TSTP Solution File: GEO036-2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GEO036-2 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n020.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 : Mon May 20 20:13:41 EDT 2024
% Result : Unsatisfiable 0.12s 0.36s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 57
% Syntax : Number of formulae : 141 ( 25 unt; 0 def)
% Number of atoms : 391 ( 32 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 446 ( 196 ~; 212 |; 0 &)
% ( 38 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 42 ( 40 usr; 39 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-6 aty)
% Number of variables : 238 ( 238 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f253,plain,
$false,
inference(avatar_sat_refutation,[],[f32,f38,f44,f49,f55,f60,f66,f70,f74,f78,f82,f87,f92,f96,f102,f106,f112,f116,f122,f126,f132,f138,f145,f152,f156,f163,f171,f175,f191,f199,f208,f213,f218,f220,f232,f237,f242,f247,f249,f252]) ).
fof(f252,plain,
( ~ spl0_26
| spl0_38 ),
inference(avatar_contradiction_clause,[],[f251]) ).
fof(f251,plain,
( $false
| ~ spl0_26
| spl0_38 ),
inference(resolution,[],[f246,f151]) ).
fof(f151,plain,
( ! [X0,X1] : between(X0,X1,X1)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f150,plain,
( spl0_26
<=> ! [X0,X1] : between(X0,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f246,plain,
( ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1)
| spl0_38 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f244,plain,
( spl0_38
<=> between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f249,plain,
( ~ spl0_26
| spl0_37 ),
inference(avatar_contradiction_clause,[],[f248]) ).
fof(f248,plain,
( $false
| ~ spl0_26
| spl0_37 ),
inference(resolution,[],[f241,f151]) ).
fof(f241,plain,
( ~ between(lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_1)
| spl0_37 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f239,plain,
( spl0_37
<=> between(lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f247,plain,
( ~ spl0_38
| ~ spl0_1
| spl0_8 ),
inference(avatar_split_clause,[],[f224,f57,f21,f244]) ).
fof(f21,plain,
( spl0_1
<=> lower_dimension_point_1 = lower_dimension_point_2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f57,plain,
( spl0_8
<=> between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f224,plain,
( ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1)
| ~ spl0_1
| spl0_8 ),
inference(superposition,[],[f59,f23]) ).
fof(f23,plain,
( lower_dimension_point_1 = lower_dimension_point_2
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f59,plain,
( ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| spl0_8 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f242,plain,
( ~ spl0_37
| ~ spl0_1
| spl0_7 ),
inference(avatar_split_clause,[],[f223,f52,f21,f239]) ).
fof(f52,plain,
( spl0_7
<=> between(lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f223,plain,
( ~ between(lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_1)
| ~ spl0_1
| spl0_7 ),
inference(superposition,[],[f54,f23]) ).
fof(f54,plain,
( ~ between(lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_1)
| spl0_7 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f237,plain,
( ~ spl0_36
| ~ spl0_1
| spl0_6 ),
inference(avatar_split_clause,[],[f222,f46,f21,f234]) ).
fof(f234,plain,
( spl0_36
<=> between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f46,plain,
( spl0_6
<=> between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f222,plain,
( ~ between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_1)
| ~ spl0_1
| spl0_6 ),
inference(superposition,[],[f48,f23]) ).
fof(f48,plain,
( ~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| spl0_6 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f232,plain,
( ~ spl0_35
| ~ spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f221,f35,f21,f229]) ).
fof(f229,plain,
( spl0_35
<=> between(lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f35,plain,
( spl0_4
<=> between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f221,plain,
( ~ between(lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_3)
| ~ spl0_1
| spl0_4 ),
inference(superposition,[],[f37,f23]) ).
fof(f37,plain,
( ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| spl0_4 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f220,plain,
( ~ spl0_26
| spl0_33 ),
inference(avatar_contradiction_clause,[],[f219]) ).
fof(f219,plain,
( $false
| ~ spl0_26
| spl0_33 ),
inference(resolution,[],[f212,f151]) ).
fof(f212,plain,
( ~ between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_1)
| spl0_33 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f210,plain,
( spl0_33
<=> between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f218,plain,
( ~ spl0_34
| ~ spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f203,f57,f29,f215]) ).
fof(f215,plain,
( spl0_34
<=> between(lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f29,plain,
( spl0_3
<=> lower_dimension_point_1 = lower_dimension_point_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f203,plain,
( ~ between(lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_2)
| ~ spl0_3
| spl0_8 ),
inference(superposition,[],[f59,f31]) ).
