9,X5,X0,X6),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity1) ).
fof(f523,plain,
spl0_57,
inference(avatar_split_clause,[],[f16,f521]) ).
fof(f521,plain,
( spl0_57
<=> ! [X10,X0,X5,X3,X1] :
( X5 = X10
| ~ between(X3,X5,X0)
| ~ between(X10,X5,X1)
| between(euclid1(X10,X3,X5,X0,X1),X1,euclid2(X10,X3,X5,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f16,axiom,
! [X3,X10,X0,X1,X5] :
( X5 = X10
| ~ between(X3,X5,X0)
| ~ between(X10,X5,X1)
| between(euclid1(X10,X3,X5,X0,X1),X1,euclid2(X10,X3,X5,X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',euclid3) ).
fof(f514,plain,
spl0_56,
inference(avatar_split_clause,[],[f37,f512]) ).
fof(f512,plain,
( spl0_56
<=> ! [X5,X10,X11,X12,X9,X3] :
( ~ between(X11,X9,X12)
| ~ between(X10,X3,X5)
| ~ equidistant(X3,X5,X9,X12)
| ~ equidistant(X10,X3,X11,X9)
| equidistant(X10,X5,X11,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f37,axiom,
! [X3,X10,X11,X9,X5,X12] :
( ~ between(X11,X9,X12)
| ~ between(X10,X3,X5)
| ~ equidistant(X3,X5,X9,X12)
| ~ equidistant(X10,X3,X11,X9)
| equidistant(X10,X5,X11,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8) ).
fof(f492,plain,
spl0_55,
inference(avatar_split_clause,[],[f15,f490]) ).
fof(f490,plain,
( spl0_55
<=> ! [X10,X0,X5,X3,X1] :
( X5 = X10
| ~ between(X3,X5,X0)
| ~ between(X10,X5,X1)
| between(X10,X0,euclid2(X10,X3,X5,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f15,axiom,
! [X3,X10,X0,X1,X5] :
( X5 = X10
| ~ between(X3,X5,X0)
| ~ between(X10,X5,X1)
| between(X10,X0,euclid2(X10,X3,X5,X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',euclid2) ).
fof(f488,plain,
spl0_54,
inference(avatar_split_clause,[],[f14,f486]) ).
fof(f486,plain,
( spl0_54
<=> ! [X10,X0,X5,X3,X1] :
( X5 = X10
| ~ between(X3,X5,X0)
| ~ between(X10,X5,X1)
| between(X10,X3,euclid1(X10,X3,X5,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f14,axiom,
! [X3,X10,X0,X1,X5] :
( X5 = X10
| ~ between(X3,X5,X0)
| ~ between(X10,X5,X1)
| between(X10,X3,euclid1(X10,X3,X5,X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',euclid1) ).
fof(f470,plain,
spl0_53,
inference(avatar_split_clause,[],[f40,f468]) ).
fof(f468,plain,
( spl0_53
<=> ! [X5,X10,X0,X3,X2,X1] :
( X3 = X10
| ~ equidistant(X5,X0,X1,X2)
| extension(X10,X3,X5,X0) = extension(X10,X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f40,axiom,
! [X2,X3,X10,X0,X1,X5] :
( X3 = X10
| ~ equidistant(X5,X0,X1,X2)
| extension(X10,X3,X5,X0) = extension(X10,X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_2) ).
fof(f466,plain,
( ~ spl0_52
| ~ spl0_24
| spl0_5
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f446,f432,f101,f196,f463]) ).
fof(f196,plain,
( spl0_24
<=> between(w,v,u) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f101,plain,
( spl0_5
<=> between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f446,plain,
( ~ between(w,v,u)
| ~ between(v1,inner_pasch(u,x,u1,v1,w),u)
| spl0_5
| ~ spl0_50 ),
inference(resolution,[],[f433,f103]) ).
