TSTP Solution File: RNG081+2 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : RNG081+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n023.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 18:14:52 EDT 2022
% Result : Theorem 1.81s 0.58s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 35
% Syntax : Number of formulae : 106 ( 12 unt; 0 def)
% Number of atoms : 1054 ( 412 equ)
% Maximal formula atoms : 76 ( 9 avg)
% Number of connectives : 1103 ( 155 ~; 153 |; 748 &)
% ( 13 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 49 ( 9 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 14 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 18 con; 0-2 aty)
% Number of variables : 322 ( 56 !; 266 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1568,plain,
$false,
inference(avatar_sat_refutation,[],[f439,f445,f484,f486,f531,f534,f787,f987,f1122,f1126,f1146,f1435,f1476,f1562]) ).
fof(f1562,plain,
( ~ spl16_53
| ~ spl16_54
| spl16_136 ),
inference(avatar_split_clause,[],[f1559,f1473,f526,f522]) ).
fof(f522,plain,
( spl16_53
<=> aScalar0(sz0z00) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_53])]) ).
fof(f526,plain,
( spl16_54
<=> sdtlseqdt0(sz0z00,sz0z00) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_54])]) ).
fof(f1473,plain,
( spl16_136
<=> sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sz0z00) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_136])]) ).
fof(f1559,plain,
( ~ sdtlseqdt0(sz0z00,sz0z00)
| ~ aScalar0(sz0z00)
| spl16_136 ),
inference(superposition,[],[f1475,f235]) ).
fof(f235,plain,
! [X0] :
( sz0z00 = sdtasdt0(sz0z00,X0)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ~ aScalar0(X0)
| ( sz0z00 = smndt0(sz0z00)
& smndt0(smndt0(X0)) = X0
& sdtpldt0(X0,sz0z00) = X0
& sdtpldt0(sz0z00,X0) = X0
& sz0z00 = sdtpldt0(X0,smndt0(X0))
& sz0z00 = sdtasdt0(sz0z00,X0)
& sz0z00 = sdtpldt0(smndt0(X0),X0)
& sz0z00 = sdtasdt0(X0,sz0z00) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( aScalar0(X0)
=> ( sz0z00 = smndt0(sz0z00)
& smndt0(smndt0(X0)) = X0
& sdtpldt0(X0,sz0z00) = X0
& sdtpldt0(sz0z00,X0) = X0
& sz0z00 = sdtpldt0(X0,smndt0(X0))
& sz0z00 = sdtasdt0(sz0z00,X0)
& sz0z00 = sdtpldt0(smndt0(X0),X0)
& sz0z00 = sdtasdt0(X0,sz0z00) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScZero) ).
fof(f1475,plain,
( ~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sz0z00)
| spl16_136 ),
inference(avatar_component_clause,[],[f1473]) ).
fof(f1476,plain,
( ~ spl16_68
| ~ spl16_136
| spl16_40
| ~ spl16_107
| ~ spl16_131 ),
inference(avatar_split_clause,[],[f1449,f1432,f1143,f436,f1473,f662]) ).
fof(f662,plain,
( spl16_68
<=> aScalar0(sdtasasdt0(xs,xs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_68])]) ).
fof(f436,plain,
( spl16_40
<=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_40])]) ).
fof(f1143,plain,
( spl16_107
<=> sz0z00 = sdtasasdt0(xt,xt) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_107])]) ).
fof(f1432,plain,
( spl16_131
<=> sz0z00 = sdtasasdt0(xs,xt) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_131])]) ).
fof(f1449,plain,
( ~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sz0z00)
| ~ aScalar0(sdtasasdt0(xs,xs))
| spl16_40
| ~ spl16_107
| ~ spl16_131 ),
inference(superposition,[],[f1438,f233]) ).
fof(f233,plain,
! [X0] :
( sz0z00 = sdtasdt0(X0,sz0z00)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f1438,plain,
( ~ sdtlseqdt0(sdtasdt0(sz0z00,sz0z00),sdtasdt0(sdtasasdt0(xs,xs),sz0z00))
| spl16_40
| ~ spl16_107
| ~ spl16_131 ),
inference(backward_demodulation,[],[f1156,f1434]) ).
fof(f1434,plain,
( sz0z00 = sdtasasdt0(xs,xt)
| ~ spl16_131 ),
inference(avatar_component_clause,[],[f1432]) ).
fof(f1156,plain,
( ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sz0z00))
| spl16_40
| ~ spl16_107 ),
inference(backward_demodulation,[],[f437,f1145]) ).
fof(f1145,plain,
( sz0z00 = sdtasasdt0(xt,xt)
| ~ spl16_107 ),
inference(avatar_component_clause,[],[f1143]) ).
fof(f437,plain,
( ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
| spl16_40 ),
inference(avatar_component_clause,[],[f436]) ).
fof(f1435,plain,
( ~ spl16_44
| spl16_131
| ~ spl16_4
| ~ spl16_104 ),
inference(avatar_split_clause,[],[f1428,f1124,f260,f1432,f464]) ).
fof(f464,plain,
( spl16_44
<=> aVector0(xs) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_44])]) ).
fof(f260,plain,
( spl16_4
<=> sz00 = aDimensionOf0(xs) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_4])]) ).
fof(f1124,plain,
( spl16_104
<=> ! [X1] :
( ~ aVector0(X1)
| sz0z00 = sdtasasdt0(X1,xt)
| sz00 != aDimensionOf0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_104])]) ).
fof(f1428,plain,
( sz0z00 = sdtasasdt0(xs,xt)
| ~ aVector0(xs)
| ~ spl16_4
| ~ spl16_104 ),
inference(trivial_inequality_removal,[],[f1424]) ).
fof(f1424,plain,
( sz0z00 = sdtasasdt0(xs,xt)
| ~ aVector0(xs)
| sz00 != sz00
| ~ spl16_4
| ~ spl16_104 ),
inference(superposition,[],[f1125,f262]) ).
fof(f262,plain,
( sz00 = aDimensionOf0(xs)
| ~ spl16_4 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f1125,plain,
( ! [X1] :
( sz00 != aDimensionOf0(X1)
| ~ aVector0(X1)
| sz0z00 = sdtasasdt0(X1,xt) )
| ~ spl16_104 ),
inference(avatar_component_clause,[],[f1124]) ).
fof(f1146,plain,
( spl16_107
| ~ spl16_42
| ~ spl16_4
| ~ spl16_103 ),
inference(avatar_split_clause,[],[f1139,f1120,f260,f456,f1143]) ).
fof(f456,plain,
( spl16_42
<=> aVector0(xt) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_42])]) ).
fof(f1120,plain,
( spl16_103
<=> ! [X1] :
( sz00 != aDimensionOf0(X1)
| sz0z00 = sdtasasdt0(xt,X1)
| ~ aVector0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_103])]) ).
fof(f1139,plain,
( ~ aVector0(xt)
| sz0z00 = sdtasasdt0(xt,xt)
| ~ spl16_4
| ~ spl16_103 ),
inference(trivial_inequality_removal,[],[f1136]) ).
fof(f1136,plain,
( ~ aVector0(xt)
| sz00 != sz00
| sz0z00 = sdtasasdt0(xt,xt)
| ~ spl16_4
| ~ spl16_103 ),
inference(superposition,[],[f1121,f446]) ).
fof(f446,plain,
( sz00 = aDimensionOf0(xt)
| ~ spl16_4 ),
inference(forward_demodulation,[],[f170,f262]) ).
fof(f170,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678_01) ).
fof(f1121,plain,
( ! [X1] :
( sz00 != aDimensionOf0(X1)
| sz0z00 = sdtasasdt0(xt,X1)
| ~ aVector0(X1) )
| ~ spl16_103 ),
inference(avatar_component_clause,[],[f1120]) ).
fof(f1126,plain,
( ~ spl16_42
| spl16_104
| ~ spl16_4 ),
inference(avatar_split_clause,[],[f1117,f260,f1124,f456]) ).