fof(f31,plain,
( lower_dimension_point_1 = lower_dimension_point_3
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f213,plain,
( ~ spl0_33
| ~ spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f202,f46,f29,f210]) ).
fof(f202,plain,
( ~ between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_1)
| ~ spl0_3
| spl0_6 ),
inference(superposition,[],[f48,f31]) ).
fof(f208,plain,
( ~ spl0_32
| ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f201,f35,f29,f205]) ).
fof(f205,plain,
( spl0_32
<=> between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f201,plain,
( ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_1)
| ~ spl0_3
| spl0_4 ),
inference(superposition,[],[f37,f31]) ).
fof(f199,plain,
( spl0_5
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f195]) ).
fof(f195,plain,
( $false
| spl0_5
| ~ spl0_26 ),
inference(resolution,[],[f151,f43]) ).
fof(f43,plain,
( ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_2)
| spl0_5 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f41,plain,
( spl0_5
<=> between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f191,plain,
( spl0_31
| ~ spl0_10
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f127,f124,f68,f189]) ).
fof(f189,plain,
( spl0_31
<=> ! [X0,X3,X2,X1] :
( ~ between(X0,X0,X1)
| ~ equidistant(X0,X1,X0,X2)
| ~ between(X0,X3,X1)
| between(X0,continuous(X0,X0,X0,X3,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f68,plain,
( spl0_10
<=> ! [X0,X1] : equidistant(X0,X1,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f124,plain,
( spl0_22
<=> ! [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_22])]) ).
fof(f127,plain,
( ! [X2,X3,X0,X1] :
( ~ between(X0,X0,X1)
| ~ equidistant(X0,X1,X0,X2)
| ~ between(X0,X3,X1)
| between(X0,continuous(X0,X0,X0,X3,X1,X2),X2) )
| ~ spl0_10
| ~ spl0_22 ),
inference(resolution,[],[f125,f69]) ).
fof(f69,plain,
( ! [X0,X1] : equidistant(X0,X1,X1,X0)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f125,plain,
( ! [X3,X10,X0,X6,X9,X5] :
( ~ equidistant(X10,X3,X10,X9)
| ~ between(X10,X3,X0)
| ~ equidistant(X10,X0,X10,X6)
| ~ between(X3,X5,X0)
| between(X9,continuous(X10,X3,X9,X5,X0,X6),X6) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f175,plain,
( spl0_30
| ~ spl0_11
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f108,f104,f72,f173]) ).
fof(f173,plain,
( spl0_30
<=> ! [X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X1,X3,X2)
| inner_pasch(X1,X3,X2,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f72,plain,
( spl0_11
<=> ! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f104,plain,
( spl0_18
<=> ! [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_18])]) ).
fof(f108,plain,
( ! [X2,X3,X0,X1] :
( ~ between(X0,X1,X2)
| ~ between(X1,X3,X2)
| inner_pasch(X1,X3,X2,X1,X0) = X1 )
| ~ spl0_11
| ~ spl0_18 ),
inference(resolution,[],[f105,f73]) ).
fof(f73,plain,
( ! [X0,X1] :
( ~ between(X0,X1,X0)
| X0 = X1 )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f105,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_18 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f171,plain,
( spl0_29
| ~ spl0_11
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f107,f100,f72,f169]) ).
fof(f169,plain,
( spl0_29
<=> ! [X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X0,X2)
| inner_pasch(X3,X0,X2,X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f100,plain,
( spl0_17
<=> ! [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_17])]) ).
fof(f107,plain,
( ! [X2,X3,X0,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X0,X2)
| inner_pasch(X3,X0,X2,X1,X0) = X0 )
| ~ spl0_11
| ~ spl0_17 ),
inference(resolution,[],[f101,f73]) ).
fof(f101,plain,
( ! [X3,X10,X0,X1,X5] :
( between(X3,inner_pasch(X10,X3,X5,X0,X1),X1)
| ~ between(X1,X0,X5)
| ~ between(X10,X3,X5) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f163,plain,
( spl0_28
| ~ spl0_14
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f98,f94,f85,f161]) ).
fof(f161,plain,
( spl0_28
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ equidistant(X0,extension(X1,X0,X2,X3),X4,X5)
| equidistant(X4,X5,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f85,plain,
( spl0_14
<=> ! [X3,X0,X5,X1] : equidistant(X1,extension(X0,X1,X5,X3),X5,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f94,plain,
( spl0_16
<=> ! [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_16])]) ).