fof(f103,plain,
( ~ between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1)
| spl0_5 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f461,plain,
spl0_51,
inference(avatar_split_clause,[],[f38,f459]) ).
fof(f459,plain,
( spl0_51
<=> ! [X10,X0,X5,X3] :
( X0 = X5
| X3 = X10
| ~ between(X10,X3,X5)
| ~ between(X10,X3,X0)
| ~ equidistant(X3,X5,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f38,axiom,
! [X3,X10,X0,X5] :
( X0 = X5
| X3 = X10
| ~ between(X10,X3,X5)
| ~ between(X10,X3,X0)
| ~ equidistant(X3,X5,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9) ).
fof(f434,plain,
spl0_50,
inference(avatar_split_clause,[],[f9,f432]) ).
fof(f9,axiom,
! [X3,X10,X0,X1,X5] :
( ~ between(X10,X3,X5)
| ~ between(X1,X0,X5)
| between(X0,inner_pasch(X10,X3,X5,X0,X1),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_pasch2) ).
fof(f430,plain,
spl0_49,
inference(avatar_split_clause,[],[f8,f428]) ).
fof(f428,plain,
( spl0_49
<=> ! [X10,X0,X5,X3,X1] :
( ~ between(X10,X3,X5)
| ~ between(X1,X0,X5)
| between(X3,inner_pasch(X10,X3,X5,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f8,axiom,
! [X3,X10,X0,X1,X5] :
( ~ between(X10,X3,X5)
| ~ between(X1,X0,X5)
| between(X3,inner_pasch(X10,X3,X5,X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_pasch1) ).
fof(f386,plain,
spl0_48,
inference(avatar_split_clause,[],[f71,f384]) ).
fof(f384,plain,
( spl0_48
<=> ! [X3,X10] : extension(extension(X10,X3,X10,X3),X3,extension(X10,X3,X10,X3),X3) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f71,plain,
! [X3,X10] : extension(extension(X10,X3,X10,X3),X3,extension(X10,X3,X10,X3),X3) = X10,
inference(definition_unfolding,[],[f43,f19,f19]) ).
fof(f19,axiom,
! [X3,X10] : reflection(X10,X3) = extension(X10,X3,X10,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflection) ).
fof(f43,axiom,
! [X3,X10] : reflection(reflection(X10,X3),X3) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r6) ).
fof(f382,plain,
spl0_47,
inference(avatar_split_clause,[],[f55,f380]) ).
fof(f380,plain,
( spl0_47
<=> ! [X10,X0,X5,X3] :
( X3 = X5
| ~ between(X10,X3,X5)
| ~ between(X3,X5,X0)
| between(X10,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f55,axiom,
! [X3,X10,X0,X5] :
( X3 = X5
| ~ between(X10,X3,X5)
| ~ between(X3,X5,X0)
| between(X10,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b7) ).
fof(f378,plain,
spl0_46,
inference(avatar_split_clause,[],[f54,f376]) ).
fof(f376,plain,
( spl0_46
<=> ! [X10,X0,X5,X3] :
( X3 = X5
| ~ between(X10,X3,X5)
| ~ between(X3,X5,X0)
| between(X10,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f54,axiom,
! [X3,X10,X0,X5] :
( X3 = X5
| ~ between(X10,X3,X5)
| ~ between(X3,X5,X0)
| between(X10,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b6) ).
fof(f374,plain,
spl0_45,
inference(avatar_split_clause,[],[f28,f372]) ).
fof(f372,plain,
( spl0_45
<=> ! [X2,X10,X0,X5,X3,X1] :
( ~ equidistant(X10,X3,X5,X0)
| ~ equidistant(X5,X0,X1,X2)
| equidistant(X10,X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f28,axiom,
! [X2,X3,X10,X0,X1,X5] :
( ~ equidistant(X10,X3,X5,X0)
| ~ equidistant(X5,X0,X1,X2)
| equidistant(X10,X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5) ).
fof(f370,plain,
spl0_44,
inference(avatar_split_clause,[],[f2,f368]) ).