fof(f1117,plain,
( ! [X1] :
( ~ aVector0(X1)
| ~ aVector0(xt)
| sz00 != aDimensionOf0(X1)
| sz0z00 = sdtasasdt0(X1,xt) )
| ~ spl16_4 ),
inference(trivial_inequality_removal,[],[f1105]) ).
fof(f1105,plain,
( ! [X1] :
( sz00 != sz00
| ~ aVector0(X1)
| ~ aVector0(xt)
| sz00 != aDimensionOf0(X1)
| sz0z00 = sdtasasdt0(X1,xt) )
| ~ spl16_4 ),
inference(superposition,[],[f176,f446]) ).
fof(f176,plain,
! [X0,X1] :
( aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X0)
| sz0z00 = sdtasasdt0(X1,X0)
| ~ aVector0(X1)
| sz00 != aDimensionOf0(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0,X1] :
( sz0z00 = sdtasasdt0(X1,X0)
| ~ aVector0(X1)
| sz00 != aDimensionOf0(X0)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X0) ),
inference(rectify,[],[f67]) ).
fof(f67,plain,
! [X1,X0] :
( sz0z00 = sdtasasdt0(X0,X1)
| ~ aVector0(X0)
| sz00 != aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1) ),
inference(flattening,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( sz0z00 = sdtasasdt0(X0,X1)
| sz00 != aDimensionOf0(X1)
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( ( aVector0(X1)
& aVector0(X0) )
=> ( ( sz00 = aDimensionOf0(X1)
& aDimensionOf0(X0) = aDimensionOf0(X1) )
=> sz0z00 = sdtasasdt0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSPZ) ).
fof(f1122,plain,
( ~ spl16_42
| spl16_103
| ~ spl16_4 ),
inference(avatar_split_clause,[],[f1118,f260,f1120,f456]) ).
fof(f1118,plain,
( ! [X1] :
( sz00 != aDimensionOf0(X1)
| ~ aVector0(xt)
| ~ aVector0(X1)
| sz0z00 = sdtasasdt0(xt,X1) )
| ~ spl16_4 ),
inference(duplicate_literal_removal,[],[f1108]) ).
fof(f1108,plain,
( ! [X1] :
( ~ aVector0(X1)
| sz00 != aDimensionOf0(X1)
| sz00 != aDimensionOf0(X1)
| sz0z00 = sdtasasdt0(xt,X1)
| ~ aVector0(xt) )
| ~ spl16_4 ),
inference(superposition,[],[f176,f446]) ).
fof(f987,plain,
( ~ spl16_44
| spl16_68
| ~ spl16_4
| ~ spl16_77 ),
inference(avatar_split_clause,[],[f986,f785,f260,f662,f464]) ).
fof(f785,plain,
( spl16_77
<=> ! [X0] :
( sz00 != aDimensionOf0(X0)
| aScalar0(sdtasasdt0(xs,X0))
| ~ aVector0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_77])]) ).
fof(f986,plain,
( aScalar0(sdtasasdt0(xs,xs))
| ~ aVector0(xs)
| ~ spl16_4
| ~ spl16_77 ),
inference(trivial_inequality_removal,[],[f980]) ).
fof(f980,plain,
( sz00 != sz00
| ~ aVector0(xs)
| aScalar0(sdtasasdt0(xs,xs))
| ~ spl16_4
| ~ spl16_77 ),
inference(superposition,[],[f786,f262]) ).
fof(f786,plain,
( ! [X0] :
( sz00 != aDimensionOf0(X0)
| aScalar0(sdtasasdt0(xs,X0))
| ~ aVector0(X0) )
| ~ spl16_77 ),
inference(avatar_component_clause,[],[f785]) ).
fof(f787,plain,
( spl16_77
| ~ spl16_44
| ~ spl16_4 ),
inference(avatar_split_clause,[],[f769,f260,f464,f785]) ).
fof(f769,plain,
( ! [X0] :
( ~ aVector0(xs)
| sz00 != aDimensionOf0(X0)
| ~ aVector0(X0)
| aScalar0(sdtasasdt0(xs,X0)) )
| ~ spl16_4 ),
inference(superposition,[],[f171,f262]) ).
fof(f171,plain,
! [X0,X1] :
( aDimensionOf0(X0) != aDimensionOf0(X1)
| aScalar0(sdtasasdt0(X1,X0))
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1] :
( ~ aVector0(X0)
| ~ aVector0(X1)
| aScalar0(sdtasasdt0(X1,X0))
| aDimensionOf0(X0) != aDimensionOf0(X1) ),
inference(flattening,[],[f105]) ).
fof(f105,plain,
! [X1,X0] :
( aScalar0(sdtasasdt0(X1,X0))
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X1)
| ~ aVector0(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,plain,
! [X1,X0] :
( ( aVector0(X1)
& aVector0(X0) )
=> ( aDimensionOf0(X0) = aDimensionOf0(X1)
=> aScalar0(sdtasasdt0(X1,X0)) ) ),
inference(rectify,[],[f34]) ).
fof(f34,axiom,
! [X1,X0] :
( ( aVector0(X1)
& aVector0(X0) )
=> ( aDimensionOf0(X0) = aDimensionOf0(X1)
=> aScalar0(sdtasasdt0(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScPr) ).
fof(f534,plain,
( spl16_54
| ~ spl16_53 ),
inference(avatar_split_clause,[],[f533,f522,f526]) ).
fof(f533,plain,
( ~ aScalar0(sz0z00)
| sdtlseqdt0(sz0z00,sz0z00) ),
inference(duplicate_literal_removal,[],[f532]) ).
fof(f532,plain,
( ~ aScalar0(sz0z00)
| ~ aScalar0(sz0z00)
| sdtlseqdt0(sz0z00,sz0z00) ),
inference(superposition,[],[f178,f235]) ).
fof(f178,plain,
! [X0] :
( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0] :
( sdtlseqdt0(sz0z00,sdtasdt0(X0,X0))
| ~ aScalar0(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( aScalar0(X0)
=> sdtlseqdt0(sz0z00,sdtasdt0(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSqPos) ).
fof(f531,plain,
spl16_53,
inference(avatar_contradiction_clause,[],[f530]) ).
fof(f530,plain,
( $false
| spl16_53 ),
inference(resolution,[],[f524,f241]) ).
fof(f241,plain,
aScalar0(sz0z00),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
fof(f524,plain,
( ~ aScalar0(sz0z00)
| spl16_53 ),
inference(avatar_component_clause,[],[f522]) ).
fof(f486,plain,
spl16_44,
inference(avatar_contradiction_clause,[],[f485]) ).
fof(f485,plain,
( $false
| spl16_44 ),
inference(resolution,[],[f466,f218]) ).
fof(f218,plain,
aVector0(xs),
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
( aVector0(xs)
& aVector0(xt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678) ).
fof(f466,plain,
( ~ aVector0(xs)
| spl16_44 ),
inference(avatar_component_clause,[],[f464]) ).
fof(f484,plain,
spl16_42,
inference(avatar_contradiction_clause,[],[f483]) ).
fof(f483,plain,
( $false
| spl16_42 ),
inference(resolution,[],[f458,f217]) ).
fof(f217,plain,
aVector0(xt),
inference(cnf_transformation,[],[f38]) ).
fof(f458,plain,
( ~ aVector0(xt)
| spl16_42 ),
inference(avatar_component_clause,[],[f456]) ).
fof(f445,plain,
~ spl16_40,
inference(avatar_split_clause,[],[f216,f436]) ).