fof(f98,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ equidistant(X0,extension(X1,X0,X2,X3),X4,X5)
| equidistant(X4,X5,X2,X3) )
| ~ spl0_14
| ~ spl0_16 ),
inference(resolution,[],[f95,f86]) ).
fof(f86,plain,
( ! [X3,X0,X1,X5] : equidistant(X1,extension(X0,X1,X5,X3),X5,X3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f95,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3)
| equidistant(X2,X3,X4,X5) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f156,plain,
( spl0_27
| ~ spl0_10
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f97,f94,f68,f154]) ).
fof(f154,plain,
( spl0_27
<=> ! [X0,X3,X2,X1] :
( ~ equidistant(X0,X1,X2,X3)
| equidistant(X2,X3,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f97,plain,
( ! [X2,X3,X0,X1] :
( ~ equidistant(X0,X1,X2,X3)
| equidistant(X2,X3,X1,X0) )
| ~ spl0_10
| ~ spl0_16 ),
inference(resolution,[],[f95,f69]) ).
fof(f152,plain,
( spl0_26
| ~ spl0_13
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f118,f90,f80,f150]) ).
fof(f80,plain,
( spl0_13
<=> ! [X3,X0,X5,X1] : between(X0,X1,extension(X0,X1,X5,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f90,plain,
( spl0_15
<=> ! [X2,X0,X1] : extension(X1,X0,X2,X2) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f118,plain,
( ! [X0,X1] : between(X0,X1,X1)
| ~ spl0_13
| ~ spl0_15 ),
inference(superposition,[],[f81,f91]) ).
fof(f91,plain,
( ! [X2,X0,X1] : extension(X1,X0,X2,X2) = X0
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f81,plain,
( ! [X3,X0,X1,X5] : between(X0,X1,extension(X0,X1,X5,X3))
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f145,plain,
spl0_25,
inference(avatar_split_clause,[],[f6,f143]) ).
fof(f143,plain,
( spl0_25
<=> ! [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_25])]) ).
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/sandbox2/benchmark/theBenchmark.p',outer_five_segment) ).
fof(f138,plain,
spl0_24,
inference(avatar_split_clause,[],[f13,f136]) ).
fof(f136,plain,
( spl0_24
<=> ! [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_24])]) ).
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/sandbox2/benchmark/theBenchmark.p',upper_dimension) ).
fof(f132,plain,
spl0_23,
inference(avatar_split_clause,[],[f18,f130]) ).
fof(f130,plain,
( spl0_23
<=> ! [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_23])]) ).
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/sandbox2/benchmark/theBenchmark.p',continuity2) ).
fof(f126,plain,
spl0_22,
inference(avatar_split_clause,[],[f17,f124]) ).
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/sandbox2/benchmark/theBenchmark.p',continuity1) ).
fof(f122,plain,
spl0_21,
inference(avatar_split_clause,[],[f16,f120]) ).
fof(f120,plain,
( spl0_21
<=> ! [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_21])]) ).
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/sandbox2/benchmark/theBenchmark.p',euclid3) ).
fof(f116,plain,
spl0_20,
inference(avatar_split_clause,[],[f15,f114]) ).
fof(f114,plain,
( spl0_20
<=> ! [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_20])]) ).
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/sandbox2/benchmark/theBenchmark.p',euclid2) ).
fof(f112,plain,
spl0_19,
inference(avatar_split_clause,[],[f14,f110]) ).
fof(f110,plain,
( spl0_19
<=> ! [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_19])]) ).
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/sandbox2/benchmark/theBenchmark.p',euclid1) ).
fof(f106,plain,
spl0_18,
inference(avatar_split_clause,[],[f9,f104]) ).
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/sandbox2/benchmark/theBenchmark.p',inner_pasch2) ).
fof(f102,plain,
spl0_17,
inference(avatar_split_clause,[],[f8,f100]) ).
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/sandbox2/benchmark/theBenchmark.p',inner_pasch1) ).
fof(f96,plain,
spl0_16,
inference(avatar_split_clause,[],[f2,f94]) ).