fof(f368,plain,
( spl0_44
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ equidistant(X0,X1,X2,X3)
| ~ equidistant(X0,X1,X4,X5)
| equidistant(X2,X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ equidistant(X0,X1,X2,X3)
| ~ equidistant(X0,X1,X4,X5)
| equidistant(X2,X3,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
fof(f353,plain,
spl0_43,
inference(avatar_split_clause,[],[f41,f351]) ).
fof(f351,plain,
( spl0_43
<=> ! [X3,X10] :
( X3 = X10
| extension(X10,X3,X10,X3) = extension(X10,X3,X3,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f41,axiom,
! [X3,X10] :
( X3 = X10
| extension(X10,X3,X10,X3) = extension(X10,X3,X3,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_3) ).
fof(f349,plain,
spl0_42,
inference(avatar_split_clause,[],[f39,f347]) ).
fof(f347,plain,
( spl0_42
<=> ! [X5,X3,X10] :
( X3 = X10
| ~ between(X10,X3,X5)
| extension(X10,X3,X3,X5) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f39,axiom,
! [X3,X10,X5] :
( X3 = X10
| ~ between(X10,X3,X5)
| extension(X10,X3,X3,X5) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_1) ).
fof(f332,plain,
spl0_41,
inference(avatar_split_clause,[],[f62,f330]) ).
fof(f330,plain,
( spl0_41
<=> ! [X10,X0,X5,X3] : equidistant(X3,extension(X10,X3,lower_dimension_point_1,lower_dimension_point_2),X0,extension(X5,X0,lower_dimension_point_1,lower_dimension_point_2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f62,axiom,
! [X3,X10,X0,X5] : equidistant(X3,extension(X10,X3,lower_dimension_point_1,lower_dimension_point_2),X0,extension(X5,X0,lower_dimension_point_1,lower_dimension_point_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_2) ).
fof(f310,plain,
spl0_40,
inference(avatar_split_clause,[],[f57,f308]) ).
fof(f308,plain,
( spl0_40
<=> ! [X10,X0,X5,X3] :
( ~ between(X10,X3,X5)
| ~ between(X10,X5,X0)
| between(X10,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f57,axiom,
! [X3,X10,X0,X5] :
( ~ between(X10,X3,X5)
| ~ between(X10,X5,X0)
| between(X10,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b9) ).
fof(f306,plain,
spl0_39,
inference(avatar_split_clause,[],[f56,f304]) ).
fof(f304,plain,
( spl0_39
<=> ! [X10,X0,X5,X3] :
( ~ between(X10,X3,X0)
| ~ between(X3,X5,X0)
| between(X10,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f56,axiom,
! [X3,X10,X0,X5] :
( ~ between(X10,X3,X0)
| ~ between(X3,X5,X0)
| between(X10,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b8) ).
fof(f302,plain,
spl0_38,
inference(avatar_split_clause,[],[f53,f300]) ).
fof(f300,plain,
( spl0_38
<=> ! [X10,X0,X5,X3] :
( ~ between(X10,X3,X5)
| ~ between(X10,X5,X0)
| between(X3,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f53,axiom,
! [X3,X10,X0,X5] :
( ~ between(X10,X3,X5)
| ~ between(X10,X5,X0)
| between(X3,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b5) ).
fof(f286,plain,
spl0_37,
inference(avatar_split_clause,[],[f49,f284]) ).
fof(f284,plain,
( spl0_37
<=> ! [X5,X3,X10] :
( X3 = X5
| ~ between(X10,X5,X3)
| ~ between(X10,X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f49,axiom,
! [X3,X10,X5] :
( X3 = X5
| ~ between(X10,X5,X3)
| ~ between(X10,X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b3) ).
fof(f282,plain,
( spl0_36
| ~ spl0_8
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f194,f178,f116,f279]) ).