fof(f216,plain,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
( ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& ( ( aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(sK1))
& ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtlbdtrb0(xs,X1) = sdtlbdtrb0(sK1,X1) )
& aScalar0(sK3)
& aScalar0(sK6)
& sdtasasdt0(sK2,sK2) = sK6
& aScalar0(sK9)
& sdtasdt0(sK5,sK9) = sK11
& aScalar0(sK12)
& aScalar0(sK13)
& sK13 = sdtasdt0(sK8,sK6)
& sK14 = sdtasdt0(sK11,sK13)
& sdtlseqdt0(sdtasdt0(sK7,sK7),sdtasdt0(sK5,sK6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(sK7,sK10),sdtpldt0(sK7,sK10)),sdtasdt0(sdtpldt0(sK5,sK8),sdtpldt0(sK6,sK9)))
& aScalar0(sK14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(sK12,sK12),sdtpldt0(sK11,sK13))
& sK12 = sdtasdt0(sK7,sK10)
& aScalar0(sK11)
& aScalar0(sK10)
& sdtasdt0(sK3,sK4) = sK10
& sK9 = sdtasdt0(sK4,sK4)
& sK8 = sdtasdt0(sK3,sK3)
& aScalar0(sK8)
& sdtasasdt0(sK1,sK2) = sK7
& aScalar0(sK7)
& aScalar0(sK5)
& sK5 = sdtasasdt0(sK1,sK1)
& aScalar0(sK4)
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = sK4
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = sK3
& aDimensionOf0(xt) = szszuzczcdt0(aDimensionOf0(sK2))
& ! [X15] :
( sdtlbdtrb0(sK2,X15) = sdtlbdtrb0(xt,X15)
| ~ aNaturalNumber0(X15) )
& aVector0(sK2)
& sziznziztdt0(xt) = sK2
& sziznziztdt0(xs) = sK1
& aVector0(sK1) )
| sz00 = aDimensionOf0(xs) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14])],[f129,f143,f142,f141,f140,f139,f138,f137,f136,f135,f134,f133,f132,f131,f130]) ).
fof(f130,plain,
( ? [X0] :
( aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(X0))
& ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtlbdtrb0(X0,X1) = sdtlbdtrb0(xs,X1) )
& ? [X2] :
( ? [X3] :
( aScalar0(X3)
& ? [X4] :
( ? [X5] :
( ? [X6] :
( aScalar0(X6)
& sdtasasdt0(X2,X2) = X6
& ? [X7] :
( ? [X8] :
( ? [X9] :
( aScalar0(X9)
& ? [X10] :
( ? [X11] :
( sdtasdt0(X5,X9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(X8,X6) = X13
& ? [X14] :
( sdtasdt0(X11,X13) = X14
& sdtlseqdt0(sdtasdt0(X7,X7),sdtasdt0(X5,X6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X7,X10),sdtpldt0(X7,X10)),sdtasdt0(sdtpldt0(X5,X8),sdtpldt0(X6,X9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13)) ) )
& sdtasdt0(X7,X10) = X12 )
& aScalar0(X11) )
& aScalar0(X10)
& sdtasdt0(X3,X4) = X10 )
& sdtasdt0(X4,X4) = X9 )
& sdtasdt0(X3,X3) = X8
& aScalar0(X8) )
& sdtasasdt0(X0,X2) = X7
& aScalar0(X7) ) )
& aScalar0(X5)
& sdtasasdt0(X0,X0) = X5 )
& aScalar0(X4)
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = X4 )
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = X3 )
& aDimensionOf0(xt) = szszuzczcdt0(aDimensionOf0(X2))
& ! [X15] :
( sdtlbdtrb0(X2,X15) = sdtlbdtrb0(xt,X15)
| ~ aNaturalNumber0(X15) )
& aVector0(X2)
& sziznziztdt0(xt) = X2 )
& sziznziztdt0(xs) = X0
& aVector0(X0) )
=> ( aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(sK1))
& ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtlbdtrb0(xs,X1) = sdtlbdtrb0(sK1,X1) )
& ? [X2] :
( ? [X3] :
( aScalar0(X3)
& ? [X4] :
( ? [X5] :
( ? [X6] :
( aScalar0(X6)
& sdtasasdt0(X2,X2) = X6
& ? [X7] :
( ? [X8] :
( ? [X9] :
( aScalar0(X9)
& ? [X10] :
( ? [X11] :
( sdtasdt0(X5,X9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(X8,X6) = X13
& ? [X14] :
( sdtasdt0(X11,X13) = X14
& sdtlseqdt0(sdtasdt0(X7,X7),sdtasdt0(X5,X6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X7,X10),sdtpldt0(X7,X10)),sdtasdt0(sdtpldt0(X5,X8),sdtpldt0(X6,X9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13)) ) )
& sdtasdt0(X7,X10) = X12 )
& aScalar0(X11) )
& aScalar0(X10)
& sdtasdt0(X3,X4) = X10 )
& sdtasdt0(X4,X4) = X9 )
& sdtasdt0(X3,X3) = X8
& aScalar0(X8) )
& sdtasasdt0(sK1,X2) = X7
& aScalar0(X7) ) )
& aScalar0(X5)
& sdtasasdt0(sK1,sK1) = X5 )
& aScalar0(X4)
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = X4 )
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = X3 )
& aDimensionOf0(xt) = szszuzczcdt0(aDimensionOf0(X2))
& ! [X15] :
( sdtlbdtrb0(X2,X15) = sdtlbdtrb0(xt,X15)
| ~ aNaturalNumber0(X15) )
& aVector0(X2)
& sziznziztdt0(xt) = X2 )
& sziznziztdt0(xs) = sK1
& aVector0(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f131,plain,
( ? [X2] :
( ? [X3] :
( aScalar0(X3)
& ? [X4] :
( ? [X5] :
( ? [X6] :
( aScalar0(X6)
& sdtasasdt0(X2,X2) = X6
& ? [X7] :
( ? [X8] :
( ? [X9] :
( aScalar0(X9)
& ? [X10] :
( ? [X11] :
( sdtasdt0(X5,X9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(X8,X6) = X13
& ? [X14] :
( sdtasdt0(X11,X13) = X14
& sdtlseqdt0(sdtasdt0(X7,X7),sdtasdt0(X5,X6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X7,X10),sdtpldt0(X7,X10)),sdtasdt0(sdtpldt0(X5,X8),sdtpldt0(X6,X9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13)) ) )
& sdtasdt0(X7,X10) = X12 )
& aScalar0(X11) )
& aScalar0(X10)
& sdtasdt0(X3,X4) = X10 )
& sdtasdt0(X4,X4) = X9 )
& sdtasdt0(X3,X3) = X8
& aScalar0(X8) )
& sdtasasdt0(sK1,X2) = X7
& aScalar0(X7) ) )
& aScalar0(X5)
& sdtasasdt0(sK1,sK1) = X5 )
& aScalar0(X4)
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = X4 )
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = X3 )
& aDimensionOf0(xt) = szszuzczcdt0(aDimensionOf0(X2))
& ! [X15] :
( sdtlbdtrb0(X2,X15) = sdtlbdtrb0(xt,X15)
| ~ aNaturalNumber0(X15) )
& aVector0(X2)
& sziznziztdt0(xt) = X2 )
=> ( ? [X3] :
( aScalar0(X3)
& ? [X4] :
( ? [X5] :
( ? [X6] :
( aScalar0(X6)
& sdtasasdt0(sK2,sK2) = X6
& ? [X7] :
( ? [X8] :
( ? [X9] :
( aScalar0(X9)
& ? [X10] :
( ? [X11] :
( sdtasdt0(X5,X9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(X8,X6) = X13
& ? [X14] :
( sdtasdt0(X11,X13) = X14
& sdtlseqdt0(sdtasdt0(X7,X7),sdtasdt0(X5,X6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X7,X10),sdtpldt0(X7,X10)),sdtasdt0(sdtpldt0(X5,X8),sdtpldt0(X6,X9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13)) ) )
& sdtasdt0(X7,X10) = X12 )
& aScalar0(X11) )
& aScalar0(X10)
& sdtasdt0(X3,X4) = X10 )
& sdtasdt0(X4,X4) = X9 )
& sdtasdt0(X3,X3) = X8
& aScalar0(X8) )
& sdtasasdt0(sK1,sK2) = X7
& aScalar0(X7) ) )
& aScalar0(X5)
& sdtasasdt0(sK1,sK1) = X5 )
& aScalar0(X4)
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = X4 )
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = X3 )
& aDimensionOf0(xt) = szszuzczcdt0(aDimensionOf0(sK2))
& ! [X15] :
( sdtlbdtrb0(sK2,X15) = sdtlbdtrb0(xt,X15)
| ~ aNaturalNumber0(X15) )
& aVector0(sK2)
& sziznziztdt0(xt) = sK2 ) ),
introduced(choice_axiom,[]) ).