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/sandbox2/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
fof(f92,plain,
( spl0_15
| ~ spl0_12
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f88,f85,f76,f90]) ).
fof(f76,plain,
( spl0_12
<=> ! [X2,X0,X1] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f88,plain,
( ! [X2,X0,X1] : extension(X1,X0,X2,X2) = X0
| ~ spl0_12
| ~ spl0_14 ),
inference(resolution,[],[f86,f77]) ).
fof(f77,plain,
( ! [X2,X0,X1] :
( ~ equidistant(X0,X1,X2,X2)
| X0 = X1 )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f87,plain,
spl0_14,
inference(avatar_split_clause,[],[f5,f85]) ).
fof(f5,axiom,
! [X3,X0,X1,X5] : equidistant(X1,extension(X0,X1,X5,X3),X5,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction2) ).
fof(f82,plain,
spl0_13,
inference(avatar_split_clause,[],[f4,f80]) ).
fof(f4,axiom,
! [X3,X0,X1,X5] : between(X0,X1,extension(X0,X1,X5,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction1) ).
fof(f78,plain,
spl0_12,
inference(avatar_split_clause,[],[f3,f76]) ).
fof(f3,axiom,
! [X2,X0,X1] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_equidistance) ).
fof(f74,plain,
spl0_11,
inference(avatar_split_clause,[],[f7,f72]) ).
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
fof(f70,plain,
spl0_10,
inference(avatar_split_clause,[],[f1,f68]) ).
fof(f1,axiom,
! [X0,X1] : equidistant(X0,X1,X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
fof(f66,plain,
( ~ spl0_9
| ~ spl0_2
| spl0_8 ),
inference(avatar_split_clause,[],[f61,f57,f25,f63]) ).
fof(f63,plain,
( spl0_9
<=> between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f25,plain,
( spl0_2
<=> lower_dimension_point_2 = lower_dimension_point_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f61,plain,
( ~ between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_2)
| ~ spl0_2
| spl0_8 ),
inference(forward_demodulation,[],[f59,f27]) ).
fof(f27,plain,
( lower_dimension_point_2 = lower_dimension_point_3
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f60,plain,
~ spl0_8,
inference(avatar_split_clause,[],[f12,f57]) ).
fof(f12,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).
fof(f55,plain,
( ~ spl0_7
| ~ spl0_2
| spl0_6 ),
inference(avatar_split_clause,[],[f50,f46,f25,f52]) ).
fof(f50,plain,
( ~ between(lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_1)
| ~ spl0_2
| spl0_6 ),
inference(forward_demodulation,[],[f48,f27]) ).
fof(f49,plain,
~ spl0_6,
inference(avatar_split_clause,[],[f11,f46]) ).
fof(f11,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).
fof(f44,plain,
( ~ spl0_5
| ~ spl0_2
| spl0_4 ),
inference(avatar_split_clause,[],[f39,f35,f25,f41]) ).
fof(f39,plain,
( ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_2)
| ~ spl0_2
| spl0_4 ),
inference(forward_demodulation,[],[f37,f27]) ).
fof(f38,plain,
~ spl0_4,
inference(avatar_split_clause,[],[f10,f35]) ).
fof(f10,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).
fof(f32,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f19,f29,f25,f21]) ).
fof(f19,axiom,
( lower_dimension_point_1 = lower_dimension_point_3
| lower_dimension_point_2 = lower_dimension_point_3
| lower_dimension_point_1 = lower_dimension_point_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_axioms_points_are_distinct) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO036-2 : TPTP v8.2.0. Released v1.0.0.
% 0.03/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun May 19 14:59:38 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % (6961)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.34 % (6962)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.35 % (6966)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)
% 0.12/0.35 % (6965)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.35 TRYING [1]
% 0.12/0.35 TRYING [2]
% 0.12/0.35 % (6968)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)
% 0.12/0.35 % (6966)First to succeed.
% 0.12/0.36 % (6968)Also succeeded, but the first one will report.
% 0.12/0.36 % (6967)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)
% 0.12/0.36 % (6966)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-6961"
% 0.12/0.36 % (6966)Refutation found. Thanks to Tanya!
% 0.12/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.36 % (6966)------------------------------
% 0.12/0.36 % (6966)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.36 % (6966)Termination reason: Refutation
% 0.12/0.36
% 0.12/0.36 % (6966)Memory used [KB]: 948
% 0.12/0.36 % (6966)Time elapsed: 0.010 s
% 0.12/0.36 % (6966)Instructions burned: 14 (million)
% 0.12/0.36 % (6961)Success in time 0.025 s
%------------------------------------------------------------------------------