fof(f279,plain,
( spl0_36
<=> between(u1,x,u) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f178,plain,
( spl0_22
<=> ! [X5,X3,X10] :
( ~ between(X10,X3,X5)
| between(X5,X3,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f194,plain,
( between(u1,x,u)
| ~ spl0_8
| ~ spl0_22 ),
inference(resolution,[],[f179,f118]) ).
fof(f118,plain,
( between(u,x,u1)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f179,plain,
( ! [X3,X10,X5] :
( ~ between(X10,X3,X5)
| between(X5,X3,X10) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f277,plain,
spl0_35,
inference(avatar_split_clause,[],[f48,f275]) ).
fof(f275,plain,
( spl0_35
<=> ! [X5,X3,X10] :
( X3 = X10
| ~ between(X3,X10,X5)
| ~ between(X10,X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f48,axiom,
! [X3,X10,X5] :
( X3 = X10
| ~ between(X3,X10,X5)
| ~ between(X10,X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b2) ).
fof(f244,plain,
spl0_34,
inference(avatar_split_clause,[],[f75,f242]) ).
fof(f242,plain,
( spl0_34
<=> ! [X3,X10] :
( X3 = X10
| extension(X10,X3,X10,X3) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f75,plain,
! [X3,X10] :
( X3 = X10
| extension(X10,X3,X10,X3) != X3 ),
inference(definition_unfolding,[],[f35,f19]) ).
fof(f35,axiom,
! [X3,X10] :
( X3 = X10
| reflection(X10,X3) != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r4) ).
fof(f240,plain,
( spl0_33
| ~ spl0_7
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f193,f178,f111,f237]) ).
fof(f111,plain,
( spl0_7
<=> between(u1,v1,w) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f193,plain,
( between(w,v1,u1)
| ~ spl0_7
| ~ spl0_22 ),
inference(resolution,[],[f179,f113]) ).
fof(f113,plain,
( between(u1,v1,w)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f235,plain,
spl0_32,
inference(avatar_split_clause,[],[f27,f233]) ).
fof(f233,plain,
( spl0_32
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X0,X5,X3,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f27,axiom,
! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X0,X5,X3,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_5) ).
fof(f231,plain,
spl0_31,
inference(avatar_split_clause,[],[f26,f229]) ).
fof(f229,plain,
( spl0_31
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X0,X5,X10,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f26,axiom,
! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X0,X5,X10,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_4) ).
fof(f227,plain,
spl0_30,
inference(avatar_split_clause,[],[f25,f225]) ).
fof(f225,plain,
( spl0_30
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X5,X0,X3,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f25,axiom,
! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X5,X0,X3,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_3) ).
fof(f223,plain,
spl0_29,
inference(avatar_split_clause,[],[f24,f221]) ).
fof(f221,plain,
( spl0_29
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X3,X10,X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f24,axiom,
! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X3,X10,X0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_2) ).
fof(f219,plain,
spl0_28,
inference(avatar_split_clause,[],[f23,f217]) ).
fof(f217,plain,
( spl0_28
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X10,X3,X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f23,axiom,
! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X10,X3,X0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_1) ).
fof(f215,plain,
spl0_27,
inference(avatar_split_clause,[],[f22,f213]) ).
fof(f213,plain,
( spl0_27
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X3,X10,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f22,axiom,
! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X3,X10,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3) ).
fof(f211,plain,
spl0_26,
inference(avatar_split_clause,[],[f21,f209]) ).
fof(f209,plain,
( spl0_26
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X5,X0,X10,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f21,axiom,
! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X5,X0,X10,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
fof(f205,plain,
spl0_25,
inference(avatar_split_clause,[],[f5,f203]) ).
fof(f203,plain,
( spl0_25
<=> ! [X3,X0,X5,X1] : equidistant(X1,extension(X0,X1,X5,X3),X5,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f5,axiom,
! [X3,X0,X1,X5] : equidistant(X1,extension(X0,X1,X5,X3),X5,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
fof(f199,plain,
( spl0_24
| ~ spl0_6
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f192,f178,f106,f196]) ).