fof(f132,plain,
( ? [X3] :
( aScalar0(X3)
& ? [X4] :
( ? [X5] :
( ? [X6] :
( aScalar0(X6)
& sdtasasdt0(sK2,sK2) = X6
& ? [X7] :
( ? [X8] :
( ? [X9] :
( aScalar0(X9)
& ? [X10] :
( ? [X11] :
( sdtasdt0(X5,X9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(X8,X6) = X13
& ? [X14] :
( sdtasdt0(X11,X13) = X14
& sdtlseqdt0(sdtasdt0(X7,X7),sdtasdt0(X5,X6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X7,X10),sdtpldt0(X7,X10)),sdtasdt0(sdtpldt0(X5,X8),sdtpldt0(X6,X9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13)) ) )
& sdtasdt0(X7,X10) = X12 )
& aScalar0(X11) )
& aScalar0(X10)
& sdtasdt0(X3,X4) = X10 )
& sdtasdt0(X4,X4) = X9 )
& sdtasdt0(X3,X3) = X8
& aScalar0(X8) )
& sdtasasdt0(sK1,sK2) = X7
& aScalar0(X7) ) )
& aScalar0(X5)
& sdtasasdt0(sK1,sK1) = X5 )
& aScalar0(X4)
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = X4 )
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = X3 )
=> ( aScalar0(sK3)
& ? [X4] :
( ? [X5] :
( ? [X6] :
( aScalar0(X6)
& sdtasasdt0(sK2,sK2) = X6
& ? [X7] :
( ? [X8] :
( ? [X9] :
( aScalar0(X9)
& ? [X10] :
( ? [X11] :
( sdtasdt0(X5,X9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(X8,X6) = X13
& ? [X14] :
( sdtasdt0(X11,X13) = X14
& sdtlseqdt0(sdtasdt0(X7,X7),sdtasdt0(X5,X6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X7,X10),sdtpldt0(X7,X10)),sdtasdt0(sdtpldt0(X5,X8),sdtpldt0(X6,X9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13)) ) )
& sdtasdt0(X7,X10) = X12 )
& aScalar0(X11) )
& aScalar0(X10)
& sdtasdt0(sK3,X4) = X10 )
& sdtasdt0(X4,X4) = X9 )
& sdtasdt0(sK3,sK3) = X8
& aScalar0(X8) )
& sdtasasdt0(sK1,sK2) = X7
& aScalar0(X7) ) )
& aScalar0(X5)
& sdtasasdt0(sK1,sK1) = X5 )
& aScalar0(X4)
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = X4 )
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = sK3 ) ),
introduced(choice_axiom,[]) ).
fof(f133,plain,
( ? [X4] :
( ? [X5] :
( ? [X6] :
( aScalar0(X6)
& sdtasasdt0(sK2,sK2) = X6
& ? [X7] :
( ? [X8] :
( ? [X9] :
( aScalar0(X9)
& ? [X10] :
( ? [X11] :
( sdtasdt0(X5,X9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(X8,X6) = X13
& ? [X14] :
( sdtasdt0(X11,X13) = X14
& sdtlseqdt0(sdtasdt0(X7,X7),sdtasdt0(X5,X6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X7,X10),sdtpldt0(X7,X10)),sdtasdt0(sdtpldt0(X5,X8),sdtpldt0(X6,X9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13)) ) )
& sdtasdt0(X7,X10) = X12 )
& aScalar0(X11) )
& aScalar0(X10)
& sdtasdt0(sK3,X4) = X10 )
& sdtasdt0(X4,X4) = X9 )
& sdtasdt0(sK3,sK3) = X8
& aScalar0(X8) )
& sdtasasdt0(sK1,sK2) = X7
& aScalar0(X7) ) )
& aScalar0(X5)
& sdtasasdt0(sK1,sK1) = X5 )
& aScalar0(X4)
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = X4 )
=> ( ? [X5] :
( ? [X6] :
( aScalar0(X6)
& sdtasasdt0(sK2,sK2) = X6
& ? [X7] :
( ? [X8] :
( ? [X9] :
( aScalar0(X9)
& ? [X10] :
( ? [X11] :
( sdtasdt0(X5,X9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(X8,X6) = X13
& ? [X14] :
( sdtasdt0(X11,X13) = X14
& sdtlseqdt0(sdtasdt0(X7,X7),sdtasdt0(X5,X6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X7,X10),sdtpldt0(X7,X10)),sdtasdt0(sdtpldt0(X5,X8),sdtpldt0(X6,X9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13)) ) )
& sdtasdt0(X7,X10) = X12 )
& aScalar0(X11) )
& aScalar0(X10)
& sdtasdt0(sK3,sK4) = X10 )
& sdtasdt0(sK4,sK4) = X9 )
& sdtasdt0(sK3,sK3) = X8
& aScalar0(X8) )
& sdtasasdt0(sK1,sK2) = X7
& aScalar0(X7) ) )
& aScalar0(X5)
& sdtasasdt0(sK1,sK1) = X5 )
& aScalar0(sK4)
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = sK4 ) ),
introduced(choice_axiom,[]) ).
fof(f134,plain,
( ? [X5] :
( ? [X6] :
( aScalar0(X6)
& sdtasasdt0(sK2,sK2) = X6
& ? [X7] :
( ? [X8] :
( ? [X9] :
( aScalar0(X9)
& ? [X10] :
( ? [X11] :
( sdtasdt0(X5,X9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(X8,X6) = X13
& ? [X14] :
( sdtasdt0(X11,X13) = X14
& sdtlseqdt0(sdtasdt0(X7,X7),sdtasdt0(X5,X6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X7,X10),sdtpldt0(X7,X10)),sdtasdt0(sdtpldt0(X5,X8),sdtpldt0(X6,X9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13)) ) )
& sdtasdt0(X7,X10) = X12 )
& aScalar0(X11) )
& aScalar0(X10)
& sdtasdt0(sK3,sK4) = X10 )
& sdtasdt0(sK4,sK4) = X9 )
& sdtasdt0(sK3,sK3) = X8
& aScalar0(X8) )
& sdtasasdt0(sK1,sK2) = X7
& aScalar0(X7) ) )
& aScalar0(X5)
& sdtasasdt0(sK1,sK1) = X5 )
=> ( ? [X6] :
( aScalar0(X6)
& sdtasasdt0(sK2,sK2) = X6
& ? [X7] :
( ? [X8] :
( ? [X9] :
( aScalar0(X9)
& ? [X10] :
( ? [X11] :
( sdtasdt0(sK5,X9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(X8,X6) = X13
& ? [X14] :
( sdtasdt0(X11,X13) = X14
& sdtlseqdt0(sdtasdt0(X7,X7),sdtasdt0(sK5,X6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X7,X10),sdtpldt0(X7,X10)),sdtasdt0(sdtpldt0(sK5,X8),sdtpldt0(X6,X9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13)) ) )
& sdtasdt0(X7,X10) = X12 )
& aScalar0(X11) )
& aScalar0(X10)
& sdtasdt0(sK3,sK4) = X10 )
& sdtasdt0(sK4,sK4) = X9 )
& sdtasdt0(sK3,sK3) = X8
& aScalar0(X8) )
& sdtasasdt0(sK1,sK2) = X7
& aScalar0(X7) ) )
& aScalar0(sK5)
& sK5 = sdtasasdt0(sK1,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f135,plain,
( ? [X6] :
( aScalar0(X6)
& sdtasasdt0(sK2,sK2) = X6
& ? [X7] :
( ? [X8] :
( ? [X9] :
( aScalar0(X9)
& ? [X10] :
( ? [X11] :
( sdtasdt0(sK5,X9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(X8,X6) = X13
& ? [X14] :
( sdtasdt0(X11,X13) = X14
& sdtlseqdt0(sdtasdt0(X7,X7),sdtasdt0(sK5,X6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X7,X10),sdtpldt0(X7,X10)),sdtasdt0(sdtpldt0(sK5,X8),sdtpldt0(X6,X9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13)) ) )
& sdtasdt0(X7,X10) = X12 )
& aScalar0(X11) )
& aScalar0(X10)
& sdtasdt0(sK3,sK4) = X10 )
& sdtasdt0(sK4,sK4) = X9 )
& sdtasdt0(sK3,sK3) = X8
& aScalar0(X8) )
& sdtasasdt0(sK1,sK2) = X7
& aScalar0(X7) ) )
=> ( aScalar0(sK6)
& sdtasasdt0(sK2,sK2) = sK6
& ? [X7] :
( ? [X8] :
( ? [X9] :
( aScalar0(X9)
& ? [X10] :
( ? [X11] :
( sdtasdt0(sK5,X9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(X8,sK6) = X13
& ? [X14] :
( sdtasdt0(X11,X13) = X14
& sdtlseqdt0(sdtasdt0(X7,X7),sdtasdt0(sK5,sK6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X7,X10),sdtpldt0(X7,X10)),sdtasdt0(sdtpldt0(sK5,X8),sdtpldt0(sK6,X9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13)) ) )
& sdtasdt0(X7,X10) = X12 )
& aScalar0(X11) )
& aScalar0(X10)
& sdtasdt0(sK3,sK4) = X10 )
& sdtasdt0(sK4,sK4) = X9 )
& sdtasdt0(sK3,sK3) = X8
& aScalar0(X8) )
& sdtasasdt0(sK1,sK2) = X7
& aScalar0(X7) ) ) ),
introduced(choice_axiom,[]) ).
fof(f136,plain,
( ? [X7] :
( ? [X8] :
( ? [X9] :
( aScalar0(X9)
& ? [X10] :
( ? [X11] :
( sdtasdt0(sK5,X9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(X8,sK6) = X13
& ? [X14] :
( sdtasdt0(X11,X13) = X14
& sdtlseqdt0(sdtasdt0(X7,X7),sdtasdt0(sK5,sK6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X7,X10),sdtpldt0(X7,X10)),sdtasdt0(sdtpldt0(sK5,X8),sdtpldt0(sK6,X9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13)) ) )
& sdtasdt0(X7,X10) = X12 )
& aScalar0(X11) )
& aScalar0(X10)
& sdtasdt0(sK3,sK4) = X10 )
& sdtasdt0(sK4,sK4) = X9 )
& sdtasdt0(sK3,sK3) = X8
& aScalar0(X8) )
& sdtasasdt0(sK1,sK2) = X7
& aScalar0(X7) )
=> ( ? [X8] :
( ? [X9] :
( aScalar0(X9)
& ? [X10] :
( ? [X11] :
( sdtasdt0(sK5,X9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(X8,sK6) = X13
& ? [X14] :
( sdtasdt0(X11,X13) = X14
& sdtlseqdt0(sdtasdt0(sK7,sK7),sdtasdt0(sK5,sK6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(sK7,X10),sdtpldt0(sK7,X10)),sdtasdt0(sdtpldt0(sK5,X8),sdtpldt0(sK6,X9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13)) ) )
& sdtasdt0(sK7,X10) = X12 )
& aScalar0(X11) )
& aScalar0(X10)
& sdtasdt0(sK3,sK4) = X10 )
& sdtasdt0(sK4,sK4) = X9 )
& sdtasdt0(sK3,sK3) = X8
& aScalar0(X8) )
& sdtasasdt0(sK1,sK2) = sK7
& aScalar0(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f137,plain,
( ? [X8] :
( ? [X9] :
( aScalar0(X9)
& ? [X10] :
( ? [X11] :
( sdtasdt0(sK5,X9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(X8,sK6) = X13
& ? [X14] :
( sdtasdt0(X11,X13) = X14
& sdtlseqdt0(sdtasdt0(sK7,sK7),sdtasdt0(sK5,sK6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(sK7,X10),sdtpldt0(sK7,X10)),sdtasdt0(sdtpldt0(sK5,X8),sdtpldt0(sK6,X9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13)) ) )
& sdtasdt0(sK7,X10) = X12 )
& aScalar0(X11) )
& aScalar0(X10)
& sdtasdt0(sK3,sK4) = X10 )
& sdtasdt0(sK4,sK4) = X9 )
& sdtasdt0(sK3,sK3) = X8
& aScalar0(X8) )
=> ( ? [X9] :
( aScalar0(X9)
& ? [X10] :
( ? [X11] :
( sdtasdt0(sK5,X9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(sK8,sK6) = X13
& ? [X14] :
( sdtasdt0(X11,X13) = X14
& sdtlseqdt0(sdtasdt0(sK7,sK7),sdtasdt0(sK5,sK6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(sK7,X10),sdtpldt0(sK7,X10)),sdtasdt0(sdtpldt0(sK5,sK8),sdtpldt0(sK6,X9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13)) ) )
& sdtasdt0(sK7,X10) = X12 )
& aScalar0(X11) )
& aScalar0(X10)
& sdtasdt0(sK3,sK4) = X10 )
& sdtasdt0(sK4,sK4) = X9 )
& sK8 = sdtasdt0(sK3,sK3)
& aScalar0(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f138,plain,
( ? [X9] :
( aScalar0(X9)
& ? [X10] :
( ? [X11] :
( sdtasdt0(sK5,X9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(sK8,sK6) = X13
& ? [X14] :
( sdtasdt0(X11,X13) = X14
& sdtlseqdt0(sdtasdt0(sK7,sK7),sdtasdt0(sK5,sK6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(sK7,X10),sdtpldt0(sK7,X10)),sdtasdt0(sdtpldt0(sK5,sK8),sdtpldt0(sK6,X9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13)) ) )
& sdtasdt0(sK7,X10) = X12 )
& aScalar0(X11) )
& aScalar0(X10)
& sdtasdt0(sK3,sK4) = X10 )
& sdtasdt0(sK4,sK4) = X9 )
=> ( aScalar0(sK9)
& ? [X10] :
( ? [X11] :
( sdtasdt0(sK5,sK9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(sK8,sK6) = X13
& ? [X14] :
( sdtasdt0(X11,X13) = X14
& sdtlseqdt0(sdtasdt0(sK7,sK7),sdtasdt0(sK5,sK6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(sK7,X10),sdtpldt0(sK7,X10)),sdtasdt0(sdtpldt0(sK5,sK8),sdtpldt0(sK6,sK9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13)) ) )
& sdtasdt0(sK7,X10) = X12 )
& aScalar0(X11) )
& aScalar0(X10)
& sdtasdt0(sK3,sK4) = X10 )
& sK9 = sdtasdt0(sK4,sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f139,plain,
( ? [X10] :
( ? [X11] :
( sdtasdt0(sK5,sK9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(sK8,sK6) = X13
& ? [X14] :
( sdtasdt0(X11,X13) = X14
& sdtlseqdt0(sdtasdt0(sK7,sK7),sdtasdt0(sK5,sK6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(sK7,X10),sdtpldt0(sK7,X10)),sdtasdt0(sdtpldt0(sK5,sK8),sdtpldt0(sK6,sK9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13)) ) )
& sdtasdt0(sK7,X10) = X12 )
& aScalar0(X11) )
& aScalar0(X10)
& sdtasdt0(sK3,sK4) = X10 )
=> ( ? [X11] :
( sdtasdt0(sK5,sK9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(sK8,sK6) = X13
& ? [X14] :
( sdtasdt0(X11,X13) = X14
& sdtlseqdt0(sdtasdt0(sK7,sK7),sdtasdt0(sK5,sK6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(sK7,sK10),sdtpldt0(sK7,sK10)),sdtasdt0(sdtpldt0(sK5,sK8),sdtpldt0(sK6,sK9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13)) ) )
& sdtasdt0(sK7,sK10) = X12 )
& aScalar0(X11) )
& aScalar0(sK10)
& sdtasdt0(sK3,sK4) = sK10 ) ),
introduced(choice_axiom,[]) ).