fof(f106,plain,
( spl0_6
<=> between(u,v,w) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f192,plain,
( between(w,v,u)
| ~ spl0_6
| ~ spl0_22 ),
inference(resolution,[],[f179,f108]) ).
fof(f108,plain,
( between(u,v,w)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f184,plain,
spl0_23,
inference(avatar_split_clause,[],[f78,f182]) ).
fof(f182,plain,
( spl0_23
<=> ! [X5,X3,X10] :
( ~ between(X10,X5,X10)
| between(X3,X5,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f78,plain,
! [X3,X10,X5] :
( ~ between(X10,X5,X10)
| between(X3,X5,X10) ),
inference(equality_resolution,[],[f45]) ).
fof(f45,axiom,
! [X3,X10,X0,X5] :
( X0 != X10
| ~ between(X10,X5,X0)
| between(X3,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b1) ).
fof(f180,plain,
spl0_22,
inference(avatar_split_clause,[],[f46,f178]) ).
fof(f46,axiom,
! [X3,X10,X5] :
( ~ between(X10,X3,X5)
| between(X5,X3,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).
fof(f176,plain,
spl0_21,
inference(avatar_split_clause,[],[f4,f174]) ).
fof(f174,plain,
( spl0_21
<=> ! [X3,X0,X5,X1] : between(X0,X1,extension(X0,X1,X5,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f4,axiom,
! [X3,X0,X1,X5] : between(X0,X1,extension(X0,X1,X5,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).
fof(f172,plain,
spl0_20,
inference(avatar_split_clause,[],[f3,f170]) ).
fof(f170,plain,
( spl0_20
<=> ! [X2,X0,X1] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f3,axiom,
! [X2,X0,X1] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
fof(f166,plain,
spl0_19,
inference(avatar_split_clause,[],[f61,f164]) ).
fof(f164,plain,
( spl0_19
<=> ! [X3,X10] : extension(X10,X3,lower_dimension_point_1,lower_dimension_point_2) != X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f61,axiom,
! [X3,X10] : extension(X10,X3,lower_dimension_point_1,lower_dimension_point_2) != X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_1) ).
fof(f162,plain,
spl0_18,
inference(avatar_split_clause,[],[f29,f160]) ).
fof(f160,plain,
( spl0_18
<=> ! [X5,X3,X10] : extension(X10,X3,X5,X5) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f29,axiom,
! [X3,X10,X5] : extension(X10,X3,X5,X5) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e1) ).
fof(f158,plain,
spl0_17,
inference(avatar_split_clause,[],[f7,f156]) ).
fof(f156,plain,
( spl0_17
<=> ! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_betweeness) ).
fof(f154,plain,
spl0_16,
inference(avatar_split_clause,[],[f36,f152]) ).
fof(f152,plain,
( spl0_16
<=> ! [X3,X10] : equidistant(X10,X10,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f36,axiom,
! [X3,X10] : equidistant(X10,X10,X3,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7) ).
fof(f150,plain,
spl0_15,
inference(avatar_split_clause,[],[f20,f148]) ).
fof(f148,plain,
( spl0_15
<=> ! [X3,X10] : equidistant(X10,X3,X10,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f20,axiom,
! [X3,X10] : equidistant(X10,X3,X10,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
fof(f146,plain,
spl0_14,
inference(avatar_split_clause,[],[f1,f144]) ).
fof(f144,plain,
( spl0_14
<=> ! [X0,X1] : equidistant(X0,X1,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f1,axiom,
! [X0,X1] : equidistant(X0,X1,X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
fof(f142,plain,
spl0_13,
inference(avatar_split_clause,[],[f47,f140]) ).
fof(f140,plain,
( spl0_13
<=> ! [X3,X10] : between(X10,X10,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f47,axiom,
! [X3,X10] : between(X10,X10,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2) ).