fof(f140,plain,
( ? [X11] :
( sdtasdt0(sK5,sK9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(sK8,sK6) = X13
& ? [X14] :
( sdtasdt0(X11,X13) = X14
& sdtlseqdt0(sdtasdt0(sK7,sK7),sdtasdt0(sK5,sK6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(sK7,sK10),sdtpldt0(sK7,sK10)),sdtasdt0(sdtpldt0(sK5,sK8),sdtpldt0(sK6,sK9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13)) ) )
& sdtasdt0(sK7,sK10) = X12 )
& aScalar0(X11) )
=> ( sdtasdt0(sK5,sK9) = sK11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(sK8,sK6) = X13
& ? [X14] :
( sdtasdt0(sK11,X13) = X14
& sdtlseqdt0(sdtasdt0(sK7,sK7),sdtasdt0(sK5,sK6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(sK7,sK10),sdtpldt0(sK7,sK10)),sdtasdt0(sdtpldt0(sK5,sK8),sdtpldt0(sK6,sK9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(sK11,X13)) ) )
& sdtasdt0(sK7,sK10) = X12 )
& aScalar0(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f141,plain,
( ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(sK8,sK6) = X13
& ? [X14] :
( sdtasdt0(sK11,X13) = X14
& sdtlseqdt0(sdtasdt0(sK7,sK7),sdtasdt0(sK5,sK6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(sK7,sK10),sdtpldt0(sK7,sK10)),sdtasdt0(sdtpldt0(sK5,sK8),sdtpldt0(sK6,sK9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(sK11,X13)) ) )
& sdtasdt0(sK7,sK10) = X12 )
=> ( aScalar0(sK12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(sK8,sK6) = X13
& ? [X14] :
( sdtasdt0(sK11,X13) = X14
& sdtlseqdt0(sdtasdt0(sK7,sK7),sdtasdt0(sK5,sK6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(sK7,sK10),sdtpldt0(sK7,sK10)),sdtasdt0(sdtpldt0(sK5,sK8),sdtpldt0(sK6,sK9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(sK12,sK12),sdtpldt0(sK11,X13)) ) )
& sK12 = sdtasdt0(sK7,sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f142,plain,
( ? [X13] :
( aScalar0(X13)
& sdtasdt0(sK8,sK6) = X13
& ? [X14] :
( sdtasdt0(sK11,X13) = X14
& sdtlseqdt0(sdtasdt0(sK7,sK7),sdtasdt0(sK5,sK6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(sK7,sK10),sdtpldt0(sK7,sK10)),sdtasdt0(sdtpldt0(sK5,sK8),sdtpldt0(sK6,sK9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(sK12,sK12),sdtpldt0(sK11,X13)) ) )
=> ( aScalar0(sK13)
& sK13 = sdtasdt0(sK8,sK6)
& ? [X14] :
( sdtasdt0(sK11,sK13) = X14
& sdtlseqdt0(sdtasdt0(sK7,sK7),sdtasdt0(sK5,sK6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(sK7,sK10),sdtpldt0(sK7,sK10)),sdtasdt0(sdtpldt0(sK5,sK8),sdtpldt0(sK6,sK9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(sK12,sK12),sdtpldt0(sK11,sK13)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f143,plain,
( ? [X14] :
( sdtasdt0(sK11,sK13) = X14
& sdtlseqdt0(sdtasdt0(sK7,sK7),sdtasdt0(sK5,sK6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(sK7,sK10),sdtpldt0(sK7,sK10)),sdtasdt0(sdtpldt0(sK5,sK8),sdtpldt0(sK6,sK9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(sK12,sK12),sdtpldt0(sK11,sK13)) )
=> ( sK14 = sdtasdt0(sK11,sK13)
& sdtlseqdt0(sdtasdt0(sK7,sK7),sdtasdt0(sK5,sK6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(sK7,sK10),sdtpldt0(sK7,sK10)),sdtasdt0(sdtpldt0(sK5,sK8),sdtpldt0(sK6,sK9)))
& aScalar0(sK14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(sK12,sK12),sdtpldt0(sK11,sK13)) ) ),
introduced(choice_axiom,[]) ).
fof(f129,plain,
( ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& ( ? [X0] :
( aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(X0))
& ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtlbdtrb0(X0,X1) = sdtlbdtrb0(xs,X1) )
& ? [X2] :
( ? [X3] :
( aScalar0(X3)
& ? [X4] :
( ? [X5] :
( ? [X6] :
( aScalar0(X6)
& sdtasasdt0(X2,X2) = X6
& ? [X7] :
( ? [X8] :
( ? [X9] :
( aScalar0(X9)
& ? [X10] :
( ? [X11] :
( sdtasdt0(X5,X9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( aScalar0(X13)
& sdtasdt0(X8,X6) = X13
& ? [X14] :
( sdtasdt0(X11,X13) = X14
& sdtlseqdt0(sdtasdt0(X7,X7),sdtasdt0(X5,X6))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X7,X10),sdtpldt0(X7,X10)),sdtasdt0(sdtpldt0(X5,X8),sdtpldt0(X6,X9)))
& aScalar0(X14)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X12,X12),sdtpldt0(X11,X13)) ) )
& sdtasdt0(X7,X10) = X12 )
& aScalar0(X11) )
& aScalar0(X10)
& sdtasdt0(X3,X4) = X10 )
& sdtasdt0(X4,X4) = X9 )
& sdtasdt0(X3,X3) = X8
& aScalar0(X8) )
& sdtasasdt0(X0,X2) = X7
& aScalar0(X7) ) )
& aScalar0(X5)
& sdtasasdt0(X0,X0) = X5 )
& aScalar0(X4)
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = X4 )
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = X3 )
& aDimensionOf0(xt) = szszuzczcdt0(aDimensionOf0(X2))
& ! [X15] :
( sdtlbdtrb0(X2,X15) = sdtlbdtrb0(xt,X15)
| ~ aNaturalNumber0(X15) )
& aVector0(X2)
& sziznziztdt0(xt) = X2 )
& sziznziztdt0(xs) = X0
& aVector0(X0) )
| sz00 = aDimensionOf0(xs) ) ),
inference(rectify,[],[f79]) ).
fof(f79,plain,
( ~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& ( ? [X0] :
( aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(X0))
& ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtlbdtrb0(X0,X1) = sdtlbdtrb0(xs,X1) )
& ? [X2] :
( ? [X4] :
( aScalar0(X4)
& ? [X5] :
( ? [X6] :
( ? [X7] :
( aScalar0(X7)
& sdtasasdt0(X2,X2) = X7
& ? [X8] :
( ? [X9] :
( ? [X10] :
( aScalar0(X10)
& ? [X11] :
( ? [X12] :
( sdtasdt0(X6,X10) = X12
& ? [X13] :
( aScalar0(X13)
& ? [X14] :
( aScalar0(X14)
& sdtasdt0(X9,X7) = X14
& ? [X15] :
( sdtasdt0(X12,X14) = X15
& sdtlseqdt0(sdtasdt0(X8,X8),sdtasdt0(X6,X7))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X8,X11),sdtpldt0(X8,X11)),sdtasdt0(sdtpldt0(X6,X9),sdtpldt0(X7,X10)))
& aScalar0(X15)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X13,X13),sdtpldt0(X12,X14)) ) )
& sdtasdt0(X8,X11) = X13 )
& aScalar0(X12) )
& aScalar0(X11)
& sdtasdt0(X4,X5) = X11 )
& sdtasdt0(X5,X5) = X10 )
& sdtasdt0(X4,X4) = X9
& aScalar0(X9) )
& sdtasasdt0(X0,X2) = X8
& aScalar0(X8) ) )
& aScalar0(X6)
& sdtasasdt0(X0,X0) = X6 )
& aScalar0(X5)
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = X5 )
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = X4 )
& aDimensionOf0(xt) = szszuzczcdt0(aDimensionOf0(X2))
& ! [X3] :
( sdtlbdtrb0(X2,X3) = sdtlbdtrb0(xt,X3)
| ~ aNaturalNumber0(X3) )
& aVector0(X2)
& sziznziztdt0(xt) = X2 )
& sziznziztdt0(xs) = X0
& aVector0(X0) )
| sz00 = aDimensionOf0(xs) ) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,plain,
~ ( ( sz00 != aDimensionOf0(xs)
=> ? [X0] :
( ? [X2] :
( aVector0(X2)
& sziznziztdt0(xt) = X2
& aDimensionOf0(xt) = szszuzczcdt0(aDimensionOf0(X2))
& ? [X4] :
( aScalar0(X4)
& ? [X5] :
( ? [X6] :
( ? [X7] :
( aScalar0(X7)
& sdtasasdt0(X2,X2) = X7
& ? [X8] :
( ? [X9] :
( ? [X10] :
( aScalar0(X10)
& ? [X11] :
( ? [X12] :
( sdtasdt0(X6,X10) = X12
& ? [X13] :
( aScalar0(X13)
& ? [X14] :
( aScalar0(X14)
& sdtasdt0(X9,X7) = X14
& ? [X15] :
( sdtasdt0(X12,X14) = X15
& sdtlseqdt0(sdtasdt0(X8,X8),sdtasdt0(X6,X7))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X8,X11),sdtpldt0(X8,X11)),sdtasdt0(sdtpldt0(X6,X9),sdtpldt0(X7,X10)))
& aScalar0(X15)
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt)))
& sdtlseqdt0(sdtpldt0(X13,X13),sdtpldt0(X12,X14)) ) )
& sdtasdt0(X8,X11) = X13 )
& aScalar0(X12) )
& aScalar0(X11)
& sdtasdt0(X4,X5) = X11 )
& sdtasdt0(X5,X5) = X10 )
& sdtasdt0(X4,X4) = X9
& aScalar0(X9) )
& sdtasasdt0(X0,X2) = X8
& aScalar0(X8) ) )
& aScalar0(X6)
& sdtasasdt0(X0,X0) = X6 )
& aScalar0(X5)
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = X5 )
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = X4 )
& ! [X3] :
( aNaturalNumber0(X3)
=> sdtlbdtrb0(X2,X3) = sdtlbdtrb0(xt,X3) ) )
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(X0,X1) = sdtlbdtrb0(xs,X1) )
& sziznziztdt0(xs) = X0
& aVector0(X0)
& aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(X0)) ) )
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(rectify,[],[f42]) ).
fof(f42,negated_conjecture,
~ ( ( sz00 != aDimensionOf0(xs)
=> ? [X0] :
( sziznziztdt0(xs) = X0
& aVector0(X0)
& aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(X0))
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(X0,X1) = sdtlbdtrb0(xs,X1) )
& ? [X1] :
( szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(xt)
& ! [X2] :
( aNaturalNumber0(X2)
=> sdtlbdtrb0(X1,X2) = sdtlbdtrb0(xt,X2) )
& sziznziztdt0(xt) = X1
& ? [X2] :
( ? [X3] :
( ? [X4] :
( sdtasasdt0(X0,X0) = X4
& ? [X5] :
( ? [X6] :
( sdtasasdt0(X0,X1) = X6
& ? [X7] :
( aScalar0(X7)
& ? [X8] :
( sdtasdt0(X3,X3) = X8
& aScalar0(X8)
& ? [X9] :
( ? [X10] :
( sdtasdt0(X4,X8) = X10
& aScalar0(X10)
& ? [X11] :
( sdtasdt0(X6,X9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( sdtasdt0(X10,X12) = X13
& sdtlseqdt0(sdtpldt0(X11,X11),sdtpldt0(X10,X12))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X6,X9),sdtpldt0(X6,X9)),sdtasdt0(sdtpldt0(X4,X7),sdtpldt0(X5,X8)))
& aScalar0(X13)
& sdtlseqdt0(sdtasdt0(X6,X6),sdtasdt0(X4,X5))
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) )
& sdtasdt0(X7,X5) = X12 )
& aScalar0(X11) ) )
& sdtasdt0(X2,X3) = X9
& aScalar0(X9) ) )
& sdtasdt0(X2,X2) = X7 )
& aScalar0(X6) )
& aScalar0(X5)
& sdtasasdt0(X1,X1) = X5 )
& aScalar0(X4) )
& aScalar0(X3)
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = X3 )
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = X2
& aScalar0(X2) )
& aVector0(X1) ) ) )
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(negated_conjecture,[],[f41]) ).
fof(f41,conjecture,
( ( sz00 != aDimensionOf0(xs)
=> ? [X0] :
( sziznziztdt0(xs) = X0
& aVector0(X0)
& aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(X0))
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(X0,X1) = sdtlbdtrb0(xs,X1) )
& ? [X1] :
( szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(xt)
& ! [X2] :
( aNaturalNumber0(X2)
=> sdtlbdtrb0(X1,X2) = sdtlbdtrb0(xt,X2) )
& sziznziztdt0(xt) = X1
& ? [X2] :
( ? [X3] :
( ? [X4] :
( sdtasasdt0(X0,X0) = X4
& ? [X5] :
( ? [X6] :
( sdtasasdt0(X0,X1) = X6
& ? [X7] :
( aScalar0(X7)
& ? [X8] :
( sdtasdt0(X3,X3) = X8
& aScalar0(X8)
& ? [X9] :
( ? [X10] :
( sdtasdt0(X4,X8) = X10
& aScalar0(X10)
& ? [X11] :
( sdtasdt0(X6,X9) = X11
& ? [X12] :
( aScalar0(X12)
& ? [X13] :
( sdtasdt0(X10,X12) = X13
& sdtlseqdt0(sdtpldt0(X11,X11),sdtpldt0(X10,X12))
& sdtlseqdt0(sdtasdt0(sdtpldt0(X6,X9),sdtpldt0(X6,X9)),sdtasdt0(sdtpldt0(X4,X7),sdtpldt0(X5,X8)))
& aScalar0(X13)
& sdtlseqdt0(sdtasdt0(X6,X6),sdtasdt0(X4,X5))
& sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) )
& sdtasdt0(X7,X5) = X12 )
& aScalar0(X11) ) )
& sdtasdt0(X2,X3) = X9
& aScalar0(X9) ) )
& sdtasdt0(X2,X2) = X7 )
& aScalar0(X6) )
& aScalar0(X5)
& sdtasasdt0(X1,X1) = X5 )
& aScalar0(X4) )
& aScalar0(X3)
& sdtlbdtrb0(xt,aDimensionOf0(xt)) = X3 )
& sdtlbdtrb0(xs,aDimensionOf0(xs)) = X2
& aScalar0(X2) )
& aVector0(X1) ) ) )
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f439,plain,
( spl16_40
| spl16_4 ),
inference(avatar_split_clause,[],[f201,f260,f436]) ).
fof(f201,plain,
( sz00 = aDimensionOf0(xs)
| sdtlseqdt0(sdtasdt0(sdtasasdt0(xs,xt),sdtasasdt0(xs,xt)),sdtasdt0(sdtasasdt0(xs,xs),sdtasasdt0(xt,xt))) ),
inference(cnf_transformation,[],[f144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : RNG081+2 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.11/0.32 % Computer : n023.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Aug 30 12:24:05 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.16/0.43 % (18731)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.16/0.44 % (18723)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.16/0.48 % (18727)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.16/0.48 % (18717)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.16/0.48 % (18718)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.16/0.48 % (18719)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.16/0.49 % (18735)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.16/0.49 % (18733)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.16/0.49 % (18725)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.16/0.50 % (18727)Instruction limit reached!