fof(f138,plain,
spl0_12,
inference(avatar_split_clause,[],[f44,f136]) ).
fof(f136,plain,
( spl0_12
<=> ! [X3,X10] : between(X10,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f44,axiom,
! [X3,X10] : between(X10,X3,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3) ).
fof(f134,plain,
~ spl0_11,
inference(avatar_split_clause,[],[f12,f131]) ).
fof(f131,plain,
( spl0_11
<=> between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f12,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension3) ).
fof(f129,plain,
~ spl0_10,
inference(avatar_split_clause,[],[f11,f126]) ).
fof(f126,plain,
( spl0_10
<=> between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f11,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension2) ).
fof(f124,plain,
~ spl0_9,
inference(avatar_split_clause,[],[f10,f121]) ).
fof(f121,plain,
( spl0_9
<=> between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f10,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension1) ).
fof(f119,plain,
spl0_8,
inference(avatar_split_clause,[],[f66,f116]) ).
fof(f66,axiom,
between(u,x,u1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_between_u_and_u1) ).
fof(f114,plain,
spl0_7,
inference(avatar_split_clause,[],[f65,f111]) ).
fof(f65,axiom,
between(u1,v1,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1_between_u1_and_w) ).
fof(f109,plain,
spl0_6,
inference(avatar_split_clause,[],[f64,f106]) ).
fof(f64,axiom,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
fof(f104,plain,
~ spl0_5,
inference(avatar_split_clause,[],[f68,f101]) ).
fof(f68,axiom,
~ between(v,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),v1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_conclusion2) ).
fof(f99,plain,
~ spl0_4,
inference(avatar_split_clause,[],[f67,f96]) ).
fof(f96,plain,
( spl0_4
<=> between(x,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),w) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f67,axiom,
~ between(x,inner_pasch(v1,inner_pasch(u,x,u1,v1,w),u,v,w),w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_conclusion1) ).
fof(f94,plain,
~ spl0_3,
inference(avatar_split_clause,[],[f60,f91]) ).
fof(f91,plain,
( spl0_3
<=> lower_dimension_point_1 = lower_dimension_point_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f60,axiom,
lower_dimension_point_1 != lower_dimension_point_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_3) ).
fof(f89,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f59,f86]) ).
fof(f86,plain,
( spl0_2
<=> lower_dimension_point_2 = lower_dimension_point_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f59,axiom,
lower_dimension_point_2 != lower_dimension_point_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_2) ).
fof(f84,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f58,f81]) ).
fof(f81,plain,
( spl0_1
<=> lower_dimension_point_1 = lower_dimension_point_2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f58,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GEO048-3 : TPTP v8.1.2. Released v1.0.0.
% 0.14/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 30 06:10:02 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (23637)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (23641)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 Detected minimum model sizes of [3]
% 0.15/0.38 Detected maximum model sizes of [max]
% 0.15/0.38 TRYING [3]
% 0.15/0.38 % (23640)WARNING: value z3 for option sas not known
% 0.15/0.38 % (23638)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (23639)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (23640)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38 % (23642)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38 % (23643)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38 % (23644)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.40 % (23642)First to succeed.
% 0.15/0.41 Detected minimum model sizes of [3]
% 0.15/0.41 Detected maximum model sizes of [max]
% 0.15/0.41 % (23642)Refutation found. Thanks to Tanya!
% 0.15/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.41 % (23642)------------------------------
% 0.15/0.41 % (23642)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.41 % (23642)Termination reason: Refutation
% 0.15/0.41
% 0.15/0.41 % (23642)Memory used [KB]: 1152
% 0.15/0.41 % (23642)Time elapsed: 0.026 s
% 0.15/0.41 % (23642)Instructions burned: 38 (million)
% 0.15/0.41 % (23642)------------------------------
% 0.15/0.41 % (23642)------------------------------
% 0.15/0.41 % (23637)Success in time 0.043 s
%------------------------------------------------------------------------------