% 0.16/0.50 % (18727)------------------------------
% 0.16/0.50 % (18727)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.50 % (18727)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.50 % (18727)Termination reason: Unknown
% 0.16/0.50 % (18727)Termination phase: Preprocessing 3
% 0.16/0.50
% 0.16/0.50 % (18727)Memory used [KB]: 1535
% 0.16/0.50 % (18727)Time elapsed: 0.003 s
% 0.16/0.50 % (18727)Instructions burned: 3 (million)
% 0.16/0.50 % (18727)------------------------------
% 0.16/0.50 % (18727)------------------------------
% 0.16/0.50 % (18725)Instruction limit reached!
% 0.16/0.50 % (18725)------------------------------
% 0.16/0.50 % (18725)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.50 % (18732)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.16/0.50 % (18724)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.16/0.51 % (18723)Instruction limit reached!
% 0.16/0.51 % (18723)------------------------------
% 0.16/0.51 % (18723)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.51 % (18724)Instruction limit reached!
% 0.16/0.51 % (18724)------------------------------
% 0.16/0.51 % (18724)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.51 % (18724)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.51 % (18724)Termination reason: Unknown
% 0.16/0.51 % (18724)Termination phase: Preprocessing 3
% 0.16/0.51
% 0.16/0.51 % (18724)Memory used [KB]: 1535
% 0.16/0.51 % (18724)Time elapsed: 0.004 s
% 0.16/0.51 % (18724)Instructions burned: 3 (million)
% 0.16/0.51 % (18724)------------------------------
% 0.16/0.51 % (18724)------------------------------
% 0.16/0.52 % (18725)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.52 % (18725)Termination reason: Unknown
% 0.16/0.52 % (18725)Termination phase: Saturation
% 0.16/0.52
% 0.16/0.52 % (18725)Memory used [KB]: 6140
% 0.16/0.52 % (18725)Time elapsed: 0.007 s
% 0.16/0.52 % (18725)Instructions burned: 7 (million)
% 0.16/0.52 % (18725)------------------------------
% 0.16/0.52 % (18725)------------------------------
% 0.16/0.52 % (18723)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.52 % (18723)Termination reason: Unknown
% 0.16/0.52 % (18723)Termination phase: Saturation
% 0.16/0.52
% 0.16/0.52 % (18723)Memory used [KB]: 7803
% 0.16/0.52 % (18723)Time elapsed: 0.125 s
% 0.16/0.52 % (18723)Instructions burned: 52 (million)
% 0.16/0.52 % (18723)------------------------------
% 0.16/0.52 % (18723)------------------------------
% 0.16/0.53 % (18719)Instruction limit reached!
% 0.16/0.53 % (18719)------------------------------
% 0.16/0.53 % (18719)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.53 % (18719)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.53 % (18719)Termination reason: Unknown
% 0.16/0.53 % (18719)Termination phase: Saturation
% 0.16/0.53
% 0.16/0.53 % (18719)Memory used [KB]: 6652
% 0.16/0.53 % (18719)Time elapsed: 0.138 s
% 0.16/0.53 % (18719)Instructions burned: 33 (million)
% 0.16/0.53 % (18719)------------------------------
% 0.16/0.53 % (18719)------------------------------
% 0.16/0.53 % (18728)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.16/0.53 % (18728)Instruction limit reached!
% 0.16/0.53 % (18728)------------------------------
% 0.16/0.53 % (18728)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.53 % (18728)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.53 % (18728)Termination reason: Unknown
% 0.16/0.53 % (18728)Termination phase: Naming
% 0.16/0.53
% 0.16/0.53 % (18728)Memory used [KB]: 1407
% 0.16/0.53 % (18728)Time elapsed: 0.003 s
% 0.16/0.53 % (18728)Instructions burned: 2 (million)
% 0.16/0.53 % (18728)------------------------------
% 0.16/0.53 % (18728)------------------------------
% 0.16/0.53 % (18714)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.16/0.54 % (18717)Instruction limit reached!
% 0.16/0.54 % (18717)------------------------------
% 0.16/0.54 % (18717)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.54 % (18717)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.54 % (18717)Termination reason: Unknown
% 0.16/0.54 % (18717)Termination phase: Saturation
% 0.16/0.54
% 0.16/0.54 % (18717)Memory used [KB]: 6780
% 0.16/0.54 % (18717)Time elapsed: 0.151 s
% 0.16/0.54 % (18717)Instructions burned: 40 (million)
% 0.16/0.54 % (18717)------------------------------
% 0.16/0.54 % (18717)------------------------------
% 0.16/0.54 % (18736)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.63/0.55 % (18718)Instruction limit reached!
% 1.63/0.55 % (18718)------------------------------
% 1.63/0.55 % (18718)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.63/0.55 % (18718)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.63/0.55 % (18718)Termination reason: Unknown
% 1.63/0.55 % (18718)Termination phase: Saturation
% 1.63/0.55
% 1.63/0.55 % (18718)Memory used [KB]: 7036
% 1.63/0.55 % (18718)Time elapsed: 0.164 s
% 1.63/0.55 % (18718)Instructions burned: 50 (million)
% 1.63/0.55 % (18718)------------------------------
% 1.63/0.55 % (18718)------------------------------
% 1.63/0.55 % (18721)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.63/0.55 % (18732)First to succeed.
% 1.63/0.56 % (18714)Instruction limit reached!
% 1.63/0.56 % (18714)------------------------------
% 1.63/0.56 % (18714)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.63/0.56 % (18714)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.63/0.56 % (18714)Termination reason: Unknown
% 1.63/0.56 % (18714)Termination phase: Saturation
% 1.63/0.56
% 1.63/0.56 % (18714)Memory used [KB]: 6396
% 1.63/0.56 % (18714)Time elapsed: 0.152 s
% 1.63/0.56 % (18714)Instructions burned: 14 (million)
% 1.63/0.56 % (18714)------------------------------
% 1.63/0.56 % (18714)------------------------------
% 1.63/0.57 % (18731)Instruction limit reached!
% 1.63/0.57 % (18731)------------------------------
% 1.63/0.57 % (18731)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.63/0.57 % (18731)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.63/0.57 % (18731)Termination reason: Unknown
% 1.63/0.57 % (18731)Termination phase: Saturation
% 1.63/0.57
% 1.63/0.57 % (18731)Memory used [KB]: 7419
% 1.63/0.57 % (18731)Time elapsed: 0.177 s
% 1.63/0.57 % (18731)Instructions burned: 99 (million)
% 1.63/0.57 % (18731)------------------------------
% 1.63/0.57 % (18731)------------------------------
% 1.81/0.57 % (18721)Instruction limit reached!
% 1.81/0.57 % (18721)------------------------------
% 1.81/0.57 % (18721)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.57 % (18721)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.57 % (18721)Termination reason: Unknown
% 1.81/0.57 % (18721)Termination phase: Saturation
% 1.81/0.57
% 1.81/0.57 % (18721)Memory used [KB]: 6140
% 1.81/0.57 % (18721)Time elapsed: 0.007 s
% 1.81/0.57 % (18721)Instructions burned: 8 (million)
% 1.81/0.57 % (18721)------------------------------
% 1.81/0.57 % (18721)------------------------------
% 1.81/0.58 % (18732)Refutation found. Thanks to Tanya!
% 1.81/0.58 % SZS status Theorem for theBenchmark
% 1.81/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 1.81/0.58 % (18732)------------------------------
% 1.81/0.58 % (18732)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.81/0.58 % (18732)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.81/0.58 % (18732)Termination reason: Refutation
% 1.81/0.58
% 1.81/0.58 % (18732)Memory used [KB]: 7036
% 1.81/0.58 % (18732)Time elapsed: 0.161 s
% 1.81/0.58 % (18732)Instructions burned: 29 (million)
% 1.81/0.58 % (18732)------------------------------
% 1.81/0.58 % (18732)------------------------------
% 1.81/0.58 % (18709)Success in time 0.24 s
%------------------------------------------------------------------------------